The correct option is B in the given Temperature problem by Calculation T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius,
T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius
According to the given information:
For the first question, we need to compare the rate of change of temperature with respect to rotation speed for both engines. We can do this by calculating the difference in temperature for a change in rotation speed of 111 cycles per second for both engines.
For the first engine, the temperature increased by:
31.2 - 28.8 = 2.4 degrees Celsius
For the second engine, the temperature increased by:
60 - 50 = 10 degrees Celsius
Since the temperature increase for the second engine is greater, we can conclude that the second engine's temperature increased more for each increase of 111 cycles per second. Therefore, the answer is (B) The second engine.
For the second question, we can use linear interpolation to estimate the temperature of each engine at 20 cycles per second.
For the first engine, we can use the two closest data points (8.8 and 11.1 cycles per second) to estimate the temperature at 20 cycles per second:
T ≈ 26.4 + (20 - 8.8) × (28.8 - 26.4) / (11.1 - 8.8) ≈ 27.7 degrees Celsius
For the second engine, we can use the same method with the two closest data points (10 and 20 cycles per second):
T ≈ 55 + (20 - 10) × (60 - 55) / (20 - 10) ≈ 60 degrees Celsius
Therefore, we can conclude that the second engine was hotter when it rotated at 20 cycles per second. The answer is (B) The second engine.
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5.explain why reaction rates decline with time and use this information to correctly process the data (by choosing the proper data points to do linear regression
Reaction rates decline with time because the reactants are consumed over time, reducing the number of reactant particles available for reaction.
What are reactants?The components that are involved in a chemical reaction are known as reactants. They are the beginning ingredients that are changed into new compounds, known as products, through a chemical process. The left side of a chemical equation is often used to represent reactants, whereas the right side is used to indicate products. The quantity and kind of reactants and products affect the kind of chemical reaction that takes place. Pure substances, such as elements or compounds, or combinations of substances, can function as reactants with time. In a chemical reaction, reactants are changed into products by chemical bonds being broken and formed, releasing or absorbing energy in the process.
How to solve?
As the number of reactant particles decreases, the rate of reaction also decreases. This phenomenon can be observed in many chemical reactions, including reactions that involve the decay of radioactive elements.To correctly process data on the decline of reaction rates with time, it is important to choose the appropriate data points for linear regression. This typically involves selecting data points at regular intervals, such as every minute or every hour, to accurately represent the decline in reaction rates over time. By choosing the right data points and performing linear regression, it is possible to accurately model the decline in reaction rates and make predictions about future reactions.
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convert 5 centimeters into yards rounded to nearest hundredth
Answer:
.05 yd
Step-by-step explanation:
5/91.44=.05468066
classify the polynomial 2x^3-5+9x^2
The category of the polynomial 2x³ - 5 + 9x² is a trinomial
How to determine the category of the expression?From the question, we have the following expression that can be used in our computation:
2x^3-5+9x^2
Rewrite this expression properly
So, we have the following representation
2x³ - 5 + 9x²
This expression can be further rewritten as
2x³ + 9x² - 5
The degree of a polynomial is the highest power of the polynomial
In this case, the degree of the above polynomial is 3
As a general rule, a trinomial is any polynomial that has a degree of 3
Hence, the expression is a trinomial
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The correspondence n matches each student in a study group to their phone number, why is n a function?
Answer:
Power functions are functions where y = x^n where "n" is any real constant number.
julie made her braclet 30 red beads and 45 blue beads julie decided to make a new braclet using the same ratio of red to blue beads Julie used 20 red beads and 30 blue beads Will the new braclet have the same ratio of red to blue beads as her own braclet? Explain.
The ratio of red to blue beads.
Own bracelets: 2 : 3
New bracelets: 2 : 3
Yes, the ratio of red to blue beads of her own bracelet and the new bracelet is the same.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Julie made her own bracelet with 30 red beads and 45 blue beads.
The ratio of red to blue beads.
= 30 : 45
= 6 : 9
= 2 : 3
Now,
The new bracelets.
The ratio of red to blue beads.
= 20 : 30
= 4 : 6
= 2 : 3
We see that,
The ratio of red to blue beads of her own bracelet and the new bracelet is the same.
Thus,
The ratio of red to blue beads.
Own bracelets: 2 : 3
New bracelets: 2 : 3
Yes, the ratio of red to blue beads of her own bracelet and the new bracelet is the same.
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A line has a slope of 3 and passes through the point (1, 1). What is its equation in
slope-intercept form?
Answer:
y = 3x - 2
Step-by-step explanation:
Slope intercept form is y= mx+b
m being the slope
and b being the y intercept
we have the slope, but we need to find the y intercept. first, plot (1,1) you can use a sheet of graph paper, demos or just a little grid on scrap paper. then you want to create another point on your graph using the slope, in this case 3 would be 3/1 so you go from your plotted point 3 units down, then 1 unit to the left. keep on plotting points until you identify your y intercept, where a plotted point goes through y axis. this is -2, which will be B in the equation.
Hello please perform indicated operation this with steps
(x+4)^2(x-2)
We can expand the given expression:
(x + 4)²*(x - 2)
To get the equivalent one:
x³ + 6x² - 32
How to perform the operation?Here we want to expand the given expression, which is:
(x + 4)²*(x - 2)
First remember the rule:
(a + b)² = a² + 2ab + b²
So we can rewrite the first factor as:
(x + 4)² = x² + 2*4*x + 4²
= x² + 8x + 16
Replacing that in our expression we get:
(x² + 8x + 16)*(x - 2)
Now we can expand that to get:
x²*x + x²*(-2) + (8x)*x + 8x*(-2) + 16*x + 16*(-2)
= x³ - 2x² + 8x² - 16x + 16x - 32
= x³ + 6x² - 32
That is the expression expanded.
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One apple weighs 1/4 IB. And another weighs 3/16IB what's the difference
Answer:
1/16IB
Step-by-step explanation:
Differnce means to subtract which means we need to subract the two fractions. First find the the lowest of common factor for both fractions. In this case it is 16 because 4 can go into 16 four times as 4x4=16.
Since we know that 4 goes into 16 four times we get the 4 and then multiply it by the numerator (the top number of the fraction) for the fracion 1/4. Now the fraction 1/4 is 4/16. Keep the 3/16 the same as the denominator (bottom number of fraction) is already our common factors between the two fractions.
Work Shown:
Orginal Equation: 1/4-3/16
Get common Denomiantors: Convert 4 to 16. 4 goes into 16 four times, multiply by 4 by numerator. 4X1=4.
Final Step: Since both are now common fractions just subtract the numerators keeping the denominators the same of the fractions.
4/16-3/16= 1/16
Final Answer: 1/16IB
Find the median of the test scores. 56, 52, 49, 52, 43, 57, 48, 52, 44, 57, 55, 45, 49, 40, 49, 53 show work
Answer: 50.5
Step-by-step explanation: To calculate the median, you add up all the #'s to get 801. Then you divide 801 by how many #'s there are (in this case 16) Then, you would get an answer close to 50.5, but since this is a test score, it would be around 51%. I hoped this helped you!
Is the line through points P(9, 7) and Q(16, 2) perpendicular to the line through points R(3, 8) and S(11, 0)? Explain.
Based on the slope formula applied, we can conclude that, the line that passes through P(9, 7) and Q(16, 2) is not perpendicular to the line that passes through R(3, 8) and S(11, 0).
How to Find the Slope of a Line?Using the slope formula, the slope of a line is calculated as:
m = change in y / change in x.
If two lines are such that one is perpendicular to the other, both lines will have slopes that are negative reciprocal to each other and will therefore have a product of -1.
For example, if the slope of a line is -1/2, the negative reciprocal of -1/2 is 2, which will be the slope of the line that it is perpendicular to.
Find the slope of PQ and RS using the slope formula:
Slope of PQ = change in y / change in x = (7 - 2) / (9 - 16) = 5/-7
Slope of PQ = -5/7
Slope of RS = change in y / change in x = (8 - 0) / (3 - 11) = 8/-8
Slope of RS = -1.
-1 is not the negative reciprocal of -5/7, this implies that both lines are not perpendicular.
Therefore, we can state that lines PQ and RS are not perpendicular to each other.
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An aquarium has 12 equal size tanks of fish on display. All together, the tanks hold 643. 8 gallons of water. How much water can each tank hold?.
Using the unitary technique, we can determine that each tank can hold 53.65 gallons of water.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
Since the tanks are equal in size then to find the volume of 1 tank
divide the total by 12
one tank = 53.65
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A company uses a new machine and an old machine to print booklets. Each
machine prints booklets at a constant rate. The graph and the equation represent the relationships between x, the number of minutes the machines print, and y, the number of booklets printed.
The company uses both machines to print a total of 1,250 booklets. Both
machines start printing at the same time. During printing, the old machine breaks down and stops printing. The new machine continues printing for an additional 14 minutes and completes the order
What is the total number of minutes the new machine prints? Show or explain all
your work. Write your answer and your work below.
By solving a linear equation, it can be calculated that
Time for which new machine prints = 64 minutes
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
For the new machine
The line passes through (0, 0) and (6, 75)
Slope = [tex]\frac{75 - 0}{6-0}[/tex] = 12.5
Equation of line for new machine
y - 0 = 12.5(x - 0)
y = 12.5x
Equation of line for old machine
y = 9x
Now,
During the 14 minutes, the number of pages printed = 12.50 [tex]\times[/tex] 14 = 175
Number of pages printed earlier = 1250 - 175 = 1050
By the problem,
12x + 9x = 1050
21x = 1050
x = [tex]\frac{1050}{21}[/tex]
x = 50
Time for which new machine prints = 50 + 14 = 64 minutes
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rita is making two recipes which will take longer to cook the walnut bread or the alfredo sauce
Answer: alfredo sauce
Step-by-step explanation:
Walnut bread will take about 30-45 minutes to cook
Alfredo sauce will take about 10-15 minutes to make
Molly wants to put a triangular fence around her garden. Use the diagram below to answer the questions.
Molly would need 43 feet of fencing to fence the triangular area.
What is Pythagorean theorem?
Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle).
According to the given question:
We can see that the area is in the form of a right-angled triangle. Since only two sides of the triangle is given, we could utilize Pythagoras theorem to our advantage to find out the third side.
In Δ ABC
AB² (base) + AC² (perpendicular) = BC² (hypotenuse)
Substituting the values of AB as 10 feet and BC as 18 feet
AC²= BC²- AB ²
∴AC²= 224
∴AC= 14.96 cm
Amount of fence required by molly would equal perimeter of the area.
⇒The perimeter of the area would equal AB+BC+AC
⇒Summing up the values of AB, AC and BC
Perimeter= 10+14.96+18= 42.96 feet which is about 43 feet
Hence, Molly would require 43 feet of fencing.
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The Scooter Company manufactures and sells electric scooters. Each scooter cost $150 to produce, and the company has a fixed cost of $2,000. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
−2x2 − 150x − 2,000
−2x2 + 250x − 2,000
−2x2 + 150x − 1,600
−300x3 − 4,000x2 + 60,000x + 800,000
The Scooter Company's total profit function is represented by -2x²+250x-2000.
Total profit of a company is the difference between total revenue and total cost.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Company earns a total revenue that can be determined by the function R(x) = 400x - 2x²
Each scooter cost $150 to produce, and the company has a fixed cost of $2,000.
Variable cost = Cost of each scooter × Number of scooter sold
Total cost = fixed cost + variable cost
= 2000 + (150×x)
Cost, C(x) = 2000 + 150x
Revenue, R(x) = 400x - 2x²
Total profit = Revenue - Cost
= 400x-2x²-(2000 + 150x)
= 400x-2x²-2000-150x
= -2x²+250x-2000
Therefore, the Scooter Company's total profit function is represented by -2x²+250x-2000.
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The length of my outdoor volleyball net is 6 m plus half its own length. How long is the net?
Answer:
12 meters
Step-by-step explanation:
The length of the volleyball net is "L"
6 + 1/2 L = L <======this is given , solve for L
6 = 1/2 L
L = 12 Meters
Help llsss happy holidays
Answer:
D) The economy has done well for a while and is at its highest point of the cycle.
Step-by-step explanation:
I believe that it is "D" considering this is the highest point on the graph. Also the fact that, that's the only statement that makes sense for point "A".
I hope this helps!!!
Answer: C
Step-by-step explanation:
A just means that the growth of the cycle will keep increasing and will not decrease, which is wrong.
B means that point A is at its lowest point in the cycle, which is wrong too.
C is correct because before the dot that’s labeled A the growth was going down. But then point A showed the cycle growing slowly.
D is incorrect because point a isn’t the highest point, point A and point C are equal.
Given triangle NEB NE is 7.5cm and TAN of B is Fill in the rest of the triangle. 3/4
A Side BN equals
A SIN of B equals
7.5
E
N
side BE equals
Using trigonometric ratios, we have been able to deduce that;
BE = 10 cm; sin B = 3/5 and cos B = 4/5
How to use trigonometric ratios?The basic trigonometric ratios for an angle θ are expressed as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
Now, looking at the given triangle NEB, we are given that;
NE = 7.5 cm
tan B = 3/4
angle E = 90°
If tan B = 3/4, then it means that;
3/4 = NE/BE
since NE = 7.5, then we can say that;
3/4 = 7.5/BE
BE = (7.5 * 4)/3
BE = 10 cm
By Pythagoras theorem, we can say that BN = 12.5 cm.
Thus;
sin B = opposite/hypotenuse = 7.5/12.5 = 3/5
cos B = adjacent /hypotenuse = 10/12.5 = 4/5
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Using trigonometric ratio, the side BN is 12.5 units, sin and cos angle of B are 36.9 degrees respectively
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
In this problem;
A)
Tan B = 3/4
BN = ?
Tan B = NE / BE
3/4 = NE / BE
BE = NE / 3/4
BE = 7.5 / 0.75
BE = 10
The side BN can found using Pythagoras theorem
BN² = BE² + NE²
BN² = 10² + 7.5²
BN = 12.5
B)
Sin B = NE / NB
sin B = 7.5 / 12.5
sin B = 0.6
B = sin⁻¹(0.6)
B = 36.9°
C)
Cos B = BE / NB
cos B = 10 / 12.5
B = cos⁻¹(10/12.5)
B = 36.9°
The length of Bn is 12.5cm, and sin and cos angle of B is 36.9 degrees respectivelt
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1. Select all the equations that represent the hanger. A. x + x + x = 1 +1+1+1+1+1 B. x. x. x = 6 C. 3x = 6 D. x + 3 = 6 E. x x .x=1.1.1.1.1.1
The equations that represent the hanger are -
x + x + x = 1 + 1 + 1 + 1 + 1 + 1 and 3x = 6.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.Given are the expressions as given in the question.
The equations that represent the hanger are -
x + x + x = 1 + 1 + 1 + 1 + 1 + 1
and
3x = 6
Therefore, the equations that represent the hanger are -
x + x + x = 1 + 1 + 1 + 1 + 1 + 1 and 3x = 6.
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HELP LIKE WHAT ELSE DO I DO???? IT WONT LET ME PROOVE THAT LINES BA AND CD ARE PARALLEL
The triangles ABC and CDA are congruent by SAS criteria.
What are the criteria for congruent triangles?Two triangles are said to be congruent when all of their corresponding sides and angles are equal. For this relation between two triangles, there are many criteria such as SSS, SAS, ASA and RHS.
Given that,
In quadrilateral ABCD, AD = BC and AD ║BC.
Now, the given relation ΔABC ≅ ΔCDA can be proved as follows,
In ΔABC and ΔCDA, it is found as,
AC = AC (Common sides)
AD = BC (Given data)
And, ∠ACB = ∠DAC (Interior angles between parallel lines AD and BC)
Thus, ΔABC ≅ ΔCDA by SAS congruence criteria.
Hence, the given relation ΔABC ≅ ΔCDA is proved by SAS criteria.
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If 9^x / 9^3 = 9^5 what is x
Answer:
since , 9^x / 9^3 = 9^5
and since there is a law for exponents that says if the bases of the exponent are equal and divided by each other we subtract the exponents
, so 9^x-3 = 9^5
then x-3 =5 , therefore the final answer will be X= 8 .
Solve for r
-2r+15=-3(-2r-7)-6
Answer:
[tex]\bf r=0[/tex]
Step-by-step explanation:
[tex]\bf -2r+15=-3\left(-2r-7\right)-6[/tex]
Expand: *-3(-2r-7)-6 = 6r+15* :-
[tex]\bf -2r+15=6r+15[/tex]
Subtract 6r from both sides:-
[tex]\bf -2r+15-6r=6r+15-6r[/tex]
[tex]\bf -8r+15=15[/tex]
Subtract 15 from both sides:-
[tex]\bf -8r+15-15=15-15[/tex]
[tex]\bf -8r=0[/tex]
Divide both sides by -8:-
[tex]\bf \cfrac{-8r}{-8}=\cfrac{0}{-8}[/tex]
[tex]\bf r=0[/tex]
__________________
Hope this helps you!
Have a good day!
Answer:
r=0
Step-by-step explanation:
-2r+15=-3(-2r-7)-6
-2r+15= 6r+21-6
-2r+15=6r+15
-6r. -6r
-8r+15=15
-15. -15
-8r=0
/-8. /-8
r=0
hopes this helps
Simplify each ratio. Make sure to convert the units when needed
1,320 feet: 1 mile (Hint: There are 5,280 feet in one mile.)
The simplification of the ratio 1320 feet : 1 mile will be 1:4
What is Ratio?
A ratio in mathematics illustrates how many times one number contains another. The term ratio is a straight borrowing from the Latin word ratio. In Latin, ratio could imply everything from "reason" to "calculation" to "proportion," and it was this last meaning that was used to create the mathematical and English ratios.
Given taht we need to simplify the ratio 1320 feet : 1 mile
For simplifying ratios we need to convert the terms in same units
and we know that 1 mile = 5280 feet
So,
1320 feet : 1 mile can be written as 1320 feet : 5280 feet
The simplification wil be 1:4
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The table compare the time at which Jayden got on the bu to chool (in minute after 8\text{ am}8 am8, tart text, pace, a, m, end text) and the duration of the ride (in minute), for everal different day. Can the duration of the ride be repreented a a function of the time Jayden got on the bu?
Time (minute after 8\text{ am}8 am8, tart text, pace, a, m, end text) Duration (minute)
202020 404040
252525 474747
181818 383838
222222 424242
303030 525252
202020 424242
222222 414141
232323 444444
Yes. The duration of the ride can be represented as a function of the time Jayden got on the bus.
We have given that,
Time (minutes) 18 20 20 22 22 23 25 30
Duration (minutes) 38 40 42 41 42 44 47 52
As we can see the duration of the ride seems to increase as the amount of time after 8 am that Jayden got on the bus.
This means that the duration of the ride and the time Jayden got on the bus have the linear relationship.
Therefore the duration of a ride can be represented as a function of the time Jayden got on the bus.
Following are the function of a time:
s(t) = distance a particle travels from tome 0 to t.
v(t) = velocity of a particle at time t.
a(t) = acceleration of a particle at time t.
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Select all statements that are true about translations.
1. The lines connecting the image and pre-image points are parallel
2. The lines connecting the image and pre-image points are perpendicular
3. The resulting image will be congruent to the pre-image
4. The resulting image will be similar but not congruent to the pre-image
5. The orientation of the image stays the same
6. All corresponding image and pre-image points are the same distance from each other.
The statements that are true about translations will be 1, 3, 5, and 6.
What is a transformation of a shape?A point, line, or numerical figure can be changed over in one of four ways, and each significantly affects the item's construction or potential position. Picture, after interpretation, alludes to the article's definitive association and position. Not long before the alludes to the material's underlying condition.
The translation does not change the shape and size of the geometry. But changes the location. And the orientation will remain the same.
The statements that are true about translations will be 1, 3, 5, and 6.
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The length of the freeway is 600 miles. If 0. 5 inch represents 50 miles, what is the length of the freeway on the map? a. 10 inches c. 12 inches b. 6 inches d. 3 inches.
When a freeway is 600 miles long, its length on a map will be 6 inches, and 50 miles will be represented by 0.5 inches.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4). The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.
Here,
Length of freeway=600 miles
if 0.5 inch make 50 miles in map,
600:x=50:0.5
=0.5*600/50
=6 inch
The length of the freeway on the map will be 6 inch when it is 600 miles long and 0.5 inch make 50 miles in map.
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Please help graph question
Answer:
a. (-2,-1)
b. y = -(1/2)x-2
Step-by-step explanation:
We will look for an equation of the form y=mx+c, where m is the slope and b is the y-intercept (the value of y when x = 0).
Put the two given points into a table to make it easier to calculate the slopes for Lines A and B. See the attachment for the table. Slope is the change in y for a change in x, often termed the "Rise/Run." Using Line A as the example, the change in y (the Rise) is obtained by taking the Point 2 value for y (7) and subtracting the Point 1 value for y (3): Rise = (7 - 3) = 4. The Run is obtained by taking the Point 2 value for x (2) and subracting the Point 1 value of x (0). The ratio of Rise/Run is 4/2, so the slope is 2. The same process is used for Line B to obtain a slope of 3 for that line.
The two equations can be written with these slopes:
Line A: y = 2x + c
Line B: y = 3x + c
We need to find a value of c for each equation that will force the line through either of their two given points. c can be determined by entering either of that line's points into the equation(s) above and solving for c:
Line A:
y = 2x + c
3 = 2*(0) + c for point (0,3)
c = 3
The equation for Line A is y = 2x + 3
Line B:
y = 3x + c
2 = 3*(-1) + c for point (-1,2)
c = 5
The equation for Line B is y = 3x + 5
The graph of these lines is attached. They intersect at point (-2,-1).
[As a note, the solution may also be found by using substitution and solving for both x and y:
y = 2x+3
y = 3x+5
The solution exists when both y's and x's are equal:
Assume y is equal:
2x+3 = 3x+5
-x = 2; x = -2
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Assume x is equal:
Rearrange:
y = 2x+3
2x = y-3
x = (y-3)/2
Use this definition of x in the second line equation:
y = 3x+5
y = 3((y-3)/2)+5
y = (3y - 9)/2 + 5
2y = 3y - 9 + 10
-y = 1
y = -1
The solution is (-2,-1), the same as was found by graphing.]
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A perpendicular line has a slope that is the negative inverse of the referenced line. For Line A, the perpendicual line would be -(1/2). The equation for this line would take the form y = -(1/2)x + c. We want this perpendicular line to intersect the same point that is the solution to the first problem: (-2,-1). Enter this point to find c:
y = -(1/2)x + c
-1 = -(1/2)*(-2) + c for (-2,-1)
-1 = 1+ c
c = -2
The perpendicular line is y = -(1/2)x - 2
See the attached graph.
Cynthia Bech want to buy a rug for a room that i 20 ft wide and ft long. She want to leave a uniform trip of 29 floor around the rug. She can afford to buy 322 quare feet of carpeting. What dimenion hould the rug have?
On solving the question, we got that - The dimensions of the rug should be 18 feet and 24 feet
What is area of rectangle?By multiplying the rectangle's length by its breadth, we may get its area.
Equiangular quadrilaterals, like rectangles, are known in this way. This is so because a rectangle is a four-sided quadrilateral shape with parallel sides that are equal to one another and four corners with 90o angles. Rectangles are sometimes known as equiangular quadrilaterals since all of its angles are 90 degrees.
the parameters provided;
The room is 20 feet by 26 feet in size.
432 feet2 is the largest area rug she can afford.
If the floor will be a uniform stripe around the rug, then each dimension should have its uniform extra length of floor = (y).
[tex]Area = Length X Width\\432 = ((20=y) X (26-y)\\432 = 520 - 20y - 26y + y^2\\y^2 - 46y+88=0\\[/tex]
here, a= 1, b= -46, c =88
[tex]y = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\[/tex]
[tex]y = \frac{-(-46) +/- \sqrt{(-46)^2 - 4X1X88} } {2} \\\\y = 44 \\or\\ y = 2[/tex]
Therefore, Length = 20-2 = 18 ft
and width = 26-2 = 24ft
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Solve for x. 6 + |4x - 1| > 10 Graph the solution on the number line.
13>10 is the answer on the number line.
What exactly is a graph solution?A system of linear equations has a solution, which is the quantity that makes all of the equations true. This is the intersection of the two graphs for two variables and two equations. The two variables in the two equations will have a solution at these coordinates.When x=6, x will remain 6 regardless of what y is. Therefore, simply draw a vertical straight line through (6, 0), parallel to the y axis, and extend it on both sides. The finished graph is there.Explanation:
x.6 + 4x -1 > 10
6.6 = 4.6 - 1
36 = 24 - 1
36 - 23 = 13>10.
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13>10 is the answer on the number line.
What exactly is a graph solution?A system of linear equations has a solution, which is the quantity that makes all of the equations true. This is the intersection of the two graphs for two variables and two equations. The two variables in the two equations will have a solution at these coordinates.
When x=6, x will remain 6 regardless of what y is. Therefore, simply draw a vertical straight line through (6, 0), parallel to the y axis, and extend it on both sides. The finished graph is there.
x.6 + 4x -1 > 10
6.6 = 4.6 - 1
36 = 24 - 1
36 - 23 = 13>10.
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A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.
Part A. Write and solve a system of equations to model this situation.
Part B. Then explain the meaning of your solution.
The system of equations to model is s=220 and a=241 when 461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students.
Given that,
461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students. Sales of tickets totaled $1624.
We have to find the system of equations to model.
We know that,
We get,
a + s = 461
s = 461 -a
The student tickets sold = s × 3 = 3 × (461-a)
The adult tix sold = 4 a
Summed they total 1624
We get system of equations as
s = 461-a
3 (461-a) + 4a = 1624
1383 -3a +4a = 1624
a = 241
Then
s = 461 -a = 220
Therefore, The system of equations to model is s=220 and a=241 when 461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students.
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