a. A function rule is a representation of dependent variable, here n, in terms of the independent variable, here P, and is expressed as ƒ(P) = 1.5n.
b. This type of reason is useful because functions in an equation can take input from many variables, but always give the same result, which is unique to that function.
What is a function rule?The connection between the input or domain and the output or range is called a function rule. When there is exactly one value in the range for each domain value, a relation is a function.
f(x), where x is the input value, is how functions are expressed.
All functions have the general form y = f(x)
On any part of the function, a vertical line is drawn. It is a function if and only if it crosses the function at that single point. It is not a function if the line crosses itself more than once.
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Given the two rectangles below. Find the area of the shaded region.10, 2, 4, 2
Applying the formula for the area of a rectangle, the area of the shaded region is calculated as: 42 units².
What is a Rectangle?A rectangle has two pairs of opposite sides that are of equal length, one pair is the length, while the other is the width.
How to Find the Area of a Rectangle?The area of a rectangle = the product of its length and its width = (length)(width).
The area of the shaded region = area of the larger rectangle - area of the smaller rectangle
Dimensions of the larger rectangle:
Length of the larger rectangle = 10 + 2 = 12 units
Width of the larger rectangle = 9 + 2 = 11 units
Area of the larger rectangle = (12)(11) = 132 units²
Dimensions of the smaller rectangle:
Length of the smaller rectangle = 10 units
Width of the smaller rectangle = 9 units
Area of the smaller rectangle = (10)(9) = 90 units²
The area of the shaded region = 132 - 90
The area of the shaded region = 42 units²
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Line ℓ has equation y=
–x–3. Find the distance between ℓ and the point I(2,5).
The distance between line y= -x-3 and the point (2,5) is 5√2units.
The distance(d) between the line ax+by+c=0 and point (x₁,y₁) is calculated using the formula
d= |ax₁+by₁+c|/√a²+b² , where a and b are the coefficients of x and y .
In the question ,
the equation of the line ℓ is given by y = -x-3
rewriting the equation in standard form x+y+3=0
So the distance between the line x+y+3 and the point (2,5) can be calculated by substituting the values in the formula, we get
d=|1(2)+1(5)+3|/√1²+1²
= |2+5+3|/√2
= 10/√2
Simplifying further , we get
= 5√2
Therefore , the distance between line y= -x-3 and the point (2,5) is 5√2 units.
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I need the answer for this question...
Expand and simplify the following 2(7s+ 4) + 6
Answer: 14s + 14
Step-by-step explanation:
- multiply in the 2 to the 7 and 4
14s + 8 +6
- add 8 + 6
14s + 14
Answer:
14s+14
Step-by-step explanation:
2(7s+4)+6
Simplify each term.
Apply the distributive property.
2(7s)+2x4 + 6
Multiply 7 by 2
14s +2 x 4 + 6
Multiply 2 by 4
14s + 8 + 6
Add 8 and 6
14+44
What are the next two terms in the sequence? 2, 12, 22, 32, ...
The graph of y=f(x) is the solid black graph below. Whoch function represents the dotted line
The function that represents the dotted line of the graph using transformation rules is; f(x - 1) - 4.
How to Interpret Translation of Graphs?For the function f(x) of the given graph, when we look at the solid line, we see that it has a root at x = -1 which means it has a zero at x = -1.
However, when observing the dashed line, we see that it has a root at x = 0 which means it has a zero at x = 0.
Thus, we can deduce from transformation rules that the function was moved by 1 unit to the right to get the new function.
Secondly, we observe that the dashed line is also below the function f(x), and we observe further that 4 was subtracted. Therefore, when we use the transformation rules again for subtracting from a function, we get the final function as; f(x - 1) - 4.
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Find the converse and determine if it is true or false.
Statement : obtuse angles are not right angles.
The converse statement is 'If an angle is not a right angles, then it is obtuse' True. Option A
What is a converse statement?The converse of a conditional statement is formed when the hypothesis and conclusion are both reversed.
In this case, the hypothesis is taken as the conclusion and the conclusion made the hypothesis.
The conditional statement is written as: a → b
The converse is written as b → a
Where;
a is the hypothesisb is the conclusionGiven that:
Original statement :Obtuse angles are not right angles
The converse statement : If an angle is not a right angles, then it is obtuse
We can see that the converse statement is true because an obtuse angle is an angle greater than 90 degrees.
Hence, the converse statement is true
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5.) Which is the better buy? Circle your answer (show supporting work)
20 cans of Mello Yello for $4.75
36 cans of Sprite for $9.50
6.)
Birth Rates and Populations around the World in 2011
Birth Rate
(per 1000 population per year)
15.53
Country
French Polynesia
Brazil
17.79
Australia
12.33
Sudan
36.12
Russia
11.05
India
20.97
Bulgaria
9.32
Source: http://www.indexmundi com/g
a.) Which country has a birth rate of 36.12?
b.) Which country has the largest birth rate?
c.) Which country has the smallest population?
Population
294,935
203,429, 800
21,766,710
45,047,500
138,739,900
1,189,173,000
7,093,635
Mello Yello
Sprite
We are spending $ 0.0263 less every Mello Yello can, therefore it is the better buy.
What is profit and loss?
Subtract the smaller value from the greater value in order to calculate the profit or loss. The selling price is always higher than the cost price when there is a profit. Selling price minus cost price is profit. In a loss scenario, the cost price is higher than the selling price. Loss = Price Cost
Given,
20 cans of Mello Yello for $4.75
Therefore cost of 1 can of Mello Yello = $4.75 / 20 = $ 0.2375
Also given,
36 cans of Sprite for $9.50
Therefore, cost of 1 can of Sprite = $9.50 / 36 = $ 0.2638
Therefore, per can we are paying $ 0.0263 less for Mello Yello.
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Complete Question:
Which is the better buy? Circle your answer (show supporting work)
20 cans of Mello Yello for $4.75
36 cans of Sprite for $9.50
Your friend says that the solutions to the inequality 9x-12x≤9 are xs-3. Solve the inequality correctly. What error did your friend
make?
holow and fill in the answer box to complete your choice
Answer:
[tex]9x - 12x \leqslant 9[/tex]
[tex] - 3x \leqslant 9[/tex]
[tex]x \geqslant - 3[/tex]
The inequality sign must be reversed when multiplying or dividing each side of an inequality by a negative number.
Which expression is equivalent to 3w-4-w-93w−4−w−9?
The most appropriate choice for simplification of algebraic expression will be given by -
-92w -17 is the correct answer
What is simplification of algebraic expression?
At first it is important to know about algebraic expression. Algebraic expression consist of numbers and variable connected by addition, subtraction, multiplication, division.
Simplification of algebraic expression is the process of calculating the algebraic expression into lower form by combining all the like terms together. Here, BODMAS rule is used. B stands for bracket, O stands for of, D stands for division, M stands for multiplication, A stands for addition, S stands for subtraction.
3w - 4 - w - 93w - 4 -w - 9
3w - w - 93w -w -4 - 4 - 9
-92w -17
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I need help with this please because I got answer C but I’m not sure I’m right
Since supplementary angles are two angles with a sum of 180°, then the supplement of ∠WTV is the angle ∠WTZ. Therefore, the answer is the option C.
The sticker on Dean's new car states that the car averages 32.6 miles per gallon. If the fuel tank holds 12.3 gallons, then how far can Dean travel on one full tank of gas?
Answer:400.98 miles on one full tank
Step-by-step explanation:
you take 32.6 and multiply it by 12.3
There are 7 red cards, 6 blue cards, 8 purple cards, and 4 green cards in a hat. In a trial, a card is drawn from the hat and then replaced. In 640 trials a red card is drawn 240 times. How much greater is the experimental probability than the theoretical probability?
Responses
Amare drops a probe into a lake. The elevation of the probe changes
by - 11 feet every second. The probe takes 50 seconds to reach
the bottom of the lake. How deep is the lake? Show your work.
The lake is 12,250 feets deep.
The elevation is changing in the downward direction and at a rate of -11ft/s.
So it means that the downward velocity of the probe is 11ft/s.
The value of downward acceleration is 9.8?m/s² which is equal to acceleration due to gravity.
The total time taken to reach down is 50seconds.
We can use the equation of motion because the acceleration is constant,
Using,
S = ut + 1/2at²
Where,
S is the depth of the pool,
U is initial velocity,
U is zero because the probe is dropped.
S = 1/2at²
S = 1/2××9.8×50×50
S = 12250 feets.
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3) Identify the center and radius
SOLUTION:
Case: Circle equations
Metho:
[tex](x-a)^2+(y-b)^2=r^2[/tex]Given:
[tex]\begin{gathered} (x+11)^2+(y-6)^2=9 \\ (x+11)^2+(y-6)^2=3^2 \end{gathered}[/tex][tex]\begin{gathered} Center(a,b)=(-11,6) \\ radius,r=3 \end{gathered}[/tex]Final answer:
Center (-11, 6)
radius, r= 3
Jim’s music library on his phone holds 1,900 songs. The songs have an average time of 3.5 minutes. Use scientific notation to find the total number of seconds the playlist will play. Express the answer to the exact decimal place.
We need to know about scientific notation to solve this problem. The number of seconds the playlist will play is 3.99 x 10^5.
Expressing a number in scientific notation means writing the number as a multiple of ten with ten raised to some power. We use scientific notation for numbers that are very small or very big. When writing numbers in scientific notation we always have one number other than zero before the decimal point. In this question we know that there are 1900 songs and each song has average time of 3.5 minutes, we need to convert the minutes into seconds and multiply the number of seconds of each song to 1900.
1 min=60 seconds
3.5 mins=3.5 x 60=210 seconds
210 x1900=399000 seconds
399000=3.99 x 10^5
Therefore the number of seconds that the playlist will play is 3.99x 10^5
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Write the ratio in the simplest form comparing the monetary value of 2 nickels to that os 1 quarter
The ratio of the simplest form of 2 nickels to 1 quarter is 2:5.
What is defined as the ratio?The ratio can be defined as a comparison of two amounts of the same unit to determine that much of one amount is present in the other. Ratios are divided into two types. The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groups. This ratio is represented by the fraction a/b. To simplify a ratio even further, we use the same method we used to simplify a fraction. a:b = a/b.For the given question;
The two monetary values are given as;
2 nickles and 1 quarter.
We know that;
1 nickles = 0.2 quarter.
For 2 nickles multiply both side by 2.
2 nickles = 2×0.2 quarter.
2 nickles = 0.4 quarter.
Find the ratio;
2 nickels to that of 1 quarter
2 nickels/ 1 quarter
Put the value of 2 nickle.
2 nickels/ 1 quarter = 0.4 quarter/1 quarter
2 nickels/ 1 quarter = 2/5
2 nickels: 1 quarter = 2:5
Thus, the ratio of 2 nickels to that of 1 quarter is found as 2:5.
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Please help I’ll mark you as brainliest if correct!!
a ) P = { a , n , c , d }
b ) {4 , 7} ⊆ { 4,7,8,12}
c ) {0,1} ⊄ { 1,4,5,6}
are the equations is mathematical symbols
What are sets and subsets ?Subsets are a component of the mathematical concept of sets. A set is anything that is contained in curly brackets, as "a,b,c,d." If set B includes the numbers 2, 4, and 6, it is said to be a subset of set A, and if set A is a collection of even integers, it is said to be the superset of set B.
Calculationa ) P = { a , n , c , d }
b ) {4 , 7} ⊆ { 4,7,8,12}
c ) {0,1} ⊄ { 1,4,5,6}
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To make orange paint he must mix yellow and red paint in the ratio 6:4 if he uses 9 litres of yellow paint how much red paint should he use
Answer:6 liters of red paint
Step-by-step explanation:
Calculate the first two terms: 34÷6
Calculate the first two terms: 6
Answer:6
find f(g(2)) if f(x)= 4x^2-1 and g(x) = 3x+2
The value of the function f(g(2)) is 255.
The two function given is f(x) = 4x^2 - 1 and g(x) = 3x + 2
We have to find the value of the function f(g(2)).
First we will find the function f(g(x))
f(g(x)) = f(3x+ 2)
=4[tex](3x +2)^{2}[/tex] - 1
= 4( 9[tex]x^{2}[/tex] + 12x + 4) - 1
= 36x² + 48x + 16 - 1
= 36x² + 48x + 15
Now we have to find f(g(2)) for which we have to put the value of x as 2.
f(g(2)) = 36(2)² + 48 (2) + 15
= 36× 4 + 48 ×2 + 15
= 144 + 96 + 15
= 255
Therefore the value of the function f(g(2)) is 255.
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Mathataur weighs 230,998,888,201 grams, and Mathamoth weighs 44,002,156 grams. About how many times greater is the weight of the Mathataur than the weight of the Mathamoth?
Answer:234534 pounds greater
Step-by-step explanation: 230,99987389x7=76
What is the correct conjunction identity for tan 0?
A. csc (90 ° - 0)
B. sec (90 ° - 0)
C. sin (90 ° - 0)
D.cos (90 ° - 0)
E. cot (90 ° - 0)
The correct cofunction identity for tan 0 is cot (90 ° - 0). Option E
What are cofunction identities?The cofunction identities are defined as trigonometric functions elaborates the relationship between the trigonometric identities.
These trigonometric identities includes;
SineCosineTangentCotangentSecant CosecantIt is crucial to note that the value of a trigonometric function of any specific angle is equivalent to the value of the cofunction of their complementary identities.
The cofunction identities are represented thus;
sin θ = cos(90 - θ)
cos θ = sin(90 - θ)
cot θ = tan(90 - θ)
tan θ = cot(90 - θ)
csc θ = sec(90 - θ)
sec θ = csc(90 - θ)
For tan 0, we have that its cofunction identity is expressed as;tan 0 = cot (90 ° - 0)
Thus, the identity is cot (90 ° - 0)
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The correct cofunction identity for tan 0 is cot (90 ° - 0). Option E.
What are cofunction identities?The cofunction identities are defined as trigonometric functions elaborates the relationship between the trigonometric identities.These trigonometric identities includes; sine,cosine, tangent, cotangent, secant cosecant.
It is crucial to note that the value of a trigonometric function of any specific angle is equivalent to the value of the cofunction of their complementary identities.The cofunction identities are represented thus;
sin θ = cos(90 - θ)cos θ = sin(90 - θ)cot θ = tan(90 - θ)tan θ = cot(90 - θ)csc θ = sec(90 - θ)sec θ = csc(90 - θ)For tan 0, we have that its cofunction identity is expressed as;tan 0 = cot (90 ° - 0)Thus, the identity is cot (90 ° - 0)
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Can you help me with this please!!
Let us find the third side of the right triangle using the Pythagora's theorem
The missing side is the opposite side because it is facing the angle
[tex]\begin{gathered} 13^2=5^2+x^2 \\ \\ x^2=169-25 \\ \\ x^2=144 \\ \\ x=\sqrt[]{144} \\ \\ x=12 \end{gathered}[/tex][tex]\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ \\ sin\theta=\frac{12}{13} \end{gathered}[/tex]Kevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces
the brakes. He works no more than 54 hours a week. He routinely completes at least 2 shocks replacements and 6
brake replacements a week. If he charges $400 for labor replacing shocks and $250 in labor for replacing brakes, how
many jobs of each type should he complete a week to maximize his income?
Answer:
18 Shocks replacments and 0 Brakes
Step-by-step explanation:
if he did That he will make 7200$ a week
I need help finding an answer, please.
Given that ΔABC is similar to ΔDFE , the value of x = 5.83 (rounded off to hundredth place)
Comparing the given pair of similar triangles,
A ↔ D
B ↔ F
C ↔ E
Now since the ΔABC ~ ΔDFE, the ratio of their sides are equal.
=> [tex]\frac{FE}{BC} = \frac{DF}{CA}[/tex] (by property of similarity of triangles)
=> [tex]\frac{x}{15} = \frac{7}{18}[/tex] (substituting respective values)
=> x = 5.83 (simplifying the algebraic equation to hundredth place)
As per the property of similarity of triangles, the corresponding sides have fixed ratio. Thus the ratio of two sides of a triangle will be numerically equal to the ratio of two corresponding sides of its similar triangle. Moreover, the corresponding angles of two similar triangles are equal in measure.
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susy goes to the grocery store, 3 apples cost 1.50 . find the unit rate in cost per apple
Answer:
1.50/3 Apples=0.5
That means each apple cost 0.5. If it's in rands gonna be R0.5 or 50 Cents per apple.
True or false,
In 60 min,the level in the pond increases 8 in
Answer:
True
Step-by-step explanation:
In 1 h, the level in the pond increases 1 ft. One way to find how many feet the level increases in 30 min is to multiply One way to find how many inches the level increases in 2- h is to multiply 2. 2 of 5 Completed
Answer:
True
Step-by-step explanation:
In 1 h, the level in the pond increases 1 ft. One way to find how many feet the level increases in 30 min is to multiply One way to find how many inches the level increases in 2- h is to multiply 2. 2 of 5 Completed so that is ture
Describe and correct the error a student made when graphing [tex]y+5=-\frac{3}{4}(x-8)[/tex].
Answer/Step-by-step explanation:
3
y + 5 = ( - ) ------- (x - 8)
4
3
y + 5 = ( - ) ------- x + 6
4
3
y + 5 = ( - ) ------- x + 6
-5 4 -5
3
y = ( - ) ------- x + 1
4
m = slope = (-3/4)
b = y-intercept = (0, 1)
----------------------------------------------------------------------------------------------------------
The student's first error was in step 1.
Step 1 should involve plotting a point at (0, 1).
Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).
Step 3, connecting the points with a line was correct.
----------------------------------------------------------------------------------------------------------
I hope this helps!
Leila is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories.Leila wants the total calorie count from the french fries and chicken wings to be less than 600 calories. Using the values and variables given, write an inequality describing this.(BOLD ANSWER WHEN FINISHED
Answer:
[tex]25f+100c<600[/tex]Step-by-step explanation:
Let f be the number of french fries in the lunch
Let c be the number of chicken wings.
Then, if Leila wants her child to eat less than 600 calories and each french fry has 25 calories and each chicken wing has 100 calories. The linear inequality that represents this situation:
[tex]25f+100c<600[/tex]a balloon is released from the top of a platform that is 50 m tall the balloon Rises at the rate of 4 meters per second identify the input variable output variable initial value and rate of change
Let's begin by identifying key information given to us:
Height = 50 m
velocity = 4m/s
The input variable is the number of seconds
The output variable is the theight of the ballon
The equation:
[tex]\begin{gathered} y=4x+50 \\ \text{Comparing this equation with the standard equation,}y=mx+b \\ \Rightarrow m=4,b=50 \\ m=4 \end{gathered}[/tex]Therefore, the rate of change equals 4
Share:
Share £20 pounds in the ratio 2:3
Share 15cm in the ratio 1:2
Divide £24 in the ratio 1:3
Share 35 sweets in the ratio 4:3
The share base on the ratio are as follows:
The share is £8 to £12The share is 5 cm to 10 cmThe share is £6 to £18The share is 20 sweet to 15 sweet.How to find the share base on the ratio?A ratio compares values. A ratio says how much of one thing there is compared to another thing.
Therefore, lets use the ratios to share the items.
Share £20 pounds in the ratio 2:3
2 / 5 × 20 = 40 / 5 = 8
Therefore, the share is £8 to £12
Share 15cm in the ratio 1:2
1 / 3 × 15 = 15 / 3 = 5 cm
Therefore, the share is 5 cm to 10 cm
Divide £24 in the ratio 1:3
1 / 4 × 24 = 24 / 4 = 6
Therefore, the share is £6 to £18
Share 35 sweets in the ratio 4:3
4 / 7 × 35 = 20 sweets
Therefore, the share is 20 sweet to 15 sweet.
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