Therefore , the solution of the given problem of angles comes out to be equation : x+ y =85°.
'
An angle is what?In Euclidean geometry, an angle is a shape that is made up of two rays, known as the tone's flanks, that meet at a midpoint known as such angle's vertex. Two rays may combine to form an angle there in plane where they are positioned. When two planes collide, an angular is also generated. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays of lines that share a termination. The origin of the English term "angle" is the Latin phrase "angulus," which meaning "horn." The vertex is the point in which the two vectors, also known as that of the faces of the angle, converge.
Here,
Given :
Let two angles be x and y is
=> x+ y =85°
So, the equation is represented as x+ y =85°.
Therefore , the solution of the given problem of angle comes out to be equation : x+ y =85°.
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if the length of the basketball court is (x+16) and the width is (x-2). what is the area
Answer:
[tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex]
Step-by-step explanation:
a basketball court is a rectangle, therefore its area is length x width.
the length given is (x+16)
the width given is (x-2)
substitute into the rectangular area equation:
length x width = (x+16)(x-2)= [tex]x^{2}[/tex]+14x-32
specific units (e.g. centimetres, meters, feet, etc) were not given so use the term 'units', and because we are dealing with area, use [tex]units^{2}[/tex].
therefore the answer is, [tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex].
i hope that helps :)
Answer:
therefore the answer is, [tex]x^{2} +14x-32units^{2}[/tex].
Step-by-step explanation:
How do I even do this?
Answer:
going to have to to get the house ready
If QR = 8, RS = x + 2, and QS = 6x, what is QS?
Answer:
QS = 12
Step-by-step explanation:
Hello!
We can see that QS is the sum of QR and RS, which is equal to 6x.
We can substitute the given values to solve for x, and then use that to find QS.
Solve for xQS = QR + RS6x = 8 + x + 2 Substitute values6x = 10 + x Combine like terms5x = 10 Subtract xx = 2 Divide by 2The value of x is 2. We can now find QS by substituting 2 for x in 6x.
QS = 12.
You decide to take a hot air balloon ride and remember to take binoculars to look around while you are airborne. As the balloon rises, you use a GPS to determine your height in meters, h, and the distance in kilometers, d, to the farthest object that you can see. The table below shows the two measurements.
Height in meters 15 30 45 60 75 90 105
Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598
1. Determine a function that could be used to model the data in the table.
Make sure to use h for height and d for distance.
2. If the balloon is 800 meters high, what is the farthest distance that you would be able to see? Round answer to the nearest whole number
3. What type of function best models the data in the table?
4. A building is 16km away. What height does the balloon have to rise for the building to be visible. Round the answer to nearest whole number.
Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex..
Explain trigonometry.Trigonometry is a discipline of mathematics that examines relationships between triangles' degrees and sides. Trigonometry is used frequently in geometry because every straight-sided form may be broken down into a group of triangles. Trigonometry and other areas of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, have a staggering amount of interrelationships.
Here,
Angle of elevation to the balloon's peak: = 28°
When the balloon is erect, a right triangle is formed by the horizontal distance to the balloon, l, the height of the balloon, h, and the distance to the top of the balloon, d.
Aside from the hypotenuse
l = The leg next to the provided reference angle
,h = The leg perpendicular to the specified angle,
Trigonometric ratios give us;
Cosx is equal to the product of the hypotenuse and adjacent lengths.
where we obtain;
Cos x equals l/d
=>Cos 28 = 30 m /d
=> d = 30m/Cos 28 ≈ 33.977
Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex.
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If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?
Answer:
If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
Use the drop-down boxes to show a function in the form y = mx + b for the line that contains the points (–6.4, –2.6) and (5.2, 9).
The equation in the slope-intercept form is y = x + 3.8
What is a slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
A line that contains the points (–6.4, –2.6) and (5.2, 9).
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
So, the equation,
y + 2.6 = {(9 + 2.6)/(5.2 + 6.4)} (x + 6.4)
y + 2.6 = x + 6.4
y = x + 6.4 - 2.6
y = x + 3.8
Therefore, the equation y = x + 3.8 is in the slope-intercept form.
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Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
X
6
-
X
The equation has Select an option
0
attempt 1 out of 2
The equation has one solution.
A value of x that makes the equation true is 6 which when substituted into the equation and simplified makes the equation turn into x = 0.
A value of x that makes the equation false is 8 which when substituted into the equation and simplified makes the equation turn into x = 2.
How to evaluate the equation?From the information provided, we have the following equation:
x - 6 = 6 - x
Rearranging the equation by collecting like terms, we have the following solution:
x + x = 6 + 6
2x = 12
x = 12/2
x = 6
Substituting the value "6" into the equation, we have the following solution;
x - 6 = 6 - 6
x - 6 = 0
Assuming x = 8, we have the following solution;
x - 6 = 8 - 6
x - 6 = 2
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Complete Question:
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
x - 6 = 6 - x
The equation has _____.
A value of x that makes the equation true is ___ which when substituted into the equation and simplified makes the equation turn into ____.
A value of x that makes the equation false is ___ which when substituted into the equation and simplified makes the equation turn into ___.
Triangle ABC has vertices A(-3, 3), B(2, 5), and C(4, - 3).
a. What is the x-coordinate of the centroid of triangle ABC?
(-,5/3)
Answer:
Step-by-step explanation:
To find the x-coordinate of the centroid of triangle ABC, we need to take the average of the x-coordinates of the three vertices of the triangle. The x-coordinates of the vertices of triangle ABC are -3, 2, and 4, so the average of these three numbers is (-3 + 2 + 4) / 3 = (3) / 3 = 1.
Therefore, the x-coordinate of the centroid of triangle ABC is 1. The correct answer is (-,1). The given answer (-,5/3) is not the correct x-coordinate of the centroid.
Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.
The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.
What does rate of change mean?
An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then the rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.
Surafce area of a prism is equal to
2(Area of base) + (perimeter of base)(height)
2b^2+4bh
[tex]S=2b^2+4bh[/tex]
[tex]\frac{ds}{dt}=4b\frac{db}{dt} + 4b\frac{db}{dt} + 4h\frac{db}{dt} \\[/tex]
It is given that db/dt= -7 and dh/dt -=10.
At a particular instant b= 4km, h=9 km.
Now we will substitute the values in this formula:
[tex]\frac{ds}{dt}=-4*4*7-4*4*7+ 4*9*10\\\frac{ds}{dt}=136[/tex]
The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.
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Lena had 149 dollars to begin with. She just spent k dollars. Using k, write an expression for the number of dollars she has left.
Therefore , the solution to the given problem of expression comes out to be 149-k =x be used it as its expression.
Define Expression .A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Here,
Given : Lena has $149
she spends k amount of money
The money left be x
=> 149-k =x
Therefore , the solution to the given problem of expression comes out to be 149-k =x be used it as its expression.
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area of 6ft 10ft 14ft figure
Answer:
209.25
Step-by-step explanation:
Calculate the areas of the triangle, rectangle, and half circle, then add them together:
triangle = 1/2bh = 1/2(6)(10) = 30
rectangle = bh = (14)(10) = 140
half circle = 1/2πr² = 1/2(3.14)(5)² = 39.25
radius = r = D/2 = 10/2 = 5
Total area = 30 + 140 + 39.25 = 209.25
Answer:
209.25 ft²
Step-by-step explanation:
To find the total area of the figure you have to add the areas of the triangle, rectangle and the semi circle.
Area of the triangle.
[tex] \sf \: A = \frac{1}{2} \times base \times height \\ \sf \: A = \frac{1}{2} \times 6 \: ft \times10 \: ft \\ \sf \: A = \frac{1}{2} \times 60 \: {ft}^{2} \\ \sf \: A =30 \: {ft}^{2} [/tex]
Area of the rectangle.
[tex]\sf \: A =length \times width \\ \sf \: A =14 \: ft \times 10 \: ft \\ \sf A =140 \: {ft}^{2} [/tex]
Area of the semi circle.
[tex] \sf \: A = \frac{1}{2} \pi {r}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times ( \frac{10}{2}) ^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times {5}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times 25 \\ \sf \: A = \frac{1}{2} \times 3.14 \times 25 \\ \sf \: A = \frac{1}{2} \times 78.5 \\ \sf \: A = 39.25 {ft}^{2} [/tex]
Add up all the areas to find the total area.
[tex] \sf \: Total \: Area = 30 {ft}^{2} + 140 {ft}^{2} + 39.25 {ft}^{2} \\ = 209.25 {ft}^{2} [/tex]
Graph the linear equation q(x)=-3x+1
The linear function q(x) = -3x + 1 is graphed and attached
How to graph the linear functionThe graph of the linear function is a straight line graph and the table of values used in making the plot is calculated as follows
For x = -20, q(x) = -3 * -20 + 1 = 61
For x = -10, q(x) = -3 * -10 + 1 = 31
For x = 0, q(x) = -3 * 0 + 1 = 1
For x = 10, q(x) = -3 * 10 + 1 = -29
For x = 20, q(x) = -3 * 20 + 1 = -59
Table of values
x y
-20 61
-10 31
0 1
10 -29
20 -59
These points are plotted in the cartesian coordinate by tracing the point of intersection of the x and y and marking it. Then the marked points are joined together to form a straight line
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All of the quadrilaterals in the shape below are squares. Find the area of the shaded
region.
Answer: I don't remember how to solve, but, I figured out the lengths of each side in the shaded region:
11, 11, 7, 7, 4, 4
Step-by-step explanation:
Hope this helps!! :D
The pairs of polygons below are similar. Give the sale factor of figure A to figure B
Answer:
Given that Figure A and Figure B are similar polygons, the scale factor of Figure A to Figure B = 5/2.
Recall:
Similar Polygons have corresponding side lengths whose ratio are equal. That is, their pairs of corresponding sides are proportional.
The ratio of any of their corresponding side length = scale factor
Given the two pairs of similar polygons, the scale factor of figure A to figure B will be calculated as follows:
A side length of Figure A = 10
Corresponding side length of Figure B = 4
Scale factor of Figure A to Figure B = 10/4 = 5/2
Step-by-step explanation:
y 10- 9 8 6 5 4 2 1 2 3 4 5 6 7 8 9 10 What is the equation of the blue line? X
Therefore , the solution of this is the required system of equation is,
y=-x+6 and y=x+10.
Explain the equation.A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.
Here,
(0,6) and the blue line pass through them (-2,8). You may figure out the equation for the blue line as,
=> y-6/x-0 = 8-6 /-2-0
=>y-6/x = 2/-2
=> y-6=-1(x)
y=-x+6
(-2, 8) and the red line pass through them (-3,7). The red line's equation can be calculated as,
y-8/x- (-2) = 8-7 /-2-(-3)
y-8 /x+2 = 1
y-8=x+2
y = x + 10
Thus, the required system of equations is,
y=-x+6 and y=x+10.
Therefore , the solution of this is the required system of equations is,
y=-x+6 and y=x+10.
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√2 (2-2√10) how do you simplify
Answer:
2√2- 4√5
Step-by-step explanation:
√2 (2-2√10)
2√2- 2√20
2√2- 2√(4*5)
2√2- 2*2√5
2√2- 4√5
Patty made a scale drawing of a park using a scale of in.=45ft. The table below shows the side lengths in her drawing. Jamie uses Patty's drawing to make a different scale of 2 in.= 35ft. Which value is one of the side lengths o Jamie's drawing?
Answer: A scale is a ratio of the size of the representation (such as a drawing) to the size of the real-world object being represented. In this case, Patty's drawing uses a scale of 1 inch = 45 feet, and Jamie's drawing uses a scale of 2 inches = 35 feet.
In order to find the side length of Jamie's drawing of one of the side length we need to use a proportion:
Jamie's side length / Patty's side length = Jamie's scale / Patty's scale
So if we know one of the side length of Patty's drawing we can find the side length of Jamie's drawing. Let's assume that the side length of Patty's drawing is x
x / Jamie's side length = 45 / 35
So we can isolate Jamie's side length by multiplying both sides by Jamie's scale of 35ft/2 inches
Jamie's side length = (x*35)/45
This is the length of one side length in Jamie's drawing using the scale of 2 inches = 35 feet. If you don't have the length of one side in patty's drawing you can't find the side length of Jamie's drawing.
Step-by-step explanation:
Let p be the statement "He is tall" and let q be the statement the following statements in symbolic form using p and q. He is handsome". Write each of /1/ He is tall and handsome. /2/ He is tall but not handsome. /3/ He is false that he is short or handsome. /4/ He is neither tall nor handsome. /5/ He is tall, or he is short and handsome /6/ It is not true that he is short or not handsome
On solving the provided question we can say that by logarithm the statement is true he is short.
what is logarithm?The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).
He is tall, or he is short and handsome
It is not true that he is short or not handsome
by logarithm,
the statement is true he is short.
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Write the equation of the ellipse with a center at (5,-2), one vertex at (2, -2) and a focus at
(5+ √5,-2)
On solving the provided question we can say that - the value of the ellipse will be (5+ , root5)
what is ellipse?In mathematics, an ellipse is a planar curve that encompasses two focus points and ensures that the sum of the two distances from any point on the curve to the focal points is constant. In doing so, the circle—a particular variety of ellipse with two equal focus points—is generalized. The ellipse, whose eccentricity is less than 1, indicates the area containing the points whose distances from its two foci add up to a certain amount. Running tracks in sporting arenas and 2D egg forms are two straightforward examples of ellipses in daily life.
here we have,
center at (5,-2), one vertex at (2, -2) and a focus at
(5+ √5,-2)
so the answer is (5+ , root5)
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Click on a factor pair of 32
Factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)
⇒ Firstly find the factors of 32
How Do You Work Out Factors of 32?
Step 1: Let's start with the whole number 1 and work our way up to the factors of 32. 32 ÷ 1= 32
Step 2: Now divide 32 by two. 32 ÷ 2= 16
Step 3: Then we get. 32 ÷ 4= 8
Step 4: Similarly, we calculate all the 32 factors.
32 factors = 1, 2, 4, 8, 16, and 32.
⇒ Secondly, find factor pairs of 32
The two numbers that, when multiplied together, give 32 are the factors of 32 in pairs. The factors of 32 are listed below in pairs.
Products of 32 Factor pair of 32
1 × 32 = 32 (1, 32)
2 × 16= 32 (2 ,16)
4 × 8 = 32 (4, 8)
∴Therefore, factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)
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1. This week Tony practiced basketball 2 hours on Tuesday, 1 hours Wednesday, and 2 hours on Friday. Next
week Tony will practice basketball for the same number of hours Tuesday, Wednesday, and Friday. What is
the total number of hours Tony will practice basketball over the 2 weeks?
For 2 weeks tony will spent time for practice basketball is 10 hours.
How do you find time in math problems?The equation for calculating time is [Time = Distance Speed]. The distance may be calculated using the time formula [Distance = Speed Time].Work completed equals Time x Rate of Work. Work Rate is equal to One/Time. Time = 1 divided by the rate of work. If a task is completed across x days, then the amount of work completed in a single day is equal to 1/x.The Greenwich hour angle, abbreviated GHA, is used to define the Equation of Time as E = GHA (apparent Sun) - GHA (mean Sun) (1). E = right ascension of the fictional mean Sun - right ascension of the apparent (real) Sun is a different formula that is frequently used in textbooks.Given data :
1st week
= Tuesday = 2 hours
= Wednesday = 1 hour
= Friday = 2 hours
same for 2nd week
so total hours = 1st week + 2nd week
= 2 + 1 + 2 + 2 + 1 + 2
= 10 hours
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A cake recipe calls for 2 1/3 cups of flour. If Gloria is planning on making 6 cakes for a bake sale, how many cups of flour will she need?
Answer: Gloria will need 14 cups of flour
Step-by-step explanation: 2 1/3 x 6 = 14
Between 2020 and 2021, the population of a town decreased by 35%
In 2021, the population of the town was 94,900
What was the population of the town in 2020?
Answer:
Step-by-step explanation:
Answer:
97611 is the correct answer
A system of linear equations with an infinite number of solutions is a(n).
_____system.
Answer:
It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.
Kendra and Dalisay practice archery. Kendra hits the target 3 times every 5 misses. Dalisay hits the target 5 times every 7 misses. Who hits the target more?
Dalisay hits the target more.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Kendra hits the target 3 times every 5 misses.
And, Dalisay hits the target 5 times every 7 misses.
Since, Kendra hits the target 3 times every 5 misses.
Hence, In 1 misses Kendra hits the target = 3/5 times
= 0.6 times
And, Dalisay hits the target 5 times every 7 misses.
Hence, In 1 misses Dalisay hits the target = 5/7 times
= 0.74 times
Thus, Dalisay hits the target more.
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whats 2+2 pls i have a test tomorrow i need to pass it
In a basket there are 18 tomatoes, 12 potatoes, and 8 carrots.identify the ratio of carrots and potatoes to tomatoes in all 3 forms.
Answer:
Step-by-step explanation:
Answer: 10:9, 10/9, 10 to 9.
Step-by-step explanation:
Solve for : -3(x+8)=30
Answer: -18
Step-by-step explanation:
Distribute the -3 to the values inside the parentheses, (x and 8) which equals -3x-24.
Then, use inverse operations by adding 24 on both sides (it will cancel on the left) to get -3x=53
Then divide -3 on both sides to get x by itself
Answer:
-18
Step-by-step explanation:
-3(x+8)=30
by dividing 3 from both sides
-(x+8)=10
by multiplying -1 for both sides
(x+8)= -10
by subtracting 8 from both sides
x = -18
what is an equation of the line that is parallel to y = - 5 x + 6 and passes through the point (-4,-1)
The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.
The equation of the line is given below.
y = - 5x + 6
The equation of the line that is parallel to the line y = - 5x + 6 is written as,
y = - 5x + c
The equation passes through (-4, -1), then we have
- 1 = - 5 (-4) + c
- 1 = 20 + c
- 21 = c
The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.
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A maple tree grows 1.5 feet each year. The table shows the yearly growth for a pibe tree
Comparing the maple tree and the pine tree growth information, the tree that grows faster is the pine tree.
How to find the tree that grow fasterA mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.
Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting or initial value
b = the base function
x = the exponents
Considering the given problem, b for maple is given as 1.5 and we calculate for pine using the data in the table. the equation is derived as follows
f(x) = a(b)ˣ
12 = a(b)¹
24 = a(b)²
dividing 24 = a(b)² by 12 = a(b)¹
b = 2
hence for pine tree the b is 2 which is greater than 1.5
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