A right triangle with coordinates A (-2,5), B (-2, 9) and C (4,5) is first rotated 90 degrees clockwise and then
translated 1 unit left and 2 units down to form triangle A'B'C'. What is the measure of angle B'A'C', in
degrees, in the resulting figure?

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:

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

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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Comparing the maple tree and the pine tree growth information, the tree that grows faster is the pine tree.

A 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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Answer: jump off a cliff and shatter your bones

Step-by-step explanation:

The linear function q(x) = -3x + 1 is graphed and attached

The 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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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.

The value of x is 2. We can now find QS by substituting 2 for x in 6x.

QS = 12.

Answer:

going to have to to get the house ready

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.

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]

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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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..

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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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:

Answer:

Step-by-step explanation:

Answer:

97611 is the correct answer

Answer: Gloria will need 14 cups of flour

Step-by-step explanation: 2 1/3 x 6 = 14

The value of the Angle A is  74.3°.

The longest side is in opposition to the longest angle, and the shortest side is in opposition to the smallest angle, respectively.

The opposite of the longest side is the greatest angle, while the opposite of the shortest side is the smallest angle. According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.

The comparable sides are proportionate and the angles are same. The sides that are opposite the same angle are the corresponding sides. For instance, if two triangles have a 90-degree angle on each side, Triangle A's opposing side will match Triangle B's opposite side.

AB/sin(c)=AC/sin(a)=BC/sin(b)

8/sin(a)=5/Sin37°

Angle= 74.3°.

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Answer:

Step-by-step explanation:

Answer: 10:9, 10/9, 10 to 9.

Step-by-step explanation:

Therefore , the solution to the given problem of expression comes out to be  149-k =x be used it as its 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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The value of fraction will be;

⇒ 101/24

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The expression is,

⇒ 7/8+ (-2/3) - (-4)

Now,

Since, The expression is,

⇒ 7/8+ (-2/3) - (-4)

Simplify as;

⇒ 7/8 - 2/3 + 4

⇒ (21 - 16)/24 + 4

⇒ 5/24 + 4

⇒ (5 + 96) / 24

⇒ 101/24

Thus, The solution is,

⇒ 101/24

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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

Step-by-step explanation:

cross multiply

12-m(3m)= 1

12-3m²-1=0

multiply by -1

3m²+1-12=0

3m²= 11

m²= 11/3

m=√11/3.

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

Answer:

If

f

(

x

)

=

2

x

4

−

3

x

+

3

f(x)=2x

4

−3x+3, then what is the remainder when

f

(

Answer:

It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.

The number of guests, g, coming for dinner is not 8, is g ≠ 8.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

The expression,

the number of guests, g, coming for dinner is not 8.

That means,

Let the number is g.

According to the question,

the number is not equals to 8.

That means,

the expression in the numerator form,

g ≠ 8.

Therefore, the term in the mathematical form g ≠ 8.

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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

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:

On solving the provided question we can say that by logarithm the statement is true he is short.

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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Answer:

Make sure to keep track of the signs of the variables. If you add or subtract a variable on one side of the equation, you must do the same to the other side.

Don't forget to distribute if you have a variable inside parentheses. For example, if you have 3x + 2(x + 4) = 7, you would need to distribute the 2 to get 3x + 2x + 8 = 7.

When solving for a variable, make sure to perform the same operation on both sides of the equation to isolate the variable. For example, if you want to solve for x in the equation 3x + 2 = 7, you would need to subtract 2 from both sides to get 3x = 5.

Dalisay hits the target more.

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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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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