The cross-section of a lean-to shelter is in the shape of a triangle. The base of the
triangle is 6 feet more than twice its height. If the area of the triangle is 88 square feet,determine the length of the base and the height of the triangle in feet

The transformation used to map AB to A'B' is not a rigid transformation since the measure of AB is greater than the measure of A'B' and not equal.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

A rigid transformation is a transformation that preserves the shape and size such as rotation, reflection and translation.

Given the points A(-1, 13), B(1, 5), A'(2, 3), and B'(6, 1), hence:

[tex]AB=\sqrt{(5-13)^2+(1-(-1))^2} =\sqrt{68}\\\\A'B'=\sqrt{(1-3)^2+(6-2)^2}=\sqrt{20}[/tex]

The transformation used to map AB to A'B' is not a rigid transformation since the measure of AB is greater than the measure of A'B' and not equal.

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Using Venn sets, it is found that:

For this problem, we consider the following sets:

2 are taking all subjects, hence:

(A ∩ B ∩ C) = 2.

8 are taking chemistry and math, hence:

(A ∩ C) + (A ∩ B ∩ C) = 8.

(A ∩ C) = 6.

6 are taking math and english, hence:

(A ∩ B) + (A ∩ B ∩ C) = 6.

(A ∩ B) = 4.

4 are taking chemistry and english, hence:

(B ∩ C) + (A ∩ B ∩ C) = 4.

(B ∩ C) = 2.

15 are taking chemistry, hence:

C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 15.

C + 6 + 2 + 2 = 15.

C = 5.

20 are taking english, hence:

B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 20

B + 4 + 2 + 2 = 20

B = 12.

18 are taking math, hence:

A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 18

A + 4 + 6 + 2 = 18

A = 6.

There is a total of 40 students, hence:

None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 40.

None + 6 + 12 + 5 + 4 + 6 + 2 + 2 = 40.

None + 37 = 40.

None = 3.

Hence:

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Answer:

140 miles

Step-by-step explanation:

Let's solve the equation step by step,

Step 1: Substract the daily charge of $25 from $39

➟ $39 - $25

➟ $14 {remaining cost except daily rate}

Step 2: Divide $14 by cost per mile

➟ $14/0.10

➟ 140 {total mile driven}

∴ He/she drove 140 miles

Answer: 140 Miles

Step-by-step explanation:

39-25= 14

14/.10 = 140

The two angles are 45° and 135°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given:

One of the same side angles of two parallel lines is three times the other angle.

According to given question we have

Let the smaller side= x,

The larger side = 3x.

The two angles are supplementary.

x + 3x = 180°

4x = 180°

Divide by 4 on both sides we get,

x = 45°

3x = 135°

Therefore,  the two angles are 45° and 135°.

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Answer:

6²

Step-by-step explanation:

6² is 6×6 which is 36

if you write it as 6² then:

6²=6^x

since the bases are equal you can cancel out the bases and it becomes:

x=2

Answer:

a. 6^2

Step-by-step explanation:

A because six times itself is equal to 36.

Answer:

49 cards in each binder

Step-by-step explanation:

If there are 5 binders and each binder contains the same amount of cards, you can just do 245 divided by 5 which gives you 49.

Answer:

17

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}9-6\\\end{array}\right]+\left[\begin{array}{ccc}-5-(9)\\\end{array}\right][/tex]

=3+14

=17

Answer:

s = 8 cm

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

given A = 64 cm² , then

s² = 64 ( take square root of both sides )

s = [tex]\sqrt{64}[/tex]

s = 8 cm

Answer:

[tex]5\sqrt{5}[/tex] = ~11.18

The correct answers would be options (A) and (C).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given two cases,

p: -3x + 8x - 5x = x

q: (3x)(5y) = 15xy

We have to need to isolate the variables:

p: -3x + 8x - 5x = x

⇒  (-3x - 5x) + 8x = x

⇒  -8x + 8x = x

⇒ x = 0

This is not always true, hence the statement is incorrect because this will hold true for only one value of x.

q: (3x)(5y) = 15xy

⇒ (3x)(5y) = 15xy

⇒ (3×5)(x×y) = 15xy

⇒ 15xy = 15xy

If both x and y are true for any value, then the statement is true.

Hence, p → q and q → p are false.

Therefore, the correct answers would be options (A) and (C).

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Answer:

English: 48 minutes

Math: 54 minutes

Biology: 18 minutes

Step-by-step explanation:

Set up each subject with the variable x as the biology homework.:

English: (x+30)

Math: (3x)

Biology: (x)

Now add them together and set it equal to 120 (2 hours into minutes):

x + 30 + 3x + x = 120

Move 120 over to the left and simplify:

5x - 90 = 0

Solve:

5(x - 18) = 0

x - 18 = 0

x = 18

So biology is 18 minutes, and then plug 18 in for all the other subjects:

English: 18+30=48 minutes

Math: 3*18=54 minutes

Biology: 18 minutes

Answer:

6^5 is equals to 7776 and 7776×6^-5 is equals to 1

Answer:

(6x² - 5)(x² + 2)

Step-by-step explanation:

6x⁴ - 5x² + 12x² - 10

(6x⁴ - 5x²)  (12x² - 10)

x²(6x² - 5) + 2(6x² - 5)

(6x² - 5)(x² + 2)

I hope this helps!

Answer:

Step-by-step explanation:

So we have 6x4-5x2+12x2-10

So we are going to add same elements

-5x2+12x2=7x2

so now we have

6x4 +7x2-10

Let u=x2

6u2+7u-10

Now we factor

(6u-5)(u+2)

Replace x2 for u

(6x2-5)(x2+2)

Hope this helps!^^

here you go :) explanation up top

The equation of line for m = 5/6 and the y -intercept is (0,12) is y = 5/6x + 12.

The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

The equation for line is y = mx + c

Given, m = 5/6, y-intercept = (0,12)

now putting the values in the equation,

y = 5/6x + 12

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to get the equation of any straight line, we simply need two points off of it, again, let's use the ones from the table in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{11}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{11}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 4 }{ 2 }\implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{2}(x-\stackrel{x_1}{2}) \\\\\\ y-7=2x-4\implies {\LARGE \begin{array}{llll} y=2x+3 \end{array}}[/tex]

Answer:

Step-by-step explanation:

Here ya go!

The current location of G is (-4,3)

If it was translated to the left by four units, that would be an extra -4

so our new coordinates are (-8,3)

Now if we translate it up 3 units, thats adding 3

so our new coordinates are

(-8,6)

Hope this helps!^^

Answer:

x=6.24

Step-by-step explanation:

cos 78° =adj/hyp=x/30

cos 78° =x/30

x=cos 78°×30

x=0.2079×30

x=6.237350725

to the nearest hundredth

x=6.24

Step-by-step explanation:

or, x + 65° = 180° [ Being Straight line]

or, x = 180° - 65°

or, x = 115°

Therefore the value of x is 115° .

Now,

or, 4x = 4 × 115° = 460° .

Step-by-step explanation:

Question no 23 : Option d

Question no 21:

angles on a straight lin is equal to 180°

150-180 = 30 (option d)

I just answered question no 23 and 21

re check the answers if you can I am a student too just trying to help as much as I can.

Answer: SA=326.56 inches

Step-by-step explanation:

[tex]SA=2\pi r^2+2\pi rh\\SA=2\pi r(r+h)\\r=4 \ inches\ \ \ \ \ h=9\ inches\ \ \ \ \ \ \pi =3.14\\Hence,\\SA=(2)(3.14)(4)(4+9)\\SA=(25.12)(13)\\SA=326.56\ inches[/tex]

By combining the like terms, the simpler form of expression -(8a+3b)+10(2a-5b)  is 12a-53b

Given,

The expression = -(8a+3b)+10(2a-5b)

Expand the terms

-(8a+3b)+10(2a-5b)= -8a-3b+20a-50b

Combining like terms

-8a-3b+20a-50b = 12a-53b

Hence, by combining the like terms, the simpler form of expression is -(8a+3b)+10(2a-5b) 12a-53b

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Answer:B. The number is composite. Its prime factors written as a product are (5*3^3*2^2)

Step-by-step explanation:

Since 540 is an even number, that means it can be divided by 2. This means that the number is composite.

You can keep dividing it by 2 until you can't anymore.

Once you divide 540 by 2 twice, then you get 135.

You can divide it by 5 because the ones digit is 5.

Then you get 27, which is 3 times itself 3 times.

You finally multiply the numbers you divided by, and you get 2*2*5*3*3*3, which is 5*3^3*2^2.

Answer:

It the square with 3/4 shaded. the point shows 0.75 and the square shows 75% which is 3/4.

Given that ∠ADB and ∠CDB are complimentary angles, the numerical measure of angle CDB is 25 degrees.

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

Given that;

Since ∠CDA is a right triangle, the sum of ∠ADB and ∠CDB sums up to 90 degrees.

∠ADB + ∠CDB = 90°

(7x +2) + (3x - 2) = 90

Solve for x

7x +2 + 3x - 2 = 90

7x + 3x - 2 +2 = 90

10x = 90

x = 90/10

x = 9

Now, the numerical measure of angle CDB will be;

m∠CDB = (3x - 2)

Plug in x=9

m∠CDB = 3(9) - 2

m∠CDB = 27 - 2

m∠CDB = 25 degrees

Given that ∠ADB and ∠CDB are complimentary angles, the numerical measure of angle CDB is 25 degrees.

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Can someone help explain how to solve

In the picture there are 4 question that are

1) [tex]A(-6,-2)\rightarrow A^{'}(-6,2)\\B(-3,-6)\rightarrow B^{'}(-3,6)\\C(-2,-2)\rightarrow C^{'}(-2,2)\\[/tex]

2)[tex]D(15,10)\rightarrow D^{'}(6,4)\\E(5,10)\rightarrow E^{'}(2,4)\\F(10,-5)\rightarrow F^{'}(4,-2)\\[/tex]

3)[tex]G(-2,7)\rightarrow G^{'}(-7,-2)\\H(-4,8)\rightarrow H^{'}(-8,-4)\\I(-3,5)\rightarrow I^{'}(-5,-3)\\[/tex]

4) [tex]J(11,-8)\rightarrow J^{'}(1,-5)\\K(6,-1)\rightarrow K^{'}(-4,2)\\L(3,-7)\rightarrow L^{'}(-7,4)\\[/tex]

The transformation has the following form:

1)[tex](x,y)\rightarrow(x,-y)[/tex]

2)[tex](x,y)\rightarrow\frac{2}{5}(x,y)[/tex]

3)[tex](x,y)\rightarrow(-y,x)\\[/tex]

4) It does not have transformation.

Geometric Transformation:

Images of triangles, quadrilaterals, pentagons, and other geometric shapes can undergo geometric transformations through the vertices in a Cartesian plane. Reflection, rotation, and translation are the three transformations; they only affect the geometric figure's location and not its size. Expansion and contraction are the two transformations that alter the geometric figure's size.

It is necessary to know the sort of transformation that took place given the points and their transformations.

1) We observe that point transformation A,B and C are transformed.

The transformation has the following form:

[tex](x,y)\rightarrow(x,-y)[/tex]

Every x-value remains constant, while every y-value flips from what it was.[tex](x,y)\rightarrow(x,-y)[/tex]

2)We observe that point transformations D, E, and F are contractions. Let's now identify the scalar that was applied to the transformation. We compute the product of the original point's coordinate and one of the transformation point's coordinates.

[tex]\frac{D^{'} _{y} }{D_{ y}} =\frac{4}{10} =\frac{2}{5}[/tex]

We multiply the coordinates of points E and F and check the results to make sure this is true.

For E:

[tex]\frac{2}{5} (5,10)=(2,4)\\Therefore,E^{'} =(2,4)[/tex]

For F:

[tex]\frac{2}{5} (10,-6)=(4,-2)\\Therefore,F^{'} =(4,-2)[/tex]

Therefore, The transformation has the following form:

[tex](x,y)\rightarrow\frac{2}{5}(x,y)[/tex]

3)We observe that point transformation G,H and I are transformed.

The transformation has the following form:

[tex](x,y)\rightarrow(-y,x)[/tex]

Every y-value flips from what it was to the opposite. The x and y values are reversed.[tex](x,y)\rightarrow(-y,x)[/tex]

4)We observe that point transformation J,K and L are not transformed.

It does not satisfy the condition of the transformation.

Therefore, this is how we solve the transformation.

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One year from now, there are 300 freshmen, 1425 sophomores, 1375 students that transferred out, and 3900 students graduated.

Each category is based on the percentages given, 25% of students transfer, 15% have to repeat the year, and 60% complete the year and the fact that once a student has transferred or graduated they have a 100% chance of staying classified that way.

Percentage, which was adapted from the Latin word "per centum", which means "by the hundred", is a fraction or a ratio in which the value of whole is always 100. It is represented by the symbol "%".

If currently there are 2,000 freshmen, 1,500 sophomores, 500 students that have transferred, and 3,000 graduates,

Among the 2000 freshmen, 25% of students transfer, 15% have to repeat the year, and 60% complete the year.

students who transfer = 25% of 2000 = 500

freshmen(repeater) = 15% of 2000 = 300

sophomore = 60% of 2000 = 1200

Among the 1,500 sophomores, 25% of students transfer, 15% have to repeat the year, and 60% complete the year.

students who transfer = 25% of 1500 = 375

sophomore(repeater) = 15% of 1500 = 225

students who graduated = 60% of 1500 = 900

Adding the total number of sophomores(freshmen who completed the year and sophomores that have to repeat the year)

sophomores = 1200 + 225 = 1425

Adding the total number of students who transfer,

500 + 500 + 375 = 1375

Adding the total number of student that graduated,

3000 + 900 = 3900

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The equation of the line in slope-intercept form with a slope of 1/2 and y-intercept of (0 , 0) is y = 1/2 x.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given that the slope of the line is 1/2 and the y-intercept is (0 , 0), write the equation of the line by simply plugging in its values.

y = mx + b

y = (1/2)x + 0

y = 1/2 x

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The distance of AO and BO are the same so the given triangle will be an isosceles triangle.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

The given vertices are making a triangle as shown below in the figure.

Distance between A(5,12) and O(0,0) is

⇒ [tex]\sqrt{(5 - 0)^2 + (12 - 0)^2}[/tex]

⇒ 13

Distance between B(13,0) and O(0,0) is

⇒ [tex]\sqrt{(13 - 0)^2}[/tex]

⇒ 13

Since the two sides are the same so triangle will be isosceles.

Hence "The distance of AO and BO are the same so the given triangle will be an isosceles triangle".

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