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The value of x in the diagram is : 75°

An isosceles triangle is a type of triangle with base angles equal and opposite sides equal.

Analysis:

Since GF = EF

∠FGE = ∠FEG = (x - 18)°( base angles of an isosceles triangle are equal)

∠FGE + ∠FEG + ∠GFE  = 180°( sum of angles in a triangle)

(x - 18)° + (x-18)° + 66 = 180

2x -36 + 66 = 180°

2x + 30 = 150

2x = 180 - 30

2x = 150°

x = 150/2 = 75°

In conclusion, the value of x in the diagram is 75°

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Explanation:

The volume of the rectangular block is:

V = L*W*H = 5*14*2 = 70*2 = 140 cubic cm.

Now move onto the triangular prism.

The triangular face has a base of 5 cm and height of 4, so the area of this face is

A = base*height/2 = 5*4/2 = 20/2 = 10 square cm

Multiplying this with the depth of the prism tells us the volume is

V = (area of the base)*(depth) = (10 sq cm)*(14 cm) = 140 cubic cm

Therefore, the prisms have the same volume.

Answer: Choice C

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Explanation:

The volume of the rectangular block is:

V = L*W*H = 5*14*2 = 70*2 = 140 cubic cm.

Now move onto the triangular prism.

The triangular face has a base of 5 cm and height of 4, so the area of this face is

A = base*height/2 = 5*4/2 = 20/2 = 10 square cm

Multiplying this with the depth of the prism tells us the volume is

V = (area of the base)*(depth) = (10 sq cm)*(14 cm) = 140 cubic cm

Therefore, the prisms have the same volume.

Answer: 60

Step-by-step explanation:

Answer:

Total Area = 24830.437[tex]m^{3}[/tex]

Step-by-step explanation:

This will be using different AREA formula to find the inner area amount

The image is color coded to each shape area

Let me know if you have any questions !

Hope this helps :)

Answer:

volume = l×b×h = 1.6 × 1.6 × 1.6 = 4.096cm³

Answer:

BC = 6 units

Step-by-step explanation:

given that B is between A and C , then

AB + BC = AC ( substitute values )

3x + 4x - 2 = 12

7x - 2 = 12 ( add 2 to both sides )

7x = 14 ( divide both sides by 7 )

x = 2

Then

BC = 4x - 2 = 4(2) - 2 = 8 - 2 = 6

Answer:

6

Step-by-step explanation:

from the question, since point B is between Ac

AC = AB + BC

12 = 3X+4X -2

3X+4X-2 = 12

7X = 12+2

7X = 14

dividing bothsides by 7

7X/7 = 14/7

X = 2

the length BC = 4X-2 = 4(2)-2 = 8-2= 6

length of BC = 6

Answer:

  $0.88/lb

Step-by-step explanation:

The end result of this units conversion is found by multiplying the fractions in the usual way. The numerator is the product of the numerators; the denominator is the product of the denominators. Of course, the division must be carried to completion to arrive at the unit price.

__

  [tex]=\dfrac{26.29\times0.074\times1}{1\times1\times2.2}\ \dfrac{\text{dollars}}{\text{lb}}=\dfrac{1.94546}{2.2}\ \dfrac{\text{dollars}}{\text{lb}}\approx\boxed{0.88\ \dfrac{\text{dollars}}{\text{lb}}}[/tex]

Answer:

See below in bold.

Step-by-step explanation:

Let t be the number of tulips you buy and r be the number of rose bushes.

a.

The system is:

t + r = 13

4t + 10r = 100

b.

Solving:

4t + 10r = 100

t + r = 13           Multiply this by 4:

4t + 4r = 52      Subtract this from the first equation:

0 + 6r = 48

r = 8.

Now substitute for r in  t + r = 13:

t + 8 = 13

t = 5.

c.

To  buy 13 plants and spend  $100 you need to buy 5 tulips and 6 rose bushes.

Answer:

(-1, 4) and (2, 7)

Step-by-step explanation:

Answer:

[tex] \longrightarrow \tt {4}^{2} + 2 + 3 \times 4 + 4[/tex]

[tex] \longrightarrow \boxed{\tt{\: 34}} \: [/tex]

---------- HappY LearninG <3 ------

Answer:

the answer is 34

Step-by-step explanation:

see the image

The perimeter of Sasha’s garden is 8x - 24 larger than the perimeter of Manual’s garden

The perimeter is given as:

P =  15 + 2x + 7 + 15 + 2x + 7

Collect like terms

P =  2x + 2x + 7 + 15 +  15  + 7

Evaluate the like terms

P = 4x + 44

The area of the garden is given as:

A = 15(2x + 7).

Expand

A = 30x + 105

Manual's expression of the area is 30x + 7

Hence, Manuel's error is that he did not multiply 15 by 7 when expanding the bracket and the actual area is 30x + 105

The side length of Sasha's design is:

L = 3x + 5 in

So, the area is:

A = (3x + 5)^2

Expand

A = 9x^2 + 16x + 25

The difference between both areas is:

Difference = 9x^2 + 16x - 30x + 25 - 105

Evaluate

Difference = 9x^2 - 14x - 80

Hence, the difference between the areas of Manual’s garden and Sasha's design is 9x^2 - 14x - 80

This is calculated using:

P = 4L

So, we have:

P = 12x + 20

The difference between both perimeter is:

Difference = 12x - 4x + 20 - 44

Evaluate

Difference = 8x - 24

Hence, the perimeter of Sasha’s garden is 8x - 24 larger than the perimeter of Manual’s garden

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Answer:

3/8

Step-by-step explanation:

1/8 + 1/4 = 1/8 + 2/8 = 3/8

Note that 1/4 = 1/4 * 2/2 = 1*2 / 4*2 = 2/8

The opposite side of the right angle triangle by using Tan.

[tex]tan \: 22 = \frac{x}{12} [/tex]

[tex]x = 12 \times tan \: 22[/tex]

[tex]x = 4.8 \: cm[/tex]

Therefore, the opposite side of the right angle triangle is 4.8 centimeters

x/12

x= 12*tan 22

x= 4.8 cm

hope this helps

The two angles are supplementary angles and form a straight line which equals 180 degrees

x = 180 - 125

X = 55 degrees

Answer:

hope this will help you

Step-by-step explanation:

x+125=180

x=180-125

x=55°

The slope within two sets of points is calculated using the slope equation [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

The slope of a line or points is the rate of change of the line.

This in other words means that, the vertical change per unit horizontal change

Assume that the points are given as:

(x1, y1) and (x2, y2)

The slope (m) of the points is:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

Hence, the equation of two sets of points is [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

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Answer:

268.08 cm

Step-by-step explanation:

we all know that the FORMULA for a sphere is v=4/3 x π x r^3, so we just SUBSTITUTE.

V=4/3 x π x 4^3

which leaves us with 268.08 cm ^2 maybe??

(hope this helps)

[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=2\\ \theta =36 \end{cases}\implies s=\cfrac{(36)\pi (2)}{180}\implies s=\cfrac{2\pi }{5}\implies s\approx 1.26~in[/tex]

Answer:

y= 4

Step-by-step explanation:

-9x-3y=6

Let x = -2

Substitute for x in the equation

-9(-2) -3y = 6

18 -3y = 6

Subtract 18 from each side

18-3y-18 = 6-18

-3y = -12

Divide by -3

-3y/-3 = -12/-3

y = 4

Answer:

*These Should be the correct answers*

1.C

2.D

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

log(5) 125 =x

5^x = 125

5^x = 5^3

x=3

Based on the calculation below, the amount that can be withdrawn each month for 10 years is a. $769.27.

First, we calculate the future value (FV) of the amount after 20 years using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = A * (((1 + r)^n – 1) / r) ................................. (1)

Where,

FV = Future value of the amount after 20 years =?

A = Monthly deposit = $235.15

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 20 * 12 = 240

Substituting the values into equation (1), we have:

FV = $235.15 * (((1 + 0.00266666666666667)^240 – 1) / 0.00266666666666667) = $78,910.41

The amount planned to be withdrawn on monthly basis can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:

P = PV / ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

P = Monthly withdrawal or payment = ?

PV = Present value = FV calculated above = $78,910.41

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 10 * 12 = 120

Substitute the values into equation (2), we have:

P = $78,910.41PV / ((1 - (1 / (1 + 0.00266666666666667))^120) / 0.00266666666666667) = $769.27

Therefore, the amount that can be withdrawn each month for 10 years is $769.27.

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The answer is A: $769.27

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Have a great day and God bless! :D

Step-by-step explanation:

−3(x−4)+x+1

Evaluate this with x=−6

−3(−6−4)+−6+1

=25

Hey there!

[tex] \displaystyle \red{ \boxed{ \green{25}}}[/tex]

-3(x - 4) + x + 1

>> Substitute -6 for x :

⇒ -3(-6 - 4) + (-6) + 1

⇒ -3(-10) - 6 + 1

⇒ 30 - 6 + 1

⇒ 24 + 1

⇒ 25

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Answer:

B

Step-by-step explanation:

We know that AB has endpoints at A(4, -3) and B(3, 7).

To find Line D, which is the perpendicular bisector of AB, we first need to find the slope of AB and its midpoint.

So, let's find the slope of AB using the slope formula:

Let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the slope formula:

So, the slope of AB is -10.

Remember that the slopes of perpendicular lines are negative reciprocals of each other.

Therefore, the slope of our Line D is the negative reciprocal of -10. Which is -10 flipped and multiplied by a negative.

So, Line D has a slope of 1/10.

Now, since Line D is also the perpendicular bisector of AB, we need to find the midpoint of AB since Line D must pass through this point.

To find the midpoint, we can use the midpoint formula:

We can again let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the midpoint formula to obtain:

Evaluate. So, the midpoint is:

Now, we can find the equation of our Line D. We know that its slope is 1/10, and that it must pass through (3.5, 2). So, we can use the point-slope form:

Where m is the slope. Let's let (3.5, 2) be (x₁, y₁) and substitute 1/10 for m. This yields:

This is the same as choice C. So, choice C is indeed an equation of Line D.

We can distribute the right to obtain:

Add 2 to both sides to acquire:

This is the same as choice D. So, choice D is indeed an equation of Line D.

Moreover, we can put this into standard form by multiply everything by 10, which gives:

Subtracting x from both sides yields:

This is the same as A. So, choice A is also an equation of Line D.

There is no way to acquire choice B. So, B is not an equation of Line D.

Therefore, our answer is B.

And we're done!

Answer:

∠A≅∠Z         AB≅ZX

∠B≅∠X          AC≅ZY

∠C≅∠Y          BC≅XY

ΔCBA≅ΔYXZ

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

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There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.

To find the total number of different sundaes possible, we need to multiply the number of choices for each category: ice cream flavors, toppings, and sizes.

Number of ice cream flavors = 20

Number of toppings = 5

Number of sizes = 3

Total number of sundaes = Number of ice cream flavors × Number of toppings × Number of sizes

Total number of sundaes = 20 × 5 × 3

Total number of sundaes = 300

There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.

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x = -2/3 or -4

see the attachment for solution

hope it helps...!!!

A linear function that models the remaining amount he would have to repay is y =620 - 50x. The slope is -50 and the y-intercept is 620.

A linear function is a function in which there is only one variable that is raised to the power of one. Linear functions usually have the form: mx + b.

Where:

The first step is to determine the amount that would be repaid each month: (620 - 320) / 6 = $50

The linear function:  =620 - 50x.

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Both the tangents are equal to each other. Then the length of BC will be 5.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

A tangent to a circle is a line that passes through the centre of the circle precisely once.

As illustrated in the diagram, there are precisely two tangents to a circle that may be drawn from a location just outside of the circle.

Then both the tangents are equal to each other.

The length of BC will be 5.

The diagram is shown below.

More about the circle link is given below.

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