Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "Cannot be determined" in place of the rule. ∆ANT ≅ ∆_____ by _____

Hey there! I'm happy to help!

Sine is a trigonometric ratio. It is the ratio of the opposite side of the angle to the hypotenuse. Since it is a ratio, it does matter how big or small the triangle is as long as the sides remain in proportion. If the opposite side is 4 and the hypotenuse is 5, the sine of x will be the same as it would be if the opposite were 16 and the hypotenuse were 20 because they simplify to the same ratio (4/5).

The sine (or any trigonometric ratio) of any number stays the same even if the triangle is dilated because the proportion between the sides stays the same no matter how big or small. So, they told us the answer at the beginning. The sine of angle x is 4/5.

Have a wonderful day! :D

Answer: 4/5

Step-by-step explanation: Took the test and got it right. I assumed it was the same because angles do not change after being dilated.

Answer:

The length of one side of the octagon is 7.65 cm

Step-by-step explanation:

The parameters given are;

A regular octagon inscribed in a circle of radius, r, of 10 cm.

The length of each side is found from the isosceles triangle formed by the radius and one side of the octagon

The sum of interior angles in a polygon, ∑θ[tex]_i[/tex] = 180 × (n - 2)

Where;

n = The number of sides of the polygon

θ[tex]_i[/tex] = The interior angle of the polygon

For the octagon, we have;

n = 8, therefore;

∑θ[tex]_i[/tex] = 180 × (8 - 2) = 1080

Given that there are eight equal angles in a regular octagon, we have;

∑θ[tex]_i[/tex] = 8 × θ[tex]_i[/tex] = 1080

θ[tex]_i[/tex] = 1080/8 = 135°

The sum of angles at the center of the circle = 360

Therefore, the angle at the center (tip angle) of the isosceles triangle formed by the radius and one side of the octagon = 360/8 = 45°

The base angles of the isosceles triangle is therefore, (180 - 45)/2 = 67.5° = θ[tex]_i[/tex]/2

The length of the base of the isosceles triangle formed by the radius and one side of the octagon = The length of one side of the octagon

From trigonometric ratios, the length of the base of the isosceles triangle is therefore;

2 × r × cos(θ[tex]_i[/tex]/2) = 2×10 × cos(67.5°) = 7.65 cm

The length of the base of the isosceles triangle = 7.65 cm = The length of one side of the octagon.

Answer:

1st triangle:

sin(C): 0.64, [tex]\frac{16}{25}[/tex]

cos(C): 0.8, [tex]\frac{4}{5}[/tex]

Second triangle:

sin(C): 0.75, [tex]\frac{\sqrt{5} }{3}[/tex]

cos(C): 0.67, [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Using SOH CAH TOA, we know that to find the sin of an angle, it's Opposite/Hypotenuse.

To find the cos of an angle, it's adjacent/hypotenuse.

In the 1st triangle:

The adjacent to C is 16, the hypotenuse is 25.

[tex]\frac{16}{25} = 0.64[/tex] is the sin of C.

The adjacent to C is 20, and the hypotenuse is 25.

[tex]\frac{20}{25} = 0.8[/tex] is the cos of C.

In the second triangle:

The opposite to C is [tex]\sqrt{5}[/tex] and the hypotenuse is 2.

[tex]\frac{\sqrt{5} }{2} \approx0.75[/tex] is the sin of C.

The adjacent to C is 2 and the hypotenuse is 3.

[tex]\frac{2}{3} \approx 0.67[/tex] is the cos of C.

Hope this helped!

Answer:

1

Step-by-step explanation:

1

Answer:

10

Step-by-step explanation

Answer:

10

Step-by-step explanation:

Answer:

200in²

Step-by-step explanation:

I separated the shaded face into two squares. Both squares would be 10 by 10.

Area of a square: [tex]a=s^2[/tex]

For each square, they have a side of 10 in.

[tex]a=10^2\\\\a=100[/tex]

The area for one square is 100in². This means that for the whole face, which is made out of 2 squares, the area would be 200in².

The second option should be the correct answer.

Answer:

Answer is  x = 24

Matches 3/2 x +1 = 4/5x-5

Step-by-step explanation:

We start with Mary 3/2x = 24 as 24/1.5 = 16 and 16 x 1/2 = 8

where 16 is 2/2 and 1/2 of 16 = 8

We find Nancy add 1 = 25 as 25/1.5 = 16.666.. and 1/2 = 8.333.

When 1 is added its done at end of both equations as multiplication occurs before hand.

Gracie has the same as Nancy =  5x+5 means   25 x 5 = 250+5 = 255 each.

50 x 5 = 250 + 5 +5= 510

510 + 24 + 1 = 535 seashells.

Because

24 + 1 = 25

matches

5/4 of 24 = 30

30 - 5 = 25

x=16 is the equation that represents this situation and identify its solution.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of shells Marry has.

Gracie has 5 more than times the number of shells Mary has.

Gracie = 1 1/4x + 5

Nancy  = 1 1/2x+ 1

Now we have given that: Gracie =Nancy

[tex]1\frac{1}{4}[/tex] x + 5 = [tex]1\frac{1}{2}[/tex]x + 1

5/4x + 5 = 3/2x + 1

5x + 20 = 6x + 4

Subtract 6x  and 20 on both sides

5x - 6x = 4 - 20

-x = - 16

x = 16.

Hence, x=16 is the equation that represents this situation.

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On a graph, points are grouped closely together to form a line and decrease.

====================================

Explanation:

Negative association is where the points decrease as you move from left to right. In other words, you move downhill as you move from left to right. There could be random upward bumps here and there, but overall the general trend is down.

Linear association is when the points are close to the same straight line, known as the regression line.

When points have strong negative linear association, we combine the two ideas mentioned above. The points are close to the same straight line and this line has a negative slope. The correlation coefficient r is close to r = -1.

Choice C is a close answer, but choice D is the better answer due to the "to form a line". If all points are on the same straight line, then r = -1 exactly and we have the strongest possible negative correlation.

The strongest negative linear association is depicted by the graph where points are grouped closely together to form a line and decrease.

Therefore, a graph with closely grouped points which forms a line and decreases infers a strong negative linear association.

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Answer: The solution for the system is (2, -7)

Step-by-step explanation:

Ok, here we have linear relationships.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, we have two lines:

ya, that passes through:

(-8, -5) and (-3, -6)

Then the slope is:

a = (-6 - (-5))/(-3 - (-8)) = (-6 + 5)/(-3 + 8) = -1/5

now, knowing one of the points like (-3, - 6) we can find the value of b.

y(x) = (-1/5)*x + b

y(-3) = -6 = (-1/5)*-3 + b

-6 = 3/5 + b

b = -6 - 3/5 = -33/5

then the first line is:

ya =  (-1/5)*x  -33/5

For the second line, we know that it passes through the points:

(-8, -15) and (-3, -11)

Then the slope is:

a = (-11 - (-15))/(-3 -(-8)) = (-11 + 15)/(-3 + 8) = 4/5

The our line is:

y(x) = (4/5)*x + b

and for b, we do the same as above, using one of the points, for example (-3, -11)

y(-3) = -11 = (4/5)*-3 + b

b = -11 + 12/5 = -(55 + 12)/5 = -43/5

then:

yb = (4/5)*x - 43/5.

Ok, our system of equations is:

ya = (-1/5)*x  -33/5

yb = (4/5)*x - 43/5.

To solve this, we suppose ya = yb

then:

(-1/5)*x + -33/5 = (4/5)*x - 43/5.

-33/5 + 43/5 = (4/5)*x + (1/5)*x

10/5 = 2 = (4/5 + 1/5)*x = x

2 = x

now we evaluate x = 2 in one of the lines:

ya = (-1/5)*2 -33/5 = -2/5 - 33/5 = -35/5 = -7

Then the lines intersect at the point (2, - 7), which is the solution for the system.

Answer:

[tex]124.63[/tex]

Step-by-step explanation:

[tex]a = \pi \times r {}^{2} = \pi \times (6.3) {}^{2} = \pi \times 39.69[/tex]

[tex]\pi \times 39.6 = 3.14 \times 39.69 = 124.63[/tex]

Hope this helps ;) ❤️❤️❤️

The area of circle will be;

⇒ 124.63 cm²

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The radius of circle = 6.3 cm

Now,

Since, The radius of circle = 6.3 cm

We know that;

Area of circle = π r²

Hence, We get;

⇒ Area of circle = 3.14 × 6.3²

                         = 3.14 × 39.69

                         = 124.63 cm²

Thus, The area of circle will be;

⇒ 124.63 cm²

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Answer:

A. 1010 FT^3

Step-by-step explanation:

19 x 14.5 x 5 = 1377.5

you need to subtract now, so the only option would be A

Answer:

[tex]1,010 ft^{3}[/tex]

Step-by-step explanation:

You can break the figure into 2 sections; one with the dimensions of 4, 5 and 7; the other with dimensions of 14.5, 5, and 12.

Multiply the first three dimensions (4, 5 and 7) to get 140 ft cubed.

Multiply the last three dimensions (14.5, 5, and 12) to get 870 ft cubed.

Now, just add both volumes together to get 1,010 ft cubed!

Hope that helps and maybe earns a brainliest!

Have a great day! :)

Answer:

D) (–5,0), (0,2), (5,0), (0,–2)

Step-by-step explanation:

The vertices are basically the x and y intercepts.

Answer:

21r +3

Step-by-step explanation:

3(7r + 1) =​

Distribute

3*7r +3*1

21r +3

Answer:

21r+3

Step-by-step explanation:

3(7r + 1)

Use the distributive property.

This property is normally used when the 2 numbers inside of the parentheses can not be added easily.

3*7r+3*1

21r+3

Answer:

24.2

Step-by-step explanation:

Answer:

[tex]f(x)=5x+12\\\\ f^{-1}(x):\\ y=5x+12\ \ \ |Subtract\ 12\\ y-12=5x\ \ \ |Divide\ by\ 5\\ \frac{y-12}{5}=x\\\\ f{-1}(x)=\frac{x-12}{5}[/tex]

Step-by-step explanation:

Answer:

f^-1(x) = x/5 - 12/5

Step-by-step explanation:

f(x) = 5x + 12

y = 5x + 12

x = 5y + 12

5y = x - 12

y = x/5 - 12/5

f^-1(x) = x/5 - 12/5

Answer:

1/3

Step-by-step explanation:

We are going to a small shape from a big shape, so the scale factor must be less than 1.

3 (which is a side on the blue figure) and 9 (a side on the green figure)

3 and 9 are easy numbers (for me...) so 3:9 is smaller than 1.

3:9 simplified is 1:3 = 1/3

so 1/3 is the scale factor.

Let's make sure it's right....

9 * 1/3 (green figure to blue figure) is = 3.

3.6 * 1/3 = 1.2

you can check it yourself on a calculator if you don't believe me

I hope this helps have a great day!!!!

Answer:

25

Step-by-step explanation:

The overall range of all scores in all three sections is 25.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

The range of 3 sections is 28, 25 and 22.

So, the overall range of all scores in all three sections

= (28+ 25+ 22)/ 3

= 75/3

= 25

Hence, the overall range of all scores in all three sections is 25.

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Answer:

The inequality shown is p>-3

Explanation:

An open hole on the number line means that the inequality will be greater or less than a number. So far we have p <or> some number.

Since the line goes to the left then we know that p is greater than some number. Now we have, p> some number.

The inequality starts at -3 so we know that the equation must be p>-3.

The inequality shown is in the given number line will be p>-3.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

An open hole on the number line refers to that the inequality will be greater or less than a number.

So far we have p <or> some number.

Since the line goes to the left then we know that p is greater than few number on the line.

Now we have, p> some number.

Thus, The inequality starts at -3, so we know that the equation must be p>-3.

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Answer:

D

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

-6x + 3y = -7

The x intercepts occur when y = 0, so

-6x + 3(o) = -7

x = -7/-6

x = 7/6

So the x-intercept =  (7/6, 0).

The y intercept:

-6(0)  + 3y = -7

y = -7/3.

So the y-intercept =  (0, -7/3.t).

Answer:

the answer must be A as it is the closest, i think its a computer error

Answer:

if the answer wasn't A i would try B since its the next closest answer

Step-by-step explanation:

Answer:

16,848+17,160+17,576+18,200+18,720+19,240+21,840=

129,584

Step-by-step explanation:

[tex]$8.10, $8.25, $8.45, $8.75, $9.00, $9.25, and $10.50\\[/tex]

Annually= Yearly, A year has 365 days.

They work 40 hours a week, 8*5=40.

There are aprox, 10 holidays in a year. (You can change this in your work)

They have 2 weeks unpaid vacation, 14 days.

There are aprox, 52 weeks in a year. (You can change this in your work)

52 weeks - 2 weeks of unpaid vacation= 50 weeks.

Now Let's calculate the weekly income, for

$8.10*40=$324 per week.

$8.25*40=$330 per week.

$8.45*40=$338  per week.

$8.75*40=$350 per week.

$9.00*40=$360  per week.

$9.25*40=$370 per week.

$10.50*40=$420  per week.

Now Let's calculate the annually income, for each clerk.

324*50=16,200 + 648=16,848

330*50=16,500 + 660=17,160

338*50=16,900 + 676=17,576

350*50=17,500  + 700=18,200

360*50=18,000 + 720=18,720

370*50=18,500 + 740=19,240

420*50=21,000 + 840=21,840

Now the total annual payroll=

16,848+17,160+17,576+18,200+18,720+19,240+21,840=

129,584

Answer:

6×[tex]10^{-4}[/tex]

Step-by-step explanation:

Answer:

The conjugate is 2+5i and the product is 29.

Step-by-step explanation:

The conjugate of a complex number [tex]a+bi[/tex] is [tex]a-bi[/tex]

Our complex number is 2-5i.

Here, a = 2 and b = -5

Thus, the conjugate of 2-5i is

[tex]2-(-5i)=2+5i[/tex]

Using this rule:

[tex](a+b)(a-b)=a^{2}-b^{2}[/tex]

And the fact that [tex]i^{2} = -1[/tex]

We can find the product of any complex number and its conjugate:

[tex](a+bi)(a-bi)=a^{2} - (bi)^{2}=a^{2} - b^{2} i^{2} = a^{2} + b^{2}[/tex]

As our complex number is [tex]2-5i[/tex], the product with its conjugate will be

[tex]2^{2} + (-5)^{2} =4+25=29[/tex]

Answer:

8.48

Step-by-step explanation:

After removing the perfect square inside √72 we get,

6√2

The given square root is,

√72

Since we know that,

A perfect square is a number that is stated as the product of an integer multiplied by itself. The perfect square is also represented as the second exponent of an integer since the same number is multiplied twice. The squares of all integers are hence referred to as perfect squares.

Simplify the square root of 72.

Factor 72 into 36 and 2,

Giving us the square root of 36 times the square root of 2.

Therefore,

√72 = √36 x √2

We know that the square root of 36 is 6,

So we can substitute that in:

√72 = 6 x √2

Hence after removing the perfect square inside √72 we get,

6√2.

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Answer:

Solution: (-4,-3)

Step-by-step explanation:

We need to complete the solution set of given graph.

We are given two graph one straight line and one parabola. We can see in graph both intersect at two points.

At x=-4 and x=-1

We can easily find the value of y corresponding to the value of x using given graph.

At x=-4,

First we draw a vertical line at x=-4 and see where it cut graph. From that point draw a horizontal line and see where y-axis cut.

The value of at x=-4 would be -3

Please see the attachment and see the vertical and horizontal line.

Thus, The Solution is (-4,-3)

Answer:

the answer is c

Step-by-step explanation:

convert the fractions to improper fractions 4/3 and 7/4 then multiply these fractions. youll get 28/ 12 and simplify to 2 1/3

Answer:

C

Step-by-step explanation:

So first, we should probably un-mix those fractions. So, we get:

4/3 x 7/4.

Multiplying this out, we get 28/12. Simplifying, we can get 2 1/3, which is C.

Answer:

7 1-yard rolls

Step-by-step explanation:

1 yard = 36 inches.

6(42 in) = 252 inches.

252 in/36 in = 7

Therefore, 7 1-yard rolls are needed.

The number of 1-yard rolls needed to sell 6 shelves each of 42 inches is 7.

Given,

A pantry contains 6 shelves.

Each shelves = 42 inches long.

The shelves are to be relined with fresh paper.

The paper is sold in 1-yard rolls.

We need to find the number of 1-yards rolls needed to sell 6 shelves.

1 yard = 36 inches.

We have,

6 shelves and each shelves is 42 inches.

1 shelves = 42 inches.

6 shelves = 6 x 42 inches

6 shelves = 252 inches.

And since,

36 inches = 1 yard

252 inches = (252/36) yard

252 inches = 7 yard

Thus the number of 1-yard rolls needed to sell 6 shelves each of 42 inches is 7 1-yard rolls.

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Answer:

28 units²

Step-by-step explanation:

→ Work out the size of the triangle if it was a full rectangle

Height = 4 and Base = 2

→ Work out area of triangle

0.5 × Height × Base ⇒ 0.5 × 4 × 2 ⇒ 2 × 2 ⇒ 4

→ Minus the area of the triangle from the "imaginary full' rectangle

Area of rectangle = Length × Width ⇒ 8 × 4 ⇒ 32

32 - 4 = 28

Answer:

[tex]\huge\boxed{28\ units^2}[/tex]

Step-by-step explanation:

The figure consists of a triangle, a square and a rectangle.

Area of Triangle:

[tex]\sf \frac{1}{2} (Base)(Height)\\Where \ Base = 2 , Height = 4 \\=> \frac{1}{2} (2)(4)\\=> 4\ units^2[/tex]

Area of Square:

[tex]\sf (Length)(Length)\\(4)(4)\\=> 16\ units^2[/tex]

Area of rectangle:

[tex]\sf (Length)(Width)\\Where \ Length = 4 , Width = 2\\=> (4)(2)\\=> 8 \ units^2[/tex]

Area of the whole figure:

=> 4 + 16 + 8

=> 28 units²