Which of the following pairs of triangles are similar?

Given:

10 boys clear a piece of land in 21 days.

To find:

The number of days it will take 7 boys to clear the same land at the same rate.

Solution:

We have,

10 boys clear a piece of land in 21 days.

Total work = [tex]10\times 21[/tex]

                 = [tex]210[/tex]

Let 7 boys clear the same piece of land in x days.

Total work = [tex]7\times x[/tex]

                 = [tex]7x[/tex]

Now, the total work is same.

[tex]7x=210[/tex]

Divide both sides by 7.

[tex]x=\dfrac{210}{7}[/tex]

[tex]x=30[/tex]

Therefore, 7 boys clear the same piece of land in 30 days.

Answer:

D.12^3 sgrt 15

Sana makatulong

The expression that is equivalent to the given expression is 12√15. Option D is correct.

Given that,
Which expression is equivalent to 21√15 - 9√15 is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
According to the question,
= 21√15-9√15
= (21 - 9 )√15
= 12√15

Thus, the expression that is equivalent to the given expression is 12√15. Option D is correct.

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Step-by-step explanation:

4) p(x)=256

p(x)=2 ^ x+2

256=2 ^ x+2

2⁸= 2 ^ x+2

8=x+2

x=8-2=6

5)243=3 ^ x+3

3×3×3×3×3 = 3 ^ x+3

3⁵= 3^ x+3

5 = x+3

x=5-3=2

Answer:

[tex]p(x) = 256 \\ p(x) = {2}^{(x + 2)} \\ {2}^{(x + 2)} = 256 \\ {2}^{(x + 2)} = {2}^{8} \\( x + 2) = 8 \\ x =( 8 - 2) \\ \boxed{x = 6}[/tex]

[tex]243 = {3}^{(x + 3)} \\ {3}^{(x + 3)} = {3}^{5} \\ (x + 3) = 5 \\ x = (5 - 3) \\ \boxed{ x = 2}[/tex]

Answer:

slope=1

Step-by-step explanation:

Rise/Run

Answer:

2, 6, 6, 8, 8

Step-by-step explanation:

First, we know that the mean is the sum of the number divided by the amount, so if we take the answer we have, 6, and multiply that by the amount of number, 5, then we get 30.

Now we add the numbers in the ratio, so 1 + 3 + 3 + 4 + 4 = 15

15 x 2 = 30

This means we need multiply the numbers in the ratio by 2 to get

2 + 6 + 6 + 8 + 8 = 30

Answer:

2, 6, 6, 8, 8

Step-by-step explanation:

The mean is calculated as

mean = [tex]\frac{sum}{count}[/tex], thus

[tex]\frac{sum}{5}[/tex] = 6 ( multiply both sides by 5 )

sum = 30

sum the parts of the ratio, 1 + 3 + 3 + 4 + 4 = 15 parts

30 ÷ 15 = 2 ← value of 1 part of the ratio, thus

3 parts = 3 × 2 = 6

4 parts = 4 × 2 = 8

Thus the 5 numbers are

2, 6, 6, 8, 8

Answer:

This is NOT a graph :)

Step-by-step explanation:

Answer

69°F

Because

12+57=69

Answer:

1/10

Step-by-step explanation:

There are 3 reds and 2 blues. He picks one and then another with no replacement. ? of getting 2 blues.

There are five marbles altogether.

First is 2/5

The second blue is 1/4

The chance of them both being blue is 2/5 * 1/4 = 2/20 = 1/10

Answer:20474.7

Step-by-step explanation:

68249 divide by 10 then multiply by 3

Answer:

ill say 75.00

Step-by-step explanation:

Answer:

[tex]f=-8[/tex]

Step-by-step explanation:

[tex]8+4f=3f[/tex]

[tex]8+4f-4f=3f-4f[/tex] (Subtract [tex]4f[/tex] from both sides of the equation to isolate [tex]f[/tex])

[tex]8=-f[/tex] (Simplify)

[tex]-f=8[/tex] (Symmetric Property of Equality)

[tex]\frac{-f}{-1} =\frac{8}{-1}[/tex] (Divide both sides of the equation by [tex]-1[/tex] to get rid of [tex]f[/tex]'s coefficient; remember that [tex]-f=-1*f[/tex], so [tex]-f[/tex] has a coefficient of [tex]-1[/tex])

[tex]f=-8[/tex] (Simplify)

Hope this helps!

Answer:

Step-by-step explanation:

Here you go mate

Step 1

8+4f=3f  Equation/Question

Step 2

8+4f=3f  Simplify

8+4f=3f

Step 3

8+4f=3f  Simplify by subtracting

f+8=0

Step 4

f+8=0  Subtract 8 frm sides

answer

f=-8

Hope this helps

Answer:

A

Step-by-step explanation:

You can use the formula change in y divided by change in x, so for this the change in y would be 2 and the change in x would be 4. This means the slope is 1/2.

In a line, the slope never changes so it's A.

Answer:

D(34)

Step-by-step explanation:

i did the math

Answer:

Step-by-step explanation:

11 is B and 12 is B. 11 is B because perimeter means to add all the outside values of the shape. 2.5+5+4+1 and then there are two missing side values which are 1.5 and 1, add them all together and the perimeter is 15. For the area, separate the small square with the big rectangle to have two full shapes. The area of the rectangle is 4x2.5=10. Area of the small square is 1x1=1. 10+1=11. Hope this helps, ask questions if you need to

Answer:

£15

Step-by-step explanation:

Angad : Nick = 5 : 1

Let

Nick share = x

Angad share = x + £60

Angad : Nick

5 : 1 = x + £60 : x

5/1 = x + 60 / x

Cross product

5 * x = 1 * x + 60

5x = x + 60

5x - x = 60

4x = 60

x = 60/4

x = 15

Nick get £15

Answer:

Root: (-5,0)

Vertical Intercept: (0,-3)

m = -3/5

b = -3

Step-by-step explanation:

Answer:

3,-2   5,-3   2,1

Step-by-step explanation:

all the points in the shaded region are the right answer

Answer and Step-by-step explanation:

To solve, you first divide 7 by 9.

Then, you divide 119 by 7/9.

[tex]\frac{7}{9} = 0.777777777777\\\\\frac{119}{0.77777777777} = 153.\\\\[/tex]

To check your work, divide 119 by 153, and you will get 0.777777777777, which is the same as 7 divided by 9.

So, the answer is A. 153

#teamtrees #WAP (Water And Plant)

Answer:

A

Step-by-step explanation:

I divided 119 by 7 which is 17. Then multiplied that by 2 because theres a gap of 2 between 7 and 9 and got 34. lastly added 119 by 34 and got 153. (Sorry if I got it wrong)

Answer:

Step-by-step explanation:

1.15

Answer:

-0.067

Step-by-step explanation:

this is a answer

Answer: 35%

Step-by-step explanation:

Given: total students in 6th grade = 160

Students said that math was their favorite subject = 56

The percentage of students who chose math as their favorite subject =

[tex]\dfrac{\text{Students like math}}{\text{Total students}}\times100[/tex]

[tex]=\dfrac{56}{160}\times100\\\\=35\%[/tex]

Hence, the percentage of students who chose math as their favorite subject = 35%.

Answer:

∠y° = ∠69°

∠x = ∠69°

Step-by-step explanation:

1) The question relates to parallel line theorem

The given parameters are;

AB is parallel to CD

∠111° and ∠y° are consecutive interior angles

∠69° and ∠x° are alternate interior angles

When two parallel lines are crossed by a common transversal, the consecutive interior angles are supplementary (sum up to 180°), and the alternate interior angles are equal

Therefore, we have;

∠111° + ∠y° = 180°

∠y° = 180° - ∠111° = ∠69°

∠y° = ∠69°

2) For the alternate interior angles, ∠69° and ∠x°, we have;

Alternate angles are equal, therefore ∠x = ∠69°

To convert from the base currency, we multiply by the exchange rate. Just like multiplying to apply a commodity price. Indeed, our base currency can be viewed as the commodity in the quote. Say we need to convert €8m into dollars, by applying the exchange rate EUR/USD 1.25.

Answer: B) −8x − 9

Step-by-step explanation:

5 − 2 (4x + 7)

Apply the distributive property.

5 − 2 (4x) − 2 ⋅ 7

Multiply 4 by −2.

5 − 8x − 2 ⋅ 7

Multiply −2 by 7.

5 − 8x − 14

Subtract 14 from 5.

−8x − 9

hope this helps :)

Answer:

b

Step-by-step explanation:

5-2(4x+7)

distribute

-8x-14

5-8x-14

5-14=-9

-8x-9

Answer:

86

Step-by-step explanation:

36 + 4 = 40 x 2 =80  

36 x 2 = 82 = 4 - 86

Hope it helps!

The special number was supposed to be; 76

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

For age 'a', the special number was

 2a +4

Tammi's mother actually calculated it as;

 2(a +4) = 2a +8

Now a value that is (2a+8) -(2a+4) = 4 more than it was supposed to be.

The special number was supposed to be;

80 -4 = 76.

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Answer:

the answer is A

Step-by-step explanation:

on edgy

The triangles △ACB ~ △DCE are similar by AA similarity theorem.

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

Given Triangle ABC with Line DE drawn inside the triangle and parallel to side AB. The line DE forms a new triangle DCE.

Because AB∥DE and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines.

Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA.

We can state ∠C ≅ ∠C using the reflexive property.

Therefore,  △ACB ~ △DCE  by the AA similarity theorem.

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Answer:

1.06

Step-by-step explanation:

To the nearest hundredth, the answer is 1.06.