The sum of three numbers is 16. The sum of twice the first​ number, 5 times the second​ number, and 6 times the third number is 85. The difference between 4 times the first number and the second number is negative 3. Find the three numbers.

Answer

7 Units left and 3 units up

Step-by-step explanation:

Rise over Run

Up 3 and to the left 7

Answer:

x = 9, y = 4 and z = 6.67

Step-by-step explanation:

Since both the polygons are similar, by the property of similarity corresponding sides of the polygons will be proportional.

Therefore, [tex]\frac{x}{6}=\frac{12}{8}[/tex]

x = [tex]\frac{12\times 6}{8}[/tex]

x = 9

Similarly, [tex]\frac{10}{z}=\frac{12}{8}[/tex]

z = [tex]\frac{10\times 8}{12}[/tex]

z = [tex]\frac{20}{3}[/tex] = 6.67

And [tex]\frac{6}{y}=\frac{12}{8}[/tex]

y = [tex]\frac{8\times 6}{12}[/tex]

y = 4

Therefore, x = 9, y = 4 and z = 6.67 will be the values.

Answer:

The dilation is an enlargement, and the scale factor is 2.  So, the answer is B.  

Step-by-step explanation:

The dilation is an enlargement, and the scale factor is 2.  

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

The image of the object undergoing transformation is given.

From the attached object, we se that CP = 4.

Also CP' = 8

Thus; Scale factor is 8/4 = 2

Now, reduction is defined as reducing the dimensions while enlargement is increasing the dimensions by a scale factor.

Thus, the denominator of the scale factor is greater than the numerator, then there is a reduction.

The scale factor of the given dilation is; 2 and the dilation is a enlargement.

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Answer:

Plz show us the figures

Step-by-step explanation:

Answer:

The answer is Figure B.

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

The formula for slope is: y1-y2/x1-x2

The points given are: (x coordinate, y coordinate)

In the formula,

y1 is the y coordinate of the first point

y2 is the y coordinate of the second point

x1 is the x coordinate of the first point

x2 is the x coordinate of the second point

This said, we can plug our points in.

5-(-1)/-3-9

Simplify.

5+1/-12

6/-12

Divide both the numerator and denominator by -6.

-1/2

Answer:

D

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x, y ) → (y, - x ) , thus

X(- 1, - 3 ) → X'(- 3, 1 )

Y(0, 0 ) → Y'(0, 0 )

Z(1, - 3 ) → Z'(- 3, - 1 )

Answer:

Step-by-step explanation:

[tex]s_{n}=3-2^{-4n}\\s_{n+1}=3-2^{-4(n+1)}=3-2^{-4n} *2^{-4}\\s_{n+1}-s_{n}=3-2^{-4n}*2^-4-3+2^{-4n}[/tex]

[tex]=2^{-4n}-2^{-4n}*2^{-4}\\=2^{-4n}(1-2^{-4})\\=2^{-4n}(\frac{2^4-1}{2^4})\\=2^{-4n}\frac{15}{16}\\U_{n+1}=15*2^{-4(n+1)}[/tex]

Answer:

the one with 47:is 43

the one with 52 is 38

the one with 63 is 27

and the one with 45 is 45

Step-by-step explanation:

these angles equal to 90

so you must subtract them from 90

Answer:

5: x=43

6: x=38

7: x=27

8: x=45

A girl has 20 marbles

10 are red, 7 are blue, and 3 are green

If she picks 5 marbles, without replacing them, what are the chances all 5 are red?

10/20 * 9/19 * 8/18 *7/17 * 6/16

1/2 * 9/19 * 4/9 * 7/17 * 3/8

1/2 * 1/19 * 3/2

1/76

Answer:

Step-by-step explanation:

Answer:

36 units³

Step-by-step explanation:

To find the volume of a prism, you must multiply the base times the height. 4×9=36.

To find the length of FE subtract t E feom F

FE = 5-2 = 3 units long

The final statement is: The property of distribution is used in the given expression.

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Given here: (x + y)(2 + z) = 2(x +y) + z(x + y)

Clearly 2 and z get distributed over (x+y)

We usually use the distributive property because the two terms inside the parentheses can’t be added because they’re not like terms

Thus this is the distributive property of multiplication.

Hence, Distributive property is the correct option.

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Answer:

x = 7

Step-by-step explanation:

The consecutive angles in a parallelogram are supplementary, thus

80 + 14x + 2 = 180

14x + 82 = 180 ( subtract 82 from both sides )

14x = 98 ( divide both sides by 14 )

x = 7

In the given parallelogram QRST, x = 7°.

In a quadrilateral, adjacent angles are the pair of angles, that come is formed by the intersection of any common line.

In the question, we are shown a parallelogram QRST and are asked to find the value of x.

We know that ∠TQR and ∠QRS are adjacent, as they include a common side, QR.

∠TQR = 80°, ∠QRS = (14x + 2)°

Now, we know that adjacent angles of a parallelogram are supplementary, that is their sum = 180°

∴ ∠TQR + ∠QRS = 180°

or, 80° + (14x + 2)° = 180°

or, 14x = 180° - 80° -2° = 98°

or, x = 98°/14 = 7°

∴ In the given parallelogram QRST, x = 7°.

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Answer:

=1.8

Step-by-step explanation:

R= Square root of volume/pie*height

R= 100/3.142*10

=100/31.42

=3.18

the square root of 3.18 is 1.78

1.78 rounded to the nearest tenth is 1.8

Answer:

Option C

Step-by-step explanation:

9/3=3

12/3=4

so, the answer is 3/4

Option C

Answer:

Think of it as 9 / 3 = 3

                       12 / 3 =  4      

so it is 3/4. The ratio is equal because 3/3 = 1 so you are dividing by 1

Hope this helps                    

Step-by-step explanation:

Answer:

a)  -2 -< x-<  2

b)  -1 < x and < 2

Step-by-step explanation:

We use -< as the numbers are included in the solution being -2 and 2

We use < as the numbers are less than -1 and 2

You know the difference i just couldn't copy and paste the inequalities for a).

They face the same way I have shown.

If the line on the number line were not central to 2 numbers and separate then they would face the opposite way and show two inequalities and we refer to that as or, but both of these mean and. they mean and as the line joins them together on each number line, the only difference is an open circle means the numbers are not inclusive so we dont enhance the arrow for non inclusive, when a) is inclusive we put a line underneath the arrow and still face them the left side as x shows the relationship of being inclusive still the same. a) has a line under the arrow i just couldn't show and hope you see the difference as we only use two types of arrows.

Answer:

2x+16

Step-by-step explanation:

2W+2P

Lets substitute the W and the P for their respective values.

2(3x+1) + 2(-2x+2)

Simplify

6x + 2 + -4x + 4

Simplify again

2x + 6

And there you have it!

Answer:

2x + 16

Step-by-step explanation:

2W + 2P

= 2(3x + 1) + 2(- 2x + 7) ← distribute both parenthesis

= 6x + 2 - 4x + 14 ← collect like terms

= 2x + 16

Answer:

it will still be zero

Step-by-step explanation:

12-12 = 0

Answer:

Numbers are 6 and 17.

Step-by-step explanation:

Let the two numbers are 'a' and 'b'.

"Sum of these numbers = 23"

a + b = 23 --------(1)

"One number is 7 less than 4 times the other"

a = 4b - 7 ---------(2)

Substitute the value of 'a' in equation (1) from equation (2)

(4b - 7) + b = 23

5b - 7 = 23

5b = 23 + 7

5b = 30

b = 6

From equation (2),

a = 4b - 7

a = 4×6 - 7

a = 24 - 7

a = 17

Therefore, the numbers are 6 and 17.

Answer: 7 and 16

Step-by-step explanation:

Let x be the smaller of the two numbers. We are told that the larger number is five less than three times the smaller number x. Therefore, our two numbers are x and 3x−5. Given that the sum is 23, we find that

x+(3x−5)=23

Solving for x, we find that x=7. So the two numbers are 7,16.

Answer:

x = 30°.

Step-by-step explanation:

To calculate the value of 'x', we can first derive the value of one of the angles that make up the triangle.

Notice that there is an angle with a measure of 100°. The angle that makes up the angle of the triangle is called a Vertical Angle. Therefore, if the angle in red is 100°, the vertical angle, or the third angle of the triangle, is 100°.

There are two congruent sides to the triangle, as seen by the congruent lines. This means that both of the other two angles must be equal. Find the value of 'x' by:

180 - 100 = 80. Since the value of one angle was 100°, and the angles in a triangle must add up to 180°, you can simply subtract to find the sum of the other two angles.

(x + 10) + (x + 10) = 80

2x + 20 = 80

2x = 60

x = 30°.

Answer:

x=30

Step-by-step explanation:

Answer:

Angle XVW is 56 degrees.

Angle XWZ is 28.5 degrees.

Angle XZW is 28.5 degrees.

Step-by-step explanation:

bcuz yes :)

Answer:

The fact that the data is univariate means that there is only one variable – age, and the fact the data is numerical means it involves numbers – age.

I'm doing the test and this is what I put for my answer

Answer:

Step-by-step explana

tion:

Ratatouille

Answer:

The probability that all of the offices are filled by members of the debate​ team is 0.0512 and the probability that none of the offices are filled by members of the debate​ team is 0.0256

Step-by-step explanation:

The offices of​ president, vice​ president, secretary, and treasurer for an environmental club will be filled from a pool of 15 candidates.

So, Number of candidates required = 4

Total number of candidates = 15

Number of candidates which are members of the debate team. = 8

So, Number of candidates which are not the members of the debate team = 15-8 =7

The probability that all of the offices are filled by members of the debate​ team = [tex]\frac{^8C_4}{^{15}C_4}=\frac{\frac{8!}{4!\left(8-4\right)!}}{\frac{15!}{4!\left(15-4\right)!}}=0.0512[/tex]

The probability that none of the offices are filled by members of the debate​ team=[tex]\frac{^7C_4}{^{15}C_4}=\frac{\frac{7!}{4!\left(7-4\right)!}}{\frac{15!}{4!\left(15-4\right)!}}=0.0256[/tex]

Hence The probability that all of the offices are filled by members of the debate​ team is 0.0512 and the probability that none of the offices are filled by members of the debate​ team is 0.0256

Answer:

  a = 20 because the rate of change is -3

Step-by-step explanation:

In order for the function to be linear, sequential values of x must match values of y that have the same first differences. Here, 23-26 = -3, so we must have a-23 = -3. That is to say, the value of "a" must be 20.

The "rate of change" is the ratio of the differences in y to the differences in x. Here, that is -3/1 = -3. The appropriate choice is ...

  a = 20 because the rate of change is -3

Answer:

Step-by-step explanation:

The third, fifth and sixth expressions (from the top) are NOT polynomials, and the reason in each case is that the expression has one or more negative powers of x in it.

Answer:

option 3

Step-by-step explanation:

each little square represents a side of a cube, so it is 81 in^2

So, lets take a square root, since all distance is positive, it is 9, since a cub'es side lengths are all the same, the dimensions are 9*9*9inches, or option 3