One more than the product of a number, x, and 7 is 5 less than that number, x. Rewrite this as an equation then solve for x.

Answer:

JK = 72

Step-by-step explanation:

JL = JK + KL = (4x+8) + (6x-6) = 10x + 2 = 162

--> x = (162-2)/10 = 16

JK = 4x + 8 = 4 . 16 + 8 = 72

f(x) = (x-8)/(x+7) and g(x) = (-7x-8)/(x-1)

To confirm that f(x) and g(x) are inverses.

f(g(x)) = x

g(f(x)) = x

f(g(x)) = (((-7x-8)/(x-1))-8)/(((-7x-8)/(x-1))+7)

f(g(x)) = (-15x² -15x)/(-15x² - 15)

f(g(x)) = -15x/-15

f(g(x)) = x

g(f(x)) = (-7((x-8)/(x+7))-8)/(((x-8)/(x+7))-1)

g(f(x)) = (-15x² - 105x)/(-15x²- 105)

g(f(x)) = -105x/-105

g(f(x)) = x

f(x) and g(x) are inverses.

Answer:

b

Step-by-step explanation:

Answer:

w = y - x is the equation to find w

Where,

w = Weight of the liquid

x = Weight of the empty can

y = Weight of the can with liquid

Step-by-step explanation:

Let

Weight of the empty can = x

Weight of the liquid = w

Weight of the can with liquid = x + w = y

x= 30 grams

w = ?

y= 47.3 grams

y = x + w

w = y - x

= 47.3 - 30

= 17.3

w= 17.3 grams

Therefore, the weight of the liquid is 17 .3 grams

Answer:

The correct answer is 12.8 J.

Step-by-step explanation:

To solve this problem, we must remember how to calculate the kinetic energy of an object.

The kinetic energy is represented by the formula K = 1/2 * m * v^2, where m represents the mass of the object and v represents the speed or velocity of the object.  If we plug in the given values into the formula, we get:

K = 1/2 * m * v^2

K = (1/2) * (0.40) * (8.0)^2

Our first step is to square the velocity.  After doing this step, we get the following:

K = (1/2) * (0.40) * (64)

Finally, we can perform the multiplication, to get:

K = 12.8

The unit for kinetic energy is joules, so the correct answer is 12.8 J.

Hope this helps!

Kinetic energy is the energy due to motion of an object

The kinetic energy of the bird is 12.5 joules

Reason:

The known parameter are;

The mass of the bird, m = 0.50 kg

The speed of the bird, v = 8.0 m/s

Required:

To find the kinetic energy of the bird

Solution:

[tex]Kinetic \ energy = \dfrac{1}{2} \cdot m \cdot v^2[/tex]

Therefore;

[tex]The \ kinetic \ energy \ of \ the \ bird = \dfrac{1}{2} \times 0.40 \ kg \times (8.0 \ m/s)^2 = 12.8 \ J[/tex]

The kinetic energy of the bird is 12.8 J

Learn more about kinetic energy here:

https://brainly.com/question/23503524

124.62 rounded to the nearest one is 125.

Rounding 124.62 to the nearest one is equivalent to finding the integer multiple of one nearest to 124.62.

" Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. "

                  124 ≤ 124.62 ≤ 125

The distance from to 124.62 to 124 is = 124.62 - 124 = 0.62

The distance from to 124.62 to 125 is = 125 - 124.62 = 0.38

So, the rounded to the nearest whole number is 125.

For more about nearest number ,

https://brainly.com/question/97416

#SPJ2

Answer:

Grades to be scored in 3rd exam = 88

Step-by-step explanation:

Given that average of 3 numbers is 85.

First two numbers are 81 and 86.

To find:

3rd number so that average is 85

Solution:

Let the third number = [tex]x[/tex]

Formula for average is:

[tex]Average = \dfrac{Sum\ of\ numbers}{Total\ count\ of\ numbers}[/tex]

Here, sum of numbers = [tex]81+86+x =167+x[/tex]

Total count of numbers = 3

[tex]85 = \dfrac{167+x}{3}\\\Rightarrow x=255-167\\\Rightarrow \bold{x=88}[/tex]

Grades to be scored in 3rd exam = 88

Answer:

5z

Step-by-step explanation:

Answer:

5z

Step-by-step explanation:

'The product of 5 and a number' would be 5 *  n.

Since the number in the question would be 'z', we will write it as '5 * z'.

However, the most ideal way to write this is '5z'. So,  "The product of 5 and a number z" would be '5z'.

Hope this helps.

Answer:

work shown and pictured

Answer:

x = - 9, x = - 4

Step-by-step explanation:

Set (x +)(x + 9) equal to zero, that is

(x + 4)(x + 9) = 0

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x + 9 = 0 ⇒ x = - 9

Thus

x = - 9, x = - 4

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

Perimeter = 74 in

The statement

The length of a rectangle picture is 5 inches more than three times the width is written as

l = 5 + 3w

Substitute the expression into the above formula and solve for the width

That's

74 = 2(5 + 3w) + 2w

74 = 10 + 6w + 2w

8w = 64

Divide both sides by 8

w = 8

Substitute this value into l = 5 + 3w and find the length

That's

l = 5 + 3(8)

l = 5 + 24

l = 29

The dimensions of the rectangle are

length = 29 inches

width = 8 inches

Hope this helps you

Answer:

ΔDEF is similar to ΔPQR by SAS similarity rule

Step-by-step explanation:

ΔDEF, with details:  

ΔPQR , with details:

As we see, the ratio of corresponding sides is:

And corresponding angles are:

Therefore,  ΔDEF is similar to ΔPQR by SAS similarity rule

Number one:

-4c - 6d + 9c + 2d

~Combine like terms

(-4c + 9c) + (-6d + 2d)

~Simplify

5c - 4d (Option A)

Number two:

2(-y + 9) + 8y

~Distribute

-2y + 18 + 8y

~Combine like terms

(-2y + 8y) + 18

~Simplify

6y + 18 (Option C)

Number three:

-3(-4y + 5) - 8y

~Distribute

12y - 15 - 8y

~Combine like terms

4y - 15 (Option C)

Number four:

6c - 8d + 3c + 4d

~Combine like terms

(6c + 3c) + (-8d + 4d)

~Simplify

9c - 4d (Option A)

Best of Luck!

It`s easy.

Real axis (-4) is the abscissa, the part with i (-8) is the ordinate. That`s why...  

Answer:

A - B  =  [  -1  3  ]

             [ -6  2  ]

             [ -4 -10 ]

Step-by-step explanation:

Since Matrix A and Matrix B have the same size, then we can simply perform the operation of subtraction on each position within the matrices to get the resulting subtracted matrix.

A =  [  4  7  ]              B =  [  5  4  ]

      [ -3  8  ]                     [  3  6  ]

      [ -5 -2  ]                    [  -1  8  ]

A - B  =  [ (4 - 5)  (7 - 4) ]

             [ (-3 - 3) (8 - 6) ]

             [ (-5 - -1) (-2 - 8) ]

A - B  =  [  -1  3  ]

             [ -6  2  ]

             [ -4 -10 ]

Cheers.

The four color theorem-No more than 4 colors are required to color the regions map

Answer and Explanations

ACT score percentile help colleges compare students with one another, rather than just looking at everyone’s score. The  score range is between 1 and 36, the highest score that one can receive on the ACT is 36. Moreover, 36 is the perfect score.

The maximum ACT score (36) is that in 2018, only 3,741 students (out of millions of test-takers) scored a perfect 36 on the ACT.  The 99th percentile of test-takers includes those who earn 35 or 34 on the ACT. We can miss up to five questions on the ACT and still earn a 36. That is a reason why the maximum ACT score is 36 at the 100th percentile.

The ACT score report will provide more information about test-taking experience in the form of sub score. The higher the score,  you will get into the colleges of your choice.

The maximum ACT score is not at the 100th percentile. because the student cannot score more than himself as well as others whom scored the same.

Although your question lacks some data a general answer have been provided above

       For the maximum score ( 36) to be at the 100th percentile the individual who scores the maximum ACT score, must have scored higher than others and also him/herself in the data set.

Even if a student scores the highest score (36) it does not mean they have scored higher than others who had the same score ( 36 ) with them or him/her self.

Hence we can conclude that the maximum ACT score ( 36 ) cannot be at the 100th percentile because the student cannot score more than himself as well as others whom scored the same.

Learn more : https://brainly.com/question/5335957

Answer:

1. Two segments are MC and AX

2. Point N

3. Three collinear points are points A, point N and point X

4. Two other names for V are quadrilateral and rectangle

5. No N, M, and X are in a different plane from R

6. Two rays are ray NR and ray NA

7. The pair of opposite rays with end point N are ray NA and ray NX and ray NM and ray NC

8. Three lines are shown in the figure

Step-by-step explanation:

1) A segment is a line portion with two end points

2) A point marks a position

3) Collinear points are points on the same line

3) A quadrilateral is a four sided figure while rectangle has 90° interior angles

4) A ray is an line extending from a point without ending

5) Opposite rays are rays extending from the same point but in opposite directions

6) A line is a straight one dimensional geometric figure  that has no width but infinite number of points extending without end in both directions

Answer:

hope it helps

Step-by-step explanation:

2x+y=10

x-2y=12

2x+y=10

2x-4y=24

y=-14/5

2x=10+14/5

2x=64/5

x=32/5

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

Explanation:

x is a variable or placeholder for a number. Think of it like a box.

1x = 1 box

2x = 2 boxes

and so on

9x = 9 boxes

5x = 5 boxes

9x+5x = 9 boxes + 5 boxes = 14 boxes = 14x

So that's one way to see how 9x+5x = 14x.

Or you could add the coefficients 9 and 5 to get 9+5 = 14. Then tack an x onto everything.

----------

The y terms are handled in a similar fashion.

-5y + 9y = 4y

which is the same as

9y - 5y = 4y

You could think of it like this

(9 yaks) - (5 yaks) = 4 yaks

So we started with 9 yaks and took away 5 of them to be left with 4 yaks.

----------

After getting the results 14x and 4y. We would then have the final answer 14x+4y

The x and y terms cannot be combined since they are not like terms. So we leave that expression as is.

Answer: mq  = 17

Step-by-step explanation:

If cm is 22   and cq  which is the whole distance,  then subtract the distance of  cm which is 22 from the distance of cq which is 39.

39 - 22 = 17

Answer:

The order of the matrix D^T × (BE) is 2 × 4

Step-by-step explanation:

In the multiplication of matrix, the number of columns in the first matrix must be equal to the number of rows of the second matrix. The resulting matrix from the product will have the same number of rows as the first matrix and the same number of column as the second matrix. For example, given Matrix A of order (m × n) and Matrix Z of order ( n × k), the product of the two matrices will give a matrix ( say Y) of order (m × k).

AZ = Y

(m x n)(n x k) = (m x k)

Now, From the question,

The order of Matrix B is 4 × 5,

the order of the matrix D is 4 × 2

and the order of the matrix E is 5 × 4.

To determine the order of the matrix D^T × (BE)

First, will find the order of (BE)

Order of BE = (4 × 5) (5 × 4)

Order of BE = (4 × 4)

Hence, the order of matrix (BE) is 4 × 4.

Now, we will determine the order of matrix D^T

D^T means the transpose of matrix D.

The transpose of a matrix is defined as a new matrix whose rows are the columns of the original matrix and the columns of the new matrix are the rows of the original matrix. This means given Matrix A of order (m × n), the transpose of Matrix A (A^T) will have an order of (n × m).

The order of the matrix D is 4 × 2

Hence, the order of the transpose of matrix D (D^T) will be 2 × 4

Now, the order of the matrix D^T × (BE) will be

Order of the matrix D^T × (BE) = (2 × 4) × (4 × 4)

Order of the matrix D^T × (BE) = 2 × 4

Hence, the order of the matrix D^T × (BE) is 2 × 4.

Answer:

fits under statistics category (also probability or math :\)

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

This is basically just a ratio in disguise. Ratios can be represented as fractions, and we can write these ratios to be equal to each other.

[tex]\frac{x}{9} = \frac{8}{12}[/tex]

We can solve for x using the cross products property:

[tex]9\cdot8=72\\\\72\div12=6[/tex]

Hope this helped!

Answer:

x=6

Step-by-step explanation:

We can write ratios to solve

x          8

----- = -----------

9           12

Using cross products

12x = 8*9

12x = 72

Divide by 12

x = 72/12

x =6

Answer: The value of x is = 5.

Step-by-step explanation:

So we are given the equation:

3x + 7 = 22​

We just have to isolate 3x and move 7 to the other side:

3x = 22 -7

3x = 15

Now divide:

x = 15/3

x = 5

There you go!

Answer:

5

Step-by-step explanation:

22-7=15 and 15 divided by 3 =5

Answer:

2k-8

Step-by-step explanation:

3k +9 -k-17

Combine like terms

3k -k    +9-17

2k         -8

Answer:Simplifying

3k + 9 + -1k + -17 = 0

Reorder the terms:

9 + -17 + 3k + -1k = 0

Combine like terms: 9 + -17 = -8

-8 + 3k + -1k = 0

Combine like terms: 3k + -1k = 2k

-8 + 2k = 0

Solving

-8 + 2k = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '8' to each side of the equation.

-8 + 8 + 2k = 0 + 8

Combine like terms: -8 + 8 = 0

0 + 2k = 0 + 8

2k = 0 + 8

Combine like terms: 0 + 8 = 8

2k = 8

Divide each side by '2'.

k = 4

Simplifying

k = 4

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

There would be 12 girl students in a class of 21 students.

"A proportion is a mathematical statement where two or more ratios are equivalent."

We have been given that, the ratio of girls to the total number of students in class is 4:7

We need to find the number of girl students if the class has 21 students in all.

Let 'n' represents the number of girl students.

⇒ [tex]\frac{4}{7} = \frac{n}{21}[/tex]

⇒ [tex]4\times 21 = n\times 7[/tex]                        ......................(cross product)

⇒ [tex]84 = n\times 7[/tex]

⇒ [tex]n=\frac{84}{7}[/tex]                                    ......................(Divide each side by 7)

⇒ [tex]n=12[/tex]

Hence, there would be 12 girls if class has 21 students in all.

Learn more about ratios and proportion here:

https://brainly.com/question/24501010

#SPJ2

Answer:

Coffees cost $2 each and bagels cost $4 each

Step-by-step explanation:

Let

Coffee=c

Bagels= b

2 coffees and 5 bagels for which he paid $24

2c + 5b= 24 (1)

he returned to buy 3 coffees and 4 bagels for

$22

3c + 4b = 22 (2)

2c + 5b= 24 (1)

3c + 4b = 22 (2)

Multiply (1) by 3 and (2) by 2

6c + 15b = 72 (3)

6c + 8b = 44 (4)

Subtract (4) from (3)

15b - 8b = 72 - 44

7b = 28

Divide both sides by 7

b= 28 / 7

= 4

b= $4

Substitute b=4 into (1)

2c + 5b= 24

2c + 5(4) = 24

2c + 20 = 24

2c = 24 - 20

2c = 4

Divide both sides by 2

c= 4 / 2

c= $2

Therefore,

Coffees cost $2 each and bagels cost $4 each