Solve the following system of equations.

3x + 2y - 5 = 0
x = y + 10

Make sure there are NO SPACES in your answer. Include a comma in your answer.

ANSWER: {(
)}

Answer:

Option A

Step-by-step explanation:

When adding two matrices, they should be of the same sizes.

Option A:

Matrix [tex]\left[\begin{array}{c}2&3\end{array}\right][/tex] has 2 rows and 1 column.

Matrix [tex]\left[\begin{array}{c}3&4\end{array}\right][/tex] has 2 rows and 1 column too.

So, these matrices can be added.

The result will be

[tex]\left[\begin{array}{c}2+3&3+4\end{array}\right]=\left[\begin{array}{c}5&7\end{array}\right][/tex]

Answer:

A

Step-by-step explanation:

E2020

Answer:

The unit rate is 1.25 seconds per jump.

Step-by-step explanation:

Given:

Will can jump rope at a rate of 8 jumps for every 10 seconds.

Now, to find the unit rate:

So, by dividing we get the unit rate.

At the rate of 8 jumps Will takes 10 seconds.

Thus, for the rate of 1 jump he will take = [tex]10\div 8=1.25\ seconds.[/tex]

Therefore, the unit rate is 1.25 seconds per jump.

Answer:

Step-by-step explanation:

If we are looking to find the composition of g(f(4)), we start at the innermost part of the problem which is to evaluate f(4).

If f(x) = x - 7, then f(4) = 4 - 7.  f(4) = -3.

Now take that -3 and evaluate the g(-3).

If g(x) = x^2, then g(-3) = (-3)^2 which is 9.

Therefore, f(g(4)) = 9

Answer:

9

Step-by-step explanation:

edg 2020

Answer:

  z = x^3 +1

Step-by-step explanation:

Noting the squared term, it makes sense to substitute for that term:

  z = x^3 +1

gives ...

  16z^2 -22z -3 = 0 . . . . the quadratic you want

_____

Solutions derived from that substitution

Factoring gives ...

  16z^2 -24z +2z -3 = 0

  8z(2z -3) +1(2z -3) = 0

  (8z +1)(2z -3) = 0

  z = -1/8  or  3/2

Then we can find x:

  x^3 +1 = -1/8

  x^3 = -9/8 . . . . . subtract 1

  x = (-1/2)∛9 . . . . . one of the real solutions

__

  x^3 +1 = 3/2

  x^3 = 1/2 = 4/8 . . . . . . subtract 1

  x = (1/2)∛4 . . . . . . the other real solution

The complex solutions will be the two complex cube roots of -9/8 and the two complex cube roots of 1/2.

Answer:

x^3 +1

Step-by-step explanation:

Hi! The correct answer is 2. g(x) = log3 (x) + 5. Message me if you need further help.

The transformation of a function may involve any change. The correct option is 2. The value will be g(x) = log₂(x+5).

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k \times f(x)

Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)

As we know to shift a function towards the left horizontally, we need to add the number of units to the value of x. Therefore, the function of g(x) will be written as,

g(x) = log₂(x+5)

Hence, the correct option is 2. The value will be g(x) = log₂(x+5).

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Answer:

The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800

Step-by-step explanation:

Let

x ----> the amount invested at 9% (first fund)

5,000-x ----> the amount invested at 13.5% (second fund)

Remember that

[tex]9\%=9/100=0.09[/tex]

[tex]13.5\%=13.5/100=0.135[/tex]

The total interest earned is equal to

[tex]\$5,531-\$5,000=\$531[/tex]

we know that

The amount earned by the first fund at 9% plus the amount earned by the second fund at 13.5% must be equal to $531

so

the linear equation that represent this situation is equal to

[tex]0.09x+0.135(5,000-x)=531[/tex]

solve for x

[tex]0.09x+675-0.135x=531[/tex]

[tex]0.135x-0.09x=675-531[/tex]

[tex]0.045x=144[/tex]

[tex]x=\$3,200[/tex]

so

[tex]\$5,000-x=\$5,000-\$3,200=\$1,800[/tex]

therefore

The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800

Answer:

184.08

Step-by-step explanation:

Answer:

Angle = 64 Degrees

Supplement of Angle = 116 Degrees

Step-by-step explanation:

Let the angle be "x"

We know

The complement of the angle is "90 - x"

and

The supplement of the angle is "180 - x"

From the statement given, we can write:

supplement is 12 LESS THAN twice the angle

The equation would be:

180 - x = 2x - 12

Now, we solve this for x:

[tex]180 - x = 2x - 12\\180+12=2x+x\\192=3x\\x-\frac{192}{3}\\x=64[/tex]

The angle is 64 degrees

The supplement of the angle is 180 - 64 = 116 degrees

Step-by-step explanation:

Since SP=TR, the differnce of PR and ST 24-15 divided by 2 is the length of PD (4.5)

Try to understand the rest from the attached picture

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. m = -1/5

2. c = -9.75

3. q = 0

Answer:

m = 89/56 = 1  33/56

(Can be simplified to 1.58)

Answer:

see explanation

Step-by-step explanation:

A translation of 4 units down means subtract 4 from the y- coordinate of the original point and a translation of 3 units left means subtract 3 from the original x- coordinate, thus translation rule is

(x, y ) → (x - 3, y - 4 )

Thus

C(8, 3 ) → C'(8 - 3, 3 - 4 ) → C'(5, - 1 )

Answer:

Step-by-step explanation:

c + 6 < -20

Subtract 6 from both side

c +6 -6 < -20-6

c < -26

So value of c should be less than -26. Value of c = { - ∞ ...... -28, - 27 }

Eg:

If c = -27

-27 + 6 = - 21 . -21 is less than -20

Answer:

√6/2

Step-by-step explanation:

Answer:

The scale is [tex]\frac{1}{60}[/tex]

Step-by-step explanation:

The correct question is

An artist is making a mural by reproducing a painting at a different scale. the original painting is 10 1/2 inches long and 4 inches wide. the mural will cover an entire wall that is 52.5 feet long and 20 feet wide. what will be the scale that relates to the original painting to the mural?

we know that

To find out the scale divide the measure of the original painting by the measure of the mural

so

Long

[tex]\frac{10.5}{52.5}\ \frac{in}{ft}[/tex]

Remember that

[tex]1\ ft=12\ in[/tex]

Convert feet to inches

[tex]\frac{10.5}{52.5*12}=\frac{10.5}{630}\ \frac{in}{in}=\frac{10.5}{630}[/tex]

simplify

[tex]\frac{1}{60}[/tex]

That means ----> 1 unit in the original painting represent 60 units in the mural

Verify the scale with the wide (both scale must be equals)

wide

[tex]\frac{4}{20}\ \frac{in}{ft}[/tex]

Remember that

[tex]1\ ft=12\ in[/tex]

Convert feet to inches

[tex]\frac{4}{20*12}=\frac{4}{240}\ \frac{in}{in}=\frac{4}{240}[/tex]

simplify

[tex]\frac{1}{60}[/tex]

That means ----> 1 unit in the original painting represent 60 units in the mural

Answer:

$15.00

A $10.00 and a $5.00 dollar bill

Step-by-step explanation:

Answer:$80

Step-by-step explanation:

3 times 20=60

2 times 10=20

either 1, $10 and 1, $5, or 3, $5 or 15, $1

Answer:

-3

Step-by-step explanation:

[tex]3 cis(180^\circ)[/tex] means [tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]

What is the [tex]x[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is -1.

What is the [tex]y[/tex]-coordinate value that corresponds to [tex]\theta=180^\circ[/tex]. That value is 0.

So this implies [tex]\cos(180^\circ)=-1 \text{ and } \sin(180^\circ)=0[/tex].

[tex]3 cis(180^\circ)[/tex]  

[tex]3(\cos(180^\circ)+i \sin(180^\circ))[/tex]

[tex]3(-1+i (0))[/tex]

[tex]3(-1+0)[/tex]

[tex]3(-1)[/tex]

[tex]-3[/tex]

Answer:

see the explanation

Step-by-step explanation:

we know that

The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

Remember that if two triangles are congruent, then its corresponding angles and its corresponding sides are congruent

In this problem

PO≅SO ----> given problem

NO≅TO ----> because O is the midpoint NT

∠PON≅∠SOT -----> by vertical angles

so

two sides and the included angle of triangle PON are congruent to two sides and the included angle of triangle SOT

therefore

Triangles PON and SOT are congruent by SAS

hence

∠N≅∠T ----> by definition of congruence (corresponding angles are congruent)

Answer:

My personal opinion to this question would be 20 times greater.

Step-by-step explanation:

This is because in a car, there is more safety as there is airbags for the driver and the passenger seat also if the people sitting on the back, lean forward from the crash, they would most probably hit their head on the headrest.

Answer:

7.125

Step-by-step explanation:

The average weight per bushel of fruits that Justin picked is calculated as the sum of all weights divided by the number of bushels, which comes out to be 7.125 pounds per bushel.

To calculate the average weight per bushel when Justin picks 3 bushels of fruits weighing 8 1/4 pounds, 6 1/2 pounds, and 6 5/8 pounds, we need to add up the weights of the bushels and then divide by the number of bushels. Here are the steps:

First, convert all fractions to decimals or common denominators for easier addition:
8 1/4 = 8.25 pounds
6 1/2 = 6.5 pounds
6 5/8 = 6.625 pounds

Add up the weights of the three bushels:
8.25 + 6.5 + 6.625 = 21.375 pounds

Finally, divide the total weight by the number of bushels to find the average:
21.375 pounds \/ 3 bushels = 7.125 pounds per bushel

The average weight per bushel that Justin picks is 7.125 pounds.

Answer:

45 remainder 3.

Step-by-step explanation:

Answer:

b 21%

Step-by-step explanation:

good luck and hurry :)

The given 22 teachers from the total of 104 teachers in the survey gives

the teachers who teach math and not English as approximately; 21%

The relative frequency table is presented as follows;

[tex]\begin{tabular}{|c|c|c|c|}&English&Not english & Total\\Math&34&22&56\\Not math&40&8&48\\Total&74&30&104\end{array}\right][/tex]

Required:

The joint relative frequency for teachers teaching math and not English

Solution:

The joint relative frequency is the ratio of the frequency of a given category to the total number of data points within the category.

The number of teachers that teach math but not English = 22

Total number of teachers in the survey = 104

Therefore;

[tex]The \ joint \ relative \ frequency = \dfrac{22}{104} \times 100\approx \mathbf{21\%}[/tex]

Therefore;

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Answer:

Step-by-step explanation:

8:5, 16:10, 24:15

these can be written as 8/5, 16/10, 24/15

8/5

16/10 reduces to 8/5

24/15 reduces to 8/5

so basically, they are all the same ratio in simplest form

Answer:

"she could have sold between 14 and 24 glasses"

Step-by-step explanation:

7 to 12 glasses sold per hour

Min 7 glasses and Max 12 glasses

If she sold for 2 hours, her minimum would be:

7 * 2 = 14 glasses

and her max would be:

12 * 2 = 24 glasses

Hence,

she could have sold between 14 and 24 glasses

Answer: $35 is the selling price and $1225 is the maximum revenue.

Step-by-step explanation:

Since we have given that

[tex]R(x)=-x^2+70x[/tex]

We need to find the maximum revenue.

So, We will first derivative it w.r.t. x.

So, it becomes,

[tex]R'(x)=-2x+70[/tex]

Now, we will find critical points.

So, R'(x) = 0

So, it becomes,

[tex]-2x+70=0\\\\-2x=-70\\\\x=\dfrac{70}{2}=35[/tex]

Now, to check whether it yields maximum revenue or not.

So, second derivative w.r.t. x, we get that

R''(x) = -2<0

So, At $35, it yields maximum revenue.

Amount of maximum revenue would be

[tex]R(35)=-(35)^2+70\times 35=-1225+2450=\$1225[/tex]

Hence, $35 is the selling price and $1225 is the maximum revenue.

Answer:

The equation of the line is 5x + y + 19 = 0

Step-by-step explanation:

The equation of the line with slope 'm' and given a point (x₁, y₁) passing through it we use the Slope - one - point form which is given by:

                                    y - y₁ = m(x - x₁)

The point given is: (-3, -4) and the slope is -5.

We get the equation of the line to be:

y - (-4) = -5(x - (-3))

⇒ y + 4 = -5(x + 3)

⇒ y + 4 = -5x - 15

⇒ 5x + y + 19 = 0. is the required equation of the line.

Answer:

$0.25 per ounce

Step-by-step explanation:

Look at this and now tell me if my deleted answer was right

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Unit rate has to do with comparison or the proportionality of an item to its unit value or unit of measure.

The unit rate for the pumpkin seeds is $0.25 per ounce.

Based on this question, unit rate is the cost of 1-ounce of pumpkin seeds

From the question:

24-ounce of pumpkin seeds = $6.00

1- ounce of pumpkin seeds = ?

Cross Multiply

1 - ounce × $6.00 / 24-ounce

= $0.25

Therefore, unit rate for pumpkin seeds is $0.25 per ounce.

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Answer:45%

Step-by-step explanation:

I believe it’s 45%

Divide 86.4 by 192 and multiply the result by 100 to get the percentage, hence it is 45%.

A figure or ratio that may be stated as a fraction of 100 is a percentage.

If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

Here we have to find:

86.4 is what percent of 192

Divide 86.4 by 192:

86.4 / 192 = 0.45

Multiply the result by 100 to convert it into a percentage,

Therefore,

0.45 x 100 = 45%

Hence,

86.4 is 45 percent of 192.

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