The value of y varies directly as x, and y is 10 when x is 5. What is the value of y when x is 4?

The solution to the system of equations is (12, 30).

Option B is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the system of equations using the substitution method,

We solve one equation for one of the variables and substitute the expression into the other equation.

Let's solve the first equation for y:

y = 2x + 6

Now, substitute y = 2x + 6 into the second equation and solve for x:

3x - y = 6

3x - (2x + 6) = 6

3x - 2x - 6 = 6

x = 12

Now that we have found x, we can substitute it back into either of the original equations to find y.

Let's use the first equation:

y = 2x + 6

y = 2(12) + 6

y = 30

Therefore,

The solution to the system of equations is (12, 30).

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[tex]Use:\\\\a^n\cdot a^m=a^{n+m}\\\\y^{-9}\cdot y^{-8}\cdot y^{10}=y^{-9+(-8)+10}=y^{-7}[/tex]

Look at the picture.

From the graph, the value of the function at x = 2 will be 9. Then the correct option is B.

A statement, principle, or policy that creates the link between two variables is known as a function.

The graph of the function is shown.

From the graph, the value of the function at x = 2 will be 9.

Then the correct option is B.

More about the function link is given below.

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Answer:

f(g(x)) = x^2 +x

Step-by-step explanation:

To find f(g)(x) , we substitute g(x) in for x in the function f(x)

f(x) = x^2 -x

f(g(x)) = g(x)^2 -g(x)

          = (x+1)^2 - (x+1)

           = (x+1)*(x+1) - (x+1)

FOIL the square

             (x+1) (x+1)

         First x*x = x^2

        outer x*1 = x

        inner 1*x = x

       last  1*1 =1

Add them together

x^2 + x+x+1 = x^2+2x+1

f(g(x)) = (x+1)*(x+1) - (x+1)

           = x^2+2x+1 -(x+1)

Distribute the -1

          = x^2 +2x+1 -x-1

          = x^2 +x

f(g(x)) is basically replacing the x with g(x).

So, f(x)=(g(x))^2 - g(x)

g(x), in turn, equals x+1

Replace g(x) with x+1

(x+1)^2 - (x+1)

Expand: x^2+x+x+1 - x - 1

Cancel out x and 1

f(g(x))=x^2+x

If you require factoring it's

f(g(x))=x(x+1)

Answer:

R is in the third quadrant and S is in the first quadrant

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y )

P(- 3, 5 ) → R(- 3, - 5 ) ← third quadrant

Under a reflection in the y-axis

a point (x, y ) → (- x , y )

P(- 3, 5 ) → S(3, 5 ) ← first quadrant

In a reflection across the x-axis, the y-coordinate is negated, and in a reflection across the y-axis, the x-coordinate is negated. Thus, Point R (-3, -5) from point P (-3, 5) is in the fourth quadrant and Point S (3, 5) is in the first quadrant.

The given point P has the coordinates (-3, 5). When a point is reflected across the x-axis, the y-coordinate changes its sign. So, the reflection of point P across the x-axis (Point R) would be at (-3, -5). This places Point R in the fourth quadrant.

Similarly, when a point is reflected across the y-axis, the x-coordinate changes its sign. Therefore, the reflection of point P across the y-axis (Point S) would be at (3, 5). This places Point S in the first quadrant.

In summary, Point R is located in the fourth quadrant and Point S is located in the first quadrant.

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Answer:

-2 > x

Step-by-step explanation:

-8x-10>7x+20

Add 8x to each side

-8x+8x-10>7x+8x+20

-10 > 15x+20

Subtract 20 from each side

-10 -20 > 15x+20-20

-30 > 15x

Divide by 15

-30/15 > 15x/15

-2 > x

[tex]p\%=\dfrac{p}{100}\\\\40\%=\dfrac{40}{100}=\dfrac{4}{10}=0.4\\\\40\%\ of\ \$1200\ is\ 0.4\cdot\$1200=\$480\\\\Answer:\ \text{He spend}\ \$480.[/tex]

Final answer:

To determine the amount Stephen spent from his $1200 at 40%, the percentage is converted to a decimal (0.40) and multiplied by $1200, resulting in $480 spent.

Explanation:

Stephen had $1200. To calculate the amount of money he spent after using 40% of his money, we need to find 40% of $1200. We can write this as 0.40 × $1200.

Step 1: Convert the percentage into a decimal: 40% = 0.40

Step 2: Multiply the decimal by the total amount of money Stephen had: 0.40 × $1200 = $480.

Hence, Stephen spent $480 out of his $1200.

Answer:

31

Step-by-step explanation:

use a step by step calculator.

Answer:

The correct answer for this problem is 200 miles.

Answer:

What do mean by equals 16?

Step-by-step explanation:

1/2x+8=16

1/2x=16-8

1/2x=8

x=8:1/2

x=8*2

x=16

Hope this helps! <3

Answer:

.224 / 7  = .032

Step-by-step explanation:

.224 / 7

7 goes into 2    0 times with 2 left over

7 goes into 22   3 times with 1 left over

7 goes into 14    2 times with 0 left over

.224 / 7  = .032

Answer:

.032

Step-by-step explanation:

Answer:

80 Cents

Step-by-step explanation:

Answer: Each person will need to pay $1.25

Step-by-step explanation: $13.75 divided by the 11 people = $2.25

Perhaps brainliest?

Answer:18 1/12

Step-by-step explanation:i first added the whole numbers 12 and 5 to get 17; i then addled 1/4 and 5/6; i did this by finding a common denominator of both fractions and converted them into 6/24 and 20/24; i added them to get 26/24 which simplifies to 1 and 2/24, which equals 1 1/12; i added 1 to 17 and got 18, then added 1/12 to get 18 1/12

The sum of 121/4 and 5 5/6 is found by converting the mixed number to an improper fraction, finding a common denominator, adding the fractions, and simplifying if possible. The final answer is 433/12, which is already in its lowest terms.

The question asks for the sum of the numbers 121/4 and 5 5/6 reduced to the lowest terms. To answer this, we must first convert the mixed number to an improper fraction and then add it to the other fraction. Here's how to do it step by step:

Convert 5 5/6 to an improper fraction: 35/6.

Add 121/4 to 35/6. To do this, find a common denominator, which would be 12 in this case.

Convert both fractions to have the common denominator: 121/4 becomes 363/12, and 35/6 becomes 70/12.

Add the two fractions: 363/12 + 70/12 equals 433/12.

Reduce the fraction if possible. In this case, 433/12 is already in its lowest terms.

Therefore, the sum of 121/4 and 5 5/6 reduced to lowest terms is 433/12.

Question

Is this a true proportion ? 3/4,8/12

Answer:

Step-by-step explanation:

3/4 = 8/12

semplify

3/4 = 2/3

or you can solve in this way

3/4 = 8/12

0.75 = 0.66≈

Answer:

x < -3

Step-by-step explanation:

First subtract 6 from both sides of the inequality.

[tex]4x+6-6<-6-6[/tex]

[tex]4x<-12[/tex]

Divide 4 on both sides.

[tex]\frac{4x}{4} < \frac{-12}{4}[/tex]

[tex]x<-3[/tex]

Answer:

I might be wrong but i think it is 90 Degree Angle

Step-by-step explanation:

Answer:

right triangle

Step-by-step explanation:

90 degrees is a right angle so it will be a right triangle

Rational root theorem is used to determine the possible root of a function.

[tex]\mathbf{(a)\ f(x)= 4x^2 - 25}[/tex]

Set to 0

[tex]\mathbf{4x^2 - 25 = 0}[/tex]

Add 25 to both sides

[tex]\mathbf{4x^2 = 25}[/tex]

Divide both sides by 4

[tex]\mathbf{x^2 = \frac{25}{4}}[/tex]

Take square roots

[tex]\mathbf{x = \pm\frac{5}{2}}[/tex]

The function has rational roots.

This means that: rational root theorem provides a complete list of all roots

[tex]\mathbf{(b)\ g(x)= 4x^2 + 25}[/tex]

Set to 0

[tex]\mathbf{4x^2 + 25 = 0}[/tex]

Add -25 to both sides

[tex]\mathbf{4x^2 = -25}[/tex]

Divide both sides by 4

[tex]\mathbf{x^2 = -\frac{25}{4}}[/tex]

Take square roots

[tex]\mathbf{x = \pm \sqrt{-\frac{25}{4}}}[/tex]

The function has complex roots.

This means that: rational root theorem does not provide a complete list of all roots

[tex]\mathbf{(c)\ h(x)= 3x^2 - 25}[/tex]

Set to 0

[tex]\mathbf{3x^2 - 25 = 0}[/tex]

Add -25 to both sides

[tex]\mathbf{3x^2 = 25}[/tex]

Divide both sides by 4

[tex]\mathbf{x^2 = 8.333}[/tex]

Take square roots

[tex]\mathbf{x = \pm 2.89}[/tex]

The function has irrational roots.

This means that: rational root theorem does not provide a complete list of all roots

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Explanation of the Rational Root Theorem and its application to polynomial functions f(x), g(x), and h(x).

The Rational Root Theorem provides a list of possible rational roots for a polynomial function. However, it does not guarantee that all roots will be rational. Let's examine the given polynomial functions:

Answer: 3a^3 b^2+3a^2 b^2

Step-by-step explanation:

3a^2(ab^2+b^2)

=(3a^2)(ab^2+b^2)

=(3a^2)(ab^2)+(3a^2)(b^2)

=3a^3 b^2+3a^2 b^2

hope this helps

please mark brainliest answer

Answer:

3a3b2 + 2a2b2

Step-by-step explanation:

3a2(ab2 + b2) =

= 3a2*ab2 + 3a2*b2

= 3a3b2 + 2a2b2

Answer:

0.19125

Step-by-step explanation:

You divided 4.59 by the amount 24-oz

Answer: A & B

Step-by-step explanation:

-7y + 2x ≤ 3

(0, 0):      -7(0) + 2(0) ≤ 3

                  0   +   0  ≤ 3      

                        0      < 3            TRUE

(1, 1):      -7(1) + 2(1) ≤ 3

               -7   +  2   ≤ 3      

                      -5     < 3               TRUE

(-3, 5):      -7(-3) + 2(5) ≤ 3

                   21   +  10   ≤ 3      

                         31        < 3          FALSE                    

Answer:

3 to 4

or

3:4

Step-by-step explanation:

Answer is shown in the attached image, in RED.

The graph shows exponential B

exponential decay is when the graph is decreasing/going down

exponential growth is when the graph is increasing/going up

The graph is shown to be increasing, so it is exponential growth

As the amount of people infected with the virus decreases, time B

If you look at the graph, as time increases, the number of infected people also increases. So when the # of infected ppl decreases, so does time

Answer:

1. Growth

2. Decreases

Step-by-step explanation:

The graph shows the number of people infected with a virus as a function of time.

1.

The graph shows exponential growth because the graph is increasing above. It is going upwards, as the time is increasing.

2.

As the amount of people infected with the virus decreases, time decreases.

As it is a growth graph, if we study this in the opposite direction, that is from upwards to downwards, we can see that as the graph is going down, the values on the y axis are also decreasing.

Answer:

[tex]\text{The quotient is }4x^2 -27x +167[/tex]

Remainder is -996          

Step-by-step explanation:

[tex]\text{Given the polynomial }4x^3-3x^2+5x+6\text{ which is to be divided by }x+6[/tex]

we have to find the quotient using synthetic division

x+6 =0 , so x=-6

We divide by -6.

The steps for synthetic division are  

Step 1: Set up the synthetic division.

Step 2:  Put down the leading coefficient to bottom row.

Step 3: Multiply divisor which is on left by the value just written on the bottom row.

Step 4: Add the column created in above step.

Step 5: continue until we reached last column.

The synthetic division is shown in attachment.

[tex]\text{The quotient is }4x^2 -27x +167[/tex]

Remainder is -996      

When you divide 4x³- 3x² + 5x + 6 by (x+6) using synthetic division, the quotient is  4x²- 27x + 162

To divide ([tex]4x^3-3x^2+5x+6[/tex]) by (x+6) using synthetic division, follow the steps provided.

Arrange the terms of the dividend in descending order of degree, filling in any missing terms with a coefficient of 0.

Set up the synthetic division table with the divisor (x+6) as the divisor and the coefficients of the dividend (4, -3, 5, 6) as the dividend.

Perform the synthetic division:

Bring down the first coefficient, 4.

Multiply the divisor (x+6) by the value in the bottom row of the divisible column (which is 4).

The result is written in the next row.

Add the value in the next row to the coefficient in the next column and write the sum in the next row.

Repeat this process until all rows are completed.

The numbers in the bottom row of the table represent the coefficients of the quotient.

The quotient for this division is [tex]4x^2 - 27x + 167.[/tex]

Therefore, the quotient of ([tex]4x^3-3x^2+5x+6[/tex])/(x+6) is [tex]4x^2 - 27x + 167.[/tex]

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Answer:

7/8 ths

Step-by-step explanation:

3 divided by 4 is .75

* 7 divided by 8 is .875

8 divided by 10 is .80

7 divided by 9 is .77

If you divide the fractions you can compare the values and the highest value is your largest fraction.

The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator. The fraction 7/9 has the largest fraction.

Given information-

The set of the fraction given in the problem is,

[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]

The order of the fraction is arranging the fraction number from the smallest to the largest number.

The fraction with largest value of numerator is largest fraction in the two or more fraction number with same denominator.

To compare the fraction, make the denominator with same.

[tex]\dfrac{3}{4}, \dfrac{7}{8}, \dfrac{8}{10}, \dfrac{7}{9}[/tex]

To make the denominator same find out the least common factor of denominators which are 4,8,10 and 9 which is 360.

Multiply and divide with 360 in the given fractions to bring the 360 in denominator,

[tex]\dfrac{3\times360}{4\times360}, \dfrac{7\times360}{8\times360}, \dfrac{8\times360}{10\times360}, \dfrac{7\times360}{9\times360}[/tex]

[tex]\dfrac{270}{360}, \dfrac{315}{360}, \dfrac{288}{360}, \dfrac{315}{360}[/tex]

As the numerator 315 is the highest among all. Hence the fraction 7/9 has the largest fraction.

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Answer:

Option 4) Probability = 30%            

Step-by-step explanation:

We are given the following information:

We have a deck of cards.

We have to find the probability of drawing a face card given that is a heart.

Formula:

[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]

Conditional probability:

The probability of happening of event A given event B:

[tex]P(A|B) = \displaystyle\frac{P(A \cap B)}{P(B)}[/tex]

[tex]P(\text{Face card}|\text{Hearts}) = \displaystyle\frac{P(\text{Face card} \cap \text{Hearts})}{P(\text{Hearts)}}\\P(\text{Hearts}) = \displaystyle\frac{13}{52}\\\\P(\text{Face card} \cap \text{Hearts}) = \frac{4}{52}\\\\P(\text{Face card}|\text{Hearts}) = \frac{4/52}{13/52} = \frac{4}{13}\\\\=\frac{4}{13}\times 100\% = 30.77\%[/tex]

Answer : The value of car will be, $11654.98

Step-by-step explanation:

Given,

Principle = $22300

Time = 6 years

Rate of depreciation = 10.25 %

Formula used :

[tex]A=P(1-\frac{R}{100})^t[/tex]

where,

A = amount

P = principle

R = rate  of depreciation

T = time

Now put all the given values in the above formula, we get:

[tex]A=P(1-\frac{R}{100})^t[/tex]

[tex]A=\$ 22300(1-\frac{10.25}{100})^{6}[/tex]

[tex]A=\$ 11654.98[/tex]

Therefore, the value of car will be, $11654.98

Answer:

658.24 m

Step-by-step explanation:

Let A be the point from where Elton started. Connect points A and C, you get triangle ABC with AB=500 m, BC=350 m and m∠B=100°. Use the cosine rule to determine the length of the segment AC:

[tex]AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot \cos \angle B,\\ \\AC^2=500^2+350^2-2\cdot 500\cdot 350\cdot \cos 100^{\circ},\\ \\AC^2=250000+122500-350000\cdot (-0.174),\\ \\AC^2\approx 433276.8622,\\ \\ AC\approx 658.24\ m.[/tex]

Answer:

658.24 m

Step-by-step explanation:

The figure makes a triangle with vertices abc.

Where ab = 500 m

           bc = 350 m

The angle abc = 100°

Using the cosine rule we can find the distance ac.

ac² = 500²+350² - 2×500×350×cos100°

      = 372,500 - -60,776.86

      = 433,276.86

ac = √433,276.86

    = 658.24 m

Answer:

[tex](3,3\frac{1}{5})[/tex]

Step-by-step explanation:

We use the formula;

[tex](\frac{mx_2+nx_1}{2},\frac{my_2+ny_1}{2})[/tex]

where m:n=2:3 and [tex]x_1=1,x_2=6,y_1=4,y_2=2[/tex]

We substitute these values to get;

[tex](\frac{2(6)+3(1)}{2+3},\frac{2(2)+3(4)}{2+3})[/tex]

We simplify to get:

[tex](\frac{15}{5},\frac{16}{5})[/tex]

[tex](3,3\frac{1}{5})[/tex]

Answer:

(3,16/5)

Step-by-step explanation:

(2)(6)+(3)(1)/(2+3),(2)(2)+(3)(4)/(2+3)=3,16/5