Solve the equation for all values of x.
|5x + 8| 8 = 3x

The solution of the system of equations are;

⇒ x = - 6 , y = 44 and z = 2

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The system of the equations are,

3x + y - 2z = 22    .... (i)

x + 5y + z = 4       .... (ii)

x = - 3z                .... (iii)

Now,

Solve the equations as;

Substitute x = - 3z in both equations, we get;

⇒ 3x + y - 2z = 22

⇒ 3 × -3z + y - 2z = 22

⇒ - 9z + y - 2z = 22

⇒ - 11z + y = 22   .... (iii)

And, x + 5y + z = 4

- 3z + 5y + z = 4

5y - 2z = 4     ... (iv)

Solve equation (iii) and (iv) we get;

⇒ y = 44 and z = 2

So, x = - 3z    

⇒ x = - 3 × 2

⇒ x = - 6

Thus, The solution of the system of equations are;

⇒ x = - 6 , y = 44 and z = 2

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Answer:

$0.8625

Explanation:

The sales tax for the t-shirt will be 7.5% of the price. So, 7.5% of $11.50 can be calculated as:

So, the sales tax for this item is $0.8625

Answer:

Step-by-step explanation:

Substitute a and b with 1/4 and 6

5b/ 32a^2

5(6)/ 32(1/4)^2

30/32(1.96)

30/62.72

0.5102 Answer

Answer: 4 tons

Step-by-step explanation:

Since the crew can clear 1/2 ton in 30 minutes, 4 hours has eight 30 minutes, which means that 8x1/2 = 4

Answer: 4 tons

Step-by-step explanation:

30 minutes multiplied by 2 is 1 hour and 1 half times 2 is 1 ton, so the crew can clear one ton every hour. 4 hours times 1 ton is 4 tons an hour.

The required answer would be (24 -3x - 4x²) / 4x = 0 which is the lcm of the rational algebraic equation 6/x+x-3/4=2.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The given equation below as:

⇒ 6/x + x - 3/4 = 2

We have to determine the lcm of the rational algebraic equation

⇒ 6/x + x - 3/4 = 2

Rearrange the term of 2 in the equation,

⇒ 6/x + x - 3/4 - 2 = 0

Take LCM in the above equation,

⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]

⇒ (24 + 4x² -3x - 8x²) / 4x = 0

Combine the likewise terms in the numerator,

⇒ (24 -3x - 4x²) / 4x = 0

Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.

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[tex] \frac{13}{5} \times - \frac{8}{3} \\ = - \frac{104}{15} [/tex]

ATTACHED IS THE SOLUTION

Answer:

(-104/15)

Step-by-step explanation:

    3              2

2 ------ × -2 -------

    5              3

5 × 2 = 10

10 + 3 = 13

3 × -2 = -6

-6 + -2 = -8

 13        -8            104

------- × ------- = (-) -------

  5          3             15

I hope this helps!

Let's begin by listing out the information given to us:

ANSWER

A = 51°

EXPLANATION

ABC is a right triangle. We know the length of the hypotenuse, AB = 44 m, and the length of the adjacent leg to angle A, AC = 28 m. To find the measure of angle A we have to use the cosine of that angle,

Solving for A,

Replace with the known values and solve,

Hence, the measure of angle A is 51°, rounded to the nearest whole number.

Given:

1 mile = 1.6 km

So, 8 miles per hour in kilometers per hour is given by:

Where x = # of kilometers

So, solve for x:

This is 12.8 km per hour

Next, the distance traveled in 2 hours is:

Substitute the values:

Answer:

Rate: 12.8 km/h

Distance traveled in 2 hours: 25.6 km

The most appropriate choice for cone and total surface area of cone will be given by-

Total surface area of the cone is [tex]198235.71 cm^2[/tex]

What is cone and total surface area of cone?

Cone is a 3 dimensional figure whose base is a circle and upper surface finally converge to a point.

Cone is obtained by revolving a right angled triangle about one of its legs.

Total surface area of the cone is the sum of curved surface area of the cone and the area of the base of the cone.

If r is the radius of the base of the cone and l is the slant height of the cone, then total surface area of the cone will be given by

[tex]\pi r(r+l)[/tex]

Here

Ratio of the slant height and radius of base of the cone = 2:1

Radius = 145cm

Slant height = [tex]145 \times 2[/tex]

                    = 290 cm

Total surface area of cone = [tex]\pi r(r+l)\\[/tex]

                                              = [tex]\frac{22}{7} \times 145\times (145+290)\\[/tex]

                                              = [tex]\frac{22}{7} \times 145 \times 435[/tex]

                                               = [tex]198235.71 cm^2[/tex]

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Complete Question

The slant height and the radius of  base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?​

The answer is in my screenshot pic.

every day she spent $35, if after 1 day she still have $315, the day before that she had $315+$35=$350

Therefore, the initial value was $350

By working with inequalities, we will see that:

Let's define:

We know that Mrs. Smith spent $50 more at a store than Mrs. Jones, then:

S = J + 50

And together they spent at most $250, then:

S + J ≤ 250

Now, replacing the equation in the inequality, we get:

(J + 50) + J  ≤ 250

2*J + 50  ≤ 250

2*J  ≤ 250 - 50

2*J  ≤ 200

J  ≤ 200/2

J  ≤ 100

So Mrs. Jones spent at most 100 dollars.

And Mrs Smith spent $50 more than that, so we can write the inequality.

50  ≤ S ≤ 150

She spends between $50 and $150.

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Total number of cards: 52

Number of face cards: 12

To calculate the percentage that the face cards represent we need to divide the number of face cards by the total number of cars, and then multiply by 100%:

The first division 12/52 will give us the proportion that the face cards represent, and by multiplying that by 100 we find the percentage.

Solving the operations:

-solving the division

-solving the multiplication:

The face cards represent 23.08%.

Rounding to the nearest tenth of a percent (one decimal place):

Answer: 23.1%

The allowance of each person is

From the question, the tape diagram that can be used in our computation is given as

you [][][][][]

friend[][][][]

Counting the number of boxes, we have

You = 5

Friend = 4

Next, we represent the boxes as a ratio

So, we have

You : Friend = 5 : 4

This means that

You = 5/9 * Total allowance

Friend = 4/9 * Total allowance

From the question, we have

Total allowance = $72

Substitute the known values in the above equation

So, we have the following equation

You = 5/9 * 72

Friend = 4/9 * 72

Evaluate the products

You = 40

Friend = 32

Hence, the amount of each person's allowance is $40 and $32, respectively

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The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.

From point A, point B is observed with an angle of 45 down from the top of the tree to the ground.

Thus, the angle of depression is 45°

The value of f(2) would be 80 which is determined by substituting the value of x = 2in the given function ​f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The given function below is:

​f(x) = 2x⁴ + 6x³ −4x² +2x + 12

​f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80

We have to determine the value of f(2).

⇒ ​f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80

Substitute the value of x = 2 in the given function,

⇒ ​f(x) = (2 −2)(2(2)³ + 10(2)² + 16(2) + 34) + 80

​⇒ f(x) = (0)(2(2)³ + 10(2)² + 16(2) + 34) + 80

​⇒ f(x) = 0 + 80

​⇒ f(x) = 80

Therefore, the value of f(2) would be 80.

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We are told that 11 mg of Achromycin per patient pound must be administered, we are also given the weight of the patient as 34 kg, in order to properly use this weight we must convert it from kg to pounds by multiplying the weight in kg by 2.2, like this:

34×2.2 = 74.8

Then, the patient weight is 74.8 lbs, by multiplying this by the 11 mg per pound of Achromycin that have to be administered we can determine the mg of Achromycin, like this:

74.8×11 = 822.8

Then, 822.8 mg of Achromycin has to be administered, by dividing this amount by 4, we can determine the amount for each dose:

822.8/4 = 205.7

Then 205.7 mg are given per dose, since 5 mL contains 125 mg, we can take the ratio of mL to mg to get:

5/125 = 1/25

By multiplying the above ratio by 205.7 we can determine the milliliters that should be given per dose, like this:

205.7×1/25 = 8.2

Then, 8.2 mL must be given per dose

Answer: Scatter plots, to show relationships among numerical variables. Line graphs, to show change over time. Histograms, to show data distributions.

Step-by-step explanation: I looked it up

Answer:

(49.4 - 39) / 4

= 10.4 / 4

= 2.6GB

Step-by-step explanation:

Given:

The equation of the ellipse is,

Explanation:

The general equation of ellipse with center (h,k) is,

The center of te given ellipse is (2,-3).

Determine the value of a and b.

The value of a is more than b. so major axis is horiontal and minor axis is vertical.

The coordinates of endpoints of major axis are,

and

The coordinates of endpoints of minor axis,

and

or we can expressed coordinates of endpoints of minor axis as,

The value of x in the given quadratic equation are; +9 and -9.

A quadratic equation is the second-order degree algebraic expression in a variable. An equation of degree 2 containing a single variable is known as the quadratic equation. Its general form is  ax² + bx + c = 0 , where variables are x and constants are a, b, and c.

As equation is  x²= 81

Taking square root on both sides;

⇒ √x² = √81

⇒ X = ± 9

Thus the value of X is  ± 9

Hence, The roots of the given quadratic equation are; +9 and -9.

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Recall the formula for the Future value of a principal amount, compounded continuously.

Rearrange the equation so that we can solve for time t.

Now substitute the following given and we have

Rounding the answer to the nearest tenth, the investment will reach $15000, in approximately 15.2 years.

To solve this exercise, we define the following variables:

• j = Japan size of shoes,

• u = United Sates size of shoes,

• k = Korea size of shoes.

From the statement of the problem, we know that:

0. In Japan, shoe size is 16 more than the size in the United States →, j = 16 + u,,

1. In Korea, shoe size is 224 more than the size in Japan →, k = 224 + j.

We must find a function for the U.S. size of a shoe (u) in terms of the shoe size in Korea (k).

1) From point 1, we have:

2) From point 2, we have:

Replacing the expression of j in terms of k in the expression of u, we get:

Replacing the value k = 250 in the last equation, we get:

Answer

The U.S. shoe size of a shoe that is 250 in Korea is equal to 10.

Solution

- The question gives us the following arithmetic sequence:

- We are asked to write out the explicit function for the sequence.

- To do this, we simply write out the terms of the sequence. After this, we would determine the common difference of the sequence.

- We will use the common difference to find the first term of the sequence and then use the formula below to find the explicit form of the arithmetic sequence:

- We have been given that the second term of the sequence is 10. We would also use this term to form our sequence.

- Let us now apply the formula for the nth term of a sequence to find the explicit formula:

- With the above formula, we can proceed to populate the table. Let us use the formula to calculate all the terms for each value of n.

- On the table, we have the values filled in below:

Final Answer

The explicit form of the sequence is:

Answer:  A) moves two places to the right

Example:

[tex]2.567 * 10^2 = 2.567 * 100 = 256.7[/tex]

The positive exponent over the 10 tells us how many places to move to the right. If the exponent was negative, then we'd move to the left. This only works when the base is 10.

Answer: The second ratio in the proportion is set up as ounces over oranges. The units should be in the same place in proportion to the first ratio.

Step-by-step explanation:

Since the student is meausuring something we conclude that this is an experiment.