Jason needed to get his computer fixed. He took it to the repair store. The technician
at the store worked on the computer for 5.75 hours and charged him $103 for parts.
The total was $419.25. What was the cost of labor, per hour?

Answer:

The other leg is 4 m long, and the hypotenuse is 5 m long

Step-by-step explanation:

Recall that the longest side of a right angle triangle is its hypotenuse, and that the legs and hypotenuse must verify the Pythagorean identity:

\(hyp^2=leg_1^2+leg_2^2\)

so, we know that the other two sides have consecutive integers for lengths. That is: if one is "x" in length, the other one must be "x+1"

So we can assume that the largest of this is the hypotenuse: "x+1"

Not, they must verify the Pythagorean identity:

\(hyp^2=leg_1^2+leg_2^2\\(x+1)^2=x^2+3^2\\x^2+2\,x+1=x^2+9\\2\,x+1=9\\2\,x=8\\x = 4\)

then, the other side is of length 4 m, and finally the hypotenuse is of length 4+1 = 5 m

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

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Answer:

3(12 + 7)

Step-by-step explanation:

To find the GCF of 36 and 21, list out their factors.

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

21: 1, 3, 7, 21

The greatest factor which both numbers share is 3.

Therefore, you can factor 36 + 21 as 3(12 + 7)

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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The type of variable being referred to is a reference variable, also known as a reference type.

In Java and other object-oriented programming languages, reference variables are used to store references to objects. Unlike primitive data types such as int or double, reference variables do not store values directly. Instead, they store the memory address of an object.

When a reference variable is passed into a method, the method receives a reference to the same object as the caller. Any changes made to the object within the method are saved, and the previous value of the object is overwritten outside the method. This is because the method operates on the same object as the caller, rather than a copy of the object.

It is important to understand the behavior of reference variables when passing them into methods, as this can have unintended consequences. For example, if the method modifies the object in a way that is not expected, the caller will also see the same change. To avoid this, it is sometimes necessary to create a new object within the method, rather than modifying the original object.

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The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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The equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

We can use the point-slope version of the equation, which is: to determine the equation of a line passing through two specified points.

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

Use the points (1,6) and (2,7) to find the equation of the line:

Using (x₁, y₁) = (1,6):

y - 6 = m(x - 1)

Now, substitute the coordinates (2,7) into the equation:

7 - 6 = m(2 - 1)

1 = m

So, the slope of the line is m = 1.

Substitute this value into the equation:

y - 6 = 1(x - 1)

y - 6 = x - 1

y = x + 5

Therefore, the equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

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Answer:800

Step-by-step explanation:1000+200x24-5000

+ 5800-5000

=800

Answer:

c

Step-by-step explanation:

~700 regular sodas to server 864 people

(the actual answer is 699.4285)

The number of regular sodas that should be bought will be 700 regular sodas.

If out of 21 people prefer diet soda to regular soda, then it means that 17 people prefer regular soda.

Since the number of people are 864 people, then the number of regular sodas that'll be bought will be:

= 17/21 × 864

= 699.42

= 700 Approximately

Therefore, the number of regular sodas that should be bought will be 700 regular sodas.

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Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

The ship started at the Position 0.14 units.

To determine the starting position of the ship, we can consider the distance sailed to the left and the distance to the treasure.

Given that you sailed 0.055 units to the left and found the treasure at 0.085 units, we can represent this situation mathematically as follows:

Starting position + Distance sailed to the left = Distance to the treasure

Let's assign a variable, "x," to represent the starting position of the ship.

The equation becomes:

x - 0.055 = 0.085

To find the value of x, we can solve this equation by isolating x on one side:

x = 0.085 + 0.055

x = 0.14

Therefore, the ship started at the position 0.14 units.

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Answer:

x=22-y^2÷2

Step-by-step explanation:

Answer:

x=44-2y^2÷2

Step-by-step explanation:

2x-3+2y^2=41

(combine like terms)

2x+2y^2=41+3

2x+2y^2=44

2x=44-2y^2

x=44-2y^2÷2

Please like my answer.

Answer:

5(n-3)

Step-by-step explanation:

There would be parenthesis because you'd subtract three from the number first.

Answer:

x = 0,-3

y = 1,-2

Step-by-step explanation:

We can substitute x+1 for x in the second equation

x(x+1) + 2x = 0

x^2 + 3x = 0

x(x+3) = 0

x = 0,-3

y = 1,-2

Answer:

just show the questions i will help

Step-by-step explanation:

In Jameson's drawing, the nose cone has an area of 5 square inches. Each of the fins has an area of 3 square inches and the total area of the drawn rocket is 22 square inches.

From the question, we have the following parameters that can be used in our computation:

The drawing (see attachment)

The area of the nose cone is

Area = 1/2 * 5 * 2

Area = 5 square inches

For the fin, we have

Fin = 1/2 * 3 * 2

Fin = 3 square inches

Lastly, we have

Total area = (4 + 2 + 1) * 2 + 5 + 3

Total area = 22 square inches

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Answer:

Hey there!

The range of this function is all numbers to three.

Thus, this can be expressed as (-∞, 3]

Let me know if this helps :)

Every six months, you will receive $21.50 back from your bond.

The 4.3% coupon is the annual interest rate, which is paid semi-annually (twice a year).

To find the amount earned every 6 months, we need to divide the annual interest rate by 2:

(4.3% / 2) = 2.15%

Next, we need to calculate the dollar amount earned every 6 months. To do this, we need to find 2.15% of the bond's face value:

2.15% of $1000 = $21.50

Therefore, you will earn $21.50 off your bond every 6 months.

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The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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Answer:

area=432

Step-by-step explanation:

use the Pythagoras theory now that you know the width and you'll get the length and the width then you multiply both of them hope it helps you.

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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The crime that is often alcohol related is domestic violence. That is option D.

Domestic violence is defined as an abusive relationship that exist between two or more individuals that are closely related by blood or marriage.

The causes of domestic violence include the following:

Therefore, alcohol intake can lead to domestic violence because it can cause the abusive partner to have a reduction in cognitive and physical functions that impair self-control, with the consequent effect of reducing the ability to resolve conflicts nonviolently.

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Answer:

She needs to win 6 more consecutive tournament games.

Step-by-step explanation:

\( \frac{3 + x}{4 + x} = \frac{9}{10} \)

\(10(3 + x) = 9(4 + x)\)

\(30 + 10x = 36 + 9x\)

\(x = 6\)

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.

Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:

P(k successes in n trials) = \(C(n , k) * p^k * (1 - p)^{(n - k)}\)

where:

Step1

Calculate the probability of rolling a seven on an 8-sided die (p).

Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),

p = 1/8.

Step 2

Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:

P(3 sevens in 10 rolls) = \(C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}\)

On subtracting gives:

=C(10,  3) * (1/8)^3 * (7/8)^{7}

Plugging the value of C(10,3) = 120 in the above equation:

= 120 * (1/8)^3 * (7/8)^{7}

Step 3:

Calculate the final answer using the formula:

P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)

≈ 0.0142

Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

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Answer:

if z square =0.64

then

z=Root under 0.64

Now

Z=0.8.

Answer:

41.93 degrees

Step-by-step explanation: