Solve the following system of equations. If there is no solution, write DNE in each coordinate of the ordered triplet. If there are an infinite number of solution, write each coordinate in terms of z
x+3=y+12
z+13=x+8
y-7=z-11
PLS

Answer:The algebraic steps you have taken are incorrect, leading to an invalid conclusion. Let's go through each step and see where the mistake is made:

X = 1 (given)

X+X = 1+X (adding X to both sides)

2X = 1+X (combining like terms)

2X = X+1 (rearranging terms)

2X-2 = X+1-2 (subtracting 2 from both sides)

2X-2 = X-1 (simplifying)

2(x-1)/(x-1) = (x-1)/(x-1) (dividing both sides by x-1, note that x cannot be 1 as it would result in division by 0)

2 = 1 (canceling out the (x-1)/(x-1) on both sides)

The error lies in dividing both sides by (x-1) in step 7. Although (x-1) appears on both sides of the equation, it is not equal to zero as x cannot be 1 due to division by zero. Dividing by (x-1) effectively cancels it out, leading to the incorrect result of 2=1.

Step-by-step explanation:

Answer:

28 hours

Step-by-step explanation:

Let's use "B" to represent the number of hours Bianca practiced.

From the problem, we know that Filipe practiced 12 fewer hours than Bianca, which means:

Filipe's practice time = Bianca's practice time - 12

We are also told that Filipe practiced for 16 hours, so we can substitute that into the equation:

16 = B - 12

To solve for B, we can add 12 to both sides:

16 + 12 = B

So, Bianca practiced for a total of 28 hours.

The requried insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.

The insurance premium of a bus is GH¢93.30 plus 15% of the insured value.

Let's first calculate 15% of¢250.00:

15% of GH¢250.00 = 0.15 x 250.00 = GH¢37.50

Now, we can add this amount to the base premium of GH¢93.30 to find the total insurance premium for the bus:

GH¢93.30 + GH¢37.50 = GH¢130.80

Therefore, the insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.

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The area of the shaded region for the normal distribution is approximately 0.6985.

We have,
To find the area of the shaded region under the standard normal distribution curve between z = -0.87 and z = 1.24, we can use a standard normal distribution table or a calculator with a standard normal distribution function.

Using a standard normal distribution table, we look up the area to the left of z = -0.87 and the area to the left of z = 1.24 and then subtract the smaller area from the larger area to find the area between z = -0.87 and z = 1.24.

The table value for z = -0.87 is 0.1949, and the table value for z = 1.24 is 0.8934.

The area between z = -0.87 and z = 1.24 is:

= 0.8934 - 0.1949

= 0.6985

So the area of the shaded region is approximately 0.6985.

Thus,

The area of the shaded region for the normal distribution is approximately 0.6985.

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Answer: The brother is 16 and she is 19.

Step-by-step explanation:

35 - 3 = 32

32 / 2 = 16

16 + 3 = 19

Answer:

(3, 0)

Step-by-step explanation:

It might be first helpful to think about the function [tex]|x-3|[/tex], we will call this [tex]g(x)[/tex]. So, [tex]g(x)=|x-3|[/tex].

The modulus (absolute value) function reflects any points on a graph that go below the x-axis up into the positive x region.

We know that the graph of [tex]y=x-3[/tex], will cross the x-axis at (3,0). We can work this out by setting y to 0 and rearranging for x. At the x-axis, y = 0.

Therefore, when the modulus comes in, a vertex will be created at (3,0).

But that is the vertex of [tex]g(x)[/tex].

Using basic algebra we can derive from previous working that [tex]f(x)=2g(x)[/tex].

Graphically, the multiplier of 2 on the outside of [tex]g(x)[/tex] stretches the graph in y-axis, and does so by the scale factor of 2.

With our vertex (3,0), the y value is 0. And if you multiply 0 and 2 together, 0 is produced. The x value will remain unchanged as a result of this transformation.

Therefore, the vertex of [tex]f(x)[/tex] is (3,0).

Answer:

[tex] {x}^{2} + 11x + 18 = [/tex]

[tex](x + 2)(x + 9)[/tex]

The two numbers are 2 and 9.

2 + 9 = 11, and 2 × 9 = 18.

The perimeter of the rectangle is P = 18 units

Given data ,

Let the rectangle be represented as ΔWXYZ

Now , the coordinates of the triangle are

W ( 3 , 3 ) , X ( 8 , 3 ) , Y ( 8 , 7 ) and Z ( 3 , 7 )

The perimeter of the rectangle = 2 ( length + width )

The width of the rectangle W = ( 7 - 3 ) = 4 units

The length of the rectangle L = ( ( 8 - 3 ) = 5 units

So , P = 2 ( 4 + 5 )

P = 2 x 9

P = 18 units

Hence , the perimeter is 18 units

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Anna will make  $1602.71 in all over 10 weeks.

Here, the first week salary of Anna = $116

i.e., the initial salary a =  $116

She was guaranteed a raise of 7% each week.

so, her salary in the next week would be,

116 + 7% of 116

7 percent of 116 is:

116 × 7/100 = 8.12

so, her salary will be $124.12

So, the equation for the salary after 'm' weeks would be,

[tex]n = 116\times (1 + 0.07)^{m - 1}\\\\n = 116\times (1 .07)^{m - 1}[/tex]

Using this equation , the salary in the second week m = 2 would be,

n = 124.12

Salary in the third week m = 3 would be,

n = 116 × [tex](1.07)^{3-1}[/tex]

n = 132.81

Salary in the fourth week m = 4 would be,

n = 116 × [tex](1.07)^{4-1}[/tex]

n = 142.11

Salary in the fifth week m = 5 would be,

n = 116 × [tex](1.07)^{5-1}[/tex]

n = 152.05

Salary in the sixth week m = 6 would be,

n = 116 × (1.07)⁶⁻¹

n = 162.7

Salary in the seventh week m = 7 would be,

n = 116 × (1.07)⁷⁻¹

n = 174.08

Salary in the eighth week m = 8 would be,

n = 116 × (1.07)⁸⁻¹

n = 186.27

Salary in the nineth week m = 9 would be,

n = 116 × (1.07)⁹⁻¹

n = 199.31

And the salary after the tenth week m = 10 would be,

n = 116 × (1.07)¹⁰⁻¹

n = 213.26

The total money after 10 weeks would be,

T = 116 + 124.12 + 132.81+ 142.11 + 152.05 + 162.7 + 174.08 + 186.27 + 199.31 + 213.26

T = $1602.71

This is the required amount.

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The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

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The correct answer is option B:

⇒ Y decreases and X increases.

Given that;

the y value starts to decrease and the x value remains the same over time.

Now, We know that;

the slope remains constant, but the y value decreases as you move along the slope in the negative y direction, while the x value increases.

Hence,

If the y value starts to decrease while the x value remains the same over time on a consistent slope,

Thus, The correct answer is option B:

⇒ Y decreases and X increases.

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The solution to the system of equations is:

x = 3, y = 2, z = 2

To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.

First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:

(3) (2x – y + 3z = 10)

6x – 3y + 9z = 30

(1) (x + 3y – 2z = 5)

x + 3y – 2z = 5

Adding the two equations gives:

7x + 7z = 35

Simplifying, we get

x + z = 5 (Equation 1)

Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:

(2) (x + 3y – 2z = 5)

2x + 6y – 4z = 10

(3) (3x – 2y + 4z = 12)

9x – 6y + 12z = 36

Adding the two equations gives:

11x + 8z = 46

Substituting x + z = 5 from Equation 1 into the above equation, we get:

11(x + z) + 8z = 46

11x + 19z = 46

Solving for z, we get:

z = 2

Substituting z = 2 into x + z = 5 from Equation 1, we get:

x + 2 = 5

x = 3

Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:

2x – y + 3z = 10

2(3) – y + 3(2) = 10

6 – y + 6 = 10

y = 2

Therefore, the solution to the system of equations is:

x = 3

y = 2

z = 2

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The surface area of the polyhedron is calculated be equal to 224 square inches.

The polyhedron can be observed to have a large rectangle between two identical triangles by the sides

area of rectangle = length × width

The large rectangle have;

length = (12 + 10 + 10) in = 32 in

width = 4 in

area of large rectangle the = 32 in × 4 in = 128 in²

area of one identical triangles = 1/2 × 12 in × 8 in = 48 in²

area of 2 identical triangles = 2 × 48 in² = 96 in²

Surface area of the polyhedron = 128 in² + 96 in²

Surface area of the polyhedron = 224 in²

Therefore, the surface area of the polyhedron is calculated be equal to 224 square inches.

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The statement that could be true for h is h(2) = 16.

Option A is the correct answer.

We have,

The function h has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25, and we know that h(8) = 19 and h(-2) = 2.

To determine which statement could be true for h, we can use the given domain and range, along with the two known function values, to narrow down the possible values of h(x) for different values of x.

h(2) = 16

We do not have enough information to determine whether this statement could be true or not.

It is possible that h(2) = 16, but it is also possible that h(2) could be a different value within the range of 1 ≤ h(x) ≤ 25.

h(8) = 21

This statement cannot be true, as we already know that h(8) = 19.

h(13) = 18

This statement cannot be true, as 13 is outside the given domain of -3 ≤ x ≤ 11.

h(-3) = -1

This statement cannot be true, as -1 is outside the given range of 1 ≤ h(x) ≤ 25.

Therefore,

The statement that could be true for h is h(2) = 16.

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Answer:

$5.50(2/3)π(6.5^3) = $3,163.45

$5.50(2/3)(3.14)(6.5^3) = $3,161.85

$3,161.85 is the correct answer.

Answer:

-6x - 2y = 12

Step-by-step explanation:

The domain and range of the graph are domain = [-2, 5] and range is [-6, 2] and the graph is not a function

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

The graph

On the graph, we have the x values to be

x = -2 to 5

On the graph, we have the y values to be

y = -6 to 2

This means that domain = [-2, 5] and range is [-6, 2]

The graph is the graph of a circle

A circle does not represent a function

Hence, the graph is not a function

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Answer:

B) 0.08 and 0.1

The answer was 0.09, which is between 0.08 and 0.1

Answer:

660,430 gallons AKA 2499.9995045071 kilograms

you would proably round it to 2500 kilograms

Step-by-step explanation:

looked it up, had the same measurements as you gave

The height will be  61.8 ft

Find the volume of prism

Volume = Base Area × Height

since height = 10 feet

5,119.5 ft³ / 10 ft

= 511.95 ft²

formula for the area of a regular polygon is:

Area = (Perimeter × Apothem) / 2

ide length of the pentagon as 's' and the apothem as 'a'

511.95 ft² = (5s × a) / 2

angle at the center of the pentagon is 360° / 5 = 72°

72 / 2 = 36  degrees

tan(36°) = (s/2) / 17.25

solve for the value of s

s = 2 × 17.25 × tan(36°)

= 12.36 ft

5 s =

5 x 12.36 ft

=  61.8 ft

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Answer:

The answer to your problem is, She spend more talking to her friend then her mother

Step-by-step explanation:

The question asking:

What fraction of the minutes did Emilia spend talking to either her mom or her best friend?

So we can see that she talks to her friend instead of her mother shown;

[tex]\frac{1}{12} < \frac{5}{12}[/tex]

The total equals to [tex]\frac{6}{12} or\frac{1}{2}[/tex]

So, She spend more talking to her friend then her mother

Thus the answer to your problem is, She spend more talking to her friend then her mother

Note that the probabilities are given below.

a) the probability of a randomly selected catch being a mouse caught by Cyd

p(Catching a mount) x p(Cyd made the catch)

= 0.5x .2

= 0.1

b) the   probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.

Thus

P(that a catch is a bird) x p(the Cyd didn't make the catch)

= 0.3 x 0.8

=0.24

c) The probability of a randomly selected catch being caught by Greg is 0.45

To calculate, we say

(0.5   x0.45) + (0.3 x 0.45) + (0.2 x .45)

= 0.45.

d)

P (mouse caught by Greg) = (0.45 x 0.5) / 1

= 0.225.

e) P(catch is a mouse caught by Ken and catch is a mouse)

= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)

= 0.05 x 0.1

= 0.005

f)

P (catch made by Cyd | catch is a mouse)

= 0.1    x 0.2 / 0.5

= 0.04

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The greatest of the given integers is 64.

Given that, the sum of four consecutive integers is 250. We need to find what is the greatest of these integers.

Let the consecutive integers be = x, x+1, x+2, x+3

Therefore,

x + x+1 + x+2 + x+3 = 250

4x + 6 = 250

2x + 3 = 125

2x = 122

x = 61

Therefore, the greatest integer = 61 + 3 = 64

Hence, the greatest of the given integers is 64.

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Answer:

43.96 = 2πr

r = 21.98/π

A = π(21.98/π)^2 = 483.1204/π = 153.78 square meters

A = 483.1204/3.14 = 153.86 square meters

An equation for the height of the rocket after t seconds is h(t) = -16t² + 352t.

The time it takes for the rocket to reach a height of 0 is 22 seconds.

The time it takes to reach the top of its trajectory is 11 seconds.

The maximum height is 1,936 feet.

The time it takes to reach a height of 968 feet is 18.8 or 3.2 seconds.

Based on the information provided, we can logically deduce that the height (h) in feet, of this rocket above the​ ground is related to time by the following quadratic function:

h(t) = -16t² + Vit

When the initial velocity is 352 feet per seconds, the height function becomes;

h(t) = -16t² + 352t

Generally speaking, the height of this rocket would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:

0 = -16t² + 352t

352t = 16t²

Time, t = 352/16

Time, t = 22 seconds.

Next, we would determine the maximum height of this rocket by taking the first derivate in order to determine the time (t) it takes;

h(t) = -16t² + 352t

h'(t) = -32t + 352

352 = 32t

t = 352/32 = 11 seconds.

h(11) = -16(11)² + 352(11)

h(11) = 1,936 feet.

At a height of 968 feet, the time is given by;

968 = -16t² + 352t

16t² - 352t + 968 = 0

t² - 22t + 60.5 = 0

Time, t = 18.8 or 3.2 seconds.

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The minimum number of people over age 30 they must include in their sample is: 829 people

The formula for calculating the standard error is:

SE = μ ± Z(σ/√N)

Where:

σ = the standard deviation,

N = the sample size,

Z = the Z value for the percent confidence level desired.

We must find the Z value, at the 85% confidence level from a Cumulative Standardized Normal table for the 99% confidence level. This gives us the value of Z = 1.44

σ = 1.4 liters

N = 0.07

Thus:

0.07 = 1.44(1.4/√N)

0.07/1.44 = 1.4/√N

1.4/√N = 0.04861

√N = 1.4/0.04861

N = (1.4/0.04861)²

N = 829 people

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