(x+26=y) and (y-12=z) if x+y+z=71 solve for x

Answer:

7.3

Step-by-step explanation:

The length of AB is found using the distance formula

We need to know the coordinates of A and B

A = (-5,-4) and B = (-3,3)

The distance is

d = sqrt ( (y2-y1)^2 + (x2-x1)^2)

   = sqrt( (3 - -4)^2 +(-3 - -5)^2)

   = sqrt( (3+4)^2 +(-3+5)^2)

   = sqrt(7^2+2^2)

   = sqrt(49+4)

  = sqrt(53)

  =7.280109889

To the nearest hundredth

 =7.3

Answer:

120⁰

Step-by-step explanation:

the top number shows the degrees

Answer:120 degrees (that's the answer

Step-by-step explanation:

According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.

To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.

Initial Debt:

Interest Calculation:

Previous Payment:

To determine the remaining debt on 1 June, we subtract the payment from the initial debt:

From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.

To calculate the interest for one month, we use the formula:

where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).

To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:

To have no debt on 30 June, Mazibane must pay the total debt amount:

Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.

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Answer:

point A

Step-by-step explanation:

Using mathematical operations, we know that the all-star players of Claremont are 2.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."

The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.

Mathematical operations include addition, subtraction, multiplication, division, and finding the root.

So, we know that 25 players in 3 cities.

1 city has 12 players.

Another city has 11 players.

So, the number of players that the 3rd city will have:

12 + 11 + x = 25

23 + x = 25

x = 25 - 23

x = 2

Therefore, using mathematical operations, we know that the all-star players of Claremont are 2.

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Answer:

8+2x-2 = 5

2x+6 =5

2x = -1

Step-by-step explanation:

8+2(x-1)=5

Distribute

8+2x-2 = 5

Combine like terms

2x+6 =5

Subtract 6

2x+6-6=5-6

2x = -1

Answer:

8 tickets

Step-by-step explanation:

Take the total cost and divide by the cost of one ticket to get the number of tickets purchased

66 / 8.25

8

Answer:

Same thing as before

Convert into improper for it to be easier to solve

11/3 - 9/5

THe common multiple is 15 here

55/15 - 27/15 = 28/15

Now 28/15 into a mixed is

1 13/15

There are 25 and 20 members in 8th grade and 7th grade respectively.

Let's call the number of 7th graders "x".

Then the number of 8th graders is 25% more than x, which is 1.25x.

We know that there are 45 total members, so as per the percent rule, we can write an equation:

x + 1.25x = 45

Combining like terms:

2.25x = 45

Dividing both sides by 2.25:

x = 20

So there are 20 7th graders, and 1.25 times as many 8th graders:

1.25x = 1.25(20) = 25

Therefore, there are 25 8th graders.

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Without additional information about the model house, it is impossible to accurately describe the surface that Molly does not need to paint. It could be any surface that will not be visible when the model house is displayed, such as the underside of a roof, the back of a wall, or the bottom of a floor.

The total length of 9 rods will be 72 units.

What is Addition?

A process of combining two or more numbers is called addition.

Given that;

The length of 6 identical iron rods is 48 unit.

Now,

Since, the length of 6 identical iron rods is 48 unit.

Hence, the length of 9 identical iron rods = 9 × 48 / 6

                                                                = 9 × 8

                                                                = 72 units

Thus, The total length of 9 rods will be 72 units.

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The value g(7) of the function g(x) = 7  / 8 x  - 1 / 2 is 45 / 8.

A function relates each element of a set with exactly one element of another set (possibly the same set).

In a simpler term, a function relates an input to an output.

Therefore, let's find the value of g(7) for the function below:

g(x) = 7  / 8 x  - 1 / 2

Hence,

g(7) = 7 / 8 (7)  - 1 / 2

g(7) = 49 / 8  - 1 / 2

g(7) =  49 - 4 / 8

Therefore,

g(7) = 45 / 8

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Answer: 3 kids take 3 pieces of candy each

Step-by-step explanation:

Let the number of children that took 3 pieces is x ( total take 3*x pieces of candy)

Number of children that took 5 pieces is y ( total take 5*y pieces of candy)

1 child took 1 piece that actually means that x+y=18 and 3*x+5*y=84.

( Because total number of all kids is 19. We just deduct one kid (Let his name is John) who took only 1 candy.  So we have 19-1 =18 kids without John. The similar is with the candies. Total number is 85. We deduct 1 piece which John has taken. )

So we have 2 equations or the system of 2 equations:

1).  x+y=18

2). 3*x +5*y=84

Multuply both sides of equation 1) by 3

We have   3*x+3*y=18*3

Deduct 3*y from both sides of this equation

3*x+3*y-3*y=54-3*y

3*x=54-3*y

Substitute 3*x in equation  2).  by 54-3*y

2) 54-3*y+5*y=84

2*y=30

y=15  ( kids take 5 pieces of candy each)

Using equation 1) find x

x+15=18

x=3 (kids take 3 pieces of candy each)

Answer:

a) The 99% confidence interval is interval B: 3.35 to 4.35

The 90% confidence interval is interval A: 3.55 to 4.15.

b) Check Explanation.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value is obtained from either the t-distribution or the z-distribution tables. It depends on sample size and for smaller sample sizes, whether there is information provided for the population mean and standard deviation.

But whether z-distribution or t-distribution, the critical value increases as the confidence level increases.

Hence, the critical value for the 99% confidence level will be higher than the critical value for the 90% confidence level.

And since all the other parameters that determine the confidence interval and it's width (sample mean and the standard error of the mean) are the same for the 90% and the 99% confidence interval, the larger critical value for the 99% confidence interval means that it has the bigger width.

Hence, of the two intervals given,

Interval A: 3.55 to 4.15

Interval B: 3.35 to 4.35

The larger interval, (3.35, 4.35) is the 99% confidence interval and the smaller interval, (3.55, 4.15) is the 90% confidence interval.

b) The data required for this second part isn't available, but the answer for the confidence interval can be obtained using the steps I have given above and below.

Like I have given above,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error = (Critical value) × (standard Error of the mean)

The sample mean and the standard error of the mean are obtained from the sample data (which is missing).

Sample mean = (Σx)/N

x = each variable

N = number of variables = 20

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation (obtained from the sample data)

90% critical value for sample size of 20 = 1.73

99% critical value for sample size of 20 = 2.86

Hope this Helps!!!

According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

1- The function is linear because 2 is added to each y value to get to the next y value.

2- It would be 111 because 109+2=111

Step-by-step explanation:

Hope this helps:)

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer:

(the relation you wrote is not correct, there may be something missing, so I will simplify the initial expression)

Here we have the equation:

\(sin^4(x) + cos^4(x)\)

We can rewrite this as:

\((sin^2(x))^2 + (cos^2(x))^2\)

Now we can add and subtract cos^2(x)*sin^2(x) to get:

\((sin^2(x))^2 + (cos^2(x))^2 + 2*cos^2(x)*sin^2(x) - 2*cos^2(x)*sin^2(x)\)

We can complete squares to get:

\((cos^2(x) + sin^2(x))^2 - 2*cos(x)^2*sin(x)^2\)

and we know that:

cos^2(x) + sin^2(x) = 1

then:

\(1 - 2*sin(x)^2*cos(x)^2\)

This is the closest expression to what you wrote.

We also know that:

sin(x)*cos(x) = (1/2)*sin(2*x)

If we replace that, we get:

\(1 - \frac{sin^2(2*x)}{2}\)

Then the simplification is:

\(cos^4(x) + sin^4(x) = 1 - \frac{sin^2(2*x)}{2}\)

Answer:

4n + 5

Step-by-step explanation:

This equation cannot be simplified further

Unless you meant 4n + 7 = 2

Then the answer would be -1.25

Answer:

4n+5 hope this helps

Step-by-step explanation:

4n+7-2

4n+5

\(\\ \tt\longmapsto 880cm{\boxed{<}}9m\)

\(\\ \tt\longmapsto 5020mg{\boxed{>}}5g\)

\(\\ \tt\longmapsto 1500HL\boxed{=}1.5L\)

Answer:

Function, function

Step-by-step explanation:

Each input corresponds to one output. Thus, by the definition of a function, both graphs represent functions

Answer:

40 terms

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

then

\(\frac{n}{2}\) (- 4 - 82) = - 1720 ( multiply both sides by 2 to clear the fraction )

- 86n = - 3440 ( divide both sides by - 86 )

n = 40

the series has 40 terms

Answer:

(5 x + 1)-(-10 x + 6)

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The sides are not equal.

Answer:

18

Step-by-step explanation:

you have to divide 72 by 4. when you get 18 you can multiply that by 4 and you would get 72.

Answer:

B: 2005

Step-by-step explanation:

Worked on edge 2022

Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

Answer:

Each side of the original square is One-fourth the length of each side of the scale model

Step-by-step explanation:

Given that the square is a scaled copy of a smaller orginal square that was scaled up using a scale factor of 4, it means that the side length of the original square was multiplied by 4 to get the new side lenght of the scaled copy given in the question, which is 8ft.

Let original lenght be x.

x * 4 = 8 ft

4x = 8

x = 8/4 = 2.

Side lenght of the original square = 2 ft

Side of the original square to side of scale model = 2 ft to 8 ft = 2/8 = ¼.

Therefore, the statement that is true is: "Each side of the original square is One-fourth the length of each side of the scale model".

Answer:

A

Step-by-step explanation:

Answer:-5

Step-by-step explanation:

5*5*5=125

-5*-5=25

25*-5= -125

or

3√-125

The equation of the line is y = 2/3x + 1

The graph represents the given parameter

From the graph, we have the following points that can be used in our computation:

(x, y) = (0, 1) and (3, 3)

The equation of the line is then calculated using the following equation

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

Where

(x, y) = (0, 1) and (3, 3)

Substitute the known values in the above equation, so, we have the following representation

y = (3 - 1)/(3 - 0) * (x - 0) + 1

Evaluate

y = 2/3 (x - 0) + 1

So, we have

y = 2/3x + 1

Hence, the line equation is y = 2/3x + 1

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