What is the solution to the system of equations?

What Is The Solution To The System Of Equations?

Answers

Answer 1
Answer:

[tex](\frac{3}{2},\frac{5}{2})[/tex]

Step-by-step explanation:

The first equation can be rearranged by subtracting y from both sides. This gives you x = 4 - y.

The second equation is x = y - 1

Therefore, as both equations are equal to x, you can say that they are equal to each other, so 4 - y = y - 1.

If you add 1 to each side, you get 5 - y = y

If you add y to each side, you get 5 = 2y

Divide both sides by 2 to get y = 5/2

Now you can substitute 5/2 for y. For example, the second equation becomes x = 5/2 - 1

x is therefore 3/2

This can  be written as [tex](\frac{3}{2},\frac{5}{2})[/tex], which is the final answer.


Related Questions

After a gas-filled balloon is released, it rises 90 feet by the end of the first minute. by the end of the second minute, the balloon rises 120 feet, and by the end of the third minute, it rises 150 feet. how many feet would the balloon rise in 8 minutes? a. 300 c. 390 b. 330 d. 660 please select the best answer from the choices provided a b c d

Answers

Answer:

330

Step-by-step explanation:

the change in hirght = 120 - 90 = 30

so 90 + (30 x 8)

= 90+240

= 330//

q=mc(T₂-T₁)
Solve for T₂

Answers

the answer is:

T2 = (q/mc) + T1

What is the maximum value of the transformed function, y = -3cos (2x - 8) + 5
A. 3 units
B. 5 units
C. 8 units
D. 11 units

Answers

Answer:

C. 8 units.

Step-by-step explanation:

The maximum value of the cosine ( cos) function is 1

So, for y = 3cos(2x - 8) + 5

Maximum value  is 3 *1 + 5 = 8.

y = -3cos(2x - 8) + 5 is the above graph reflected in the y axis so the maximum value is also 8.

The graph of a linear relation passes through the point (-3,-5) and has a slope of 3.
Determine an equation for this linear relation in slope intercept form.

Answers

Answer:

y = 3x + 4

Step-by-step explanation:

Substituting into point-slope form and converting to slope-intercept form,

[tex]y+5=3(x+3) \\ \\ y+5=3x+9 \\ \\ \boxed{y=3x+4}[/tex]

An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 634" by 412" on the drawing, how large is the bedroom?

Answers

For a bedroom measuring 6 3/4" by 4 1/2" on the drawing, the dimensions of the bedroom are 18 ft. by 27 ft.

Option (C) is correct.

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.

According to the question,

The scale of an architectural sketch is 1/4" = 1'. If, according to the drawing, a bedroom has the dimensions 6 3/4 by 4 1/2 inches.

Then, the dimensions of the bedroom in feets are calculated as follows:

As 1/4" = 1'

6 3/4" = 27'= 27 ft.

Similarly,

4 1/2" = 18' =18 ft.

Thus, the dimensions of the bedroom are: 18 ft. by 27 ft.

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what is ratio (maths short definition)​

Answers

Answer:

division

Step-by-step explanation:

ratio means those 2 nunbers are being divided

division is how the numbers are related or compared

much of it is describing some of all something

like 2 out 3 dentists like chrwing gum

If amy cuddy and her research team originally established a sample size of n=200 (100 in each group) and then discovered that 86% of the high-power group (86 of 100) took a gambling risk while 60% of the low-power group (60 of 100) took the risk, then the p-value would have been much lower than that originally found in question 1. this p-value would have been less sensitive and would have provided stronger evidence for the researcher's hypothesis. state the p-value, rounding to 5 decimal places.

Answers

The p-value that would be given as the evidence would be given as p-value = 0.00002 and also P value = 0.00003

How to solve for the p value

The sample size of the first sample = 100

x1 = success 0f 86%

We have to find the proportion of this = 0.86

The sample size of the second sample n2 = 100

x12 = success 0f 60%

We have to find the proportion of this = 60/100

= 0.6

The difference = 0.86-0.6= 0.26

Next we have to find the pooled proportion. This is taken given as p = (x1+x2)/(n1+n2) this gives us 0.73

Next we have to find the standard error

= √(p*(1-p)*(1/n1+ 1/n2)= 0.06279

Z stat = (0.26-0)/0.0628= 4.1411

From here the p value would have to be

p-value = 0.00002 and also

P value = 0.00003

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Use distributive properties for 5(8+r)

Answers

Answer:

40 + 5r

usually you put the one with the variable infront

so 5r+40

Step-by-step explanation:

5(8+r)

5*8 + 5*r

40 + 5r

Izzo's Pizza sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found. Type of Crust Number Sold

Thin crust 307

Thick crust 224

Stuffed crust 161

Pan style 191

Based on this information, of the next 2000 pizzas he sells, how many should he expect to be stuffed crust or pan style? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answers

Answer:

797

Step-by-step explanation:

First, we need to find the number of pizzas sold last week by finding the sum of the pizzas sold:

307 + 224 + 161 + 191 = 883

Next, we need to find the proportion of stuffed crust and pan style pizzas sold last week by adding the number of both sold and dividing by the total number of pizzas sold:

(191+161) / 883 = 352 / 883

Now we need to multiply this proportion by 2000 to find the expected number of stuffed crust or pan style pizzas:

(352 / 883) * 2000 = 797.28 = 797

Pls help …. Need it immediately ….

Answers

The answer is 10.73 years.

Here, the formula we can use is :

[tex]\boxed {Children = \frac{Boys+Girls}{2}}[/tex] (for the average)

Substitute the values mentioned in the question.

10.54 = (10.35 + Girls)/2

21.08 = 10.35 + Girls

Girls = 10.73 years

The logarithmic functions, f(x) and g(x), are shown on the graph.
What is the equation that represents g(x)? Explain your reasoning.

Answers

Answer:

g(x) = log(x + 1) + 4

Step-by-step explanation:

The graph of g(x) is shifted 1 unit left and 4 units right from its parent function.

The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:

Answers

Answer:

11, 11, 24, 34, 45 and 23

===========================

Given data

9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45

Five-number summary

Minimum:

The smallest number of data ⇒ 11

Maximum:

The largest number of data ⇒ 45

Median:

The middle number of the data if data consists of odd number of elements ⇒ 24

Lower quartile:

The median of the lower half of data, 9, 11, 11, 16, 16 ⇒ 11

Upper quartile:

The median of the upper half of data, 28, 30, 34, 42, 45 ⇒ 34

Interquartile rangeThe difference of upper and lower quartiles, 34 - 11 = 23

Which function in vertex form is equivalent to f(x) = 4 + x² - 2x?
O f(x) = (x - 1)² + 3
O f(x) = (x-1)² + 5
O f(x) = (x + 1)² + 3
O f(x) = (x + 1)² +5

Answers

Answer:

f(x)=(x-1)^2+3

Step-by-step explanation:

Both equations vertexes equal (1, 3) while the rest do not match.

f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.

We can use the technique of completing the square to rewrite the given function f(x) in vertex form.

f(x) = 4 + x² - 2x

f(x) = (x² - 2x) + 4

Adding and subtracting (1) inside the parentheses

f(x) = (x² - 2x + 1) + 4 - 1

f(x) = (x - 1)² + 3

So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.

Therefore, the correct option is f(x) = (x - 1)² + 3.

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what is the range 42,43,44,44,49,40,39

Answers

Answer:

range is 10

Step-by-step explanation:

highest number is 49

loweest number is 39

49 - 39 = 10

Answer:

10

Step-by-step explanation:

The range is found by taking the largest number and subtracting the smallest number

The largest number is 49

The smallest number is 39

The range is 49-39 = 10

Rod waxes two thirds of his car with one fourth bottle of car wax. What fraction of the bottle of car wax will Rod need to wax his entire car?

Answers

Answer is 3/8
Step by step

Use x for car wax

2/3x = 1/4 × 1 car
2/3x = 1/4

Divide both sides by 2/3 to solve for x

x = 1/4 divided by 2/3

Note to divide fractions flip the 2/3 and multiply

x = 1/4 × 3/2 multiply across

x = 3/8.

factor (16x^2-8x+1)
Please show your work lol

Answers

Answer:

(4x - 1)^2.

Step-by-step explanation:

16x^2 - 8x + 1

Multiplying the first and last coefficients:

16 * 1 = 16

We need 2 numbers whose product is 16 and whose sum is -8.

These are - 4 and -4.

So we now write:

16x^2 - 4x - 4x + 1

Now factor by grouping :

= 4x(4x - 1) - 1(4x - 1)

= (4x - 1)(4x - 1)

= (4x - 1)^2

This method of factoring quadratics is called the 'ac' method - you split the middle term ( in this case the -8x) into 2 parts.

Answer:

[tex](4x-1)^2[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]16x^2-8x+1[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b:

[tex]ac = 16 \times 1 = 16[/tex][tex]b = -8[/tex]

Therefore, two numbers are: -4 and -4

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 16x^2-4x-4x+1[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 4x(4x-1)-1(4x-1)[/tex]

Factor out the common term (4x - 1):

[tex]\implies (4x-1)(4x-1)[/tex]

Apply the exponent rule:  aa = a²

[tex]\implies (4x-1)^2[/tex]

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Find the area of the figure below

Answers

Answer:

140 in^2

Step-by-step explanation:

Take the outside dimensions of the LARGE rectangle

11 x 17 = 187 in^2

 subtract the two corner cutout rectangles

    187 - 8x4   -  3 x 5   = 140 in^2

Diagram

Which graph represents the function f(x)=(x+4)(x+1)(x−3)?

Answers

Answer:

your answer will be C .

Step-by-step explanation:

please help im stuck its math

Answers

Answer:

y = 5x - 6

Step-by-step explanation:

We are given a line, which is parallel to the line y=5x+3.

We also know that this line passes through the point (3,9).

We want to find the equation of this line.
Parallel lines have the same slopes, yet different y intercepts.
So, let's find the slope of the line y=5x+3.

The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.

As 5 is in the place of where the slope (m) is, 5 is the slope of the line.

It is also the slope of the line parallel to it (which is the line we are trying to find).

We can write the equation of this new line in slope-intercept form as well, which is also the format your system wants.

Before we write the equation of the line in slope-intercept form, we can write it in point-slope form, then convert it into slope-intercept form.

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.

As we have already found the slope (5), we can immediately plug it into the formula.

[tex]y-y_1=5(x-x_1)[/tex]

Now, remember that we were also given a point, that passes through the line. This point is (3,9).

We can use its values in the formula.

Substitute 3 as [tex]x_1[/tex] and 9 as [tex]y_1[/tex].

y - 9 = 5(x-3)

Now, we have written the line in point-slope form.

However, we're not done yet; remember that we want it in slope-intercept form.

We can solve the equation for y to get slope-intercept form.

So, on the right, open up the parentheses and distribute 5 to both x and -3.

y - 9 = 5x - 15

Now add 9 to both sides.

y = 5x - 6

A computer chip factory produces 520 chips in 13 minutes. at this rate, how many chips does it produce in 1 hour?

Answers

They could do 2,400 chips in an hour

-5/12 - (-9/3) what is the answer for this equation

Answers

Answer:

2 7/12

Step-by-step explanation:

Simple fraction problem

What's the circumference of a
circle with a diameter of 31 inches?
Use 3.14 for I.
C = [?] inches
Enter the number that belongs in the green
box. Do not round your answer.
Hint: C = nd

Answers

Answer: C = 97.34 inches

Step-by-step explanation:

C = πd

= 3.14(31)

= 97.34

determine the rate of change of the function.

decreasing at increasing rate
increasing at a decreasing rate
decreasing at a decreasing rate
increasing at an increasing rate

Answers

it would be C
Deceasing at a decreasing rate

1. Convert the numeral to a numeral in base ten.
3205 six
43
125
4325
725

Answers

Expanding the digits, we have

[tex]3205_6 \equiv 3\cdot6^3 + 2\cdot6^2 + 0\cdot6^1 + 5\cdot6^0 = \boxed{725}[/tex]

Please help and explain.

Answers

Considering the given graph, we have that:

The slope of the graph of the function is equal to 1 for x between x = -3 and x = -2.The slope of the graph is equal to 0 for x between x = 3 and x = 4.The greatest value of y is y = 4.The smallest value of y is y = -3.

How to find the slope of a function?

The slope of a function, given two points, is given by the change in y divided by change in x.

When x = -3, y = -3, and while x = -2, y = -2, hence when x changes by 1, y also changes, hence the slope of the graph of the function is equal to 1 for x between x = -3 and x = -2.

When x = 3, y = 4, and when x = 4, y = 4, hence the slope of the graph is equal to 0 for x between x = 3 and x = 4.

Looking at the vertical axis:

The greatest(top) value of y is y = 4.The smallest(bottom) value of y is y = -3.

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If 2 pounds is equal to 3 dollars, which of the following is incorrect?
A. 28 pounds is 44 dollars
B. 23 pounds is 34.50 dollars
C. 11 pounds is 16.50 dollars
D. 10 pounds is 15 dollars

Answers

Answer:

A

Step-by-step explanation:

Find the ratio of pounds to dollars, [tex]\frac{3}{2}[/tex] or 1.5.

Next test each option by multiply the pounds by that ratio.

A: 28*1.5=42

B: 23*1.5=34.5

C: 11*1.5=16.5

D: 10*1.5=15

You can see A is the incorrect answer as 28 pounds would be 42 dollars, not 44.

What additional information could be used to prove that the triangles are congruent using aas? select two options.

Answers

Two angles and a non-included side of one triangle.

The AAS rule states that:

If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

In the diagrams below, if AC = QP,

∠ A = ∠ Q,

∠ B = ∠ R,

then triangle ABC ≅ QRP.

What is meant by congruence of triangles?

Congruence of triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

There are 5 main rules of congruency for triangles:

SSS Criterion: Side-Side-Side.

SAS Criterion: Side-Angle-Side.

ASA Criterion: Angle-Side- Angle.

AAS Criterion: Angle-Angle-Side.

RHS Criterion: Right angle- Hypotenuse-Side.

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Suppose you live in a country with a proportional tax system. you make $20,000 a year and pay $5,000 in taxes. your friend makes twice as much money as you. what amount can your friend expect to pay in taxes this year? $2,500 $5,000 $10,000 $20,000

Answers

Answer:

10,000

Step-by-step explanation:

Tbh this was pretty simple. If he makes twice the money as you, he pays twice as much too. Meaning he makes 40k a year and pays 10k for taxes

the x and y intercept

Answers

x intercept: (7/6, 0)
y intercept: (0, -7/3)

Evaluate the following expression. "5 less than 15"
A. -10
B. 8
C. 20
D. 10

Answers

Answer: 10

Step-by-step explanation: 5 less than 15 is 10 because 15 - 5 is 10. If it was 15 less from 5, only then it would be -10.

Answer:

5 less than 15 is Option D, 10. This is because using mathematical symbols, it says 15-5 which equals to 10.

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