Answers
[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
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.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ5
BRAINLIEST!
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
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
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
q=mc(T₂-T₁)
Solve for T₂
Answers
T2 = (q/mc) + T1
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.
A computer chip factory produces 520 chips in 13 minutes. at this rate, how many chips does it produce in 1 hour?
Answers
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.
Which graph represents the function f(x)=(x+4)(x+1)(x−3)?
Answers
Answer:
your answer will be C .
Step-by-step explanation:
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 data9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45Five-number summaryMinimum:
The smallest number of data ⇒ 11Maximum:
The largest number of data ⇒ 45Median:
The middle number of the data if data consists of odd number of elements ⇒ 24Lower quartile:
The median of the lower half of data, 9, 11, 11, 16, 16 ⇒ 11Upper quartile:
The median of the upper half of data, 28, 30, 34, 42, 45 ⇒ 34Interquartile rangeThe difference of upper and lower quartiles, 34 - 11 = 23-5/12 - (-9/3) what is the answer for this equation
Answers
Answer:
2 7/12
Step-by-step explanation:
Simple fraction problem
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]
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.
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.More can be learned about the graph of a function at https://brainly.com/question/19376563
#SPJ1
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.
To learn more about concurrency of triangles from the given link
https://brainly.com/question/15552454
#SPJ4
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.
the x and y intercept
Answers
y intercept: (0, -7/3)
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
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]
Learn more about factoring quadratics here:
https://brainly.com/question/27956741
https://brainly.com/question/27947331
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
Deceasing at a decreasing rate
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//
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
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 valueThe 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
Read more on p value here:
https://brainly.com/question/4621112
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
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
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
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.
Learn more about dimensions here:
https://brainly.com/question/19819849
#SPJ1
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
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.
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]
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
