Final answer:
To simplify the expression −5x + 8y + 2x − 3y, combine like terms, resulting in −3x + 5y.
Explanation:
To simplify the expression −5x + 8y + 2x − 3y, you want to combine like terms. The like terms are those with the same variable raised to the same power. In this expression, −5x and 2x are like terms, as are 8y and −3y.
Combine −5x and 2x: (−5 + 2)x = −3x
Combine 8y and −3y: (8 − 3)y = 5y
After combining like terms, the simplified expression is −3x + 5y.
Zack wants to make a profit of more than $300 for painting 4 identical rooms. The profit he makes is equal to the amount he is paid minus the cost of supplies. The cost of supplies is $32.50 for each room. Which inequality and solution represent the dollar amount, n, that zack must be paid for each room if he is to make a profit of more than 300$
A: n-4(32.5) > 300;n > 430
B: (n - 32.5) > 1,200; n > 332.5
C. (n-32.5)>300;n> 107.5
D 4n-32.5 > 300; n > 83.125
Answer: A
n-4(32.5) > 300;n > 430tep-by-step explanation:
given that Zack wants to make a profit of more than $300 for painting 4 identical rooms. That is
Profit > $300
Then, the profit he makes is equal to the amount he is paid minus the cost of supplies. The cost of supplies is $32.50 for each room. That is
n - 32.5 and
P + 32.5 × 4
Where 4 = number of rooms
P + 130
The minimum profit = 300 + 130 = $430
Therefore, the inequality and solution that represent the dollar amount, n, that zack must be paid for each room if he is to make a profit of more than 300$ is
n-4(32.5) > 300;n > 430
Final answer:
The correct inequality to represent the amount Zack must be paid per room to make a profit of more than $300 is C: (n-32.5) > 300; n > 107.5. After solving the inequality, it shows that n must be greater than $107.5 per room.
Explanation:
Zack aims to make a profit of more than $300 for painting 4 identical rooms. The cost of supplies per room is $32.50, and Zack's profit is based on what he's paid minus the supplies costs. To find the minimum amount, n, he needs to be paid per room to achieve this profit, we set up an inequality where the total amount paid for all rooms minus the total cost of supplies is greater than the desired profit.
The correct inequality is:
4n - 4(32.5) > 300
When simplified, this inequality becomes:
4n > 300 + 4(32.5)
4n > 300 + 130
Now, we solve for n:
4n > 430
n > 107.5
This means each room must be paid for an amount greater than $107.5 for Zack to make his desired profit. Therefore, the correct answer is C.
Solve 3z divided by 2=9
Answer:
z=6
Step-by-step explanation:
3z/2=9
3x6=18/2=9
A rectangle made of square tiles measures 10 tiles long and 8 tiles wide. what is the width of a similar rectangle whose length is 15 tiles?
Answer:
12 or 13
hope this helps
Answer:
13
Step-by-step explanation:
Write the following number in expanded form: fifty-four and elght tenths
Answer:
50 + 4 + . 8/10 I think
Step-by-step explanation:
54.8
The number 'fifty-four and eight tenths' in expanded form is represented as 50 + 4 + 0.8. Each digit's place value is broken down in this representation.
Explanation:The number 'fifty-four and eight tenths' is typically represented in decimal form as 54.8. In expanded form, we break down each digit's place value. Here are the steps:
Look at the digits in the number 54.8. The '5' is in the tens place and the '4' is in the ones place. Express the '5' in the tens place as 50 because 5 tens equals 50. Express the '4' as 4 because it is in the ones place. The '.8' represents eight tenths, so it can be written as 0.8.
When combined, the expanded form of 54.8 is 50 + 4 + 0.8.
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what is the solution to the system of equations below?
{2y=x+6
{3x=y+7
Answer:
x=4, y=5
Step-by-step explanation:
2y=x+6
3x=y+7
If you subtract 6 from both sides of the first equation, x will be isolated and you can plug it into the second equation. The new first equation is 2y-6=x, which when plugged into the second equation yields:
3(2y-6)=y+7
6y-18=y+7
5y=25
y=5
x=4
Hope this helps!
Final answer:
To solve the given system of linear equations, we use substitution to express x in terms of y from one equation and substitute it into the other, giving us the solution x = 4, y = 5.
Explanation:
The solution to a system of linear equations can be found by various methods, including substitution or elimination. The given system, which appears to be:
2y = x + 63x = y + 7This can be solved by using these methods. First, we will express one variable in terms of the other from one of the equcations and then substitute this into the second equation. Taking the first equation:
2y = x + 6
we can solve for x:
x = 2y - 6
Now, we substitute x in the second equation:
3(2y - 6) = y + 7
This simplifies to:
6y - 18 = y + 7
Now, let's solve for y by isolating it on one side:
6y - y = 7 + 18
5y = 25
y = 5
With the value of y, we can now substitute back into the equation x = 2y - 6 to find x:
x = 2(5) - 6
x = 10 - 6
x = 4
Therefore, the solution to the system of equations is x = 4, y = 5.
The equation y = 23.67x + 13.12 fits the scatterplot of the values for stock
ABC over the past month with an r-value of 0.9957. How much do you think
ABC will be worth at x = 28 days?
A. 13.12
B. 23.67
C. 698.74
D. 675.88
Step-by-step explanation:
The given equation is y = 23.67x + 13.12, where y is the value of the stock ABC and x is the number of days. The r-value of 0.9957 indicates a strong positive correlation between the two variables, which suggests that the equation is a good fit for predicting the value of the stock.
To find the value of the stock ABC at x = 28 days, we need to substitute x = 28 into the equation and solve for y:
y = 23.67(28) + 13.12
y = 663.76 + 13.12
y = 676.88
Therefore, the predicted value of the stock ABC at x = 28 days is $676.88.
The closest answer option is D. 675.88, but the correct answer is actually slightly higher at $676.88.
We are given a linear equation y = 23.67x + 13.12, where 'x' is the number of days and 'y' is the stock value.
Now, we need to predict the stock value for 'x' equals to 28 days. To do so, we substitute x = 28 into the equation.
Start by multiplying the given value of x with the slope:
23.67 times 28 equals 662.76.
Next, add the y-intercept to the result from the first step. So you take 662.76 and you add 13.12.
The sum is 675.88.
So, according to our calculation, the ABC stock would be worth 675.88 on the 28th day.
So, the answer is
Answer: D. 675.88.
Witch is not a characteristic of an exponential parent function
Answer:
All exponential functions try to cross the x axis but never do
Step-by-step explanation:
Two angles in a triangle measure 28° and 939. What is the measure of the third angle?
59
87
121
152
Which of the following describes the function −x4 + 1
where are the choices for the question?
Write an equation in which the quadratic expression 4x^2-26x+42 equals 0. Must show all work to receive credit.
Show the expression in factored form
Explain what your solutions mean for the equation in complete sentences.
HIGH POINT AND BRAIN LIST
Answer:
(a) (x + 3)(2x + 7) = 0
(b) These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.
Step-by-step explanation:
(a) We set 4x² -26x + 42 equal to 0:
4x² -26x + 42 = 0
Let's divide both sides by 2 to simplify this a bit:
2x² - 13x + 21 = 0
Now, we need factors a and b of 2 and c and d of 21 such that ac + bd = -13. The factors of 2 are: 1 and 2, so let's say a = 1 and b = 2. The factors of 21 are: (1, 21), (3, 7), (-1, -21), and (-3, -7). We see that if c = -7 and d = -3, this works:
ac + bd = 1 * (-7) + 2 * (-3) = -7 - 6 = -13
So, the factored form is:
(x - (-3))(2x - (-7)) = 0
(x + 3)(2x + 7) = 0
(b) So now we need to solve this. Set each of the two parenthetical expressions equal to 0:
x + 3 = 0
x = -3
AND
2x + 7 = 0
x = -7/2
These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.
Answer:
a) 2(x - 3)(2x - 7) = 0
b) function is 0 when x = 3 or 7/2
Step-by-step explanation:
4x² - 26x + 42 = 0
2(2x² - 13x + 21) = 0
2[2x² - 6x - 7x + 21] = 0
2[2x(x - 3) - 7(x - 3)] = 0
2(x - 3)(2x - 7) = 0
Solutions:.
x = 3, 7/2
Question 7
3 pts
(02.03 MC)
Which of the following statements is most likely correct about a rock found in Europe and a
rock found in America, both having the same kinds of fossils?
The rocks are the same age.
They are different types of rocks.
The mineral composition of the rocks is identical.
They were exposed to the same agents of weathering
Answer:
They were exposed to the same agents of weathering
Suppose a number cube is rolled twice. what is the probability that an odd number will show both times?
Answer:
1/4 or 25%Step-by-step explanation:
Suppose half on numbers are odd, then for each roll the probability is 1/2
So for two rolls the probability is:
1/2*1/2 = 1/4 or 25%Subtract 75 - 50.50 = ___ using mental math
Answer:
24.5
Step-by-step explanation:
First, I subtracted 50 from 75.
75 - 50 = 25
Then, subtract 0.5 from 25.
25 - 0.5 = 24.5
I hope this helps!
445% as a decimal rounded to the thousands place
Answer:
4.45
Step-by-step explanation
Answer:
Step-by-step explanation:
445
First, we move the decimal 2 spaces which give us 4.45
4.45 rounded is 4.45 so that is our answer
What is the shape of the graph of the function?
h(x) =2.05*3^x
Answer: A
Step-by-step explanation:
help, Find the circumference of the circle. Round your answer to the nearest hundredth.
Answer:
18.85
Step-by-step explanation:
2 x π x 3
18.8496
Rounded to nearest hundredth: 18.85
Mr. Sam took 1 h 15 minute drive from his home to his office.if the distance between his home and office was 50 miles, at what average speed did Mr. Sam drive?
Find the value of x in the triangle above
Answer: x = 8
Step-by-step explanation: So you have 3 sides and 3 numbers. Identify the side that has a number without a variable. (This goes for both triangles) Then you divide the 1st number by the 2nd. In this case it would be 20 or side "B" divided by 5 or side "E", which equals 4. You then take 4 and multiply it by 4 or side "D" (Because it's the only other side that does not have a variable) and you take your answer (16) and 2x or side "A", and make an equation. The equation would be : 2 * x = 16. Now solve the equation. Your answer is : x = 8.
What is the measure of angle A?
(3y + 27)
What is the measure of angle B?
(5y - 3)º
Answer:
72
108
Why?
It came back as correct
Jace gathered the data in the table. He found the approximate line of best fit to be y = –0.7x + 2.36.
A 2-column table with 5 rows. The first column is labeled x with entries 0, 1, 4, 5, 7. The second column is labeled y with entries 3, 1, 0, negative 2, negative 2.
What is the residual value when x = 5?
Answer:
B on ed!!!!
Step-by-step explanation:
(-0.86)
The residual value when x = 5 is -0.86.
What is meant by Residual Value?Residual value is defined as the difference of the value that we predicts with that of the observed value.
It is given that,
Line of best fit is,
y = –0.7x + 2.36
Predicted value at x = 5 is,
y = -0.7 × 5 + 2.36 = -1.14
Observed value at x = 5 is y = -2
Residual value = Observed value - Predicted value
= -2 - -1.14
= -0.86
Hence the residual value is -0.86.
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Which is a way to find the area of this rectangle?
4+3
6
Answer:
Height x Width (length x breadth)
Step-by-step explanation:
4X3=12
Abdul returned home from school on the school bus. The bus traveled 9 km north
and then 12 km west. How far is Abdul's house from the school? Round to the
nearest whole number. (PLEASE SHOW WORK)
Answer:
15 km
Step-by-step explanation:
The formula to find the hypotenuse of a right triangle
Is the square root of [tex]a^{2} +b^{2}[/tex]
a and b represent the side lengths so just plug in the side lengths for a and b
it doesn't matter which side you make a or b
square a and b
square root of 144+81
add them
[tex]\sqrt{225}[/tex]
solve
15
add your units and you're done
15 km
Find the area of the regular polygon with the given apothem a and side length s.
octagon, a=66.4 in, S =55 in
Answer:
Area is 14608in²
Step-by-step explanation:
this problem is based on mensuration of flat shapes, polygon
Octagon number of sides n= 8
The expression for the area of polygon given apothem and side
Is
Area= (n*s*a)/2
Given n= 8
s= 55in
a= 66.4in
Substituting our given data we have
Area = (8*55*66.4)/2
Area = 29216/2
Area = 14608in²
The area of the regular octagon is [tex]\( 14608 \)[/tex] square inches.
The area of a regular polygon can be calculated using the formula:
[tex]\[ A = \frac{1}{2} \times a \times p \][/tex]
where [tex]\( A \)[/tex] is the area, [tex]\( a \)[/tex] is the apothem, and [tex]\( p \)[/tex] is the perimeter of the polygon.
For a regular octagon, the perimeter [tex]\( p \)[/tex] is given by:
[tex]\[ p = n \times s \][/tex]
where [tex]\( n \)[/tex] is the number of sides and [tex]\( s \)[/tex] is the length of one side. Since an octagon has 8 sides:
[tex]\[ p = 8 \times s \][/tex]
Given that [tex]\( s = 55 \)[/tex] in, we can calculate the perimeter:
[tex]\[ p = 8 \times 55 \text{ in} = 440 \text{ in} \][/tex]
Now, we can calculate the area of the regular octagon with the given apothem [tex]\( a = 66.4 \)[/tex] in and side length [tex]\( s = 55 \)[/tex] in:
[tex]\[ A = \frac{1}{2} \times a \times p \][/tex]
[tex]\[ A = \frac{1}{2} \times 66.4 \text{ in} \times 440 \text{ in} \][/tex]
[tex]\[ A = 33.2 \text{ in} \times 440 \text{ in} \][/tex]
[tex]\[ A = 14608 \text{ in}^2 \][/tex]
What is one way to summarize all of the values of a data set with a single number?
Thank you
Answer:
A measure of central tendency
Step-by-step explanation:
A measure of central tendency summarizes all of the values in a data set with one number.
A measure of central tendency describes how the values in a data set vary with a single number.
the three main measure of central tendency are the mean, median, and mode, all this three are single values attributed to values of a distribution.
The mean is the average value of a distribution
while the median is the middle value of a distribution and
the mode is the most occurrence value among the distribution.
SOMEONE PLEASE HELPP!!
Answer:
Only the x-value changes.
Step-by-step explanation:
When a point is reflected over the y-axis, it is the x-axis number that will flip it's sign.
When a point is reflected over the x-axis, it is the y-axis number that will flip it's sign.
~
Find the circumference of a circle of 1 1/2 inches.
Answer:
The circumference of a circle with radius length of 1 1/2 units is:
6.2832 units.
Step-by-step explanation:
Answer:
[tex]9.42[/tex]
Step-by-step explanation:
I used the equation [tex]C=2[/tex]π[tex]r[/tex]. I hope I could help you :))
A right circular cylinder has a base radius of 6 centimeters and a height of 12 centimeters. What is the volume of this cylinder? A. 432cm B.450cm C.275cm D.360cm
Answer:
The volume of the cylinder is 432π
Step-by-step explanation:
Volume of a Cylinder is, πr²h where r = radius and h = height of the cylinder.
so, πr²h = π×6²×12 = 432π
Answered by GAUTHMATH
Answer:
A) 432
Step-by-step explanation:
prove that 7 + 3 root 2 is not a rational number
Answer:
Step-by-step explanation:
let 7 + 3√2 be an rational number where
7+3√2 = a/b [ a and b are coprime and b is not equal to zero]
3√2= a/b-7
3√2 =( a-7b) /b
√2 = (a-7b) /3b .....(i)
Now ,from equation (i) ,we get that √2 is rational but we know that √2 is irrational. so actually 7 + 3√2 is irrational not rational. thus our assumption is wrong. The number is irrational.
Answer:
Prove by contradiction.
See below.
Step-by-step explanation:
Assume it is rational, then:
Let x = 7 + 3√2 = p/q where p and q are integers and p/q is in simplest form.
x^2 = 49 + 42√2 + 18 = p^2/q^2
67q^2 = p^2 - 42√2q^2
67q^2 - p^2 = -42√2 q^2
67q^2 - p^2 is rational and q^2 is rational so that makes -42√2 rational.
but we know that -42√2 is irrational, so our original assumption is not true.
Which statement is true?
The solution is x = 3.
The solutions are x = -2 and x = 3.
There are no solutions.
There are infinite solutions.
DONE
Answer:
its c
Step-by-step explanation:
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Use the graph to estimate the solution of the system. x + 2y = 5, –x + 3y = 6 Which integers is the x-value between? What is the x-value to the nearest tenth? Which integers is the y-value between? What is the y-value to the nearest tenth?
Answer:
look at this and there’s ur answer
Step-by-step explanation:
The solution of the given system of equations using the graph is (0.6,2.2) so x is between 0 and 1 and y is between 2 and 3.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
As per the given system of equations,
x + 2y = 5, –x + 3y = 6
Both systems of the equation have been plotted below.
The intersection point will be a solution as (0.6,2.2).
0 < 0.6 < 1 and 0.6 can be rounded to the nearest tenth as 0.6.
2 < 2.2 < 3 and 2.2 can be rounded to the nearest tenth as 2.2.
Hence "The solution of the given system of equations using the graph is (0.6,2.2) so x is between 0 and 1 and y is between 2 and 3".
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