The price of 1 yard of blue fabric and 1 yard of green fabric is obtained by solving the system of linear equations and it is $8
Let
x = price of blue fabric per yard
y = price of green fabric per yard
"The blue fabric costs $2 more per yard than the green fabric" means:
x = y + 2 (Equation 1)
" LaTanya buys 6 yards of blue fabric and 9 yards of green fabric and pays $57" means:
6x + 9y = 57 (Equation 2)
Substitute equation 1 into equation 2:
6x + 9y = 57
6 (y + 2) + 9y = 57
6y + 12 + 9y = 57
15 y = 45
y = 3
Substitute y = 3 into equation 1
x = 3 + 2 = 5
Hence, the price of blue fabric is $5 per yard while the green fabric is $3 per yard.
The price of 1 yard of blue fabric and 1 yard of green fabric = x + y = 3 + 5 = $8
Complete question:
LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and 1 yard of green fabric?
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10. Dan paid 20% down on 8 new car that cost
$16,584.00. He will pay the balance in
24 equal monthly installments.
He will pay S Drop-cown each month.
A. 1,105.60
B. 667.18
C. 552.80
D. 132.20
Answer:
552.8
Step-by-step explanation:
16584/8=2073
2073*0.8=1658.4
1658.4*8=13267.2
13267.2/24=552.8
Helpppppppppppppppppppppppp
the actual amount is 78000 dollar
Step-by-step explanation:
one pack cigarettes cost 25 dollar
3 pack cigarettes costs 75 dollar
20 years × 52 =1040
1040 weeks
1040 × 75 dollar
78000 dollar
Write an equation in point-slope form of the line that passes through the given point and with the given slope m. A. (1, -8) m= -9
The point-slope form of a line is:
y = mx + b
where m is the slope and b is the y-intercept
Replacing with point (1, -8) and m= -9, we get:
-8 = (-9)(1) + b
-8 = -9 + b
-8 + 9 = b
1 = b
Then, the equation is:
y = -9x + 1
A pile of sand has a weight of 65 kg.
Some of the sand is put into a small sack.
The rest of the sand is put into a large sack.
The sand in the large sack weighs 15 kg more than the sand in the small sack.
What is the weight of the sand in the small sack?
Answer:
25kg
Step-by-step explanation:
65=x+x+15
65-15=2x
50=2x
25=x
URGENTTTY PLS PLS HELP !! GRAPH TOO PLS !!
A store sells 5 T-shirts for $48.60. What is the unit cost per T-shirt? A. $9.72 B. $8.10 C. $43.60 D. $0.10
Answer:$9.72
Step-by-step explanation: 48.60 DIVIDED BY 5 EQUALS 9.72
GIVE ME BRAINLEST PLSS
You need a 30% alcohol solution. On hand, you have a 75 mL of a 10% alcohol mixture. You also have 55% alcohol mixture. How much of the 55% mixture will you need to add to obtain the desired solution?
60 ml of the 55% solution is required to get the desired solution.
A unique kind of homogenous mixture made up of two or more substances is called a solution.
A solute is a substance that has been dissolved in a solvent, which is the other substance in the mixture. Polarity effects of chemicals are engaged in the mixing of a solution at a scale that leads to interactions that are very specific to solvation. When the solvent makes up a significant large portion of the combination, as is frequently the case, the solution typically or normally has the condition of the solvent. The concentration of a solution, which measures how much solute is present in a given volume of solution or solvent, is one crucial parameter.Let x ml of 55% solution is taken.
therefore alcohol = 0.55x ml
water = 0.45x ml
Now it is added to 10% 75 ml solution.
Alcohol = 10% of 75 = 7.5ml
Water = 67.5 ml
New mixture = 75 + x
Alcohol = 30% of (75+x) = 22.5 + 0.3x
Therefore 22.5 + 0.3x = 7.5 + 0.55x
or, x = 60 ml
Therefore 60 ml of the 55% solution is required.
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Which ordered pair would form a proportional relationship with the point graphed below?
-60-40-20 20 40 60 80 ×
x
*
O (-10, 30)
O (30, -15)
O (-30, 10)
10.0
40
30
20
10
20
30-
40-
(60,-20)
Answer: (-30, 10)
Step-by-step explanation:
A proportional relationship is of the form y=kx for some constant k.
From the point (60, -20), we know that k = -1/3.
So, we are looking for a point where the y coordinate is -1/3 of the x coordinate. This is satisfied by option 3.
scores on an iq test are normally distributed. the test is designed so that the mean is 100 and standard deviation is 15. (a) what percentage of the population has an iq above 120?
From the normal distribution it is calculated that 9.18% of people has an iq over 120.
Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued regressors with unknown distributions.
Some of their significance can be attributed to the central limit theory. This claim states that, in some cases, the average of many samples (observations) of a stochastic process with limited mean and variance constitutes itself as a random variable, whose distribution merges to a normal distribution as the number of samples increases.Because of this, the distributions of physical values, such as error margins, which are expected to be the sum of many independent events, are frequently near to normal.We have to find P( X > 120 )
Thus find z score for x =120
[tex]z=\frac{x-\mu}{\sigma}=\frac{120-100}{15}=\frac{20}{15}=1.33[/tex]
Thus we get:
P(X>120) = P(Z>1.33)
P(X>120) = 1 - P(Z<1.33)
P( Z < 2.67) = 0.9082
Thus
P(X>140) = 1 - P(Z<2.67)
P(X>140) = 1 - 0.9082
P(X>140) = 0.0918
Percentage = 9.18%
Therefore 9.18% of people has an iq over 120.
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Help me with this i need to submit this assignment tyy
i think its ez but yk.. im lazy
Answer:
3x3x3x3=81
.......................
what are the steps of simplifying the fraction 1244/2000 to its lowest term?
can you help with these two questions please
MATH PLEASE DO THIS FOR BRAINLYIST
Answer: The percent of change in the perimeter is 100 percent and
the percent of change in the area is 300 percent .
Step-by-step explanation:
Rectangle is the closed shaped polygon with 4 sides. Opposite sides of the rectangle are equal. when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.
Find x of the triangle
Answer: The answer is 20°
Step-by-step explanation:
I think it’s 20° but I’m only in the 6th grade and I got my 180 ruler for this into the screen
I NEED HELP!!!
50 POINTS!!!
slope is 3;
rise/run = y/x
6/2 = 3/1
Consider the line y = - - X+4.4.***4.Find the equation of the line that is perpendicular to this line and passes through the point (-9, 6).Find the equation of the line that is parallel to this line and passes through the point (-9, 6).Note that the ALEKS graphing calculator may be helpful in checking your answer.Equation of perpendicular line: 0-Equation of parallel line:X0P
ANSWER:
[tex]\begin{gathered} \text{perpendicular} \\ y=\frac{4}{3}x+18 \\ \text{parallel} \\ y=-\frac{3}{4}x-\frac{3}{4} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation of a line in its slope and y-intercept form is the following:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}[/tex]Now, when two equations are perpendicular, the slope of both are opposite, that is, the product between them is equal to -1, like this:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{3}{4}\cdot m_2=-1 \\ m_2=\frac{4}{3} \end{gathered}[/tex]We replace the values of the point (-9, 6) and the slope to calculate the value of the y -intercept:
[tex]\begin{gathered} 6=-9\cdot\frac{4}{3}+b \\ b=12+6 \\ b=18 \end{gathered}[/tex]Therefore, the perpendicular equation that also passes through the point (-9,6) is:
[tex]y=\frac{4}{3}x+18[/tex]Now, when two lines are parallel, the slope is the same, therefore we calculate directly that it passes through the point (-9, 6)
[tex]\begin{gathered} 6=-9\cdot-\frac{3}{4}+b_{} \\ b=6+9\cdot-\frac{3}{4} \\ b=-\frac{3}{4} \end{gathered}[/tex]therefore, the equation of the line that is parallel to this line and passes through the point (-9, 6) is:
[tex]y=-\frac{3}{4}x-\frac{3}{4}[/tex]<
Find the time-and-a-half pay rate by multiplying the hourly wage, $22 by
by 1-1/2
When the hourly wage is $22, the time-and-a-half pay rate is $
(Simplify your answer.)
consequently, the time and a half rate will be 33 dollars per hour according to the query.
What is the logic behind time and a half pay rate and how tocalculate it?A higher rate of pay known as "time and a half" is normally only applied to hours that are over 40 in a workweek or that are worked extra.
Companies have different overtime pay practices, with time and a half as a typical rate.
Simply said, it means that for each hour performed within the time and a half window, the employee will receive payment in addition to their regular hourly rate of one half of that amount.
Time and a Half Rate = Hourly Rate * 1.5
According to the given question:
Time and a half rate =22$*1-1/2
=22$*1.5
=33$ per hour
Therefore, According to the question given the Time and a pay half rate will
be 33$ per hour.
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Help Please!!
Unit 4 lesson 11 geometry Parallel and Perpendicular Lines Unit Test
I have been doing well in this test till this question... any help is appreciated!!
The values of x = 14 and y = 12
In the diagram given, there are two parallel lines and three angles formed by cutting the parallel lines.
So here, angles (2x+7)° and (3x-7)° are corresponding angles.
That is they occupy relatively same position, that is both are above each parallel line.
So they are equal angles.
i.e., 2x+7 = 3x-7
⇒ 3x-2x = 7 +7
⇒ x = 14
Now the angles 2x+7° and 12y+1° are supplementary angles.
Supplementary angles are formed on a straight line between a line cutting the straight line.
That is their sum = 180°
i.e., 2x+7° + 12y+1° = 180
⇒ 2 x 14 + 7 + 12y +1 = 180
⇒ 28 + 8 +12y = 180
⇒ 36 +12y = 180
⇒ 12y = 180 -36
⇒ 12y = 144
⇒ y = 12
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Ethan and Adrian are reading the same book. At the beginning of the month, Ethan was on page 18 and Adrian was on page 45. Ethan will read 12 pages per day and Adrian will read 9 pages per day. Let E represent the page of the book that Ethan is on at the end of t days into the month, and let A represent the page of the book that Adrian is on at the end of t days into the month. Write an equation for each situation, in terms of t, and determine whether Ethan or Adrian is farther along in the book after 4 days.
The equations are e = 18+12t and a = 45+9t
Adrian will be father along in the book after 4 days. She will be 15 pages ahead of Ethan
Ethan's page number at the beginning of the month = 18
Adrian's page number at the beginning of the month = 45
Pages read by Ethan each day = 12 pages
Pages read by Adrian each day = 9 pages
Let e represent the page of the book that Ethan is on at the end of t days into the month. Let a represent the page of the book that Adrian is on at the end of t days into the month.
Formulating the equation we get the following:
e = 18 + 12t
a = 45 + 9t
Finding the page number of both Ethan and Adrian after 4 days by substituting the values in the equations we get:
e = 18+12(4)
e = 66
a = 45 + 9(4)
a = 81
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Find the value of c that makes t^2 - 22t+ c a perfect square trinomial.
Write the expression as the square of a binomial.
The expression is
The expression is a perfect square trinomial if and only if c = 121.
How to get the value of c?
A perfect square trinomial is written as:
(a + b)^2 = a^2 + b^2 + 2ab
In this case, we have:
t^2 - 22t + c
We can rewrite this as:
t^2 - 2*11*t + c
Then we have:
a = t
b = -11
And we will have that:
c = b^2 = (-11)^2 = 121
Then we have:
t^2 - 2*11*t + 121
Which is a perfect square trinomial:
(t - 11)^2 = t^2 - 22t + 121
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1) Apples cost $16 for an 8 pound bag at the local price
club, but the club has a membership fee of $50.
Write and solve an equation to determine how many
pounds (p) of apples you can buy for $58.
Answer:
4 pounds with a membership
29 pounds without
i just added both because i didnt know if you meant 58 extra dollars after bbuying membership or not
Step-by-step explanation:
58 -50(membership fee)=8
16 divide by 8=2
16$=8 pounds
8$=4 pounds
---------------------------------------
without membership you could buy 29 pounds of apples
58 divide by 16=3.625
3.625 x 8=29
What is the value of −5 + (−14) + 53?
Answer:
34
Step-by-step explanation:
The value would be 34
Help me please!! due at 8pm tonight 10/12/22
Answer:
y=3x+3
Step-by-step explanation:
Use rise/run
Answer:
y=-9x+5
Step-by-step explanation:
Homework #5
Question 9 of 12
AMORTIZATION Car loans are often spread into multiple regular payments over time. This process is called amortization. Each payment
reduces the remaining principal, and the interest accrued for the next payment is based on the reduced principal. The monthly payment is
fixed; so, with each subsequent payment, an increasing portion goes toward principal, and a decreasing portion goes toward interest. Lori
takes out a car loan of $15,000 for 3 years, with a 3% interest rate. When the loan is amortized into monthly payments, the total interest paid by
the end of the loan term will be $704.
Calculate the simple interest Lori would pay if the loan was not amortized and the entire loan was paid at the end of 3 years.
$15
The simple interest Lori would pay if the loan was not amortized and the entire loan was paid at the end of 3 years is $ 1,350.
It is given in the question that:-
Principal = $15,000
Time period = 3 years
Interest rate = 3 %
Total interest paid by Lori, if the loan was amortized = $ 704.
We have to find the simple interest Lori would pay if the loan was not amortized and the entire loan was paid at the end of 3 years.
We know that,
Simple interest = (Principal*Rate*Time)/100
Hence,
Simple interest = (15000*3*3)/100 = $ 1350.
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44+400 divided by (4+62)-24
Answer:
10.57
Step-by-step explanation:
44+400=444
(4+62)-24=
66-24=42
444/42=10.57
this graph shows the height of a tree over a 5 year growing peroid calculate the rate of change of height per year
Need explanation on how to solve ASAP
Answer: It jupes by 2 each year the rate is 2 to 1 year
Step-by-step explanation:
In zero years it alretey 1m so we can go to 1 where its 3 it juped by two more
An angle measures 58° more than the measure of its supplementary angle. What is the measure of each angle?
Answer: 61° and 119°
Step-by-step explanation:
So for the smaller angle you have to do:
1. 180-58=122
2. 122/2=61
Then you just add 61+58=119 for the larger angle
If Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10}
When Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10) Q ∩ P = { 1, 9}
How to calculate the value?Set theory simply means the branch of mathematical logic that deals with sets, that can be described as collections of objects.
It should be noted that perfect squares are the numbers that can be divided to give same number.
Q = {all perfect squares less than 30}. This will be 1, 4, 9, 16, 25
P ={ all odd numbers from 1 to 10}. This will be 1, 3, 5, 7, and 9.
In this case, the common numbers to set of P and Q are 1 and 9.
Therefore, the numbers are 1 and 9 since they're common to both sides.
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If Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10}. Find Q ∩ P.
The quadratic equation [tex]( k - 1 )x^{2} + 2x + ( 2k - 3 ) = 0[/tex] , where k is R, has real distinct roots.
Find the range of possible values for k.
The possible values of k such that the quadratic equation has real distinct roots are 1 / 2 and 2.
What are the possible values of k associated to quadratic equation?
In this problem we find the case of a quadratic equation, of which the values of a variable k must be found such that the polynomial have real distinct roots. This can be done by using the discriminant of the quadratic formula, which is defined below:
For a · x² + b · x + c = 0, the discriminant is:
b² - 4 · a · c > 0
Then, if we know that a = k - 1, b = 2 and c = 2 · k - 3, then the possible values of k are:
2² - 4 · (k - 1) · (2 · k - 3) > 0
4 - (4 · k - 4) · (2 · k - 3) > 0
4 - (8 · k² - 8 · k - 12 · k + 12) > 0
8 · k² - 20 · k + 8 > 0
Whose form form is shown below:
8 · (k² - (20 / 8) · k + 1) = 0
8 · (k² - (5 / 2) · k + 1) = 0
8 · (k - 2) · (k - 1 / 2) = 0
The possible values of k are 1 / 2 and 2.
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In Montyville, the value of homes has experienced an annual change of -2 percent. If the rate continues, what will be
the change over 10 years?
Answer:
I believe the answer would be -20 percent