At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on 4.25 yards of silk and cotton fabrics for a dress. Silk is $16.90 per yard and cotton is $4 per yard.
Let 'x' represent the number of yards of silk and 'y' represent the number of yards of cotton.
Here is a system of equations that represent the constraints in the situation.
x+y=4.25
16.90x+4y=36.35
Find the solution to the system of equations. You may use any method you want, but you must explain your reasoning and methods fully.
Answer:
Step-by-step explanation:
The yards of silk bought is 1.49 yards and the yard of cotton bought is 2.76 yards.
The two equations are known as simultaneous equation. They would be solved using elimination method.
x + y = 4.25 equation 1
16.90x + 4y = 36.25 equation 2
where:
x = yards of silk bought
y = yards of cotton bought
In order to determine the value of x, multiply equation 1 by 4.
4x + 4y = 17 equation 3
Subtract equation 3 from 2
19.25 = 12.90x
Divide both sides of the equation by 12.90
x = 1.49 yards
In order to determine the value of y, substitute for x in equation 1
1.49 + y = 4.25
y = 4.25 - 1.49
y = 2.76 yards
Answer:
Step-by-step explanation:
The yards of silk bought is 1.49 yards and the yard of cotton bought is 2.76 yards.
The two equations are known as simultaneous equation. They would be solved using elimination method.
x + y = 4.25 equation 1
16.90x + 4y = 36.25 equation 2
where:
x = yards of silk bought
y = yards of cotton bought
In order to determine the value of x, multiply equation 1 by 4.
4x + 4y = 17 equation 3
Subtract equation 3 from 2
19.25 = 12.90x
Divide both sides of the equation by 12.90
x = 1.49 yards
Please help me I keep getting the last row wrong.
Answer:
B = 48°
b = 29.7
c = 39.1
Step-by-step explanation:
You have made a Mistake which is C = 102° Not 120°
So, Lets begin with the Problem
Since the Sum of Interior Angles of the Triangle = 180 °
Then A+B+C=180
Then 30+B+102=180
Then B+132=180
Subtract 132 from Both sides
B = 180 - 132 = 48°
Applying Law of Sines
[tex]\frac{a}{sinA} =\frac{b}{sinB}=\frac{c}{sinC}[/tex]
by substituting
[tex]\frac{20}{sin30} =\frac{b}{sin48}=\frac{c}{sin102}[/tex]
Then [tex]b=\frac{20sin48}{sin30} =29.7[/tex]
Then [tex]c=\frac{20sin102}{sin30} =39.1[/tex]
Juan is clearing land in the shape of a circle to plant a new tree. The diameter of the space he needs to clear is 52 inches. By midday, he has cleared a sector of the land cut off by a central angle of 140 . What is the arc length and the area of land he has cleared by midday?
The central angle of 140 degrees illustrates the degree measure of the arc
The arc length cleared is 63.54 inches and the area of the land cleared is 826.00 square inches
How to determine the arc lengthThe given parameters are:
Central angle = 140 degrees
Diameter = 52 inches
The length of the arc is then calculated s:
[tex]L = \frac{\theta}{360} * \pi d[/tex]
Substitute known values in the equation
[tex]L = \frac{140}{360} * 3.142 * 52[/tex]
Evaluate the products
[tex]L = \frac{22873.76}{360}[/tex]
Evaluate the quotient
[tex]L = 63.54[/tex]
Hence, the arc length cleared is 63.54 inches
How to determine the area of the land clearedThe area is calculated s:
[tex]A = \frac{\theta}{360} * \pi (d/2)^2[/tex]
Substitute known values in the equation
[tex]A = \frac{140}{360} * 3.142 * (52/2)^2[/tex]
Evaluate the products
[tex]A = \frac{297358.88}{360}[/tex]
Evaluate the quotient
[tex]A = 826.00[/tex]
Hence, the area of the land cleared is 826.00 square inches
Read more about arc lengths at:
https://brainly.com/question/2005046
Answer:
64 and 826
Step-by-step explanation:
The land Juan has cleared by midday has an arc length of about 64 inches and an area of about 826 square inches.
someone help me please
Rectangle ABCD is rotated by 90 degrees
clockwise about the origin and then translated
2 units left and 3 units down to form A'B'C'D'.
What is the length, in units, of line segment A'B'
if AB was 4 units?
Rotation involves moving the rectangle ABCD around a fixed point
The length of side A'B' is 4 units, if AB was 4 units
How to determine the length of A'B'From the question, we have the following transformations
RotationTranslationBoth transformations are rigid transformations, and they do not change the length of the shape
Hence, the length of side A'B' is 4 units, if AB was 4 units
Read more about transformation at:
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A large box of biscuit mix costs $6.48. The box contains 72 servings of biscuit mix. One serving is equal to ¼ cup of biscuit mix. This table shows the amount of mix and water needed to make different numbers of biscuits.
Part A
What is the total number of cups of biscuit mix in one box? Show your work or explain your answer.
Part B
What is the total number of biscuits that can be made using one box of the biscuit mix? Show your work or explain your answer.
Part C
What is the cost, in dollars and/or cents, per biscuit? Show your work or explain your answer.
A large box of biscuit mix costs $6.48. The box contains 72 servings of biscuit mix. One serving is equal to ¼ cup of biscuit mix. This table shows the amount of mix and water needed to make different numbers of biscuits.
Answer:
Part A: 18 cups
Part B: 56 biscuits
Part C: $0.16
Step-by-step explanation:
Part A
72 * 1/4 = 18
Part B
18 total cups/ 2 cups/biscuit = 9 cups able to be used (dk how else to explain it)
6 * 9 = 56 biscuits
Part C
$6.48/56 = $0.16
If 1 serving of stir fry uses 3/5 cup of rice , how many cups are in 12 servings
Answer:
36/5 cups of rice.
Step-by-step explanation:
12x3/5 is the equation. 36/5 is the answer, which is 7 1/5 or 36/5
what is [7a-21a+10b]*[2a+5b]
Answer:
-28a2 - 50ab + 50b2
Step-by-step explanation:
[7a-21a+10b]*[2a+5b]
[-14 + 10b]*[2a+5b]
Hope it helps!!!!!!!!!brainliest pls!!!!!!!!!Help plssss geometry!!
Answer:
x=4
Step-by-step explanation:
both angles add up to 90* because it is a right angle
10x + 12x + 2 = 90
22x + 2 = 90
subtract 2 from both sides of the equation
22x = 88
divide both sides by 22
x = 4
HELP MEEEEE IM DESPERATE 30 POINTS!!!!!!
find x
Answer:
D
Step-by-step explanation:
the measure of a secant- tangent angle is half the difference of the intercepted arcs, then
[tex]\frac{1}{2}[/tex] (154 - (12x + 2) ) = 6x + 4 ( multiply both sides by 2 to clear the fraction )
154 - 12x - 2 = 12x + 8 , that is
152 - 12x = 12x + 8 ( subtract 12x from both sides )
152 - 24x = 8 ( subtract 152 from both sides )
- 24x = - 144 ( divide both sides by - 24 )
x = 6
What is 80% of 150? Please help
14. Danny works part-time at Tom's Toy Store. He
worked 84 hours in May and June. Danny worked
one-third as many hours in May as in June.
How many hours did he work in each month?
Answer:
21 hours in May, 63 hours in JuneStep-by-step explanation:
Set up equationsm - May, j - Junem + j = 84m = 1/3jSolve by substitution, fin the value of j1/3j + j = 844/3j = 84j = 84*3/4j = 63Find mm + 63 = 84m = 84 - 63m = 21May be y and June be x
x+y=84y=1/3xNow
Put y from (2) in eq(1)
x+1/3x=843x+x)3=844x/3=844x=3(84)x=3(21)x=63Find y
y=1/3(63)y=21find the equation of the line that passes through the point (3,5) and is parallel to the equation of the line y=2×-5
Answer:
y=2x-1
Step-by-step explanation:
Since it is parallel to y=2x-5, they have the same slope of 2.
Now you're going to plug the point and slope into the following equation: y-(y value of point) = slope ×(x-(x value of point))
y-5= 2 (x-3)
Now you simplify:
y-5=2x -6
y=2x-1
The distance between AB is 24 units, Endpoint A is (-5.8) and B(1,y) is A?
Determine the y coordinates of B.
Answer:
y=2.89
explanation
square root of 24=square root of (6)^2+(y-8)^2
4.89=6+y-8
4.89-2=y
2.89=y
Can someone help me solve this Function Notation.
Answer:
1
Step-by-step explanation:
What ever is in the parenthesis needs to be substituted into the equation
So,
3(-2) + 7 =
-6 + 7
1
f(-2) = 1
Answer:
f(-2) = 1
Step-by-step explanation:
1. Replace x with -2
f(-2) = 3(-2) + 7
2. Multiply 3 by -2
f(-2) = -6 +7
3. Add -6 and 7
-6 + 7 = 1
f(-2) = 1
Find g(x), where g(x) is the translation 17 units right and 15 units down of f(x)=
–
3(x+8)2–6.
Answer:
Step-by-step explanation:
Square B is a dilation of square A. What is the scale factor?
Answer:
54:45
6:5
this is the scale factor
PLS HELP FAST
A plane in which the coordinates of a point are its distances from two intersecting perpendicular lines called axes.
Which term is defined in the above statement?
Question 6 options:
Air Plane
Coordinate Plane
Quadrant
Ordered Pair
Answer:
Coordinate plain
Step-by-step explanation:
airplane... i think you know what that is, and quadrant is the squares sectored off by a coordinate plane.
Classify each pair of numbered angles.
Drag and drop the descriptions into the boxes to correctly classify each pair of numbered angles. Each description may be used more than once.
Answer:
1 and 2 are vertical
3 and 4 adjacent
ANYONE GOOD AT MATH!!!! HELP WITH 3 QUESTIONS
Answer: a) I believe it is 2 out of 8
b) 6 out of 8
c) 50/50 chance
d) 3 out of 8
Not 100% sure so please double-check.
Step-by-step explanation:
The pinwheel has a total of 8 places. There are only 2 purple squares, there are 4 evens and 4 odds, and there are 3 numbers less than 4, (1,2,3).
HELP WILL GIVE BRAINLEST QUICKKK SP and SR are tangent to circle Q. If SP = 10x - 18 and SR = 2x + 6, find x.
A. 2
B. -1
C. 3
D. -3
Answer:
C.3
Step-by-step explanation:
SP and SR are tangent to circle Q.
-> SP = SR
-> 10x - 18 = 2x + 6
-> 10x - 2x = 18 + 6
-> 8x = 24
-> x = 24/8
-> x = 3
Answer:
C. 3
Step-by-step explanation:
125 g of yoghurt provides 4.5 g of protein. How many grams of protein does 100 g of yoghurt provide
Answer:
3.6g
Step-by-step explanation:
the protein thats in 125g of yoghurt is 4.5g
the protein thats in 1g of yoghurt is 4.5/125
the protein thats in 100g of yoghurt is
4.5/125 x 100
0.036 x 100
3.6g
I need to find the answer for 21.60÷1.35
Answer: 16
Step-by-step explanation: 21.60 / 1.35 = 16
The result of the division 21.60÷1.35 is: 16.
To find the answer for 21.60 ÷ 1.35, you can perform the division operation:
21.60 ÷ 1.35
Divide 21.60 by 1.35:
21.60 ÷ 1.35 ≈ 16
The result of 21.60 ÷ 1.35 is approximately 16.
When dividing decimals, it's essential to align the decimal points and then perform the division as you would with whole numbers.
In this case, dividing 21.60 by 1.35 gives us an approximate quotient of 16.
Hence, The result of the division 21.60÷1.35 is: 16.
To learn more on division click:
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#SPJ6
In an extensive government study conducted this year a simple random sample of 500 households was obtained and 80 had experienced property damage due to a crime. Calculate and interpret a 95% confidence interval for the true proportion of households that have experienced property damage due to crime
Using the z-distribution, the 95% confidence interval is (0.1279, 0.1921), and it means that we are 95% sure that the proportion for the entire population is between these two values.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem:
A sample of 500 households was obtained and 80 had experienced property damage due to a crime, hence [tex]n = 500, \pi = \frac{80}{500} = 0.16[/tex].95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].Hence:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.16 - 1.96\sqrt{\frac{0.16(0.84)}{500}} = 0.1279[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.16 + 1.96\sqrt{\frac{0.16(0.84)}{500}} = 0.1921[/tex]
The 95% confidence interval for the true proportion of households that have experienced property damage due to crime is (0.1279, 0.1921), and it means that we are 95% sure that the proportion for the entire population is between these two values.
More can be learned about the z-distribution at https://brainly.com/question/25890103
Greatest common factor of 42,60
3 A scientist takes four random samples of a population of 700 trees. Each sample is
the same size. The first sample indicates that 30% of the trees are oak, while the
second sample indicates that only 15% of the trees are oak. The third sample
indicates that 26% of the trees are oak. The fourth sample indicates that 29% of
the trees are oak. Based on the data, about how many of the 700 trees are oak?
Using proportions, it is found that about 175 trees are oak.
What is a proportion?A proportion is a fraction of a total amount.
For the four samples, the proportions are: {0.3, 0.15, 0.26, 0.29}.
Hence, the mean proportion is given by:
M = (0.3 + 0.15 + 0.26 + 0.29)/4 = 0.25
Out of 700 trees:
700 x 0.25 = 175.
About 175 trees are oak.
More can be learned about proportions at https://brainly.com/question/24372153
Round 83,461 to the nearest thousand.
Answer:
See below.
Step-by-step explanation:
83,461
/\
This is the thousand place.
5 and above is rounded up, 4 and below is rounded down.
83,000 is the answer.
-hope it helps
Help me solve this please
Answer:
x=-3 im pretty sure
Step-by-step explanation:
so if y=4 and 4 is something plus 7, 7+-3=4 so im abut 98% its -3
7 added to the product of 14 and f
I need help please I’ll give u a brainliest
Answer:
k=4
Step-by-step explanation:
Hope this helps!