Answer:
Step-by-step explanation:
x = small barrettes
y = large barrettes
13x + 11y = 142.......multiply by -1
13x + 12y = 149
-----------------------
-13x - 11y = -142 (result of multiplying by -1)
13x + 12y = 149
------------------------add
y = 7..........large barrettes used 7 yards
13x + 11y = 142
13x + 11(7) = 142
13x + 77 = 142
13x = 142 - 77
13x = 65
x = 65/13
x = 5........small barrettes used 5 yards
Final answer:
Kimberly uses 5 yards of ribbon for each small barrette and 7 yards of ribbon for each large barrette. The problem was solved using a system of equations and the elimination method.
Explanation:
To solve the problem using a system of equations and the elimination method, we first need to define variables for the unknown quantities we are trying to find. Let's let x represent the number of yards of ribbon used for each small barrette and y represent the number of yards of ribbon used for each large barrette.
From the information given, we can set up the following system of equations representing the two craft fairs:
For Rockport: 13x + 11y = 142
For Westminster: 13x + 12y = 149
Now, we will solve these equations using the elimination method. To eliminate one of the variables, we can subtract the first equation from the second equation.
13x + 12y - (13x + 11y) = 149 - 142This simplifies to:
y = 7
Using the value of y, we can substitute it back into either equation to find x. Plugging it into the first equation:
13x + 11(7) = 142
13x + 77 = 142
13x = 142 - 77
13x = 65
x = 65 / 13
x = 5
Therefore, Kimberly uses 5 yards of ribbon for each small barrette and 7 yards of ribbon for each large barrette.
PLEAE HELP MISSING NJMEBR
Answer:
114
Step-by-step explanation:
the answer is not geomatic but you just have to think harder not smarter. ;)
Answer:
104
Step-by-step explanation:
80 = 8 * 10
88 = 8 * 11
? = 8 * x
128 = 8 * 16
160 = 8 * 20
11 - 10 = 1
x - 11 = 2
16 - x = 3
20 - 16 = 4
x = 13
13 * 8 = 104
Can you show work to for y=4x-3?
Answer:
Is the equation that you need answered
y = 4x - 3 ?
That is not a real equation, therefore you can not answer that/show work
Answer:
Step-by-step explanation:
Not sure what they are looking for here.
you can plug in different x and get a y
x = 0 y = -3
x = -3 y = -15
x = 4 y = 13
Is your roller coaster a function? Why or why not?
A roller coaster can usually be considered a function if each time point corresponds to exactly one location of the car. However, there may be exceptions, such as during loops. The roller coaster also demonstrates conversions between potential and kinetic energy.
Explanation:In mathematical terms, a roller coaster can be described as a function if each input (in this case, time) corresponds to exactly one output (the position of the roller coaster car). For a typical roller coaster, this would be the case, as at each moment in time during the ride, the car is at one specific location.
However, there might be exceptions. For example, if the roller coaster has a loop, there's a point in time where the car reaches the top of the loop, descends, goes around the loop, and ends up at the same vertical location as before but upside down. Two different positions correspond to the same 'height' input, hence it wouldn't be considered a function in regards to height.
The physics of roller coasters also involves conversions between potential and kinetic energy. The car gains potential energy as it climbs to the top of a hill then it loses potential energy but gains kinetic energy as it descends a hill.
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Evelyn is creating a rectangular garden in her backyard. The length of the garden is 11 feet. The perimeter of the garden must be at least 56 feet and no more than 82 feet. Use a compound inequality to find the range of values for the width w of the garden.
The range of values for the width w of the garden is 17 ≤ w ≤ 30.
Step-by-step explanation:
Given,
The length of the garden = 11 feet.
The perimeter of the garden = 56 feet (at least is the minimum value)
The perimeter of the garden = 82 feet (not more than is the maximum value)
step 1 :
Perimeter of a rectangle = 2 (length + width)
⇒ 56 = 2 (11 + width)
⇒ 56 = 22 + 2 width
⇒ 34 = 2 width
⇒ width = 34/2
∴ width = 17 feet
step 2 :
Perimeter of a rectangle = 2 (length + width)
⇒ 82 = 2 (11 + width)
⇒ 82 = 22 + 2 width
⇒ 60 = 2 width
⇒ width = 60/2
∴ width = 30 feet
step 3 :
The range of values for width 'w' is 17 ≤ w ≤ 30.
Answer:
[17,30]
Step-by-step explanation:
At a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2. A) how many kids are there? B) how many men are there? C) how many ladies are there?
A) There are 16 kids.
B) There are 32 men.
C) There are 24 ladies.
Hope this helps. :)
Which expressions can be represented by the model?
Check all that apply.
10+ 4 + 10 + 4
14 x 2
18 x 2
0 24₃2
28 = 2
The expressions that can be represented by a model for the value of 28 are "10 + 4 + 10 + 4" and "14 x 2". The expression "18 x 2" equals 36 and does not represent a value of 28, and the meanings of the last two expressions ('0 24₃₂' and '28 = 2') are not clear without additional context.
To determine which expressions can be represented by a mathematical model, it's important to pay attention to the operations and numbers involved. In the list provided, there are various expressions that could potentially represent the same numerical value. For example, the expression 10 + 4 + 10 + 4 represents the sum of these numbers, which equals to 28. Similarly, 14 x 2 represents the product of 14 and 2, which also equals to 28. On the other hand, 18 x 2 equals 36, which is different from the previous two expressions.
We can look at these expressions and evaluate them:
10 + 4 + 10 + 4 = 28
14 x 2 = 28
18 x 2 = 36
Thus, from the expressions listed, only 10 + 4 + 10 + 4 and 14 x 2 can be represented by a model that reflects the value of 28. The expression 18 x 2 represents a model for the value of 36, not 28. The last two expressions, '0 24₃₂' and '28 = 2', are either typos or not clear enough to deduce a meaningful mathematical operation. If '24₃₂' indicates some form of mathematical notation or operation, it isn't standard and therefore cannot be verified without further context.
Mr. Norris is paid a 5% commission on each boat he sells. What is his commission on a boat that he sells for $125,000?
Answer:
His commission on the boat he sells is $6250.
Step-by-step explanation:
Given:
Mr. Norris is paid a 5% commission on each boat he sells.
Now, to find his commission on a boat that he sells for $125,000.
Commission = 5%.
Boat he sell for = $125,000.
Now, to get the commission on the boat he sells:
5% of $125,000.
[tex]=\frac{5}{100} \times 125000[/tex]
[tex]=0.05\times 125000[/tex]
[tex]=\$6250.[/tex]
Therefore, his commission on the boat he sells is $6250.
Final answer:
Mr. Norris's commission on a boat sold for $125,000, with a commission rate of 5%, is $6,250.
Explanation:
Mr. Norris earns a commission based on a fixed percentage of the sales price. To calculate his commission for selling a boat priced at $125,000, we apply the 5% commission rate to the sale price.
Here's the calculation:
Commission = Sale Price × Commission Rate
Commission = $125,000 × 0.05
Commission = $6,250
Hence, Mr. Norris's commission for selling a boat that he sells for $125,000 is $6,250.
The height of a parallelogram is 10ft more than its base
The area is 1200ft
Solve b and h
Answer:
The answer is b = 30 ft and h = 40 ft.
Step-by-step explanation:
Given:
The height of a parallelogram is 10ft more than its base
The area is 1200 ft².
Now, to solve for b and h.
Let the base (b) be [tex]x.[/tex]
And the height (h) is = [tex]x+10.[/tex]
Area = 1200 ft².
Now, to solve we put formula of area:
[tex]Area =b\times h[/tex]
[tex]1200=x\times (x+10)[/tex]
[tex]1200=x^2+10x[/tex]
Subtracting both sides by 1200 we get:
[tex]0=x^2+10x-1200\\x^2+10x-1200=0[/tex]
Now, solving the quadratic equation:
[tex]x^2+40x-30x-1200=0[/tex]
[tex]x(x+40)-30(x+40)=0[/tex]
[tex](x+40)(x-30)=0[/tex]
[tex]x+40=0[/tex] and [tex]x-30=0[/tex]
Subtracting Adding both sides
both sides by 30 we get:
by 40 we get:
[tex]x=-40.[/tex] [tex]x=30.[/tex]
So, we will take the positive result.
[tex]x=30.[/tex]
Thus, the base (b) = 30 ft.
Now, getting the height (h) by substituting the value of [tex]x[/tex]:
[tex]x+10\\=30+10\\=40\ ft.[/tex]
Therefore, the answer is b = 30 ft and h = 40 ft.
If f (x) = one-ninth x minus 2, what is f-1(x)
Answer:
[tex]f^{-1}[/tex](x) = 9x + 18
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )
y + 2 = [tex]\frac{1}{9}[/tex] x
Multiply through by 9 to clear the fraction
9y + 18 = x
Change y back into terms of x
[tex]f^{-1}[/tex] (x) = 9x + 18
The inverse of the function is 9y+18
What is inverse of function?An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
Given:
f f (x) = one-ninth x minus 2
f(x)= 1/9 x - 2
let f(x)=y
Now, solve for x
y = 1/9x -2
y+2 = 1/9x
9y+18 = x
Hence, the inverse of the function is 9x+18.
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marco is limited to 7 hours of screen time each week. he decides to watch a movie that is 1 hour and 20 minutes on sunday. if he divides the remainder of time equally amongst the other six days, then how many minutes can h.e watch each day? write and solve an inequality.
Marco can watch TV for at most 56 minutes each day.
Step-by-step explanation:
Given,
Time of screen each week = 7 hours
1 hour = 60 minutes
7 hours = 60*7 = 420 minutes
Length of movie = 1 hour + 20 minutes = 60 + 20 = 80 minutes
Time left for other days = 420 - 80 = 340 minutes
Number of days = 6
Let,
x be the time per day for remaining 6 days.
Number of days * Time per day ≤ Time remaining
[tex]6x\leq 340[/tex]
Dividing both sides by 6
[tex]\frac{6x}{6}\leq \frac{340}{6}\\x\leq 56.66[/tex]
Marco can watch TV for at most 56 minutes each day.
Keywords: inequality, division
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Finding the length of NM?
Because the triangles are congruent we know that NM = ST = 50.
answer: 50
The length of NM line segment for the considered situation is given by: Option D: 50 mi
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF\\[/tex]
(|AB| denotes length of line segment AB, and so on for others).
For these cases, the two triangles in the image are congruent.
So their corresponding sides must be of same measures.
The three sides of triangle RST are of measures 75, 67 and 50 miles
The two sides of triangle NLM are 67 miles and 75 miles. So obviously third one can be nothing except 50 miles so that the triangle NLM also have sides of same measure as of the triangle RST.
Thus, the length of NM line segment for the considered situation is given by: Option D: 50 mi
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how to solve −6/5x + 10= -7
Subtract 10 on both sides: -6/5x=-17
Multiply both sides by 5: -6x=-85
Divide both sides by -6: x= 14 1/6
Hope this helped!
Answer:X=6/85
Step-by-step explanation:
What are the factors of -12?
Answer:
− 12 , − 6 , − 4 , − 3, −2, −1, 1, 2, 3, 4, 6 , 12
Step-by-step explanation:
-12 * 1 = -12
-6 * 2 = -12
-4 * 3 = -12
-3 * 4 = -12
-2 * 6 = -12
-1 * 12 = -12
1 * -12 = -12
2 * -6 = -12
3 * -4 = -12
4 * -3 = -12
6 * -2 = -12
12 * -1 = -12
Apply the multiplication property of equality to write an equation equivalent to 7n=28
The value of n from the equation 7n = 28 is n = 4
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
7n = 28 be equation (1)
On simplifying the equation , we get
Divide by 7 on both sides of the equation , we get
n = 28/7
n = 4
Another equation which satisfies the relation is 4n = 16
n = 4
Therefore, the value of n is 4
Hence , the value of the equation is 4
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the radius of a circle is 1 kilometer. What is the circle’s circumference?
Answer:
[tex]2\pi[/tex]
Step-by-step explanation:
Formula of circumference is [tex]C = 2\pi r[/tex]
r = radius
plug in the numbers into formula to get
[tex]2\pi (1)[/tex] which will eqaul [tex]2\pi[/tex]
Final answer:
The circumference of a circle with a radius of 1 kilometer is approximately 6.28318 kilometers, calculated using the formula C = 2πR.
Explanation:
Given that the radius of a circle is 1 kilometer, we can calculate the circumference of the circle using the formula C = 2πR, where R is the radius of the circle and π (pi) is approximately 3.14159. Since the radius is 1 kilometer, we plug that value into the formula to get:
C = 2 × 3.14159 × 1 km
C = 6.28318 km
Therefore, the circle's circumference is approximately 6.28318 kilometers.
What is 927 divided by 9
Answer:103
Step-by-step explanation:
find the slope of the line passing through the points (-4, 6) and (3, -8)
Answer:
The slope of the line is 2.
Step-by-step explanation:
slope = y2 - y1/x2 - x1
= -8 - 6/3 - (-4)
= 14/3 + 4
= 14/7
= 2
Answer: Use the slope formula to find the slope m .
m = -2
Step-by-step explanation:
3. You are constructing a 95% confidence interval of a sample space consisting of n = 40 values
and a population standard deviation of 2.6. The population appears to be skewed. Determine
whether a margin of error should be calculated using a critical value of Za/2, a critical value of
ta/2, or neither.
a critical value of ta/2
a critical value of za/2
neither
Given the provided conditions which are a known population standard deviation and a sample size (n = 40) greater than 30, the critical value of Za/2 is appropriate for calculating the margin of error in a skewed population.
Explanation:In this scenario, a 95% confidence interval is being constructed for a population that is skewed. Given a sample size, n, of 40, the population standard deviation (σ) is 2.6. When we construct confidence intervals for such a scenario, we refer to either a Z-distribution (critical value of Za/2) or a T-distribution (critical value of ta/2) based on certain conditions.
A critical value of Za/2 is used when the population standard deviation is known, and the sample size is large enough (typically n > 30). A critical value of ta/2 is referred to when the population standard deviation is unknown, or the sample size is too small (typically n < 30).
In this case, the population is skewed, the standard deviation is known, and the sample size (n = 40) is larger than 30. Therefore, we should use the critical value of Za/2 for calculating the margin of error.
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Solve: 2.8 X +12=-1.4 X -9
Answer:
X= -5
Step-by-step explanation:
Expression: 2.8X+12=-1.4X-9
Order it: 12+9=-1.4X-2.8X
Simplification: 21=-4.2X
Results: x=-5
Which expression is equivalent to 210d² – 63d
o
21d(10d-3)
o 21(10d+3)
o
21d(10d+3)
Answer:
21d(10d-3)
Step-by-step explanation:
21d x 10d = 210d^2
21d x 3 = -63d
so it would be 210d^2 - 63d
The expression which is equivalent to 210d² − 63d would be 21d(10d- 3).
What is factorization?factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
From the given expression;
210d² − 63d
A factor which is common to both terms of the expression;
21d.
On this note, the factorisation of the expression yields,
21d(10d- 3).
21d x 10d = 210d^2
21d x 3 = -63d
so it would be 210d² − 63d.
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if x+7=23,then x=16 what property is this
The property used in this equation is the addition property of equality.
Explanation:The property used in this equation is called the addition property of equality. According to this property, if two numbers are equal, then adding the same number to both sides of the equation will still result in an equality.
In the given equation, x + 7 = 23, we need to isolate the variable x. To do this, we can subtract 7 from both sides of the equation, using the subtraction property of equality. This simplifies the equation to x = 16.
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Triangle 2 and triangle 3 were created by drawing an altitude in triangle 1. What is the relationship between the green highlighted
segment in triangle 2 and the blue highlighted segment in triangle 1?
A. The highlighted segments are corresponding sides of triangles 1 and 3.
B. The highlighted segments are corresponding sides of triangles 2 and 3.
C. The highlighted segments have no corresponding relationship.
D. The highlighted segments are congruent.
Answer:
Triangle 1 line segment AB and triangle 2 line segment BA correspond to each other
Step-by-step explanation:
Point b and point a don't correspond to anything else
triangle 1 and 2 are congruent my answer would be a 50/50 guess between C and D If it were me id risk it and go D but it is up to you.
Cynthia plans to build a treehouse that is 1/3 the size of Andrew's tree house. Cynthia plans to make the area of her tree house at least 13 square feet. Write and solve an inequality to find the area of Andrew's tree house. Let x be the area of Andrew's tree house. Describe how you know which tree house is larger without solving the inequality.
Answer:
The area of Andrew's tree house must be greater than or equal to 117 square feet
Step-by-step explanation:
Let
x -----> the area of Andrew's tree house in square feet
y ----> the area of Cynthia's tree house in square feet
we know that
Cynthia plans to make the area of her tree house at least 13 square feet.
The word "at least" means "greater than or equal to"
so
[tex]y\geq 13[/tex] ----> inequality A
Cynthia plans to build a tree house that is 1/3 the size of Andrew's tree house
so
Remember that
When two figures are similar, the ratio of its areas is equal to the scale factor squared
In this problem the scale factor is given
The scale factor is 1/3
The scale factor squared is 1/9
That means
The area of Andrew's tree house is 9 times greater than the area of Cynthia's tree house
or
The area of Cynthia's tree house is 9 times smaller than the area of Andrew's tree house
[tex]y=\frac{1}{9}x[/tex] ----> equation B
substitute equation B in the inequality A
[tex]\frac{1}{9}x\geq 13[/tex]
solve for x
[tex]x\geq 117\ ft^2[/tex]
so
The area of Andrew's tree house must be greater than or equal to 117 square feet
we know that Andrew's tree house is larger than Cynthia's tree house, because the problem states that Cynthia's tree house is 1/3 the size of Andrew's tree house
That means
The size of Andrew's tree house is 3 times greater than the size of Cynthia's tree house, without solving the inequality
Final answer:
To find the size of Andrew's treehouse, let's assume the area as x square feet. Using the given information, we can write and solve the inequality (1/3)x ≥ 13 to find the area of Andrew's treehouse. Without solving the inequality, we know that Andrew's treehouse is larger because the area must be greater than or equal to 39 square feet.
Explanation:
To find the area of Andrew's tree house, let's assume that his tree house has an area of x square feet.
According to the information given, Cynthia plans to build a treehouse that is 1/3 the size of Andrew's tree house. Therefore, the area of Cynthia's tree house would be (1/3)x square feet.
We are told that Cynthia plans to make the area of her tree house at least 13 square feet. So we can write the inequality as follows:
(1/3)x ≥ 13
To solve the inequality, we need to multiply both sides by 3 (since the coefficient of x is 1/3). This will give us:
x ≥ 39
This means that the area of Andrew's tree house must be greater than or equal to 39 square feet.
Without solving the inequality, we can see that Andrew's tree house is indeed larger than Cynthia's tree house because the area of Andrew's tree house must be greater than or equal to 39 square feet.
solve the simultaneous equations:
y=3x+5
y=4x²+x
Give your answer correct to 2 decimal places
Answer:answer to the questions are x=1.396 or -0.896 and y=9.188 or 2.312
Step-by-step explanation: see attachment
Thanks for drawing my attention to my mistake. I appreciate.
Answer:
The solutions (x, y) are (1.40, 9.19) and (-0.90, 2.32) correct to 2 decimal places.
Step-by-step explanation:
As the 2 expressions in x are both equal to y we can write:
4x^2 + x = 3x + 5
4x^2 - 2x - 5 = 0
x = [ -(-2) +/- sqrt(4 - 4*4*-5)] / 2*4
= 0.25 +/- (sqrt 84)/8
x = 1.396, -0.895.
When x = 1.396, y = 3(1.396) + 5 = 9.188
when x = 0.895, y = 3(-0.895) + 5 = 2.315.
If 108 is 90% of x, what is the value of x?
Answer:
x=120
Step-by-step explanation:
108 = 90%
divide everything by 9
12 = 10%
multiply everything by 10
120 = 100%
x=120
Answer:
120
Step-by-step explanation:
set a relation. Because 108 is 90%, you do 90%/100% = 108/x (write vertically so its easier. So you see what number you multiply 90 by to get 108 and multiply that by 100 to get the total amount.
Rachel bought a piece of fabric 2.3 meters long and a piece of fabric 3.45 meters long. She needs 10 meters of fabric altogether. How much more does she need to buy?
4. Write the steps that tell how to find the answer.
?
Which of these plans will work?
Add the length of one piece to the length of the other piece. Add the sum to the length needed.
Add the length of one piece to the length of the other piece. Subtract the sum from the length needed.
Answer:
She needs to buy 4.25 m cloth
Step-by-step explanation:
Add the length of one piece to the length of the other piece. Subtract the sum from the length needed.
2.3 + 3.45 = 5.75
10 - 5.75 = 4.25m
Answer:
4.25, B
Step-by-step explanation:
2.3+3.45= 5.75 you need 4.25 more to have 10 meters
solve 6x^2 - 42 = 0 for the exact values of x
Answer:
The values of x are
[tex]x=-\sqrt{7} , x=\sqrt{7}[/tex]
Step-by-step explanation:
we have
[tex]6x^{2}-42=0[/tex]
Solve for x
Adds 42 both sides
[tex]6x^{2}-42+42=0+42[/tex]
[tex]6x^{2}=42[/tex]
Divide by 6 both sides
[tex]6x^{2}/6=42/6[/tex]
simplify
[tex]x^2=7[/tex]
square root both sides
[tex]x=\pm\sqrt{7}[/tex]
therefore
The values of x are
[tex]x=-\sqrt{7} , x=\sqrt{7}[/tex]
The exact solution for the values of x in the given equation are: +√7 and -√7.
What are the exact values of x in the equation?From the task content; it follows that the given equation is; 6x² - 42 = 0.
On this note, the evaluation for the values of x can be done as follows;
6x² - 42 = 0
6x² = 42
x² = 7
x = ±√7.
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Which of the following fractions is not equivalent to 6/21
Answer:
3/7 and 4/14
Step-by-step explanation:
a) 3/7 is not an equivalent of 6/21 because when you multiply the numerator and the denominator by 2 you get: 6/14
b) 4/14 is not an equivalent
Answer:
3/7
Step-by-step explanation:
6/21 = 6 ÷ 3 / 21 ÷ 3 = 2 / 7
6 / 21 = 4 ÷ 2 / 14 ÷ 2 = 2 / 7
6/21 = 12 ÷ 6 / 42 ÷ 6 = 2 / 7
please help !!! 30 points and i’m struggling
graph the equation
Y+5= -2(x-4)
PLEASE HELP
Step-by-step explanation:
y+5-5=-2(x-4)
-5, first let's put it in the form y=mx+b.
y+5-5=-2(x-4)-5
y=-2x+3, so in this, m=slope and b=y-intercept. On your graph, plot three on the y line, and the slope is negative two, so go down two then over one to the left side, because it is decreasing. Also slope is rise over run or just rise/run.
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)
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