The given line has a slope of -1.
The slope of a perpendicular line is the negative reciprocal.
The slope of the new line would be positive 1.
Now using the point slope form, use the given pint to find the equation:
y -y1 = m(x -x1)
Replace x1 and y1 with the given point:
y - (-2) = 1(x -3)
Simplify:
y +2 = x -3
Subtract 2 from both sides:
y = x-5
Answer:
y = x-5
Step-by-step explanation:
Worst Buy, a local electronics store, advertises a sale price of 25% off all televisions 42" or bigger. Model the sale price (original price minus discount) of those televisions, y, as a function of the regular price of the TV, x.
25% off means it would be selling for 75% of the original price ( 100% - 25% = 75%).
To find the sale price you would multiply the regular price by 75%:
The equation would be y = 0.75x
3.3(x – 8) - x = 1.2
Answer:
3.3 x - (3.3*8) - x = 1.2
2.3 x - (3.3*8) = 1.2
2.3 x - 26.4 = 1.2
2.3 x - 26.4 + 26.4 = 1.2 + 26.4
2.3 x = 27.6
2.3 x / 2.3 = 27.6 / 2.3
x = 12
A rectangular prism with a volume of 555 cubic units is filled with cubes with side lengths of \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction unit.
How many \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction unit cubes does it take to fill the prism?
135 cubes are required to fill the prism
Solution:
Given that a rectangular prism with volume of 5 cubic units is filled with cubes with side lengths of [tex]\frac{1}{3}[/tex] units
Then the number of cubes required to fill the prism will be given by:
[tex]\text { number of cubes }=\frac{\text {volume of rectangular prism}}{\text {volume of cube}}[/tex]
Volume of rectangular prism = 5 cubic units
[tex]\text{ Volume of cube}=(\text { side })^{3}$[/tex]
[tex]\text { Volume of cube }=\left(\frac{1}{3}\right)^{3}=\frac{1}{27}[/tex]
Therefore number of cubes required to fill the prism are:
[tex]\text { number of cubes }=\frac{5}{\frac{1}{27}}=5 \times 27=135[/tex]
Therefore 135 cubes are required to fill the prism
Answer:
135
Step-by-step explanation:
The scatterplot represents the total fee
for miles traveled on a toll road.
The line of best fit for the data is
y = 0.043x + 0.324.
Use the line of best fit to predict the toll
when 100 miles are driven.
Answer:
[tex]4.624[/tex]
Step-by-step explanation:
[tex]y=0.043x+0.324\\given \ miles \ x=100\\y= 0.043\times100+0.324\\=4.3+0.324\\=4.624[/tex]
please help I need to get this done today
Answer:
18) If ∠1 = 124° , then ∠4 = 56°.
19) if ∠2 = 48°, then ∠3 = 132°.
20) if ∠4 = 55°, then ∠2 = 55°.
21) if ∠6 = 120° , then ∠8= 120°.
22) if ∠7 = 50.5 , then ∠6= 50.5°.
23) if ∠3 = 118.7°, then ∠2= 61.3°
Step-by-step explanation:
Given two parallel lines a and b.
And other line, which is called transversal line cuts these two parallel lines to make 8 angles.
Now,
18) Given, ∠1 = 124°
Now, sum of consecutive interior angles made by transversal line with parallel lines = 180° .
⇒∠1 + ∠4 = 180°
⇒∠a = 180° - 124° = 56°.
19) ∠2 = 48°.
as sum of consecutive interior angles made by transversal line with parallel lines = 180° .
∠2 + ∠3 = 180°.
⇒ ∠3 = 180° - 48° = 132°.
20) ∠4 = 55°
Alternate angles made by transversal line with parallel lines are equal .
⇒∠2 = ∠4 = 55°.
21) ∠6 = 120°
As corresponding angles made by transversal line with parallel lines are equal. ∠6 = ∠3 = 120°.
now, also opposite angles are equal
⇒ ∠3 = ∠8 = 120°.
22) ∠7 = 50.5
As corresponding angles made by transversal line with parallel lines are equal. ∠7 = ∠2 = 50.5°.
now, also opposite angles are equal
⇒ ∠2 = ∠6 = 50.5°.
23) ∠3 = 118.7°
as sum of consecutive interior angles made by transversal line with parallel lines = 180° .
∠3 + ∠2 = 180°.
⇒ ∠2 = 180° - 118.7° = 61.3°
Emily has $3.15 worth of dimes and quarters. She has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Emily has.
Answer:
The number of dimes is 14 and the number of quarters is 7.
Step-by-step explanation:
Given:
Emily has $3.15 worth of dimes and quarters.
She has twice as many dimes as quarters.
Now, to determine the number of dimes and the number of quarters.
Let the number of quarters be [tex]x.[/tex]
And the number of dimes be [tex]2x.[/tex]
So, the total worth of dimes and quarters = $3.15.
Now, to get the number of dimes and quarters:
According to question:
[tex]0.10(2x)+0.25x=3.15[/tex]
[tex]0.20x+0.25x=3.15[/tex]
[tex]0.45x=3.15[/tex]
Dividing both sides by 0.45 we get:
[tex]x=7.[/tex]
Thus, the number of quarters = 7.
So, the number of dimes = [tex]2x=2\times 7=14.[/tex]
Therefore, the number of dimes is 14 and the number of quarters is 7.
help a girl out
(2a^3−5a)−(7a+3a^2)
For this case we must simplify the following expression:
[tex](2a ^ 3-5a) - (7a+ 3a ^ 2) =[/tex]
By definition of the law of multiplication signs we have to:
[tex]- * + = -[/tex]
Rewriting the expression we have:
[tex]2a ^ 3-5a-7a-3a ^ 2 =[/tex]
We add similar terms taking into account that:
Equal signs are added and the same sign is placed.
[tex]2a ^ 3-3a ^ 2-12a[/tex]
ANswer:
[tex]2a ^ 3-3a ^ 2-12a[/tex]
Which fraction is the reciprocal of 2 5/7 ASAP!!!
7/19
bc 2 5/7 = 19/7. the reciprocal is a fraction reversed. or upside down that is. So, your answer is 7/19
Answer:
7/19
Step-by-step explanation:
2 5/7=19/7
Two-thirds of a number added to itself is 20. What is the number?
Answer:
12
Step-by-step explanation:
2/3 x + x = 20
2/3 x + 3/3x = 20
5/3 x = 20 ... times 3/5 both sides
x = 12
check: 2/3 x 12 + 12 = 8 + 12 = 20
a 20.00 pair of jeans is discounted 20%. What is the final price of the jeans?
Answer:
16.00
Step-by-step explanation:
When you divide twenty percent(0.20) to 20.00 you will get sixteen or 4.00 dollars off
The base of a triangle is 10 cm greater than the height. The area is 28 cm2. Find the height and the
base.
Absolute value of 225
225
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Answer: 3x-x+2=4
Step-by-step explanation:
absolute value of 225 = | 225 | = 225
here is an inequality 2x + 5 > 50 explain the steps you would use to solve the equation for x what would the graph look like
Answer:
[tex]x>22.5[/tex]
Step-by-step explanation:
Given linear inequality:
[tex]2x+5>50[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 5.
[tex]2x+5-5>50-5[/tex]
[tex]2x>45[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}>\frac{45}{2}[/tex]
∴ [tex]x>22.5[/tex]
The graph of the inequality is shown below.
The line is represented by dotted line because the inequality sign is only greater than which means 22.5 is not included in the solution.
Janet charges an upfront fee of $20 plus $7.50 an hour for babysitting. Lisa does not charge an upfront fee, but charges $8.75 an hour. After how many hours will their charge be equal?
After 16 hours, the charges will be same.
Step-by-step explanation:
Given,
Janet's upfront fee = $20
Charges per hour = $7.50
Let,
x be the number of hours.
J(x) = 7.50x+20
Lisa has no upfront fee.
Charges per hour = $8.75
L(x) = 8.75x
For the charges to be equal;
J(x) = L(x)
[tex]7.50x+20=8.75x\\20=8.75x-7.50x\\20=1.25x\\1.25x=20[/tex]
Dividing both sides by 1.25
[tex]\frac{1.25x}{1.25}=\frac{20}{1.25}\\x=16[/tex]
After 16 hours, the charges will be same.
Keywords: function, division
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solve the inequality for x: -3(2x+5) < -45
Answer:
x>5
Step-by-step explanation:
-3(2x+5)<-45
2x+5<-45/-3
2x+5<15
2x<15-5
2x<10
x<10/2
x<5
x>5
Is x-4 equivalent to x3•x-7
Answer:
No.
Step-by-step explanation: Assuming you mean x^3*x-7, these two equations do not produce the same line.
Answer:
YESStep-by-step explanation:
[tex]x^3\cdot x^{-7}=x^{3+(-7)}=x^{-4}\\\\\text{used}\ a^n\cdot a^m=a^{n+m}\\\\\text{Other way}\\\\a^{-n}=\dfrac{1}{a^n}\\\\x^3\cdot x^{-7}=x^3\cdot\dfrac{1}{x^7}=\dfrac{x^3}{x^7}=\dfrac{x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1}{x\!\!\!\!\diagup_1\cdot x\!\!\!\!\diagup_1 \cdot x\!\!\!\!\diagup_1 \cdot x\cdot x\cdot x\cdot x}=\dfrac{1}{x^4}=x^{-4}[/tex]
which formula can be used to find an ?
Answer:
Step-by-step explanation:
an = 6n - 13
If n = 10 , a10 = 6*10 - 13 = 60-13 = 47
If n = 11 , a11 = 6*11 - 13 = 66-13 = 53
If n = 12 , a12 = 6*12 - 13 = 72-13 = 59
The formula to find the nth term of the sequence an, is a(n) = -13 + 6n
How to determine the formula to find an ?From the question, we have the following parameters that can be used in our computation:
a(10) = 47
a(11) = 53
a(12) = 59
a(13) = 65
The nth term of an arithmetic sequence can be represented as
a(n) = a(1) + (n - 1) * d
Where,
common difference,
d = 6
So, we have
a(n) = a(1) + (n - 1) * 6
Using the 12th term, we have
a(1) + (12 - 1) * 6 = 59
a(1) = 59 - 66
a(1) = -7
So,, we have
a(n) = -7 + (n - 1) * 6
Expand
a(n) = -13 + 6n
Hence, the formula to find an is a(n) = -13 + 6n
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Choose the point-slope form of the line passing through (3,5) with a slope of -3.
O y -3'= -3 (ix – 5)
0 -3(y – 5) = x - 3
y - 5 = -3 (0 - 3)
O 3x - 5y = -3
O
Answer:
answer is y-5=-3(x-3)
Step-by-step explanation:
your y-coordinate is 5 s you would write y-5 and your slope is -3 with your x-coordinate as 3 so that would be written as -3(x-3). The equation put together correctly would be y-5=-3(x-3)
Answer:
y-5=-3(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-3(x-3)
Is the following relation a function?
Answer:
No
Step-by-step explanation:
A function is a relation in which no two ordered pairs have the same first element.
A function associates each element in its domain with one and only one element in its range.
What is a rational number equivalent to ——
3.12
Answer:
[tex]\frac{78}{25}[/tex]
Step-by-step explanation:
A rational number has the form
[tex]\frac{a}{b}[/tex] ← where a and b are integers
3.12 = [tex]\frac{312}{100}[/tex] ← divide numerator/denominator by 4, thus
3.12 = [tex]\frac{78}{25}[/tex] ← in simplest form
Which number line best shows how to solve −8 − (−6)?
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 6.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to negative 8.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to 2.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Answer:
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Step-by-step explanation:
find the number line best shows how to solve −8 − (−6)
In the number line first we start with -8 . negative and negative becomes positive
from -8 move 6 units to the right. So it ends at -2
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
What is the slope of the line shown below?
Answer:
B
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 8) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line
m = [tex]\frac{-4-8}{2+1}[/tex] = [tex]\frac{-12}{3}[/tex] = - 4 → B
Answer:
The slope of the given line is -4.
So, option (B) is correct.
Step-by-step explanation:
We know that, slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂) is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Now, the given line passes through the point (-1, 8) and (2,-4).
So, (x₁, y₁) = (-1, 8) and (x₂, y₂) = (2, -4)
So, by using the above formula, we get
Slope(m) of the given line passing through (-1, 8) and (2, -4) is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-4-8}{2-(-1)}[/tex]
[tex]\implies\;m = \frac{-12}{3}=-4[/tex]
∴The slope of the given line is -4.
Hence, option (B) is correct.
What is the point (5, -3) after a rotation of 90 degrees counterclockwise
Answer:
It would be (3,5)
Step-by-step explanation:
On a coordinate plane it would be changed in which the 2nd number becomes first & the + or - changes. Same for the first number.
please help me I need it.
Deon needs 50g of shugger to make 15 biscuits.
she also needs three times as much flour as sugar
two times as much butter as sugar
Deon is going to make 60 biscuits
work out the amount of flour she needs.
Answer:
200g of sugar, 600g of flour, 400g of butter
Step-by-step explanation:
50g sugar = 15 biscuits
3 x 50g = flour --) 150g = flour
2 x 50g = butter --) 100g = butter
60/15 = 4; 4 times as much
4 x 50g = 200g of sugar
4 x 150g = 600g of flour
4 x 100g = 400g of butter
The amount of flour she needed is 600g.
Given that,
Deon needs 50g of shugger to make 15 biscuits. she also needs three times as much flour as sugar two times as much butter as sugar. Deon is going to make 60 biscuits.Based on the above information, the calculation is as follows:
50g sugar = 15 biscuits
[tex]= 3 \times 50g\\\\ = 150g\ flour[/tex]
And.
[tex]= 2 \times 50g \\\\= 100g \ butter[/tex]
Now
[tex]= 60\div15[/tex]
= 4 times
Therefore, the amount of floor should be
[tex]= 150 \times 4[/tex]
= 600 grams.
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A candy store sells caramels and milk chocolate by the pound the table below shows the total cost in dollars for a pound of each type of candy the store sells
Caramels: $10.28
Milk Chocolate: $13.85
How much more is the cost for 1 3/4 pounds of milk chocolate than the cost for 1 3/4 pounds of caramels?
The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.
Step-by-step explanation:
Given,
Cost of one pound of Caramels = $10.28
Cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel = [tex]10.28*1\frac{3}{4}[/tex]
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]10.28*\frac{7}{4}=\frac{71.96}{4}= \$17.99[/tex]
Cost of one pound of chocolate milk = $13.85
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]13.85*1\frac{3}{4}=13.85*\frac{7}{4}[/tex]
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]\frac{96.95}{4}=\$24.24[/tex]
Difference = 24.24 - 17.99 = $6.25
The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.
Keywords: difference, multiplication
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Final answer:
The cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels, after calculating the total cost of each based on their per pound price.
Explanation:
To find out how much more the cost for 1 3/4 pounds of milk chocolate is than the cost for 1 3/4 pounds of caramels, we first need to calculate the cost of 1 3/4 pounds of each type of candy. Since the cost per pound of caramels is $10.28 and the cost per pound of milk chocolate is $13.85, we can set up our calculations as follows:
Total cost of caramels = 1.75 (pounds) * $10.28 (per pound) = $17.99
Total cost of milk chocolate = 1.75 (pounds) * $13.85 (per pound) = $24.24
Now, we subtract the total cost of caramels from the total cost of milk chocolate to find the difference:
Cost difference = $24.24 - $17.99 = $6.25
So, the cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels.
How many 3/4 cup servings are in 12 cups of cherries?
Answer:
16 serving.
Step-by-step explanation:
Given: 3/4 cup servings.
Now, computing the number of serving in 12 cups of cherries.
Using unitary method to solve.
∴ Number of serving= [tex]total\ cups \times number\ of\ serving\ per\ cup[/tex]
Number of serving in one cup is [tex]\frac{4}{3}[/tex]
Number of serving in 12 cups = [tex]12\times \frac{4}{3} = 16 \ serving[/tex]
Number of serving in 12 cups= [tex]16\ serving[/tex]
∴ There are 16 serving is possible in 12 cups of cherries.
Final answer:
To calculate the number of 3/4 cup servings in 12 cups of cherries, divide 12 by 3/4, which equals 16 servings.
Explanation:
To determine how many 3/4 cup servings are in 12 cups of cherries, we can divide the total number of cups by the size of one serving.
First, we express the serving size and the total amount in the same units: 3/4 cup and 12 cups.
Next, we divide the total amount of cherries by the serving size: 12 cups ÷ 3/4 cup.
To perform the division, we can multiply 12 by the reciprocal of 3/4, which is 4/3 (12 × 4/3 = 16).
The result is that there are 16 servings of 3/4 cup in 12 cups of cherries.
Someone please help!
Answer:
See explanation
Step-by-step explanation:
1. Lines l and k are parallel. These lines are cut be transversal n. Angles 2 and 7 are corresponding angles when parallel lines l and k are cut by transversal n. By Corresponding Angles Ttheorem, angles 2 and 7 are congruent.
2. Lines m and n are parallel. These lines are cut be transversal k. Angles 2 and 10 are alternate interior angles when parallel lines m and n are cut by transversal k. By Alternate Interior Angles Theorem, angles 2 and 10 are congruent.
3. Angles 2 and 7 are congruent (see 1)
Angles 2 and 10 are congruent (see 2)
Hence, angles 7 and 10 are congruent by transitive property.
Please help! A chemist has 100ml of 25% acid solution. How much of the solution does she need to drain and replace with 70% acid solution to obtain 100ml of 60% acid solution?
Answer:
77.78
Step-by-step explanation:
Answer:
77.78
Step-by-step explanation:
i had this ? on rsm student portal.
3x + 4x − 2x = − 76 + 96
Answer:
4
Step-by-step explanation:
first add up the xs that gives you 5x because first 3x+4x gives you 7 then minus that with 2x that gives you five,
now add the numbers -76+96 that gives you 20 now the equation becomes
5x=20
now divide 20 by 5 that gives you 4
Determine the y-intercept of x 12 + y 3 = 2
The y-intercept of [tex]\(12x + y^3 = 2\) is at \((0, \sqrt[3]{2})\).[/tex]
To find the y-intercept of the equation [tex]\(12x + y^3 = 2\)[/tex], we first need to understand what the y-intercept represents. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of this point is 0.
To find the y-intercept, we set [tex]\(x = 0\)[/tex] in the equation and solve for y:
[tex]\[12(0) + y^3 = 2\][/tex]
[tex]\[y^3 = 2\][/tex]
To solve for y, we take the cube root of both sides:
[tex]\[y = \sqrt[3]{2}\][/tex]
So, the y-intercept of the equation is [tex]\((0, \sqrt[3]{2})\).[/tex]