the the original price be x
[tex]x - \frac{30}{100} x = 84 \\ \frac{100x - 30x}{100} = 84 \\ 70x = 8400 \\ x = \frac{8400}{70} \\ x = 120[/tex]
so the original price was $120
Answer: original price b4 30% discount was $120
Step-by-step explanation:
If at 30% discount, baseball glove is $84
It means 70% = 84
100% = x
Cross multiply
70x = 8400
x = 120
What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x − 6y = 15?
3
1) y−9=−2(x−6)
2
2) y−9= 3(x−6)
3
3) y+9=−2(x+6)
4) y+9=23(x+6)
Given:
The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is [tex]4 x-6 y=15[/tex]
We need to determine the equation of the line.
Slope:
Let us convert the equation to slope - intercept form.
[tex]-6 y=15-4x[/tex]
[tex]y=\frac{2}{3}x-\frac{5}{2}[/tex]
From the above equation, the slope is [tex]m_1=\frac{2}{3}[/tex]
Since, the lines are perpendicular, the slope of the line can be determined using the formula,
[tex]m_1 \cdot m_2=-1[/tex]
[tex]\frac{2}{3} \cdot m_2=-1[/tex]
[tex]m_2=-\frac{3}{2}[/tex]
Therefore, the slope of the equation is [tex]m=-\frac{3}{2}[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the point (6,9) and the slope [tex]m=-\frac{3}{2}[/tex] in the above formula, we get;
[tex]y-9=-\frac{3}{2}(x-6)[/tex]
Simplifying the terms, we get;
[tex]2(y-9)=-3(x-6)[/tex]
[tex]2y-18=-3x+18[/tex]
[tex]3x+2y=36[/tex]
Thus, the equation of the line is [tex]3x+2y=36[/tex]
The equation of a line that is perpendicular to the line 4x - 6y = 15 and passes through the point (6,9) is 3x + 2y = 36. This is because the slope of the new line is the negative reciprocal of the slope of the given line, and the line passes through the given point (6,9).
Explanation:The subject of this question is mathematics, specifically in the topic of linear equations. To find the equation of a line that is perpendicular to a given line and passes through a certain point, we first need to find the slope of the given line. The standard form of the equation of a line is Ax + By = C. The given line is 4x - 6y = 15. We can find its slope by taking the negative reciprocal of the coefficient of x (A) over the coefficient of y (B), so the slope of the given line is -4/-6 = 2/3. Since we want a line that is perpendicular to the given line, the slope of the line we are looking for would be the negative reciprocal of the slope of the given line, which would be -3/2, because perpendicular lines have slopes that are negative reciprocals of each other. Using the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, the equation of the line we are looking for is y - 9 = -3/2(x - 6), which simplifies to 2y - 18 = -3x + 18 and further simplifies to 3x + 2y = 36. So the answer is none of the given options.
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If 8x - 4 = 6x - 10, find the value of 5x
Answer:
5x=-15
Step-by-step explanation:
8x-6x=4-10
2x=-6
x=-3
5x=-15
five friends split the cost of parking at an amusement park. each of them also buys a $30 ticket. Write an algebraic expression that represents the amount of money each friend spends.
Answer: A/5+30*5
Step-by-step explanation:
A 23-year-old female buys 25/50/100 liability insurance, collision insurance with a $250 deductible, and comprehensive insurance with a $100 deductible. What is her total annual premium? Use the base premium and rating factor tables used to calculate the annual car insurance premium of a person.
Answer: $1090.80
Step-by-step explanation:
Answer:
$1,090.80
Step-by-step explanation:
Bodily injury; 25/50=$220
Property; 100=$375
Collision deductibles;$250=$185
Comprehensive deductibles;$100=$129
220+375+185+129 = 909
909*1.2=1,090.8
Took the test
The lid of a jewelry box is in the shape of a triangular prism. The lid has a height of 10 inches. The triangular base of the lid has a base of 6 1/2 inches and a height of 3 1/2 inches. What is the volume of the lid to the nearest tenth?
The volume of the lid is approximately 113.8 cubic inches.
Explanation:The volume of the lid can be found by multiplying the area of the triangular base by the height of the lid. The area of a triangle can be found by using the formula: Area = (base x height) / 2. In this case, the base is 6 1/2 inches and the height is 3 1/2 inches. Plugging these values into the formula, we get: Area = (6.5 x 3.5) / 2 = 11.375 square inches. Now, to find the volume of the lid, we multiply the area by the height: Volume = 11.375 x 10 = 113.75 cubic inches. Rounding to the nearest tenth, the volume of the lid is 113.8 cubic inches.
The volume of the lid is 113.8 cubic inches.
To determine the volume of the lid of the jewelry box, we need to use the formula for the volume of a triangular prism, which is V = (1/2 * base * height of triangular base) * height of the prism.
First, calculate the area of the triangular base:
Base of the triangular base: 6.5 inchesHeight of the triangular base: 3.5 inchesArea = 1/2 * 6.5 inches * 3.5 inches = 11.375 square inchesNext, multiply the area of the triangular base by the height of the prism:
Height of the prism: 10 inchesVolume = 11.375 square inches * 10 inches = 113.75 cubic inchesTherefore, the volume of the lid to the nearest tenth is 113.8 cubic inches.
Jorge is setting up his tent. He is using two nylon ropes to pull the tent taut and stabilize it at each end. If the tent is 5 feet tall, and Jorge stakes the ropes into the ground 3 feet from the tent, what is the total length of nylon rope he will use, to the nearest tenth of a foot? Show all of your work. PLEASE HELP ME !!!!!!!!!!
Answer: 5.8 ft
Step-by-step explanation:
We can use the Pithagorean Theorem in this problem, in order to find the length of the rope:
[tex]h^{2}=a^{2}+b^{2}[/tex]
Where:
[tex]h[/tex] is the length of the rope (the hypotenuse of the right triangle formed by the height of the tent, the rope and the ground)
[tex]a=5 ft[/tex] is the height of the tent (one of the legs of the right triangle)
[tex]b=3 ft[/tex] is the other leg of the right triangle
Solving the equation with the given data:
[tex]h^{2}=5^{2}+3^{2}[/tex]
Finding [tex]h[/tex]:
[tex]h=\sqrt{(5 ft)^{2}+(3 ft)^{2}}[/tex]
[tex]h=\sqrt{25 ft+9 ft}[/tex]
[tex]h=5.83 ft \approx 5.8 ft[/tex] This is the total length of nylon rope
mrs.darby works at the local bakery as a cake decorator if it takes her 1 1/3 hours to decorate one cake how many cakes can she dcorate in a 30-hour week
Answer:
22 1/2 cakes
Step-by-step explanation:
1 cake = 1 1/3 hours
Number of cakes in 30-hour week
= 30 ÷ 1 1/3
= 30 ÷ 4/3
= 30 x 3/4
= 90/4
= 45/2
= 22 1/2
Answer: 22 1/2 cakes
Can someone please help me answer this?
On Saturday, local hamburger shop sold a combined total of 450 hamburgers and cheeseburgers. The number of cheeseburgers old was two times the number of hamburger sold. How many hamburgers were sold on Saturday?
Answer:
There was 150 hamburgers sold on Saturday
Step-by-step explanation:
Step 1: Make an equation
2x + x = 450
Step 2: Solve for x
2x + x = 450
3x / 3 = 450 / 3
x = 150
Answer: There was 150 hamburgers sold on Saturday
Final answer:
The local hamburger shop sold 150 hamburgers on Saturday. This was found by setting up a system of equations where H represents hamburgers and C represents cheeseburgers, and solving for H.
Explanation:
To determine how many hamburgers were sold on Saturday, we can set up a system of equations based on the information given:
Let H represent the number of hamburgers sold.
Let C represent the number of cheeseburgers sold.
We are told that the total number of hamburgers and cheeseburgers sold is 450, so:
H + C = 450
We also know that the number of cheeseburgers sold was two times the number of hamburgers sold, so:
C = 2H
Now we substitute the second equation into the first one to solve for H:
H + 2H = 450
3H = 450
H = 450 / 3
H = 150
Therefore, on Saturday, the local hamburger shop sold 150 hamburgers.
A cable television provider offers six
different news stations. If 25% of the
stations offered are news, how many
stations are offered by the provider?
Answer:
24 stations
Step-by-step explanation:
we know that
six stations represent 25% of the stations offered
so
using a proportion
Find out how many stations represent a percentage of 100%
[tex]\frac{6}{25\%}=\frac{x}{100\%}\\\\x=6(100)/25\\\\x=24\ stations[/tex]
=
Initial Knowledge Check
Question 8
A veterinarian treated 7 dogs this morning. The list below gives the weights (in pounds) of each dog.
66, 8, 12, 74, 36, 66, 7
Find the range of the data set.
x
?
The range of the data set is 67 pounds.
Explanation:The range of a data set is the difference between the maximum and minimum values. In this case, the weights of the 7 dogs are 66, 8, 12, 74, 36, 66, and 7 pounds. To find the range, we subtract the smallest value (7) from the largest value (74):
Range = 74 - 7 = 67
So, the range of the data set is 67 pounds.
The length and width of a rectangle are 4 feet and 3 feet, respectively. A similar rectangle has a length of 10 feet. What is the width of the second rectangle?
KNOWLEDGE CHECK: ALEKS
The value of x that satisfies the equation 41 - x = 157 is x = -116.
To solve for x in the equation 41 - x = 157, we need to isolate x on one side of the equation.
Let's go step by step:
Step 1: Start with the given equation.
41 - x = 157
Step 2: Get rid of the constant term on the left side (41) by subtracting it from both sides of the equation.
(41 - x) - 41 = 157 - 41
Simplifying the left side:
41 - 41 - x = 157 - 41
0 - x = 116
Step 3: We have -x on the left side, and we want to solve for x, so we need to get rid of the negative sign in front of x.
To do that, we can multiply both sides of the equation by -1.
When we multiply a number by -1, the sign changes.
(-1) * (-x) = (-1) * 116
Simplifying the left side:
x = -116
Step 4: Now we have found the value of x, which is x = -116.
To verify our solution, we can substitute the value of x back into the original equation and see if it holds true:
41 - (-116) = 157
Simplifying:
41 + 116 = 157
157 = 157
Since both sides of the equation are equal after simplification, our solution x = -116 is correct.
Therefore, the value of x that satisfies the equation 41 - x = 157 is x = -116.
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Evaluate 60 • x-60 · 15, when x=8.
Step 1 60• x-60 • 15 = 60(x - 15)
Step 2
Step 3
= 480 – 15
Step 4
465
Where is the error
Answer:
The right answer is, -420
Step-by-step explanation:
Because we use common factor:
60 (x - 15)
We multiply for each term:
60 (x) - 60 (15)
60 (8) - 60 (15)
We solve:
480 - 900 = -420
In ΔGHI, the measure of ∠I=90°, the measure of ∠G=21°, and GH = 31 feet. Find the length of IG to the nearest tenth of a foot.
Answer:
[tex]IG=28.9\ ft[/tex]
Step-by-step explanation:
we know that
In the right triangle GHI
[tex]cos(G)=\frac{IG}{GH}[/tex] ----> by CAH )adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(21^o)=\frac{IG}{31}[/tex]
solve for IG
[tex]IG=cos(21^o)(31)=28.9\ ft[/tex]
see the attached figure to better understand the problem
Answer:
24.6
Step-by-step explanation:
Makoto's summer job is mowing and edging lawns. He charges $20 to mow a lawn and $10 to edge a lawn. Makoto earned $180 mowing some lawns and edging 4 lawns. How many lawns did he mow?
Answer:
7
Step-by-step explanation:
to edge a lawn =10.he edged 4 lawn =10multiplied by 4=40
2nd. total -40=180-40=140
3rd. when he mows 1 lawn he is paid 20 what about when he is paid 140=140 divided by 20 =7
Makoto mowed 7 lawns to earn $180.
Let's denote the number of lawns Makoto mowed as m. Since he edged 4 lawns, that part of the income is 4 times $10, which sums up to $40. The total income from mowing is then $20 times the number of lawns he mowed, which is m. The equation representing Makoto's earnings is:
20m + 40 = 180
Subtracting 40 from both sides gives us:
20m = 140
Dividing both sides by 20 to solve for m gives us:
m = 7
For every 6 children there is 1 adult so if there’s 66 children how many adults are there?
Answer:
11
Step-by-step explanation:
6 : 1
66 : X
X/66 = 1/6
X = 11
Write a division equation that has the solution x= 16
Answer:
2x ÷ 4 = 8
Step-by-step explanation:
2x ÷ 4 = 8
2x/4 = 8
2x = 32
x = 16
6. Use the image below to find the missing value.
Using the segment addition postulate, find the value of m.
AB = 4m - 15
BC = Sm - 6
AC = 15
Option C:
The value of m is 4.
Solution:
Given data:
AB = 4m – 15
BC = 5m –6
AC = 15
To find the value of m:
Using segment addition postulate,
AB + BC = AC
4m – 15 + 5m –6 = 15
Arrange the like terms together.
4m + 5m – 15 – 6 = 15
9m – 21 = 15
Add 21 on both sides of the equation,
9m = 36
Divide by 9 on both sides of the equation.
m = 4
The value of m is 4.
Option C is the correct answer.
Answer:
is 4
Step-by-step explanation:
i got it right on the test
how do i find the area of this stop sign using subtraction?
Answer:
745.12
Step-by-step explanation:
30 x 30 = 900 which is the sign if it were a square
then you subtract the four corner pieces
900 - 4([tex]\frac{1}{2}[/tex](8.8 x 8.8))
900 - 2(77.44)
900 - 154.88
= 745.12
A trapezoid was made by joining a pentagon and a triangle. the dimensions of the trapezoid are- height: 1 feet, bases 1/2 feet and 1 1/2 feet. the dimensions of the triangle are- height: 1/2 feet, base 1/2 feet. what is the area of the pentagon
Answer
3
Step-by-step explanation:
the formulas say it
evaluate the following 7 = 5x+y÷3-3y
Answer:
5x + 22y = 21
or
5x + 22y - 21 = 0
Step-by-step explanation:
evaluate 7 = 5x+y÷3-3y
7 = [5x + y]/[3-3y]
Don't forget 7 can also be expressed in form 7/1,
so the step to follow is using a cross multiplication technique.
we have ;
5x + y = 7(3 - 3y)
5x + y = 21 - 21y
Collect the like terms (note when the negative sign crosses over the equal to sign it changes to positive and the same thing applies to positive sign it changes to negative respectively.)
5x + y + 21y = 21
5x + 22y = 21
5x + 22y - 21 = 0
Which property is demonstrated in the equation 4×7×3 = 7×4×3
A)Symmetric
B)associative
C)property of zero
D)cummutative
Answer:
B) associative
Step-by-step explanation:
The associative property of multiplication says you can choose which pair of numbers to multiply first, so when every operation is multiplication, you can move parentheses without changing the answer.
The given equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. This is the property which states that the order in which numbers are multiplied or added does not affect the result.
Explanation:The equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. In mathematics, the Commutative Property refers to the fact that the order in which numbers are multiplied does not change the result of the multiplication. This is why we can rearrange the factors 4, 7, and 3 in any order and still get the same product.
For instance, we can express the commutative property of multiplication as a×b = b×a. So, in your example, the equation 4×7×3 = 7×4×3, is an application of this principle as you are simply rearranging the order of numbers being multiplied.
Please remember that this rule applies only to addition and multiplication, not subtraction or division.
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What is the volume of the pyramid?
km
Answer:
V=lwh/3
Step-by-step explanation:
(2x^3+4x^2-3)+(6x^3+4x-4)
Answer:
8x^3 + 4x^2 + 4x -7
Step-by-step explanation:
Add like terms.
Answer: everything is explained in the picture
Step-by-step explanation:
The length of a rectangle is 2 units more than the width. The area of the rectangle is 48 units. What is the width, in units, of the rectangle?
Final answer:
To find the width of a rectangle when the length is 2 units more than the width and the area is known to be 48 units, you can use algebraic equations to determine the width. In this case, the width of the rectangle is 6 units.
Explanation:
To find the width of the rectangle:
Let x be the width of the rectangle.
Since the length is 2 units more than the width, the length is x + 2.
Given that the area is 48 units, use the formula for the area of a rectangle: width x length = area. Therefore, x(x + 2) = 48.
Solve for x by setting up the equation: x^2 + 2x - 48 = 0.
Factor the quadratic equation: (x + 8)(x - 6) = 0.
Since the width cannot be negative, the width of the rectangle is 6 units.
The width of the rectangle is 6 units.
According to the question, the length is 2 units more than the width, so we can express the length as ( w + 2 ) units.
The area of a rectangle is given by the product of its length and width. Therefore, we can set up the following equation to represent the area of the rectangle:
[tex]\[ \text{Area} = \text{length} \times \text{width} \] \[ 48 = (w + 2) \times w \][/tex]
Expanding the right side of the equation, we get:
[tex]\[ 48 = w^2 + 2w \][/tex]
To find the value of w, we need to solve the quadratic equation. Let's rearrange the equation to set it equal to zero:
[tex]\[ w^2 + 2w - 48 = 0 \][/tex]
Now, we can factor this quadratic equation:
[tex]\[ (w + 8)(w - 6) = 0 \][/tex]
Setting each factor equal to zero gives us two possible solutions for w:
[tex]\[ w + 8 = 0 \quad \text{or} \quad w - 6 = 0 \][/tex]
Solving for w, we get:
[tex]\[ w = -8 \quad \text{or} \quad w = 6 \][/tex]
Since the width of a rectangle cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is:
[tex]\[ w = 6 \text{ units} \][/tex]
PAGE 15
1) Describe the relationship shown in the table of values.
X 5 4 0
Y 8 9 13
A Relation only.
B Function only.
C Both relation and function.
D Neither relation nor function.
Answer:
C Both relation and function.
Step-by-step explanation:
This would pass the vertical line test so it is both a relation and a function
ava bought 6 packages of tulip bulbs and 12 bags of dafodill bulbs for a total of $198 grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs
Answer:
Answer:
Step-by-step explanation:
Let x represent the cost of one package of tulip bulbs.
Let y represent the cost of one bag of daffodil bulbs.
Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that
6x + 12y = 198- - - - - - - - - - - - -1
Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that
14x + 12y = 254- - - - - - - - - - - - 2
Subtracting equation 2 from equation 1, it becomes
- 8x = - 56
x = - 56/-8
x = 7
Substituting x = 7 into equation 1, it becomes
6 × 7 + 12y = 198
42 + 12y = 198
12y = 198 - 42
12y = 156
y = 156/12
y = 13
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Step-by-step explanation:
Answer:
Step-by-step explanation:
Let x represent the cost of one package of tulip bulbs.
Let y represent the cost of one bag of daffodil bulbs.
Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that
6x + 12y = 198- - - - - - - - - - - - -1
Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that
14x + 12y = 254- - - - - - - - - - - - 2
Subtracting equation 2 from equation 1, it becomes
- 8x = - 56
x = - 56/-8
x = 7
Substituting x = 7 into equation 1, it becomes
6 × 7 + 12y = 198
42 + 12y = 198
12y = 198 - 42
12y = 156
y = 156/12
y = 13
4
answers left
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Ask your own homework questions
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A map has a scale of 1 inch =35 miles what is the distance if the distance on the map is 3.5
Answer: 122.5 Miles.
Step-by-step explanation: This is because if you multiply 35 miles by 3.5 inches, you get 122.5 miles.
Hope this helps!
Find two numbers, if
Their sum is − 1/3 and their difference is 18
Let the two numbers be [tex]x,y[/tex].
We have
[tex]\begin{cases}x+y=-\frac{1}{3}\\x-y=18\end{cases}[/tex]
From the second equation, we derive [tex]x=18+y[/tex]
Plugging this value in the first equation, we have
[tex]18+y+y=-\dfrac{1}{3} \iff 2y=-\dfrac{1}{3}-18\iff 2y=-\dfrac{55}{3} \iff y=-\dfrac{55}{6}[/tex]
And we derive
[tex]x=18+y=18-\dfrac{55}{6}=\dfrac{53}{6}[/tex]
Answer:
The two numbers are: -9.17 and 8.83
Step-by-step explanation:
Let the two numbers represent 'x' and 'y'
Their sum is − 1/3 ==> x + y = -1/3 .................(eqn 1)
Their difference is 18 ==> x − y = 18 ....................(eqn 2)
from equation 2,
x = 18 + y
therefore, substitute for 'x' in (eqn 1) to get y
(18+y) + y = -1/3
18 + 2y = -1/3
2y = -1/3 − 18
2y = -[tex]18\frac{1}{3}[/tex]
2y = - 55/3
y = (-55/3) / 2
y = -55/3 x 1/2
y = -55/6 = -9.17
Substitute for 'y' in either equation
picking (eqn 2)
x − (-9.17) = 18
x + 9.17 = 18
x = 18 − 9.17
x = 8.83