The original price before a 25% discount, when the sales price is $40, is calculated as $40 divided by 0.75, resulting in $53.33.
Explanation:To find the original price before a 25% discount, we can set up the equation where original price minus 25% of the original price equals the sales price. Let's call the original price 'P'. Then 0.25P is the amount discounted. The equation is P - 0.25P = $40. This simplifies to 0.75P = $40. To find P, divide both sides by 0.75, giving us P = $40 / 0.75. So, the original price P = $53.33.
The original price is $53.33.
If you have the sales price and the percent of discount, you can calculate the original price using the following steps:
Let P be the original price.Since the discount is 25%, you pay 75% of the original price.We know that 75% of the original price is $40.To find the original price, we set up the equation:
0.75P = 40
Next, solve for P by dividing both sides by 0.75:
P = 40 / 0.75
P = $53.33
So, the original price of the item was $53.33 before the 25% discount was applied.
The jones family drove 1,200 miles in 3 days on the first day they traveled 1/4 of the total distance how many miles did they travel the first day
Answer:
They drove 300 miles on the first day
Step-by-step explanation:
They drove 1200 miles
They drove 1/4 on the first day
1200 * 1/4 = 300 miles
They drove 300 miles on the first day
Terry bakes bread. He uses the equation 3x-18=y to find the profit, y , in dollars. He paid $18 for supplies and earns $3 for each loaf he sells. What does x represent?
Answer:
The number of loaves sold
Step-by-step explanation:
What is the diameter of a circle with a circumference of 66 ft? Use 22/7 for pie
Answer:
21 ft
Step-by-step explanation:
Diameter = Circumference/Pi
Diameter = 66/(22/7)
Diameter = 21
Jill bought a 9 pound bag of cat food for her cats. She had used 4/5 of the bag. How many pounds has she used?
A. 9 4/5
B. 8 4/5
C. 8 3/5
D. 7 1/5
Answer:
D. 7 1/5
Step-by-step explanation:
We would calculate the amount of pounds she used by multiplying the total amount of cat food = 9 to the amount she has used = 4/5
= [tex]9 * \frac{4}{5}[/tex]
= [tex]\frac{36}{5}[/tex]
= [tex]7 \frac{1}{5}[/tex]
(An image is attached for the calculation)
Julie drew a picture of her rectangular garden,. In her picture,the length of her garden is 7/8 inches and the width is 3/4 inches. She thinks the area of her picture is 21/32 inches. do you agree or disagree with Julie ? JUSTIFY YOUR ANSWER.(Area=Length X Width)
Answer:
21/32 square inches.
Step-by-step explanation:
The area of a rectangle = length x width
The area of her picture = length x widht
= 7/8 x 3/4
= 21/32
The area of her picture is 21/32 square inches.
Yes, I agree the area of the picture is 21/32 square inches.
The area must be in square inches. So she need to specify it.
Thank you.
What are the x–coordinates of the three points where the graphs of the equations intersect? x3 – 10x = x2 – 6
Answer:
(- 3, 0), (2 + [tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)
Step-by-step explanation:
rearrange the equation equating to zero
x³ - x² - 10x + 6 = 0
note that when x = - 3
(- 3)³ - (- 3)² - 10(- 3) + 6 = - 27 - 9 + 30 + 6 = 0, hence
x = - 3 is a root and (x + 3) is a factor of the polynomial
dividing x³ - x² - 10x + 6 ÷ (x + 3) gives
(x + 3)(x² - 4x + 2) = 0
solve x² - 4x + 2 = 0 using the quadratic formula
with a = 1, b= - 4 and c = 2
x = (4 ± [tex]\sqrt{16-(4(1)(2)}[/tex])/ 2
= (4 ± [tex]\sqrt{8}[/tex]) / 2
= (4 ± 2[tex]\sqrt{2}[/tex]) / 2
= 2 ±[tex]\sqrt{2}[/tex], hence
x = 2 + [tex]\sqrt{2}[/tex], x = 2 - [tex]\sqrt{2}[/tex]
intersect at (- 3, 0), (2 +[tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)
Answer: [tex]\bold{x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2} }}[/tex]
Step-by-step explanation:
First, move all terms to one side with zero on the other side so the Zero Product Property can be applied:
x³ - x² - 10x + 6 = 0 Possible rational roots are: ±{1, 2, 3, 6}
Use synthetic division to find one of the roots. Let's try x = -3
-3 | 1 -1 -10 6
| ↓ -3 12 -6
1 -4 2 0 ← remainder is zero, so x = -3 is a root/intercept
Next, evaluate the reduced polynomial x² - 4x + 2 = 0
This can not be factored so use the quadratic formula to find the remaining roots/intercepts: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 1, b = -4, c = 2
[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)}}{2(1)}[/tex]
[tex]=\dfrac{4\pm\sqrt{16-8}}{2}[/tex]
[tex]=\dfrac{4\pm\sqrt{8}}{2}[/tex]
[tex]=\dfrac{4\pm2\sqrt{2}}{2}[/tex]
[tex]=2\pm\sqrt{2}[/tex]
[tex]x=2+\sqrt{2}\qquad x=2-\sqrt{2}[/tex]
Intercepts are [tex]x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2}}[/tex]
what is 3w - 60 if the perimiter is 449 yards?
Answer:
sooo sorry im in the third grade and notised that this is not my onw level but i really thought i could help u sorry ;(
Step-by-step explanation:
Molly ran 2/3 of a mile in 8 minutes. If Molly runs at the same speed, how long will it take her to run one mile
Answer:
It will take 12 minutes
Step-by-step explanation:
We can use ratio's to solve the problem
2/3 mile 1 miles
------------ = ------------------
8 minutes x minutes
Using cross products
2/3 * x = 8*1
Multiply each side by 3/2 to isolate x
3/2 * 2/3 x = 3/2 * 8
x = 12
Given that lines a and b are parallel, what angles formed on line b when cut by the transversal are congruent with ∠3?
A) ∠5 and ∠6
B) ∠5 and ∠7
C) ∠6 and ∠7
D) ∠6 and ∠8
Answer:
C) ∠6 and ∠7
Step-by-step explanation:
We have been given that lines a and b are parallel. We are asked to find the angle on line b that will be congruent to angle 3.
We can see that angle 3 is under the line a and on the left side of transversal.
We know that the corresponding angles and alternate interior angles formed by two parallel lines are equal.
We can see that angle 7 corresponds to angle 3 and angle 6 is alternate interior angle of angle 3.
Therefore, angle 7 and angle 6 will be congruent with angle 3 and option C is the correct choice.
Jeff Jones earns $1,200 per week. He's married and claims four withholding allowances. The social security rate is 6.2% on $118,500, and Medicare is 1.45%. Each paycheck, his employer also deducts $42.50 for health insurance. What's his net pay?
Jeff's net pay is $1,065.70 per week.
To calculate Jeff Jones's net pay, we need to consider several deductions from his gross pay.
1. Gross Pay: Jeff earns $1,200 per week.
2. Social Security Deduction: Social Security tax is 6.2% of the first $118,500 of earnings. Jeff's earnings are below this threshold, so his Social Security deduction is 6.2% of his gross pay.
Social Security deduction = 6.2% of $1,200 = 0.062 * $1,200 = $74.40
3. Medicare Deduction: Medicare tax is 1.45% of all earnings.
Medicare deduction = 1.45% of $1,200 = 0.0145 * $1,200 = $17.40
4. Health Insurance Deduction: $42.50 is deducted for health insurance.
5. Total Deductions: Add up all deductions.
Total deductions = Social Security deduction + Medicare deduction + Health insurance deduction
= $74.40 + $17.40 + $42.50
= $134.30
6. Net Pay: Subtract total deductions from gross pay.
Net pay = Gross pay - Total deductions
= $1,200 - $134.30
= $1,065.70
Therefore, Jeff's net pay is $1,065.70 per week.
18 × 106) + (5 × 104)
Answer:
2,428
Step-by-step explanation:
(18 × 106) + (5 × 104)
1908 + 520
= 2,428
I'm really sorry if this isn't what you meant... but if it is then... Hope this helps you! :)
5y - 10 = -25
ok try this one buster.
Answer:
Y= -3
Step-by-step explanation:
5y-10=-25 Add 10 on both sides
5y=-15 Divide by 5 on both sides
y=-3
what is the value of the lower quartile?
a.0
b.8
c.6
d.2
thank you!
Answer:
D
Step-by-step explanation:
From the box- plot the left hand side of the box represents the lower quartile
that is [tex]Q_{1}[/tex] = 2 → D
A moving walkway at an airport moves at a pace of 1.75 feet per second. If you stand on the walkway as it moves, how long will it take to transport you 280 feet? CLEAR CHECK 160 seconds 278.25 seconds 490 seconds 625 seconds
Answer:
2 minutes 40 sec
Step-by-step explanation:
Recall that distance = rate times time.
Thus, time = distance / rate.
Here,
time = 280 ft / (1.75 ft/sec) = 160 sec, or 2 minutes 40 sec
To calculate the time it takes to travel 280 feet on a moving walkway at an airport moving at a pace of 1.75 feet per second, we use the formula time = distance/pace. This equates to approximately 160 seconds.
Explanation:The question is asking about the time it takes to transport someone along a distance of 280 feet by a moving walkway in an airport, given that the pace of the walkway is 1.75 feet per second. To answer this, you use the formula of time = distance/pace. So we have time = 280 feet / 1.75 feet per second. This calculation will give you the answer in seconds. When you do this calculation, you will find that it takes approximately 160 seconds to cover that distance on the moving walkway.
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Four friends went to a local amusement park. Three of the friends bought ride tickets for x dollars, plus a game pass for $10. The other friend bought just a ride ticket. Write and simplify an expression showing the amount of total money spent.
Answer:
4X + 30 = TOTAL AMOUNT OF MONEY
Step-by-step explanation:
All of them bought a ride ticket (that explains the 4x)
3 of them also bought a game pass thet costs $10 each. That explains the 30
going deeper: If the total amount of money was $70
The tickets would've costed $10 each.
Look:
4x + $30 = $70
4x = 70 - 30
4x = 40
x = 40/4
x =$10
Three bricklayers from the Emerald Construction Company are working on the new addition to an office building. The first bricklayer laid 8,792 bricks; the second laid 9,491 bricks; and the third laid 9,629 bricks this week. How many bricks did they lay in all?
This question is asking us to find the sum.
8,792 + 9,491 + 9,629 = 27, 912
They lay 27, 912 bricks in all.
Hope helps!-Aparri
Answer: Three bricklayers from the Emerald Construction Company are working on the new addition to an office building. The first bricklayer laid 8,792 bricks; the second laid 9,491 bricks; and the third laid 9,629 bricks this week. They lay a total of 8,792 + 9,491 + 9,629 = 27, 912 bricks.
Step-by-step explanation:
First Brick Layer Laid: 8,792
Second Brick Layer Laid: 9,491
and lastly the
Third Brick Layer Laid 9,629
Now if you take all the bricks that each Brick layer has laid and add them all up (break down)
8,792+9,491+9,629= 27,912 bricks laid in all
that's the break down I hope this helps you all
plz help me with these two questions :)
will give brainliest
What is the simplified form of 72x16/50x36 ? Assume x ≠ 0.
Answer:
72 / 50 = 36/25
x^16 / x^36
= x^-20
Answer:
[tex]\frac{36}{25x^{20} }[/tex]
Step-by-step explanation:
In order to simplify this function, we have to divide by the maximum common divisor:
[tex]\frac{72x^{16} }{50x^{36} }\\ 72/2=36\\50/2=25\\\frac{36}{25} \\(x^{16} )(x^{-36})=x^{-20}=\frac{1}{x^{20} } \\\frac{36}{25x^{20} }[/tex]
By doing this you can simplify the function into the simplified form.
The Science Club went on a two-day field trip. The first day the members paid $30 for transportation plus $12 per ticket to the planetarium. The second day they paid $90 for transportation plus $9 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club.
Answer: Total: 30 + 20y + 85 + 17y This is the not simplified version.
37y+115 This is the simplified version. Hope this helps
Step-by-step explanation: I really don't know the steps.?
Mr. Jensen is a salesperson for an insurance company. His monthly paycheck includes a base salary of $2,175 and a commission of $250 for each policy he sells. Write an equation, in slope-intercept form, that represents the total amount, y, in dollars, of Mr. Jensen's paycheck in a month when he sells x policies. Do not include dollar signs in the equation.
Answer:
y = 250x + 2175
Step-by-step explanation:
Mr. Jensen month pay = 2175
Commission per policy = 250
Let "x" be the number of policy he sells and "y" is the total paycheck including the commission.
y = 250x + 2175
Thank you.
Answer:
y = 250x + 2175
Step-by-step explanation:
The coordinates of the vertices of JKL are J(-5, -1), K(0, 1) , and L(2, -5). Which statement correctly describes whether JKL is a right triangle?
Answer:
It is NOT a right triangle.
Step-by-step explanation:
You must figure out the slopes of the segments of the triangle to see if it is a right triangle. If they are perpendicular (meaning the slopes are negative reciprocals of each other), they form a right angle, making it a right triangle.
[tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex] This formula finds slope using two points.
Let's figure out the slope of JK.
(-1-1)/(-5-0) = m
Simplify.
-2/-5 = m
A negative divided by a negative makes a positive.
2/5 = m
Now LK.
(-5-1)/(2-0) = m
Simplify.
-6/2 = m
Divide.
-3/1 = m
Now JL.
(-1+5)/(-5-2) = m
Simplify.
4/-3 = m
None of these slopes are negative reciprocals of each other, thus deeming it not a right triangle.
Given: ABCD is a trapezoid, AB=CD, MN is a midsegment, MN=30, BC=17, AB=26 Find: m∠A, m∠B, m∠C, and m∠D
Answer:
m∠A=m∠D=60°, m∠B=m∠C=120°
Step-by-step explanation:
Consider isosceles trapezoid ABCD with midsegment MN. Draw two trapezoid heights BF and CE. Then quadrilateral FBCE is rectangle and EF=BC=17 units.
By the trapezoid midsegment theorem,
[tex]MN=\dfrac{AD+BC}{2},\\ \\30=\dfrac{AD+17}{2},\\ \\60=AD+17,\\ \\AD=60-17=43\ units.[/tex]
Segments FA and ED are equal to [tex]\dfrac{43-17}{2}=13\ units.[/tex]
In right triangle ABF, the hypotenuse AB is twice greater than the leg FA, then m∠FBA=30°.
m∠B=m∠FBA+m∠CBF=30°+90°=120°.
In isosceles trapezoid
m∠B=m∠C=120°,
m∠A=m∠D and m∠A=180°-m∠B=180°-120°=60°=m∠D.
In a trapezoid with equal bases and a midsegment, the angle measures of the trapezoid can be determined using the properties of the figure. In this case, the angle measures are 90 degrees for each angle.
Explanation:In a trapezoid ABCD, the midsegment MN is parallel to the bases AB and CD, and its length is equal to the average of the lengths of the bases. Given that AB = 26, CD = 26, and MN = 30, we can set up the equation: MN = (AB + CD) / 2. Substituting the given values, we get 30 = (26 + 26) / 2. Solving for the angle measures, we can use the fact that the opposite angles in a trapezoid are congruent. So, m∠A = m∠C and m∠B = m∠D. Since the sum of the interior angles of a trapezoid is always 360 degrees, we can use the equation: m∠A + m∠B + m∠C + m∠D = 360. Substituting the angle measures we found, we get 2(m∠A) + 2(m∠B) = 360. Solving for the angle measures, we get m∠A = m∠C = 90 degrees and m∠B = m∠D = 90 degrees.
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How would u convert 5 feet 6 inches in inches
1 feet is 12 inches.
We have 5 feet and 6 inches. First, let's convert the feet to inches. 5 times 12 is 60, so 5 feet is 60 inches.
Now add 60 inches to the 6 inches that we didn't mention. 60 plus 6 is 66. Thus, 5 feet and 6 inches is 66 inches.
Answer:
The answer is 66
Step-by-step explanation: 1 foot is 12 inches so you do 12 times 5 and get 60 and then add the next 6 inches... :)
multiplying integers
3(-7)
Answer:
-21
Step-by-step explanation:
3(-7)
3*7 =21
A positive times a negative is a negative
-21
Answer:
3x-7=21 ( i think )
Step-by-step explanation:
when you have a parenthesis beside a number you always multiply. A negative times a positive is a negative,
What is the pattern and slope ? Please answer !!
Answer:
The slope is 3
Step-by-step explanation:
To find the slope we can use the formula
m = (y2-y1)/ (x2-x1)
Using the points (5,14) and (-5,-16)
m= (-16-14)/ (-5-5)
= -30/-10
= 3
Hello! Can someone please help me with this? There are four answers in total. :D
Problem 1
a) y = 8 and c) x = 2 are perpendicular lines to one another. The first is horizontal and the second is vertical.
The other two lines are not perpendicular because their slopes (1/8 and 8) do not multiply to -1. This rule only applies to lines that are neither horizontal nor vertical.
Answers: A and C.
============================================
Problem 2
Equations b) y = (-1/2)x - 4 and c) y-4 = 2(x+3) are perpendicular. Equation B has a slope of -1/2, while equation C has a slope of 2. Those two values multiply to -1. One slope is the negative reciprocal of the other. It might help to think of 2 as 2/1.
The other two equations are not perpendicular to each other, nor are they perpendicular to B or C. Equation A has a slope of 0. Equation D has a slope of -2.
Answers: B and C
Given cos a= 3/5, sin B = 5/13 and a and B are first quadrant angles find cos(a + B)
A. 1/3
B. 16/65
C. -33/65
Please explain
Answer:
Option B is correct.
Value of cos(a+B) is, [tex]\frac{16}{65}[/tex]
Step-by-step explanation:
Using the formula:
[tex]\cos(a+B) = \cos a \cos B -\sin a \sin B[/tex]
Given the values:
[tex]\cos a = \frac{3}{5}[/tex] and [tex]\sin B = \frac{5}{13}[/tex]
Using trigonometric identity:
[tex]\sin^2 \theta + \cos^2 \theta =1[/tex]
or
[tex]\sin \theta = \sqrt{1-\cos^2 \theta}[/tex]
or
[tex]\cos \theta = \sqrt{1-\sin^2 \theta}[/tex]
Find the value of sin a and cos B;
Using trigonometric identity:
[tex]\sin a = \sqrt{1-\cos^2 a}[/tex]
[tex]\sin a = \sqrt{1-(\frac{3}{5})^2}[/tex] = [tex]\sqrt{1-\frac{9}{25}} = \sqrt{\frac{25-9}{25}}=\sqrt{\frac{16}{25} } =\frac{4}{5}[/tex]
Similarly;
[tex]\cos B = \sqrt{1-\sin^2 B}[/tex]
[tex]\cos B = \sqrt{1-(\frac{5}{13})^2}[/tex] = [tex]\sqrt{1-\frac{25}{169}} = \sqrt{\frac{169-25}{169}}=\sqrt{\frac{144}{169} } =\frac{12}{13}[/tex]
Substitute these given values equation [1] we have;
[tex]\cos(a+B) =\frac{3}{5} \cdot \frac{12}{13}-\frac{4}{5} \cdot \frac{5}{13}[/tex]
[tex]\cos(a+B) =\frac{36}{65}-\frac{20}{65}[/tex]
then;
[tex]\cos(a+B) =\frac{36-20}{65}=\frac{16}{65}[/tex]
Since, the angles a and B are in first quadrant angles therefore the value of cos(a+B) is, [tex]\frac{16}{65}[/tex]
To find cos(a + B), use the formula cos(a + B) = cos(a)cos(B) - sin(a)sin(B). Substitute the given values of cos(a) = 3/5 and sin(B) = 5/13, and solve for cos(B) using the Pythagorean identity. Then substitute all the values into the formula and simplify to find cos(a + B) = 16/65.
Explanation:To find cos(a + B), we can use the formula:
cos(a + B) = cos(a)cos(B) - sin(a)sin(B)
Given that cos(a) = 3/5 and sin(B) = 5/13, we can substitute these values into the formula:
cos(a + B) = (3/5)(cos(B)) - (sin(a))(5/13)
To find cos(B), we can use the Pythagorean identity:
cos²(B) + sin²(B) = 1
Substituting the given value of sin(B), we can solve for cos(B):
cos(B) = √(1 - (5/13)²)
Now we can substitute the values of cos(a), sin(B), and cos(B) into the formula for cos(a + B):
cos(a + B) = (3/5)(√(1 - (5/13)²))) - (5/13)(5/13)
Simplifying this expression gives us the final answer: cos(a + B) = 16/65.
20 POINTS ANSWER SOON PLEASE
Which table represents a proportional situation?
x f(x)
–1 –3
0 0
1 3
4 12
x f(x)
–2 2
0 4
2 6
3 7
x f(x)
–1 –5
0 –2
1 1
2 4
x f(x)
–1 5
0 1
1 –1
2 –3
Answer:
78
Step-by-step explanation:
Is the system of equations consistent, consistent and coincident, or inconsistent? y=3x+4y=3x+3 Select the correct answer from the drop-down menu.
Answer: Inconsistent
Step-by-step explanation:
y = 3x + 4 → m = 3, b = 4
y = 3x + 3 → m = 3, b = 3
These equations have the same slope but different y-intercepts so they are parallel lines which means they will never intersect.
NOTES
one solution: consistent & independent lines crossinfinite solutions: consistent & dependent same lineno solution: inconsistent parallel linesAnswer:
Inconsistent
Step-by-step explanation:
What is the pattern in this sequence?
1,9,17,25,33,...
Select from the drop down box to correctly complete the rule.
First Box
Add
Multiply by
Subtract
Divide by
Second box
9
8
-5
-9
Choose one from each box!
2. The ordered pairs model an exponential growth function
{(-1, 21.875), (0,35), (1,56), (2, 89.6)}
what is the function equation?
Enter your answer in the box
F(x)=
Answer in #1 it ads up by 8
Number 1 is Add by 8
& I'm not sure about number 2