Final answer:
The algebraic expression for the problem is '8n - 20 = 3n + 80', which simplifies to 'n = 20'. Therefore, the number in question is 20.
Explanation:
The question presents a classic algebra problem where we have to find the value of a variable that satisfies a given condition. Specifically, this problem states:
"If 8 times a number is decreased by 20, the result is the same as 3 times the number increased by 80."
To solve this, we'll convert the words into an algebraic equation and solve for the number. Let's use 'n' to represent the number:
8n - 20 = 3n + 80This equation tells us that when you multiply the number by 8 and subtract 20, it's equal to the result of multiplying the number by 3 and adding 80. To find 'n', we combine like terms and solve:
8n - 3n = 80 + 205n = 100n = 100 / 5n = 20Thus, the number we're looking for is 20.
Graph y+6=4/5(x+3) using the point and slope given in the equation. Use the line tool and select two points on the line.
Answer:
Look at pic...
The points were (-3,-6) and (2,-2)
Step-by-step explanation:
You could just use desmos graphing calculator
The equation of a line is a form of representing the set of points, which form a line in a coordinate system.
The two points on the line are (0, -3) and (1, -11/5).
What is equation of a line?The equation of a line is a form of representing the set of points, which form a line in a coordinate system.
The general equation of a straight line is given as:
y = mx + c,
where m = slope of the line and c = y-intercept.
We have,
y + 6 = 4/5 ( x + 3 )
Subtract 6 on both sides.
y = 4/5 ( x + 3 ) - 6
y = (4/5)x + 4/5 x 3 - 6
y = (4/5)x + 12/5 - 6
y = (4/5)x + (12 - 30)/6
y = (4/5)x - 3
The y-intercept is at -3.
We have a point as (0, -3).
For x = 1,
y = (4/5) x 1 - 3
y = 4/5 - 3
y = (4 - 15) / 5 = -11/5
The other point is (1, -11/5)
Thus,
The two points on the line are (0, -3) and (1, -11/5).
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Perimeter of the rectangular playing field is 470 yards. the length of the field is 5 yards less than triple the width, what are the dimensions of the playing field
Jane has a 5x7 inch photograph that she wants enlarged to a 10x14inch photograph. What is the scale factor from the original photograph to the enlarged photograph?
List the next three terms in the following sequence: 1, 2, 4, 8, 16, 32,... a. 48, 80, 128 b. 64, 96, 160 c. 64, 128, 256 d. 46, 92, 184
The graph of a proportional relationship contains the point (8, 4).
What is the corresponding equation?
Enter your answer as a fraction in simplest form
Heather and her family are going to the grand opening of a new amusement park. There is a special price on tickets this weekend. Tickets cost $42 each. This is 70% of the cost of a regular price ticket. What is the cost of a regular price ticket? Please explain! thanks!
David cycles x km in 3 hours. if he maintains the same average speed, how far can he cycle in 12y minutes
David can cycle [tex]\( \frac{xy}{15} \)[/tex] kilometers in 12y minutes if he maintains the same average speed.
To find out how far David can cycle in 12y minutes, we first need to convert the time from minutes to hours, since David's speed is given in kilometers per hour.
Since there are 60 minutes in an hour, we can convert 12y minutes to hours by dividing by 60:
[tex]\[ \text{12y minutes} = \frac{12y}{60} = \frac{y}{5} \text{ hours} \][/tex]
Now, we know that David cycles x kilometers in 3 hours, so we can find his average speed:
[tex]\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} \]\[ \text{Average speed} = \frac{x \text{ km}}{3 \text{ hours}} \][/tex]
Now, using the average speed, we can find the distance David can cycle in [tex]\( \frac{y}{5} \)[/tex] hours:
[tex]\[ \text{Distance} = \text{Average speed} \times \text{Time} \]\[ \text{Distance} = \left( \frac{x}{3} \right) \times \left( \frac{y}{5} \right) \]\[ \text{Distance} = \frac{xy}{15} \][/tex]
if your average stride length is 2.6 feet how many strides will it take you to walk to grandparents house
The distance from your house to your grandparents house is 3.67 miles or 19377.6 ft.
So the total number of strides needed would be:
strides needed = 19377.6 ft / (2.6 ft / stride)
strides needed = 7,452.92 = 7,453 strides
As children grow, dosages for medications gradually approach those for adults. Clark’s rule is often used to determine the correct dosage for children.
Child’s dose = Adult dose x (Weight of child in pounds)/(150 pounds)
What dosage should be administered to a child weighing 28 pounds if the adult dose of a certain drug is 80 milligrams? Round your answer to the nearest whole milligram.
How much would a child have to weigh to receive the adult dosage? Explain why your answer is reasonable.
what is 7,925 divided by 72?
Please help with this question thank you!
Can you show me the steps for this equation and answerF(x)=(x-3)^2+2
Sue spent $40 on one pair of shoes and earned $35 baking cookies. Write an expression using positive and/or negative integers to represent this situation. Evaluate the expression and interpret what it means.
Solve the compound inequality shown below. Show steps.
-4< 3x -1<5
A bakery offers a sale price of $2.55 for 4 muffins. What is the price per dozen? The price per dozen muffins is $ .
Final answer:
To find the price per dozen, divide the sale price of $2.55 by 4 to get the price per muffin, then multiply by 12. The price per dozen muffins is $7.65.
Explanation:
To calculate the price per dozen muffins at the bakery when the sale price is $2.55 for 4 muffins, you first need to determine the price of one muffin. You can do this by dividing the sale price by the number of muffins in the offer:
$2.55 ÷ 4 = $0.6375 per muffin.
Next, because a dozen consists of 12 items, you would find the price per dozen by multiplying the price per muffin by 12:
$0.6375 × 12 = $7.65
Therefore, the price per dozen muffins is $7.65.
What are the x-intercepts of the graph of the function below? y=x^2+4x-32
Answer:
Option B is correct.
Step-by-step explanation:
Given Function is,
y = x² + 4x - 32
X-intercepts of the graph of given function is the solution of the equation when y is equal to 0 is substituted.
y = 0
x² + 4x - 32 = 0
x² + 8x - 4x - 32 = 0
x ( x + 8 ) - 4 ( x + 8 ) = 0
( x + 8 ) ( x - 4 ) = 0
x + 8 = 0 and x - 4 = 0
x = -8 and x = 4
So x-intercept are ( -8 , 0 ) and ( 4 , 0 )
Therefore, Option B is correct.
What is the remainder when the polynomial 8x^2+4x−3 is divided by 2x−1?
Answer:
1
Step-by-step explanation:
Given: A polynomial [tex]8x^{2} +4x-3[/tex] is divided by another polynomial [tex]2x-1[/tex]
To find: Remainder when [tex]8x^{2} +4x-3[/tex] is divided by [tex]2x-1[/tex]
Solution:
To find the remainder when [tex]8x^{2} +4x-3[/tex] is divided by [tex]2x-1[/tex]
First, equate [tex]2x-1[/tex] with 0.
Now, [tex]2x-1=0[/tex]
[tex]\implies2x=1[/tex]
[tex]\implies x=\frac{1}{2}[/tex]
Now, to find the remainder put [tex]x=\frac{1}{2}[/tex] in [tex]8x^{2} +4x-3[/tex]
So, we have
[tex]8\times(\frac{1}{2})^{2}+4(\frac{1}{2} )-3[/tex]
[tex]=8\times\frac{1}{4} +2-3[/tex]
[tex]=2+2-3[/tex]
[tex]=4-3[/tex]
[tex]=1[/tex]
Hence, the remainder is 1.
how do you graph a function
Mr. Rose spent $63 for a sport jacket and a pair of slacks. If the jacket cost $33 more than the slacks, how much did he pay for each?
Which system of equations represents the word problem if j is the jacket price and s is the price of the slacks?
j + s = 63 and s - j = 33
j + s = 63 and j - s = 33
js = 63 andj/s = 33
Answer:
The system of the equations is: j+s=63 and j-s=33
The Jackets price is j=48
The slacks prices is s=15
Step-by-step explanation:
You know for the problem that:
j+s=65
And
j= s+33; from this equation you get j-s=33
Then you replace j "j=s+33" in the first equation:
(s+33)+s=63
2s+33=63
2s=63-33
s=(63-33)/2
s=15
and you know that: j=s+33
Then, j=15+33=48
and j+s=63
48+15=63
96 points here, having to ask same question again - please help a brother out.
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation. Show your work.
1. cot x sec^4 x = cot x + 2 tan x + tan^3 x
2. (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos^2 x
3. 1 + sec^2 x sin^2 x = sec^2 x
4. ((sin x)/(1-cos x)) + ((sin x)/(1+cos x))=2csc x
5. - tan^2 x + sec^2x = 1
the equation is - tan2 x + sec2 x = 1.
Left hand side identity : - tan2 x + sec2 x.
Trigonometric function : tan x = sin x / cos x,
Reciprocal identity : sec x = 1/cos x.
- tan2 x + sec2 x = - (sin x/cos x)2 + (1/cos x)2
= - sin2 x/cos2 x + 1/cos2 x
= (1 - sin2 x)/cos2 x
Pythagorean identity : sin2 x + cos2 x = 1 .
= cos2 x / cos2 x
= 1
135in.=___ft ___ in.
convert
1 foot = 12 inches
135 / 12 = 11.25 feet 0.25 feet = 0.25 * 12 = 3 inches
answer is: 11 feet 3 inches
The length to width ratio of a wide-screen tv is 16:9. if a tv is 30 inches long, how wide is it?
Shelly can cut a lawn with a riding mower in 22 hours less time than it takes william to cut the lawn with a push mower. if they can cut the lawn in 33 hours working together find how long to the nearest tenth of an hour it takes for william to cut the lawn alone.
it is not d it is c i just took the test
Bananas cost $0.70 each, and peaches cost $0.90 each. If you want to spend exactly $21.20 at the stand and you need to buy 11 bananas, how many peaches can you buy? Write an equation in standard form modeling this situation then see how many peaches you can buy. Let be represent the number of bananas you buy and p represent the number of peaches you buy. [2 points]
Standard Form Equation: _______________________
p = ________
Ian wants to promote his band on the internet. Site a offers website hosting for $4.95 per month with a $49.99 startup fee. Site b offers website hosting for $9.95 per month with no startup fee. Write and solve an inequality to determine how many months lan could have his wedsite on site b and still keep his total cost less than site a
Ian could have his website on site B for less than 10 months for it to be cheaper than hosting on site A.
Explanation:To solve this question, we need to find when the costs between site a and site b equal each other. Since site a charges $4.95 per month plus a $49.99 startup fee, the cost of site a can be modelled by the equation: 4.95x + 49.99. Site b charges $9.95 per month with no startup fee, so its cost can be modelled by the equation 9.95x. We can now set up the inequality as follows:
4.95x + 49.99 > 9.95x
To solve for x, we will subtract 4.95x from both sides of the inequality, getting 49.99 > 5x. Finally, we divide each side by 5 to solve for x, resulting in x < 10. So Ian could have his website on site b for less than 10 months and still keep his total cost less than site a.
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Which is bigger, 978 centimeters or 12 meters?
The sum of three consecutive integers is 16 more than 2 times the smallest integer. find the integers
A store owner ordered 132 boxes of erasers. There are 8 erasers in each box. Use place value and expanded form to write an expression that shows how to multiply 8 x 132.
Simplify (4x3+ 13x − 7) − (6x2+ 9x + 2). −2x2+ 4x − 9 −2x2+ 22x − 5 4x3− 6x2+ 4x − 9 4x3− 6x2+ 22x − 5