Answer:
Length = 8 inches
Width = 15 inches
Step-by-step explanation:
A rectangular painting has a diagonal measure of 17 inches and an area of 120 square inches. Use the formula for the area of a rectangle and the Pythagorean Theorem to find the length and width of the painting.
Let:
a = length of painting
b = width of painting
Area of painting = 120 = ab
Pythagorean Theorem says
a² + b² = Diagonal²
a² + b²= 17²
[120 =ab means b= 120/a]
a² + (120/a)² = 17²
Multiply through by a²
a⁴ + 14400 = 289
z² + 14400 = 289z [for now, substitute z for a²]
z² - 289z + 14400 = 0
z² - 64z - 225z + 14400 = 0
z(z - 64) -225(z - 64) = 0
(z - 64)(z - 225) = 0
z - 64 = 0
z = 64
z - 225 = 0
z = 225
Note that:
z for a²
Hence:
a² = 64
a = √64
a = 8 inches
The same applies for b
b² = 225
b = √225
b = 15 inches
If (x^2 – 4) ÷ (x + 2) = x -2, which polynomial should fill in the blank below?
(x + 2) × ____= x^2 - 4
O x² – 4
O x-2
O x +2
O x² – 2
Answer:
x - 2
Step-by-step explanation:
(x + 2)(x - 2) = x^2 - 4
When graphing inequalities, where can the solutions be found?
Solutions will be located in the shaded region. Since this is a “less than” problem, ordered pairs on the boundary line are not included in the solution set. These values are located in the shaded region, so are solutions. (When substituted into the inequality x–y<3.
When solving systems of inequalities, the solutions are the regions where all the inequalities are true and will be represented by the intersection of the shaded areas.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
When graphing inequalities, the solutions can be found on the side of the number line or the coordinate plane where the inequality is true.
For example, if the inequality is x > 3, the solutions would be all the values of x that are greater than 3. These solutions would be represented by shading the area to the right of line x = 3 on the coordinate plane.
Similarly, if the inequality is y < 2, the solutions would be all the values of y that are less than 2. These solutions would be represented by shading the area below the line y = 2 on the coordinate plane.
It's important to note that when solving systems of inequalities, the solutions are the regions where all the inequalities are true and will be represented by the intersection of the shaded areas.
Learn more about inequalities here:
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5x – 3y = -21
2x - 9y = 54
Answer:
I'm confused
Step-by-step explanation:
What am I suposed to do?
Two eighth-grade classes are selling chocolate bars to raise money for an end-of-year field trip. One class is selling chocolate bars for $3.00 each and has already raised $275.00. The other class is selling chocolate bars for $3.50 each and has already raised $250.00. Which equation can be used to calculate c, the number of additional chocolate bars each class needs to sell, so that the total amount raised is the same for both classes?
Answer:
Step-by-step explanation:
you add both $275.00 and $250.00 ($525.00) then and $3.00 and $3.50 ($6.50) then divide $525.00 by $6.50 and then you answer would be $88.00
so c = $88.00
Answer:
3.50c + 250.00 = 3.00c + 275.00
Step-by-step explanation:
Every morning for the past 12 days, Beth used Two-thirds of a cup of milk on her cereal. To determine how much milk she used in total, she set up the equation, Two-thirds times 12 = question mark ?. What is the total amount of milk that Beth used
Answer:
It would be 8
Step-by-step explanation:
Answer:
(c) 8 Cups
Step-by-step explanation:
Tommy Thomas’s tankard holds 480ml when it is one quarter empty. How much does it hold when it is one quarter full?
Answer:
Tommy Thomas's tankard holds 160ml when it is one-quarter full.
Step-by-step explanation:
When Tommy's tankard holds 480ml when it's one-quarter empty. There are three other quarters in the tankard. So, you would divide 480 by 3 to see how much is in each of the other 3 quarters. The answer comes down to 160ml per quarter, which equals one-quarter full.
Angel got paid $332.50. He had to pay income tax of 30%. How much money did he have left?
Answer:
$232.75
Step-by-step explanation:
Because the tax takes 30% of his pay, he will be left with 70%.
Multiply his pay by 0.7 to get the answer:
332.50 * 0.7 = 232.75
Hope that helps! :D
Find the quotient: 189 divided by 9
1. 21
2. 22
3. 23
4. 24
The quotient is 21. the correct answer is option 1) 21.
To find the quotient of 189 divided by 9, we divide 189 by 9.
When dividing 189 by 9, we find that 9 can be subtracted from 189 a total of 21 times without going into negative values. Therefore, the quotient is 21.
So, the correct answer is option 1) 21.
When we divide 189 by 9, the result is 21, which means that 21 is the number of times that 9 can be subtracted from 189 without remainder. The quotient represents the whole number part of the division, indicating the number of groups of 9 that can be formed from 189.
Learn more about quotient here
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solve for x pls help
Answer:
23
Step-by-step explanation:
51+(2x+3)=100
54+2x=100
-54 -54
2x=46
x=23
what is the value of ? pls help
PLS HELP ME!
You buy 3.17 pounds of peaches, 1.15 pounds of pears, and 2.26 pounds of grapes. What is your total bill?
Answer:
Step-by-step explanation:
just add
3.17
1.15
2.26
-------
7. 48 lbs
im pretty sure
what is the slope of the line thru (-9,6) and (-6,-9) ??
Answer:
-5
Step-by-step explanation:
Answer:
−5
Step-by-step explanation:
there is a 30% sale today. what would the shoes that normally cost $125 now cost?
Answer:
$37.50
Step-by-step explanation:
$125 times30%=$37.50
Container A and container B have leaks. Container A has 800 ml of water, and is
leaking 6 ml per minute. Container B has 1000 ml, and is leaking 10 ml per minute.
How many minutes will it take for the two containers to have the same amount of
water?
**Write an equation to represent the situation (first blank). Use the variable m, for
minutes.
**Then solve for m (second blank).
**Finally, use your solution to determine the water level at that time (third blank).
The equation
can represent this situation. It will take
minutes for the two containers to have the same amount of water. At this time,
both containers will have ml left.
Answer:
a) 50 minutes
b) The water level at 50 minutes for Container A and B would be 500ml
Step-by-step explanation:
a) Let number of minutes at which both containers leak be represented by m.
Container A has 800 ml of water, and is leaking 6 ml per minute.
800ml - 6ml × m
800 - 6m
Container B has 1000 ml, and is leaking 10 ml per minute.
1000ml - 10ml × m
1000 - 10m
How many minutes will it take for the two containers to have the same amount of water?
Container A = Container B
800 - 6m = 1000 - 10m
Collect like terms
-6m + 10m = 1000 - 800
4m = 200
m = 200/4
m = 50 minutes
It will take 50 minutes for the two containers to have the same amount of water.
b) Finally, use your solution to determine the water level at that time.
Since m = 50 minutes
Container A = Container B
800 - 6m = 1000 - 10m
800 - 6 × 50 = 1000 - 10 × 50
800 - 300 = 1000 - 500
500 ml = 500 ml
Therefore, the water level at 50 minutes is 500 ml
Solve for AB
a: 3.6
b: 15
c: 4
d: 10
Solve the equation for y. 2x−14y=1
Answer:
y = 1/7x + -1/14
Step-by-step explanation:
2x−14y+−2x=1+−2x
−14y=−2x+1
−14y /−14 = −2x+1 /−14
The 4th term of a sequence is 108. Each term after the first is three times the previous term. Write an expression that represents all 4 terms. Write an equation that represents the 4th term. What are the 4 numbers?
Answer:
First 4 terms are a, 3a, 3^2 a and 3^3 a.
The numbers are:
4, 12, 36, 108.
Step-by-step explanation:
This is a geometric sequence and we can write it as:
a, ar, ar^2, ar^3 <---- the first 4 terms.
Here the common ratio r = 3 and the 4th term is 108 so:
a(3)^3 = 108
So the first term a = 108 / 3^3
= 108/27
= 4.
So the second number = 3*4 = 12 and 3rd is 12*3 = 36.
Help asap cuz idk what’s going on
Answer:
The answer is the first one or 9.5
Step-by-step explanation:
This is because you need to use a^2+b^2=c^2
Plug in 9 and 3
To get 81+9
To get 90
Now find the square root of 90
It is around 9.48
Which is closest to 9.5
which of the following is a solution to
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]x < - 3 \: \: \: and \: \: \: x > 4[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Please help! Due tonight!
Answer:
x = square root of 119
Step-by-step explanation:
Because it is only a little bigger than the side it opposes
HURRYYY HELPP!! Are the triangles below congruent by Side-Side-Side, Side-Angle-Side, or neither?
Answer:
b
Step-by-step explanation:
09) The ratio of the number of jackfruit in baskets P, Q
and R is 6:2:5. The total number of jackfruit
in basket Pis 48 more than the number of
jackfruit in basket Q. Calculate the total number
of jackfruits in the three baskets.
A 121 B 144 C 156 D 169
Answer:
156 jackfruits
Step-by-step explanation:
Let there are 6x jackfruit in baseket P, 2x in basket Q and 5x in basket R.
The total number of jackfruit in basket P is 48 more than the number of jackfruit in basket Q. ATQ,
6x = 48 + 2x
Solving for x.
6x - 2x = 48
4x = 48
x = 12
Jackfruits in basket P = 6x = 6(12) = 72
Jackfruits in basket Q = 2x = 2(12) = 24
Jackfruits in basket R = 5x = 5(12) = 60
Total no of jackfruits = 72 + 24 + 60
= 156
So, there are 156 jackfruits in the three baskets.
What graph represents the equation y = -1/2x + 1?
Answer:
The answer to your question is A.
Step-by-step explanation:
Jody's older brother is only three years less than twice Jody's age. If the sum of their ages is 30, write an equation (do not solve) to find the age of Jody's brother.
Answer:
y = 2x-3
Step-by-step explanation:
Twice the age means 2x
three less means -3
2x -3 = y
y = 2x -3
Brainliest appreciated!
How do you Solve 3x-12= 3x+4? Please explain how you did it.
Answer:
Step-by-step explanation:
There are no values of
x
that make the equation true.
No solution
Johny and Rahul divided the benefit of the business in the ratio 7:9. If
Rahul got 4878 rupees as benefit did Johny get?
Answer:
Step-by-step explanation:
7:9 = x:4878
4878/9 times 7
3794 would be your answer
Answer:
3,794 rupees
Step-by-step explanation:
Johny got 7 parts of the benefit while Rahul got 9. This can be represented as a fraction: 7/9
To solve this problem, we can use cross multiplication, where x represents the amount of rupees Johny got:
[tex]\frac{7}{9}[/tex] = [tex]\frac{x}{4878}[/tex]
Multiply 7 by 4,878: 34,146
Multiply 9 by x: 9x
Now the equation looks like this:
9x = 34,146
Divide both sides of the equation by 9 to isolate the x:
9x/9 = 34,146/9
x = 3,794
Johny got 3,794 rupees.
Seema sells two cookers for Rs.2574 each. On one she gains 10% and on the other she loses 10%.Find her gain or loss percent in the whole transaction.
Answer:
18.18%
Step-by-step explanation:
Selling price of one coker = Rs.2574
If she loose 10% on one;
%loss = Cost price - Selliing price/cost price * 100
10 =Cp-2574/Cp * 100
10/100 = Cp-2574/Cp
0.1Cp = Cp-2574
0.1Cp - Cp = -2574
-0.9Cp = -2574
Cp = 2574/0.9
Cp = Rs. 2860
Amount lost = 2860-2574 = Rs. 286
If she gains 10% on the second
%loss =Sp-Cp/Cp * 100
10 = 2574-Cp /Cp * 100
10/100 = 2574-Cp /Cp
0.1Cp = 2574-Cp
1.1Cp = 2574
Cp = 2574/1.1
Cp = Rs. 2340
Amount gained = 2340-2574 = Rs. 234
Total Loss = Amount lost - Amount gained
Total loss = 286 - 234
Total loss = Rs. 52
Total loss % = 52/286 * 100
Total loss % = 5200/286
Total loss % = 18.18%
25 pts
At birth, a puppy weighed 14 lbs. At one years old, the puppy weighs 35 times its birth weight. How much does the puppy
weigh now?
Answer:
490lbs.
Step-by-step explanation:
Answer:
490 lbs
Step-by-step explanation:
times means multiplication, so 35 times means 14 rows of 35 (and vice versa).
14 x 35
490
(Check the attached file for a full count)
Giving 15 point plz help me
Answer:
3
Step-by-step explanation:
Looking at the first three values of the table- when the x increases by 1, the y increases by 3.
Answer:
It's 3, I believe.
Step-by-step explanation:
If it isn't I'll remove my answer so someone else can answer. :)
14. A satellite orbits 22, 300 miles above the equator. It completes one revolution in 24 hours. Assume that the radius of the Earth is 3, 960 miles. How far will the satellite travel in one day?
Answer:
Displacement = 0 mi
Distance = 164,996.45 mi
Step-by-step explanation:
In this case, the displacement will be zero because the satellite goes back to its starting point after one day. If there is no distance traveled between the starting point and the ending point, then the Displacement will be zero.
When it comes to the distance, we will need to calculate the perimeter of the circle the satellite describes when making one whole turn around the earth.
The perimeter of a circle is given by the equation:
[tex]p=2\pi r[/tex]
so we need to start by finding what the radius of the circle is. This radius if found by adding the radius of the earth and the distance above the equation the satellite is located at, so we get that:
[tex]r=r_{earth}+h[/tex]
where h is the height of the satellite, so the radius of the circle is:
[tex]r=22,300mi + 3,960 mi[/tex]
so
r=26,260 mi
so now we can use the perimeter equation to get:
[tex]p=2\pi r[/tex]
[tex]p=2\pi (26,260)[/tex]
So the distance traveled by the satellite in one day will be:
P=164,996.45 mi.