Answer:
16
Step-by-step explanation:
Using the Remainder theorem
f(x) divided by (x + h) then the remainder is the value of f(- h)
here the divisor is (x + 3), thus remainder is f(- 3)
remainder = 5(- 3)² + 9(- 3) - 2 = 5(9) - 27 - 2 = 45 - 29 = 16
PLS HELP GIVING BRAINLIEST Turner Middle School has 525 boys, 625 girls, 58 teachers, and a supporting staff of 12 employees. The school uses an average of 1,267,760 gallons of water per month. Assuming that the water usage is proportional to the number of people in the school, about how much water do the students consume per week? a. 17,940 gal c. 316,940 gal b. 299,000 gal d. 1,196,000 gal
Answer:
d. 1,196,000 galStep-by-step explanation:
Number of students = 525+625=1 150
The number of people = 525+625+58+12=1 220
let x represent the amounot of water consumed by students
1220———————>1 267 760
1150———————> x
then
x = (1 150×1 267 760)÷1 220 = 1 195 019.67213115
:)
I really need help can ya'll please help. ://
Thank you
a) Wayne's savings before he spent $28 is $30
b) Stef's savings after she spent $28 is $8
Step-by-step explanation:
step 1 :
let,
Wayne's savings = 5x
Stef's savings = 6x
step 2 :
After spending $28 each of them, The ratio becomes 1/4.
⇒ (28 - 5x) / (28 - 6x) = 1/4
⇒ 4(28 - 5x) = 1 (28 - 6x)
⇒ 112 - 20x = 28 - 6x
⇒ 112 - 28 = 20x - 6x
⇒ 84 = 14 x
x = 84/4 = 6
step 3 :
a) Wayne's savings before he spent $28 = 5x
substitute x=6,
Wayne's savings = 5(6) = $30
step 4 :
b) Stef's savings after she spent $28 = Total savings - $28
= 6x - 28
= 6(6) - 28
∴ Stef's savings after she spent $28 = 36 - 28 =$8
(a) Wayne's savings before he spent $28 is $30.
(b) Stef's savings after she spent $28 is $8.
Solution:
Ratio of Wayne's savings to Stef's savings = 5 : 6
Let x be the common amount they have.
After spending $28 each, the ratio becomes 1 : 4.
5x – 28 : 6x – 28 = 1 : 4
This can be written in a fraction form.
[tex]$\Rightarrow\frac{5x-28}{6x-28}=\frac{1}{4}[/tex]
Do cross multiplication.
[tex]$\Rightarrow 4(5x-28)}=1({6x-28})[/tex]
[tex]$\Rightarrow 20x-112=6x-28[/tex]
Arrange like term one side.
[tex]$\Rightarrow 20x-6x=112-28[/tex]
[tex]$\Rightarrow 14x=84[/tex]
⇒ x = 6
(a) Wayne's savings before he spent $28 = 5x = 5(6) = $30
(b) To find stef's savings after spent $28:
Stef's savings before she spent $28 = 6x = 6(6) = $36
Stef's savings after she spent $28 = $36 – $28 = $8
Hence Wayne's savings before he spent $28 is $30
Stef's savings after she spent $28 is $8.
A triangular pane of glass has a height of 30 inches and an area of 270 square inches.What is the length of the base of the pane
Answer: 18in
Step-by-step explanation: Since area of triangle is A = 1/2 x b x h 30×18 = 540 and 540 Divided by two = 270 square inches
Can someone please help first answer gets brainlist
Answer:
3/5
Step-by-step explanation:
0.6 is actually 6/10 as a fraction. You divide bot the 6 and the 10 by 2 to get 3/5
What does -8/3 simplify to ?
Answer:
exact form: -8/3
decimal form: -2.6666666
mixed number: -2 2/3
Step-by-step explanation:
oakwood has a mass of 2.85 kilograms and a volume of 4100 cubic centimeters. determine the density of oak in grams per cubic centimeter.
Answer:
The density of oak is 0.695 grams per cubic centimeter.
Step-by-step explanation:
Given:
Oakwood has a mass of 2.85 kilograms and a volume of 4100 cubic centimeters.
Now, to find the density of oak in grams per cubic centimeter.
Mass (m) = 2.85 kilograms.
So, using conversion factor we convert into grams:
[tex]2.85\times 1000=2850\ grams.[/tex]
Volume (v) = 4100 cubic centimeters.
Now, to get the density by using formula:
[tex]Density=\frac{mass}{volume} \\Density=\frac{m}{v}[/tex]
[tex]Density=\frac{2850}{4100}[/tex]
[tex]Density=0.695\ grams\ per\ cubic\ centimeter.[/tex]
Therefore, the density of oak is 0.695 in grams per cubic centimeter.
Write an equation of a line that passes through the x-intercept 4 and y-intercept -2
Answer:
[tex]y=\frac{1}{2} x-2[/tex]
Step-by-step explanation:
We have the two points (4,0) and (0,-2)
Find the slope
[tex]m=\frac{-2-0}{0-4} =\frac{-2}{-4} =\frac{1}{2}[/tex]
y-intercept is -2
[tex]y=\frac{1}{2} x-2[/tex]
one year, super bowl commercial time sold for 4 million for 30 seconds of air time. What was the price per second? Round to the nearest cent
Final answer:
To calculate the cost per second for a $4 million Super Bowl ad that runs for 30 seconds, divide the total cost by the number of seconds, yielding a cost of approximately $133,333.33 per second.
Explanation:
The question asks us to calculate the cost per second for Super Bowl commercial air time when 30 seconds of air time sold for $4 million. To find the price per second, we divide the total cost by the total number of seconds.
Price per second = Total cost ÷ Number of seconds
Price per second = $4,000,000 ÷ 30 seconds
Price per second = $133,333.33 (rounded to the nearest cent)
Therefore, the price per second for Super Bowl commercial air time was approximately $133,333.33.
A business woman invests $41,500 into two accounts: one that returns 8% annual interest and one that returns 15% annual interest. After 1 year, she earns $5490. How much did she invest in each account?
$10,500 in the 8% interest account, $31,000 in the 15% interest account.
$11,500 in the 8% interest account, $30,000 in the 15% interest account.
$9,500 in the 8% interest account, $32,000 in the 15% interest account.
$32,000 in the 8% interest account, $9,500 in the 15% interest account.
Answer:
$10,500 in the 8% interest account,
$31,000 in the 15% interest account
Step-by-step explanation:
Let
x ---> the amount invested in the 8% interest account
41,500-x ----> the amount invested in the 15% interest account
we know that
The amount invested in the 8% interest account multiplied by the interest in decimal form plus the amount invested in the 15% interest account multiplied by the interest in decimal form, must be equal to $5,490
so
The linear equation that represent this problem is
[tex]0.08x+0.15(41,500-x)=5,490[/tex]
solve for x
[tex]0.08x+6,225-0.15x=5,490\\0.15x-0.08x=6,225-5,490\\0.07x=735\\x=\$10,500[/tex]
so
[tex]41,500-x=41,500-10,500=\$31,000[/tex]
therefore
$10,500 in the 8% interest account,
$31,000 in the 15% interest account
What is the slope intercept form of 6x+2y=8
Answer: y = -3x + 4
Step-by-step explanation:
subtract the 6x on both sides (2y = -6x + 8)
divide on both sides by 2 to isolate y ( y = -3x + 4)
Done :)
18. You run along a path at a constant speed of 5.5 miles per hour. How far do you travel in 1.5 hours? in 3.8 hours?
Answer:
the travel of only 1.5 hours:8.25
The travel in 3.8 hours:20.9
Step-by-step explanation:
1.5(5.5)
1.5(3.8)
“An A grade will be given to students having at least 450 total test points. There are two more tests to take before the semester is over. Lesha wants to know what she needs to score in order to get an A. Write and solve an equation to determine what score she needs to average on the next two tests if each question is with 1 point. Explain your reasoning.”
The required average on next two tests are:
[tex]t\geq \frac{450-p}{2}[/tex]
Solution:
An A grade will be given to students having at least 450 total test points
Let p represent her present test point total, and t represent the necessary average on the next two tests
There are two more tests to take before the semester is over
Therefore,
[tex]p+2t\geq 450[/tex]
A grade is given to students having at least 450 total test points
"at least" means greater than or equal to
So we have used greater than or equal to symbol
Solve the inequality for "t"
[tex]p+2t\geq 450\\\\Subtract\ p\ from\ both\ sides\\\\2t\geq 450-p\\\\Divide\ both\ sides\ by\ 2\\\\t\geq \frac{450-p}{2}[/tex]
Thus the required average on next two tests are:
[tex]t\geq \frac{450-p}{2}[/tex]
Find the x-coordinates of the points where the graph crosses the x-axis.
y = (x - 3)(x + 8)
To find the x-coordinates of the points where the graph crosses the x-axis, set y = 0 and solve for x. The x-coordinates are 3 and -8.
Explanation:The question asks for the x-coordinates of the points where the graph of the equation y = (x - 3)(x + 8) crosses the x-axis. To find these points, we need to determine the values of x that make y equal to zero. Setting y = 0, we get (x - 3)(x + 8) = 0. This equation will be true if either (x - 3) = 0 or (x + 8) = 0. Solving each equation gives us x = 3 and x = -8, respectively. These are the x-coordinates of the points where the graph crosses the x-axis.
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To find the x-coordinates where the graph of y = (x - 3)(x + 8) crosses the x-axis, set y to zero and solve for x, yielding the points (3, 0) and (-8, 0).
To find the x-coordinates where the graph crosses the x-axis, we need to set the y-value to zero and solve the equation. This is because when a graph crosses the x-axis, its y-coordinate is always zero. The equation given is y = (x - 3)(x + 8).
To find the x-coordinates, we set y to zero:
x = -8
Thus, the graph crosses the x-axis at the points (3, 0) and (-8, 0).
what is x+3y=15 and 4×2y=30
Answer:
For the first one, x is 9 and y is 2. 9 + 3(2) = 15. The second is y = 3.75
What is 83.9 rounded two decimal places
Expressed as the product of prime factors,
198 = 2 x 32 x 11 and 90 = 2 x 32 x 5.
Use these results to find
(a) the smallest integer, k, such that 198k is a perfect
square,
Answer:
22
Step-by-step explanation:
198 = 2×3×3×11
For a perfect square, factors have to occur in pairs
198×2×11 (because 3 is already twice)
198×2×11
198×22
198k = 198×22
k = 22
The value of k as smallest integer is 22 if 198k is a perfect square.
What is prime factor?A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11,.....
The given numbers are 198 and 90.
The prime factor of 198 = 2 x 3 x 3 x 11
The prime factor of 90 = 2 x 5 x 9
(a)
to make 198 perfect square,
The prime factor must be in square,
198k = 2 x 2 x 3 x 3 x 11 x 11
k = 2 x 11
k = 22
The value of k is 22 if 198k is a perfect square.
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What percent of 140 is 50.4?
Answer:
36
Step-by-step explanation:
X/100% x 140 = 50.4
X x 140 = 50.4 x 100
X x 140 = 5040
X = 5040/140
X = 36
What is ED?
I've been trying to solve this for a while and I just can't figure anything out.
Answer:
ED=12 units
Step-by-step explanation:
From the diagram triangle EAB is similar to triangle EDC.
The corresponding sides will be proportional.
EA/ED=AB/DC
This implies that:
[tex] \frac{2x + 4}{x + 4} = \frac{9}{6} [/tex]
We cross multiply to get:
[tex]6(2x + 4) = 9(x + 4)[/tex]
We expand to get:
[tex]12x + 24 = 9x + 36[/tex]
Group similar terms to get:
[tex]12x - 9x = 36 - 24[/tex]
Combine the similar terms to get:
[tex]3x = 12[/tex]
Divide through by 3 to get:
[tex]x = \frac{12}{3} [/tex]
This will simplify to:
[tex]x = 4[/tex]
Therefore ED=2*4+4=8+4=12
Astronomers sometimes use angle measures divided into degrees, minutes, and seconds. One degree is equal to 60 minutes, and one minute is equal to 60 seconds. Suppose that ∠J and ∠K are complementary and that the measure of ∠J is 41 degrees, 38 minutes, 9 seconds. What is the measure of ∠K?
Pleaseee answer now!!!
The measure of ∠K is 49 degrees 22 minutes 51 seconds.
Step-by-step explanation:
Given that ∠J and ∠K are complementary.
∠J = 41°38'9".
∠K = ?
When a sum of two angles result is 90°, then it is called as complementary angles.
Since ∠J and ∠K are complementary, then their sum is 90°.
∠J +∠K=90°.
∠K= 90° - ∠J.
=90°60'60" - 41°38'9".
=49°22'51".
∠K= 49 degrees 22 minutes 51 seconds.
The coordinates of the vertices if triangle ABC are A (1,-1) , B (1,4) , and C (8,4). What is the length in units of the line segment that connects vertex A and vertex B?
Length of the line segment is 5 units.
Step-by-step explanation:
Step 1: Length of the line segment that connects A and B is the distance between the points A (1, -1) and B(1, 4). x1 = 1, x2 = 1, y1 = -1, y2 = 4Step 2: Calculate the distance using distance formula √(x2 - x1)² + (y2 - y1)²⇒ Length = √(1 - 1)² + (4 - -1)² = √5² = 5 units
An office remodeling project costs $15,880. If you pay $3,680
towards the project, how much do you finance?
Answer:
23.17%
Step-by-step explanation:
The project costs $15,880 of which you contributed $3,680. To know the percentage of how much you finance,
(amount paid / cost)*100%
= (3680/15880)*100%
= (0.231738035)*100%
= 23.1738035%
Thus the amount contributed is 23.17% of the cost.
Which expressions are equivalent to 7 (negative three-fourths x minus 3)? Select two options.
The equivalent expressions are:
[tex]7(-\frac{3}{4}x - 3) = (7 \times \frac{-3}{4}x) + (7 \times -3)\\\\7(-\frac{3}{4}x - 3) = \frac{-21x}{4} - 21[/tex]
Solution:
Given expression is:
[tex]7(-\frac{3}{4}x - 3)[/tex]
We have to find the equivalent expressions
By distributive property,
a(b + c) = ab + ac
Therefore,
[tex]7(-\frac{3}{4}x - 3) = (7 \times \frac{-3}{4}x) + (7 \times -3)\\\\7(-\frac{3}{4}x - 3) = \frac{-21x}{4} - 21[/tex]
Thus equivalent expressions are found
Answer:
Im pretty sure its a and e
Step-by-step explanation:
lmk if im wrong or right
Write 80/100 as tenths in fraction form and decimal form
Answer:
0.8
Step-by-step explanation:
IF A LIQUID WEIGHS 2 POUNDS AND HAS A CApacity of 3 gallons. what is its density
Answer:
0.08 g/cm³
Step-by-step explanation:
We are given;
Mass of the liquid = 2 poundsBut; 1 pound = 453.592 g
Therefore, mass = 907.184 g
Volume of the liquid = 3 gallonsBut; 1 gallon = 3785.41 cm³
Thus, volume = 11356.23 cm³
We are required to determine the density of the liquid;
We need to know that;
Density = Mass ÷ Volume
Therefore;
density of the liquid = 907.184 g ÷ 11356.23 cm³
= 0.0799 g/cm³
= 0.08 g/cm³
Thus, the volume of the liquid is 0.08 g/cm³
Determine whether the statement is true of false and support your reasoning:
Mr. Flores has 100 pictures in a photo album. Of these pictures, 20 show his friends, 50 show his family, and 30 show his pet dachshund, Frou-Frou.
Based on this information, the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family.
Answer:
The statement that the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family is FALSE. We can clearly see that the probability of selecting a picture of his family is greater than the probability of selecting a picture of Frou Frou.
Step-by-step explanation:
the probability of randomly selecting a picture of Frou Frou is = 30/100 = 0.3
The probability of randomly selecting a picture of his family = 50/100 = 0.5
The statement that the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family is FALSE. We can clearly see that the probability of selecting a picture of his family is greater than the probability of selecting a picture of Frou Frou.
The president of a company creates a graph of the price of the company’s stock over one year. He describes the graph as follows: • The price of the stock rose to about $17 before falling to about $3. • There have only been two periods during which the price of the stock decreased. • The price of the stock is expected to increase in the long run. Which graph correctly shows the price of the stock?
Answer:
Option D
Just took test on ed2020 it is the last graph. Option D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
A cyclist traveled 9 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 45 kilometers, the skater had gone 30 kilometers. What’s the speed of the skater?
Final answer:
The speed of the skater is 18 km/h.
Explanation:
To find the speed of the skater, we can set up a proportion using the information given. Let's let the speed of the skater be x km/h. Since the cyclist traveled 9 km/h faster than the skater, the speed of the cyclist would be x + 9 km/h. Now, we can set up the proportion:
(x + 9 km/h)/(45 km) = x km/h)/(30 km).
To solve this proportion, we can cross-multiply and solve for x:
(x + 9 km/h)(30 km) = (x km/h)(45 km)
30x + 270 = 45x
270 = 45x - 30x
270 = 15x
x = 18
Therefore, the speed of the skater is 18 km/h.
the table shows the distance a small motor scooter can travel using one gallon of gasoline comeplete the table to find the number of miles the scooter can travel for other amounts of gasoline
By using the information that the scooter can travel 118 miles with 1 gallon of gasoline as a reference, we calculate that it can travel 11.8 miles with 0.1 gallons and 1180 miles with 10 gallons.
To complete the table and find the number of miles the scooter can travel for other amounts of gasoline, we can use the given information that the scooter can travel 118 miles with 1 gallon of gasoline as a reference point. We can calculate the mileage for different amounts of gasoline using this information.
Here's how we can complete the table:
Gallon 0.1:
We can calculate the distance for 0.1 gallons by taking 10% of the mileage for 1 gallon:
0.1 * 118 miles = 11.8 miles
Gallon 10:
Similarly, we can calculate the distance for 10 gallons by multiplying the mileage for 1 gallon by 10:
10 * 118 miles = 1180 miles
So, the completed table would look like this:
Gallon 0.1: 11.8 miles
Gallon 1: 118 miles
Gallon 10: 1180 miles
This table provides the number of miles the scooter can travel for different amounts of gasoline, including 0.1 gallons, 1 gallon, and 10 gallons.
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Find the missing side length, m.
Answer:
m=5
Step-by-step explanation:
Since we know that triangle ABC is similar to QRS, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of m.
Choose whole numbers to make the division easier
[tex]\frac{QR}{AB} = \frac{QS}{AC} \\\frac{10}{6} = \frac{m}{3} \\\frac{10*3}{6} =m\\m=10*3/6 = 5[/tex]
The missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].
The missing side length, [tex]$m$[/tex], can be found using the fact that triangles [tex]$ABC$[/tex] and[tex]$QRS$[/tex] are similar. This means that their corresponding side lengths are proportional. We can set up a proportion like this:
(m)/(3)=(10)/(6)
Cross-multiplying, we get:
[tex]$$6m[/tex] =[tex]30$$[/tex]
Solving for [tex]$m$[/tex], we get:
[tex]$$m[/tex] =[tex]5$$[/tex]
Therefore, the missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].
what is the measure of b if a=20 and c=29. using the pythagorean theorem
Since a^2+b^2=c^2 becomes 20^2+b^2=29^2, we solve for b:
400+b^2=841
b^2=441
b=21
So the length of b is 21 units.
Hope this helped!
Answer:
Step-by-step explanation:
b=21
a Leg
20
c Hypotenuse
29