Answer:
-27
(negative number)
Step-by-step explanation:
-b/2a = -(-16)/2(1) = 16/2 = 8
x + 8
x x^2 8x
+
8 8x 64
So we got 64, but 64 is not 37 so we need to change that by subtracting 27 from it.
64 - 27 = 37
So the final answer (in vertex form) is:
(x+8)^2 - 27
(-27) is the number being added
What does absolute value represent?
Step-by-step explanation:
The distance from zero that a number is on the number line without considering Direction
a group of four numbers has an average of 15. The first three numbers are 12,19 and 7. What is the other number
Answer:
22
Step-by-step explanation:
12 + 19 + 7 + _?_ = 15
38 + _?_ = 15
-38 -38
-----------------------
? = 23
12 + 19 + 7 + 23 = 61
-1
12 + 19 + 7 + 22 = 60
60 ÷ 4 = 15
I hope this helps!
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $54 . The total cost to rent 5 chairs and 3 tables is $36 . What is the cost to rent each chair and each table?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The cost of each chair is $2.25.
The cost of each table is $8.25.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x + 4 = 5 is an equation.
We have,
Cost of each chair = x
Cost of each table = y
Now,
2x + 6y = 54 _____(1)
5x + 3y = 36 ______(2)
From (1) we get,
2x = 54 - 6y
x = (54 - 6y)/2 ______(3)
Now,
Putting (3) in (2) we get,
5(54 - 6y)/2 + 3y = 36
270/2 - 30y/2 + 3y = 36
135 - 15y + 3y = 36
99 = 12y
y = 99/12
y = 8.25 ______(4)
Now,
Putting 4 in (3) we get,
x = (54 - 6 x 8.25) / 2
x = 4.5/2
x = 2.25
Thus,
The cost of each chair is $2.25.
The cost of each table is $8.25.
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Susan has a collection of 60 nickels and dimes. If the number of nickels is four times the number of dimes, how many nickels and how many dimes does she have?
Answer: 12 dimes, 48 nickles.
Step-by-step explanation:
Let x = the number of dimes
Let 4x = the number of nickels
x + 4x = 60
5x = 60
x = 12 dimes
4x = 48 nickles
She has 48 nickels and 12 dimes.
Equation
At first, we have to express the sentence into equation:
Given:
x = nickels
y = dimes
Susan has a collection of 60 nickels and dimes --> x + y = 60 ............. (1)
the number of nickels is four times the number of dimes --> x = 4y ......(2)
then we must input the equation (2) into the equation (1):
x + y = 60
4y + y = 60
5y = 60
y = 60/5
y = 12
As we know the value of y, we can calculate the value of x from the equation (2):
x = 4y
x = 4 * 12
x = 48
Thus, Susan has 48 nickels and 12 dimes
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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide. 7 and 2
24 units is the area of the shaded region if the "frame" is 2 units wide.
What is Area of Rectangle?The area of Rectangle is length times of width
We know that the frame is 2 units wide, and the measure of the rectangle and the frame are:
width = 7 units
length = 12 units
Now, if we remove the frame, we will remove 2×2 units = 4 units for each measure (because for each measure we have the frame in both sides).
So the measures for the shaded rectangle are:
width = 7 units - 4 units = 3 units
length = 12 units - 4 units = 8 units.
And the area of a rectangle is given by the product between the width and length, then we have:
A = (3 units)*(8 units) = 24 square units.
Hence, 24 units is the area of the shaded region if the "frame" is 2 units wide.
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9(2n+1) help please brooooooo
Answer:
18n + 9
Step-by-step explanation:
Distribute 9 into the expression.
9*2n = 18n
9*1 = 9
18n + 9
Malik spent $7.00 for a drink and a sandwich. His drink cost $ 2.00. Did he have a ham sandwich for $ 3.00, a tuna sandwich for $ 5.00, or a turkey sandwich for $ 4.00 Use the equation s + 2.00 = 7.00 to justify your answer.
Answer: tuna sandwich
Step-by-step explanation: 2+5=7
Can somebody help me with this please?
Answer: -16.66
Reason: 10*-5/3=−16.66666667 or −50/3
Jason uses his car for business. he must keep accurate records so his company will reimburse him for his car expenses. when he started his trip, the odometer read 43,156.1. Jason's car gets 35 miles per gallon. his tank was full at the beginning of the trip. when he filled the tank, it cost $34.24. what price did he pay per gallon of gas on this fill-up?
The price Jason paid per gallon of gas on this fill-up is $0.03 per gallon
What is the price per gallon?Based on the given task content; this can be solved using the division method.
Total miles = 43,156.1Jason's miles per gallon = 35 miles per gallonTotal cost to fill Jason's car = $34.24Total 35 miles in Jason's odometer = Total miles / 35
= 43,156.1 / 35
= 1233.031428571428
Approximately,
1,233.03 of 35 miles per gallon
Amount Jason paid per gallon of gas on this fill-up = 1,233.03 / $34.24
= 0.027768991833126
Approximately,
$0.03 per gallon
In conclusion, the amount Jason paid per gallon of gas is $0.03 per gallon
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Find the present value (the amount that should be invested now to accumulate the following amount) if the money is compounded as indicated.
$6800 at 4% compounded quarterly for 3 years
The present value the amount that should be invested now to accumulate is $7662.24.
What is meant by compound interest?Compound interest is the adding of interest to the principal amount of a loan or deposit, or interest on interest + principal. It is the outcome of reinvesting interest, or adding it to lent capital, rather than paying it out or requesting payment from the borrower, so that interest is received on the principle sum plus previously accumulated interest in the next month. In finance and economics, compound interest is common.
Compound interest differs from simple interest in that previously collected interest is not added to the current period's main amount, resulting in no compounding. The simple annual interest rate is calculated by multiplying the interest amount per period by the number of periods in a year.
Given,
Principle P=$6800
T=3 years
And also given that the money is compounded quarterly.
Present value=P[tex](1+(R/4)^{4t}[/tex]
=6800[tex](1+(4/400)^{12}[/tex])
=6800[tex](1+(1/100))^{12}[/tex]
=6800[tex](101/100)^{12}[/tex]
=6800[tex](1.01)^{12}[/tex]
=6800×1.1268
=$7662.24
The present value the amount that should be invested now to accumulate is $7662.24
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The weather report suggested that your city’s temperature increased from -10 degree celsius to 20 degree celsius. What is the rise in temperature?
Answer:
The temperature increased in 30 degrees Celsius
Step-by-step explanation:
what is the slope of a line that is parallel to the line connecting point O (-5,1) and point P (2,3)?
Answer:
2/7
Step-by-step explanation:
2 parallel lines have the same slope
we just need to find the slope of the line with the point’s connecting O and P
We use y2-y1/x2-x1 to find slope
3-1/2-(-5)
2/7
2/7 is the slope
Hopes this helps please mark brainliest
given the slope of the line and one point the passage through (2,-1) m=5/4
Answer:
slope intercept form:
y = [tex]\frac{5}{4}[/tex] x - [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
m = 5/4
x = 2 from the point (2,-1)
y = -1 from the point (2,-1)
y = mx + b
-1 = [tex]\frac{5}{4}[/tex] ([tex]\frac{2}{1}[/tex]) + b
-1 = [tex]\frac{10}{4}[/tex] + b
-1 = [tex]\frac{5}{2}[/tex] + b Subtract [tex]\frac{5}{2}[/tex] from both sides
[tex]\frac{-2}{2}[/tex] -+ [tex]\frac{-5}{2}[/tex] = b
[tex]\frac{-7}{2}[/tex] = b
y = mx + b
y = [tex]\frac{5}{4}[/tex] x - [tex]\frac{7}{2}[/tex]
Answer:
if you need the equation: y + 1 = [tex]\frac{5}{4}[/tex] (x-2) or y + 1 = [tex]\frac{5}{4}[/tex] x [tex]-\frac{5}{2}[/tex]
the answer: y = [tex]\frac{5}{4}[/tex] x [tex]-\frac{7}{2}[/tex]
Step-by-step explanation:
Kind of explanatory you have a slope and a point, your formula is going to be y-y₁ = m(x-x₁)
A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built
The dimensions of the rectangle for the most economical fence are length, L = 50 feet and width, W = 25 feet
How to find the dimensions of the rectangle for the most economical fence?Given: Area = 1250 square feet, , cost of material along three sides = $6 per foot, cost of material for fourth sides = $18 per foot
In order to calculate the dimension of the fence
Let L and W represent the length and width of the fence respectively
Thus, the area of the fence can be represented as:
A = L × W = 1250 ---- (1)
L = 1250/W
Let the total cost to construct the fence be 'C' can be obtained if we construct the shorter side with material with a cost of $18 per foot
C = 6×(2W + L) + 18×L
C = 12W + 24L ---- (2)
Substituting the value of L from equation 1 into equation 2 we have:
C = 12W + 24×(1250/W)
To minimize the cost we differentiate both sides with respect to W and equate the result to zero:
C = 12W + 24×(1250/W)
dC/dW = d/dW (12W + 30000/W)
0 = 12 - 30000/W²
12W² = 30000
W² = 2500
W = 50 feet
Since L = 1250/W
L = 1250/50
L = 25 feet
Therefore, the dimensions of the rectangle are length of 25 feet and width of 50 feet
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Jordan is helping his dad build a doghouse. The floor is rectangle-shaped with a width of 5 feet and an area of 36.25 ft2. What is the length of the rectangular floor?
The length is 7.25 feet
Here the detail
The formula for rectangled-shaped area is multiply length and width
Area = Length x Width
In this case, we know that the area is 36.25 ft2 and the width is 5 feet
so we can divided the area and the width to solve the length
Area = Length x Width
36.25 = Length x 5
Length = 36.25 : 5
Length = 7.25 feet
Hence the length of the rectangular floor is 7.25 feet
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15 points!! Is the triangle a right triangle?
Answer: Yes.
Step-by-step explanation:
Answer:
yes, it is because the right side is the bigger side.
Step-by-step explanation:
See in a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse.
Sydney’s fitness app says she has completed `70\%` of her goal for the week. Her goal is `50` miles. How far has she biked?
Sydney has biked `35` miles.
pls help me with this question
Answer:
[tex]\frac{13}{30}[/tex]
Step-by-step explanation:
The diagram shows a shape with all side lengths measured in centimetres. All the angles are right angles.
Write an expression, in terms of
x, for the total shaded area.
The expression for the total shaded area is in terms of x is
Area = (x + 5)(x - 3)
How to find the total shaded areaThe top side of the diagram shows that the dimension for the shaded area has length = x + 5
The width of the shaded area is x - 3
Area of a rectangle is given by the formula
Area = Length * width
Area = (x + 5) * (x - 3)
Area = x² - 3x + 5x - 15
Area = x²+ 2x - 15
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Can you guys awnser the questions in the boxes below
Answer:35 divide by 10.50= 3.33 = 4 hrs
Step-by-step explanation:
What percentage of 2000 is 1200
question below answer quick
The x-intercept is (5,0)
The y-intercept is (0,10)
What is intercept ?
A y-intercept, also known as a vertical intercept, is the point where the graph of a function or relation intersects the y-axis of the coordinate system in analytical geometry, using the widely used convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. As a result, x = 0 is satisfied at these sites.
A line's x-intercept and y-intercept are the points at which the x- and y-axes cross, respectively.
To find x-intercept we put y = 0 to the equation
4x + 2y = 20
4x = 20
x = 5
To find y-intercept we put x = 0 to the equation
4x + 2y = 20
2y = 20
y = 10
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In your own words, tell me the difference between a geometric and an arithmetic sequence.
As several differences are there between them and is differentiated below.
What is Sequence?
A list of numbers in a specific order is called a sequence. The terms of the sequence are the various numbers that appear in it.
Let a sequence's terms be a1, a2, a3,..., an,..., etc.
The term's position is indicated by the subscripts. That implies,
Initial phrase = a1
term two = a2
term three Equals a3
….
The nth term, indicated by an, is the number that appears in the sequence at the nth place. This phrase is also known as the sequence's general phrase.
Geometric Sequence:
It is a sequence of numbers in which each new term is calculated by multiplying by a non-zero and fixed number.Multiplication or Division is done in every step.A common ratio between 2 successive terms is the common ratio.It is of the Exponential Form.Arithmetic Sequence:
It is a list of numbers, in which every new term alters from another preceding term by a definite quantity.Addition or Subtraction is done in every step.A common ratio between 2 successive terms.It is of the Linear Form,To learn more about Sequence, visit:
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Jaxon goes to a restaurant and the subtotal on the bill was x dollars. A tax of 8% is applied to the bill. Jaxon decides to leave a tip of 23% on the entire bill (including the tax). Write an expression in terms of x that represents the total amount that Jaxon paid.
Answer:
Step-by-step explanation:
If the equation is going off of what is the traditional, and correct way to tip, the tip would be based off the total BEFORE tax.
Therefore, the expression for the total cost would be: x + .23x +.08x, which, simplified, would be 1.33x.
Ahmed earns $450/week. He receives a 4% increase in pay.
What is Ahmed’s weekly pay after his increase?
In an animal rescue facility are 21 animals.14 cats and 7 dogs. During the day 5 animals were adopted.what is the probabity that 3 cats and 2 dogs were adopted? Review ch 7 on probability
Answer:
0.3756
Step-by-step explanation:
I believe this is a combinatorics probability problem.
We first figure out in how many ways we can choose 3 cats out of 14 cats
Then we figure out how many ways we can choose 2 dogs out of 7 dogs
The total number of ways to select 3 cats and 2 dogs will be the product of these two
We then figure out in how many ways we can select 5 animals out of a total of 21 animals
The product we computed divided by the above number will give the probability
The number of ways we can choose k items out of n items is given by nCk i.e n Choose k
The formula is rather complicated but almost all calculators should be able to compute this given n and k
Let's deal with the selection of 3 cats from the population of 14 cats
This is given by 14C₃ which works out to 364
Number of ways for selecting 2 dogs from 7 dogs = 7C₂ = 21
Number of ways of selecting 5 animals from 21 = 21C₅ = 20349
The probability of selecting 3 cats and 2 dogs is therefore:
[tex]\dfrac{364 \times 21}{20349} = 0.3756[/tex]
That, I believe is the answer. Please let me know if it is correct and if you need more info.
The power P (in W) generated by a particular windmill is given by P=0.015V where V is the velocity of the wind (in
mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 5.9 mph. Round
your answer to the nearest tenth.
OA. 0.3 W/mph
OB. 3.5 W/mph
OC. 1.6 W/mph
D. 6.2 W/mph
The instantaneous rate of change of power with respect to velocity is 1.6 W/mph.
What is the rate of change function?
The pace at which one quantity changes in relation to another is known as the rate of change function.
Given, P = 0.015[tex]V^{3}[/tex]
Differentiating P with respect to V:
P′=(0.015)(3)[tex]V^{2}[/tex]
At V = 5.9 mph, then
P′=(0.015)(3)[tex]5.9^{2}[/tex] = 1.6 W/mph
Hence, the instantaneous rate of change of power is 1.6 W/mph.
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Explain why the slope(m) of this line is
2/6
The slope is 2/6 because the rise is 2 while the run is 6
rise 2
------- = -------
run 6
during basketball season josh made 3 out of every 7 free throw attempts in the last game josh attempted 28 free throws how many free throws would he have been expected to make
There are 12 free throws would he have been expected to make.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities.
Given that;
During basketball season josh made 3 out of every 7 free throw attempts in the last game.
Now,
Since, During basketball season josh made 3 out of every 7 free throw attempts in the last game.
Hence, Let number of free throws would he have been expected to make for attempted 28 free throws = x
So, We can formulate;
⇒ 3/7 = x/28
Solve for x as;
⇒ 3 × 28 / 7 = x
⇒ x = 3 × 4
⇒ x = 12
Thus, There are 12 free throws would he have been expected to make.
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Does the table represent a
function? Explain.
x
-3 -2 0 -3 -2
y 9 4 0 -9 -4
keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.