You just need to factor a to get
[tex]a(1+2+3+4) = 10a[/tex]
What is assumed mean
Answer: as·sume
verb
past tense: assumed; past participle: assumed
1.
suppose to be the case, without proof.
"it is reasonable to assume that such changes have significant social effects"
synonyms: presume, suppose, take it, take for granted, take as read, take it as given, presuppose, conjecture, surmise, conclude, come to the conclusion, deduce, infer, draw the inference, reckon, reason, guess, imagine, think, fancy, suspect, expect, accept, believe, be of the opinion, understand, be given to understand, gather, glean; More
2.
take or begin to have (power or responsibility).
"he assumed full responsibility for all organizational work"
synonyms: accept, shoulder, bear, undertake, take on, take up, take on oneself, manage, handle, deal with, get to grips with, turn one's hand to
"the children are to assume as much responsibility as possible"
seize (power or control).
"the rebels assumed control of the capital"
synonyms: seize, take, take possession of, take over, take away, appropriate, commandeer, expropriate, confiscate, requisition, hijack, wrest, usurp, preempt, arrogate to oneself, help oneself to, claim, lay claim to
"Edward I used the conflict to assume control of Scotland"
Step-by-step explanation:
suppose to be the case, without proof.
"I assumed you were done with the dishes"
The function c(f) = 5/9 (f-32) allows you to convert degrees to Fahrenheit to degrees Celsius. Find the inverse of the function so that you can convert degrees Celsius back to degrees Fahrenheit
For this case we have the following function:
[tex]c (f) = \frac {5} {9} (f-32)[/tex]
We must find the inverse function. For this we follow the steps below:
Replace c (f) with y:
[tex]y = \frac {5} {9} (f-32)[/tex]
We exchange variables:
[tex]\frac {5} {9} (y-32) = f[/tex]f = \frac {5} {9} (y-32)
We solve for "y":
[tex]\frac {5} {9} (y-32) = f[/tex]
We multiply by[tex]\frac {9} {5}[/tex]on both sides of the equation:
[tex]y-32 = \frac {9} {5} f[/tex]
We add 32 to both sides of the equation:
[tex]y = \frac {9} {5} f + 32[/tex]
We change y by[tex]c^{ -1} (f):[/tex]
[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]
Answer:
[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]
Answer:
[tex]f(c)=\frac{9}{5}c+32[/tex]
Step-by-step explanation:
Given function that is used to convert degrees to Fahrenheit to degrees Celsius,
[tex]c(f)=\frac{5}{9}(f-32)[/tex]
Let y represents the output value of the function and x represents the input value,
[tex]y=\frac{5}{9}(x-32)[/tex]
Switch x and y,
[tex]x=\frac{5}{9}(y-32)[/tex]
Isolate y,
[tex]9x=5(y-32)[/tex]
[tex]\frac{9}{5}x=y-32[/tex]
[tex]\implies y = \frac{9}{5}x+32[/tex]
[tex]\implies f(c)=\frac{9}{5}c+32[/tex]
Which is the required function.
Beth is making fruit salad. She adds 5 grapes for every 2 strawberries. If she uses 16 strawberries, how many grapes will she use?
A.
10
B.
160
C.
80
D.
40
Answer:
D
Step-by-step explanation:
Well, we know that for every 2 strawberries are 5 grapes.
What times 2 is 16? 8.
so, it would be 40 grapes.
(This is now making me hungry.)
PLEASE HELP! URGENT! WHAT'S B
Answer:
"B" represents the area of the base so if the base is a square than a capital "B" means to find the area of the base (square). To find the area of a square it would be length x width.
Step-by-step explanation:
Given a = -3 and b = 4 and c = -5, evaluate -1/5 1/5 -7/5
The input (-1/5 1/5 -7/5) without specified operations and unused variables a, b, and c, make it difficult to evaluate as a standard mathematical question. There may likely be a mistake in the original question.
Explanation:Given the numbers a = -3, b = 4 and c = -5, the provided expression (-1/5 1/5 -7/5) appears to be a sequence of standalone fractions, not a standard mathematical operation or equation. To evaluate fractions, generally, we perform a calculation like addition, subtraction, multiplication, or division. However, the query lacks any specified mathematical operation to apply to these fractions. It seems there might be a mistake in the original question since the given values a, b, and c are also unused. To make it a valid mathematical question, we need to know what needs to be done with the fractions and variables given.
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Final answer:
The question appears to involve solving a quadratic equation using the quadratic formula, but there seems to be a typo in the provided figures. Nevertheless, the solution process entails substituting the given values into the quadratic formula and solving for x, which may result in two possible solutions depending on the discriminant.
Explanation:
The question involves solving a quadratic equation of the form ax² + bx + c = 0 using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). Based on the provided values of a, b, and c, we would substitute these into the quadratic formula to find the solutions to the equation. It seems there may be a typo in the original question, as the given values do not match any standard form of a quadratic equation nor the matrix form of a linear system. However, I will provide a general step-by-step solution for the quadratic equation based on the format provided in the reference information.
First, calculate the discriminant using the formula √(b² - 4ac). Then, use the values of a, b, and c to evaluate the positive and negative solutions of x using the quadratic formula. For example, if a = 1, b = 0.0211, and c = -0.0211, the solutions would be found as follows:
-0.0211 ± √(0.0211)² - 4(1)(–0.0211)
2(1)
It is important to note that this structure is indicative of the process and the actual computations will differ with the correct values provided for a, b, and c.
Select the correct answer.
Which operation should be performed first for calculations involving more than one arithmetic operation?
A. parentheses
В. exponents
C.multiplication
D.division
Answer:
parenthesis
Step-by-step explanation:
A common technique that is being used in solving with several arithmetic operations is the PEMDAS. It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". It is the order to be followed when calculating involving more than one arithmetic operation.
The correct first operation to perform in a calculation involving multiple arithmetic operations is parentheses, as per the order of operations, known as PEMDAS or BEDMAS.
The correct operation that should be performed first for calculations involving more than one arithmetic operation is parentheses. According to order of operations, the sequence you would follow is: Parentheses (or grouping symbols), Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). This is also commonly remembered by the acronym PEMDAS in the American system or BEDMAS in the Canadian system, indicating the sequence: Parentheses/Brackets, Exponents, Multiplication/Division, and Addition/Subtraction.
Milan uses a probability simulator to roll a six-sided number cube 100 times and to flip a coin 100 times. The results of the experiment are shown below:
Number on the Cube Number of Times Rolled
1 10
2 8
3 33
4 29
5 11
6 9
Heads Tails
29 71
Using Milan's simulation, what is the probability of rolling a 5 on the number cube and the coin landing on tails?
rolling a 5= 11/100
getting tails=71/29
i’m pretty sure you times the fractions together to get an overall probability
The probability of rolling a 5 on number cube and tail on coin is:
[tex]P(A\bigcap B)=\dfrac{781}{10000}[/tex]
or
[tex]P(A\bigcap B)=0.0781[/tex]
Step-by-step explanation:Let A denote the event of rolling a 5 on the number cube.
and B denote the event of coin landing on tails.
Let P denote the probability of an event.
Also, event A is independent of event B.
( Since, both the events are not affected by happening of each other )
We are asked to find the probability: P(A∩B)
We know that:
[tex]P(A\bigcap B)=P(A)\cdot P(B)[/tex]
( Since, both the events are independent )
Also,
[tex]P(A)=\dfrac{11}{100}[/tex]
( Since, 5 occurs 11 times out of a total of 100 times on the number cube )
and
[tex]P(B)=\dfrac{71}{100}[/tex]
Hence, we have:
[tex]P(A\bigcap B)=\dfrac{11}{100}\times \dfrac{71}{100}[/tex]
i.e.
[tex]P(A\bigcap B)=\dfrac{781}{10000}[/tex]
i.e.
[tex]P(A\bigcap B)=0.0781[/tex]
help quick. One car traveled 220 miles and drove 10 mph hour slower than a second car which drove 260 miles. If the cars were traveling for the same time, how fast was the first car traveling?
65 mph
75 mph
55 mph
85 mph
Answer:
55mph
Step-by-step explanation:
car A distance, d1= 220
car b distance, d2= 260
speed of car A, s1= speed of car B- 10
let speed of car B be s2
s1= s2-10
speed = distance/time
time= distance/speed
As time of car A= time of car B
distance of Car A/speed of Car A=distance of Car B/speed of Car B
220/s2-10= 260/s2
s2=(s2-10)260/220
s2=65
s1= s2- 10
= 65-10
=55
hence speed of first car is 55mph !
Answer: 55 mph
Step-by-step explanation:
the base and hight is 5 and 5
Tariq also designs hot tubs. The diameter of the hot tub is 3 meters. What is the area of the deck that surrounds the hot tub? If necessary, round to the nearest tenth.
3.3 m2
7.1 m2
17.9 m2
18.8 m2
Answer:
The area of the deck that surrounds the hot tub is 17.9 m².
Step-by-step explanation:
Base of deck = 5 m
Height of deck = 5 m
Area of deck = base*height
= 5*5
= 25 m²
A circular hot tub is placed in the deck whose diameter is 3 m.
Radius = diameter/2
= 1.5 m
Area of the circular hot tub = πr²
= 3.14*(1.5*1.5)
= 7.07 m²
Area of the deck that surrounds the hot tub = Area of deck - Area of tub
= 25 - 7.07
= 17.93 m²
= 17.9 m²
Answer:
17.9
Step-by-step explanation:
A.3.3
B.7.1
C.17.9
D.18.8
Geometry question please help due tomorrow
Find the fifth term in the sequence
that is defined as follows:
an = n/n+1
Answer:
5/6
Step-by-step explanation:
Just plug in five where n is.
In this case, it would be:
5/(5+1) or 5/6
Identify, graph, and state the symmetries for the polar equation r=2+2sintheta.
Which are the critical points in the graph? please help
Answer:
Graph = Cardioid
Axis of symmetry = y-axis
Critical points= [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]
Step-by-step explanation:
General equation for this type of cardioid is:
a ± b sinθ
Condition for a cardioid = [tex]\frac{a}{b} = 1[/tex]
Axis of symmerty according to the graph of 2 + 2 sinθ is along y-axis.
Critical points:
r = 2 + 2 sinθ ⇒ r = 2(1 + sinθ) ⇒ r' = 2 cosθ
∵derivative of 1 + sinθ = cosθ
For finding critical point the derivative is equal to zero,
2 cosθ = 0 ⇒ cosθ = 0
the value of cosθ is equal to zero at intervals: [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]
So, critical points = [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]
Karl used 2 inch by 2 inch square tile to cover a 14 inch by 12 inch piece of cardboard. Each tile weighs 3 ounces. What is the combined weight of the tiles Karl used to cover the piece of cardboard?
First, we need to find the area of both the tile and cardboard, so we can calculate how much tile will fit in the cardboard
Final answer:
Karl used a total of 42 square tiles to cover the piece of cardboard, with each tile weighing 3 ounces. Therefore, the combined weight of all the tiles is 126 ounces.
Explanation:
Karl used 2 inch by 2 inch square tiles to cover a 14 inch by 12 inch piece of cardboard. To find out how many tiles he used, we need to calculate the area of the cardboard and divide it by the area of a single tile. The area of the cardboard is 14 inches * 12 inches = 168 square inches. The area of one tile is 2 inches * 2 inches = 4 square inches. So, the number of tiles used is 168 divided by 4, which equals 42 tiles.
Now that we know Karl used 42 tiles, and each tile weighs 3 ounces, we can find the combined weight. The combined weight is 42 tiles * 3 ounces per tile = 126 ounces.
which trinomial is the product of the expression below? (3x+2)(2x-3)
A. 6x^2-13x-6
B. 6x^2+5x-6
C. 6x^2-5x-6
D. 6x^2+13x-6
Answer:
C
Step-by-step explanation:
Expand the factors to obtain the product.
Each term in the second factor is multiplied by each term in the first factor
(3x + 2)(2x - 3)
= 3x(2x - 3) + 2(2x - 3) ← distribute both parenthesis
= 6x² - 9x + 4x - 6 ← collect like terms
= 6x² - 5x - 6 → C
Which number line shows the solution to 4 + (-4)
The answer is the third one because the answer to 4-4 is 0.
The Number line which shows the solution 4 + (-4) is the third number line.
The solution to the statement 4 + (-4) is correctly given by the third number line.
The solution given by plot 1 is : (-4) + (-4) as both arrows points 4 units to the left.
The solution given by plot 2 is : ( 4 + 4) as both arrows points 4 units to the right.
The solution given by plot 3 is (4) + (-4) as one arrow points 4 units to the left and the other points 4 units to the right.
The solution given by the plot 4 is (-4 + 8) as one arrow points 4 units to the left and the other points 8 units to the right.
Therefore, the Number line which shows the solution 4 + (-4) is the third number line.
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john has a spinner with eight equal sectors with labels from 1 to 8. he spins the spinner once. what is the probability that he gets a number less than 4 or a multiple of 4?
3/4
3/32
1/2
5/8
Answer:
3/32
Step-by-step explanation:
Labels from 1 to 8:
The probability that he gets a number less than 4 (1, 2, 3) is 3/8
The probability to get a multiple of 4 (4, 8) is 2/8 = 1/4
So
The probability that he gets a number less than 4 or a multiple of 4:
= 3/8 x 1/4
= 3/32
Answer
3/32
Answer:
The answer is 5/8.
I saw an answer that gave 3/32, and since I knew that was wrong I wanted to give my answer to not lead others astray.
Step-by-step explanation:
There are 8 numbers john can pick.
Numbers less than 4 are (1, 2, 3)
Numbers that are a multiple of 4 are (4, 8)
The word "or" in the question implies addition, and adding 3/8 and 2/8 yields a result of 5/8. This is also the answer in the test that I took.
if y=-3x, find x's and y's value in 4x-2y=-20
Answer:
x=-2
Step-by-step explanation:
Answer:
x = - 2
y = 7
Step-by-step explanation:
4x - 2y = - 20
Now substitute - 3x for y.
4x - 2(-3x) = -20 combine the xs in the brackets
4x + 6x = - 20 Make the addition
10x = - 20 Divide by 10
x = - 20/10 Do the division
x = - 2
===============
3x - 2y = - 20 Put - 2 in for x
3(-2) - 2y = - 20 remove the brackets
- 6 - 2y = - 20 Add 6 to both sides
-2y = - 20 + 6 Combine
-2y = - 14 Divide by - 2
y = - 14/-2
y = 7
jack sold magazine subscriptions for $2 each receiving 25% commission on his sales. how much did he earn for each subscription
Answer: $42
Step-by-step explanation:
Answer:
$0.50
Step-by-step explanation:
We have been given that Jack sold magazine subscriptions for $2 each receiving 25% commission on his sales. We are asked to find Jack's income for each subscription.
Jack's income for each subscription will be equal to 25% of $2.
[tex]\text{Jack's income}=\$2\times \frac{25}{100}[/tex]
[tex]\text{Jack's income}=\$2\times 0.25[/tex]
[tex]\text{Jack's income}=\$0.50[/tex]
Therefore, Jack's income for each subscription will be $0.50.
Which function has only one x-intercept at (-6, 0)?
f(x) = x(x - 6)
Of(x) = (x - 5)(x-6)
f(x) = (x + 6)(x - 6)
f(x) = (x + 6) (x + 6)
These prisms are similar. Find the volume of the larger prism in decimal form. Need help please.
Answer:
518.4 in³
Step-by-step explanation:
The ratio of the sides of the prisms = 5 : 6, hence
the ratio of their volumes = 5³ : 6³ = 125 : 216
let x be the volume of the larger prism then by proportion
[tex]\frac{125}{300}[/tex] = [tex]\frac{216}{x}[/tex] ( cross- multiply )
125x = 216 × 300 ( divide both sides by 125 )
x = [tex]\frac{216(300)}{125}[/tex] = 518.4
The volume of the larger prism is 518.4 in³
Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. Kelly ran at an average speed of 8 miles per hour. When will Ava and Kelly be 3/4 mile apart?
To find out when Ava and Kelly will be 3/4 mile apart, we can set up a distance equation based on their average speeds. The time it takes for Ava and Kelly to be 3/4 mile apart is 22.5 minutes.
Explanation:To find out when Ava and Kelly will be 3/4 mile apart, we can set up a distance equation based on their average speeds.
Let's assume that the time it takes for Ava and Kelly to be 3/4 mile apart is t. Ava's distance can be represented by the equation 6t, while Kelly's distance would be 8t. We can set up the equation:
6t - 8t = 3/4
Simplifying, we have -2t = 3/4. To solve for t, we can multiply both sides of the equation by -1/2 to eliminate the negative sign:
t = (3/4) * (-1/2) = -3/8
Since time cannot be negative, we can conclude that Ava and Kelly will be 3/4 mile apart after 3/8 of an hour or 22.5 minutes.
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Answer:
They will 3/4 miles apart after 3/8 hours.
Step-by-step explanation:
To find out when Ava and Kelly will be 3/4 miles apart, we can set up an equation.
[tex]d = 8t-6t=2t[/tex]
t is the time in hours and d is the distance between the two girls in miles. Kelly runs at 8 miles/hour (represented by 8t) and Ava runs at 6 miles/hour (represented by 6t), and the distance between them can be calculated by subtracting Ava's distance from Kelly's distance.
To find out when they will be 3/4 miles apart, set d to 3/4 and solve for t.
[tex]\frac{3}{4} =2t\\\frac{3}{8}=t[/tex]
So, they will 3/4 miles apart after 3/8 hours.
What value is equivalent to 8 · 9 − 2 · 5?
It’s important to keep PEMDAS in mind (order of operations) when solving this.
PEMDAS stands for: Parentheses, exponents, multiplication, division, addition, subtraction.
So when doing this problem we can see that there are two multiplication problems (8 • 9) and (2 • 5) so let’s put those to the side and solve those.
8 • 9 = 72
2 • 5 = 10
Now we can put the problem back together as 72-10
So ... 72-10=62
Will mark BRAINLIEST! Help me!
Answer:
The answer is 5 people.
Step-by-step explanation:
.25 * 20 people surveyed = 5.
Chad left his house to go on a road trip. He drove due north at 60 mph for the first two hours of the trip, and then drove due east at 50 mph for the next hour. After those three hours of driving, approximately how far was Chad from his house?
A
78 mi
B
130 mi
C
156 mi
D
170 mi
Answer: C: 156 mi
Step-by-step explanation:
Driving north then east or west is 90 degrees rotation internally. Distance of Chad from his home to his final location is Option B: 130 mi
The Pythagoras theorem:If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
What is a right angled triangle?A right angled triangle is a triangle having one of its angle with measure of 90 degrees.
The slant side of that triangle is called Hypotenuse and it is the longest side in that triangle.
Referring to the diagram attached below, as Chad moved from north driving to east driving, thus, he made a 90 degrees angle internally as perpendiculars are with 90 degrees. Then joining his first and final position, we get a right angled triangle. Thus,
Distance of Chad from final point to his home = length of AC = |AC|
Measuring length of AB:A is the starting point of Chad. His speed was 60 mph for the first travel in the north direction. He traveled 2 hours. Since each hour he travels 60 miles(from his speed), and he spent 2 hours so 60 + 60 = 120 miles covered.
Thus, |AB| = distance traveled in north direction is 120 miles.
Measuring length of BC:Similarly, as he traveled in east for 1 hour with speed 50 mph, thus, he traveled 50 miles. Thus,
Length of BC = |BC| = 50 miles.
His distance from his home A to his final position C is calculated as follows.
Using Pythagoras theorem, we get:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{120^2 + 50^2} = \sqrt{16900} = 130 \: \rm miles\\\\[/tex]
(we took positive root since |AC| is length's measure., which is a non-negative quantity)
Thus,
Distance of Chad from his home to his final location is Option B: 130 mi
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There are 27 questions on an algebra test. All of the questions are multiple choice or constructed response. The number of constructed response questions on the test is six less the ten times the number of multiple choice questions. How many of each.
The measure of angle O is 110°. what is the angle of r and p?
Answer:
Choice D for Angle R
70 degrees for Angle P
Step-by-step explanation:
Google "central angles and inscribed angles geometry" for an explanation.
It's actually a poorly worded question.
You are in charge of buying the chips and soda for
a party. You must spend $52. The chips cost $5
per bag and the soda costs $3 for a gallon bottle.
You want to buy 14 items. How many
bottles of soda should you buy?
Show work
Answer:
9 bottles of soda can be bought.
Step-by-step explanation:
Let chips represented by x
and soda represented by y
then
x + y = 14 eq(1)
and
5x + 3y = 52 eq(2)
Solving the equations simultaneously we can find the value of x and y
Multiplying eq(1) with 5 and subtracting from eq(2)
5x + 3y = 52
5x + 5y = 70
- - -
___________
-2y = -18
y = -18/-2
y = 9
Putting value of y in eq(1)
x + y =14
x + 9 = 14
x = 14 - 9
x = 5
As y represents the soda, so 9 bottles of soda can be bought.
please help ASAP! will give brainlist.
Your friend George is 6 feet tall and his shadow is 10 feet long. At the same time, the shadow of the flagpole was 85 feet long. What is the height of a flagpole?
A. 141.6 feet.
B. 51 feet.
C. 1.4 feet.
D. 60 feet.
Answer: 51 feet
Since we know George's height, the length of George's shadow, and the length of the flagpole's shadow we have all the information we need
Now we can set up a relationship between George and the flagpole:
[tex] \frac{6}{10} = \frac{x}{85} [/tex]
6 represents George's height
10 represents the length of George's shadow
x is the unknown height of the flagpole
85 is the length of the flagpole's shadow
Now you solve for x:
[tex]x = \frac{85 \times 6}{10} \\ x = \frac{510}{10} \\ x = 51[/tex]
So, the height of the flagpole is 51 feet
Heidi has 6 pounds of tomatoes from her garden. She used 3/4 of all the tomatoes to make sauce and gave 2/3 of the rest of the tomatoes to her neighbor. How much ounces of tomatoes did Heidi give her neighbor?
Answer:
She gives 16 ounces to her neighbor
Step-by-step explanation:
How much did you use to make sauce
6 * 3/4 = 18/4 =9/2 = 4.5 lbs
That leaves 6-4.5 = 1.5 lbs
She give 2/3 of this to her neighbor
1.5 * 2/3
Changing the decimal to a fraction
3/2 * 2/3 = 1
She gives 1 pound to her neighbor, but we want it in ounces
16 ounces equals 1 pound
She gives 16 ounces to her neighbor
6 consecutive integers starting with 3
the set of 6 consecutive integers starting with -3:
{ -3,-2,-1,0,1,2 }
Answer:
Step-by-step explanation:
let :
x , x+1 , x +2 , x + 3 , x+4 , x+5 ....... ( 6 consecutive integers )
x +( x+1 ) + (x +2) + (x + 3)+ (x+4) + ( x+5) = - 3
6x+16 = - 3
6x = - 3 - 16
6x = - 18
x v= -18/6
x = - 3
6 consecutive integers are : -3 ; - 2 ; - 1 ; 0 ; 1 ; 2