Answer:
[tex]\displaystyle m=\frac{-5}{6}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (8, 8)
Point (20, -2)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute [SF]: [tex]\displaystyle m=\frac{-2-8}{20-8}[/tex][Fraction] Subtract: [tex]\displaystyle m=\frac{-10}{12}[/tex][Fraction] Simplify: [tex]\displaystyle m=\frac{-5}{6}[/tex]A certain star is 1.135 × 10^14 km away from Earth. If light travels at 9.4607 × 10^12 km per year, how long will it take for light from the star to reach Earth?
Answer:
Approximately 11.99 years
Step-by-step explanation:
This is just a type of problem like finding how long it will take for you to get somewhere. Like in finding how fast you need to go to go to a place that is 60 miles in one hour. All you have to do is divide the distance of the star by the speed of light, and you get the amount of time it will take for the star's light to reach the Earth.
The time taken by the light to travel from a star to Earth is required.
It would take 12 years for the light to reach Earth.
Distance of star from Earth = [tex]1.135\times 10^{14}\ \text{km}[/tex]
Speed of light from star = [tex]9.4607\times 10^{12}\ \text{km/year}[/tex]
Time is given by
[tex]t=\dfrac{\text{Distance}}{\text{Speed}}\\\Rightarrow t=\dfrac{1.135\times 10^{14}}{9.4607\times 10^{12}}\\\Rightarrow t=11.996\approx 12\ \text{years}[/tex]
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A person ate 2400 calories in a day. Of these, 36% came from fat. How many calories came from fat?
Answer:
864 calories came from fat. What I did was just subtract 2400 from 36% and got it.
Step-by-step explanation:
The calories that come out from fat will be 864 calories.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
A person ate 2400 calories in a day. Of these, 36% came from fat.
36% of 2400 = (36/100)2400
⇒ 864 calories.
Hence "The calories that come out from fat will be 864 calories".
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It costs Raquel 5$ in tolls to drive to work and back each day, plus she uses 3 gallons of gas. It costs her a total of 15.50$ to drive to work and back each day. How much per gallon is Raquel paying for her gas?
Answer:
$3.50
Step-by-step explanation:
Let x be the cost of per gallon gas.
We have been given that it costs Raquel 5$ in tolls to drive to work and back each day, plus she uses 3 gallons of gas. It costs her a total of 15.50$ to drive to work and back each day.
We can represent this information as:
[tex]3x+5=15.50[/tex]
[tex]3x+5-5=15.50-5[/tex]
[tex]3x=10.50[/tex]
[tex]x=\frac{10.50}{3}[/tex]
[tex]x=3.50[/tex]
Therefore, Raquel is paying $3.50 for per gallon gas.
Tossing coins imagine tossing a fair coin 3 times. (a) what is the sample space for this chance process? (b) what is the assignment of probabilities to outcomes in this sample space?
Answer:
(a) what is the sample space for this chance process?
If we toss a coin three times then there are total [tex]2^{3}=8[/tex] outcomes
The sample space associated with the given chance process is:
[tex]S= \left \{ HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\right \}[/tex]
(b) what is the assignment of probabilities to outcomes in this sample space?
Since the given sample space has eight outcomes and we know that a fair coin is tosses three times. Therefore, the probability of all the events mentioned in the given sample space is same. Hence we have:
[tex]Probability = \frac{1}{8}[/tex]
When tossing a fair coin three times, the sample space includes all combinations of heads (H) and tails (T). With a fair coin, the probability of each possible outcome (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT) is equal, at 0.125.
Explanation:When we're discussing the tossing of a fair coin three times, we're delving into the area of probability. (a) The sample space in this scenario is all the possible outcomes we could have. Those outcomes are: TTT, TTH, THT, THH, HTT, HTH, HHT, and HHH (Remember: H represents a head and T represents a tail).
(b) When we talk about the assignment of probabilities, we mean the likelihood of each potential outcome occurring. With a fair coin, it's equally likely to land on heads or tails - a 0.5 chance for each. Therefore, each of the eight possible outcomes has a 1/8 or 0.125 probability of occurring, granted that all outcomes are equally likely. So, for for instance, the probability of getting one head and two tails (HHT, HTH, THH) is 3/8 or 0.375, and similarly for all other cases.
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Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest tenth of an hour, will it take them to paint the room together?
BRAINLIEST GOES TO FIRST CORRECT ANSWER, NO STEPS NEEDED
If the roots of a quadratic equation are 1±√5, then the product of the roots is:
a) -24
b) -4
c) 26
Answer:
Its option B -4
Step-by-step explanation:
Answer:
b) -4
Step-by-step explanation:
The roots are (1-sqrt5) and (1+sqrt(5)
FOIL
first:1*1 =1
outer: 1 * sqrt(5) = sqrt(5)
inner -1*sqrt(5) = -sqrt(5)
last sqrt(5) * - sqrt(5) = -5
Add them together: 1+sqrt(5) - sqrt(5) -5 = -4
Help me with these math questions......
Answer: y = 0
Step-by-step explanation:
[tex]\frac{x^{0}}{x^{2}}[/tex]
exponent of denominator > exponent of numerator so, y = 0
*****************************************************************************
Answer: [tex]y=\frac{x^{2}+8}{3}[/tex]
Step-by-step explanation:
y = [tex]\sqrt{3x-8}[/tex]
To find the inverse, swap the x's and y's and solve for "y":
x = [tex]\sqrt{3y-8}[/tex]
x² = 3y - 8
x² + 8 = 3y
[tex]\frac{x^{2}+8}{3}=y[/tex]
*****************************************************************************
Answer: -6x - 3h
Step-by-step explanation:
f(x + h) = 7 - 3(x + h)²
= 7 - 3(x² + 2xh + h²)
= 7 - 3x² - 6xh - 3h²
-f(x) = -(7 - 3x²)
= -7 + 3x²
f(x + h) - f(x) = 7 - 3x² - 6xh - 3h² -7 + 3x²
= -6xh - 3h²
= h(-6x - 3h)
[tex]\frac{f(x+h)-f(x)}{h}=\frac{h(-6x-3h)}{h}[/tex]
= -6x - 3h
The formula for the lateral surface area of a cylinder is S=2πrh , where r is the radius of the bases and h is the height. Solve for r. r=2hπ/S r=S/2πh r=2Sπh r=h/2πS
Answer:
Option B is correct.
[tex]r = \frac{S}{2\pi h}[/tex]
Step-by-step explanation:
It is given that :
The formula for the lateral surface area of a cylinder is [tex]S = 2\pi rh[/tex]
where
S represents the lateral surface area of cylinder,
r represents the radius of the bases and
h represents the height of the cylinder.
Solve for r;
Given: [tex]S = 2\pi rh[/tex]
Divide both sides by [tex]2 \pi h[/tex],
[tex]\frac{S}{2\pi h} =\frac{2\pi rh}{2\pi h}[/tex]
Simplify:
[tex]r = \frac{S}{2\pi h}[/tex]
Therefore, the radius of the bases of the cylinder is, [tex]r = \frac{S}{2\pi h}[/tex]
Final answer:
The radius of the base of a cylinder, denoted as 'r', can be solved from the lateral surface area formula 'S=2πrh' by rearranging the formula to 'r = S / (2πh)'.
Explanation:
The question requires solving for r (the radius of the bases) from the formula for the lateral surface area of a cylinder, which is S=2πrh. To solve for r, we start by isolating r on one side of the equation. Here's how we can do it step by step:
Start with the formula for lateral surface area: S=2πrh.Divide both sides of the equation by 2πh to isolate r: S / (2πh) = r.Thus, the formula for r is r = S / (2πh).This equation shows that the radius can be found by dividing the lateral surface area by twice the product of π and the height of the cylinder.
Someone help please!
PLEASE HELP ME!!! (LINK) find the missing value in the solution to the equation. thank you!!
Answer:
4
Step-by-step explanation:
x = - 3
y - 4 = - 2.(x + 3)
y - 4 = - 2.(- 3 + 3)
y - 4 = - 2.0
y - 4 = 0
y = 4
I hope I helped you.
(-3, ?)
To find the missing value, which is "y", since you know x = -3, you can plug it into the equation to find "y"
y - 4 = -2(x + 3)
y - 4 = -2(-3 + 3)
y - 4 = -2(0)
y - 4 = 0 Add 4 on both sides
y = 4
A store Is having a 20% off sale on all merchandise if my buyers one item and save $13 what was the original price of their of her precio is having a 20% off sale on all merchandise if my buyers one item and save $13 what was the original price of her purchase
If the arc length of a sector in the unit circle is 3 radians, what is the measure of the angle of the sector?
A) 1.5 radians
B) 3 radians
C) 6 radians
D) 9 radians
Answer:
B) 3 radians
Step-by-step explanation:
The arc length is the product of the radius and angle. You have ...
... 3 radians = 1 × angle
so
... 3 radians = angle
_____
Comment on units
The formula is
... s = rθ . . . . . where s is the arc length, r is the radius, and θ is the central angle in radians.
The units of both s and r are units of length, so the units of angle are ...
... (length units)/(length units) = <no units>
That is, "radians" are fully equivalent to "no units."
The trouble with this problem statement is that it expresses "arc length" in units of "radians." This only works if the units of the radius of the unit circle are "no units". Ordinarily, that would not be the case. The length of the radius of the unit circle is usually "one length unit." If the central angle is 3 radians, then the arc length is "3 length units," not "3 radians."
45 trucks, each with 3.5-ton payload, are needed to unload a freight train. How many trucks with a 2.5-ton payload would be needed to do the same job?
Answer:
The answer is 63 trucks.
Step-by-step explanation:
If we need 45 trucks with 3.5 ton each to do the job; then we have a 157.5 ton payload. So if we divide the 157.5 ton into 2.5 ton trucks we get a total of 63 trucks.
3.5 x 45 = 157.5
2.5 x 63 = 157.5
The number of trucks required with 2.5 payloads will be 32.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that 45 trucks, each with a 3.5-ton payload, are needed to unload a freight train.
The number of trucks for 2.5 tons of payloads will be calculated as,
3.5 Tons of payload = 45 Trucks
2.5 Ton = ( 45 x 2.5 ) / 3.5
2.5 Ton = 32 Trucks
Therefore, the number of trucks required with 2.5 payloads will be 32.
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How many rows are needed to seat all students. When there are 846 students and each row holds 18 people
If Sue rides 10 miles per hour on her bike, and this relationship is graphed, which ordered pair would not be on the graph?
(2, 20)
(5, 50)
(6, 60)
(8, 85)
Answer:
(8, 85) Would make this relationship not a function because every time you count up 1 it goes up 10 and 8 would match to 80 not 85 making 8, 85 the ordered pair would not be on the graph.
Given Sue's speed of 10 miles per hour, we're looking for an ordered pair that does not fit the relationship y = 10x. While (2,20), (5,50), and (6,60) all fit this relationship, the pair (8,85) does not, hence it won't be on the graph.
Explanation:Sue's speed on her bike is 10 miles per hour. This relationship can be graphed as a straight line in a coordinate plane because the speed remains constant - the distance covered increases uniformly over time. So, for each hour (x), she covers a distance of 10x miles (y). Therefore, we can identify the ordered pair that does not belong on the graph by determining which one does not fit the relationship y = 10x.
(2,20): y=10*2=20, so the pair (2,20) fits the relationship.(5,50): y=10*5=50, therefore the pair (5,50) fits the relationship.(6,60): y=10*6=60, hence the pair (6,60) fits the relationship.(8,85): y=10*8=80, but the given y-value is 85, therefore the ordered pair (8,85) does not fit the relationship and would not be on the graph.Learn more about Linear Relationships here:https://brainly.com/question/31693063
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Sherman goes golfing every 6^\text{th}6 th day and Brad goes golfing every 7^\text{th}7 th day. If Sherman and Brad both went golfing today, how many days until they will go golfing on the same day again? Days
Answer:
42 days.
Step-by-step explanation:
We have been given that Sherman goes golfing every 6th day and Brad goes golfing every 7th day.
To find the number of days after that both will go golfing on the same day we will find LCM of 6 and 7.
Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48,..
Multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56,...
We can see that least common multiple of 6 and 7 is 42, therefore, both will go golfing on the same day again on 42nd day.
What is the domain of the following list of ordered pairs? (-3,-1) , (0,-2), (4,3),(1,5)
Answer:
the domain is X so
Step-by-step explanation:
(-3,0,4,1) is the answer
A rectangular garden has a total area of 48 square yards.Draw and label2 possiblerectangular garden with different side lengths that have the same area.
Two possible rectangular gardens with different side lengths and an area of 48 square yards are:
Square garden: 6 yards by 6 yards
Long and narrow garden: 8 yards by 6 yards
Explanation:Given:
Total area of the garden = 48 square yards
Objective:
Find possible combinations of side lengths for rectangular gardens with the same area.
Step 1: Square Garden
Let the side length of the square garden be x.
Area of the square garden = x^2
Set the area equation: x^2 = 48
Solve for x:
Take the square root of both sides: x = √48
Approximate the value: x ≈ 6.928 yards
Therefore, a square garden with sides of approximately 6.93 yards will have an area of 48 square yards.
Step 2: Long and Narrow Garden
We know the total area is 48 square yards.
Try different values for the width (w) and calculate the corresponding length (l) using the area formula: l * w = 48
For example, if w = 6 yards:
Calculate the length: l = 48 / w = 48 / 6 = 8 yards
Verify that the area matches: l * w = 8 * 6 = 48 square yards
Therefore, a long and narrow garden with a length of 8 yards and a width of 6 yards will also have an area of 48 square yards.
Type the correct answer in the box. Jason builds doghouses for a pet store. Each doghouse is a wooden structure with a rectangular base that has an area of 21 square feet and a length that is 4 feet more than its width. If x represents the width of the doghouse, write an equation in the given form that can be used to determine the possible dimensions of the base of the doghouse.
The equation that represents the area of the doghouse base is 21 = x * (x + 4), where x is the width and x + 4 is the length.
Explanation:Jason is building a doghouse with a rectangular base, where the area is known to be 21 square feet. If the width is x feet and given the length is 4 feet longer than the width, the length can be represented as x+4. As such, we can create an equation representing the area of the rectangular base as:
Area = Width * Length
By substituting the given values, we get the equation:
21 = x * (x + 4).
This algebraic equation can guide the solution to find the possible values of x, that is, the width of the doghouse.
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To determine the possible dimensions of the base of the doghouse, use the equation x^2 + 4x - 21 = 0.
Explanation:To find the possible dimensions of the base of the doghouse, we can use the given information that the area of the base is 21 square feet and the length is 4 feet more than its width.
We can represent the width as x. So, the length would be x + 4.
The equation for the area of the rectangle is length x width.
Substituting the values, we get x(x + 4) = 21.
Simplifying the equation, we can rewrite it as x^2 + 4x - 21 = 0.
This equation can be used to determine the possible dimensions of the base of the doghouse.
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Type the correct answer in the box.
An airplane takes off from point A in a straight line, as shown in the diagram.
The distance from A to E is ____ feet.
Answer:
11700
Step-by-step explanation:
The triangles are similar (presumably) because their ratios are the same for all three corresponding sides.
Equation
Set up the proportionAB/AC = AD /AEGivens
AB = 5600 feetAD = 5200 feetAC = 5600 + 7000 = 12600 feetAD = ?Solution
5600 / 12600 = 5200 / x Cross multiply5600x = 12600 * 5200 Simplify the right.5600x = 65,520,000 Divide by 5600x = 65,520,000/5600 Do the divisionx = 11,700Answer:
11700
Step-by-step explanation:
simplify
12+4x+8
(25)×y×(1/25)
18+7x+4
Answer:
a) 4x + 20
b) y
c) 7x + 22
Step-by-step explanation:
Assuming these were originally 3 questions? Simply pack together the numbers and the numbers with letters.
Answer: 144x2y+11x+16
that is the correct answer. 144x2y+11x+16
Which real numbers are zeroes of the function f(x)=2x^3-x^2-8x+4
Answer:
2, -2 and 1/2
Step-by-step explanation:
As the the first coefficient is 2 and the last number is 4 1/2, 2, -2 seem likely zeros ( By the rational roots theorem).
f(2) = 2*8 - 4 -16 + 4 = 0 so 2 is a zero.
f(-2) = -16 - 4 +16 + 4 = 0 so -2 is a zero
f(1/2) = 2*1/8 - 1/4 - 4 + 4 = 0 so 1/2 is the other zero.
Since the highest degree is 3 the maximum number of zeroes is 3.
Answer:
Try math
way if you need help on apex
Step-by-step explanation:
Kelly saved $150. That is 50% of the money she earned this summer. How much did Kelly earn this summer?
Question
Kelly saved $150. That is 50% of the money she earned this summer. How much did Kelly earn this summer?
Answer:
300$Step-by-step explanation:
50% = 1/2 = 0.5
150 is the 50% of the money she earned this summer.
Solution
150 * 2 = 300$
Answer:
$300
Step-by-step explanation:
If 150 is 50% you multiply 150 by 2 to get 300 and that would make it 100% of what she got that summer.
The following ordered pairs are solutions to a linear equation: (-20, 11.5), (-21, 12), and (-22, 12.5).
Which of the following graphs shows all of the ordered pairs in the solution set of this linear equation?
Answer:
option A
Step-by-step explanation:
The following ordered pairs are solutions to a linear equation: (-20, 11.5), (-21, 12), and (-22, 12.5).
Frame the equation of line y=mx+b using ordered pairs
(-20, 11.5), (-21, 12)
[tex]slope m = \frac{y_2-y_1}{x_2-x_1} =\frac{12-11.5}{-21+20}=-0.5[/tex]
m= -0.5
Now plug in (-21,12) and find out b
y=mx+b
12= -0.5(-21) + b
12= 10.5 +b
Subtract 10.5 on both sides
So b= 1.5
Equation of line is y=-0.5x + 1.5
Slope is negative so graph will be decreasing
Option A and option C graphs are decreasing
y intercept is the b values = 1.5
y intercept is (0,1.5)
Lets find x intercept
Plug in 0 for y in the equation y=-0.5x+1.5
0 = -0.5x+1.5
subtract 1.5 on both sides
1.5 = -0.5x
Divide by -0.5
so x= 3
So x intercept is (3,0)
Option A graph has x intercept (3,0) and y intercept (0,1.5)
Sheldon harvest the strawberries and tomatoes in his garden. He picks 1 2/5 kg lesss strawberries in the morning tha in the afternnoon. If sheldon picks 2 1/4 in the morning, how many kilograms of strawberries does he pick in the afternoon?
Answer:
[tex]3\frac{13}{20}=3.65[/tex] kg.
Step-by-step explanation:
Let S be amount of strawberries picked in the afternoon.
We have been given that Sheldon harvest the strawberries and tomatoes in his garden. He picks 1 2/5 kg less strawberries in the morning than in the afternoon and the strawberries picked in morning are [tex]2\frac{1}{4}[/tex] kg.
To find the amount of strawberries picked by Sheldon in the afternoon we will add [tex]2\frac{1}{4}[/tex] and [tex]1\frac{2}{5}[/tex] :
[tex]S= 2\frac{1}{4}+1\frac{2}{5}[/tex]
Upon converting our given mixed fractions into improper fraction we will get,
[tex]S= \frac{9}{4}+\frac{7}{5}[/tex]
Now let us have a common denominator.
[tex]S=\frac{9*5}{4*5}+\frac{7*4}{5*4}[/tex]
[tex]S=\frac{45}{20}+\frac{28}{20}[/tex]
[tex]S=\frac{45+28}{20}[/tex]
[tex]S=\frac{73}{20}[/tex]
[tex]S=3\frac{13}{20}[/tex]
[tex]S=3.65[/tex]
Therefore, Sheldon picked [tex]3\frac{13}{20}=3.65[/tex] kg of strawberries in the afternoon.
Sheldon picks approximately 0.85 kg of strawberries in the afternoon.
Explanation:To find out how many kilograms of strawberries Sheldon picks in the afternoon, we need to subtract 1 2/5 kg from the total he picks in the morning.
Given that Sheldon picks 2 1/4 kg of strawberries in the morning, we can subtract 1 2/5 kg from it:
2 1/4 kg - 1 2/5 kg = 9/4 kg - 7/5 kg = 45/20 kg - 28/20 kg = 17/20 kg.
Therefore, Sheldon picks 17/20 kg or approximately 0.85 kg of strawberries in the afternoon.
The amount of water in a bottle is reduced by 85% to 20 milliliters. How much water was originally in the bottle?
To find the original quantity when given the percent it was reduced and the amount left, divide the amount left by the percentage that is left:
The bottle was reduced by 85%, which means there is 15% left left in the bottle ( 100% - 85% = 15%)
Now divide the amount left by the percentage left:
20 / 0.15 = 133.33
The original amount was 133.33 milliliters ( Round answer as needed)
What is the surface area of a rectangular prism that has a length of 9 feet, a width of 5 feet, and a height of 7.5 feet?
A. 300 ft2
B. 150 ft2
C. 337.5 ft2
D. 43 ft2
Hello.
The Answer: A. 300 ft^2
Step-by-step explanation: Find the area of two sides (Length*Height)*2 sides.
Find the area of adjacent sides (Width*Height)*2 sides.
Find the area of ends (Length*Width)*2 ends.
Add the three areas together to find the surface area.
Formula: A= 2( W l + H L + H W)
Have a nice day.
Answer:
A 300 ft2
Hope this help's!
A store is having a sale where school supplies are 30% off theirr original price. A backpack is on sale for 11.20. What was the original price of the backpack?
Answer:
$16
Step-by-step explanation:
x*0.7=11.20
11.20/0.7=16
15(x+2000)=3300 is my question on common core. I don't know how to solve this correctly.
m x 5 = 30
m = ?
A) 3
B) 4
C) 5
D) 6 what the answer
Answer:
M= D) 6
Step-by-step explanation:
just do 30 divided by 5=M
Answer:
D) 6 is your answer
Step-by-step explanation: You have to substitute the #'s in for m then multiply it by 5, and if it equals 30, it's your answer... But it has to be a true statement...
A) 3:
m x 5 = 30
3 x 5 = 30
15 = 30
FALSE
B) 4:
m x 5 = 30
4 x 5 = 30
20 = 30
FALSE
C) 5:
m x 5 = 30
5 x 5 = 30
25 = 30
FALSE
D) 6:
m x 5 = 30
6 x 5 = 30
30 = 30
TRUE