Answer
y = 2(x - 8)(x + 2)
Step-by-step explanation:
A(x - 8)(x + 2)
A × -8 × 2 = -32
-16A = -32
A = 2
y = 2(x - 8)(x + 2)
The triangular prism has
lateral faces.
square
The triangular prism has a lateral area of
inches.
Answer: 3 and 240
Step-by-step explanation:
Edg 2020
Answer:
The triangular prism has
✔ 3
lateral faces.
The triangular prism has a lateral area of
✔ 240
square inches.
Step-by-step explanation:
study it and got it rightIf (− 4, −8) and (−10, −12) are the endpoints of a diameter of a circle, what is the equation of the circle?
A) (x + 7)^2 + (y + 10)^2 = 13
B) (x + 7)^2 + (y − 10)^2 = 12
C) (x − 7)^2 + (y − 10)^2 = 169
D) (x − 13)^2 + (y − 10)^2 = 13
Answer:
Correct option: A
(x + 7)^2 + (y + 10)^2 = 13
Step-by-step explanation:
First we need to find the center of the circle. We can find it calculating the midpoint of the diameter.
the x-coordinates of the diameter are -4 and -10, so the midpoint is:
(-4 -10)/2 = -7
the y-coordinates of the diameter are --8 and -12, so the midpoint is:
(-8 -12)/2 = -10
Now we need to find the radius of the circle, so we find the diameter and then find half of it.
The lenght of the diameter is the distance of the endpoints:
D = sqrt((-4+10)^2 + (-8+12)^2) = 7.21
radius = 7.21/2 = 3.605
The generic equation of the circle is:
(x - xc)^2 + (y - yc)^2 = r^2
So we have:
(x + 7)^2 + (y + 10)^2 = 13
Correct option: A
The sum of two numbers is 7. The larger number is 16 more than 2 times the smaller number. What are the numbers? *
Answer:
-3, 10
Step-by-step explanation:
Let s represent the smaller number. Then 7-s is the larger one.
7-s = 16 +2s
-9 = 3s . . . . . . . add s-16
-3 = s
7-s = 10
The smaller number is -3, the larger one is +10.
A truck rental company charges a weekend rate of $50.75 plus $8.25 for each hour a truck is rented.You have at most $125.00 to spend on a truck rental.Let x represent the number of hours you rent a truck.Which inequality describes the number of hours you can rent a truck?
Answer:
Step-by-step explanation:
Let x represent the number of hours for which you can rent the truck.
truck rental company charges a weekend rate of $50.75 plus $8.25 for each hour a truck is rented. It means that the cost of renting the truck for x hours would be expressed as
50.75 + 8.25x
You have at most $125.00 to spend on a truck rental. Therefore, the inequality that describes the number of hours you can rent the truck is
50.75 + 8.25x ≤ 125
A Pontiac Grand am I Pinterest so will Roger turn pike traveling at 50 mph. Once half an hour later a ford Mustangs enter the turnpike at the same location and travel in the same distance at 80 mph. How long would it take for the mustang to catch up to the grand am ?When it catch up how far will the two cars have traveled on the turnpike
Answer:
It will take 0.8333h for the mustang to catch up to the grand am.
The two cars will have traveled 66.664 miles on the turnpike
Step-by-step explanation:
The position for each car can be modeled by equations in the following format:
[tex]S(t) = S(0) + vt[/tex]
In which S(t) is the position t hours after the last car(the Ford Mustang) has left, S(0) is the position of each car when the Ford Mustang left and v is the speed of each car, in miles per hour.
Pontiac
Traveling at 50 mph, which means that [tex]v = 50[/tex].
The Ford Mustang leaves half an hour after the Pontiac. The Pontiac travels at 50 mph, which means that in this interval, the Pontiac will have traveled 0.5*50 = 25 mph. This means that S(0) = 25. So
[tex]S_{P}(t) = 25 + 50t[/tex]
Ford Mustang
Leaves from position 0, so S(0) = 0.
Travel in the same distance at 80 mph, so [tex]v = 80[/tex]. So
[tex]S_{M}(t) = 80t[/tex]
How long would it take for the mustang to catch up to the grand am ?
This is t when
[tex]S_{M}(t) = S_{P}(t)[/tex]
[tex]80t = 25 + 50t[/tex]
[tex]30t = 25[/tex]
[tex]t = \frac{25}{30}[/tex]
[tex]t = 0.8333[/tex]
It will take 0.8333h for the mustang to catch up to the grand am.
When it catch up how far will the two cars have traveled on the turnpike
This is either [tex]S_{M}(0.8333)[/tex] or [tex]S_{P}(0.8333)[/tex], since they will be in the same position. So
[tex]S_{M}(t) = 80t[/tex]
[tex]S_{M}(0.8333) = 80*0.8333 = 66.664[/tex]
The two cars will have traveled 66.664 miles on the turnpike
The Ford Mustang will catch up to the Pontiac Grand Am in 18.75 minutes and they will have traveled a total of 25 miles on the turnpike.
Explanation:To find out how long it takes for the Ford Mustang to catch up to the Pontiac Grand Am, we need to determine the time it takes for the Mustang to cover the same distance that the Grand Am has already traveled. The Grand Am has a head start of half an hour at a speed of 50 mph, so it has covered a distance of:
Distance = Speed x Time = 50 mph x 0.5 hr = 25 miles
Now, we can calculate the time it takes for the Mustang to cover this distance:
Time = Distance / Speed = 25 miles / 80 mph = 0.3125 hr = 18.75 minutes
Therefore, it will take the Mustang 18.75 minutes to catch up to the Grand Am.
When the two cars catch up, they will have traveled a total distance of 25 miles, which is the distance covered by the Grand Am in the half-hour head start.
Leila, Charlie, and Joe have a total of $144 in their wallets. Joe has 4 times what Leila has. Charlie has $6 more than Leila. How much does each have?
Answer:
The amounts of money each has are:
Joe = $92
Charlie = $29
Leila = $23
Step-by-step explanation:
To solve this, we will convert the statements into an equation, and use that to solve for the unknowns, as follows:
total amount = $144
Let Leila's share be S
Joe's share = 4 times Leila's = 4S
Charlie's share = $6 + Leila's share = 6 + S
Joe's share + Charlie's Share + Leila's Share = $144
4S + (6 + S) + S = 144
4S + 6 + S + S = 144
4S + 2S + 6 = 144
6S + 6 = 144
6S = 144 - 6 = 138
S = 138 ÷ 6 = $23
Therefore Leila's share 'S' = $23
Joe share= 4S = 4 × 23 = $92
Charlie's share = 6 + 23 = $29
18. Ms. Acosta works in the lab at a pharmaceutical company. She needs to make 21 liters of a 32% acid solution to
test a new product. Her supplier only ships a 28% and a 35% solution. Ms. Acosta decides to make the
32% solution by mixing the 28% solution with the 35% solution. How much of the 28% solution will Ms. Acosta
need to use?
A. 6L
B. 9L
C. 12L
D. 21L
Answer:
vbighughyuogytifvyigguhui
Step-by-step explanation:
How do you find the arc length in a circle given any angle?
You find the circumference and multiply it by the central angle. If the central angle is in degrees, you divide that by 360. If the central angle is in radians, you divide by 2pi.
Which function has an initial value of 0.2?
Group of answer choices
Function Three
Function Four
Function Two
Function One
PICTURE IS BELOW
Answer:
Function 4
Step-by-step explanation:
5-x= -(x - 5)
how many solutions does this equation have
Answer:
Infinitely many solutions
Step-by-step explanation:
5-x= -(x - 5) ➡ 5 - x = -x + 5 add x to both sides and subtract 5 from both sides
5 - x - 5 + x = -x + x - 5 + 5 ➡0 = 0 in this case we say the equation has infinitely many solutions because whatever value you give for x there will always be a solution.
How do i solve -1=-3r +2r
To solve this, you need to isolate/get the variable "r" by itself in the equation:
-1 = -3r + 2r Combine like terms(terms that have the same variable and power/exponent.) The only like terms you can combine are -3r and 2r
-1 = -r Divide -1 on both sides to get "r" by itself
[tex]\frac{-1}{-1} =\frac{-r}{-1}[/tex] (two negative signs cancel each other out and become positive)
1 = r or r = 1
Answer:R=-1
Step-by-step explanation: You would have to first do the math for the equation, then you would have to work in the "R" and given the answer is smaller than the equation itself we can tell that the "R" is a negative. So, if we add the -3 and the 2 we get 1,so we can say that the "R" are both equal to -1 then we put it in the equation. We get -1=1 we add the "R's" then get -1
Sandra biked 7 kilometers on Wednesday. She biked 3 times as many kilometers on Thursday. How many total
meters did she bike?
What do you know? What do you need to find?
What question do you need to answer first?
How many meters did Sandra bike in all?
Which of the following sentences do you know? Select all that apply.
DA. Sandra biked 7 kilometers on Wednesday
OB. She biked 3 times as many kilometers on Thursday.
OC. How many total meters did she bike?
Answer:
A and B
Step-by-step explanation:
From what we know, Sandra biked 7 kilometers on Wednesday because of the statement, followed by how she biked 3x as many miles on Thursday. We do not know how many total meters she biked because it does not give us that information. Hope this helps!
The Lopez family took a taxi to there next destination. The cost of the taxi was 4 dollars plus 3 dollars for each mile traveled.When they arrived the total cost 37 dollars how far did they go in the taxi
Answer: 8.3
Step-by-step explanation: 37 divided by=12.3 then 12.3 - 4
Answer: the taxi travelled 11 miles
Step-by-step explanation:
Let x represent the number of miles that the taxi traveled.
The cost of the taxi was 4 dollars plus 3 dollars for each mile traveled. It means that the total cost of renting and driving the taxi over x miles is
4 + 3x
The Lopez rented the taxi and when they arrived at their destination, the total cost 37 dollars. It means that
4 + 3x = 37
3x = 37 - 4
3x = 33
x = 33/3
x = 11 miles
Use the law of cosines to find each missing side. Round to the nearest tenth.
(I'm doing each individual question)
Answer:
x = 9.3
Step-by-step explanation:
The Law of Cosines
[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]
[tex] x^2 = 15^2 + 13^2 - 2(15)(13) \cos 38^\circ [/tex]
[tex] x^2 = 225 + 169 - 2(15)(13) \cos 38^\circ [/tex]
[tex] x^2 = 394 - 390(0.7880) [/tex]
[tex] x^2 = 86.6758 [/tex]
[tex] x = \sqrt{86.6758} [/tex]
[tex] x = 9.3 [/tex]
Scott runs 4 sprints of 20 yards each. If he continues his routine, how many practices will it take for Scott to have sprinted a total of 2 miles combined?
Answer:
It will take 44 practices for Scott to have sprinted a total of 2 miles combined
Step-by-step explanation:
This question can be solved using rules of three.
First step:
Scott practice is measured in yards.
We want to know how many practices it will take for him to have sprinted 2 miles.
So we pass 2 miles to yards
Each mile has 1760 yards.
So 2 miles is 1760*2 = 3520 yards.
A practice:
4 sprints of 20 yards each.
So 4*20 = 80 yards.
A practice is 80 yards. How many practices for 3520 yards?
1 practice - 80 yards
x practices - 3520 yards
80x = 3520
x = 3520/80
x = 44
It will take 44 practices for Scott to have sprinted a total of 2 miles combined
Antoine wants to get a subscription to a local library. There are two libraries, each of which charges a monthly subscription free plus a fee for each book instead
Answer:
b then a
Step-by-step explanation:
Answer:
Step-by-step explanation:
Find an equation for the line that passes through the points (-3,-2) and (1,4)
Answer:
y=2/3x
Step-by-step explanation:
First, we have to find the slope, which is [tex]\frac{(y_{1} -y_{2})}{(x_{1}-x_{2}}[/tex]
(-3-1)/(-2-4)
-4/-6
2/3 is slope.
y=2/3x+-___
substitute in -3 from first point
y=-2+__=-2
y=2/3x+0
y=2/3x
Answer:
y + 2 = (3/2) (x+3) (point slope form)
Step-by-step explanation:
(see attached for reference)
Given
(x₁, y₁) = (-3,-2)
(x₂, y₂) = (1,4)
Since we are given 2 points, it would be easiest to express the equation of the line in point-slope form (see attached)
(y - y₁) = m (x - x₁)
we already have the values for x₁ and y₁, hence we only need to find the slope m (see 2nd attached graphic)
m = (y₂-y₁) / (x₂ - x₁)
= [4 - (-2) ] / [1 - (-3)]
= (4+2) / (1+3)
= 6/4
= 3/2
substituting the value for m and the values for x₁ and y₁:
(y - y₁) = m (x - x₁)
[y - (-2)] = (3/2) [x - (-3)]
y + 2 = (3/2) (x+3)
If f(x) = -x^2 – 1, and
g(x) = x + 5, then
g(f (x)) = [? ]x^2+[ ]x + [ ]
Answer:
g(f(x)) = - x² + 4
Step-by-step explanation:
To evaluate g(f(x)), substitute x = f(x) into g(x), that is
g(f(x))
= g(- x² - 1)
= - x² - 1 + 5
= - x² + 4
Sara and her family went to eat at Pappasito's for dinner. The total cost of the meal is $76.50. Sara left a 10% tip.
Determine their total cost, including the tip.
Answer:
The answer to your question is $84.15
Step-by-step explanation:
Data
cost of the meal = $76.50
tip 10%
total cost = ?
Process
1.- Calculate the 10% of $76.50 using proportions and cross multiplication.
$76.50 --------------- 100%
x ----------------- 10%
x = (10 x 76.5) / 100
x = 765/100
x = 7.65
2.- Calculate the total cost
Total cost = cost of the meal + tip
-Substitution
Total cost = $76.50 + $7.65
-Result
Total cost = $84.15
4. *Each pair of polygons is similar. Find the value of x.
Step-by-step explanation:
since both objects and sides are similar, you can set each side equal, then you cross multiply, and do subtraction, then find x.
Final answer:
To find the value of x in similar polygons, justify the similarity, write an equation relating the sides, algebraically solve for x, calculate, and then check that the result is reasonable.
Explanation:
The subject of this question is Mathematics, and it is likely at the high school level, as it involves finding a missing length in similar polygons, which requires knowledge of ratios and properties of similar figures, often covered in high school geometry courses.
Steps to find the value of x:
Justify that the triangles are similar: This can typically be done by verifying that the triangles meet the criteria of similarity, such as having identical angles or corresponding sides in proportion.
Write an equation that relates the sides of the triangles: Utilize the properties of similar triangles to write ratios that compare the lengths of corresponding sides.
Algebraically isolate the unknown quantity x.
Plug in numbers and calculate the answer.
Check the answer to ensure it seems reasonable.
It's also important to remember that if two triangles are similar, their corresponding lengths are proportional, which you can express algebraically with a statement such as AB/CD = EF/GH where AB, CD, EF, and GH are corresponding sides of the similar triangles.
Jayden’s family took a road trip to the Grand Canyon. Jayden fell asleep 15% of the way through the trip if the total length of the trip was 1000 miles, how many miles had they travelled when Jayden fell asleep?
Answer:
150 miles
Step-by-step explanation:
0.15x1000=150
The bricklayer exerted 150 newtons of force as he pushed the pushcart of bricks down
an alley that is 20 meters long. When the bricklayer reached the end of the alley, how
much work had he done?
Answer:
3000 N
Step-by-step explanation:
The work done by a force on an object is given as the product of the force applied on the object and the distance moved by the object.
Mathematically:
W = F * d
The force applied by the man is 150 N and the distance moved is 20 m. Hence, the work done by the man is:
W = 150 * 20 = 3000 J
The work done by the man is 3000 Joules.
What is the volume of a sphere with a radius of 3 inches ? Use 3.14 for pi
Final answer:
The volume of the sphere is 113.04 cubic inches.
Explanation:
The volume of a sphere can be calculated using the formula V = (4/3)×πr³. In this case, the radius is given as 3 inches. Plugging in the value, we get:
( V) volume of the sphere = (4/3)×3.14×3³ = (4/3)×3.14×27 = 113.04 cubic inches.
What value of x is a solution to x3 = 216?
Answer:
X=72
Step-by-step explanation:
216/3= 72
Erika is making cookies the recipe she has makes 20 cookies but she wants to make 60 cookies if she needs 2 cups of flour for 20 cookies how many cups of flour will she need for 60 cookies?
Answer:
The answer is 6 cups.
Step-by-step explanation:
If 20 cookies are 2 cups, that means that 10 cookies are 1 cup. If you see the pattern, the answer would easily be 6 cups.
find the volume of a cylinder with a height of 2 and a radius of 3. Use terms of pi
Answer:
56.55
Step-by-step explanation:
The formula to find the volume of a cylinder is V=πr2h so you would just need to plug the numbers in to get 56.55.
There are 4 green marbles and 6 yellow marbles in a bag. You want to find the compound probability of picking a green marble and a yellow marble. However, you do not put back the marble back into the bag. Is this an example of a dependent event or independent event?
Answer:
Dependent event because the sample space depends on the first event
Step-by-step explanation:
10 marbles total
4 green
6 yellow
1st pick green: Probability= 4/10
2nd pick yellow: Probability= 6/9
Dependent event because the sample space depends on the first event
A recent study showed that the modern working person experiences an average of 2.1 hours per day of distractions (phone calls, emails, impromptu visits, etc.). A random sample of 50 workers for a large corporation found that these workers were distracted an average of 1.8 hours per day and the population standard deviation was 20 minutes. Estimate the true mean population distraction time with 90% confidence, and compare your answer to that of the study.
Answer:
True mean population distraction time with 90% confidence is
C.I[103.34 ,112.66] at 108
Step-by-step explanation:
Given:
Study Average hrs =2.1 =2.1 *60=126 minutes
For sample mean =1.8 *60= 108 minutes
S.D=20 and n=50
To Find:
True mean population distraction time with 90% confidence,
Solution:
90% C.I. means 90 % will fall in true mean and other will not .
So for that calculating the
Standard error=S.D/Sqrt(n)
S.E=20/Sqrt(50)
S.E=2.828
For 90% Confidence interval Z=1.65
C.I= mean±Z*Standard error
C.I=108±1.65*2.828
C.I=108±4.662
Hence C.I will range from 103.34 to 112.66
Study mean =126 minutes .
Here it ranges from 103.34 to 112.66
In this exercise we have to use the knowledge of probability to calculate this we will use percentage as:
[tex]C.I= 108[/tex]
Given the following information in the text we find that:
Study Average=126 minutesFor sample mean =108 minutesS.D=20 and n=50Then calculating the probability we find that:
[tex]Standard error=S.D/\sqrt(n)\\ S.E=20/\sqrt(50)\\ S.E=2.828\\ Z=1.65\\ C.I=108+4.662 [/tex]
See more about probability at brainly.com/question/795909
5(3x+2)=8(2x-4) solve for x
Answer:
x = 42 i hope this helps! :)
Step-by-step explanation:
given 5(3x + 2) = 8(2x - 4)
distribute the 5 to both the 3x and the 2 15x + 10 = 8(2x - 4)
now distribute the 8 to both the 2x and the -4 15x + 10= 16x - 32
subtract 15x from both sides 10 = x - 32
add 32 to both sides 42 = x
flip the equation around so the x is first x = 42
answer x = 42
A regulation baseball can weigh no more than 149 grams. A factory produces baseballs with weights that are normally distributed with a mean of 146 grams and a standard deviation of 2.3 grams.
Answer:
0.9032
Step-by-step explanation:
Given that:
mean (μ) = 146 grams and standard deviation (σ) = 2.3 grams
The z score is a measurement used in statistics to calculate how far a value is from the mean in a normal distribution. The z score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
For the baseball not to weigh more than 149 grams i.e x = 149 g
[tex]z=\frac{x-\mu}{\sigma}=\frac{149-146}{2.3} =1.30[/tex]
From the probability distribution table, P(x < 149) = P(z < 1.30) = 0.9032 = 90.32%