Answer:
y + 4 = a(x - 7)^2
Step-by-step explanation:
The standard vertex form of a parabola with vertex at (h, k) is
y - k = a(x - h)^2
and if we start with the simplest case, y = a(x)^2 and translate its graph 7 units to the right and 4 units down, we get y - {-4] = a(x - 7)^2, or
y + 4 = a(x - 7)^2
The answer is y + 4 = a(x - 7)^2.
The standard vertex form of a parabola with vertex at (h, k) is
y - k = a(x - h)^2
And if we start with the simplest case,
y = a(x)^2 and
translate it Into 7 units to the right and 4 units down,
we get
y - {-4] = a(x - 7)^2
then we get the equation is y + 4 = a(x - 7)^2.
Learn more about parabola: https://brainly.com/question/284411
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What is the product? 6(x^2-1) times 6x-1 over 6(x+1)
(36x^3-36x-1)/6x+6 or 6x^2-6x+(-1/6x+6)
For this case we must find the product of the following expression:
[tex]6 (x ^ 2-1) * \frac {6 (x-1)} {6 (x + 1)}[/tex]
We can rewrite [tex]x ^ 2-1[/tex] as:
[tex](x + 1) (x-1)[/tex], then:
[tex]6 (x + 1) (x-1) * \frac {6 (x-1)} {6 (x + 1)} =[/tex]
Canceling similar terms of the numerator and denominator:
[tex](x-1) * 6 (x-1) =\\6 (x-1) ^ 2[/tex]
ANswer:
[tex]6 (x-1) ^ 2[/tex]
You have an ant farm with 24 ants. The population of ants in your farm will
double every 3 months. The table shows the population over nine months. Decide
whether the table represents a linear function or a nonlinear function. After one
year, how many ants will be in the ant farm?
The population growth of the ants represents a non-linear function or exponential growth. After one year, the ant farm will contain 384 ants.
Explanation:Exponential growth is evident in this situation as the number of ants in the farm doubles every three months. This doubling is characteristics of exponential functions, therefore, this population growth is a non-linear function, not a linear function. In terms of how many ants will be in the farm after a year, there will be four 3-month periods in a year. So, the ants double four times. Using the formula of exponential growth 2n (where 'n' is the number of cycles), we can precisely calculate the final number of ants. Therefore, the total number of ants after one year, or four 3-month cycles, would be 24 ants * 24 = 24 ants * 16 = 384 ants.
Learn more about Exponential Growth here:https://brainly.com/question/12490064
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Find the area of the figure.
A-56cm^2
B-88cm^2
C-112cm^2
D-384cm^2
Answer:
88cm^2
Step-by-step explanation:
cot(x)=square root three
ty!!
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
tanx = [tex]\frac{1}{cotx}[/tex], then
tanx = [tex]\frac{1}{\sqrt{3} }[/tex]
x = [tex]tan^{-1}[/tex]( [tex]\frac{1}{\sqrt{3} }[/tex]) = [tex]\frac{\pi }{6}[/tex]
Hence x = [tex]\frac{\pi }{6}[/tex] + kπ ( k ∈ Z )
A steel oil tank is a cylinder with a diameter of 12 ft and a height of 18 ft. How many square feet of steel were needed to make the tank
To calculate the amount of steel needed to construct the oil tank, we need to find the surface area of the cylinder. A cylinder's surface area is composed of two parts: the area of its circular top and bottom (which are identical), and the area of its side.
Let's start by calculating the area of the two circular ends of the cylinder.
1. The area of one circle (either the top or the bottom) is given by the formula:
\[ A_{\text{circle}} = \pi r^2 \]
where \( r \) is the radius of the circle.
Since the diameter is twice the radius, we have:
\[ d = 12 \ \text{ft} \]
\[ r = \frac{d}{2} = \frac{12 \ \text{ft}}{2} = 6 \ \text{ft} \]
Now, we calculate the area of one circle:
\[ A_{\text{circle}} = \pi (6 \ \text{ft})^2 = \pi \times 36 \ \text{ft}^2 \]
\[ A_{\text{circle}} = 36\pi \ \text{ft}^2 \]
Since there are two circles (top and bottom), we double this area:
\[ A_{\text{circles}} = 2 \times 36\pi \ \text{ft}^2 \]
\[ A_{\text{circles}} = 72\pi \ \text{ft}^2 \]
2. Next, we calculate the area of the side of the cylinder. The side is essentially a rectangle that is wrapped around the circular ends. The width of this rectangle is the height of the cylinder, and the length is the circumference of the circle.
The circumference of the base circle is given by:
\[ C = 2\pi r \]
Using the radius we found before:
\[ C = 2\pi \times 6 \ \text{ft} = 12\pi \ \text{ft} \]
The area of the side is then:
\[ A_{\text{side}} = C \times \text{height} \]
\[ A_{\text{side}} = 12\pi \ \text{ft} \times 18 \ \text{ft} \]
\[ A_{\text{side}} = 216\pi \ \text{ft}^2 \]
3. The total surface area of the steel needed to make the tank is the sum of the areas of the circular ends and the side:
\[ A_{\text{total}} = A_{\text{circles}} + A_{\text{side}} \]
Substitute the values found above:
\[ A_{\text{total}} = 72\pi \ \text{ft}^2 + 216\pi \ \text{ft}^2 \]
\[ A_{\text{total}} = 288\pi \ \text{ft}^2 \]
To find a numerical value, we use the approximation \( \pi \approx 3.14159 \) (you can use a more precise value based on your requirements):
\[ A_{\text{total}} \approx 288 \times 3.14159 \ \text{ft}^2 \]
\[ A_{\text{total}} \approx 904.77792 \ \text{ft}^2 \]
So approximately 904.78 square feet of steel are needed to make the tank.
arlo rented a car. it cost $29.99 plus 0.26 per mile. is arlo paid 75.49 for the car rental. how many miles did he drive the car.
Arlo rented a car, and after accounting for the base price of the rental, it is determined he drove 175 miles
Arlo's total cost for car rental is the base price plus the cost per mile driven. To find out how many miles Arlo drove, we use the equation total cost = base price + (cost per mile imes number of miles). Arlo paid $75.49, which includes the base price of $29.99 and $0.26 per mile.
We first subtract the base price from the total cost to find out how much was spent on the mileage:
$75.49 - $29.99 = $45.50 spent on mileage
Now, we divide the amount spent on mileage by the cost per mile to get the number of miles driven:
$45.50 / $0.26 per mile = 175 miles driven
Arlo drove 175 miles with his rented car.
The student asked how many miles Arlo drove when he rented a car, given that the total cost was $75.49, with an initial fee of $29.99 and an additional charge of $0.26 per mile. To calculate the number of miles driven, we first subtract the initial fee from the total cost:
Total cost - Initial fee = Cost for miles
$75.49 - $29.99 = $45.50
Next, we divide the remaining cost for the miles by the per-mile charge to find the distance driven:
Cost for miles / Charge per mile = Number of miles
$45.50 / $0.26 = 175 miles
Therefore, Arlo drove 175 miles with the car he rented.
Answer to B pleaseeeeee???????
Answer:
if i did my math right then the answer is 244
Step-by-step explanation:
Answer:
92
Step-by-step explanation:
Substitute the given values for a and b into the expression
2a² + 5b²
= 2(- 6)² + 5(2)²
= (2 × 36) + (5 × 4)
= 72 + 20
= 92
First you need to replace all of the letter A's with -6 and all of the B's with 2.
The equation would look like this
2(-6)^2+5(2)^2
Second, you solve what in is the parenthesis 2(-6)=-12 5(2)= 10
Third, you rewrite the problem. -12^2+10^2
Fourth, you need to figure out what the final answer would be.
-12^2=-144 and 10^2=100
The answer would be -144+100=-44
Sorry!!! This is probably Wrong, I didn't use an algebra calculator or anything to check the answer. I didn't remember if I needed to bring the number in parenthesis to the power before or after multiplying.
Which expression is equivalent?
[tex]c)x^{2/3}[/tex]
what is the graph of the solution to the following compound inequality?
Answer:
C.Step-by-step explanation:
<, > - open circle
≤, ≥ - solid circle
<, ≤ - draw to the left
>, ≥ - draw to the right
[tex]3-x\geq2\qquad\text{subtract 3 from both sides}\\\\-x\geq-1\qquad\text{change the signs}\\\\\boxed{x\leq1}\\\\4x+2\geq10\qquad\text{subtract 2 from both sides}\\\\4x\geq8\qquad\text{divide both sides by 4}\\\\\boxed{x\geq2}[/tex]
Find the missing value so that the two points have a slope of -2 (1,y)and (6,-5)
Final answer:
To find the missing value so that the two given points have a slope of -2, substitute the values into the slope formula and solve for y. The missing value is y = 5.
Explanation:
To find the missing value for the given points (1, y) and (6, -5) so that the two points have a slope of -2, we can use the formula for finding the slope between two points:
Slope = (y₂ - y₁) / (x₂ - x₁)
Substituting the given values into the formula, we have:
(-5 - y) / (6 - 1) = -2
Simplifying this equation:
-5 - y = -2(6 - 1)
-5 - y = -2(5)
-5 - y = -10
Solving for y:
y = -5 + 10
y = 5
Therefore, the missing value 'y' is 5.
300 children are divided into 2 groups. There are 50 more children in the first group than in the 2nd group. How many children are there in the 2nd group?
Hei there!
Let's start by letting x be the number of children in the 2nd group. So we can make an equation:
(50+x)+x=300
Next, open parenthesis and combine like terms. Then solve for x.
50+x+x=300
2x=300-50
2x=250
x=125
So, there are 125 kinds in the 2nd group.
Hope I helped, sorry if I'm wrong ouo.
~Potato.
Copyright Potato 2019.
Answer: 125 children
We have an unknown amount of children in the second group, so let us call this x. The number of children in the first class must be x + 50. In other words, the total number of children in both classes would be x + x + 50, which equals to 2x+50, and you have a total of 300 children. Let us start with this equation:
2x + 50 = 300
Subtract 50 from both sides
2x + 50 - 50 = 300 - 50
Simplify
2x = 250
Divide both sides by 2
2x / 2 = 250 / 2
Simplify
x = 125
Again, we said, x is an unknown amount of children in the second group. As you can see, x = 125, so there are 125 children in the second group.
125 + 50 = 175
Since, there are 50 more children in the first group, you would add 50 to 125, and that will give us a total of 175 children in the first group.
Geometry question :) could use some help
Answer:
statement A
Step-by-step explanation:
If the ratio
[tex]\frac{QT}{TR}[/tex] = [tex]\frac{QU}{US}[/tex]
then TU is parallel to RS
[tex]\frac{QT}{TR}[/tex] = [tex]\frac{32}{36}[/tex] = [tex]\frac{8}{9}[/tex]
[tex]\frac{QU}{US }[/tex] = [tex]\frac{40}{45}[/tex] = [tex]\frac{8}{9}[/tex]
Since the ratios are equal then line segment TU is parallel to line segment RS
Help me Again for 46 points ill go higher I have over 900+ points to spend also with my alt acc so please help me
For the first question there is no mode because none of the numbers are the same. Mode means the popular number.
Answer: There is no mode.
For the second question , the answer is 3. Median means the middle number.
Answer:
5. ○ There is no mode.
6. ○ 3
Step-by-step explanation:
6. Median means the "midst" term [greatest to least (or vice versa)]:
5, 3,5, 3, 2,3, 2,2
5. Mode means "Most Often". We do not see any replicas in the data chart, therefore there is no mode.
I am joyous to assist you anytime.
Which is an equation PLS HELP MEEEE
Answer:
It should be D if that is an option.
Step-by-step explanation:
The equation is y= -3/2 x + 3
The slope is -3/2. It goes down 3 and over 2 to the right.
The y-intercept is positive 3. It intersects with the y-axis at the point (3,0).
Answer:
y = -3/2x + 3
Step-by-step explanation:
To find the equation for the graph, first you must find the slope. Pick 2 random points on the line, [for example (2,0) and (0,3)] You can find the slope by using the formula rise/run [rise over run]. To get from point (2,0) to point (0,3) you have to go up 3 and left 2 [resulting in the negative infront of 3/2. if you went right, ti would've been positive.] Then you have your slope, -3/2x
Next find the y-intercept [the point where the line hits the y-axis]
The line hits the y-axis at (0,3), so your y-intercept s 3.
Therefore, the equation is -3/2x+3
There were two containers of oil. There was twice as much oil in the second container as in the first one. After using 13 liters of oil from the first container and 7 liters from the second one, the second container still had 3 times more oil than the first one. How many liters of oil in total were in both containers originally?
PleASE HELP
Answer:
There are 96 liters of oil in both containers originally
Step-by-step explanation:
* Lets change the story problem to mathematics equation
- Let the first container had A liters of oil and the second container
had B liters of oil
- The quantity of oil B in the second container is twice the quantity
of oil in A in the first container
∴ B = 2A ⇒ (1)
- After using 13 liters from the quantity of oil A in the first container,
the container had (A - 13) liters
- After using 7 liters from the quantity of oil B in the second container,
the container had (B - 7) liters
- After that the quantity of oil in the second container is 3 times
more oil than the first one
∴ B - 7 = 3(A - 13) ⇒ simplify
∴ B - 7 = 3A - 39 ⇒ add 7 and subtract 3A from both sides
∴ B - 3A = -39 + 7
∴ B - 3A = -32 ⇒ (2)
- Substitute the value of B from (1) into (2)
∴ 2A - 3A = -32
∴ -A = -32 ⇒ × -1
∴ A = 32 liters
- Find the value of B by substitute value of A in (1)
∴ B = 2(32) = 64 liters
- Now find the total liters of oil in both containers
∴ A + B = 32 + 64 = 96 liters
* There are 96 liters of oil in both containers originally
Which function shows the final number of tires, y, produced by two of each machine working for x number of hours?
y = 55x – 1
y = 57x – 3
y = 110x – 2
y = 114x – 6
Answer:
y=110x-2... I might be wrong...
Step-by-step explanation:
Answer:
y=114x-6
Step-by-step explanation:
i got a 100 on ed2021 good luck yall
which of these tables represents a linear function
Answer:
Option B
Step-by-step explanation:
Given are three tables in x and y and we have to find which table shows a linear relation.
We know in a linear relation between x and y the graph would be a straight line and also the slope would be constant
i.e. change of y/change of x for any pair in the table would be a constant.
Out of three tables given, only second table satisfies this.
Hence B is the answer
10 points someone help me please!?
Answer:
[tex]\large\boxed{b=\sqrt{95}}[/tex]
Step-by-step explanation:
Use the Pyhagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=b,\ leg=7,\ hypotenuse=12[/tex]
Substitute:
[tex]b^2+7^2=12^2[/tex]
[tex]b^2+49=144[/tex] subtract 49 from both sides
[tex]b^2=95\to b=\sqrt{95}[/tex]
In your piggy bank, you dropped $1.00 on May 1, $1.75 on May 2, $2.50 on May 3 and so on until the last day of May. a) How much did you drop in the piggy bank on May 19? b) What is the total amount in your piggy bank at the end of May? Show all work.
Answer:
A. $14.5 B. $23.5
Step-by-step explanation:
You are adding .75 cents to your bank account each day so you can do .75 *18 days plus one dollar from day one to get $14.5 dollars on may 19. If you do 30 * .75 you get 22.5 plus a dollar from what you start with to get $23.5 at the end of may in your account. Hope this helped you!!
Find the slope and the y-intercept of the equation 4x + 5y = -9.
A. slope = 4/5' and y-intercept = '-(9)/(5)
B. slope = `-(4)/(5) and y-intercept = (9)/(5)
Oc. slope = *-(4)/(5) and y-intercept = *-(9)/(5)
D. slope = °(4)/(5) and y-intercept = "9/59
Answer:
slope= -4/5
y intercept= - 9/5
Step-by-step explanation:
The expression 4x^2 represents
(4x)(4x)
(4)(x)(x)
(4)(x)(2)
The answer is (4)(x)(x) because it’s 4 times 2 x’s
Answer:
(4)(x)(x)
Step-by-step explanation:
The square ONLY effects the x
I appreciate for those who are trying to help
Answer:
3 * pi
B
Step-by-step explanation:
The diameter is 3 inches.
radius = diameter / 2
radius = 3 / 2 = 1.5 inches.
The circumference of a circle = 2*pi*r where r is the radius, and pi = 3.14
C = 2 * pi * 1.5
C = 3 * pi
B
Solve the following equation. Then place the correct number in the box provided. x/9 = 1
First, we need to isolate the variable x.
To isolate x, we simply need to multiply both sides by 9, which would result in x = 9
[tex] \frac{x}{9} = 1 \\ \\ 1. \: x = 1 \times 9 \\ \\ 2. \: x = 9[/tex]
A chemist is using 388 milliliters of a solution of acid and water. If 19.7% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
____________________________________________________
Answer:
Your answer would be 76.4.
____________________________________________________
Step-by-step explanation:
First, lets take out some key information in the question:
------------------------
Key information:
388 milliliters
19.7%
------------------------
With the information above, it will make it easier to find the answer for your question.
To find the answer to your question, we would need to find how much is 19.7% of 388 millimeters
Therefore, we would need to multiply 388 and 19.7% to get our answer.
In order for this to work, we would need to move the decimal places to times to the left from 19.7; 19.7 will turn to .197. After you move the decimal place, we can now multiply.
[tex]388 * .197=76.436[/tex]
In the question, it asks that we need to round to the nearest tenth, so that's the place right after the decimal place.
The 3 is not a big enoug hnumber to change the number before it, so we would keep the tenth place the same.
It would be rounded up as 76.4
76.4 would be your FINAL answer. There are 76.4 milliliters of acid
____________________________________________________
Three girls are selling cases of popcorn to earn money for a band trip. In their first week, emily sold 2 3/4 cases,brenda sold 4 1/4 cases, and shannon sold 31/2 cases. How many cases of popcorn have the girls dold in all?
Well convert all of them into fourths. 3 1/2 = 3 2/4. Add all the whole numbers 2 + 4 + 3 = 9 and then add the fractions 1/4 + 3/4 + 2/4 = 6/4 = 1 2/4. Finally add the whole number and fraction together, 10 2/4 or 10 1/2.
10 1/2 cases of popcorn.
The total number of cases of popcorn sold by Emily, Brenda, and Shannon is 10 1/2 cases. We arrived at this number by converting their sales to improper fractions, finding a common denominator, and then adding the fractions together.
The question asks us to calculate the total number of cases of popcorn sold by three girls: Emily, Brenda, and Shannon. Emily sold 2 3/4 cases, Brenda sold 4 1/4 cases, and Shannon sold 3 1/2 cases. To find the total, we need to add these amounts together.
To perform the addition, convert any mixed numbers to improper fractions:
Emily: 2 3/4 = 11/4 cases
Brenda: 4 1/4 = 17/4 cases
Shannon: 3 1/2 = 7/2 cases
Now, add these improper fractions together:
(11/4) + (17/4) + (7/2)
To add these fractions, we need a common denominator, which is 4 in this case. So, we need to multiply the numerator and denominator of Shannon's sales by 2 to get 14/4.
Now we have:
(11/4) + (17/4) + (14/4) = 42/4
After adding the fractions, we get 42/4, simplifying to 10 1/2 cases. Therefore, the girls sold a total of 10 1/2 cases of popcorn in all.
which of the following represents the area of a rectangle whose length is 5x-3 and whose width is x+7
Answer:
The answer is 5x^2+32x-21
Step-by-step explanation:
To find the area of a rectangle, you have to multiply the length by the width. Then, you will get the equation of (5x-3)(x+7). Then, multiply these two together, therefore getting 5x^2+32x-21.
The sum of 5 consecutive integers is 110.
What is the fourth number in this sequence?
Answer:
Step-by-step explanation:
let: x , x+1 , x+2 ,x+3 , x+4 ....( 5 consecutive integers is 110)
x+x+1 +x+2 +x+3+x+4=110
5x +10 = 110
5x =100
x=100/5
x=20
the fourth number in this sequenceis : x+3 so : 23
A right cylinder has a radius of 2 units and height of 5 units. What is the volume of the cylinder? Round to the nearest tenth. ____ cubic units
Hi,
The volume of the cylinder is :
V = π × r^2 × h
V = 3,142 × (2)^2 × 5
V = 62, 8319 cm^3
π : Pi => 3,142
r : radius of the cylinder (2 units).
h : height of the cylinder (5 units).
The base of the cylinder is a circle , so to calculate the area we have to use the formula : area = π × r^2. And to find the volume , we have to multiply the area by the height.
•It was nice to help you, Bellalocc!
4(x+7)=9(x-1)+22 solve for x
Answer:
x=3
Step-by-step explanation:
First we will distribute the 4 into the (x+7) and 9 into (x-1).
You should then got
4x+28=9x-9+22
Afterwards we combine like-terms
4x+28=9x+13
Then, we put all the alike values on the same side together.
4x+28=9x+13
-4x -4x
___________
28=5x+13
-13 -13
____________
15=5x
You then divide both sides by 5 to isolate x
15/5= 3
x=3
What is next term in sequence 54,-18,6
Answer:
-2
Step-by-step explanation:
its a geometric sequence where every term is being divided by -3
Answer:
-2
Step-by-step explanation:
This is a geometric sequence. We need to find the common ratio
Take the second term and divide by the first
-18/54 = -1/3
Take the third term and divide by the second
-18/6 = -1/3
The common ratio is -1/3
The next term is the third term times the common ratio
6 * -1/3 = -2
The fourth term is -2