Hey There!! ☄️ The general vertex to The general vertex form is this:
v(x) = a (x-h)2 + k
where (h,k) is the coordinates of the of vertex.
and a indicates the widening or shrinking of the function compared to another parabolic function. If a become bigger, the graph becomes narrower. If a becomes negative, the graph is reflected over the x-axis.
Comparing f(x) = x2 with g(x) = -3(x+6)2 + 48, we have the following transformations:
The graph is reflected over the x-axis
The graph is made narrower.
The graph is shifted 6 units to the left.
The graph is shifted 48 units up.
From the choices we only have:
The graph of f(x) = x2 is made narrower
The graph of f(x) = x2 is made narrower.
It is given that f(x) = x2 and g(x) = –3x2 – 36x – 60.
To find the transformations applied to the graph.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The general vertex to The general vertex form is this:
v(x) = a (x-h)2 + k
where (h,k) is the coordinates of the of vertex.
Indicates the widening or shrinking of the function compared to another parabolic function. If a become bigger, the graph becomes narrower. If a becomes negative, the graph is reflected over the x-axis.
Comparing f(x) = x2 with g(x) = -3(x+6)2 + 48, we have the following transformations:
The graph is reflected over the x-axis.
The graph is shifted 6 units to the left.
The graph is shifted 48 units up.
From the choices we only have:
So, the graph of f(x) = x2 is made narrower.
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Jess borrows 250 from the bank. The band chargEs 11% simple interest over 2 years.
How much will Jess owe the bank at the end of 2 years?
Answer:
$305
Step-by-step explanation:
You have to use the following formula to calculate the accrued amount:
A=P(1 + rt), where:
A= accrued amount
P= principal amount= $250
r= rate of interest= 11%
t= time period= 2 years
Now, you have to replace the values in the formula:
A=250*(1+0.11*2)
A=250*(1+0.22)
A=250*1.22
A=305
According to this, at the end of 2 years, Jess owes the bank $305.
2w^3 – 32w
Factor a difference of squares
Answer:
[tex]=2w\left(w+4\right)\left(w-4\right)[/tex]
Step-by-step explanation:
[tex]2w^3 - 3\\\\\mathrm{Factor\:out\:common\:term\:}2w:\quad 2w\left(w^2-16\right)\\=2w\left(w^2-16\right)\\\\\mathrm{Factor}\:w^2-16:\quad \left(w+4\right)\left(w-4\right)\\=2w\left(w+4\right)\left(w-4\right)[/tex]
Answer:
[tex]=2w\left(w+4\right)\left(w-4\right)[/tex]
Step-by-step explanation:
[tex]2w^3 - 32w\\[/tex]
Factor out 2w from the expression
[tex]2w(w^2+16)[/tex]
Factor (w^2+16) according to difference of two squares principle
[tex](w^2 +16) = (w+4)(w-4)\\2w((w+4)(w-4)))[/tex]
What’s the measure for angle C?
Answer:
152°
Step-by-step explanation:
Angles B and A of the isosceles triangle have the same measures, so we have ...
∠B = ∠A
(x -14)° = (x/2)°
2x -28 = x . . . . . . divide by °, multiply by 2
x = 28 . . . . . . . . . .add 28-x to both sides
Then the base angles, A and B, both have measure (x/2)° = 14°.
The third angle, C, will bring the total to 180°.
∠A + ∠B + ∠C = 180°
∠C = 180° - 2(14°)
∠C = 152°
is x=y^2 a function or not
Answer:yes
Step-by-step explanation:
Please Help! I'm Stuck!
Answer:
The area of P is 9 times the area of Q
Step-by-step explanation:
From P to Q
The side lengths are
6 : 2
Divide each side by 2
3:1
From length to area we square the scale factor
3^2 : 1^2
9 : 1
P to Q area is 9 to 1
The area of P is 9 times the area of Q
Find a irrational number that is between 5.2 and 5.5.
Answer:
5.35
Step-by-step explanation:
Answer:
5.29150262213
Step-by-step explanation:
There is no pattern that repeats and it cannot be written as a fraction of two whole numbers.
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU VERY MUCH :)
Answer: 45 1/2
Step-by-step explanation:
Volume = 3 1/2 x 4 x 3 1/4
= 91/2
= 45 1/2 or 45.5
Answer:
45. 1/2 cubic inches
Step-by-step explanation:
Since volume of a cube = length x width x height, or V=Bh, we need to multiply 3 1/2, 4, and 3 1/4 together. 3.5 (3 1/2) x 4 = 14. 14 x 3.25 (3 1/4) is 45.5. This is also 45 1/2 in fraction form.
00:00
The weights of babies born at a hospital in November are shown in a line plot.
How many more babies weighed 8 pounds than 61 pounds?
Newborn Weights
0
.
.
6
7
Pounds
Answer:
I think its 1 baby because the 6 1/4 is 2 babies and the 8 1/2 is 3 babies so if you subtract 3 from 2 you get 1.
One more baby weighed [tex]8\frac{1}{2}[/tex] pounds than [tex]6\frac{1}{4}[/tex] pounds.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that The weights of babies born at a hospital in November are shown in a line plot.
The babies weighed at [tex]8\frac{1}{2}[/tex] pounds are 3 babies.
The babies weighed at [tex]6\frac{1}{4}[/tex] pounds are 2 babies.
We have to find the number of babies weighed [tex]8\frac{1}{2}[/tex] pounds than [tex]6\frac{1}{4}[/tex] pounds.
So we have to subtract 2 from 3
3-2 is one
Hence, One more baby weighed [tex]8\frac{1}{2}[/tex] pounds than [tex]6\frac{1}{4}[/tex] pounds.
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5(x + 3) - (9x - 4)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf - 4x + 19}}}}[/tex]
Step-by-step explanation:
[tex] \sf{5(x + 3) - (9x - 4)}[/tex]
Distribute 5 through the parentheses
⇒[tex] \sf{5x + 15 - (9x - 4)}[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression. Also, remove the parentheses
⇒[tex] \sf{5x + 15 - 9x + 4}[/tex]
Collect like terms
⇒[tex] \sf{5x - 9x + 15 + 4}[/tex]
⇒[tex] \sf{ - 4x + 15 + 4}[/tex]
Add the numbers : 15 and 4
⇒[tex] \sf{ - 4x + 19}[/tex]
Hope I helped!
Best regards!!
The bill in a restaurant is $102.25. A tip of 20% is added to the bill. What id tyhe final amount paid?
Answer: $117.59
Step-by-step explanation:
One integer is 7 more than another. Their product is 98. Find the integers,
Answer:
- 14, - 7 or 7, 14
Step-by-step explanation:
Let the the two integers be x and (x + 7)
[tex] \therefore \: x(x + 7) = 98 \\ {x}^{2} + 7x - 98 = 0 \\ {x}^{2} + 14x - 7x - 98 = 0 \\ x(x + 14) - 7(x + 14) = 0 \\ (x + 14)(x - 7) = 0 \\ (x + 14) = 0 \: or \: (x - 7) = 0 \\ x = - 14 \: or \: x = 7 \\ \\ when \: x = - 14 \\ x + 7 = - 14 + 7 = - 7 \\ \\ when \: x = 7 \\ x + 7 = 7 + 7 = 14 \\ [/tex]
Hence the required integers are - 14, - 7 or 7, 14
96,187 square miles. Round the area to the nearest ten.
Answer:
96,190 sq m
Step-by-step explanation:
96,187
7 is greater than 5 so we round up
8 + 1 is 9
Therefore 96,187 rounded to the nearest ten is 96,190
Hope this helped~
Your local smart crackhead
Eric Shotwell borrows $24,600 from a certain bank. The interest charge amounts to $8,592. What equal monthly payments (in $) must Eric make in order to pay back the loan, with interest, in 36 months?
Answer:
He will pay $922 Eve month where
$238.6667 is the interest in the payment
Step-by-step explanation:
Eric Shotwell borrows $24,600 from a certain bank. The interest charge amounts to $8,592 to be paid back in 36 months monthly.
Total money to be paid back
= 24600+8592
Total money to be paid back
= $33192
Now for each month in 36 months, a certain amount must be paid
That amount= 33192/36
= $922
But if the interest wasn't added
He'll pay= 24600/36
=$683.333
So the interest amount in the payment every month= 922-683.333.
= $238.6667
He will pay $922 Eve month where
$238.6667 is the interest in the payment
The calculation is as follows:Total money to be paid back
= 24600+8592
= $33192
Now for each month in 36 months, a certain amount must be paid
That amount= [tex]33192\div36[/tex]
= $922
Now in the case when the interest wasn't added
He'll pay= [tex]24600\div 36[/tex]
=$683.333
So the interest amount in the payment every month is
= 922-683.333.
= $238.6667
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If 2x + 5 = -25 and -3m - 6 = 48, what is the product of x and m?
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.171 ounces, with a sample standard deviation of 0.052 ounce.1. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.01level of significance.)2. State the null and alternative hypotheses.H0:μ ( ≥, ≤, =, <, >,≠ ) ________H1:μ ( ≥, ≤, =, <, >,≠ ) ________(Type integers or decimals.)3. The critical value(s) is(are) _____(Round to four decimal places as needed. Use a comma to separate answers as needed.)4. The test statistic is _______(Round to four decimal places as needed.)5. Reject/ Do not reject H0. There is sufficient/insufficient evidence to conclude the population mean amount is different from 8.17ounces.6. The p-value is _______(Round to four decimal places as needed.)7. Interpret the meaning of the p-value. Choose the correct answer below.A. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounce below 8.17if the null hypothesis is false.B. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounce away from8.17 if the null hypothesis is true.A. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001ounce aboveB. The p-value is the probability of not rejecting the null hypothesis when it is false.
Answer:
We conclude that the mean amount packaged is equal to 8.17 ounces.
Step-by-step explanation:
We are given that in a particular sample of 50 packages, the mean amount dispensed is 8.171 ounces, with a sample standard deviation of 0.052 ounces.
Let [tex]\mu[/tex] = population mean amount packaged.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 8.17 ounces {means that the mean amount packaged is equal to 8.17 ounces}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 8.17 ounces {means that the mean amount packaged is different from 8.17 ounces}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean amount dispensed = 8.171 ounces
s = sample standard deviation = 0.052 ounces
n = sample of packages = 50
So, the test statistics = [tex]\frac{8.171-8.17}{\frac{0.052}{\sqrt{50} } }[/tex] ~ [tex]t_4_9[/tex]
= 0.1359
The value of t-test statistics is 0.1359.
Also, the P-value of test-statistics is given by;
the meaning of the p-value is that the p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounces away from8.17 if the null hypothesis is true.
P-value = P( [tex]t_4_9[/tex] > 0.136) = More than 40% {from the t-table}
Since the P-value of our test statistics is more than the level of significance of 0.01, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean amount packaged is equal to 8.17 ounces.
How do i find the ratio between 16 and 20
Answer:
divide 16/20
Step-by-step explanation:
Answer:
4 : 5
Step-by-step explanation:
ratio between 16 and 20
[tex] = \frac{16}{20} = \frac{4 \times 4}{4 \times 5} = \frac{4}{5} = 4 : 5 \\ [/tex]
Write the following sentence using mathematical symbols. Twice the difference of x and 7 is greater than the reciprocal of 10.
Answer:
2(x-7) > 1/10
Step-by-step explanation:
The statement says, twice the difference of x and 7. This implies that it wants the difference of x and 7, x - 7, and it wants twice that difference so:
2 ( x - 7 )
The statement continues that this twice the difference of x and 7 is greater than the reciprocal of 10. The reciprocal of 10 is 0.1 or 1/10.
Hence, the statement should be written as such:
2 ( x - 7 ) > 1/10 OR 2 ( x - 7 ) > 0.1
Cheers.
The perimeter of a rectangle is 42 cm. The width is 7 cm less than the length.
Answer:
Length = 14Width =7Step-by-step explanation:
[tex]Let \:the\:length\:be \:x\\Perimeter = 42 cm\\Width = x -7\\\\P = 2(l+b)\\\\42 = 2(x+(x-7))\\\\42 = 2(x +x-7)\\42 = 2(2x-7)\\42 = 4x -14\\Collect\:like\:terms\\\\42+14=4x\\56 = 4x\\\\Divide \:both\:sides\:of\:the\:equation\:by \:4\\\frac{56}{4} = \frac{4x}{4} \\\\14 =x\\Length = 14\\Width = x-7\\Width = 14-7\\\\Width = 7[/tex]
why is tan(20) = 3.64 in decimals instead of fractions or whole number?
tan(20) can be written in fractions if you want to, but it is easier to write it in a decimal number when it is punched into a calculator.
You can find the exact value of sin, cos, and tan for some values.
tan() is a trigonometric function that is used when calculating angles or side lengths in a triangle.
solve for θ. sinθ = cos(θ+10)
a. 6°
b.66°
c.84°
d.40°
Answer: d. 40°
Step-by-step explanation:
Use the Cofunction Identity: sin Ф = cos (90° - Ф)
sin Ф = cos (Ф + 10) = cos (90° - Ф)
⇒ Ф + 10 = 90 - Ф
2Ф + 10 = 90
2Ф = 80
Ф = 40
if it -9 now the temperature will drop 5 in two hours what will the temperature be in two hours?
Answer:It will be -14 degrees, because in the negative side, droping or subtracting, would instead be adding. -9 - 5 = -14.
9 + 5 = 14
Step-by-step explanation:
If 7x + 4 = -19 + 5x, then 2x – 14 equals A) 23 B) -23 C) -3 D) 16 E) NOTA
Answer:
2x-14 = -37
Step-by-step explanation:
7x + 4 = -19 + 5x,
Subtract 5x from each side
7x-5x + 4 = -19 + 5x -5x
2x +4 = -19
Subtract 4 from each side
2x +4-4 = -19 -4
2x = -23
We want to find 2x -14
2x = -23
2x-14
-23-14
-37
Answer:
-37
Step-by-step explanation:
First, let's solve for x.
7x+4= -19+5x
Subtract 5x from both sides of the equation.
(7x-5x)+4= -19 (+5x-5x)
(7x-5x)+4=-19
2x+4=-19
Subtract 4 from both sides of the equation.
2x(+4-4)=(-19-4)
2x=(-19-4)
2x= -23
Divide both sides of the equation by 2.
2x/2= -23/2
x= -23/3
x= -11.5
Next, let's find what 2x-14 is equal to. Substitute -11.5 in for x.
2x-14
2(-11.5)-14
Multiply 2 and -11.5
-23-14
Subtract 14 from -23.
-37
2x-14 is equal to -37.
9. Find the slope of a line parallel to 3x - y = 1.
Answer:
slope = 3
Step-by-step explanation:
The slope of a line parallel to the given equation share the same slope. Note the slope intercept formula:
y = mx + b
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
First, isolate the variable, y. Subtract 3x from both sides:
3x (-3x) - y = 1 (-3x)
-y = -3x + 1
Next, divide -1 from both sides:
(-y)/-1 = (-3x + 1)/-1
y = 3x - 1
You are solving for the slope of a line parallel to the given equation. Since you are solving for parallel, the slope would be shared.
3 would be the slope of the line.
~
16 p = 208 p = Pls help quick
Answer:
p=0
Step-by-step explanation:
When you isolate both variables, one side becomes 0.
Answer:
p = 0
Step-by-step explanation:
16p=208p
Subtract 208p from both sides.
16p−208p=0
Combine 16p and −208p to get −192p.
−192p=0
Product of two numbers is equal to 0 if at least one of them is 0. Since −192 is not equal to 0, p must be equal to 0.
p=0
(a) An astronomer's infrared telescope is able to detect radiation with a wavelength of 5.32 x 10-6 meters. Write this number in standard notation.
(b) The diameter of Saturn at its equator is approximately 121,000 kilometers. Write this number in scientific notation.
Answer:
a, 0.00000532 metersb, 1.21*10^5Step-by-step explanation
In this problem. we are required to re-write the given number from scientific notation to standard notation and from standard notation to scientific notation
Exercise a
5.32 x 10-6 meters.
Since we have 10-6, this tells us that we are meant to shift 6 decimal points to the left that is we have
0.00000532 meters
Exercise b
In this example, we are expected to shift 5 decimals away from the decimal point to the right to arrive at the answer therefore we have to multiply by 10^5
hence the equivalent figure in scientific notation is 1.21*10^5 hence
121,000 meters.
1.21*10^5 meters
( -8x + 3x 4 ) - ( -7x - 6x 4 )
Answer:
9x^4 -x
Step-by-step explanation:
( -8x + 3x^4 ) - ( -7x - 6x^4 )
Distribute the minus sign
( -8x + 3x^4 ) +7x + 6x^4
Combine like terms
3x^4 + 6x^4 -8x +7x
9x^4 -x
Answer:
x + 9x^4
Step-by-step explanation:
There is some confusion here. You likely meant by "3x 4" the power term 3x^4 and by "6x 4" the power term 6x^4. " ^ " indicates exponentiation.
Step 1: Eliminate the parentheses. Simply drop them from the first term.
The first term becomes -8x + 3x^4 and the second term becomes 7x + 6x^4.
Now combine like terms:
-8x + 3x^4
+ 7x + 6x^4
------------------
x + 9x^4
Stefen earns $88 in 8 hours. At this rate, how many dollars will he warn in 40 hours
Answer:
$440
Step-by-step explanation:
You need to find the unit rate by dividing how much he earned (88)by how many hours he worked (8) which equals $11 per hour.Then you take the unit rate (11) and multiply it by 40 which equals $440.
if each hash mark represents a spacing of 10 in which of the following ranges of values would you find |x|
Answer:
B, Between -40 and -50
Step-by-step explanation:
Because, X lies between hask mark 4 and 5 to the left of 0, which would make it -40 and -50.
A swimming pool holds exactly 184 cubic yards of water. Assuming that the depth of the pool is the same everywhere, what is the depth in meters if the pool is exactly 30.0 feet long and 20.0 feet wide
Answer:
The depth of the swimming pool is 2.52 meters
Step-by-step explanation:
To solve this problem properly, the first thing we are to do is to ensure that we are working in the same units at all points in time during the solution.
First of all, we will convert the length and breadth of the pool from feet to yards.
1 foot = 0.3333 yards
30 feet = 10 yards
20 feet = 6.67 yards.
The next step is to find the depth of the swimming pool using the volume and the available dimensions.
From the dimensions given, we can tell that the swimming pool will have a cuboidal shape. This means that the volume will be = length X breadth X depth.
hence we have
184 = 10 X 6.67 X depth
depth = 2.76 yards.
The final step will be to convert the answer we obtained in yards to meters.
1 yard = 0.9144metres
2.76 yards = 2.52 meters
The depth of the swimming pool is 2.52 meters
Find the measure of angle in the figure shown below (Please help)
Answer:
ans is 58°
Step-by-step explanation:
it is a straight line so the angle is 180°
so the angle of CED is
CED + 122° = 180°
CED = 180 - 122 = 58°