Answer:
x = -1
Step-by-step explanation:
The graph's turning point is at ( -1 , 1 ), therefore the line of symmetry is at x = -1.
Answer: x = -1
Step-by-step explanation:
The formula to find the axis of symmetry in a function y = ax² + bx + c is:
[tex]x=\frac{-b}{2a}[/tex]
For y = x² + 2x + 2, where:
a = 1b = 2c = 2The axis of symmetry would be:
[tex]x=\frac{-b}{2a} =\frac{-2}{2(1)} =\frac{-2}{2} =-1[/tex]
A ball is dropped from 248 feet above
the ground level and after the second
bounce it rises to the height of 62 feet.
If the height to which the ball rises
after each bounce is always the same
fraction of the height reached on its
previous bounce, what is this
fraction?
Let us say
The Height from which the ball was first dropped as H0 = 248 feet
The Height reached by the ball after second bounce is H1
The Height reached by the ball after second bounce is H2 = 62 feet
Given , Height the ball reaches after bounce is a fraction of the height the ball reached in the previous bounce
The Height reached by the ball after second bounce = H2 = X of H1
==> 62 = X * H1 ...................Equation 1
The Height reached by the ball after first bounce = H1 = X of H0
==> H1 = X * 248 ...................Equation 2
Substituting value of H1 from Equation 2 to Equation 1
62 = X * H1 = X * X * 248
X^2 = 62/248 = 31/124 = 1/4
X = 1/2
Answer is A. 1/2
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if D is the center of the circle below and AC measures 48, what is the mesure of ABC
Answer:
A. 24
Step-by-step explanation:
48/2=24. Hope this helps:)
[tex]\sqrt{x} 3500[/tex]
Step-by-step explanation:
Download gauthmath it will help
IBM issued 30-year bonds with an annual simple interest rate of 6.22%. Find the semiannual interest payment on a$5,000 bond.
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Answer:
$155.50
Step-by-step explanation:
The interest is given by the formula ...
I = Prt
where P is the principal earning interest at annual rate r for t years. The interest period here is 1/2 year.
I = $5000×0.0622×1/2 = $155.50
The semiannual interest payment is $155.50 on this bond.
four consecutive numbers have a sum of –30. What number is x?
Answer:
- 9
Step-by-step explanation:
Let the four consecutive numbers be x, x + 1,
x + 2 and x + 3.
x + x + 1 + x + 2 + x + 3 = - 30
x + x + x + x + 1 + 2 + 3 = - 30
4x + 6 = - 30
4x = - 30 - 6
4x = - 36
x = - 36 / 4
x = - 9
Find the common denominator 2/7 and 7/10
Answer:
70
Step-by-step explanation:
Finding the common denominator is really just finding the gcf of 7 and 10. The gcf of 7 and 10 is 70. So the common denominator is 70.
Corinne solved the equation below:
5x = 95
5x − 5 = 95 − 5
x = 90
Is Corinne's solution correct? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation.
Answer:
The solution is incorrect
Step-by-step explanation:
5x = 95
We need to do the opposite
We are multiplying x by 5 so we need to divide by 5
5x/5 = 95/5
x = 19
Corinne's solution is incorrect.
The mistake occurred when she subtracted 5 from both sides of the equation.
We have,
To solve the equation correctly, we need to isolate the variable x. Here are the correct steps:
Starting with the equation:
5x = 95
To isolate x, we divide both sides of the equation by 5:
(5x) / 5 = 95 / 5
x = 19
Thus,
The correct solution to the equation is x = 19.
Learn more about equations here:
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Two friends went to get ice cream sundaes. They each chose a flavor of ice cream from a list of vanilla and chocolate and toppings from a list of hot fudge, strawberries, sprinkles, peanuts, and whipped cream. Use the sets below describing their choices and find B'.
Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}
Let B = {vanilla, hot fudge, sprinkles, whipped cream}
Let C = {chocolate, hot fudge, peanuts, whipped cream}
The complement of set B denoted by B' is are {chocolate, strawberries, peanuts}
What is a Venn Diagram?A Venn diagram is a diagrammatic illustration showing the various components of a set in a diagram. The venn diagram for each set is usually enclosed in a circle and those circle(s) are inscribed in a rectangle known as the Universal Set.
A complement of a set is a set that is not from the Universal Set.
Let's assume that we use the initials of each word to represent them in a Venn diagram. Then;
Universal Set (U) = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream} Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}Let B = {vanilla, hot fudge, sprinkles, whipped cream}Let C = {chocolate, hot fudge, peanuts, whipped cream}The complement of Set B denoted at B' = {chocolate, strawberries, peanuts}
Learn more about Venn Diagrams here:
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The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 mm
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Answer:
8000π mm^3/s ≈ 25,133 mm^3/s
Step-by-step explanation:
The rate of change of volume is found by differentiating the volume formula with respect to time.
V = 4/3πr^3
V' = 4πr^2·r'
For the given numbers, this is ...
V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s
_____
Additional comment
By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.
The product of two numbers is 60 and thei r sum is it, find the Numbers
A line with a slope of 4 passes through the point (2, 3) . What is its equation in slope -intercept form?
Answer:
y=4x-5
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y intercept.
Plug in what you know to solve for b.
3 = 4(2) + b
3 = 8 + b
3-8 = b
b = -5
now put b and m back into the slope- int form.
y = 4x-5
Polynomial: 3x^4 + 5x - 4; Divisor: x - 1
Answer:
3x³+3x²+3x+8+[tex]\frac{4}{x-1}[/tex]
Step-by-step explanation:
You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.
What is 5% of 483759????
Step-by-step explanation:
5% of 483759 is 24187.95
Answer: The answer is 24,187.95
Step-by-step explanation:
483759 Multiplied by 0.05 = 24,187.95
50 POINTS PLEASE HELP ME
Hello!
f(g(x)) = 4 - 2 × (3x²) <=>
<=> f(g(x)) = 4 - 6x²
Answer: B. f(g(x)) = 4 - 6x²
Good luck! :)
Let we find the composition,
→ f(g(x)) = 4 (-2 × 3x²)
→ f(g(x)) = 4 -6x²
Hence, option (B) is the answer.
The Science Club arranged a trip to Smithsonian. Only 2/3 of the members were able to attend, which left one seat empty on the 25-passenger bus. How many members does the Science Club have?
Answer:
36 members
Step-by-step explanation:
Let x = the number of science club members
There are 24 people on the bus (1 seat empty on the 25 seat bus)
2/3 of the club attended and that equals 24 people on the bus
2/3x = 24
Multiply each side by 3/2
3/2 * 2/3x = 24 * 3/2
x = 36
what is 2 1/2 divided by 1/3 {pls hurry the teacher is not letting us use brainly}
Answer:
7 1/2
Step-by-step explanation:
2 1/2 ÷ 1/3
Change to an improper fraction
(2*1+2)/2 ÷ 1/3
5/2 ÷1/3
Copy dot flip
5/2 * 3/1
15/2
Change to a mixed number
7 1/2
what fraction of 3 weeks is 18 days?
Answer:
18/21
Step-by-step explanation:
1 week is 7 days
3 weeks is 21 days
so the answer is 18/21
If the cost, C, for manufacturing x units of a certain product is given by c=x^2-5x+65, find the number of units manufactured at a cost of 13,865.
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Answer:
120
Step-by-step explanation:
I find it pretty easy to obtain the solution by graphing ...
c(x) -13865 = 0
The positive value of x that makes this so is x = 120.
120 units will have a cost of 13,865 to manufacture.
__
If you like to solve this algebraically, you can probably do it most easily by completing the square.
x^2 -5x = -65 +13865
x^2 -5x +6.25 = 13806.25 . . . . . add the square of (-5/2)
(x -2.5)² = 13806.25
x -2.5 = √13806.25 = 117.5 . . . . only the positive square root is interesting
x = 117.5 +2.5 = 120
Select the correct answer from each drop-down menu?
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Answer:
second3firstisStep-by-step explanation:
We observe that the second equation of System B has had the x-term eliminated. That can be accomplished by adding 3 times the first equation to the second.
"To get System B, the second equation in System A was replaced by the sum of that equation and 3 times the first equation. The solution is the same as the solution to System A."
If my saving x$ grows 10% every year how much will I have in:
1 year
2 year
5 year
Answer:
[tex]1.1x, 1.21x, 1.61051x[/tex]
Step-by-step explanation:
If you saving grows [tex]10 \%[/tex] every year, then your saving is [tex]1.1\\[/tex] times your saving from last year. Therefore, after one year, you will have [tex]1.1x\\[/tex], then after [tex]2[/tex] years, you will have [tex](1.1)^2 \cdot x=1.21x[/tex], then after [tex]5[/tex] years, you will have [tex](1.1)^5 \cdot x = 1.61051x[/tex].
Answer:
$1.1x, $1.21x, $1.61x
Step-by-step explanation:
convert the following decimals to a simplified fraction, showing all wok
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Have a nice day
Answer:
first let y=1.33 (with a _ on top of the threes after the decimal) then let 100y=133.33( with a _on top of the threes after the decimal)then subtract eq(ii) -eq(I) which is left side 100y-y= 99yright side 133.33-1.33=132then 99y=132then y=132/99 hence converted to fractionThe feet of the average adult woman are 24.6 cm long, and foot lengths are normally distributed. If 16% of adult women have feet that are shorter than 22 cm, approximately what percent of adult women have feet longer than 27.2 cm?
Answer:
Approximately 16% of adult women have feet longer than 27.2 cm.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The feet of the average adult woman are 24.6 cm long
This means that [tex]\mu = 24.6[/tex]
16% of adult women have feet that are shorter than 22 cm
This means that when [tex]X = 22[/tex], Z has a p-value of 0.16, so when [tex]X = 22, Z = -1[/tex]. We use this to find [tex]\sigma[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1 = \frac{22 - 24.6}{\sigma}[/tex]
[tex]-\sigma = -2.6[/tex]
[tex]\sigma = 2.6[/tex]
Approximately what percent of adult women have feet longer than 27.2 cm?
The proportion is 1 subtracted by the p-value of Z when X = 27.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27.2 - 24.6}{2.6}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84.
1 - 0.84 = 0.16
0.16*100% = 16%.
Approximately 16% of adult women have feet longer than 27.2 cm.
If IC Rs 100 is equal to Rs 160 NC, convert IC Rs 150 into NC rupees.
Answer:
240 NC rupees.
I need two examples of rounding to the thousandths place. SHOW ALL WORK!
Answer:
3.418
Step-by-step explanation:
3.4175
3.4178
u round if the number behind it is higher than 5
Your help would be very much appreciated I will mark you brainliest as well! :D
Given the similarity statement
AJKL ANOP, what's the
corresponding side of ON ?
Answer:
ON = KJ
Step-by-step explanation:
JKL = NOP
We know the angles match
<J = <N
<K = <O
< L = <P
And we know
JK = NO
KL = OP
JL = NP
We are looking for ON = KJ
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Answer:
(d) KJ
Step-by-step explanation:
The segment of interest is named using the 2nd and 1st letters of the right side of the similarity statement.
The corresponding segment will be named using the 2nd and 1st letters of the left side of the similarity statement: KJ.
Which answer explains the correct way to move the decimal to find the quotient of 14.6 ÷ 10,000?
three places to the right.
three places to the left.
four places to the left.
four places to the right
Answer:
Four places to the left.
Step-by-step explanation:
14.6/10000
=> 1.46/1000 [Shifted 1 decimal place after dividing by 10]
=> 0.146/100 [Shifted 1 decimal place after dividing by 10]
=> 0.0146/10 [Shifted 1 decimal place after dividing by 10]
=> 0.00146 [Shifted 1 decimal place after dividing by 10]
Number of decimal places = 1+1+1+1=4
Four places to the left.
On her summer abroad in France, Jane bought a pair of shoes for 54.82 euros. The store owner only had francs to give her as change. She gave him 55 euros. How much did he give her back in francs
Answer:
0.19
Step-by-step explanation:
Jane bought a shoe for 54.82 euros
She gave the store owner 55 euros
= 55-54.82
= 0.18 euros to franc
= 0.18× 1.08222
= 0.19 franc
Simplify and express the following as a rational number
[tex]( \frac { - 4 } { 3 } ) ^ { 8 } \div ( \frac { - 4 } { 3 } ) ^ { 12 }[/tex]
Answer:
81/256
Step-by-step explanation:
(-4/3)^8 divide (-4/3)^12
= (-4/3)^8-12
= (-4/3)^-4
= (3/-4)^4
=81/256
Answer:
The answer is 81/256
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST! Also please explain the answer
Answer:
Each triangle is a right triangle.
Step-by-step explanation:
You can see each one has one 90 degree corner.
Answer:
13. True
14. True
15. False
Step-by-step explanation:
By using the Pythagorean Theorem a^2+b^2=c^2, you can evaluate whether or not the triangles are right triangles.
13. 8^2+15^2=17^2 -> 64+225=289 -> TRUE
14. 50^2+120^2=130^2 -> 2500+14400=16900 -> TRUE
15. 12^2+35^2=36^2 -> 144+1225 =/=1296 -> FALSE
