Answer: To get function g, shift f DOWN by 7 units and to the RIGHT by 2 units
Step-by-step explanation: g(x)= (x-2)^2-7 since they’re both negatives it should be the opposite. An example would be g(x)=(x+3)^2+5, f goes UP for positive by 5 units, left by 3 units.
Write the equation of the line that passes through the given points.
(1,2.5) and (0,6.5)
let's change the decials first off to fractions and get the slope and line
[tex]2.\underline{5}\implies \cfrac{25}{1\underline{0}}\implies \cfrac{5}{2}~\hfill 6.\underline{5}\implies \cfrac{65}{1\underline{0}}\implies \cfrac{13}{2} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{\frac{5}{2}})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{\frac{13}{2}})[/tex]
[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{13}{2}}-\stackrel{y1}{\frac{5}{2}}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{1}}}\implies \cfrac{~~ \frac{8}{2}~~}{-1}\implies \cfrac{4}{-1}\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{-4}(x-\stackrel{x_1}{1})[/tex]
[tex]y-\cfrac{5}{2}=-4x+4\implies y=-4x+4+\cfrac{5}{2}\implies y = -4x+\cfrac{13}{2}[/tex]
There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 212.5 grams of this cereal.
Answer: 131.76 calories
Step-by-step explanation:
110 calories x
----------------- = ----------------
177.4 grams 212.5 grams
cross multiply and divide
(110x212.5)
23, 375 / 177.4 grams
x= 131.76
Consider the set {7,8,9; the elements of this set include?
a. 7,8,9
b. 9, 10, 11
c. none of these
Answer:
The correct answer is "Option A".
Step-by-step explanation:
Hope this helps :)
Mr. Walthour is building a storage in a conical shape. The base of the shed is 4 meters in diameter and the height of the shed is 3.8 meters. What is the volume of the shed? Round to the nearest tenth.
Please HELP ME!!!
[tex]x=1+i[/tex] is a solution to which of the following equations?
a: [tex]x^{2}+1=0[/tex]
b:[tex]x^{2} -2x+2=0[/tex]
c: [tex]x^{2} -2x+1=0[/tex]
d:[tex]x^{2} -1=0[/tex]
If you could please share you're thought process and work with me as well, so I can better understand how you found the answer. Thanks a bunch!
Answer:
b. x² - 2x + 2 = 0Step-by-step explanation:
Solve each to confirm answer
a.
x² + 1 = 0x² = - 1x = √ -1x = iFALSEb.
x² - 2x + 2 = 0(x - 1)² + 1 = 0(x - 1)² = - 1x - 1 = √-1x - 1 = ix = 1 + iTRUEc.
x² - 2x + 1 = 0(x - 1)² = 0x - 1 = 0x = 1FALSEd.
x² - 1 = 0x² = 1x = √1x = ± 1FALSEAnswer:
Option B
Step-by-step explanation:
[tex]\\ \sf\longmapsto x^2-2x+2=0[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(2)}}{2(1)}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2\pm\sqrt{4-8}}{2}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2\pm\sqrt{-4}}{2}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2\pm 2i}{2}[/tex]
[tex]\\ \sf\longmapsto x=1\pm i[/tex]
Verified
Please help me out with thisbeen stuck on this for like a day
Check the picture below, that'd be more or less the pattern of the sprinklinkg, so when we find it's vertex, we'd find how far along the ground at the maximum and its maximum height.
[tex]h(x)=160x-16x^2\implies h(x)=-16x^2+160x+0 \\\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ h(x)=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+160}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left( -\cfrac{160}{2(-16)}~~,~~0-\cfrac{160^2}{4(-16)} \right)\implies \left( \cfrac{160}{32}~~,~~\cfrac{25600}{64} \right) \\\\\\ (\stackrel{\stackrel{\textit{along the ground}}{\downarrow }}{5}~~,~~\underset{\stackrel{\uparrow }{\textit{maximum height}}}{400})[/tex]
well, as you may notice from the picture, the water will hit the ground again when h(x) = 0 or namely y = 0, so let's do that to find out
[tex]h(x)= 160x-16x^2\implies \stackrel{h(x)}{0}= 160x-16x^2 \\\\\\ \stackrel{\textit{common factoring}}{0=16x(10-x)} \implies x = \begin{cases} 0&\leftarrow \textit{hits the ground first}\\ 10&\leftarrow \textit{hits \underline{the ground again}} \end{cases}[/tex]
1. Suppose that in the population of American college students the average number of alcoholic drinks consumed per week is 22. What is the probability of randomly selecting a sample (n = 30) with a mean of 24 and a standard deviation of 5? (Hint: Tell me the two probabilities it will be between using a 2-tailed value)
im not sure on the full awnser.
what number is its own oppositie?
Answer:
0Step-by-step explanation:
what number is its own oppositie?
The number 0 is the only number that is its own opposite.
A bike race takes place over a 3 mile course. How many feet is it?
a
15280 ft
b
3000 ft
c
15,840 ft
d
15000 ft
Answer:
A
Step-by-step explanation:
Here is ur answer
- BRAINLIEST answerer
kyle took at total of 8 quizzes in the first 4 weeks of school. How many weeks of school will he have to attend before he will have taken a total of 12 quizzes?
Answer:
6 weeks
Step-by-step explanation:
8 quizzes = 4 weeks
So 2 quizzes/week
It will take her 12/2 weeks (6) to finish 12 quizzes
-Chetan K
the area of a square is 36 centimeters. how long is each side of the square?
Answer:
6cm
Step-by-step explanation:
square root of 36 because the area of a square is base x height and a square has equal sides
what is multiple integrals
am 7. If the base of the parallelogram is equal to ir and the height is r, then what is the area of the parallelogram?
Step-by-step explanation:
The area of a parallelogram is just base x height, same as a rectangle.
[tex]a=b*h\\a=ir*r[/tex]
If ir is 2 separate variables rather than just 1, that can be simplified to this:
[tex]a=ir^2[/tex]
I need help with b .
Answer:
Finding a common denominator is the same as finding a common multiple. You can multiply the denominators by each other, or list out the multiples of each denominator. Multiplying by others' unique factors gives the least common denominator.
Natalie and her sister opened a savings account at the same time. Natalie deposited $100 and will deposit $10 each month. Her sister deposited $25 and will deposit $25 each month. When will Natalie have less money in her account that her sister?
Answer:
6 months
Step-by-step explanation:
We can think of Natalie as 100 + 10x and her sister as 25 + 25x. If we put them together, we will get 100 + 10x < 25 + 25x, We can simplify it by moving the 25 to the left side and 10x to the right side. Then we will get 75 < 15x, and the smallest solution is 6 because 5 * 15 is equal to 75
A map has a scale of 1 cm to 20km. Rewrite the scale as a ration in its simplest form.
BRAINLIEST HELP PLS !!!!!
Answer:
1 : 2000000
Step-by-step explanation:
we have to convert 20km into cm so
20km×100000
=2000000
So ratio is 1:2000000
MARK ME BRAINLIEST PLS!Answer:
1:2000000.
Step-by-step explanation:
1 km = 1000m = 100*1000
= 100,000 cm
20 km = 2,000,000 cm.
Vhich number line represents the solution of 4x - 9> -21?
Answer:4x -9 >= -21
4x >= -12
x >= -12/4
x >= -3
so this number line started with -3 and go away till + infinity
hope this will help you
Step-by-step explanation:
please help me with this sum I will mark you as brainest
Answer:
Step-by-step explanation:
3/6 x 8
= ( 3 x 8 ) / 6
= 24 / 6
4/7 x 2
= ( 4 x 2 ) / 7
= 8 / 7
9/2 x 3
= ( 9 x 3 ) / 2
= 27 / 2
8/5 x 7
= ( 8 x 7 ) / 5
= 56 / 5
3/9 x 5
= ( 3 x 5 ) / 9
= 15/9
7/4 x 4
= ( 7 x 4 ) / 4
= 28 / 4
6/2 x 6
= ( 6 x 6 ) / 2
= 36 / 2
8/3 x 9
= ( 8 x 9 ) / 3
= 72 / 3
9/4 x 8
= ( 9 x 8 ) / 4
= 72 / 4
5/3 x 6
= ( 5 x 6 ) / 3
= 30 / 3
2/7 x 3
= ( 2 x 3 ) / 7
= 6 / 7
8/4 x 7
= ( 8 x 7 ) / 4
= 72 / 4
6/4 x 2
= ( 6 x 2 ) / 4
= 12 / 4
What is the next number in the series shown?
132, 123, 115, 108, 102
One integer is 8 less than another integer. The sum of the two integers is 72. Find the two integers. Step 2 of 2: What are the two integers? Separate values with a comma.
Answer:
40 and 32
Step-by-step explanation:
This is a linear systems equation problem.
a + b = 72
a = b - 8
Use substitution. Substitute b-8 for a in a+b=72
b-8+b=72
2b-8=72
add 8 to both sides
2b=80 (divide both sides by 2)
b = 40
Plug the value of b into the a=b-8
a=40-8
a=32
Check: 40 + 32 = 72 So the two integers are 40 and 32
Select the geometric figure that correctly matches with the following formula:
A=[tex]\pi r^{2}[/tex]
Answer:
Circle
Step-by-step explanation:
The area of a circle is
[tex]\pi r^{2}[/tex]
A. circle
The area of a circle is 2[tex]\pi[/tex]r²
What is the formula for the circle?The Circle Formulas are expressed as,
the Diameter of a Circle. D = 2 × r. Circumference of a Circle. C = 2 × [tex]\pi[/tex] × r.Area of a Circle A = 2[tex]\pi[/tex]r²The collection of all points equidistant from a fixed point in a plane is called a circle.
the circle is a closed 2-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”. Every line that passes through the circle forms the line of reflection symmetry.
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Help pls ASAP plssss
Answer:
y=2x-1
Step-by-step explanation:
The y-intercept is -1
The slope is 2
Fill in the blank to make each equality true. _ divided by (1/2x^3)=16x^6y^4.
PLS HELP!
Answer:
(8x^9 x y^4) : (1/2x^3)=16x^6y^4
Step-by-step explanation:
8 : 1/2 = 16
x^9 : x^3 = x^6
Equation - [tex]8x^3y^4[/tex] divided by (1/2x^3)=16x^6y^4.
What is equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign. A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The meanings of the word equation as well as its cognates in other languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions.
Let the required term be z.
[tex]z/ (1/2x^3)=16x^6y^4[/tex]
[tex]z=(16x^6y^4) }{(1/2x^3)}[/tex]
[tex]z = 8x^3y^4[/tex]
Hence, [tex]8x^3y^4[/tex]
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Find the additive inverse and the multiplicative inverse, if it exists, of the given number. 5 in modulo 8 arithmetic
The additive inverse of 5 modulo 8 is the number a such that
5 + a ≡ 0 (mod 8)
Then
a ≡ -5 ≡ -5 + 8 ≡ 3 (mod 8)
The multiplicative inverse is m such that
5m ≡ 1 (mod 8)
Use the Euclidean algorithm:
8 = 1•5 + 3
5 = 1•3 + 2
3 = 1•2 + 1
Then
1 = 3 - 1•2
1 = 3 - 1•(5 - 1•3) = 2•3 - 1•5
1 = 2•(8 - 1•5) - 1•5 = 2•8 - 3•5
and so
1 ≡ 2•8 - 3•5 ≡ (-3)•5 (mod 8)
which means the inverse of 5 is
-3 ≡ 8 - 3 ≡ 5 (mod 8)
A researcher claims that 89% of people sleep with a pillow. In a random sample of 1000 people, 825 say that they sleep with a pillow
A loan is paid in 15 years with a total of $192.000. It had a 4% interest rate that compounded monthly. What was the principal?
Round your answer to the nearest dollar and do not include dollar sign
Harold and his brother collected 2019 cans a 1-year period. Each boy collected the same number of cans. About how many cans did each boy collect? Explain how you found your answer.
Answer:
1008.5 cans
Step-by-step explanation:
2019/2=1008.5
if you wanted per day, 1008.5/365=2017/730
Which of the following is not a question to ask to determine the reasonability of a solution?
A. Do the units match what is given in the word problem?
B. Does the answer match what the question is asking for in the problem?
C. Does the numerical answer match up with the correct variable?
D. Is the magnitude of the numeric portion of the answer within an expected range?
Answer:
D IS THE ANSWER
Step-by-step explanation:
HOPE IT HELPS
The image of the point (4, -9) under a translation is (9, -14). Find the coordinates
of the image of the point (-9, -8) under the same translation.
9514 1404 393
Answer:
(-4, -13)
Step-by-step explanation:
When the translation (T) is added, the image is formed.
(4, -9) +T = (9, -14)
T = (9, -14) -(4, -9) = (9-4, -14-(-9)) = (5, -5)
The same holds for the second point:
(-9, -8) +T = (-9, -8) +(5, -5) = (-9 +5, -8 -5) = (-4, -13)
The image of the second point under the same translation is (-4, -13).
Assume the average amount of caffeine consumed daily by adults is normally distributed with a mean of 240 mg and a standard deviation of 47 mg. In a random sample of 600 adults, how many consume at least 320mg of caffeine daily?
The confidence interval is between (48.2%, 57.7%)
Using the proportion formula expressed as:
[tex]CI=p\pm z\cdot \sqrt{\frac{p(1-p)}{n} }[/tex]
Get the proportion:
p = 320/600 = 0.53
[tex]z=\frac{x- \mu}{\sigma}[/tex]
[tex]z = \frac{320-240}{47}\\z=\frac{80}{47}\\z= 1.70[/tex]
Substitute into the formula to get the confidence interval to have:
[tex]CI=0.53\pm 1.7\cdot \sqrt{\frac{0.47}{600}}\\CI = 0.53\pm 0.04757\\CI = (0.53-0.04757, 0.53+0.04757)\\CI = (0.482, 0.577)[/tex]
Hence the confidence interval is between (48.2%, 57.7%)
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