Answer:
[tex]g(x)=(x-3)^{2}[/tex]
Step-by-step explanation:
Options 2 and 3 are discarded because those are traslations to up and down.
Now, the point (0,0) is in the function [tex]f(x)=x^{2}[/tex] and after being traslated it needs to be (3,0). The option [tex]g(x)=(x+3)^{2}[/tex] doesn't satisfice that because the image of 3 is 36 and needs to be 0. On the other hand, [tex]g(x)=(x-3)^{2}[/tex] is the only option that contains the point (3,0) so it is the correct answer.
Answer..
D) g(x) = (x − 3)2
PLEASE HELP, OFFERING 30 POINTS!!
If a plus b plus c equals 68 and ab plus bc plus ca equals 1121, where a, b, and c are all prime numbers, find the value of abc.
The answer is 1978 but I need an explanation on how to get that.
Answer:
This looks a lot harder than it is, because with some clever observations we can quickly eliminate most solutions.
The first thing that springs to mind is a,b,c cannot all be odd, because then the LHS is even and the RHS is odd. Thus at least one of them must be even and therefore equal to 2. So let’s break this into two cases:
Case 1: c=2.
Hence we get
a(a+b)=122=2×61
Now a must be a positive prime factor of this number, and a+b is clearly more than a, so the only solution in this case is (a,b,c)=(2,59,2). Note here that we must check 59 is prime; fortunately it is.
Case 2: c≠2.
Now the RHS is odd, so a certainly can’t be even. But then b must be even, so b=2. Then we have
a(a+2)=120+c
Adding one to each side and factorising shows
(a+1)2=121+c
from which
c=(a+12)(a−10)
(if you are confused about this step think about difference of two squares factorisations).
But we know c is a prime number, so it can’t have any non-trivial factors. Thus one of the brackets must be 1, so a=11, which yields the solution (a,b,c)=(11,2,23). Once more we must check this solution is valid — again, it is, since 11 and 23 are prime. And those are the only two solutions since our cases cover every possibility.
Step-by-step explanation:
Answer:
1978
Step-by-step explanation:
This looks a lot harder than it is, because with some clever observations we can quickly eliminate most solutions.
The first thing that springs to mind is a,b,c cannot all be odd, because then the LHS is even and the RHS is odd. Thus at least one of them must be even and therefore equal to 2. So let’s break this into two cases:
Case 1: c=2.
Hence we get
a(a+b)=122=2×61
Now a must be a positive prime factor of this number, and a+b is clearly more than a, so the only solution in this case is (a,b,c)=(2,59,2). Note here that we must check 59 is prime; fortunately it is.
Case 2: c≠2.
Now the RHS is odd, so a certainly can’t be even. But then b must be even, so b=2. Then we have
a(a+2)=120+c
Adding one to each side and factorising shows
(a+1)2=121+c
from which
c=(a+12)(a−10)
(if you are confused about this step think about difference of two squares factorisations).
But we know c is a prime number, so it can’t have any non-trivial factors. Thus one of the brackets must be 1, so a=11, which yields the solution (a,b,c)=(11,2,23). Once more we must check this solution is valid — again, it is, since 11 and 23 are prime. And those are the only two solutions since our cases cover every possibility.
Which of the following equations is not equivalent to the others?
O y=-3X-4
O y=-3x+(-4)
O y=-4 + 3x
Oy=-4-3x
What’s the answer please
Answer:
d) 6
Step-by-step explanation:
you multiply 3 by 6 because the reciprocal of 1/6 is 6/1
Answer: Last option.
Step-by-step explanation:
When you divide fractions you can multiply the first fraction by the reciprocal of the second fraction.
To find the reciprocal of the fraction, you need to flip it. Then the original denominator will be the new numerator and the original numerator will be the new denominator.
Then, the reciprocal of the fraction [tex]\frac{1}{6}[/tex] is:
[tex]\frac{6}{1}=6[/tex]
Therefore, you can find the quotient of [tex]3[/tex]÷[tex]\frac{1}{6}[/tex] by multiplying 3 by 6:
[tex]3[/tex]÷[tex]\frac{1}{6}=3*6=18[/tex]
Help plz thank you so much
Answer:
x=0.73
Step-by-step explanation:
(+16) 2x^2+12x-16= -3(+16)
2x^2+12x=13/12
2x^2= 1.08/2
x^2=.54
sqrt x^2=.54
x=0.73
Answer:
[tex]x_1=-6.9\\x_2=0.9[/tex]
Step-by-step explanation:
The first step is to move all the terms from the right side to the left side of the equation and then add the like terms:
[tex]2x^2+12x-16=-3\\\\2x^2+12x-16+3=0\\\\2x^2+12x-13=0[/tex]
Now we can apply the Quadratic formula. This is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
In this case we can identify that:
[tex]a=2\\b=12\\c=-13[/tex]
Finally, we must substitute these values into the Quadratic formula. Then we get:
[tex]x=\frac{-12\±\sqrt{((12)^2-4(2)(-13)}}{2(2)}[/tex]
[tex]x_1=-6.9\\x_2=0.9[/tex]
Simplify -26a^7+(-25a^7)
Answer:
-51a^7
Step-by-step explanation:
-26a^7+(-25a^7) may be re-written as a^7(-26 - 25), or -51a^7
The probability of winning a particular game at the Game Place is 1 4 14 . Find the odds against winning the game.
Answer:
3:1
Step-by-step explanation:
The probability of winning is
P(win) = 1/4 = winning/ total
1 win
4 total
total - wins = losses
4-1 = 3
There are 3 losses
To find the odds against winning is finding the odds of losing
We need to compare losing to not losing
3:1
Which of the possible correlations is not possible?
A. -.65
B. .00
C. 1.00
D. 1.25
Answer:
D. 1.25
Step-by-step explanation:
The values of the correlation coefficient must be between -1 and 1 (they can include -1 and 1)
The only value outside that range is 1.25
1.25 is not a possible correlation coefficient
what is the percent change from 45 to 56? round to the nearest percent
Step-by-step answer:
Percentage difference = (new value-old value)/old value*100%
=(56-45)/45*100%
=11/45%100%
= 24.4%
Answer: 24
Step-by-step explanation:
its just 24 have the same question ^^
You bought a magazine for $3 and some
candy bars for $2 each. You spent a total.
of $19. How many candy bars did you do
buy?
Answer:
8 candy bars
Step-by-step explanation:
Transform the question to an equation:
3 + 2x = 19
Solve:
2x = 16
x = 8
Check the answer:
3 + 2 (8) = 19
3 + 16 = 19
True
Hello There!
A magazine costs $3 and some candy bars. Let’s represent the number of candy bars as “X”
19-3=16 so that’s how much money is spent on candy bars.
If $16 is spent on candy bars then 8 candy bars were bought.
Which ratios are equivalent to 10:16? Check all that apply.
30 to 48
25:35
8:32
5 to 15
Answer:
30:48
Step-by-step explanation:
because 30 divides into 10 and 48 divides into 16
Answer:
Option A is correct
30 to 48
Step-by-step explanation:
Given the ratio:
10 : 16
We have to find the ratios are equivalent to 10:16.
Option A.
30 to 48
⇒[tex]\frac{30}{48}[/tex]
Divide numerator and denominator by 3 we have;
⇒[tex]\frac{10}{16}[/tex]
Option B.
25:35
⇒[tex]\frac{25}{35}[/tex]
Divide numerator and denominator by 5 we have;
⇒[tex]\frac{5}{7}[/tex]
or
5 : 7
Option C:
8 : 32
⇒1 : 4
Option D:
5 to 15
⇒[tex]\frac{5}{15}[/tex]
Divide numerator and denominator by 5 we have;
⇒[tex]\frac{1}{3}[/tex]
or
1 : 3
Therefore, the ratio equivalent to 10:16 is, 30 to 48.
What’s the median?
8.74, 3.44, 6.09, 5.0
Answer:
5.545
Step-by-step explanation:
place them in order
3.44, 5.0, 6.09, 8.74
since there are four numbers you add the middle two together and divide in half.
5.545
Median means middle. You must find the middle of this set of data. To do this you must first order the data from least to greatest:
3.44, 5.0, 6.09, 8.74
Now on each "level" remove the largest and the smallest number until you get to the middle number(s)
3.44, 5.0, 6.09, 8.74
5.0, 6.09
Since there isn't exactly one number in the middle you must take the mean (average) of the two numbers left. To do this you must add the remaining numbers, 5.0 and 6.09, together then divide by 2
5.0 + 6.09 = 11.09
11.09 ÷ 2 = 5.545
The mean of this data set is 5.545
Hope this helped!
~Just a girl in love with Shawn Mendes
According to the general equation for conditional probability, if P(A n B) = 3/10 and P(B)= 2/5 what is p(alb)
Answer:
P(A given B) = 3/4
Step-by-step explanation:
As we know that it is conditional probability, where the probability of an event depends on the event that has certain probability of occurrence.
The formula for conditional probability is:
P(A given B) = P(A ∩B) / P(B)
Where a and B are events. The probability of event B is known and we also know probability of A∩B
So, putting the values in the formula:
[tex]P(A\ given\ B) = \frac{P(A and B)}{P(B)}\\= \frac{\frac{3}{10} }{\frac{2}{5} } \\=\frac{3}{10} *\frac{5}{2}\\=\frac{3}{4}[/tex]
So, the probability of A given B is 3/4 ..
Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism.
How are the surface areas of the figures related?
Answer:
The surface area of the larger triangular prism is 4 times the surface area of the smaller triangular prism
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor and the ratio of its surface areas is equal to the scale factor squared
Let
z ----> the scale factor
In this problem
z=2
therefore
z²=2²=4
The surface area of the larger triangular prism is 4 times the surface area of the smaller triangular prism
Answer:
The surface area of the larger prism is 4 times the surface area of the smaller prism.
Step-by-step explanation:
Was right on edge
Your clothing store is open seven days a week from 9 am to 9 pm you are the manager of three employees each of whom want to work at least 24 hours a week. Each employee can work the 9 am to 3 pm shift or the 3 on to 9 pm shift and at least one weekend day. No one can work both shifts on the same day make up a schedule that will meet these requirements
1 represents they are scheduled to work the 9am-3pm shift
2 represents they are scheduled to work the 3pm - 9pm shift
0 represents they are not scheduled to work that day
[tex]\begin{array}{c||c|c|c|c|c|c|c}&Mon&Tue&Wed&Thu&Fri&Sat&Sun\\Employee\ 1&1&1&1&1&0&0&1\\Employee\ 2&0&2&2&2&2&2&0\\Employee\ 3&2&0&0&0&1&1&2\end{array}[/tex]
Employees 1 & 2 will work 30 hours and have 2 days off in a row
Employee 3 will work 24 hours and have 3 days off in a row
What is the measure of XZ?
Check the picture below.
The measure of XZ is 72
What is an arc?A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that might be created by joining the arc's two ends. A semicircular arc is one whose length is exactly half that of a circle.
Given
θ = arc / 2
36 = arc/2
XZ= [tex]36*2[/tex]= 72
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Complete the statement with the choice that best
describes the relationship between the polynomial
and its rational zeroes.
A polynomial, P, has a leading coefficient of 1 and
a constant term. The rational roots of P are all
_______
1. Factors of the leading coefficient
2. Factors of the constant term
3. Multiples of the constant term
Answer:
Factors of the constant term
Step-by-step explanation:
A polynomial, P, has a leading coefficient of 1 and a constant term. The rational roots of P are all factors of the constant term.
The correct option is (2).
What is rational roots of a polynomial?The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials. A polynomial doesn't need to have rational zeros.
Given statement is:
A polynomial, P, has a leading coefficient of one and a constant term. The rational roots of P are all
We know by Rational Zeros Theorem states:
If P(x) is a polynomial with integer coefficients and if is a zero of P(x)
(P( ) = 0), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).
So, from the above statement it is clear that p is a factor of the constant term.
Hence, The rational roots of P are all factors of the constant term.
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Marc bought a pair of sneakers and a sweatshirt for $120. If the sweatshirt cost one-half the price of sneakers, find the cost of each
Answer:
The pair of sneakers cost 80 dollars.
The sweatshirt costs 40 dollars.
Step-by-step explanation:
Let x represent the pair of sneakers
Let y represent the sweatshirt
x + y = 120
The sweatshirt costs one-half the price of sneakers, which is represented by:
y = 1/2(x)
Use the substitution method
x + y = 120
x + 1/2(x) = 120
Multiply the equation by 2
2x + x = 240
3x = 240
x = 80
The cost of the sneakers is 80 dollars
To determine the cost of the sweatshirt subtract 120 by 80/
120 - 80 = 40
The cost of the sweatshirt is 40 dollars
Which equation represents the graphed function?
Answer:
y = -2x + 3
Step-by-step explanation:
The three is the y-intercept, so when x=0, y will equal 3. (0,3)
The slope is negative (-2x), because the minus is present infront of x. So the line's going down.
And we can confirm that it's the function
y = -2x + 3 by letting one point in the line from the graph enter the function.
For example (1,1)
1 = -2x + 3. (let y = 1.)
1 = -2(1) + 3 (let x = 1)
1 = 1
so we can see when we let 1 = -2(1) + 3 it equals the y value on the line.
Answer:
Step-by-step explanation:
y= -2x + 3
What is the length of the hypotonic the triangle ?
Answer:
37 ftStep-by-step explanation:
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]lef=12ft,\ leg=35ft,\ hypotenuse=AB[/tex]
Substitute:
[tex]AB^2=12^2+35^2\\\\AB^2=144+1225\\\\AB^2=1369\to AB=\sqrt{1369}\\\\AB=37[/tex]
The clock face in a famous clock tower has a radius of about 3 meters. What is the area of the clock face to the nearest square meter?
Answer: 28.27
Step-by-step explanation:
A=3.14r^2
A=3.14•3^2
A=3.14•9
A=28.27
Answer: a = 28.3 m²
Step-by-step explanation:
a = πr²
a = π3²
a = 28.3 m²
(pls mark me brainliest)
name the property of equation 8.2 + (-8.2)=0
Answer:
Inverse property of addition.
Round 228 to the nearest 100
What number is 264% of 25?
Answer:
9.47
Step-by-step explanation:
Fill in each square with a digit 1-9, and fill in
each circle with an operator +, -, *, -. Use each
digit and each operator exactly once. The
resulting equation should be true. Use the
standard order of operations (PEMDAS).
What is the largest possible three-digit result
that can be obtained on the right side of the
equation?
Answer:
532
Step-by-step explanation:
To make the right hand side as large as possible, the numerator must be as large as possible and the denominator must be as small as possible. But we can only use each digit once.
Through trial and error:
(9 × 8 + 4) / (1 − 6 ÷ 7) = 532
532 is the largest possible three digit that can be obtained on the right side of equation.
What is PEMDAS?
PEMDAS is short form of parentheses, exponents, multiplication , division, addition and subtraction.
To get the the largest possible three digit from given condition, we have to make the denominator as small as possible by using subtraction and division. And we can increase the numerator.
Now, through trial and error method
we have (9 * 8 + 4) / ( 1 - 6 / 7 ) = 76 * 7 = 532
Hence 532 is the largest possible three digit that can be obtained on the right side of equation.
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What number, when substituted for x in the following problem, will make the problem true? 6x + 8x = 10x
Answer:
There is no number when substituted for x that will make the statement true.
Step-by-step explanation:
First you would simplify the left side:
6x + 8x= 14x
14x=10x
This statement isnt true no matter what you plug in the sides will never be equal
Answer: If you substitute the number 2 for x in the problem, you’ll make it true.
6x + 8x = 10x
62 + 82 = 102
36 + 64 = 100
100 = 100
Step-by-step explanation
pennfoster
Use the graph to find the indicated function value y=f(x). Find f(-2)
Answer:
f(-2)=3
Step-by-step explanation:
we know that
f(-2) is the value of the function f(x) for the value of x equal to -2
so
Observing the graph
For x=-2
f(-2)=3
The result is found by substituting -2 into the equation of the function. Using the provided line of best fit equation, we find f(-2) to be approximately -3207.324, but this is just an approximation.
Explanation:To find f(-2) using the given equations, we first identify the equation associated with the given function, which in this case, is not explicitly provided in the given information. By convention, the general format for a linear function is y=f(x). The value is found by substituting the value of x into the equation and solving for y.
However, since the equation of the function isn't provided but we have details about the line of best fit, we could use that if it closely represents the graph of our function. In the case of the line of best fit given as ŷ = −3204 + 1.662x, we simply plug in -2 for x:
ŷ = -3204 + 1.662*(-2) = -3204 - 3.324 = -3207.324
So, if we were using this line of best fit as a representation for our function f(x), then f(-2) would be approximately -3207.324. Always remember though, that the line of best fit is an approximation and the real value might slightly differ based on the actual function.
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Fill in the blank.In the triangle below,z degrees =
Not enough information, please attach a photo next time.
ANSWER ALL TO GET ALL POINTS
Q1: How do you identify which side is the hypotenuse of right triangles?
Q2: What does it mean to be a Pythagorean Triple? Given an example of a Pythagorean Triple.
Q3: Explain why Volume must always have cubic units.
Answer:
hypotenuse is always opposite the right angle and it is always the longest side of the triangle
Pythagorean Triple consists of three positive integers a, b, and c, such that a² + b² = c² example 3, 4, 5).
volume occupies a three dimensional space. Distance is measured in one unit of length
Step-by-step explanation:
Ordered pairs for y=3^x
Answer:
[-2, ⅑], [-1, ⅓], [0, 1], [1, 3], [2, 9]...
Step-by-step explanation:
You are simply creating an x-y value value chart and simply plugging in integers for "x" to get your "y".
5/9 of students at a school are girls. If there are 3708 students at the school, how many are boys?
Answer:
1648 are boys.
Step-by-step explanation:
You divide the 3708 by 9 and get 412. Then you multiply that by 4 and get 1648
To find how many boys are in the school, first calculate the number of girls by multiplying the total students, 3708, by 5/9, resulting in 2060 girls. Subtracting this from the total gives 1648 boys.
The question asks how many students are boys in a school if 5/9 of the students are girls, and the total number of students is 3708. To solve this, first, we need to calculate the number of girls by multiplying the total number of students (3708) by 5/9. Then, to find the number of boys, we subtract the number of girls from the total number of students.
Calculate the number of girls:Therefore, there are 1648 boys in the school.