write a quadratic function whose graph passes through (4,-7) and has a vertex of (1,6)
REmember that
The equation of a vertical parabola in vertex form is equal to
y=a(x-h)^2+k
where
(h,k) is the vertex
a is the leading coefficient
substitute the given values
(h,k)=(1,6)
y=a(x-1)^2+6
Find the value of a
we have the point (4,-7)
so
For x=4
y=-7
substitute
-7=a(4-1)^2+6
-7=a(9)+6
solve for a
9a=-7-6
9a=-13
a=-13/9
therefore
y=(-13/9)(x-1)^2+6Decide whether the given ordered pair is a solution to the system of equations.
y = −4x
y =1/2x+7
(-2,8)
Answer:
No, the ordered pair is not a solution to the system of equations
Step-by-step explanation:
Plug x and y into the equations and if both equations are true, then the ordered pair is a solution. Y is 8 and X is -2
8 = -4(-2) is correct
8= 1/2(-2) + 7 is not correct, the equation is equal to 6, not 8.
Find the volume of the oblique rectangular prism below. (2 points)
15
10
8
Enter your answer and your work or explanation in the space provided. Round your answer to the nearest hundredth.
Using the formula we know that the volume of the oblique rectangular prism is 1,200units³ respectively.
What is an oblique rectangular prism?A prism with oblique bases is one in which the bases are not parallel to one another.
An oblique rectangular prism is a rectangular prism with bases that are not arranged one over the other.
The following qualities describe an oblique prism: It seems to be slanted or skewed. Parallelograms make up an oblique prism's faces.
The height is gauged from the outside.
The two bases are not positioned next to one another exactly.
So, the volume formula for the oblique rectangular prism:
V=l⋅w⋅h
Now, insert values:
V=l⋅w⋅h
V=15*10*8
V=1,200 units ³
Therefore, using the formula we know that the volume of the oblique rectangular prism is 1,200units³ respectively.
Know more about an oblique rectangular prism here:
https://brainly.com/question/25670236
#SPJ1
(WILL GIVE BRAINLIEST PLS HELP) Marco is saving for tuition costs at a state university. He deposited $8500 in a 4-year certificate of deposit that earns 7.25% per year. What equation represents this scenario?
f(x)=4*7.25^x
f(x)=8500*4^x
f(x)=1.0725*8500^x
f(x)=8500*1.0725^x
Answer:
($8500)(0.0725)(4)
The expression f(x) = 8500*0.0725*x represents the b best scenario. None of them are correct.
Equation that fit the scenario of He deposited $8500 in a 4-year certificate of deposit that earns 7.25% per year, to determine.
Equation are link of variables that contain equal sign.
Here,
He deposited $8500 in a 4-year certificate,
f(x) = 8500
Earns 7.25% per year,
f(x) = 8500*0.0725*4
Thus, the expression f(x) = 8500*0.0725*x represents the b best scenario.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ2
how to find the length of EF?
\(CD = \frac{HG + EF}{2} \Leftrightarrow EF = 2CD - HG\)
\(2x - 2 = 2x - x + 3\\2x - 2x + x = 3 + 2\\x = 5\)
\(EF = 2 * 5 - 2 = 10 - 2 = 8\)
Answer: 8.
Answer:
EF=8
Step-by-step explanation:
HG=x-3
CD=x
EF=2x-2
Since HG is 3 less than CD, EF has to be 3 more than CD
x+3=2x-2
3+2=2x-x
5=x
x=5
HG=2
CD=5
EF=8
Commitment to goals can be promoted in which of the following ways?
Commitment to goals can be promoted in through:
by imagining how you will feel when you achieve themby identifying who or what might keep you from achieving themWhat is goal commitment?Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain outcomes, are significant. Commitment helps you stick to your goals in both good and bad times, when obstacles arise. Commitment is influenced by two factors: importance and
Goal commitment is generally defined as an individual's determination to devote time and effort to achieving a goal.
Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain.
Learn more about goal on:
https://brainly.com/question/24693533
#SPJ1
30 POINTS HELPPPPP PLS Simplify the following. Do not Evaluate
30^7
Which sequences are geometric? Select three options.
Answer:
there are no sequences pls edit or repost so i can help : )
a shirt was originally marked as $24.95 rings up at the register as 19.96 what is the percent discount on the shirt
Answer:
The discount is 20% off
hope this helps!
express 28x-35y=-7,inthe form ax+by+c=0and find the value of a,b,&c
Answer:
a = 28, b = -35 and c =7
Step-by-step explanation:
Given expression is :
28x-35y=-7
We need to express it in the form of ax+by+c=0 and then find the value of a,b and .
Adding 7 to both sides.
28x-35y+7=-7+7
28x-35y+7=0
or
28x+(-35y) +7=0
It is in the form of ax+by+c=0.
On comparing,
a = 28, b = -35 and c =7
y x1 x2
10 1 16
11 5 11
15 5 14
15 9 11
20 7 1
23 11 8
27 16 7
32 21 3
a. Using technology, construct a multiple regression model with the given data.
b. Interpret the meaning of the values for b1 and b2.
Answer:
ŷ = 0.964X1 - 0.336X2 + 13.066
b1 = 0.964 which is the unit change in the value of y when x1 changes.
b2 = - 0.336 which is the unit change in the value of y when x2 changes
Step-by-step explanation:
Y
10
11
15
15
20
23
27
32
X1
1
5
5
9
7
11
16
21
X2
16
11
14
11
1
8
7
3
The general form of a multiple regression equation is in form:
ŷ = b1x1 + b2x2 + c
Where,
ŷ = predicted or dependent variable
b1 and b2 = slope or gradient Coefficient for the independent or predictor variables x1 and X2 respectively.
c = intercept (constant)
Using the online multiple regression calculator, the model obtained by Inputting the values is written below:
ŷ = 0.964X1 - 0.336X2 + 13.066
Value of b1 = 0.964 which is the unit change in the value of y when x1 changes.
Value b2 = - 0.336 which is the unit change in the value of y when x2 changes
The average length of a baby at birth is 19 inches long. There are 2.54 centimeters in 1 inch. What is the average length of a baby at birth in centimeters.
Answer:
16.46 I don't know
Step-by-step explanation:
3/4n=-1 3/4n-18
Step by step please
Answer:
Solving the expression \(\frac{3}{4}n=-1\frac{3}{4}n-18\) we get \(\mathbf{n=-\frac{36}{5} }\)
Step-by-step explanation:
We need to solve the expression: \(\frac{3}{4}n=-1\frac{3}{4}n-18\)
Solving:
\(\frac{3}{4}n=-1\frac{3}{4}n-18\)
First we convert mixed fraction into improper fraction
\(\frac{3}{4}n=-\frac{7}{4}n-18\)
Now adding 7/4 n on both sides
\(\frac{3}{4}n+\frac{7}{4}n=-\frac{7}{4}n-18+\frac{7}{4}n\\\frac{3}{4}n+\frac{7}{4}n=-18\)
Now, taking LCM on left side
LCM of 4 and 4 is 4
\(\frac{3}{4}n+\frac{7}{4}n=-18\\\frac{3*1n+7*1n}{4}=-18\\\frac{3n+7n}{4}=-18\\\frac{10n}{4}=-18\)
Now, multiply both sides by 4/10
\(\frac{10n}{4}\times \frac{4}{10} =-18\times \frac{4}{10}\\n=-\frac{36}{5}\)
So, solving the expression \(\frac{3}{4}n=-1\frac{3}{4}n-18\) we get \(\mathbf{n=-\frac{36}{5} }\)
log2(1/128)=x, then x =
The value of x will be -7. The expression is solved using the identity.
What is the definition of a logarithm?Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.
Given expression;
\(\rm log_2(\frac{1}{128}) = x\)
The expression is solved using the identity as;
\(\rm log_e1 = x\\\ e^x=1\)
Apply the identity;
\(\rm log_2(\frac{1}{128}) = x \\\\ 2^x = \frac{1}{128}\\\\ 2^x = \frac{1}{2^7} \\\\ 2^x = 2^{-7} \\\\ x = -7\)
Hence the value of x will bed -7.
To learn more about the logarithm refer;
https://brainly.com/question/7302008
#SPJ1
Last week Tom earned $4.50 for every car he washed.
He washed cars over the weekend and now has $63.
Which equation shows x, the number of cars he washed?
Ο Α.
$6x = $4.50
$4.50x = $63
O B.
O C.
O D.
x = $4.50 = $63
$4.50 $63 = x
Plz help
Answer:
4.50x=63
Step-by-step explanation:
in sum 14 cars washed
Leslie buys a large circular pizza that is divided into eight equal slices. She measures along the outer edge of the crust from one piece and finds it to be 5.5 inches. What is the diameter of the pizza to the nearest inch?
Answer:
i believe it's 4.5
Step-by-step explanation:
Answer:
14 in. hope this helps!!:)
Step-by-step explanation:
Which shows the solution set to the
inequality below?
2x+35-5
A. H
-5 -4 -3 -2 -1
0 1
++
2 3 4 5
-
B. +
HHHHHH
-5 -4 -3 -2 -1 0 1 2 3 4 5
C. HA
++++
-5 -4 -3 -2 -1 0 1
0 1 2 3 4 5
D.
-5 -4 -3 -2 -1
+++++
0 1 2 3 4 5
Answer:
The answer is C hope this can help you out!
I will give you the second part of the question.What fraction chose flight ?
As shown in the table :
The total number of students who chose the flight = 37
And the total number of the students = 100
So, the fraction will be : 37/100
the answer is option C. 37/100
A system of equations is given.
Equation 1: 4x − 6y = 10
Equation 2: 9x + 2y = 7
Explain how to eliminate x in the system of equations.
Step-by-step explanation:
To eliminate x in the system of equations:
1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:
Equation 1: 36x -54y = 90
Equation 2: -36x - 8y = -28
2. Add the two equations together to eliminate x:
(36x - 54y) + (-36x - 8y) = 90 - 28
Simplifying, we get:
-62y = 62
3. Solve for y:
y = -1
4. Substitute y = -1 into one of the original equations, say Equation 1:
4x - 6(-1) = 10
Simplifying, we get:
4x + 6 = 10
5. Solve for x:
4x = 4
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.
What's 2+5^3, and how exactly would I solve it
The result of the expression 2 + 5^3 is 127.
To solve the expression 2 + 5^3, you need to follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
In this case, the exponentiation should be performed first.
Step 1: Calculate 5^3
5^3 means raising 5 to the power of 3, which is equivalent to multiplying 5 by itself three times: 5 * 5 * 5 = 125.
Step 2: Add 2 to the result from Step 1.
2 + 125 = 127.
Therefore, the result of 2 + 5^3 is 127.
For more such questions on result , Visit:
https://brainly.com/question/29248277
#SPJ11
Solve by Factoring:
2x^2 - x - 3 = 0
Answer:
x = 3/2 or x = -1
Step-by-step explanation:
2x² - x - 3 = 0
2*(-3) = -6
Factors of -6:
(-1, 6), (1, -6), (-2, 3), (2, -3)
We need to find a pair that adds up to the co-eff of x which is (-1)
Factors :(2,-3)
2 - 3 = -1
so, 2x² - x - 3 = 0 can be written as:
2x² + 2x - 3x - 3 = 0
⇒ 2x(x + 1) -3(x + 1) = 0
⇒ (2x - 3)(x + 1) = 0
⇒ 2x - 3 = 0 or
x + 1 = 0
⇒ 2x = 3 or x = -1
⇒ x = 3/2 or x = -1
The ratio of 36 apples to 18 children
It could be 1:1 or 2:1 if you dont give them more than 1 apple and save some
Step-by-step explanation:
Question 10 of 20 :
Select the best answer for the question.
10. If five times a number plus two is 17, what is the number?
A. 2
B. 5
ООО
C.3
D. 7
Mark for review (Will be highlighted on the review page)
<< Previous Question
Next Question >>
Answer:
C. 3
Step-by-step explanation:
3 x 5 = 15, 15 + 2 = 17 :)
A bag contains 8 red balls and 3 white balls. Two balls are drawn without replacement. (Enter your probabilities as fractions.) (a) What is the probability that the second ball is white, given that the first ball is red
Answer:
12/55
Step-by-step explanation:
Probability is the ratio of the number of possible outcomes to the number of total outcomes.
Given that the bag contains 8 red balls and 3 white balls, the probability of picking a red ball
p(r) = 8/(8+3) = 8/11
Probability of picking a white ball
= 3/11
when a red ball is picked first, the total number of balls reduces to 10 hence the probability that the second ball is white, given that the first ball is red
=8/11 * 3/10
= 24/110
= 12/55
What is 20% of 80 I need help
Answer:
16
Step-by-step explanation:
20% = 0.2
80 x 0.2 = 16
Please mark me Brainliest :)
Answer:
16 is 20 percent out of 80
Step-by-step explanation:
given the following table with selected values of f(x) and g(x) evaluate f(g(1))
The value of f(g(1) from the table of functions is given as 1.
What is Functions ?Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.
when x = 1
g(x) = 3
or f(g(1) = f(3) = 1
The value of f(g(1) from the table of functions is given as 1.
To learn more about Functions refer to :
https://brainly.com/question/30169765
#SPJ1
The value of coin A is twice the value of coin B. Together, the total value of the two coins is $30.00 What is the value of each coin?
Find the slope of the line that passes through (56, 49) and (-18, 35).
Answer:
\(\displaystyle \frac{7}{37}\)
Step-by-step explanation:
\(\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-49 + 35}{-56 - 18} = m \hookrightarrow \frac{-14}{-74} = m \\ \\ \boxed{\frac{7}{37} = m}\)
I am joyous to assist you at any time.
what would be your first step in completely factoring 6a^2-15a+6
The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).
In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:
3(2a^2 - 5a + 2)
Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.
The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:
3(2a - 1)(a - 2)
Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
for similar questions on factoring.
https://brainly.com/question/28260513
#SPJ8
Todd rolled a 12-sided die marked with the numbers 1 to 12. These are his experimental probabilities.
P(odd number) = 18/48
P(greater than 8) = 16/48
P(9) = 12/48
1. Which experimental probability matches the theoretical probability exactly?
2. Which experimental probability is farthest from the theoretical probability?
The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.
Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.
Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.
The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.
The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.
Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.
The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.
The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.
However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.
For more such questions on possible outcomes
https://brainly.com/question/30241901
#SPJ8
I buy 4 5/8 blue fabric and 2 1/8 green fabric how much blue than green did i buy
Answer:
2.5
Step-by-step explanation:
We Know
You buy 4 5/8 blue fabric and 2 1/8 green fabric .
4 5/8 = 37/8 = 4.625 blue fabric
2 1/8 = 17/8 = 2.125 green fabric
How much blue than green did you buy?
We Take
4.625 - 2.125 = 2.5
So, you buy 2.5 blue more than green.