Answer:
Step-by-step explanation:
Answer:
[tex]y=(x-7)^2-1[/tex]
Step-by-step explanation:
We want to convert the equation:
[tex]\displaystyle y=x^2-14x+48[/tex]
Into vertex form, given by:
[tex]\displaystyle y=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
There are two methods of doing this. We can either: (1) use the vertex formulas or (2) complete the square.
Method 1) Vertex Formulas
Let's use the vertex formulas. First, note that the leading coefficient a of our equation is 1.
Recall that the vertex is given by:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -14, and c = 48. Find the x-coordinate of the vertex:
[tex]\displaystyle x=-\frac{(-14)}{2(1)}=7[/tex]
To find the y-coordinate, substitute this value back into the equation. Hence:
[tex]y=(7)^2-14(7)+48=-1[/tex]
Therefore, our vertex (h, k) is (7, -1), where h = 7 and k = -1.
And since we already determined a = 1, our equation in vertex form is:
[tex]\displaystyle y=(x-7)^2-1[/tex]
Method 2) Completing the Square
We can also complete the square to acquire the vertex form. We have:
[tex]y=x^2-14x+48[/tex]
Factor out the leading coefficient from the first two terms. Since the leading coefficient is one in this case, we do not need to do anything significant:
[tex]y=(x^2-14x)+48[/tex]
Now, we half b and square it. The value of b in this case is -14. Half of -14 is -7 and its square is 49.
We will add this value inside the parentheses. Since we added 49 inside the parentheses, we will also subtract 49 outside to retain the equality of the equation. Hence:
[tex]y=(x^2-14x+49)+48-49[/tex]
Factor using the perfect square trinomial and simplify:
[tex]y=(x-7)^2-1[/tex]
We acquire the same solution as before, with the vertex being (7, -1).
If the relationship is proportional, what is the missing value from the table
x
-12
-1
?
-10
-30
O-8
-6
-5
04
Given:
Consider the below figure attached with this question.
The table represents a proportional relationship.
To find:
The missing value from the table.
Solution:
If y is proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is a constant of proportionality.
The relationship passes through the point (-3,-1). Substituting [tex]x=-3,y=-1[/tex] in (i), we get
[tex]-1=k(-3)[/tex]
[tex]\dfrac{-1}{-3}=k[/tex]
[tex]\dfrac{1}{3}=k[/tex]
Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get
[tex]y=\dfrac{1}{3}x[/tex] ...(ii)
We need to find the y-value for [tex]x=-12[/tex].
Substituting [tex]x=-12[/tex] in (ii), we get
[tex]y=\dfrac{1}{3}(-12)[/tex]
[tex]y=-4[/tex]
Therefore, the missing value in the table is -4. Hence, option D is correct.
what much is 1/2 - 1/4
Answer:
1/4
Step-by-step explanation:
The answer is 1/4.
1/2 is equivalent to 2/4.
2/4-1/4=1/4
An environmentalist would like to estimate the true mean weight of all cars. To do so, she selects a random sample of
30 cars and determines that the 90% confidence interval for the true mean weight to be 2.8 to 3.4 tons. Which of the
following would increase the margin of error for this confidence interval?
O selecting another sample
O increasing the sample size
O increasing the confidence level
O decreasing the confidence level
If the confidence level will increase, the margin of error will also increases.
What is margin of error?The margin of error is defined a range of values below and above the sample statistic in a confidence interval.
What is confidence interval?The confidence interval is a way to show what is uncertainty is with a certain statistic.
According to the given question
Environmentalist estimating true mean weight or all cars.
For the true mean weights of 2.8 to 3.4 tons the confidence level is 90%.
Since, the confidence level increases, the critical value increases and hence the margin of error increases.
Therefore, if the confidence level will increase, the margin of error will also increases.
Find out more information about confidence interval and margin error here:
https://brainly.com/question/15079850
#SPJ2
Please HELP!
How many pairs (A, B) are there where A and B are subsets of {1, 2, 3, 4, 5, 6, 7, 8} and A ∩ B has exactly two elements?
Answer:
There are 256 pairs in all.
The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (-); for example, enter y as x^3. Do
not include "G(x) =" in your answer.
Answer:
The graphs below have the same shape. What is the equation of the blue graph? A. G(x) = (x + 3)^3 B. G(x) = x^3 + 3 C. G(x) = x^3 - 3 D. G(x) = (x - 3)^3
The blue graph is a horizontal shift to the left by 3 units of F(x) = x³.
G(x) = (x + 3)³.
What is translation?In mathematics, translation is the process of moving an object from one position to another without changing its shape, size, or orientation.
It involves sliding the object in a particular direction by a certain distance.
We have,
From the graph, the blue graph is G(x) = (x + 3)³.
The function f(x) = (x + 3)³ is a transformation of the function f(x) = x³.
Specifically, it is a horizontal shift to the left by 3 units.
To see why,
Let's consider the effect of replacing x with x + 3 in the original function f(x) = x³.
f(x + 3) = (x + 3)³
Notice that f(x + 3) is equal to f(x) translated horizontally to the left by 3 units.
For example, when x = 0, we have:
f(0) = 0³ = 0
f(0 + 3) = 3³ = 27
So the point (0, 0) on the graph of f(x) = x³ is transformed to the point
(-3, 27) on the graph of f(x) = (x + 3)³.
Similarly, we can see that every point on the graph of f(x) = x³ is shifted horizontally to the left by 3 units to obtain the graph of f(x) = (x + 3)³.
Therefore,
The blue graph is G(x) = (x + 3)³.
Learn more about translation here:
https://brainly.com/question/12463306
#SPJ7
A student sees a newspaper ad for an apartment that has 1330. How many square meters of area are there
Answer:
[tex]Area = 123.55 m^2[/tex]
Step-by-step explanation:
Given
[tex]Area = 1330ft^2[/tex]
Required
Convert to [tex]m^2[/tex]
To convert from square feet to square meter, we simply divide by 3.281^2
So, we have:
[tex]Area = \frac{1330}{3.281^2}m^2[/tex]
[tex]Area = \frac{1330}{10.765}m^2[/tex]
[tex]Area = 123.55 m^2[/tex]
Four brands of lightbulbs are being considered for use in the final assembly area of the Ford F-150 truck plant in Dearborn, Michigan. The director of purchasing asked for samples of 200 from each manufacturer. The numbers of acceptable and unacceptable bulbs from each manufacturer are shown below. At the 0.10 significance level, is there a difference in the quality of the bulbs?
Manufacturer
A B C D
Unacceptable 29 17 9 22
Acceptable 171 183 191 178
Total 200 200 200 200
H0: There is no relationship between quality and manufacturer.
H1: There is a relationship.
1) State the decision rule using 0.10 significance level. (Round your answer to 3 decimal places.)
Reject H0 if chi-square >
2) Compute the value of chi-square. (Round your answer to 3 decimal places.)
Chi-square value
Answer:
Decison region :
Reject H0 : if χ² > 6.251
12.229
Step-by-step explanation:
Given :
Manufacturer A B C D
Unacceptable 29 17 9 22
Acceptable 171 183 191 178
Total 200 200 200 200
H0: There is no relationship between quality and manufacturer.
H1: There is a relationship.
Testing using the goodness of fit :
Chisquare = (observed - Expected)² / Expected
Expected Values:
19.25 19.25 19.25 19.25
180.75 180.75 180.75 180.75
Chi-Squared Values:
4.93831 0.262987 5.45779 0.392857
0.525934 0.0280083 0.581259 0.0418396
χ² = 4.93831 + 0.262987 + 5.45779 + 0.392857
+ 0.525934 + 0.0280083 + 0.581259 + 0.0418396 = 12.229
Degree of freedom, df = (4-1)(2-1) = 3*1= 3
The critical value,
χ² at 0.10, 3 = 6.251
Decison region :
Reject H0 : if χ² > 6.251
Reject H0 : 12.229 > 6.251
If the bearing of P and
Q is
145°. What is the bearing of
Q from P?
9514 1404 393
Answer:
325°
Step-by-step explanation:
The bearing in the reverse direction is 180° more (or less) than the bearing in the forward direction.
145° +180° = 325°
The bearing of Q from P is 325°.
If the bearing of P and
Q is 145°
Soo,
the bearing of Q from P is 145+180=325°
Because it is reserve in the forward direction
[tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
anyone have sna pc hat ??
mine is rince9253
Answer:
Yeah the answer is n o .
Answer:
yes i do have but i dont use it
What is the distance between -10.2 and 5.7?
Answer:
15.9
Step-by-step explanation:
The distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
Two numbers on a number line:
-10.2 and 5.7
As we know, a number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
Indicating the above numbers on a number line:
= 5.7 -(-10.5)
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
= 5.7 + 10.5
= 15.9
Thus, the distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.
Learn more about the number line here:
brainly.com/question/13189025
#SPJ5
on a piece of paper graph y=-2x^2+10x-12 and identify the zeros. Select the choice that matches the graph that you drew and correctly identifies the zeros
Answer:
C. 2 and 3 opens down
Step-by-step explanation:
see graph
Look at the graph shown below:
which equation best represents the line?
A: y=3x+3
B: y=1/2x-3
C: y= 1/2x+3
D: y=3x+ 1/2
Answer:
the answer is C
the y intercept is +3
if you do rise over run, the slope will be 1/2
The quadratic function y = -10x2 + 160x - 430 models a store's daily profit (y), in dollars, for selling T-shirts priced at x dollars.
Answer:
shall I have to answer for x pls tell
Answer:
D, B, C, A
Step-by-step explanation:
What is the image point of (1,-2) after a translation right 4 units and down 4units
Answer:
(-4, -1)
Step-by-step explanation:
y + x + z =762500
z : x = 15/9 : 2
y : x = 1 : 3/4
Step-by-step explanation:
true
What is the y-intercept of y = 3x-
2?
Answer:
-2
Step-by-step explanation:
y = mx + b
y = 3x - 2
y-intercept = b
Which law would you use to simplify the expression
(P/q)^3?
power of a power
power of a quotient
quotient of powers
power of a product
Answer: Power of a quotient
Step-by-step explanation:
The power of quotient basically is:
[tex](\frac{P}{q})^{3} =\frac{P^3}{q^3}[/tex]
A bank gives you a loan of 1,500,000 Baht to buy a house. The interest rate of the loan is 0.01% per day (Using 1 year = 365 days) How much interest you pay after 10 years
Answer:
547 500
Step-by-step explanation:
Interest for 1 year:
0.01%×365=3.65 a year
3.65×10=36.5% for 10 years
36.5×1,500,000÷100=547 500
The interest paid after 10 years is 547 ,500 Baht.
What is Interest ?Interest is the amount paid or earned when a loan is taken or an investment is done respectively.
It is given that
Principal = 1,500,000 Baht
Rate = 0.01 % per day
Time period = 10 years
Interest = ?
Interest = P *R *T/100
Interest = 1500000 * 0.01 *365* 10 / 100
Interest = 547,500 Baht
Therefore the interest paid after 10 years is 547 ,500 Baht.
To know more about Interest
https://brainly.com/question/13324776
#SPJ2
The greatest number of elements possible in
Answer:
4
9
Step-by-step explanation:
If X has 5 elements, and Y has 4 elements, and all 4 of Y's elements are the same as 4 of X's elements, then the intersection of the sets has 4 elements.
If X has 5 elements and Y has 4 elements, and they are all different, then the union of the sets has 9 elements.
Answer:
4
9
You get GPS units from two manufacturers, A and B. You get 43% of your units from A and 57% of your units from B. In the past, 2% of the units from A have been defective, and 1.5% of the units from B have been defective. Assuming this holds true, if a GPS unit is found to be defective what is the probability that it came from manufacturer A (think Bayes Theorem AND round to two decimal places)
Answer:
0.5015 = 50.15% probability that it came from manufacturer A.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Defective
Event B: From manufacturer A.
Probability a unit is defective:
2% of 43%(from manufacturer A)
1.5% of 57%(from manufacturer B). So
[tex]P(A) = 0.02*0.43 + 0.015*0.57 = 0.01715[/tex]
Probability a unit is defective and from manufacturer A:
2% of 43%. So
[tex]P(A \cap B) = 0.02*0.43 = 0.0086[/tex]
What is the probability that it came from manufacturer A?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0086}{0.01715} = 0.5015[/tex]
0.5015 = 50.15% probability that it came from manufacturer A.
Solve the right triangle ABC, with C = 90.00◦ , a = 15.21 cm, b = 17.34 cm. Round to two decimal places.
Answer:
the hypotenuse side, c = 23.1 cmangle A = 41.26 ⁰angle B = 48.74 ⁰Step-by-step explanation:
Given;
first leg of the right triangle, a = 15.21 cm
second leg of the right triangle, b = 17.34 cm
Angle C = 90 ⁰
The missing parameters;
the hypotenuse side = cangle Aangle BUse Pythagoras theorem to calculate the missing side "c", which is the hypotenuse
c² = a² + b²
c² = (15.21)² + (17.34)²
c² = 532.02
c = √532.02
c = 23.1 cm
The missing angle A is calculated as;
[tex]tan(A) = \frac{a}{b} \\\\tan(A) = \frac{15.21}{17.34} \\\\tan(A) = 0.8772 \\\\A = tan^{-1} (0.8772)\\\\A = 41.26^0[/tex]
The missing angle is calculated as;
B = 90⁰ - A
B = 90⁰ - 41.26⁰
B = 48.74⁰
10=−4x+3x^2 solve
please help!
Answer:
-1.28 AND 2.61
Step-by-step explanation:
[tex]10= -4x+3x^2\\ 3x^2 -4x - 10 = 0\\\\[/tex]
use quadratic formula
x = [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] x = [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]
Solution/X-Intercepts: -1.28 AND 2.61
What is the area of the sector that is not shaded?
12Pi units squared
24Pi units squared
120Pi units squared
144Pi units squared
Answer:
120Pi units squared
Step-by-step explanation:
π*12²*(360-60)/360
= π*144*300/360
= π*144*5/6
= π*720/6
= π*120
= 120π or 120Pi units squared
Answer:
120Pi units squared
Step-by-step explanation:
on edge
I need a fast help please
Answer:
(5) c
(6) c
(7) b
(8) a
Step-by-step explanation:
(5) The multiplicative inverse of a number n, is the number which when multiplied by n will give a result of 1 which is a multiplicative identity. The multiplicative inverse of a number is actually the reciprocal of that number. For example, the multiplicative inverse of n is 1/n. The multiplicative inverse of 5 is 1/5. The multiplicative inverse of 5/6 is 6/5.
Therefore, the multiplicative inverse of [tex]\frac{-11}{15}[/tex] is [tex]\frac{-15}{11}[/tex]
(6) To solve 7m + 12 = -4m + 78, follow these steps;
i. Collect like terms by putting terms with m on the left hand side and the terms without m on the right hand side as follows;
7m + 4m = 78 - 12
ii. Now solve both sides;
11m = 66
iii. Divide both sides by 11;
[tex]\frac{11m}{11} = \frac{66}{11}[/tex]
m = 6
(7) Let the number be x;
10 more than twice number is 22 implies that
10 + 2x = 22
Now solve the equation;
2x = 22 - 10
2x = 12
x = 6
(8) The interior angles of a given polygon are the angles of its vertices that are within or inside of the polygon.
The sum of the interior angles of a polygon is given by;
(n-2) x 180°
where;
n = number of sides of the polygon.
For example;
For a triangle, which has n = 3 sides, the sum of these interior angles is (3 - 2) x 180° = 180°
For a rectangle/square, which has n = 4 sides, the sum of these interior angles is (4 - 2) x 180° = 360°.
For a pentagon, which has n = 5 sides, the sum of these interior angles is (5 - 2) x 180° = 540°
Therefore, depending on the number of sides n, the sum of the interior angles of a given polygon is given by;
(n-2) x 180°
Ghgshsvssbdbdbbdbxbxbxbdbdbdbdbdndndjd
So a Quadratic function,A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero
Please answer!<333 xx
12. X= 6
14. B= -11
16. N= 15
Answer:
q12. [tex]x=6[/tex]
q14. [tex]b=-11[/tex]
q16. [tex]n=15[/tex]
Step-by-step explanation:
Q12.
[tex]-1=\frac{x}{-6}[/tex]
Flip the equation:
[tex]\frac{x}{-6} =-1[/tex]
Multiply both sides by 6/(-1)
[tex](\frac{6}{-1} )[/tex] × [tex](\frac{-1}{6}x )[/tex] = [tex](\frac{6}{-1} )[/tex] × [tex](-1)[/tex]
[tex]x=6[/tex]
Q14.
[tex]5b=-55[/tex]
[tex]b=\frac{-55}{5}[/tex]
[tex]b=-11[/tex]
Q16.
[tex]-3n=-45[/tex]
[tex]n=\frac{-45}{-3}[/tex]
[tex]n=15[/tex]
hope this helps.....
What value of b will cause the system to have an infinite number of solutions?
V = 6x + b
-3 x + 1/2 V = -3
Answer:
-6
Step-by-step explanation:
V = 6x + b
1/2 V -3 x = -3
V - 6x = -6
V - 6x = b
You play basketball at your school's
indoor stadium. You have two payment
options. Option A is to buy a membership
card for $20 and pay $2 each time you
go to the gym, t. Option B is to pay $4
each time you go. Write a a linear
equation to show how many trips to the
gym would the cost be the same?
Answer:
20 + 2x = 4x
Step-by-step explanation:
So you are setting the two expressions equal to each other.
buying a membership card and paying each time looks like this: 20 + 2x where x is the number of times you go to the gym. 20 dollars base then 2 each time you go.
4 each time you go is just 4x
so just set the two equal to each other.
20 + 2x = 4x
If you solve it you will get x = something, which would be the number of times to make the two equal.
The sum of a number and 2 times its reciprocal is -3
Answer:
(-2,-1)
Step-by-step explanation:
let the number=x
its reciprocal=1/x
x+2(1/x)=-3
x+2/x=-3
x²+2=-3x
x²+3x+2=0
(x+2)(x+1)=0
x=-2,-1
(c2−4c+7) -(7c2−5c+3).
The required solution for the given expression (c² - 4c + 7) - (7c² - 5c + 3) is -6c² + c + 4.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
(c² - 4c + 7) - (7c² - 5c + 3)
Simplify the expression by solving bracket terms,
c² - 4c + 7 - 7c² + 5c - 3
Further, solve the expression by using mathematical operations,
-6c² + c + 4
The solution for the given expression is -6c² + c + 4.
To know more about Algebraic expression on:
https://brainly.com/question/19245500
#SPJ1