Answer:
f(x) = (x - 3)² - 1
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
Add/subtract ( half the coefficient of the x- term )² to x² - 6x
f(x) = x² + 2(- 3)x + 9 - 9 + 8
= (x - 3)² - 1
6 times a number plus 21 is greater than 6
A. 6 x plus 21 greater than 6
B. 6 x plus 21 less than or equals 6
C. 6 x plus 21 greater than or equals 6
D. 6 x plus 21 less than 6
PLEASE HELP MEHHH
Which of the following represents a function?
Answer: The top one
Step-by-step explanation:
Because there can only be one input for one output. (X’s can’t repeat)
If f(x) = -4x2 - 6x- 1 and g(x) = -x2 - 5x + 3, find (f+ g)(x).
O A. (f+ g)(x) = 5x2 + 11x+ 4
O B. (f+ g)(x) = - 5x2 - 11x + 2
O C. (f+g)(x) = -5x2 - x-4
O D. (f+9)(x) = 3x2 + x+4
Answer:
Step-by-step explanation:
f(x) = -4x^2 - 6x - 1 ........ g(x) = -x^2 - 5x + 3
find (f + g)(x)
-4x^2 - 6x - 1 + (-x^2 - 5x + 3) =
-4x^2 - 6x - 1 - x^2 - 5x + 3 =
-5x^2 - 11x + 2 <====
Answer: B
Step-by-step explanation:
-4x2 + (-x2)= (-6x2) (-6x) + ( -5x)= (-11x) (-1) + 3= 2-6x2-11x+2Lesson 8-5
Using the Distributive Property
b (b + 12) = 0
The value of b is -12
Solution:
The given equation, b (b + 12) = 0
On distributing the b inside the parentheses we get,
[tex]\Rightarrow\bold{ b\times b+b\times12=0}[/tex]
[tex]\bold{\Rightarrow b^{2}+12b=0}[/tex]
[tex]\bold{\Rightarrow b^{2}=-12b}[/tex]
[tex]\bold{\Rightarrow 1=\frac{-12b}{b^2}}[/tex]
[tex]\bold{\Rightarrow 1=\frac{-12}{b}}[/tex]
[tex]\bold{\Rightarrow b=-12}[/tex]
Steps to use distributive property to solve an equation:
Multiply the term outside of the parentheses by each term in the parentheses.Distribute a negative number together with its negative sign.Combine like termsSolve the equation.For fractions:
Identify any fractional coefficients or constants.Find the lowest common multiple (LCM) for all denominators.Multiply all terms of the equation by the LCM.Combine like terms and solve the equation.James has pennies nickels and dimes in his bank he is has more than $1.60 and less than $2.00 in the bank there are 5 times as many pennies as dimes there is an equal number of nickels dimes what’s exact amount of money in his bank
James has pennies, nickles and dimes in his bank. he has more than $1.60 and less than $2.00 in the bank. there are 5 times as many pennies as dimes. there is an equal number of nickels and dimes. what is the exact amount of money in his bank?
Answer:
The exact amount of money in his bank is $ 1.8
Solution:
Let "p" be the number of pennies
Let "d" be the number of dimes
Let "n" be the number of nickels
Given that,
There are 5 times as many pennies as dimes
Number of pennies = 5 times the number of dimes
p = 5d ----------- eqn 1
There is an equal number of nickels and dimes
n = d -------- eqn 2
We know that,
value of 1 dime = 0.10 dollar
value of 1 nickel = 0.05 dollar
value of 1 penny = 0.01 dollar
The total value of coins is:
total value = d(0.10) + n(0.05) + p(0.01)
Substitute eqn 1 and eqn 2
total value = d(0.10) + d(0.05) + 5d(0.01)
total value = 0.2d
Given that he has more than $1.60 and less than $2.00 in the bank
Therefore, 0.2d must be greater than 1.60 and less than 2.00
Try for d = 8
total value = 0.2 x 8 = 1.6
But value must be greater than 1.6
Try for d = 9
total value = 0.2 x 9 = 1.8
Thus 1.8 is greater than 1.60 and less than 2.00
Therefore, the exact amount of money in his bank is $ 1.8
Read the following scenarios. Who is better positioned to invest in bonds and why?
Jim is 24 and earns $62,000 a year. He wishes to invest for his newborn daughter's college education, which is 18 years away. Inflation is currently running at 4.1%, while real interest rates are rising.
Elizabeth is 63 years old and earns $137,000 a year. She wishes to invest for retirement, which is four years away. Inflation is currently running at 1.1%, while real interest rates are falling.
Select the best answer from the choices provided.
A.
Jim is better positioned to invest in bonds because he makes less and has longer before his investment matures.
B.
Jim is better positioned to invest in bonds because inflation is high.
C.
Elizabeth is better positioned to invest in bonds because she has less time before her investment matures.
D.
Elizabeth is better positioned to invest in bonds because real interest
rates are falling.
Answer:
The correct answer is A. Jim is better positioned to invest in bonds because he makes less and has longer before his investment matures.
Step-by-step explanation:
Jim is better positioned to invest in bonds for two reasons:
1. He can invest and take advantage of long-term bonds, between 12 and 20 years of term of maturity, that are those that usually have the highest interest rate. His goal is to invest and save for his daughter's college education, that is a newborn.
2. The real interest rates are rising. It means the bonds interest rates are clearly above the inflation rate in the country where Jim and his family live, having a better return for his investment.
Which point is the y-intercept of the graph of 5x - 3y = 15 ?
(-5, 0)
(3, 0)
0, -5)
(0,3)
Answer:
c
Step-by-step explanation:
How do you workout 28 divided by 812
Answer:
29
Step-by-step explanation:
Look at image
I need help please and thank you
Answer:
75
Step-by-step explanation:
6 and 4 are alternate interior angles meaning they have the same value
$5000 at 4% interest for 3 years?
Answer:
Simple Interest =$5600 (Principal and Interest)
Compound Interest = $5624.32 (Principal and Interest)
Step-by-step explanation:
Using Simple interest, use the formulae, Principal X Rate X Time
= 5000*4%*3
= $600 Interest
Principal plus Interest = $5600
Using compound Interest, use the formulae P(1+r)^n
P means Principal
R means rate
N means number of years
= 500(1+4%)^3
= $5624.32 (Principal with Interest)
is 0.325 a rational or irrational
Answer:
rational number
Step-by-step explanation:
Answer:
It's a rational. You can convert this to a simplified fraction
An irrational number is a number which cannot be expressed in a ratio of two integers. In rational numbers, both numerator and denominator are whole numbers, where the denominator is not equal to zero. While an irrational number cannot be written in a fraction.
2. Tickets to a play cost $344.50 for a group of 12 adults and 10 children. Each aduit ticket cost
$18.50. What is the cost of one child's ticket?
Brainliest if you are right
Answer:
e
Step-by-step explanation:
because the lines are less scattered and they all are going straight up. they are also higher then all of the other ones.
-3(x+5) = -9
Please answer asap
Steps to solve:
-3(x + 5) = -9
~Distributive Property
-3x - 15 = -9
~Add 15 to both sides
-3x - 15 + 15 = -9 + 15
~Simplify
-3x = 6
~Divide -3 to both sides
-3x/-3 = 6/-3
~Simplify
x = -2
Best of Luck!
Answer:
x= -2
Step-by-step explanation:
First, distribute the 3 into the parenthesis.
(-3)x+ (-3)5= -9
Then, multiply.
-3x-15= -9 *The negative makes it into becoming subtraction.
Now, add 15 to both sides since that's the opposite of subtraction.
-3x-15= -9
+15 +15
Then, divide by 3 to both sides to isolate the variable.
-3x= 6
-3 -3
x= -2
The width of a rectangle is 4 1/6 feet, and its area is 35 square feet. What is the perimeter of this rectangle?
The perimeter of rectangle is 25.13 feet
Solution:
Given that,
width of a rectangle = [tex]4\frac{1}{6} \text{ feet }[/tex]
Convert the mixed fraction to improper fraction
[tex]\rightarrow 4\frac{1}{6} = \frac{6 \times 4 + 1}{6} = \frac{25}{6}[/tex]
Therefore,
[tex]\text{width of rectangle } = \frac{25}{6} \text{ feet }[/tex]
Area of rectangle = 35 feet
The area of rectangle is given by formula:
[tex]area = length \times width[/tex]
Substituting the given values, we get
[tex]35 = length \times \frac{25}{6}\\\\length = 35 \times \frac{6}{25} = \frac{42}{5}[/tex]
Thus we get,
[tex]\text{length of rectangle } = \frac{42}{5} \text{ feet }[/tex]
The perimeter of rectangle is given as:
perimeter = 2(length + width)
[tex]perimeter = 2(\frac{42}{5} + \frac{25}{6})\\\\perimeter =2(8.4+4.167)\\\\perimeter = 2(12.567)\\\\perimeter = 25.13[/tex]
Thus perimeter of rectangle is 25.13 feet
Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4. Nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power of 4 to get StartFraction r Superscript negative 20 Baseline s Superscript negative 12 Baseline Over r Superscript 32 Baseline s Superscript 8 Baseline EndFraction. Calvin claims the first step to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4. Who is correct and why?
Answer:
Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step
That is [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex] Calvin's step is the correct step.Because this is the correct way to do simplify the rational expression. And also because Nadine made a blender mistake in her operations in step
Step-by-step explanation:
Given that Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4
Their expression can be written as below
[tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}[/tex]
Nadine's first step is to simplify the expression is to raise the numerator and denominator to the power of 4 to get StartFraction r Superscript negative 20 Baseline s Superscript negative 12 Baseline Over r Superscript 32 Baseline s Superscript 8 Baseline EndFraction
That is [tex]\frac{r^{20}s^{12}}{r^{-32}s^8}[/tex]
Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4
That is [tex]r^{-13}s^{-1}[/tex]
Now simplify the given expression to check whose step is correct:
[tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}[/tex]
[tex]=(r^{-5}s^{-3}r^{-8}s^{2})^{-4}[/tex] ( using the property [tex]\frac{1}{a^m}=a^{-m}[/tex] )
[tex]=(r^{-5-8}s^{-3+2})^{-4}[/tex]
[tex]=(r^{-13}s^{-1})^{-4}[/tex]
Therefore [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex]
Therefore Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step.
That is [tex](\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}[/tex] Calvin's step is the correct step .Because this is the correct way to do simplify the rational expression.And also because Nadine made a blender mistake in her operations in step
Evaluate a Composit
Given f(x) = x - 7 and g(x) = x2
Find g(4)).
G(f(4)) =
g(x) = x²
g(4) = 4² = 16
g(f(4)) = (f(4))² = (4-7)² = (-3)² = 9
Given that the points (-7, 6), (3, 6), (3, -6), and (-7, -6) are vertices of a rectangle, how much longer is the length than the width?
Answer:
Therefore,
The Length is longer than Width by 2 units.
[tex]Length=Width+2[/tex]
Step-by-step explanation:
Given:
Let the vertices of a Rectangle be
A ( -7 , 6)
B ( 3 , 6)
C ( 3 , -6)
D ( -7 ,-6)
To Find:
Relation between Length and Width = ?
Solution:
First we will find the Length and Width of Rectangle by Distance Formula ,
[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
Substituting the values we get
[tex]l(AB) = \sqrt{((3-(-7))^{2}+(6-6)^{2} )}[/tex]
[tex]l(AB) = \sqrt{((10)^{2}+(0)^{2} )}\\l(AB)=\sqrt{100}=10\ unit[/tex]
Similarly for BC we will have,
[tex]l(BC) = \sqrt{((3-3)^{2}+(-6-6)^{2} )}\\l(BC)=\sqrt{144}=12\ unit[/tex]
Now
Length = 12 units.
Width = 10 units.
Therefore,
Let Length be denoted by "L" and Width by "W" then
[tex]Length=Width+2=10+2=12\\\\\therefore L=W+2[/tex]
Therefore,
The Length is longer than Width by 2 units.
[tex]Length=Width+2[/tex]
Find the inverse of f(x)=5x+11
Answer:
f^-1 (x)=1/5x-11/5
Step-by-step explanation:
y=5x+11
x=5y+11
5y=x-11
y=1/5x-11/5
the table shows the melting points of various elements is the absolute value of the melting point of neon greater than or less than the absolute value of the melting point of hydrogen
The absolute value of the melting point of neon greater than the absolute value of the melting point of hydrogen.
Step-by-step explanation:
In positive numbers, when the number gets larger then it is considered to be the greatest number.
for example: 20 > 5.
Meanwhile, For negative numbers, when the number gets larger then it is considered to be the smallest.
For example: -21 > - 40.
From the given table, we are given with the values of Melting point:
Hydrogen= -259.
Neon = -248.
Oxygen = -218.
We have to compare the melting points of hydrogen and neon,
⇒ - 248 > - 259.
Thus the melting point of the neon is greater than the melting point of the hydrogen.
Emelina wrote the equation of a line in point-slope form as shown below.
(y + 4) = 3 (x + 2)
What is Emelina’s equation in slope-intercept form?
y = 3x + 2
y = 3x +10
y = 3x – 4
y = 3x – 10
Answer:
y = 3x +2
Step-by-step explanation:
The first answer
The track team needs new uniforms. The students plan to sell plush toy hawks (the school mascot) for $5 each. The students find three companies on line that sell stuffed mascots. Company A sells 18 hawks for $49.14. Company B sells 12 hawks for $33.12. Company C charges $40.65 for 15 hawks. Which company has the Best Buy?
After calculating the cost per hawk for each company, Company C offers the best buy at $2.71 per hawk.
The goal is to find out which company offers the best buy for the plush toy hawks. To do so, we'll calculate the cost per hawk from each company and compare them.
Company A: 18 hawks for $49.14 so $49.14 ÷ 18 = $2.73 per hawkCompany B: 12 hawks for $33.12 so $33.12 ÷ 12 = $2.76 per hawkCompany C: 15 hawks for $40.65 so $40.65 ÷ 15 = $2.71 per hawkCompany C offers the lowest cost per hawk at $2.71, thus they have the best buy.
A 41-foot ladder is placed against a vertical wall of an apartment building. The base of the ladder is 9 feet from the base of the apartment building
The ladder reaches 40 feet up the wall.
41 squared (1681) minus 9 squared (81) is 1600. 40 is the square root of 1600.
The required distance between the top of the ladder and the ground is 40 feet.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
We can use the Pythagorean theorem to solve this problem. Let's call the distance from the base of the ladder to the wall "x", and let's call the length of the ladder "y".
According to the problem statement, we know that the ladder is 41 feet long and that the base of the ladder is 9 feet from the base of the apartment building.
y = 41 feet
x = 9 feet
We can use the Pythagorean theorem to solve for the distance between the top of the ladder and the ground. The Pythagorean theorem tells us that:
y² = x² + z²
where "z" is the distance between the top of the ladder and the ground. Plugging in the values we know,
(41 feet)² = (9 feet)² + z²
1681 = 81 + z²
1600 = z²
z = 40 feet
Therefore, the distance between the top of the ladder and the ground is 40 feet.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
#SPJ5
How do you get the answer to
459.74 x 7.66
Answer:
You multiply, the answer is 3,521.6084.
Step-by-step explanation:
Answer:
3521.6084
Step-by-step explanation:
Remove decimalsMultiply Count the amount of numbers behind decimalTake the number: 35216084Then count the numbers and add the decimalFind the cosine of ∠U. A) 15 17 B) 17 15 C) 8 15 D) 8 17
The calculated cosine of the angle U is 8/17
How to determine the cosine of the angle U
From the question, we have the following parameters that can be used in our computation:
The triangle
By definition:
The cosine of the angle is calculated using
cos(U) = VW/UW
Where
VW = 8 and UW = 17
Substitute the known values into the equation
cos(U) = 8/17
Hence, the cosine of the angle U is 8/17
(I will give brainliest, a thanks, 30 points, and 5 stars if you can answer these 2 questions)
1.C=6π yd, find area, answer in terms of π
2. C=22π in^2, find area, answer in terms of π
Answer:
1. 9 pi, 2. 121 pi
Step-by-step explanation:
The formula for circumference is pi d. So for the first question the radius would be three. The you do pi r ^2 for area so 3 times pi squared. Which is 9 pi. For the second you will do the same thing you will do 22 pi divided by 2 which is 11 pi then you will square 11pi and get 121 pi
equation in slope intercept form for a line that passes through (1,5) and (1,1)
Answer:
x = 1
Step-by-step explanation:
If you graph this, you will see that you will get a line that is straight up and down (or perpendicular to the x axis). No matter what y is, x will always be 1.
solve the system of linear equations 4x-2y=8 y=3/2x-2
The solution to the system of linear equations 4x - 2y = 8 and y = (3/2)x - 2 is x = 4 and y = 4, found by substituting y in the first equation with the expression from the second equation and solving for x.
The student is asking to solve a system of linear equations. The equations provided are:
4x - 2y = 8
y = (3/2)x - 2
We will solve this system using substitution since the second equation is already solved for y. Here are the steps:
Substitute y in the first equation with the expression from the second equation: 4x - 2((3/2)x - 2) = 8.
Simplify the equation: 4x - 3x + 4 = 8.
Solve the simplified equation for x: x + 4 = 8, which leads to x = 4.
Substitute x back into the second equation to find y: y = (3/2)4 - 2.
Calculate the value of y: y = 6 - 2, which leads to y = 4.
The solution to the system of equations is x = 4 and y = 4.
Above, a right triangle is removed from a rectangle. What is the area of the remaining figure?
[tex]48 {in}^{2} [/tex]
Answer: B . 48 in²
Step-by-step explanation:
First o all complete the block and find the area
The area of the completed block which looks like a rectangle
= L x B
= 9 x 6
= 54 in²
Step 2 : Find the area of the removed right angled triangle using the formula
= ¹/₂b x h
where the base is 3 in and the height is 4 in
= ¹/₂ x 3 x 4
= 6 in².
Therefore, to find the area of the remaining figure :
Area of the complete block less the area of the right angled triangle
= ( 54 - 6 ) in²
= 48 in²
The option therefore is B
Solve -3(2x-3)+10x=3q
Answer:
4x+9=3q
Step-by-step explanation:
-3(2x-3)+10x=3q
-6x+9+10x=3q
4x+9=3q
Answer:
q = 4/3x + 3
Step-by-step explanation:
-3(2x-3)+10x=3q
Multiply the -3 at the beginning by (2x - 3), the parenthesis
-6x + 9 + 10x = 3q
Now combine the like terms (add x's and variables separately)
(-6x + 10x) + 9 = 3q
4x + 9 = 3q
Divide both sides of the equation by 3
(4x + 9) ÷ 3 = q
4x/3 + 9/3 = q
Simplify
q = 4/3x + 3
Hope this helps :)