Answer: Second option.
Step-by-step explanation:
Given the function f(x):
[tex]f(x) = x^2 - 2x + 8[/tex]
Find [tex]f(x -2)[/tex]:
[tex]f(x -2)=(x-2)^2 - 2(x-2) + 8[/tex]
Remember that:
[tex](a\±b)^2=a^2\±2ab+b^2[/tex]
Then, simplifying:
[tex]f(x -2)=x^2-2(x)(2)+2^2 - 2x+4+ 8\\\\f(x-2)=x^2-6x+16[/tex]
So the function g(x) is:
[tex]g(x)=x^2-6x+16[/tex]
Use the following formula to find the x-coordinate of the vertex of g(x):
[tex]x=\frac{-b}{2a}[/tex]
In this case:
[tex]a=1\\b=-6[/tex]
Then:
[tex]x=-\frac{-(-6)}{2(1)}=3[/tex]
Substitute this value into the function g(x) in order to find the y-coordinate of the vertex. Since [tex]g(x)=y[/tex], you get:
[tex]y=3^2-6(3)+16=7[/tex]
Therefore, the vertex of g(x) is:
[tex](3,7)[/tex]
Answer:
Second one
Step-by-step explanation:
I have 86 hours divided into 15 days how many hours per day
Answer:
86/15 hours/day or 5.73333333333 hours/day
Step-by-step explanation:
divide 86 by 15 to get your answer
don't forget units
Answer: 86 hours divided into 15 days would approximately be 6 hours per day (or 5.733 if you aren't rounding the amount).
A man was surprised when he found an old bank account statement in his mother’s attic. Money had been left for 30 years in a bank account paying simple annual interest. The statement showed that originally $500 had been put into the account. When he called the bank, he found that there is now $1550 in the account! What is the annual interest rate?
Answer:
7%
Step-by-step explanation:
Answer:
7% is the correct answer
3. After hiking to the top of a mountain, Raul starts to descend at the rate of 350
feet per hour. What real number represents his vertical change after 1 1/2 hours?
Answer: 525 ft
Step-by-step explanation:
350 = 1 hour
350 / 2 = 175 in half an hour
350 + 175 = 525 ft
List the angles of rotation, separated by commas, less than 360° if the figure has rotational symmetry. If
the figure does not have rotational symmetry, enter the number zero.
The list of angles of rotation is
Answer:
The list of angle of rotation is zero
Step-by-step explanation:
* Lets revise some definitions about isosceles trapezoid
- An isosceles trapezoid is a trapezoid with congruent base angles
- An isosceles trapezoid has congruent legs
- An isosceles trapezoid has 1 axis of symmetry
- An isosceles trapezoid has no rotational symmetry
* Lets solve the problem
- From the attached figure:
∵ The figure is quadrilateral
∵ The quadrilateral has only a pair of parallel sides
∵ The parallel side not equal in length
∵ The other two sides of the quadrilateral are equal in length
∴ The quadrilateral is an isosceles trapezoid
∵ The isosceles trapezoid has no rotational symmetry
∴ There is no angle of rotation
∴ The list of angle of rotation is zero
Answer:
the answer is 0
Step-by-step explanation:
Which expression is equivalent to (2r2+r - 1) – (3r2+48 - 5)?
-p2 – 3r+4
°-p2 + 58 - 6
5r²+5r-6
5r2 - 3r + 4
The specified expression simplifies to -r² + r - 44. Steps to find equivalent expressions include gathering like terms and utilizing the distributive property.
Explanation:
The expression (2r²+r-1) – (3r²+48-5) can be rewritten as 2r²+r-1 - 3r² - 48 +5. For the r² terms, combine 2r² and -3r² to get -r². For the constant terms, combine -1, -48 and +5 to get -44. And there's only one r term which is r. Together, these give the equivalent expression as -r² + r - 44.
Learn more about Equivalence expressions here:https://brainly.com/question/27911936
#SPJ12
The expression equivalent to (2r2 + r - 1) - (3r2 + 48 - 5) is -r2 + r - 44.
Explanation:To find the equivalent expression, we need to distribute the negative sign into the second set of parentheses.
Then, combine like terms.
The expression becomes: (2r2 + r - 1) - 3r2 - 48 + 5.
Combining like terms further, we have: 2r2 + r - 1 - 3r2 - 48 + 5
Now, combine the like terms again: (2r2 - 3r2) + r + (-1 - 48 + 5). Simplifying this gives us: -r2 + r - 44
Therefore, the expression equivalent to (2r2 + r - 1) - (3r2 + 48 - 5) is -r2 + r - 44.
Learn more about Equivalent expressions here:https://brainly.com/question/34140345
#SPJ12
if the federal reserve sets the reserve rate at 12.5% what is the resulting money multiplier
Answer:
Currently the U.S. is on a downwards spiral and will fall soon.
Step-by-step explanation:
The resulting money multiplier is 8
What is a money multiplier?The money multiplier represents the greatest amount the supply of money increase on the bases of an increase in reserves within the banking system.
How to find the resulting money multiplier ?The given rate is 12.5%So, rate = 12.5/100 = 0.125
The resulting money multiplier (M) = 1/r∴ (M) = 1/0.125 = 8
The resulting money multiplier is 8
Find more about "Money multiplier" here: https://brainly.com/question/13988758
#SPJ2
a ^-4 / a ^-6 please simplify and show your work if possible <:D
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{a^{-4}}{a^{-6}}\implies a^{-4}\cdot a^6\implies a^{-4+6}\implies a^2[/tex]
what is the answer to 5 over 35 simplalifying
Answer:
1/7
Step-by-step explanation:
Divide each number by 5.
5/5=1
35/5=7
Answer:
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 5 and 35 is 5
Divide both the numerator and denominator by the GCD
5 ÷ 5
35 ÷ 5
Reduced fraction:
1
7
Evaluate the expression if x = 3 and y = 11. 3x + 2y
Answer:
31
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
3(3)+2(11)=31
Find the area of the parallelogram that has a base of 2 1/2 ft and a height of 1 1/4ft
Answer:
The area of the parallelogram is [tex]3\frac{1}{8}ft^{2}[/tex]
Step-by-step explanation:
Remember that a mixed fractions are composed for a whole number, a numerator and a denominator. For example in the mixed fraction [tex]2\frac{1}{3}[/tex]: 2 is the whole number, 1 is the numerator and 3 is the denominator.
If you want to convert to a improper fraction you need to multiply the whole number by the denominator and add to the numerator. The result will be the numerator of the improper fraction. The denominator remains the same.
[tex]2\frac{1}{3}=\frac{(2*3)+1}{3} =\frac{7}{3}[/tex]
1. Convert the mixed fractions in the improper fraction type, as follows:
[tex]Base= 2\frac{1}{2}=\frac{5}{2} \\ \\Height= 1\frac{1}{4}=\frac{5}{4}[/tex]
2. Replace the data in the equation of a parallelogram
[tex]Area= Base*Height[/tex]
[tex]Area= Base*Height\\Area=\frac{5}{2}ft *\frac{5}{4}ft\\Solve...\\Area=\frac{25}{8}ft^{2}[/tex]
3. Convert the improper fraction in a mixed fraction
[tex]Area=\frac{25}{8}ft^{2}=3\frac{1}{8}ft^{2}[/tex]
The area of the parallelogram is [tex]3\frac{1}{8}ft^{2}[/tex]
2x + 5 = 4 (5/4 - 1/2 x)
Answer:
x=0
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2x+5=−2x+5
Step 2: Add 2x to both sides.
2x+5+2x=−2x+5+2x
Step 3: Subtract 5 from both sides.
4x+5−5=5−5
4x=0
Step 4: Divide both sides by 4.
4x/4=0/4
X=0
43tens×3tens=how many hundreds
Answer:
129 hundreds
Step-by-step explanation:
Owen has enough materials to build up to 10 birdhouses in shop class. Each birdhouse needs 12 square feet of wood. The function W(b) = 12b represents the total amount of wood that Owen would need to build b birdhouses. What domain and range are reasonable for the function?
A.
D: 10 ≤ b ≤ 12
R: 0 ≤ W(b) ≤ 120
B.
D: 0 ≤ b ≤ 120
R: 0 ≤ W(b) ≤ 10
C.
D: 0 ≤ b ≤ 10
R: 12 ≤ W(b) ≤ 120
D.
D: 0 ≤ b ≤ 10
R: 0 ≤ W(b) ≤ 120
Each birdhouse uses 12 sq ft of wood.
He has enough to build 10 birdhouses, so he has 120 sq ft of wood.
The function has an input of the number of birdhouses, b, and has an output of the amount of wood needed, W. b is the input or the domain, and W is the output or the range. The domain is 0 to 10. The range is 0 to 120.
Answer: B. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120
Enjoy! Hope this helped you! :)
if log x - log(2x-1)=1 find x
Answer:
x = 10/19
Step-by-step explanation:
[tex]log(x)-log(2x-1) = 1\\log\frac{x}{2x-1}=log(10)\\\frac{x}{2x-1}=10\\x = \frac{10}{19}[/tex]
The solution to the equation log x - log(2x-1) = 1 is x = 10/19.
We have,
To solve the equation log x - log(2x-1) = 1, we can use logarithmic properties to simplify the equation.
First, we can apply the quotient rule of logarithms, which states that
log a - log b = log(a/b).
Applying this rule to the equation, we get:
log(x / (2x-1)) = 1
Next, we can rewrite the equation in exponential form, using the definition that log base a of b is equivalent to a raised to the power of the logarithm equals b.
In this case, the base is 10 since we are using common logarithms (log base 10):
[tex]10^1[/tex] = x / (2x-1)
Simplifying the left side, we have:
10 = x / (2x-1)
To eliminate the denominator, we can multiply both sides of the equation by (2x-1):
10(2x-1) = x
Expanding the left side:
20x - 10 = x
Now, we can isolate the variable x:
20x - x = 10
19x = 10
Dividing both sides by 19:
x = 10/19
Therefore,
The solution to the equation log x - log(2x-1) = 1 is x = 10/19.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Select the correct answer.
Elizabeth is selling jam at a farmers market, and she earns $5.00 for each jar of jam that she sells. Her goal for the weekend is to earn at least $450.00, and she has already made $95.00 from jam sales as well as $24.00 from leading a demonstration. What is the minimum number of jars Elizabeth must sell at this point to reach her goal?
A.
60
B.
66
C.
67
D.
70
Answer:
Option C. 67
Step-by-step explanation:
Elizabeth is selling jam at a farmers market, and she earns $5.00 for each jar of jam that she sells.
She has already made $95.00 from jam sales and $24.00 from leading a demonstration.
She has made money = 95 + 24 = $119.00
Her goal for the weekend is to earn at least $450.00
Now She is away from her goal = 450 - 119 = $331
To achieve the goal she has to sell the number of jar of jam = [tex]\frac{331}{5}[/tex]
= $66.2
To make at least $450 she must sell 67 jars of jam.
The required minimum number of jars must sell by Elizabeth at this point of time to reach her goal is given by option b. 66.
To find out how many jars Elizabeth needs to sell to reach her goal,
Need to subtract the amount she has already earned from her goal.
Goal earnings: $450.00
Already earned from jam sales: $95.00
Earned from demonstration: $24.00
Total earnings so far: $95.00 + $24.00 = $119.00
Remaining earnings needed to reach the goal:
$450.00 - $119.00 = $331.00
Since Elizabeth earns $5.00 for each jar of jam sold,
determine the minimum number of jars she needs to sell by dividing the remaining earnings needed by the earnings per jar:
Number of jars needed = Remaining earnings / Earnings per jar
Number of jars needed = $331.00 / $5.00 ≈ 66.2
Nearest integer value to 66.2 is 66.
Therefore, as Elizabeth can't sell a fraction of a jar she needs to sell minimum number of 66 jars to reach her goal , the correct answer is option b. 66
Learn more about minimum number here
brainly.com/question/29198746
#SPJ3
What does an author's claim contain?
an opinion about a toplo
the support for the argument
the entire argument
the reasons for the claim
Final answer:
An author's claim is a specific statement that represents the main argument, supported by evidence and reasoning, and serves as the backbone of the thesis structure in academic writing.
Explanation:
An author's claim contains an opinion about a topic that is presented as a specific statement or assertion for which the author will provide support throughout their work. The claim is often a summation of the author's main argument or thesis statement and is supported by evidence, including facts, statistics, anecdotes, and quotations. In addition to presenting the argument, the claim is backed by reasoning, and the author must use analysis to show how the evidence relates to and supports the claim.
The effective use of a claim involves stating it clearly and supporting it with credible evidence, thereby forming the backbone of the thesis-first or thesis-last structure in an academic paper. It's critical for the claim to be directly connected to evidence through logical reasoning, such as cause and effect or comparison and contrast, to ensure that the argument is coherent and compelling.
How do cows buy gifts
Answer:they dont
Step-by-step explanation:
3 1/4 yards of fabric costs $27.95. what is the cost per yard
Answer:
8.6
Step-by-step explanation:
because 27.95 divided by 3.25=8.6
Julias text messaging plan costs $8 for the first 400 messages and 20e for each additional text message. If she owes $24.00 for text messaging in the month of
September, how many text messages did she send that month?
Julia sent 401 text messages in the month of September.
Explanation:To find the number of text messages Julia sent, we can set up an equation using the given information.
Let's assume she sent x additional messages.
The cost of the additional messages would be 20x.
Since her total cost is $24, we can write the equation:
8 + 20x = 24
Subtracting 8 from both sides gives:
20x = 16
Dividing both sides by 20 gives:
x = 0.8
Since x represents the additional messages sent, we can round it to the nearest whole number.
Therefore, Julia sent 1 additional text message.
In order to find the total number of messages sent, we can add the initial allowance of 400 messages to the additional message:
Total messages sent = 400 + 1 = 401 text messages.
Final answer:
Julia sent a total of 401 text messages in September.
Explanation:
Julia's text messaging plan costs $8 for the first 400 messages and $20 for each additional text message. To find out how many text messages she sent in September, we need to determine the number of additional text messages she sent beyond the first 400. Let's assume she sent x additional text messages. The additional cost for these text messages would be 20 * x. We can set up an equation to solve for x:
$8 + 20x = $24
Subtracting $8 from both sides gives:
20x = $16
Dividing both sides by 20, we get:
x = $16 / 20 = 0.8
Since we cannot have a fraction of a text message, Julia must have sent 1 additional text message beyond the first 400. Therefore, she sent a total of 401 text messages in September.
what is the simplified form of the following expression? 3 sqrt 4x/5
Final answer:
The simplified form of the expression [tex]3 \sqrt(4x/5) \ is\ 6 \sqrt(5x) / 5[/tex]after performing the square root separately on the numerator and denominator, and then rationalizing the denominator.
Explanation:
The expression given is [tex]3 \sqrt(4x/5)[/tex]. To simplify this expression, we observe that the square root of 4 is a perfect square and equals 2. The square root of the fraction can be taken by applying the square root to the numerator and the denominator separately. Therefore, we have:
[tex]3 \times \sqrt(4) \times \sqrt(x) / \sqrt(5)[/tex]
Upon simplifying, we get:
[tex]3 \times 2 \times \sqrt(x) / \sqrt(5)[/tex]
This simplifies further to:
[tex]6 \sqrt(x) / \sqrt(5)[/tex]
However, it's not common to leave a square root in the denominator, so we can multiply both the numerator and the denominator by sqrt(5) to rationalize the denominator.
The final simplified form is:
[tex]6 \sqrt(5x) / 5[/tex]
c.
5 tomatoes for $3.10. What was the cost per tomato?
The cost per tomato is $0.63.
Answer:
The cost of each tomato is $0.62
Step-by-step explanation:
Consider the provided information.
5 tomatoes for $3.10.
We need to determine the cost per tomato.
To find this divide the number of tomatoes from the cost of tomatoes.
[tex]\frac{3.10}{5}=0.62[/tex]
Hence, the cost of each tomato is $0.62
Add. 4 7/12+2 3/4+7 5/12
A.13 3/4
B.14 1/4
C.14 3/4
D.15 1/4
Add.
4/5+3 1/10
Enter the sum in the box as a mixed number in simplest form.
Answer:
C.14¾
3 9⁄10
Step-by-step explanation:
[tex] \frac{4}{5} + 3 \frac{1}{10} = \frac{8}{10} + 3 \frac{1}{10} = 3 \frac{9}{10} [/tex]
[tex]4 \frac{7}{12} + 2 + \frac{3}{4} + 7 \frac{5}{12} = 13 \frac{12}{12} + \frac{3}{4} = 14 + \frac{3}{4} = 14 \frac{3}{4} [/tex]
I am joyous to assist you anytime.
How many solutions does this problem have? 3(y+41)=3y+123
Answer:
The answer is many solutions
Answer:
infinite
Step-by-step explanation:
3 x 41 = 132 so
3y +132 =3y +132
Barry and Lou entered a hot dog eating contest. The winner of the contest is the person who can eat the most hot dogs in the allotted amount of time. Barry can eat 12 hot dogs in 9 minutes. Lou can eat 20 hot dogs in 16 minutes. Barry thinks with his rate he will win the contest.
Is Barry correct?
Answer:
Yes
Step-by-step explanation:
If you divide 12 by 9, you get 1.33... and if you divide 20 by 16, you get 1.25 so Barry can eat more hot dogs in less amount of time than Lou can.
Answer:
yes
Step-by-step explanation:
What is the coefficient of b in the expression b + 10? Explain.
Answer:
The coefficient of b is 1
Step-by-step explanation:
we know that
In a mathematical equation, a coefficient is a constant by which a variable is multiplied
so
A coefficient is a constant multiplied by a variable.
In this problem we have
b+10
Rewrite'
b+10=(1)b+10
therefore
The coefficient of b is 1
Write 5.48 as a mixed number in simplest form.
5.48=
Answer:
5 12/25
Step-by-step explanation:
The first step is to separate the whole number number from the decimal.
that would be 5
Next would to see in which place the decimal number is in. .48 is in the hundredths place so we put 48 over 100 like this 48/100
So now we have the whole number 5 and the fraction 48/100
Lastly we simplify the fraction. 48 divided by 2 and 100 divided by 2
This equals 24/50
This can be simplified even more
24 divided by 2 and 50 divided by 2
This equals 12/25
Then we put the whole number in front and your final answer is
5 12/25
Martin paid $6 for 4 avocados at a farm stand. He wants to know what the price would be for buying different numbers of avocados? What is the price of 2 avocados?
Answer:
$3
Step-by-step explanation:
4/$6 = 2/$3
Answer:
3
Step-by-step explanation:
ywwwwww
Simplify the expression (StartFraction 1 Over 4 a b EndFraction) Superscript negative 2. Assume a not-equals 0, b not-equals 0.
Answer:
The simplest form of the expression is 16 a²b²
Step-by-step explanation:
* Lets explain how to solve the problem
- To simplify any fraction with exponent you must put it with positive
exponent
- Ex: the fraction [tex](\frac{2}{3})^{-1}[/tex] not in the simplest form
because it has negative exponent
- To change the negative exponent to positive exponent reciprocal the
fraction, [tex](\frac{3}{2})^{1}[/tex] and this is the simplest form of the fraction
* Now lets solve the problem
∵ The expression is [tex](\frac{1}{4ab})^{-2}[/tex], where a and b ≠ 0
- At first reciprocal the fraction
∴ [tex](\frac{1}{4ab})^{-2}=(\frac{4ab}{1})^{2}[/tex]
- Then solve the power
∵ 4² = 16
∵ (ab)² = a²b²
∴ (4ab)² = 16 a²b²
* The simplest form of the expression is 16 a²b²
Answer:
16 a²b² is option D on e2020
Step-by-step explanation:
100% on test
Converting Point-Slope Use the point-slope form of a line to write the equation of a line that has a slope of 2 and passes through the point (–4, 3). Write the equation in slope-intercept form. Choose the equation of the line.
A) y = 2x – 7
B) y = 2x + 11
C) y = –4x + 14
D) y = 3x +14
Here is HOW to do it.....:
Input Data :
Coordinates
(
x
A
,
y
A
)
(xA,yA)
= (5, 4)
Slope (m) = 8
Objective :
Find slope of a straight line?
Formula :
y
−
y
A
=
m
(
x
−
x
A
)
y-yA=m(x-xA)
Solution :
y - 4 = 8 (x - 5)
y - 4 = 8x - 40
y = 8x - 40 + 4
y = 8x - 36
8x - y - 36 = 0
Answer:
the answer is B
Step-by-step explanation:
How many packs of DVD's can you buy with 180 dollars if one pack costs 12 dollars?
Final answer:
With $180 and each pack costing $12, you can buy 15 packs of DVDs.
Explanation:
Calculating the Number of DVD Packs
To determine how many packs of DVDs you can buy with $180 when one pack costs $12, you need to perform a simple division operation. You divide the total amount of money you have by the cost of one pack of DVDs:
$180 ÷ $12 per pack = 15 packs.
Therefore, with $180, you can buy 15 packs of DVDs.