Answer:
[tex]F(x)=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.[/tex]
Step-by-step explanation:
Consider the function [tex]F(x)=2x^2+13x+20.[/tex]
Rewrite it as follows:
[tex]F(x)=(2x^2+13x)+20=2\left(x^2+\dfrac{13}{2}x\right)+20=2\left(x^2+\dfrac{13}{2}x+\left(\dfrac{13}{4}\right)^2-\left(\dfrac{13}{4}\right)^2\right)+20=2\left(x^2+\dfrac{13}{2}x+\dfrac{169}{16}\right)-2\cdot \dfrac{169}{16}+20.[/tex]
Since
[tex]x^2+\dfrac{13}{2}x+\dfrac{169}{16}=\left(x+\dfrac{13}{4}\right)^2,[/tex]
you get
[tex]F(x)=2\left(x+\dfrac{13}{4}\right)^2+20-\dfrac{169}{8}=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.[/tex]
Answer:
the correct answer is: f(x)=2(x+13/4)²+-9/8. i hope it help
Show 326 using hundreds, tens, and ones
Answer:
using hunreds 300
using tens 20
using ones 6
300+20+6= 326
Step-by-step explanation:
All you got to do is break them apart into the places.
Plzzz mark brainlest and thank me
HELP
GIven:
QRS is an isosceles triangle
If M is midpoint of RQ, then triangle SMQ is congruent to triangle SRM
True or false
Answer:
true
Step-by-step explanation:
Find the percent of decrease. Round your answer to the nearest tenth of a percent where necessary.
5. 57 to 19
A. 38%
B. 66.7%
C. 200%
D. 20%
Find the percent of markup. Round to nearest whole percent.
6. Store’s Cost:$136.50
Selling price:$184.70
A. 48%
B. 26%
C. 14%
D. 35%
Answer:
Number 5: Answer B
Number 6: Answer B
Step-by-step explanation:
5) The percent of decrease from 57 to 19 is:B. 66.7%
6) The percent of markup is: D. 35%
How to find the percentage?6) To find the percent of decrease from 57 to 19, we can use the formula:
percent decrease = (original value - new value) / original value x 100%
Substituting the given values, we get:
percent decrease = (57 - 19) / 57 x 100%
percent decrease = 38 / 57 x 100%
percent decrease = 0.6667 x 100%
percent decrease = 66.7%
Therefore, the percent of decrease from 57 to 19 is 66.7%. The answer is option B.
6) To find the percent of markup, we can use the formula:
percent markup = (selling price - cost) / cost x 100%
Substituting the given values, we get:
percent markup = (184.70 - 136.50) / 136.50 x 100%
percent markup = 48.20 / 136.50 x 100%
percent markup = 0.353 x 100%
percent markup = 35.3%
Therefore, the percent of markup is 35%. The answer is option D.
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Please help quick!!!
Which table shows a proportional relationship between x and y?
x 1 3 4 5
y 50 150 200 250
x 1 2 3 6
y 1.5 3 6 9
x 3 5 7 8
y 1.5 2.5 3 4.5
x 2 4 5 6
y 6 12 18 21
Answer:
the most accurate answer would be option 3 relatively speaking
Step-by-step explanation:
5.5 ÷ .25 plz show work
Answer:
22
Step-by-step explanation
that is how many times .25 goes into 5.5
Question
5.5 ÷ .25 and plz show work
Answer:
22
Step-by-step explanation:
5.5 : 0.25 =
55 : 2.5 =
550 : 25 =
22
HELP
GIven:
QRS is an isosceles triangle
If M is midpoint of RQ, then triangle SMQ is congruent to triangle SRM
True or false
Answer:
True
Step-by-step explanation:
Given: QRS is an isosceles triangle that is QS=SR and M is the mid point of QR.
To prove: ΔSQM≅ΔSRM
Proof: It is given that QRS is an isosceles triangle that is QS=SR and M is the mid point of QR, thus from ΔSQM and ΔSRM, we have
QS=SR (Given)
QM=MR (Mid point)
SM=MS (Reflexive)
Thus, by SSS rule of congruence,
ΔSQM≅ΔSRM
Hence the given statement is true, that is if M is teh point of RQ, then ΔSQM≅ΔSRM.
Hence proved.
A car is traveling 10 miles per hour during rush hour. How far does the car travel in 5 minutes
Write an equation represents the number of bracelets b Carly will have if she works t hours making bracelets in the next 2 weeks and averages one bracelet every 2 hours
Which rules of exponents will be used to evaluate the expression. PLZ answer (MEGA NEEDS HELP :( Quick!!!!!!!!!!!!!!!!!!!!!!!! Check all that apply [( 7^5)(7^3)]-4
.quotient of powers
.product of powers
.power of a power
.power of a product
.negative exponent
.zero exponent
Answer:
Product of powers; power of a power; negative exponent
Step-by-step explanation:
A jeweler orders necklaces from a website that offers $6 shipping for any-size order. Each necklace costs $7. The jeweler wants to know the total cost of ordering n necklaces.What is the dependent (output) variable?
Answer: 6x7=n
Step-by-step explanation:
Answer:
A jeweler orders necklaces from a website that offers $6 shipping for any-size order. Each necklace costs $7. The jeweler wants to know the total cost of ordering n necklaces.
What is the independent (input) variable?
✔ n, the number of necklaces
What is the dependent (output) variable?
✔ c, the total cost (in dollars)
What is the domain?
✔ n=0, 1, 2, 3,...
Which equation expresses the order’s total cost, c, as a function of the number of necklaces, n?
✔ c(n)=7n + 6
Which expression means “the total cost, including shipping, of 5 necklaces”?
✔ c(5)
Step-by-step explanation:
What is the ratio of a to b 9/17= 3a/ a+b
3/14
6/17
13/17
50/9
Answer:
3/14
Step-by-step explanation:
We want to find the ratio of a to b, or a/b
9/17 = 3a/ (a+b)
Multiply each side by 17
17*9/17 =17* 3a/ (a+b)
9 = 51 a/ (a+b)
Multiply each side by (a+b)
9 (a+b) = 51a
Distribute the 9
9a +9b = 51a
Subtract 9a from each side
9a-9a +9b =51a-9a
9b = 42a
Divide each side by b
9b/b = 42a/b
9 = 42a/b
Divide each side by 42
9/42 = a/b
But we can simplify 9/42 because each is divisible by 3, so divide 9 and 42 by 3
3/14 = a/b
What is the sum of 5(−3.4k−7) (3k+ 21) =
Answer:
welp i got -891k - 357 but that seems really big
Step-by-step explanation:
i distributed the 5 to the -3.4k and the -7 and got -17k-35. then i foiled that out with the 3k+21 and got -51k -357 - 105k -735k. then i combined like terms and got -891k -357
hope this helps rip sorry
Which is the best first step when solving the following system of equations?x+y=3 and 4x-y=7
I Need Answer ASAP
I think it would be x+y=3
Hope this helps
X/2 + 3 = -4
/=fraction
Given the equations `2x + 4/3 y = 1` and `y - 9/13 x = 9`, by what factor would you multiply the first equation so that combining the two equations would eliminate x? A. `-9/26` B. `9/26` C. `1/2` D. `-9/13`
Answer:
B. 9/26.
Step-by-step explanation:
You need to change the coefficient of x in the first equation to 9/13 so that adding the 2 equations would eliminate x.
So you would multiply by
= 9/13 / 2
= 9/13 * 1/2
= 9/26 (answer)
Answer:
The correct option is B) [tex]\frac{9}{26}[/tex]
Step-by-step explanation:
Consider the provided equations:
[tex]2x+\frac{4}{3}y=1[/tex] and [tex]y-\frac{9}{13}x=9[/tex]
The above equation can be written as:
[tex]2x+\frac{4}{3}y=1[/tex] and [tex]-\frac{9}{13}x+y=9[/tex]
As it is given that we need to eliminate the variable x.
Multiplying the equation [tex]2x+\frac{4}{3}y=1[/tex] with [tex]\frac{9}{26}[/tex].
Therefore,
[tex]\frac{9}{26}2x+\frac{9}{26}\times{\frac{4}{3}y}=1\times{\frac{9}{26}}[/tex]
[tex]\frac{9}{13}x+\frac{9}{26}\times{\frac{4}{3}y}=1\times{\frac{9}{26}}[/tex]
Therefore, the correct option is B) [tex]\frac{9}{26}[/tex]
How can this quadrilateral be classified?
Answer:
I am pretty sure it is all but trapezoid.
Step-by-step explanation:
Answer:
B. Trapezoid
Step-by-step explanation:
We have been given image of a quadrilateral. We are asked to classify our given quadrilateral.
Let us check our given choices one by one.
A. Parallelogram.
We can see that our given quadrilateral is square as its all sides are equal and perpendicular to each other.
Since sides of square are parallel to each other and opposite sides has equal measure, therefore, it is a parallelogram.
B. Trapezoid
We know that a trapezoid has one pair of parallel sides.
Since square has two pair of parallel sides, therefore, our given quadrilateral is not a trapezoid.
C. Rhombus
We know that each square is a rhombus, therefore, our given quadrilateral is a rhombus as well.
D. Square.
Our given quadrilateral is square as its all sides are equal and perpendicular to each other. Therefore, option D is correct as well.
What is n in the equation -5(1+6n)=5n-5?
Answer:
0 is your answer
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Remember to follow PEMDAS.
First, distribute -5 to all terms within the parenthesis
-5(1 + 6n) = (-5)(1) + (-5)(6n) = -5 - 30n
-30n - 5 = 5n - 5
Isolate the variable, n. Subtract 5n and add 5 to both sides
-30n (-5n) - 5 (+5) = 5n (-5n) - 5 (+5)
-30n - 5n = -5 + 5
-35n = 0
Isolate the n, Divide -35 from both sides
(-35n)/-35 = (0)/-35
n = 0
0 is your answer
~
The lenght of sydney's tennis racket is 2 rulers long. How many feet long is sydeney's tennis racket
Answer:
2 feet or 24 inch.
Step-by-step explanation:
Matthew can buy an 8-ounce jar of salsa for $2.85 or a 15-ounce jar of salsa for $5.65. Which jar is the best buy and what is the unit rate?
Answer:
The $2.85 jar is the better buy.
Step-by-step explanation:
Start by finding the two separate unit rates. Then compare them:
$2.85
---------- = $0.36/oz
8 oz
$5.65.
----------- = $0.38/oz
15 oz
The $2.85 jar is the better buy, as its unit cost is lower.
Final answer:
The 8-ounce jar of salsa at $0.35625 per ounce is the better buy compared to the 15-ounce jar at $0.37667 per ounce.
Explanation:
The student wants to determine which jar of salsa provides the best value in terms of cost per ounce. To find the unit rate, we need to divide the price of each jar by the number of ounces it contains.
For the 8-ounce jar of salsa:
Unit rate = $2.85 / 8 oz = $0.35625 per ounce
For the 15-ounce jar of salsa:
Unit rate = $5.65 / 15 oz = $0.37667 per ounce
Comparing the unit rates, the 8-ounce jar of salsa has a lower unit rate, making it the better buy.
1.32:3 1/7 =(1.4y): 5/6
Answer:
y=0.25 please mark brainliest i worked very hard to figure this out.
Step-by-step explanation:
3 1/7=22/7
22/7/6/5=132/35
1.32=132/100
132/100/132/35=1.4y=35/100
35/100*14/10=0.25
hence, y=0.25
Which values from the specified set make up the solution set of the inequality?
5w–10>20 ; {5,6,7,8}
Select each correct answer.
5
6
7
8
5w - 10 > 20 add 10 to both sides
5w > 30 divide both sides by 5
w > 6
Answer: 7 and 8.Answer: 7 and 8
Step-by-step explanation:
A department store sells logo shirts at an original price of $20. Every month that a shirt doesn’t sell, the store reduces the selling price by 25%. The store employees get a 50% markdown off the current price. Macy works at the store and sees the shirts going into the second markdown month. She decides that since 25% + 25% + 50% = 100%, the shirts must be free to employees. What is Macy’s error?
Answer: The pre-tax price of the shirt for Macy will be $5.63
Step-by-step explanation:
Given:
Original price = 20
reduces selling price by 25% every month it's not sold.
First markdown month:
20 * (100%-25%) = 20 * 75% = 15
Second markdown month
15 * 75% = 11.25
Macy, employee gets a 50% discount off the current price.
11.25 * 50% = 5.625
11.25 - 5.625 = 5.625 or 5.63
hope it helps! :)
Answer:
teacher's response
Step-by-step explanation:
Macy was calculating the employee price off the original amount each time instead of off the new selling price each month. Macy cannot add up all the discounts; she must apply them one by one.
An image point has coordinates B'(7, -4). Find the coordinates of its pre-image if the translation used was (x + 4, y + 5).
Answer:
The coordinate of pre-image is, B(3 , -9).
Step-by-step explanation:
Given an image point has coordinate B'(7, -4).
We have to find the coordinates of its pre-image:
The rule of translation on pre-image (x, y) is given by;
[tex]B(x, y) \rightarrow B'(x + 4, y + 5)[/tex]
then;
(7, -4) = (x+4, y+5)
on comparison we have;
x+4 = 7 and y + 5 = -4
First solve for x;
[tex]x + 4 = 7[/tex]
Subtract 4 from both sides we have;
x + 4 -4 =7-4
Simplify:
x = 3
To solve for y;
y+5 = -4
Subtract 5 from both sides we get;
y = -9
Therefore, the coordinate of pre-image is, B(3, -9)
Answer:
The coordinate of pre-image is, B(3 , -9).
Step-by-step explanation:
Given an image point has coordinate B'(7, -4).
We have to find the coordinates of its pre-image:
The rule of translation on pre-image (x, y) is given by;
then;
(7, -4) = (x+4, y+5)
on comparison we have;
x+4 = 7 and y + 5 = -4
First solve for x;
Subtract 4 from both sides we have;
x + 4 -4 =7-4
Simplify:
x = 3
To solve for y;
y+5 = -4
Subtract 5 from both sides we get;
y = -9
Therefore, the coordinate of pre-image is, B(3, -9)
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Step-by-step explanation:
Suppose Department X is 8,000 square feet, Department Y is 5,000 square feet, and Department Z is 6,000 square feet. What's the percent of overhead expense applied to Department Z?
Answer:
31.6%
Step-by-step explanation:
it is given that
Area of Department X = 8,000 square feet
Area of Department Y = 5,000 square feet
Area of Department Z = 6,000 square feet
now the total area = [tex]8000+5000+6000[/tex]
=[tex]19,000[/tex] square feet
Percentage of area covered by Department Z = [tex]\frac{area of Department Z}{total area }100[/tex]%
=[tex]\frac{6000}{19000} 100[/tex] %
=[tex]31.6[/tex] %
percentage of overhead expenses applied to Department Z = percentage of area covered by Department Z
hence we have,
percentage of overhead expenses applied to Department Z = 31.6%
I will give you literally 40 points if you answer this. In a stadium, there are 31 chairs in the first row and 37 in the second row. The number of chairs in a row continues to increase by 6 with each additional row. a) write the first 5 numbers of this sequence b)what is the explicit tilde for the number of seats in n rows c)use the rule you wrote in 1b to determine which row has 103 seats. SHOW ALL WORK
A) 1st Row = 31 seats
2nd row = 37 seats
3rd row = 37+6 = 43 seats
4th row = 43+6 = 49 seats
5th row = 49+6 = 55 seats
B) The formula for finding the number of seats in any row number is:
Number of seats in nth row = 31 + (n-1) *6
C) To find the row with 103 seats, set the equation in B to equal 103 and solve for n:
103 = 31 + (n-1)*6
Subtract 31 from each side:
72 = (n-1)*6
Divide both sides by 6:
12 = n-1
add 1 to each side:
n = 13
The 13th row has 103 seats.
What is the value of n in the equation 8n + 7 =31
Answer:
The answer is the third choice 3
Step-by-step explanation:
First you undo by doing the opposite 31 - 7 = 24 now we undo the 8 by undoing 24 divided by 8 is 3
Question
What is the value of n in the equation 8n + 7 =31
Answer:
3Step-by-step explanation:
8n + 7 = 31
8n = 31 - 7
8n = 24
n = 24 : 8
n = 3
--------------------
check
8 * 3 + 7 = 31
24 + 7 = 31
31 = 31
The answer is good
What is the solution set of the compound inequality 8< 4 - x <10
Answer:
-6 < x < -4
Step-by-step explanation:
8 < 4 - x < 10
Split this up into 2 inequalities:
4 - x > 8
-x > 8 - 4
-x > 4 Divide both sides by -1
x < -4 (Note that sign flips when dividing by a negative).
Also 4 - x < 10
-x < 6
x > -6
So the solution is -6 < x < -4
find the angle of elevation of the sun if a building 100 feet tall casts a shadow 150 feet long.
The angle of elevation of the sun can be determined using trigonometry by finding the inverse tangent of the ratio of the building height to the shadow length, which is approximately 33.69 degrees.
To find this, we can use trigonometry, specifically the tangent function, which is the ratio of the opposite side over the adjacent side in a right-angled triangle. Here, the building height represents the opposite side, and the shadow length represents the adjacent side.
Using the formula tangent = opposite/adjacent, we have:
tangent(\(\theta\)) = 100 / 150tangent(\(\theta\)) = 2/3Now, we need to find the angle whose tangent is 2/3. By using a calculator or a trigonometry table, we find:
\(\theta\) = tan-1(2/3) \(\approx\) 33.69 degreesTherefore, the angle of elevation of the sun is approximately 33.69 degrees.
Two large single-topping pizzas cost $25.00. What is the constant of proportionality (k)?
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{c}cost directly proportional to \underline{p}izzas}}{c=kp} \\\\\\ \textit{we know that } \begin{cases} p=2\\ c=25 \end{cases}\implies 25=k(2)\implies \cfrac{25}{2}=k\implies 12\frac{1}{2}=k[/tex]
The same king cobra is 4.237 meters long. Round the length to the nearest meter.
Answer:
4 is the closest meter you can round to. So your answer would be 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
since 2<5, 4.237 ≈ 4