Answers
x² + 4x = 192
Step 2:
Take x common:
x ( x + 4) = 192
Length is x and width is x+4
Step 3:
x² + 4x - 192 = 0
Step 4:
x² + 16x - 12x - 192 = 0
x(x+16) - 12(x+16) = 0
(x-12)(x+16) = 0
⇒ x=12, x=-16
Because the length can't be -16, the length is 12.
Factoring x²+4x, you get x(x+4). If you call the length x, then the width is the other factor, x+4.
Step 4: {16}
You know this two ways. -192/-12 = 16, and 4 -(-12) = 16, where 4 is the coefficient of x in step 3.
Last line: {-16, 16}
The values of x that make the factors zero are -16 and 12. Since these are supposed to represent lengths, an appropriate answer cannot be negative (-16). The width is x+4 = 12+4 = 16.
Related Questions
Question# 12, find the slope
Answers
(0,1) and (-4, -2)
Slope = m = (-2 - 1)/(-4 -0 ) = -3/-4 = 3/4
So the slope of given line is 3/4
Thus the correct answer is option B
m = (y2-y1) / (x2-x1)
We choose the ordered pairs:
(x1, y1) = (0, 1)
(x2, y2) = (4, 4)
Substituting values we have:
m = (4-1) / (4-0)
m = (3) / (4)
m = 3/4
Answer:
The slope for this case is given by:
m = 3/4
option 2
A theater received $8,917 in ticket sales for one performance of a play. Tickets for preferred seats cost $45 each and regular seats cost $34 each. All of the theaters 75?preffered seats were sold out that evening. How many tickets were sold?
Answers
P = Number of ticket for preferred seats costing $45 per seat
R = Number of regular seats costing $34 per seat.
Total revenue = P*45 + R*34 =8,917
45P + 34R = 8917
But, number of preferred seats is 75 or P=75 seats
Then,
45*75 +34R = 8917
3375 +34R = 8917
34R = 5542
R = 5542/34 = 163
Total number of seats = P+R = 75+163 = 238 seats. If each seat is sold for one ticket, then 238 tickets wee sold.
given that an arithmetic sequence can be expressed as a linear function in the form f(x)=mx+b, write a linear function to describe the sequence {10,15,20,25,30,35...}
Answers
m = (y2-y1) / (x2-x1)
m = (15-10) / (2-1)
m = 5/1
m = 5
Then,
y-yo = m (x-xo)
where,
(xo, yo) = (1, 10)
Substituting:
y-10 = 5 (x-1)
y = 5x -5 + 10
y = 5x + 5
Answer:
a linear function to describe the sequence is:
y = 5x + 5
Answer:
a linear function to describe the sequence is:
y = 5x + 5
Step-by-step explanation: ik ur on usa te$t prep
Quadrilateral has angles 45 degrees, 150 degrees, 65 degrees, and N degrees
Answers
other angles=260
all interior angles of a quadrilateral add up to 360
Q # 8 please solve the question
Answers
Their sum is 20, so we can write
x + y = 20
Their difference is 14, so we can write:
x- y = 14
Adding the two equations, we get:
2x = 34
x = 17
Using the value of x, in first equation, we get:
17 + y = 20
so,
y = 3
Thus the two numbers are 17 and 3.
So, option a is the correct answer
x + y = 20
x-y = 14
Where,
x: real number
y: real number
Solving the system we have:
x = 17
y = 3
Therefore, the numbers are:
17 and 3
Answer:
17 and 3
option 1
A lunch in a fancy restaurant is three times as expensive as a lunch in a cafeeria. The lunch in the fancy restaurant costs 36. In five day workweek Mary eats at the fancy restaurant once and in the cafeteria the rest of the days. How much does she spend on lunches in that week
Answers
3x = 36
where x is the cost of eating in cafeteria.
The value of x from the equation is 12.
In a five-day workweek, she eats at the fancy restaurant once and four times in cafeteria. To determine the total cost,
T = 4(12) + 36
T = 84
Thus, the answer to this item is 84.
f = fancy restaurant price
c = cafeteria price
f = 3c
f = 36
c = 36/3 = 12
36 + 12*4 = 84
she spends 84 on lunches for a fiveday workweek
Regina's mom bought her some bracelets. There were a total of 85 bracelets in 5 packages.
Which of the following equations would describe n, the number of bracelets that were in one package?
A. n + 5 = 85
B. n ÷ 5 = 85
C. n - 5 = 85
D. n × 5 = 85
Answers
What is the ratio (fraction) of minivans to all vehicles on the forecourt?
A)1/120
B)1/20
C)1/6
D)1/4
Answers
20/120
1/6
I hope this helps
do u do keystone
? im just wondering i do
An electrolyte solution has an average current density of 111 ampere per square decimeter \left( \dfrac{\text{A}}{\text{dm}^2}\right)( dm 2 A )left parenthesis, start fraction, A, divided by, d, m, start superscript, 2, end superscript, end fraction, right parenthesis. What is the current density of the solution in \dfrac{\text{A}}{\text{m}^2} m 2 A start fraction, A, divided by, m, start superscript, 2, end superscript, end fraction?
Answers
We have to find the average current density of the solution in ampere per square meter.
1 decimeter = [tex] \frac{1}{10} [/tex] meter
Squaring both sides we get
1 decimeter square = [tex] \frac{1}{100} [/tex] meter square
Current density = [tex]1 \frac{A}{dm^{2} } =1 \frac{A}{ \frac{1}{100} m^{2} } =100Am^{-2} [/tex]
Thus, the density of electrolyte solution is 100 ampere per square meter
Answer:
Answer is 100
Step-by-step explanation:
Nan and sato are designing a coffee table would you sing 4 inches tile Nan uses 30 tiles and sato uses half as many many total tiles did they use
Answers
it is assumed that the tile is square
area of the square=b²
b is the length side of a square
b=4 in
area of the tile=4²----> 16 in²
Part 1) How many total tiles did they use?
Nao uses 30 tiles
and
Sato uses (1/2)*30=15
so
Nao and Sato uses----> 30+15----> 45 tiles
the answer Part 1) is
45 tiles
Part 2) If the area of the table is 36 inches by 26 inches, will they have enough tiles for the table?
find the area of the table
area of the table=36*26----> 936 in²
area of one tile=4*4----> 16 in²
if 1 tile------------------> 16 in²
x tiles-------------> 936 in²
x=936/16----> x=58.5 tiles
58.5 > 45
so
there are not enough tiles for the table
the answer part 2) is
there are not enough tiles for the table
Part 3) If not, how many more will they need?
tiles required=58.5-45------> 13.5-----> 14 tiles
the answer part 3) is
14 tiles
Nan and Sato together used 45 tiles for their coffee table design.
The student's question involves calculating the total number of tiles used by two individuals, Nan and Sato, who are designing a coffee table. Nan uses 30 tiles, and Sato uses half as many tiles as Nan does. To find out how many tiles Sato uses, we divide Nan's number of tiles by 2.
So, Sato uses 15 tiles because half of 30 is 15. To find out the total number of tiles used, we add Nan's tile count to Sato's tile count:
30 tiles (Nan) + 15 tiles (Sato) = 45 tiles in total.
Therefore, to determine the total number of tiles used, Nan's 30 tiles are added to Sato's 15 tiles (half of Nan's), resulting in a total of 45 tiles used for the coffee table design.
hey can you please help me posted picture of question
Answers
C. G(x)=(x-2)^3
The explanation is shown below:
1. You have the the red graph has the equation F(x)=x^3
2. If you shifted two units to the right, you must add -2 to the function x^3, as below:
G(x)=(x-2)^3
3. If you want to verify this is correct, you need to give values to the variable x and plot each point.
4. You will see that the correct answer is the option mentioned above.
Ezra is training for a track race. He starts by sprinting 100 yards. He gradually increases his distance, adding 5 yards a day for 21 days.
Answers
Is that what you meant for the problem
or do u want to know how many yards he sprinted total for the 21 days
If it is,
he sprinted a total of 3390 yards
On Apex the correct one is 200 yards.
Given: triangle ABC, AB = BC Perimeter of ΔABC = 50 Perimeter of ΔABD = 40 Find: BD
Answers
The measure of angle ABC and BDC is 80° and 90° respectively.
What is the triangle?In geometry, a triangle is a closed, two-dimensional shape with three straight sides. A triangle is also a polygon.
Given the ΔABC in which AB ≅ BC, m∠ABD = 40° and BD is the median of ΔABC.
We have to find the measure of angle ∠ABC and ∠BDC.
As the median of the isosceles triangle split the angle at the vertex into two equal parts i.e ∠ABC is twice the angle ∠ABD.
[tex]\rm \angle ABC=2\angle ABD\\\\\angle ABC=2 \times 40\\\\\angle ABC=80[/tex]
Also, the median of an isosceles triangle is perpendicular to the opposite side i.e to the base. Here, BD is perpendicular to AC.
∠BDC=90°
Therefore, the measure of angle ABC and BDC is 80° and 90° respectively.
To know more about triangles click the link given below.
https://brainly.com/question/12636178
#SPJ3
Cards are dealt, one at a time, from a standard 52-card deck. a if the first 2 cards are both spades, what is the probability that the next 3 cards are also spades?
Answers
Then third card being spades would be 11 / 50
Now there are 10 spades and 49 cards left.
So the probability for fourth card would be 10 / 49
Fifth card would be 9 / 48.
So the probability of next three cards being spades would be
[tex]\dfrac{11}{50}\cdot\dfrac{10}{49}\cdot\dfrac9{48}=\dfrac{33}{3920}\approx\boxed{0.00842}[/tex]
Hope this helps.
what is the value of x sin x + 11 degrees equals cos 2x + 22 degrees enter your answer in the Box
Answers
(x + 11) + (2x + 22) = 90
Simplifying,
3x + 33 = 90
Further simplification,
3x = 90 - 33 = 57
The value of x from the equation is 19.
Answer: x = 19
Answer:
it is 19
Step-by-step explanation:
I just took this test and got 100 :)
A line passes through the ordered pairs (4,1) and (2,8). What is the slope? Please help due today
Answers
find 1/9 as many as 3 divided by 5
Answers
Final answer:
To find 1/9 as many as 3/5, you multiply 3/5 by 1/9 to get 3/45, which simplifies to 1/15.
Explanation:
To solve the student's question, we need to find what is 1/9 as many as 3/5. This involves multiplying the fraction 3/5 by the fraction 1/9. Here is the step-by-step calculation:
Multiply the numerator of the first fraction (3) by the numerator of the second fraction (1) to get the numerator of the answer.Multiply the denominator of the first fraction (5) by the denominator of the second fraction (9) to get the denominator of the answer.Combine these to get the answer in fractional form.The calculation will look like this: (3/5) × (1/9) = 3/45 = 1/15.
Thus, 1/9 as many as 3/5 is 1/15.
Brad has 3 pairs of pants, 7 tee shirts, and 2 pairs of sneakers. How many different outfit combinations can he wear
Answers
Answer:
42
Step-by-step explanation:
What is the distance d across the lake?
Answers
Answer-
The distance d across the lake is 90ft.
Solution-
In the picture,
ΔABC ≈ ΔCDE
Because,
∠ACB = ∠DCE (∵ vertical opposite angles)∠B = ∠D = 90°∠ACB = ∠CED (∵ as other two angles are same and sum of those two angles when subtracted from 180° will result the same)So, from similarity properties
[tex]\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{DC}[/tex]
[tex]\Rightarrow \dfrac{120}{20}=\dfrac{d}{15}[/tex]
[tex]\Rightarrow d=\dfrac{120\times 15}{20}=90[/tex]
In which type of investment do you lend your money to a government agency or a corporation for a fixed period of time and earn interest?
a) bonds
b) stocks
c) mutual funds
Answers
Answer: a. Bonds
Step-by-step explanation:
Bond is a kind of money investment issued by private corporations or government banks.
Buying a bond is like issuing a loan to the issuer. The issuer will pay back the face value of the issued loan along with interest money. It is issued for a fixed period of time.
Answer:
a) bonds
Step-by-step explanation:
was right
A display that shows how the values in a data set are distributed
Answers
Answer: Line Plot
Step-by-step explanation: A line plot is a display that shows how the values in a data set are distributed.
Answer: histogram
Step-by-step explanation:
What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet? Use 3.14 for π.
Answers
ω = d/(t*r) = (14.13 ft)/((3 s)*(6 ft))
ω = 0.785 radians/second
There are 180/π degrees per radian, so the angular velocity can also be written as ...
ω = 45 degrees/second
Which answer shows a correct order to solve this story problem? Maurine had to pay $2.52 tax on her purchases. She bought 3 books for $12.99 each, 2 pens for $0.69 each, and a magazine for $2.99. How much did Maureen spend? A. Step 1: Add the price of a book and a pen. Step 2: Multiply by 3 and then by 2. Step 3: Add $2.99 to that result. Step 4: Add the tax to the total of the purchases. B. Step 1: Calculate the total price of the 2 pens. Step 2: Add $2.99 to that total. Step 3: Calculate the total price of the 3 books. Step 4: Add the tax to the price of the 3 books C. Step 1: Calculate the total price of the 3 books. Step 2: Calculate the total price of the 2 pens. Step 3: Add $2.99 to the total of the cost of the books and pens. Step 4: Add the tax to the total of the purchases. D. Step 1: Add $2.99 to the amount of the tax. Step 2: Calculate the total price of the 2 pens. Step 3: Calculate the total price of the 3 books. Step 4: Add the prices of the pens to the price of the books.
Answers
C. Step 1: find the price of the books; Step 2: find the price of the pens; Step 3: add the prices of the books, pens, and magazine; Step 4: add the tax.
_____
You can, of course, find and add the constituent prices in any order. Generally, you need to know that subtotal in order to figure the tax, which is then added to that subtotal. If you've ever done any shopping at a store where bills are added manually, or if you pay attention to any cash register receipt, you know this is the process.
From a group of 3 men and 4 women, a delegation of 2 is selected. let x be the random variable that represents the number of women selected. write the probability distribution and find the expected number of women in the delegation?
Answers
x values are 0, 1, 2, 3
The corresponding probabilities are:
P(x=0)= 3C2/7C2=3/21
P(X=1)=3C1*4C1/7C2=12/21
P(X=2)=3C2/7C2=3/21
P(X=3)=3C2/7C2=3/21
Hence the expected value will be:
E(x)=[0*3+1*12+2*3+3*3]/21
E(x)=27/21=1.29
Find the length of JK and the measure of M
Answers
You have two different situations, but both of them are solved the same way.
Step One
Solve for the 2 equal sides.
21x - 9 = 3x + 27 Add 9 to both sides.
21x = 3x + 27 + 9
21x = 3x + 36 Subtract 3x from both sides.
21x - 3x = 36
18x = 36 Divide by 18
x = 36/18
x = 2
That's not quite the answer
Step Two
Find JK
JK = 21x - 9
JK = 21*2 - 9
JK = 42 - 9
JK = 33 <<<<<<< Answer
Step Three
Solve for y
5y + 11 = 12y - 10 Subtract 5y from both sides.
11 = 12y - 5y - 10
11 = 7y - 10 Add 10 to both sides.
11 + 10 = 7y
21 = 7y Divide by 7
21/7 = y
3 = y
Step Four
Solve for M
M = 12y - 10
M = 12*3 - 10
M = 36 - 10
M = 26 <<<<< Answer
M = 74
Hope this Helped!
;D
Brainliest??
If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction. Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"?
Answers
x / y
Where,
x = numerator
y = denominator:
If the numerator of a fraction is increased by 3, the fraction becomes 3/4:
(x + 3) / y = 3/4
If the denominator is decreased by 7, the fraction becomes 1:
x / (y-7) = 1
Solving the system of equations we have:
x = 9
y = 16
The original fraction is:
9/16
Answer:
the original fraction is:
9/16
"If the numerator of a fraction is increased by 3, the fraction becomes 3/4" is:
(x + 3) / y = 3/4
PLEASE HELP!
1. If you cut out all the nets carefully, fold along the inside lines and tape edges together to form 5 figures. Describe the figures formed. What shapes are they? Are any the same?
2. What does the fact that the figures fit together to make the prism tell you about their combined volume?
Answers
The first picture is A. The rest should be in order like this: A, B, E, D,C.
Yes I know I did a crummy job at taping but hey, I tried.
A snow storm left 1.25 feet of snow on the ground overnight. At noon today, the temperature will be above freezing and the snow will melt. If the melting snow is modeled by the equation y = -1 3 x + 1.25, how long will it take for the snow to melt away?
Answers
0 = -13x + 1.25
-1.25 = -13x
3.75 = x
then,
3.75 hours to 3 hours 45 minutes
Two graphs are shown below:
graph A shows scatter points 1, 1 and 2, 2 and 3, 3 and 4, 4 and 5, 5graph A shows scatter points 1, 4 and 2, 4 and 3, 4 and 4, 4 and 5, 4
Which scatter plot shows a positive correlation between x and y?
Only graph A
Only graph B
Both graph A and graph B
Neither graph A nor graph B
Answers
The correct answer is graph A
David is making a mosaic using 63 glass tiles 105 ceramic tiles and 84 marble tiles he wants to put the same number of each type of tile and Rose what is the maximum number of times you can have in each row
Answers
David can put 21 of each kind of tile in a row.
_____
These numbers are 3*21, 4*21, and 5*21, respectively.