Answer:
x = 3 ± [tex]\frac{\sqrt{10} }{-2}[/tex]
Step-by-step explanation:
To find the roots of this equation, we can either use facotring or the quadratic formula. Because this equation isn't facotrable, we will use the quadratic formula to solve it
-2[tex]x^2[/tex] + 12x - 13 = 0
x = [tex]\frac{-12 +- \sqrt{12^2 - 4(-13)(-2)} }{-4}[/tex]
x = [tex]\frac{-12 +- \sqrt{144-104} }{-4}[/tex]
x = [tex]-\frac{-12 +- \sqrt{40} }{-4}[/tex]
x = 3 ± [tex]\frac{\sqrt{10} }{-2}[/tex]
5
volume of the solid figure.
7 yd 3 yd
4 yd
1 yd
12 yd
9 yd
4 yd
8 yd
lume is
Answer:
Hope the picture will help you.Make sure to mark me brilliant
There is exactly 1 pair of parallel sides in the following shape.
The 7 unit side and the unit 10
since they are both perpendicular to the same 8 unit side
:)
If AC= 8x-14 and EC = 2x + 11, solve for x.
Step-by-step explanation:
AC= 8x-14
AC+14=8x
x=(AC+14)÷8
EC=2x+11
EC-11=2x
x=(EC-11)÷2
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
A mother invests $7000 in a bank account at the time of her daughter's birth. The interest is 18) compounded quarterly at a rate of 8%. What will be the value of the daughter's account on her twentieth birthday, assuming no other deposits or withdrawals are made during this period?
well, from birth to your twentieth birthday that'll just be 20 years, so
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=7000\left(1+\frac{0.08}{4}\right)^{4\cdot 20}\implies A=7000(1.02)^{80}\implies A\approx 34128.07[/tex]
the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 56 in, find its length and width
Answer:
Step-by-step explanation:
Let the width of the rectangle = x
As length is 5 inches longer than width, we have to add 5 to width
Length = x + 5
Perimeter of ractangle = 56 in
2* (length + width) = 56
2*( x + 5 + x) = 56
2* (2x + 5) = 56
Use distributive property: a*(b +c) =(a*b) + (a * c)
2*2x + 2*5 = 56
4x + 10 = 56
Subtract 10 from both sides
4x = 56- 10
4x = 46
Divide both sides by 4
x = 46/4
x = 11.5
Width = 11.5 in
length = 11.5 + 5
= 16.5 in
A manager drew this box-and-whisker plot to represent the number of minutes each of his 27 employees took on their break. Each employee took a different amount of time.
How many employees took a break longer than 49 minutes?
Enter your answer in the box.
Answer:
6
Step-by-step explanation:
Longer than 49 is only 25% percentile.
27 X .25 = 6.75
Employees are whole numbers, therefore the answer is 6.
Answer:
6
Step-by-step explanation:
C
X
A parabola has a focus at ( 1.5, 0) and a directrix of x= -1.5. Which of the following equations represent the parabola?
Step-by-step explanation:
Since the focus lies on the x axis, and the diretcrtirx is a vertical line, we have a sideways parabola so we have the equation
[tex](y - k) {}^{2} = 4p(x - h)[/tex]
where h,k is the vertex and
p is the distance from the vertex to the focus or the distance fromcthe vertex to the directrix.
Since the focus is 1.5, and the directrix is -1.5 the vertex is (0,0) so we have
[tex]y {}^{2} = 4px[/tex]
We know p is 1.5 so we have
[tex] {y}^{2} = 6x[/tex]
[tex] \frac{1}{6 } {y}^{2} = x[/tex]
The number of men and women participating in the Winter Olympic Games has been steadily increasing in recent years. In the 19th Winter Olympics, 1389 men and 787 women participated. 1660 men and 1121 women participated in the 22nd Winter Olympics.
Part A
Which system describes the number of men and women participating if x represents the number of winter games after the 22nd Winter Olympics?
Multiple choice question.
A)
y=1389x+1660y=787x+1121
B)
y=2713x+1121y=3343x+1660
C)
y=2713x+1389y=3343x+787
D)
y=2713x+1660y=3343x+1121
Using a system of equations, it is found that the correct option is:
A) 1389x+1660y=787x+1121y.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, considering the amounts in each olympics(1389 men and 787 women participated on the 19th, 1660 men and 1121 women in the 22th), the system is:
A) 1389x+1660y=787x+1121y.
More can be learned about a system of equations at https://brainly.com/question/24342899
The graph of f(x) = 8 - x and line l which is tangent to f at x =1 is
shown in the figure to the right. The equation for line l is y =-3x +10.
Region R is the shaded region between line l, the graph off and the
y-axis while S is the shaded region between line l, the graph off and
the x-axis.
(a) Find the area of the shaded region R.
By taking the integral of the difference between the two given lines, we will see that R = 0.75.
How to find the area of the region R?Notice that the area will be given by the integral of the difference between the line L and our function on the interval [0, 1]
Then we just need to compute:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx[/tex]
Solving that we will get:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx = \int\limits^1_0 ({-3x + 10 - 8 + x^3} )dx\\\\\R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\\\[/tex]
[tex]R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\R = \frac{-3}{2}*(1)^2 + 2*1 + \frac{1^4}{4} = 0.75[/tex]
So the area of region R is 0.75 square units.
If you want to learn more about integrals, you can read:
https://brainly.com/question/14502499
5.Joan Robinson opens her own law office on July 1, 2012. During the first month of operations, the following transactions occurred. 1. Joan invested $11,000 in cash in the law practice. 2. Paid $800 for July rent on office space. 3. Purchased office equipment on account $3,000. 4. Provided legal services to clients for cash $1,500. 5. Borrowed $700 cash from a bank on a note payable. 6. Performed legal services for client on account $2,000. 7. Paid monthly expenses: salaries and wages $500, utilities $300, and supplies $100. 8. Joan withdraws $1,000 cash for personal use
Step-by-step explanation:
i will go you in the bank in co2 in the man
A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a square base. Express the
surface area A of the box in terms of the width w of the base. If the material for the base and top costs 10 dollars/ft2
and that for the sides costs 20 dollars/ft express the total cost C as a function of the width.
The total surface area is 2w² + 8/w, while the total cost is $(20w² + 160/w)
What is volume?Volume is the amount of space occupied by a three dimensional shape or object.
Let w represent the width of the base and h represent the height. Hence:
w²h = 2
h = 2/w²
The surface area = 2w² + 4(hw) = 2w² + 4(2/w² * w) = 2w² + 8/w
The total cost = 2w² * $10 + (8/w) * $20 = $(20w² + 160/w)
The total surface area is 2w² + 8/w, while the total cost is $(20w² + 160/w)
Find out more on volume at: https://brainly.com/question/12410983
Find all the factors of 18.
A) 2, 9
B) 1, 2, 3, 6, 9, 18
C) 1, 2, 3, 4, 6, 8, 9, 18
Answer:
B)1, 2, 3, 6, 9, 18
Step-by-step explanation:
1×18
2×9
3×6
HOPE IT HELPS YOU
Can someone please help with this. I’m stuck.
Answer:
567 ghbvc. the high but
Step-by-step explanation:
solve accordingly to the picture
hope it helps
Sketch a graph x - y =5
Answer:
Step-by-step explanation:
*View attached graph*
Hope this helps!
Answer quickly help please !!
Answer:
z = 104°
Step-by-step explanation:
A straight line is 180° which helps us to solve this problem.
180° - 76° = 104°
This means that angle y will be 76° and x will be 104° because of vertical angles.
Please help me I don’t understand
Answer:
y=-2x + 5
Step-by-step explanation:
y=mx+b
m=slope
b= y intercept
since on the y line the line intercepts on 5 you replace 5 with the b.
As for the m(slope) when the line is decreasing (going down) its automatically a negative number. and since (0,5) (1,3) 5-3=2 -2 would be ur slope.
solve this sum urgent no spam
Answer:
Step-by-step explanation:
YES IS THE ANSWER BECAUSE X=9
AND 11+3=87
Antonio weighs four pounds more than twice his brother weight. If Antonio weighs 97 pounds, how much does his brother weigh? Write and solve equation.
Answer:
The bother's weight is 46.5 lb.
Step-by-step explanation:
Let the brother's weight be b.
Antonio's weight is 2b + 4.
Antonio's weight is 97 lb.
2b + 4 = 97
2b = 93
b = 46.5 lb
Answer: The bother's weight is 46.5 lb.
Seven times a number is between – 28 and 28.
Answer:
four and negative four
Step-by-step explanation:
7*4 =28 7 *-4 = -28
What is the solution set?
Answer:
5'3
Step-by-step explanation:
trust me I know what im talking about
What would be the corresponding angles ( similar figures ). Any help with this question will be gladly appreciated . Thank you
Answer:
x=4.8
I think ur supposed to solve for x. Since the rectangles are similar, we can set a proportion for the sides
5/3 = 8/x (then just solve for x)
24=5x
4.8=x
-5 x + 10 -20 need help with this
Answer:
-5(x+2)
Step-by-step explanation:
For f(x) = 3x^3 - 9x^2 - 5x + 2
A. Find f(-1)
B. Find f(2)
Answer:
(3x2 + 3x - 1) • (x + 2)
Step-by-step explanation:
3.4 Polynomial Long Division
Dividing : 3x3+9x2+5x-2
("Dividend")
By : x+2 ("Divisor")
dividend 3x3 + 9x2 + 5x - 2
- divisor * 3x2 3x3 + 6x2
remainder 3x2 + 5x - 2
- divisor * 3x1 3x2 + 6x
remainder - x - 2
- divisor * -x0 - x - 2
remainder 0
Quotient : 3x2+3x-1 Remainder: 0
Eliana draws a quadrilateral that has sides measuring 12 centimeters, 10 centimeters , 12 centimeters, and 10 centimeters in length. The angles are NOT right angle. What type of quadrilateral did Eliana draw?
Answer:
parallelogram
Step-by-step explanation:
opposite sides are congruent so this meets the minimum requirement to be a parallelogram.
Can someone help me please?
Answer:
11/2
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
This is because each dot represents one plot, and the only number with one plot above it is 1 and 1/2, aka D
Please help me to answer this
Find the lateral surface area of the rectangular prism in centimeters
Answer:
180 cm2 is the answer you can multiply all sides
Answer:
Step-by-step explanation:
length = l = 9 cm
Width = w= 3 cm
height = h = 4 cm
Lateral surface area = 2 *( lh+ lw)
= 2*( 9*4 + 9*3)
= 2 * (36 + 27)
= 2 * 63
= 126 square cm
*Pls help me*
No links
Answer:
See below ↓
Step-by-step explanation:
a. 4 ÷ (2/3) = 12/3 ÷ 2/3 = 12 ÷ 2 = 6
b. 4 ÷ 1 = 4
Attachment below.
Answer:
1: 6
2:4
Step-by-step explanation:
What is the sum of 8 of the interior angles of a regular decagon?
Answer:
1152°
Step-by-step explanation:
interior angles of polygon = (n - 2) x 180, where n is the number of sides.
Decagon has 10 sides. 10 - 2 = 8 and 8 x 180 = 1440
Since there are 10 angles, Each angle a= 1440 / 10, which equals 144.
Finally, multiply 144 by 8 and you get 1152°
A certain brand of laundry detergent is manufactured for $3.85 and then marked up 40% by the local store before selling. The store offers a 20% discount with the purchase of three or more bottles of the detergent. Showing all work, determine the total cost, before tax, of five bottles of detergent. (10 points)
Answer:
$21.56
Step-by-step explanation:
Original price = $3.85Marked up by 40% = 3.85 x 1.4 = $5.39 per bottleCost and discount of 5 bottles
Cost = 5 x 5.39 = $26.95Discount of 20% = 26.95 x 0.8 = $21.56Answer:
$21.56
Step-by-step explanation:
Original cost of one bottle of detergent = $3.85
Cost of one bottle after 40% mark up = 1.4 × $3.85 = $5.39
Cost of 5 bottles = 5 × $5.39 = $26.95
Cost of 5 bottles after applying 20% discount = 0.8 × $26.95 = $21.56
Therefore, the total cost of 5 bottles of detergent is $21.56
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Information about percetange increase/decrease
If you increase the price of something by 40% then it will be 140% of the original price (the original price is 100% and 100% + 40% = 140%).
Convert to decimal form: 140% = 140/100 = 1.4
Therefore, to calculate an increase of 40%, multiply the original price by 1.4
If you decrease the price of something by 20% then it will be 80% of the previous price (the original price is 100% and 100% - 20% = 80%).
Convert to decimal form: 80% = 80/100 = 0.8
Therefore, to calculate a decrease of 20%, multiply the previous price by 0.8