Answer:
[tex]\rightarrow \sf x^2=\:17x\:+\:60[/tex]
change sides
[tex]\rightarrow \sf x^2 -17x -60 = 0[/tex]
breakdown, (60 : 20 * 3)
[tex]\rightarrow \sf x^2 -20x +3x-60 = 0[/tex]
factor the following
[tex]\rightarrow \sf x(x -20) +3(x-20) = 0[/tex]
collect into groups
[tex]\rightarrow \sf (x +3)(x-20) = 0[/tex]
final answer
[tex]\rightarrow \sf x=-3, \ 20[/tex]
Answer:
(x-20) (x+3) =0
Step-by-step explanation:
x ^ 2 = 17x + 60
Subtract 17x from each side
x ^ 2 - 17x = 60
Subtract 60 from each side
x ^ 2 - 17x - 60=0
What 2 numbers multiply by -60 and add to -17
-20 * 3 = -60
-20 +3 = -17
(x-20) (x+3) =0
can someone help me with this ?
Answer:
yes I can help you with this but I don't know it
Julia’s gross pay was $4,500 last year. the federal income tax withholding from her pay was 13% of her gross pay. julia determined the federal income tax she owes is $495. how much of a refund can julia expect? $64.35 $90.00 $430.65 $585.00
The amount of the refund Julia gets as a federal income tax will be $90.
What will be Julia's refund?It is given in the question:
Julia's gross pay = $500
federal income tax withholding from her pay was 13% of her gross pay
federal income tax she owes is = $495
To find out the refund we will first find the amount of Federal income which is 13% of the gross pay.
[tex]\rm federal \ amount =\dfrac{4500\times 13}{100} =585[/tex]
The refund Julia will get will be
[tex]=585-495=90[/tex]
Hence the amount of the refund Julia gets as a federal income tax will be $90.
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The amount of money Camilla earns varies directly with the number of hours she works. If she earns $150 when she works 20 hours, how much will she earn for working 60 hours?
What is k ? (k = y/x)
What is the equation for the direct variation situation? (y = kx)
How much will she earn for working 60 hours?
What is k ? (k = y/x)
If y is dollars earned and x is hours worked,
k = y/x
k = 150 dollars /20 hours
k = 7.50 dollars per hour
What is the equation for the direct variation situation? (y = kx)
y = kx
y = (7.50)(60)
y = 450
How much will she earn for working 60 hours?
y = $450
She will earn $450 after working for 60 hours.
Write the polar equation 0= pi/3
Answer:
1
(
π
3
)
)
Step-by-step explanation:
Explanation:
Substitute
tan
(
y
x
)
for
θ
tan
(
y
x
)
=
π
3
Obtain
y
x
on the left by using the inverse tangent on both sides:
tan
−
1
(
tan
(
y
x
)
)
=
tan
−
1
(
π
3
)
y
x
=
tan
−
1
(
π
3
)
Multiply both sides by x:
y
=
(
tan
−
1
(
π
3
)
)
x
What percent represents the shaded part of the hundredths grid shown? Please help asap!
Answer:
C. 5%
Step-by-step explanation:
if u count the shaded part it is 5 shaded out of 100 so that fraction is 5/100 which is .05 as a decimal and 5% as a percent
A pizza box is 20 inches wide, 18 inches long, and 2 inches tall.
How many square inches of cardboard were used to create the box?
Answer:
872 square in.
Step-by-step explanation:
The formula for the surface area of a rectangular prism is:
[tex]A=2(wl*wh*lh)[/tex]
Where w is the width of the prism, l s the length of the prism, h is the height of the prism, and A is the surface area.
Plugging in the numbers given, you get the following equation:
[tex]A=2((20*18)*(20*2)*(18*2))[/tex]
Which when calculated out, is 872 square in.
-2x + 22 < 18
It is an inequality
Answer:
Solving for x;
-2x + 22 < 18
Get rid of constants:
-22 -22
-2x < -4
Isolate x, by dividing by -2 from both sides since the inverse operation of multiplication is division, and remember when dividing or multiplying by negative integers, you flip the inequality symbol around:
÷-2 ÷-2
x > 2
Answer:
[tex]x > 2[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x > 2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(2,\:\infty \:\right)\end{bmatrix}[/tex]
Given:
-2x + 22 < 18
Solve:
[tex]\mathrm{Subtract\:}22\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x+22-22 < 18-22[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-2x < -4[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
[tex]\left(-2x\right)\left(-1\right) > \left(-4\right)\left(-1\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]2x > 4[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}2[/tex]
[tex]\frac{2x}{2} > \frac{4}{2}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x > 2[/tex]
~Lenvy~
17. Billy purchased 100 shirts at a cost of $15 each and planned to resell them. The first
week he sold some of them for $25 each. The second week he sold the rest for $20 each.
If his total profit was $600, how many shirts did he sell the first week?
Answer:
2100
Step-by-step explanation:
Answer pls in fractions
Answer:
4/5 yd^3
Step-by-step explanation:
(2/3)(3/1)(2/5) = 12/15 = 4/5
Answer:
4/5 I believe?
Step-by-step explanation:
Multiply all the numbers together :)
Sherlene bought 3 pounds of coffee and 2 pounds of chocolate for a total of $24. Which equation, written in standard form, correctly represents this scenario and correctly indicates what the variables represent? A) The correct equation is 3x + 2y = 24, where x is the price per pound of coffee and y is the price per pound of chocolate. B) The correct equation is 5x + y = 24, where x is the combined price per pound of coffee and chocolate, and y is the total number of pounds purchased. C) The correct equation is 3x + 2x + y = 24, where x is the combined price per pound of coffee and chocolate, and y is the total number of pounds purchased. D) The correct equation is 3x + 2y = 24, where x is the price per pound of chocolate and y is the price per pound of coffee.
Regina created a playlist on her cell
phone. The playlist includes 3 pop songs, hip-hop songs, and 1 blues song. Regina will randomly choose 2 songs, without repeating a song, to play through her new earbuds. What is the probability that Regina will choose a pop song first and a hip-hop song second?
Answer: a 5/24
Step-by-step explanation:
3 + 5 + 1 = 9
First = Pop Song P = 3/9 = 1/3
Seconed = Hip Hop Song P2 = 5/9-1 = 5/8
So P = 1/3 x 5/8 = 5/24
So that makes A the correct answer
Annie wants to use the problem-cause-solution order to organize a persuasive speech to reduce violence on campus. she begins by offering statistics of incidents to show that there is a need for action. what is a possible next step
The possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.
What is a persuasive speech?It should be noted that a persuasive speech simply means a speech that is used to convince an individual to agree to a particular perspective.
In this case, the possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.
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The length of a square is 3x - 4 units. Find the area in terms of x.
Answer:
9x^2 - 24x + 16 is area in terms of x alternativly (3x-4)^2 is also true
Step-by-step explanation:
L * W = area length = width on a sqare so L * L = area too
(3x - 4) * (3x - 4)
use foil method
9x^2 - 24x + 16
Answer:
9x^2 − 24x + 16
Step-by-step explanation:
To find the area of a square, you use the formula
A = x^2
So we plug in 3x-4 for x
A = (3x-4)^2
A = 9x^2 − 24x + 16
MARKING BRAINLEIST IF CORRECT
Answer:
A) (-5,0) and (-4,0)...
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♪[/tex]
X - intercepts are the points where the curve cuts x - axis ~
for the given curve (parabola), the intercepts are :
[tex]\qquad \sf \dashrightarrow \:(-5,0) \: \: and \: \: (-4, 0)[/tex]
The Correct choice is A
[tex]➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖[/tex]
In 2010 Elmbrook Middle School had 100 students in the eighth grade. In 2011 the number of eighth
graders decreased by 10%. The 2012 eighth grade Class increased in size by 10% from 2011. How many
eighth grade students were enrolled at Elmbrook Middle School in 2011
Answer:
90 students
Step-by-step explanation:
So, if you have 100 students to start and it decreases by 10% then take the 100 and multiply it by .10. You should get 10. Then, subtract 10 from 100 and you end up with 90.
Answer:
hello
2010 = 100 students
2011 = 100 x 0.9 = 90
2012 = 90 x 1.1 = 99
Step-by-step explanation:
Researchers are recording how much of an experimental medication is in a person's bloodstream every hour. they discover that half-life of the medication is about 6 hours.
By using the known half-life, we can see that if the initial dose is 500mg, after 4 days the medication will be 0.0076 mg.
What is the half-life?
We define half-life as the time such that the initial amount is reduced to its half.
So, if a given substance has a half-life T, then the amount of substance as a function of time, we have:
S(t) = A*e^{-t*ln(2)/T}
Where t is the variable in time units.
We know that T = 6 hours, and A, the initial dose, is 500 mg, so the formula is:
S(t) = 500mg*e^{-t*ln(2)/6h}
Then after 4 days (or 4*24h = 96h) the amount of medication is:
S(96h) = 500mg*e^{-96h*ln(2)/6h} = 0.0076 mg.
If the initial dose was 750mg, after 4 days the person would have:
S(96h) = 750mg*e^{-96h*ln(2)/6h} = 0.0114 mg
So the person would have:
0.0114 mg - 0.0076 mg = 0.038 mg more of medication.
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What is the mean absolute deviation of Madison's exercise times?
Madison's
Exercise Times
20
25
35
40
55
Answer:
5
Step-by-step explanation:
Answer:
The mean absolute deviation would be 10.
Step-by-step explanation:
I calculated the answer in Microsoft excel. I used a bunch of excel formulas. I do not know how to insert some of the math symbols neccessary to show you my steps. Here is a picture of the formula.
A frame contains 4 pounds of gold. suppose gold is worth $1,277 per ounce. how much would the gold in the frame be worth?
Answer:
$81,728
Step-by-step explanation:
For reference: 1 pound = 16 ounces.
Therefore, 4 pounds of gold must be 16 * 4 = 64 ounces.
Since each ounce is $1,277, we must have the total cost of the gold to be $1,277 * 64 = $81,728.
The key word here is "per", which means to multiply.
Answer:Answer:5,108
Step-by-step explanation:
[tex]y+2=(x^2/2)-2sin(y)[/tex]
the assumption being that "y" is encapsulating a function in "x" terms.
[tex]y+2=\cfrac{x^2}{2}-2sin(y)\implies \stackrel{\textit{taking the derivative to both sides}}{\cfrac{dy}{dx}+0=\cfrac{1}{2}(2x)\underset{chain~rule}{-2cos(y)\cdot \cfrac{dy}{dx}}} \\\\\\ \cfrac{dy}{dx}=x-2cos(y)\cfrac{dy}{dx}\implies \cfrac{dy}{dx}+2cos(y)\cfrac{dy}{dx}=x \\\\\\ \cfrac{dy}{dx}\left[ 1+2cos(y) \right]=x\implies \cfrac{dy}{dx}=\cfrac{x}{1+2cos(y)}[/tex]
The two figures are congruent. Find the values of the unknown variables.
Answer:
y = 71
z = 18
x = 14
Step-by-step explanation:
Figure on the right is simply figure on the left but flipped on its side. we know this because the question tells us the shapes are congruent (which means equal, the same)
Which one is it? Im stumped.
Answer:
rational
Step-by-step explanation:
Hope this helps!
If not I am sorry
let's keep in mind that that same/same = 1 always, so then we can say
[tex]\cfrac{spaghetti}{spaghetti}~~ = ~~\cfrac{hippopotamus}{hippopotamus}~~ = ~~\cfrac{meatballs}{meatballs}~~ = ~~\cfrac{dog}{dog}~~ = ~~\cfrac{0.\overline{55}}{0.\overline{55}}~~ = ~~\textit{\huge 1}[/tex]
well, "1" is a whole number
"1" is also an integer oddly enough
"1" can be written as a ration like 1/1, so is also rational.
4 2/4 + 1/9 =
what is the answer i need to know now
Answer:
4.61
Step-by-step explanation:
Step-by-step explanation:
[tex] = 4 \frac{2}{4} + \frac{1}{9} \\ = \frac{4 \times 4 + 2}{4} + \frac{1}{9} \\ = \frac{18}{4} + \frac{1}{9} [/tex]
Find the LCM
[tex] = \frac{18}{4} \times \frac{9}{9} + \frac{1}{9} \times \frac{4}{4} \\ = \frac{162}{36} + \frac{4}{36} \\ = \frac{166}{36} [/tex]
Convert into lowest term
[tex] \frac{83}{16} \\ [/tex]
A skydiver in a computer game free-falls from a height of 3000 meters at a
rate of 55 meters per second. Which equation can be used to find the
height of the skydiver after tseconds?
Solve 7x -4 = 5x + 15 for x.
19/12
11/2
19/2
Answer:
Third option
Step-by-step explanation:
Given the following question:
[tex]7x-4=5x+15[/tex]
To find the answer we need to use inverse of operations to simplify the equation in till we isolate the variable and find the value of x.
[tex]7x-4=5x+15[/tex]
[tex]-4+4=0[/tex]
[tex]15+4=19[/tex]
[tex]7x=5x+19[/tex]
[tex]5x-5x=0[/tex]
[tex]7x-5x=2x[/tex]
[tex]2x=19[/tex]
[tex]2x\div2=x[/tex]
[tex]19\div2=\frac{19}{2}[/tex]
[tex]=\frac{19}{2}[/tex]
Your answer is the third option or "19/2."
Hope this helps.
A total of 275 people took a driving theory test on Monday. Of these people, 68% passed the test.
a) (i) What percentage of people who took the test on Monday did not pass the test?
(ii) How many of the 275 people who took the test on Monday passed the test?
Answer:
a. 32%
B.8B.88
Step-by-step explanation:
100 -68=32%
32/100=x/275
100x=8800
x=88
the first day of shooting a movie, a director uses 30% of a film reel. The strip of
film used was 90 meters long.
What is the standard length on a film reel?
Answer:
27
Step-by-step explanation:
30% of 90 can be written as 30% × 90
= 30/100 × 90
= 27
F(X)= -x^2 + 10x - 12
Answer:
(0, -22)
Step-by-step explanation:
The y-intercept is the value of y when x is 0,
f(x) = -x² + 10x - 22
f(0) = -(0)² + 10(0) - 22
f(0) = - 22
The y-intercept is -22 at point (0, -22).
-> We can also see this when graphing, please see attached.
Note: If you want me to solve for f(x) = -x² + 10x - 12 as you wrote in text and not f(x) = -x² + 10x - 22 as the picture shows, let me know.
by finding tan θ in 2 different triangles find the value of m
Answer:
m = 3.75
Step-by-step explanation:
tanθ = 3/4θ = 37°⇒ Angle opposing 3 in the left triangle is 53°
sin53° ⇒ 4/5 = 3/m4m = 15m = 15/4m = 3.75This is getting more difficult!
The equation [tex]y = x^2 - 8x + 3[/tex] is an illustration of a quadratic equation
The vertex of the quadratic equation [tex]y = x^2 - 8x + 3[/tex] is (4,-13)
How to determine the vertex?The equation is given as:-
[tex]y = x^2 - 8x + 3[/tex]
A quadratic equation is represented as:
[tex]y = ax^2 + bx + c[/tex]
By comparison, we have:
a = 1; b = -8; c = 3
The x-coordinate of the vertex is:
[tex]x = -\frac b{2a}[/tex]
So, we have:
[tex]x = \frac 8{2*1}[/tex]
[tex]x = 4[/tex]
Substitute 4 for y in [tex]y = x^2 - 8x + 3[/tex]
[tex]y = 4^2 - 8 * 4 + 3[/tex]
[tex]y = -13[/tex]
When x = 2 and 3, we have:
[tex]y = 2^2 - 8 * 2 + 3 = -9[/tex]
[tex]y = 3^2 - 8 * 3 + 3 = -12[/tex]
When x = 5 and 6, we have:
[tex]y = 5^2 - 8 * 5 + 3 = -12[/tex]
[tex]y = 6^2 - 8 * 6 + 3 = -9[/tex]
So, the table of values is:
x y
2 -9
3 -12
4 -13
5 -12
6 -9
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The owner of a music store ordered new compact disks. Of the new compact disks ordered,1/4 are Jazz, 2/7 are Classical, and the rest of the compact disks are Soft Rock. What fraction of the compact disks ordered are Soft Rock?
The fraction of the compact disks ordered by the owner of the music store that are Soft Rock is 13/28.
What are fractions?A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above while the denominator is the number below.
What fraction is Soft Rock?1 - (1/4 + 2/7)
1 -[ (7 + 8) /28]
1 - 15/28 = 13/28