Answer:
number of adult shirts sold (a) = 20
number of youth shirts sold (b) = 10
Step-by-step explanation:
a = number of adult shirts sold
y = number of youth shirts sold
30 = a + y
$324.50 = 11.50a + 9.45y
This is the resulting system of equations from the given information in the problem.
Solve for y in the first equation and then substitute the equation for y into the second equation :
a+y=30 --> y=30-a
324.50 = 11.50a + 9.45(30-a)
Solve for a.
324.50 = 11.50a + 283.5 - 9.45a
41 = 2.05a
a = 20
Now that we have solved for a, we can back substitute into our equation for y and solve.
y=30-(20)
y = 10
CHECK:
(20)+(10) = 30 True
(11.50)(20) + (9.45)(10) = 324.5 True
What is the solution to the equation? −12x=−3 Enter your answer as a simplified fraction in the box. x =
Answer:
1/4
Step-by-step explanation:
This is because you want to get x alone, so if you divide -12 on one side you have to do it on the other side, so you get -3/-12 which can be divided by -3 to be simplified to 1/4. Hope this helps!
Answer:
1/4Step-by-step explanation:
-12x = -3
x = 12 : -3
x = 1/4
--------------------
check
-12 * 1/4 = -3
-3 = -3
the answer is good
calculate (3×10^5) × (4×10^4) in standard form.
NEED HELP ASAP.
Answer:
12000000000
Step-by-step explanation:
did I add too many zeros????
10 to the 5 is multiply by 10 five times (100,000)
100,000 x 3 = 300,000
For the second thing, 10 to the 4 = 10,000
10,000 x 4 = 40,000
300,000 x 40,000 = 12000000000
Sketch the graph of each line
The standard equation of a line is y = mx+ b
where:
m is the slope of the lineb is the y-intercept of the lineThe y-intercept is the point where the line cuts the y-axis
For the equation y = -2x -4
For the equation, the line will cut the y-intercept at y = -4 with a negative slope of -2.For the equation y = -5/2x
For the equation, the line will cut the y-intercept at y = 0 with a negative slope of -5/2.Find the graphs attached.
Learn more on graphs here: https://brainly.com/question/25020119
Lily has 7 fewer ribbons than Dora. Lily has 13 ribbons. How many ribbons does Dora have?
Answer: 6
Step-by-step explanation:
13-7=6
Evaluate the expression when c=−4 and y=2
-y+4c
Answer:
-2 - 16 = -18
Step-by-step explanation:
-y+4c
You take the values for c and y and substitute them in the original equation.
It would then look like:
-(2) + 4(-4)
Solving that would be -2 -16 = -18
Answer:
-18
Step-by-step explanation:
-(2)+4(-4) Plug in the values of y and c.
-2+(-16) Simplify.
-2-16
-18
Hope this helps you out!! Have an amazing day <3
Find the discriminant and describe the nature of the root(s) of the equation: 6x2 - 2x - 4 = 0)
Answer:
discriminant= 100, nature of the root= real numbers.
Step-by-step explanation:
discriminant formula: b^2-4ac
-2^2-4(6)(-4)
4+96=100.
Find the factors of f(x) given that x = 5 is a zero.
f(x) = x3 − 6x2 − x + 30.
(x − 5)(x + 3)(x − 2)
(x − 5)(x − 3)(x + 2)
(x + 5)(x − 3)(x + 2)
(x + 5)(x + 3)(x − 2)
Answer:
B.(x − 5)(x − 3)(x + 2)
Hope you could get an idea from here.
Doubt clarification - use comment section.
this is for 8th grade pls answer .
Step-by-step explanation:
We have that
[tex](x + \frac{1}{x} ) {}^{2} = 3[/tex]
We are trying to find the number value so that we can apply in the later equation.
Qe first simplify.
Remeber that
[tex](a + b) {}^{2} = a {}^{2} + 2ab + {b}^{2} [/tex]
Also remeber that
[tex] \frac{1}{x} = {x}^{ - 1} [/tex]
so
[tex](x + x {}^{ - 1} ) {}^{2} = {x}^{2} + 2x {}^{0} + {x}^{ - 2} = 3[/tex]
We then simply remeber that x^0=1 so
[tex] {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 3[/tex]
Multiply both sides by x^2.
[tex] {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{2} [/tex]
Subtract both sides by 3x^2
[tex] {x}^{4} - {x}^{2} + 1 = 0[/tex]
Notice that x^4= (x^2)^2.
So our reformed equation is
[tex]( {x}^{2} ) {}^{2} - {x}^{2} + 1 = 0[/tex]
Let a variable , w equal x^2. This means that we subsitute variable, w in for x^2.
[tex]w {}^{2} - w + 1 = 0[/tex]
Now we use the quadratic formula
[tex] w = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
and
[tex]w = - b - \frac { \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
Let a=1 b=-1 and c=1.
[tex]w = \frac{1 + \sqrt{1 - 4(1)} }{2} [/tex]
[tex]w = \frac{1 - \sqrt{1 - 4} }{2} [/tex]
Now, we get
[tex]w = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]
and
[tex]w = \frac{1}{2} - \frac{ i\sqrt{3} }{2} [/tex]
Now since we set both of these to the x^2 we solve for x.
and
[tex] {x}^{2} = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]
and
[tex] {x}^{2} = \frac{1}{2} - \frac{i \sqrt{3} }{2} [/tex]
We can represent both of these as complex number in the form of a+bi. Next we can convert this into trig form which is
[tex] {x}^{2} = 1( \cos(60) + i \: \sin(60) [/tex]
and
[tex] {x}^{2} = 1( \cos(300) + i \: sin(300))[/tex]
Next we take the sqr root of 1 which is 1, and divide the degree by two.
[tex] {x} = 1( \cos(30) + i \: sin \: 30)[/tex]
and
[tex]x = 1( \cos(150) + i \: sin(150)[/tex]
We are asked for the 2nd root so just add 180 degrees to this and we have
[tex]x = 1 \cos(210) + i \: sin \: 210)[/tex]
and
[tex]x = 1( \cos(330) + i \: sin(330)[/tex]
which both simplified to
[tex]x = - \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]
and
[tex]x = \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]
Now we must find
x^18+x^12+x^6+1.
We just use demovire Theorem. Which is a complex number raised to the nth root is
[tex] {r}^{n} (cos(nx) + i \: sin(nx)[/tex]
So let plug in our first root.
[tex]1( \cos(330 \times 18)) + i \: sin \: (330 \times 18))) + 1( \cos(12 \times 330)) + i \: sin(12 \times 330) + 1( \cos(6 \times 330) + i \: sin(6 \times 330))) + 1[/tex]
To save time we multiply the angle and use rules of terminals angle and we get
[tex]1( \cos(180) + i \sin(180) ) + 1( \cos(0) + i \: sin \:( 0) + 1( \cos(180) + i \: sin(180) + 1[/tex]
And we get
[tex] - 1 + 1 + - 1 + 1 = 0[/tex]
So one of the answer is x=0
And the other, let see
[tex]1 \cos(210 \times 18) + i \: \sin(210 \times 18) + 1 \: cos(210 \times 12) + i \: sin(210 \times 12) + 1 \cos(210 \times 6) + \:i sin(210 \times 6) + 1[/tex]
[tex] \cos(180) + i \: sin(180) + 1 \cos(0) + i\sin(0) +1( \cos(0) + i \sin(0) + 1[/tex]
We get
[tex] - 1 + 1 + 1 + 1 = 2[/tex]
So our answer are 2.
So the answer to the second part is
0 and 2.
How i can answer this question
Answer:
3(2q+1)
Step-by-step explanation:
6q+2
3(2q+1)
Define the domain: {(2,3),(0,3),(4,2),(5,6)}
A. 2, 0, 4, 5
B. 0
C. 6
D. 3, 2, 6
After looking through different hotel options, Gabriela and Luis decided to estimate a budget of $1,200
$
1,200
for hotel costs. They want to stay 6
6
nights at a hotel. In addition, they know they should plan to pay $240
$
240
in taxes and tips. Let c
c
represent the total cost per night they should plan for the hotel.
What is the solution to the equation that represents this situation?
Answer:
The equation will be. c= 1200 / 240 + 6 = 440. C=440 (I don't know if this is correct)
Let $F,$ $G,$ and $H$ be collinear points on the Cartesian plane such that $\frac{FG}{GH} = 1.$ If $F = (a, b)$ and $H = (7a, c)$, then what is the $x$-coordinate of $G$?
F, G, and H all lie on the same line. If FG/GH = 1, then FG = GH, which is to say the distance between F and G is equal to the distance between G and H. This means either F and H are the same point, or G is the midpoint of F and H.
They're not the same point, because the x-coordinate of H is 7 times that of F. So G must be halfway between F and H.
Then the x-coordinate of G is
(a + 7a)/2 = 8a/2 = 4a
what is the value of k makes the equation trur
Answer:
where is the equation??
pls attach that
Find the x in the figure. Assume a and b are parallel
Answer:
x = 15
Step-by-step explanation:
(4x - 30) and (2x) are alternate angles and are congruent , then
4x - 30 = 2x ( subtract 2x from both sides )
2x - 30 = 0 ( add 30 to both sides )
2x = 30 ( divide both sides by 2 )
x = 15
Calculate the volume of the storage tank to the nearest hundredth.
F.2,840.04 m3
G.8,520.12 m3
H.11,360.16 m3
J.34,080.47 m3
Answer:
gang gang shii
Step-by-step explanation:
gang gang.
Please Help Me Out Show You Work :) I will appreciate much
Step-by-step explanation:
6)
[tex]k = \frac{6}{4} \\ k = \frac{3}{2} [/tex]
7)
[tex] \frac{ab}{mn} = \frac{bc}{no} = \frac{cd}{op} = \frac{da}{pm} [/tex]
8)
[tex]y = 8 ( \frac{3}{2} ) \\ y = 12[/tex]
[tex]z = 6 ( \frac{3}{2} ) \\ z = 9[/tex]
9)
[tex]5k = 8 \\ k = \frac{8}{5} \\ x( \frac{8}{5}) = 32 \\ x = 20ft[/tex]
what is n? solve for n+5=2n-6
Answer:
n = 11
Step-by-step explanation:
n+5=2n-6
you add 6 on both sides and you get
n+11=2n
you then subtract n on both sides and get
11=n
Step-by-step explanation:
n+5 = 2n - 6 -> Original equation
5 = n - 6 -> Take n away from both sides
11 = n -> Add 6 to both sides
n = 11 -> Final answer
*Remember, we are trying to get n by using inverse operations.
Elena received a $30 gift for her birthday. She plans to use it to buy one or more books. Elena will have to pay 8% sales tax on the books and $1.50 bus fare to get to and from the shopping center. If c = the amount in dollars Elena spends on books, this situation can be represented by the inequality below.
1.08c + 1.5 ≤ 30
The cost of book has to be less than or equal to 26.39.
The amount of money Elena can buy has to be less than or equal to $30. Thus, the inequality sign to be used is the less than or equal to sign.
(1 + tax)cost of books + cost of bus fare ≤ value of the gift
1.08c + 1.5 ≤ 30
In order to determine the maximum cost of books, take the following steps:
Combine similar terms
1.08c ≤ 30 - 1.5
Add similar terms together
1.08c ≤ 28.50
Divide both sides of the equation by 1.08
c ≤ 28.50 / 1.08
c ≤ 26.39
To learn more about taxes, please check: https://brainly.com/question/25311567
Solve the system of linear equations by substitution
6x-9=y
y=-3x
Answer:USE SUBSTITUTION METHOD. Algebra work right here
Step-by-step explanation:
1) The height, h, in feet of a ball above the ground is given by h = -16t2 + 64t+ 80, where t is the time in seconds. How long does it take the ball to hit the ground? es A) 3 seconds B) 4 seconds 95 seconds D) 6 seconds
Answer:
C) 5 seconds
Step-by-step explanation:
[tex]h = - 16t {}^{2} + 64t + 80[/tex]
When the ball hits the ground, the height is 0.
[tex]0 = - 16t {}^{2} + 64t + 80[/tex]
Factor out the greatest common factor: 16
[tex]0 = - 16(t {}^{2} - 4t - 5)[/tex]
Find numbers whose sum is -5 and product is - 4.
Those numbers are - 5 and 1: - 5 × 1 = - 5, - 5 + 1 = - 4
[tex]0 = - 16(t - 5)(t + 1)[/tex]
[tex]t - 5 = 0[/tex]
Or
[tex]t + 1 = 0[/tex]
So,
[tex]t = 5[/tex]
Or
[tex]t = - 1[/tex]
Since time cannot be a negative value the correct answer is 5 seconds.
Pointing to a photograph, a man said, "I have no brother, and that man's father is my father's son." Whose photograph was it?
The man’s son. Since the man has no brothers and the father of the man in the photograph is the man’s father’s son, the father of the man in the photograph must be the man. That means that the man in the photograph is the man’s son.
Which of the following correctly simplifies the expression
(3^2 X 5^0 /4) ^2
What is √101.6064 in to 1 decimal place and in standard form?
NEED ASAP
Note that
10² = 100
0.08² = 0.0064
and
101.6064 = 100 + 1.6 + 0.0064
It also happens that
1.6 = 2 • 10 • 0.08
which means
101.6064 = 100 + 1.6 + 0.0064
101.6064 = 10² + 2 • 10 • 0.08 + 0.08²
101.6064 = (10 + 0.08)²
101.6064 = 10.08²
which means
√101.6064 = 10.08
which, to one decimal place, is approximately 10.1.
Question 1 of 10
In order to solve the following system of equations by addition, which of the
following could you do before adding the equations so that one variable will
be eliminated when you add them?
2x - 4y= 5
6x – 3y=10
O A. Multiply the top equation by 3 and the bottom equation by 4.
B. Multiply the top equation by-3 and the bottom equation by 2.
ООО
C. Multiply the top equation by-2.
D. Multiply the top equation by-3.
Answer:
D.
Step-by-step explanation:
Help me with this
-22*3 +12*2 -6*2 +4+2
[tex]\red{\bf{ {Answer = \: \: - 48}}} [/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-22 \times 3} + \underbrace {12 \times 2} - \underbrace {6\times 2} + 4 + 2[/tex]
We carry out the three multiplications.
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-66 \: + \: 24} \: - \: 12 \: + \: \underbrace {4 \: + \: 2}[/tex]
Now we make the ones that are marked.
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-42} \: \: - 12 \: \: + \underbrace {6} \: \: [/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-36 \: \: \: - \: \: \: 12}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf -48[/tex]
What is the value of the expression [−18+(−22)]−43+12?
Answer:
-71
Step-by-step explanation:
Answer:
-71
Step-by-step explanation:
[-18+(-22)]-43+12
=(-18+22)-43+12
=-40-43+12
=-83+12
=-71
16. You and a friend are going shopping. You leave school and drive 10 miles
due west on 26th Street. You then drive 7 miles NW on Raspberry Street to the
grocery store. Your friend leaves school and drives 10 miles due east on 26th Street.
He then drives 7 miles SE on Cascade Street to the movie store. Each of you has
driven 17 miles. Which of you is farthest from your school?
Answer:
My friend is farthest from my school
Step-by-step explanation:
Let the distance from the movie store to school be x and the distance from the grocery store to school be y
Using Cosine rule,
x²= 10²+7² - 2×10×7Cos120
x²= 149 -140(-0.5)
x²= 149+70
x²= 219
x= √219
= 14.8miles
y²= 10²+7² - 2×10×7Cos100
y²= 149 -140(-0.1736)
y²=149+24.2704
y²=173.2704
y=√173.2704
y=13.4miles
Ralph has 9 cards, each with a number on it. What is the probability that the number chosen is a multiple of 4 ?
Answer:
2/9.
Step-by-step explanation:
There are 2 multiples of 4 in the 9 cards, 4 itself and 8.
So the required Probability is 2/9.
What are the steps to convert a number from standard notation to scientific notation?
Answer:
Step-by-step explanation:
The goal in scientific notation is to express a value in terms of a number that contains a single unit before the decimal point.
Examples:
10000: 1.0 x 10^4
23456: 2.3456x10^4
In both cases, the x10^4 is telling us to multiply the first number by 10,000. 10^4 is the same as 10x10x10x10 = 10,000
The justification for scientific notation is that is makes expression large and small numbers much easier, as well as reduces errors due to an incorrectly placed decimal.
An example: Divide 2500000000 by 5000. That would normally require setting up a long-hand division problem that not only wastes paper and pencil, but is also prone to decimal point errors.
Do the same problem with scientific notation:
Count the places you want to move the decimal point backwards to just beyond the 5 in 2500000000. It takes nine steps to move the decimal point to between the 2 and 5: 2.5 followed by 8 zeros. That's a total of next steps to go in front of the 5. This is written 2.5 x 10^9
5000 is represented by 5.0x10^4
Now when we divide the same numbers, but in scientific format, it is easier to see the answer:
(2.5x10^9)/(5.0x10^4)
2.5/5 = 0.5
10^9/10^4 = 10^5 [The exponents are subtracted when dividing with exponents: 9-4 = 5]
Put them together to find the final answer: 0.5x10^5
Then move the decimal point one spot to the right and reduce the exponent by 1:
5.0x10^4
------
Add exponents when multiplying: 10^3 x 10^5 = 10^8 (3+5=8)
Subtract when dividing: 10^7/10^2 = 10^5 (7-2=5)
Multiply when there is an exponent raised to another exponent: (10^4)^3 = 10^12 (4x3 = 12)
31. One serving of party drink is comprised of 3oz of syrup, 4oz of water, and 3oz of apple juice. If a large bowl of the drink contains 237oz of apple juice, how much of the total drink is in the bowl
Answer:
790 oz
Step-by-step explanation:
Ratio:
3oz syrup : 4oz water : 3oz apple juice: 1 serving: 10oz total mixture
We know there is 10oz total mixture because 3oz of syrup + 4oz of water + 3oz of apple juice = 10oz total mixture
We want to find
237oz apple juice: ?oz total mixture
To do this, we can multiply the ratio
3oz apple juice: 10oz total mixture by 237/3, because 237/3 * 3 = 237, getting us to 237oz apple juice on one side and maintaining the ratio so that we can find the total mixture amount, so we have
237oz apple juice: 10*237/3 oz total mixture = 10*79 = 790 oz