#1
Solve the system using the elimination method.
x + y- 2z = 5
-x + 2y + z = 2
2x + 3y – z= 9
Answer:x=1, y=2, z=-1
Step-by-step explanation:
x = 1; y = 2; z = -1
This involves solving simultaneous equations using elimination method.
We are given the equations;x + y - 2z = 5 - - - (eq 1)
-x + 2y + z = 2 - - - (eq 2)
2x + 3y – z = 9 - - - (eq 3)
Looking at the 3 equations, let's multiply equation 2 by 3 and multiply eq 1 and eq 3 by 1 to get;x + y - 2z = 5 - - - (eq 4)
-3x + 6y + 3z = 6 - - - (eq 5)
2x + 3y – z = 9 - - - (eq 6)
Add eq 4, 5 & 6 together to get;
10y = 20
y = 20/10
y = 2
Similarly, let's repeat this proves by multiplying eq 1 by -1 and eq2 & eq 3 by 1 to get;-x - y + 2z = - 5 - - - (eq 7)
-x + 2y + z = 2 - - - (eq 8)
2x + 3y – z = 9 - - - (eq 9)
Add eq 7, 8 and 9 together to get;
4y + 2z = 6
From earlier, we saw that y = 2. Thus;
4(2) + 2z = 6
8 + 2z = 6
2z = 6 - 8
2z = -2
z = - 2/2
z = - 1
Putting -1 for z and 2 for y into;
x + y - 2z = 5
Gives; x + 2 - 2(-1) = 5
x + 4 = 5
x = 5 - 4
x = 1
Thus; x = 1; y = 2; z = -1
Read more at; brainly.in/question/18335432
A box contains cards number 1-10. A card is drawn at random, without replacement, and a second card is drawn. What is the probability that the first number is a multiple of five and the second number is a multiple of three?
Answer:
Step-by-step explanation:
Total outcome is 10 and favorable outcome is 2 ⇒ the probability that the first number is a multiple of five is [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]
Total outcome is 9 and favorable outcome is 3 ⇒ the probability that the first number is a multiple of three is [tex]\frac{1}{3}[/tex] if first draw was successful, and [tex]\frac{2}{9}[/tex] if the first number was multiple of three.
Using conditional probability, it is found that there is a 0.0667 = 6.67% probability that the first number is a multiple of five and the second number is a multiple of three.
A probability is the number of desired outcomes divided by the number of total outcomes.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: First number is a multiple of 5.Event B: The second number is a multiple of 3.There are 10 numbers, of which 2(5 and 10) are multiples of 5, hence [tex]P(A) = \frac{2}{10} = 0.2[/tex]
Then, supposing a multiple of 5 is taken, there will be 9 numbers, of which 3(3, 6 and 9) are multiples of 3, hence [tex]P(B|A) = \frac{3}{9} = \frac{1}{3} = 0.3333[/tex]
Then:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A)P(B|A)[/tex]
[tex]P(A \cap B) = 0.2(0.3333)[/tex]
[tex]P(A \cap B) = 0.0667[/tex]
0.0667 = 6.67% probability that the first number is a multiple of five and the second number is a multiple of three.
A similar problem is given at https://brainly.com/question/14398287
Question 8 If f (2) = (1 + 3) and g (2) VO+ 7, find g (f (x)). 9(f()) = 1 + 10 O g(f ()) = VI + 3 +7 Og(f (x)) = v= + 10 Og(f (2)) = 2? + 10
Answer:
x+10
Step-by-step explanation:
f(x) = (x+3)^2 and g(x) = sqrt(x)+7
g(f(x)) =
Replace f(x) in for x in the function g(x)
= sqrt((x+3)^2)+7
= x+3 +7
= x+10
Which decimal is equivalent to 48 over 100
a. 0.048
b. 0.48
c. 4.08
d. 4.8
Answer:
0.48
Step-by-step explanation:
hope it can work for you mark me as a brain liest
Points A, B, and C are collinear. Point B is between A and C. Solve for x. Find x if BC = 2x+10, AC = x+21, and AB = 11.
the answer choices:
*0 *-4 *-11 *-1
Answer:
x = 0
Step-by-step explanation:
Since the points are collinear , then
AB + BC = AC , that is
11 + 2x + 10 = x + 21
2x + 21 = x + 21 ( subtract x from both sides )
x + 21 = 21 ( subtract 21 from both sides )
x = 0
what is |x-4| if x>4
Answer:
x-4
Step-by-step explanation:
If x>4, |x-4|>0 which means |x-4|=x-4
If n equals 5 and b equals 4 what is n + b * 5
Answer:
25Step-by-step explanation:
Given,
n = 5
and, b = 4
Equation:
n + b × 5
= 5 + 4 × 5
= 5 + 20
= 25 (Ans)
Challenge: For a particular job, the Amax Employment Agency charges a fee that is equal to 15% of the first
month's pay. If the job pays X dollars annually, express the agency fee algebraically.
Answer:
0.0125x or x/80
Step-by-step explanation:
Salary: x dollars per year
To find the pay per month, we divide the annual pay by 12.
The monthly pay is x/12
15% of the first month's salary is
15% of x/12 = 0.15 * x/12 = 0.0125x = x/80
Answer: 0.0125x
what is the answer to 4.7 x 10^-8
Answer:
0.000000047
Step-by-step explanation:
Which of these is NOT an integer
A) 3 raised to the power of -5
B) -3 raised to the power of 5
C) (1/3) raised to the power of -5
Hi there!
»»————- ★ ————-««
I believe your answer is:
Option A
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Option A:}}\\\\3^{-5}\\\\\rightarrow \frac{1}{3^5}\\\\\rightarrow \frac{1}{243}\\\\\ \text{This is \textbf{NOT} an integer.}}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Option B:}}\\\\-3^5\\\\\rightarrow -3 * -3 * -3 * -3 * -3 \\\\\rightarrow \boxed{-243}\\\\\\\text{This \textbf{IS} an integer.}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Option C:}}\\\\\frac{1}{3}^{-5} \\\\\rightarrow \frac{1}{(\frac{1}{3})^5}\\\\\rightarrow \frac{1}{\frac{1}{243} }\\\\\rightarrow \boxed{243}\\\\\\\text{This \textbf{IS} an integer.}[/tex]
⸻⸻⸻⸻
[tex]\text{Option \textbf{A} does not simplify into an integer.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
1)
-2x - 5 = x - 17
-2x - 5 + 5 = x - 17 + 5
* cancel out 5 on each side of equal sign.
2)
-2x = x - 12
-2x - x = x - x - 12
* cancel out x on each side of equal sign.
3)
-3x = -12
-3x/ -3 = -12/-3
* cancel out -3x on each side of equal sign.
4) Simplify
x = 4
Hope this helps, good luck! :)
Have a great day!!
[tex]x + 0.25 = -0.25[/tex]
Answer:
x = -0.5
Step-by-step explanation:
x + 0.25 = -0.25
x = -0.25 - 0.25
x = -0.5
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:6
B. 1:1
C. 1:3
D. 1:5
Answer:
either it's 1:3 or 1:6
Step-by-step explanation:
3 students went to the zoo, and 15 students went to the aquarium.
15 plus 3 is 18.
3/18 then reduces to 1/6
therefore it is:
1:6
(before, I got my answer deleted so, maybe it is 1:3, but I solved it and got 1:6)
express p/q form of 0.375
Answer:
15/40
Step-by-step explanation:
[tex]0.375 = \frac{375}{1000} \\ \\ = \frac{15}{40} [/tex]
HELPPP!
Suppose that you head an insurance company. Your most popular insurance policy has a premium of $600 and a deductible of $1,000. This insurance policy provides your state’s minimum coverage of $30,000 for injury or death to one person, $50,000 for injury or death to two or more people, and $10,000 for damage to property, which is called 30/50/10 coverage. Assume that, on average, 2 of your 100 customers have an accident every year. One of the accidents causes damage to property and the other causes injury or death to one person. Both drivers file for the maximum claims
Now assume that you are one of the customers purchasing this popular insurance policy with the company. Considering only your premiums, deductible, and claims, what is the break-even period after which you could make a $10,000 claim for property damage without the insurance company suffering a loss? Explain your answer.
Considering only this customer's premiums, deductible, and claims, the break-even period after which the customer could make a $10,000 claim for property damage without the insurance company suffering a loss is 15 months.
At this break-even period, the company will not make a profit or a loss.
Data and Calculations:
Monthly insurance premium payable = $600 (assumed to be paid monthly)
Deductible on the insurance policy = $1,000
Minimum coverage = 30/50/10
Coverage for injury or death to one person = $30,000
Coverage for injury or death to two or more people = $50,000
Coverage for damage to property = $10,000
Average accidents every year = 2
Total claims cost to the insurance before deductibles = $40,000 ($30,000 + $10,000)
Break-even period = 15 ($10,000 - $1,000)/$600
This break-even period is computed by deducting the deductible from the claim that the customer makes, and then dividing the result by the monthly insurance premium.
Thus, the customer could make a $10,000 claim for property damage without the insurance company suffering a loss after 15 months' break-even period.
Learn more about break-even here: https://brainly.com/question/22875945
in the first quarter austin played for 4 minutes and 30 seconds. wyatt played for 310 seconds who had more playing time
Answer:
wyatt
Step-by-step explanation:
4:30 mins is 270 seconds
A grocery store is having a "buy 2 get 1 free" promotion on their six-pack cans of orange juice. If Mrs. VanCleave decides to take advantage of this promotion everyday for a week, how many cans of orange juice will she have at the end of the week?
Picture shown!
If f(x) = x + 1, and g(x) = 2x,
then
f(g(x)) = [ ? ]x + [ ?]
Answer:
2x+1
Step-by-step explanation:
f(x) = x + 1
g(x) = 2x
f(g(x)) = Replace x in the function f(x) with the function g(x)
f(g(x)) = g(x) +1
= 2x+1
Answer:
f(g(x)) = 2x + 1
Step-by-step explanation:
Substitute x = g(x) into f(x) , that is
f(g(x))
= f(2x)
= 2x + 1
Please help solve this. 10points worth it
Answer:
The function is a growth function so I guess A, B and D
suggest a growth curve
Step-by-step explanation:
PLEASE simplfy 8^15÷8^−3
Answer:
8^18
Step-by-step explanation:
We know that a^b ÷ a^c = a^(b-c)
8^15÷8^−3
8^(15 - -3)
8^(15+3)
8^18
Circle the graphs of the functions.
How did you know which graphs showed a function?
i will mark brainliest
Answer:
Step-by-step explanation:
Relations are only functions if they do not share any x values at all! The 2 graphs there that do not have any of the same x values are graphs A and D. Notice that on graph B, there are several y values that share the x value of 2; on graph C, there are several y values that share the x value of 2.
Answer:
A and D only
Step-by-step explanation:
A function is a relation where each input has its own output ( each x values has its own corresponding y value ) If an input has more than one output than the relation is not a function.
We can tell if a graph shows a function or not by using the vertical line test. If you draw vertical lines on the graph and more than one point is on the vertical line drawn then the graph does not show a function.
For graph B if you draw a vertical line at x = -2 more than 1 point will be on the line meaning that the graph does not show a function.
For Graph C if you draw a vertical line at x = 2 more than 1 point will be on the line meaning that Graph C also does not show a function.
For Graphs A and D you can draw a vertical line anywhere on the graph and no more than 1 point will be on the line therefore Graphs A and D show functions.
1. Which of these is most likely to describe the number of yards lost in a football game?
A. rational number
B. whole number
C. real number
D. integer
Answer:
Step-by-step explanation:
whole number with the occasional jump into rational numbers when a down like 2nd and 5 1/2 to go.
HELP! TRIGONOMETRY QUESTION!!
Use the law of cosines, which says
189² = 215² + 123² - 2×215×123 cos(∠P)
==> cos(∠P) = 25,633/52,890
==> ∠P ≈ 61.06°
I don’t understand how to find the height
Answer:
height, x is 235 ft
Step-by-step explanation:
From trigonometric ratios:
[tex] \cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]
but:
[tex] \theta = 90 \degree - 36 \degree \\ \theta = 54 \degree[/tex]
adjacent is x
hypotenuse is 400 ft
[tex] \ \cos ( 54 \degree) = \frac{x}{400} \\ \\ x = 400 \ \cos (54 \degree) \\ x = 235 \: \: feet[/tex]
Answer:
[tex]235\ ft[/tex]
Step-by-step explanation:
In this problem, one is given two parallel lines and a few transversals that form a triangle between these parallel lines. The parallel lines, one from the parasailer, and one from the boat have an angle of depression between them. This means the angle of elevation from the boat to the parasailer is also (36) degrees. This is due to the alternate interior angles theorem, which states that when two parallel lines are intersected by a transversal, then the alternate interior angles are congruent.
The triangle formed in this situation is a right triangle, this is indicated by the box around one of the angles. Now that one has found another angle measure in this triangle, one can use right angle trigonometry. Right angle trigonometry is a series of ratios that describe the relationship between the sides and angles of a right triangle. These ratios are as follows:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Please note that the names (opposite) and (adjacent) are subjective, and change relative to the angle one is looking at, however (hypotenuse) refers to the side opposite the right angle. This side doesn't change its name. In this situation, it would be most logical to use the ratio of sine, (sin), as one has the measure of the hypotenuse, and one is trying to find the measure of the side opposite the angle. Substitute the given information into the ratio of (sin) and solve to find the unknown:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]sin(36)=\frac{x}{400}[/tex]
Inverse operations,
[tex]sin(36)=\frac{x}{400}[/tex]
[tex]400(sin(36))=x[/tex]
[tex]235.114=x[/tex]
A book, a person and a box cost Rs 45 and Rs 54 respectively . Find the smallest sum of money with which the exact number of books , pens and boxes can be purchased.
Answer:
99
Step-by-step explanation:
If you like my answer than please mark me brainliest
Answer: 99
Step-by-step explanation:
please click thanks and mark brainliest if you like :)
PLEASE HELP ME ANSWER THESE !!!
1 There are 63 students marching in a band, and they’re marching in 7 rows. How many students are in each row?
2 A candy factory made 54 boxes of chocolates. Each box weighs 2 pounds. They packed the boxes in 6 cases with the same number of boxes in each case. How many pounds of chocolates were there in each case?
3 Max bought tools costing $75. He made a $30 down payment and plans to pay off the rest of the money in 5 monthly installments. How much will Max’s monthly payments be?
4 Harry has decided to give his collection of 24 old coins to his four grandsons. John, the oldest, gets half the collection. Walt, Matt, and Richie will divide the remaining coins evenly among themselves. How many coins will each boy receive?
5 Mr. and Mrs. Pierotti are remodeling their kitchen. They need 9 square yards of covering for the floor. Jackson Interiors quoted them a price of $81 for 9 square yards of linoleum. Carpet Master told them that carpeting would cost $6 per square yard. Which is cheaper—the linoleum or the carpeting
Answer:
1)9 2)18 3)9. 4)4. 5)carpeting
Step-by-step explanation:
1) divide 63 by 7 = 9
2)multiply 54 by 2 = 108 total weight of the boxes then divide 108 by 6 to get 18
3) 75 -30 to get remaining amount which is 45 then divide by 5 to get how much he will pay each month which is 9
4 24- 12= 12 the remaining for the 3 and divide by 3 to get 4
5) multiply 6 * 9 which is $54 which is cheaper than the $81
13 Water is pulled up from a well in a bucket on a rope. The rope winds on a cylindrical drum 15 cm in diameter. It takes 28 turns of the drum to pull the bucket up from the bottom of the well. How deep is the well? (Use the value 2 for m.)
Write the quadratic expressions in the numerator and the
denominator in factored form
4x^2-14x+6/
X^3-7x^2+12x
I have to give 2 Ans form my question so sorry
Can you find the area of the figure?
Answer:
Below
Step-by-step explanation:
First I found the area of the triangle on the right
A = bh/2
A = (9)(4.5) / 2
A = 20.25 ft^2
Next, the area of the rectangle in the middle
A = lw
A = (7.5)(9)
A = 67.5 ft^2
And now the area of the right triangle on the left
A = bh/2
A = (5)(9) / 2
A = 22.5 ft^2
Add em all up : 20.25 + 67.5 + 22.5 = 110.25 ft^2
Hope this helps!
Solve the proportion below.
Answer:
Does the answer help you?
