The answers are:
1
[tex]x=2[/tex]
2
[tex]y=-4[/tex]
3
[tex]z=4[/tex]
4
[tex]x=-5[/tex]
Why?Solving for each of the given equations and variable, we have:
1[tex]-2x + 5 = 4x - 7[/tex]
Solving for "x", we have:
[tex]-2x + 5 = 4x - 7\\\\-2x-4x=-7-5\\\\-6x=-12\\\\x=\frac{-12}{-6}=2[/tex]
So, we have that:
[tex]x=2[/tex]
2[tex]12y+4=8y-12[/tex]
Solving for "y", we have:
[tex]12y+4=8y-12\\\\12y-8y=-12-4\\\\4y=-16\\\\y=\frac{-16}{4}=-4[/tex]
So, we have that:
[tex]y=-4[/tex]
3[tex]7z-18 =-2z+18[/tex]
Solving for "z", we have:
[tex]7z-18 =-2z+18\\\\7z+2z=18+18\\\\9z=36\\\\z=\frac{36}{9}=4[/tex]
So, we have that:
[tex]z=4[/tex]
4[tex]10x+15 =5x-10[/tex]
Solving for "x", we have:
[tex]10x+15 =5x-10\\\\10x-5x=-10-15\\\\5x=-25\\\\x=\frac{-25}{5}=-5[/tex]
So, we have that:
[tex]x=-5[/tex]
Hence, the answers are:
1
[tex]x=2[/tex]
2
[tex]y=-4[/tex]
3
[tex]z=4[/tex]
4
[tex]x=-5[/tex]
Have a nice day!
Brody and four of his friends purchased tickets to a movie. The total was $32. How much did each person spend on their ticket? Use the equation 5x = 32 to solve.
x = $6.00
x = $6.40
x = $27.00
x = $160.00
Assume that the probability of a driver getting into an accident is 7.6%, the average cost of an accident is $16,412.05, and the overhead cost for an e company per insured driver is $105. What should be this drivers insurance premium?
Answer:
1,352.32
Step-by-step explanation:
If you take 7.6 and multiply it to 16,412.05 (.076)(16,412.05), you get 1,247.32. You then add the overhead cost of 105 to get 1352.32. (Apex verified too)
The drivers insurance premium is:
$ 1352.3158
Step-by-step explanation:The probability of a driver getting into an accident is 7.6%.
The average cost of an accident is $16,412.05.
This means that the expected amount that will be paid to each of the driver by the company on accident will be: 0.076×16412.05
= $ 1247.3158
Also, the overhead cost for an e company per insured driver is $105.
This means that the insurance premium of driver is:
= 105+1247.3158
= $ 1352.3158
The Sudsy car wash loses $40 on rainy days and gains $150 on sunny days. If the probability of rain is 15%, what its he expected value of the net profit?
-40*.15 + 150*(1-.15)= 121.50
Given the probabilities of sunny and rainy days and the respective profits, the Sudsy car wash's expected net profit per day, considering the rain probability, is $121.5.
Explanation:The subject of the question is about Expected Value, a concept in Probability Theory. Considering the Sudsy car wash's situation, we know that it loses $40 on rainy days and gains $150 on sunny days. The probability of having a rainy day is given as 15%, which means the probability of having a sunny day is 85% (100% - 15%).
The expected value of the net profit can be calculated by the formula for Expected Value: E[X] = ∑[x*P(X=x)]. In the context of this problem, we can write out the expected value E[N] of the net profit N as E[N] = (-$40 * 0.15) + ($150 * 0.85) = -$6 + $127.5 = $121.5. So, it is expected that the Sudsy car wash will have a net profit of $121.5 per day, on average.
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What is the quotient (6x4 − 15x3 + 10x2 − 10x + 4) ÷ (3x2 + 2)?
2x + 6
2x − 6
2x + 4
2x − 4, r = 1
Answer:
The quotient is [tex]2x^2-5x+2[/tex]
Step-by-step explanation:
We want to simplify:
[tex]\frac{6x^4-15x^3+10x^2-10x+4}{3x^2+2}[/tex]
We factor the numerator to get:
[tex]\frac{(x-2)(2x-1)(3x^2+2)}{3x^2+2}[/tex]
We cancel out the common factors to get:
[tex](x-2)(2x-1)[/tex]
Therefore the quotient is [tex]2x^2-5x+2[/tex]
⊙X≅⊙Y and RQ = 35.6. Identify ED, rounded to the nearest tenth.
Answer:
Your answer is 7.0
Step-by-step explanation:
If the circles are congruent and RQ measures 35.6, then so does CB. That means that half of it (the radius XD which measures 26 cuts the length of CB in half) is 17.8. If the base of that right triangle is 17.8 and the hypotenuse is 26, then Pythagorean's Theorem tells us that the height of the triangle is 18.95151709. Subtract that from the radius length of 26 and you'll have the length of DE
The value of length ED would be, 7.0
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
⊙X≅⊙Y
And, Length of RQ = 35.6
Now, We get;
⇒ CB = RQ = 35.6
Hence, EB = 1/2CB
= 1/2 (35.6)
= 17.8
Applying Pythagoras theorem,
⇒ XE² = XB² - EB²
⇒ XE² = 26² - 17.8²
⇒ XE² = 19
Thus, The length of ED is,
⇒ ED = XD - XE
⇒ ED = 26 - 19
⇒ ED = 7.0
Therefore, The value of length ED would be, 7.0
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The area of an oil spill is doubling in size every day. At the start of the day on May 1, the oil spill covers 20 square meters. During which day will the area exceed 500 square meters?
Answer:
May 6
Step-by-step explanation:
20 x 2 = 40 40 x 2 = 80 80 x 2 = 160 x 2 = 320 320 x 2 = 640 after 5 days on may 6 it will surpass 500 meters.
The oil spill, doubling in size each day from an initial 20 square meters, will exceed 500 square meters on the 6th of May.
Explanation:Based on the information provided, let's calculate how long it will take for the oil spill to exceed 500 square meters if it doubles in size each day starting from an initial size of 20 square meters. On May 1, the spill is 20 square meters. On May 2, it would be 40 square meters (20*2). If we continue this pattern, we can find the day the spillage area will exceed 500 square meters:
May 3: 80 square metersMay 4: 160 square metersMay 5: 320 square metersMay 6: 640 square meters
Therefore, the area of the oil spill exceeds 500 square meters on May 6.
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Please please help me
Answer:
y = 13
Step-by-step explanation:
If it's a parallelogram then its consecutive angles are supplementary (add up to 180°).
6x - 12 + 132 - x = 180°,
5x + 120 = 180
5x = 60
x = 12
6x - 12 = 6(12) - 12 = 72 - 12 = 60
Parallelogram, opposite angles are equal
so
6y + 18 = 6x - 12
6y - 18 = 60
6y = 78
y = 13
What is (f ⋅ g)(x)?
f(x) = x^4 − 9
g(x) = x^3 + 9
(f ⋅ g)(x) =
Answer:
x⁷ + 9x⁴ - 9x³ - 81
Step-by-step explanation:
(f⋅g)(x) is just another way of writing f(x) ⋅ g(x).
f(x) ⋅ g(x)
(x⁴ - 9) (x³ + 9)
If you wish to simplify:
x⁷ + 9x⁴ - 9x³ - 81
A company launches 4 new products.
The market price, in dollars, of the four products after a different number of years, x, is shown in the following table:
Product 1 | f(x)=3^x |$3 | $9| $27
Product 2 | g(x)= x^2+4| $5 | $8 | $13
Product 3 |h(x)=3x+8| $11| $14| $17
Product 4 | j(x) = x^3| $1 | $8 | $27
Based on the data table, for which product does the price eventually exceed the others?
A. product 1
B. Product 2
C. Product 3
D. Product 4
Answer:
A. product 1
Step-by-step explanation:
An exponential function (with a base larger than 1) will eventually exceed the value of any polynomial function. Product 1 has a price described by an exponential function, so its price will exceed all others. (One only need to compute the values for x=4 to see this.)
_____
The attachment extends the table and plots the functions up to the point where Product 1 exceeds the others.
Marlye posted a story on her blog. On the first day there were 80 responses and on the second day there were 180 responses. What percent is the increase, 100, of the original number of responses, 80?
55%
80%
100%
125%
Answer:
80 * 80% = 64 So it's not A
80 * 55% = 44 so it's not B
80 * 100% = 80 so it's not C
80 * 125% = 100 so D is your answer
Step-by-step explanation:
Answer:
125%
Step-by-step explanation:
Given,
Responses on first day or original responses = 80
While responses on second day or final responses = 180,
Thus, the percentage increase in the responses
[tex]=\frac{\text{ final responses- original responses}}{\text{original responses}}\times 100[/tex]
[tex]=\frac{180-80}{80}\times 100[/tex]
[tex]=\frac{10000}{80}[/tex]
[tex]=125\%[/tex]
Hence, fourth option is correct.
Renee is playing a game with marbles and a spinner. The spinner has four sections: orange, black, purple, and white. The marbles are kept in a bag and come in three colors: orange, black, and purple. Renee first spins the spinner and then picks a marble from the bag without looking. What is the probability that the color of the marble matches the color on which the spinner lands? brainly
Answer:
[tex]\frac{1}{16}[/tex] Is the chance of the colours matching.
Step-by-step explanation:
The possibility of the spinner landing on an orange side is [tex]\frac{1}{4}[/tex]
and the possibility of the marble being orange is [tex]\frac{1}{4}[/tex] in this case you have to remember, in the fraction, you have 4 possibilities and 1 desirable outcome, when you have two dependant possibilities you have to multiply them:
[tex]\frac{1}{4} * \frac{1}{4}[/tex]
And the result of that multipliction is [tex]\frac{1}{16}[/tex] which is the probability of the marble and the spiner colours matching.
Answer:
Step-by-step explanation:
1/4
Triangles are formed in a cube by connecting three vertices.
Which triangles are right triangles? Check all that apply.
1. triangle AEG
2. triangle AEH
3. triangle DAE
4. triangle BFH
5. triangle GDH
6. triangle CFG
7. triangle DFH
8. triangle BCF
Answer:
B: triangle AEH
C:triangle DAE
E: triangle GDH
F: triangle CFG
H: triangle BCF
Step-by-step explanation:
just took the unit test hope it helps ;)
Right angle triangles are triangle AEG , triangle AEH , triangle DAE , triangle BFH , triangle CFG , triangle BCF .
Right angle triangle :
A Right triangle states that if one of the angles of a triangle is a right angle - 90º .
So , In the figure given below we get :
→ In triangle AEG : the angle between AE and AG is 90 ^ º .
→ In triangle AEH : the angle between AE and EH is 90 ^ º .
→ In triangle DAE : the angle between DA and AE is 90 ^ º .
→ In triangle BFH : the angle between BF and FH is 90 ^ º .
→ In triangle GDH : the angle at G , D and H is 60 ^ º .
→ triangle CFG : the angle between CG and GF is 90 ^ º .
→ triangle DFH : the angle between sides is not 90^ º .
→ triangle BCF : the angle between BC and BF is 90 ^ º .
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Hannah made 0.7 of her free throws in a basketball game. Abra made 9/10 of her free throws. Dena made 3/4 of her free throw. Who was the best shooter?
Abra is the best shooter because 9/10 is almost a 1 where 3/4 is .75.
The triangles are similar. What is the value of x? Enter your answer in the box. X=
[tex] \frac{4x + 12}{32} = \frac{15}{8} \\ ( = )32x + 96 = 480 \\ ( = )x = 12[/tex]
Answer:
x = 12
Step-by-step explanation:
Since the triangles are similar then the ratio of corresponding sides are equal, that is
[tex]\frac{4x+12}{15}[/tex] = [tex]\frac{32}{8}[/tex] = 4, thus
4x + 12 = 4 × 15 = 60 ( subtract 12 from both sides )
4x = 48 ( divide both sides by 4 )
x = 12
The base of a hexagonal prism has an apothem measuring 10 inches and an area of 346.41 square inches. The prism is 12 inches tall. What is the approximate lateral area of the prism? Round to the nearest whole number.
Answer:
The approximate lateral area of the prism is [tex]831\ in^{2[/tex]
Step-by-step explanation:
we know that
The lateral area of the prism is equal to
[tex]LA=PH[/tex]
where
P is the perimeter of the base of the prism
H is the height of the prism
Find the perimeter of the hexagonal base
Remember that the area of the hexagonal base is equal to
[tex]A=\frac{1}{2} P(a)[/tex]
where
P is the perimeter
a is the apothem
we have
[tex]A=346.41\ in^{2}[/tex]
[tex]a=10\ in[/tex]
substitute and solve for P
[tex]346.41=\frac{1}{2} P(10)[/tex]
[tex]P=346.41/5=69.282\ in[/tex]
Find the lateral area
[tex]LA=PH[/tex]
we have
[tex]P=69.282\ in[/tex]
[tex]H=12\ in[/tex]
substitute the values
[tex]LA=(69.282)(12)=831\ in^{2[/tex]
Answer:
831 In^3
Step-by-step explanation:
Edge 2020
Gabriel is making a mixture of compost and soil to use for a special plant. He wants his final mix to be 2 parts compost to 6 parts potting soil. He wants to end up with 10 kilograms of mix.
how many kilograms of compost should Gabriel use?
Answer:
5/2 kg
Step-by-step explanation:
The ratio here is 2:6. 2 plus 6 is 8.
Then (2/8) times 10 kg represents the amount of compost needed; that comes to 20/8 kg, or 10/4 kg, or 5/2 kg.
Gabriel should use 2.5 kilograms of compost to create a 10-kilogram mix that has a ratio of 2 parts compost to 6 parts potting soil.
Gabriel is making a mixture for a special plant which requires a ratio of 2 parts compost to 6 parts potting soil. He aims to make 10 kilograms of this mix in total. To calculate the amount of compost he should use, we first have to find the total number of parts in the mix:
Add the parts of compost to the parts of potting soil: 2 parts (compost) + 6 parts (soil) = 8 parts (total).
Determine the weight of each part: 10 kilograms (total mix) / 8 parts = 1.25 kilograms per part.
Multiply the weight of each part by the number of parts for compost: 1.25 kilograms per part × 2 parts (compost) = 2.5 kilograms of compost.
Therefore, Gabriel should use 2.5 kilograms of compost for his special plant mix.
One hundred football players were asked how many broken bones they have suffered. The probability distribution shows the probability of the number of bones broken by a football player.
What is the probability that a football player has suffered more than 3 broken bones?
Enter your answer, as a decimal, in the box.
Answer:
0.25
Step-by-step explanation:
The probability that a football player has suffered more than 3 broken bones is equal to the probability they suffered 4 or 5.
P(x>3) = P(4 or 5)
P(x>3) = P(4) + P(5)
P(x>3) = 0.10 + 0.15
P(x>3) = 0.25
What is the mean of the following set of numbers?
121, 347, 45, 21, 300, 614, 312, 333, 421
A. 312
B. no mean
D. 251.4
C. 279.3
Answer:
C. 279.3
Step-by-step explanation:
To find the mean of a set of numbers you have to add all of them together and divide them by how manys numbers there are
If we add all the numbers together it equals 2514
There are 9 numbers here
2514/9=279,333333
Therefore, the answer is C
The mean is the same as the average!
To find mean ...
add up all the numbers121+
347+
45+
21+
300+
614+
312+
333+
421
__________________
2,514
Then we divide by how many numbers there are total[tex]\frac{2,514}{9} = 279.33[/tex]
Final answer is D. (279.3)
If f(x) = 2x – 1 and g(x) = – 2, find [g ◦ f](x).
Answer:
[tex][g\circ f](x)=-2[/tex]
Step-by-step explanation:
By the definition
[tex][g\circ f](x)=g(f(x))[/tex]
You are given
[tex]f(x)=2x-1\\ \\g(x)=-2[/tex]
So,
[tex][g\circ f](x)=g(f(x))=g(2x-1)=-2[/tex]
In which direction does the graph of the function shown below open?
[tex]f(x) = 2x^2+5x-4[/tex]
A. Down
B. Left
C. Right
D. Up
Answer:
D. Up
Step-by-step explanation:
When a parabola has the form [tex]y=ax^2+bx+c[/tex] , It is vertical (opens up or down).
Because the variable "x" is squared.
If "a" is positive, then the parabola opens up, but if it is negative, then the parabola opens down.
In this case you have the quadratic function:
[tex]f(x) = 2x^2+5x-4[/tex]
Which can be rewritten as:
[tex]y = 2x^2+5x-4[/tex]
Therefore, it is vertical, because it has the form: [tex]y=ax^2+bx+c[/tex]
You can observe that the value of "a" is:
[tex]a=2[/tex]
Then, since "a" is positive, the parabola opens up.
Please help me out please
Answer:
w = 54°
Step-by-step explanation:
w is the inscribed angle subtended on the same arc with measure of 108°
w is half the size of the central angle, that is
w = 0.5 × 108° = 54°
I found an odd thing idk what I’m doing wrong, I think i calculated it right but?
Because 3.14 * 30^2 * 110 = 310860 just as 3.14 * 900 * 110 since its pi and 900 is just 30x30, but when I input the actual TT pi symbol or do pi * 900 * 110 a result of 311017
am I an idiot?
Answer:
Step-by-step explanation:
No, you're not an idiot. You are just misunderstanding pi. Pi is an irrational number, meaning it goes on forever. Literally, forever, with no end. Some weird guy actually memorized the first 100,000 places of it or something crazy like that. Anyway, if you use 3.14 you have rounded so incredibly, that you lose a lot of your precision. Your calculator uses the first 9 places of the decimal or something like that.
Noa was paid a 25 percent commission for selling a used car If she was paid $1,631.24, what was the selling price of the car?
Answer:
$6,524.96
Step-by-step explanation:
Take the commission total which is $1631.24 divide it by 25% or .25.
$1,631.24 ÷ .25=$6,524.96 cost of the used car
Check your answer by taking your answer and multiple it by 25%.
$6,524.96 (cost of the car) × .25 =$1,631.24 commission
Answer:
$6,524.96
Step-by-step explanation:
Step One: Because the amount she is paid is the 25% commission, multiply the 1,631.24 by 4 ( 4 because she is paid 1 out of 4 parts of the total selling price)
Step Two: the answer is 6,524.96
There is a beach ball with radius 24cm and a ping pong ball with radius 4cm. Find how many times greater the volume of the beach ball is as that of the ping pong ball.
It is 36 times greater.
It is 128 times greater.
It is 6 times greater.
It is 216 times greater.
Answer:
216
Step-by-step explanation:
Which type of climate is the most common in Australia's Outback?
A) Dry desert climate
B) Tropical climate
C) Humid and rainy climate
D) Mild climate with seasonal monsoons
OOPS i put it as mathematics IM SO SORRY!
Please answer QUICK if can!
i think its letter A. The outback seems very dry and desert like
Answer:
Dry desert
Step-by-step explanation:
did the quiz
Who originated the metric system and when
Gabriel Mouton
Early development. Most historians agree that Gabriel Mouton, the vicar of St. Paul's Church in Lyons, France, is the “founding father” of the metric system. He proposed a decimal system of measurement in 1670.
is anyone willing to answer this question?
ANSWER
[tex]4(x + 6)(x - 2)[/tex]
EXPLANATION
The given rational expression is:
[tex] \frac{1}{ {x}^{2} + 4x - 12} + \frac{3x}{4x - 8} [/tex]
We can factor the denominators to obtain:
[tex] \frac{1}{(x + 6)(x - 2) } + \frac{1}{4(x - 2)} [/tex]
The common denominator is least common multiples of the denominators.
The common denominator is of the given rational expression is
[tex]4(x + 6)(x - 2)[/tex]
Valentina has a 30% chance of randomly drawing a blue marble from a bag. If she does the random drawing 50 times, how many times can she expect to get a blue marble
A-30
B-5
C-35
D-15
Answer:
d
Step-by-step explanation:
30% of 50 is 15 because 30 % means 30out of 100
and if you half 100 you also half 30
Valentina, with a 30% probability, can expect to draw a blue marble 15 times out of 50 draws. This is calculated by multiplying the total number of draws by the probability of drawing a blue marble.
Explanation:The question revolves around the concept of probability. The probability of an event is the measure of the likelihood that the event will occur. In Valentina's case, she has a 30% chance of drawing a blue marble. Therefore, if she were to draw a marble 50 times, we would expect her to draw a blue marble 30% of those 50 times. Probability is often expressed as a fraction or decimal, and in this case, 30% translates to 0.30 in decimal form.
To calculate how many times we can expect Valentina to draw a blue marble, we multiply the total number of draws (50) by the probability of drawing a blue marble (0.30).
So, 0.30 * 50 = 15.
Therefore, Valentina can expect to draw a blue marble 15 times out of 50 draws.
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Help with slope intercept!
It the second equation. I used subsitution to find that out.
The second one y = 1/2x + 3/4 is the correct answer. I first graphed the two points then started graphing the equations to find which line went through those two points.
There are 18,076 books in our public library. How should this number be written in expanded form? A) 10,000 + 8,000 + 70 + 6 B) 10,000 + 8000 + 700 + 6 C) 18,000 + 700 + 60+ 0 D) 18,000 + 70 + 60 + 0
Answer:
A) 10,000 + 8,000 + 70 + 6
Step-by-step explanation:
Write one digit at a time, with the others shown as zero. The sum of those numbers is the expanded form.
___
There are other ways to write a number in expanded form. One I like uses exponents to show the place value.
1×10⁴ +8×10³ +0×10² +7×10¹ +6×10⁰
Understanding this form can help you write the number in scientific notation.