Functions are written in terms of variables. The value of the function when x is -8 is 124
Functions and valuesFunctions are written in terms of variables. Given the function below;
g(x) = 2x^2 - 4
If the value of x is -8, substiute
g(-8) = 2(-8)^2 -4
g(-8) = 2(64) - 4
g(-8) = 124
Hence the value of the function when x is -8 is 124
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3/4(2x-3) = 2/3 x+5 with detailed explanation
Answer:
x = 11
Step-by-step explanation:
3/(3(2x-3)) = 2/(3x+5)
3(2x-3) = 6x - 9
3/(6x-9) = 2/(3x+5)
3(3x+5) = 2(6x-9)
9x + 15 = 12x - 18
12x - 9x = 15 + 18
3x = 33
x = 11
Answer:
[tex]\mathrm x= \dfrac{87}{10} \quad or \quad 8.7[/tex]
Explanation:
[tex]\longrightarrow \sf \dfrac{3}{4} (2x-3)=\:\dfrac{2}{3}\:x+5[/tex]
Distribute inside parenthesis[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{9}{4} =\:\dfrac{2}{3}\:x+5[/tex]
Group the variables[tex]\longrightarrow \sf \dfrac{3}{2} x-\dfrac{2}{3}x=5+\dfrac{9}{4}[/tex]
Add or Subtract[tex]\longrightarrow \sf \dfrac{5}{6} x=\dfrac{29}{4}[/tex]
Cross Multiply[tex]\longrightarrow \sf x=\dfrac{29(6)}{4(5)}[/tex]
Simplify the following[tex]\longrightarrow \sf x=\dfrac{87}{10} \quad or \quad 8.7[/tex]
What is 5 over 8 expressed as a percent?
Answer: 62.5%
Step-by-step explanation:
5/8 = 0.625
0.625 x 100 = 62.5
Which of the following points is not coplanar with points C, D and E?
The point R is the point which is not coplanar with points C, D and E.
We need to find the point which is not coplanar with points C, D and E.
What are coplanar points?The points that lie on the same plane are called coplanar points.
In the given figure there are five planes which are as follows:
BCUD, BRAE, BRAC, BTDE, ACUDE
Now, points C,D and E lie in plane ACUDE.
In the plane ACUDE points A, C, U, D, E and S lies.
From the options point, R is not lining in the same plane as C, D and E lies.
Therefore, the point R is the point which is not coplanar with points C, D and E.
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The graph of function g (x) predicts the profit of jimmy's famous Jer*y for a week. The x-axis represents the number of employees earning overtime for the week. The y-axis is the business's profit for the week in hundreds of dollars.
By identifying the maximums, we see that in each blank we need to write:
1) 2
2) 2
3) greater.
How to complete the given statement?
First, we need to find the maximum of the function g(x).
You can see that for x = 2 we have the maximum of the parabola, which gives y = 9.
Then the maximum profit is got when 2 employees earn overtime.
We also need to find the maximum for the table. Notice that the maximum value of the table also happens for x = 2, and this time the maximum is y = 16.
So we can see that the maximum of Cathy's cupcakes is larger than the maximum of Jimmy's.
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Match the vocabulary words with their definitions. 1. an arrangement of data in logical order predict 2. to tell something in advance chart 3. a list of facts from which a conclusion can be drawn random sample 4. an opinion of the amount, value, or worth of something average 5. dividing the total number by the number being counted estimation 6. every member of a large group has an equal chance of being chosen data
Answer:
sorting, predict, data, access, divisor, sampling
Step-by-step explanation:
Find the distance between the points (5,0) and (-5,3)
Answer:
10.4
Step-by-step explanation:
√(5--5)²+(0-3)²
√100+9
√109=10.4
Type the expression that results from the following series of steps:
Start with
y
, subtract 7, multiply by 3, then add 6.
Answer:
3y-15
Step-by-step explanation:
(y-7)3=3y-21
3y-21+6=3y-15
What is (f−g)(x) ?
f(x)=x3−3x2+2x−3
g(x)=4x2−5x+7
Enter your answer in the box.
(f−g)(x)=
Answer:
Step-by-step explanation:
(F-G)(X)=x^4-x^3+2x-6
The total area of town C and town D is 120,000 square miles. The area of town C is 30,000 square miles more than that of town D. Find the area land of each town.
Answer:
Find the area land of each town.
Let x be the area of town D
then, x+ 30000 is the area of town C
we know that,
the total area of town C and town D is 120,000 square miles.
x+x+30000=120000
2x= 90000
x=45000
Area of town D= 45000 square miles
Area of town C= 45000+30000= 75000 square miles.
What is the solution to the trigonometric inequality sin^2(x) > cos(x) over the interval 0<= x <= 2pi radians?
The solutions to the trigonometric inequality in the interval is given by:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex], or [tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
What is the trigonometric inequality?It is given by:
[tex]\sin^{2}{x} > \cos{x}[/tex]
We have the following identity:
[tex]\sin^2{x} = 2\sin{x}\cos{x}[/tex]
Hence:
[tex]2\sin{x}\cos{x} > \cos{x}[/tex]
[tex]2\sin{x} > 1[/tex]
[tex]\sin{x} > \frac{1}{2}[/tex]
Between the first and second quadrant, the solution is:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex]
Between the third and fourth quadrants, the solution is:
[tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
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Given: ABCD is a parallelogram.
Prove: ∠A ≅ ∠C and ∠B ≅ ∠D
Parallelogram A B C D is shown.
By the definition of a ▱, AD∥BC and AB∥DC.
Using, AD as a transversal, ∠A and ∠
are same-side interior angles, so they are
. Using side
as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary.
Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠
.
A parallelogram is a quadrilateral with four sides and the opposite sides of the parallelogram are equal and parallel.
How to show the proof?In the given figure, AB||DC. AD is the transversal, such that:
∠A + ∠D = 180-degrees.
The parallelogram is a quadrilateral with equal such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees.
From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.
From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.
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Determine the value of y.
135°
27°
24°
45°
Which of the following fraction pairs is equivalent?
12/20 and 20/25 18/27 and 10/15 6/24 and 5/15 3/25 and 5/25
Answer:
b
Step-by-step explanation:
answer is b
Factor by grouping
5y^3(y-2)-15y(y-2)
5y³(y-2)-15y(y-2)
= (y-2)×(5y³-15y)
Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below:
A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 1 meter.
What is the maximum length of the seesaw?
Using the slope concept, it is found that the maximum length of the seesaw is of 1.73 meters.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The vertical change is of 1 m.The horizontal change is the length l.The angle is of 30º.Hence:
tan(30º) = 1/l
l = 1/tan(30º)
l = 1.73.
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Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write the expression for the number of sweets Sue and Tony now have
Answer:
Sue : 13 - x Tony : x/2 + 9Step-by-step explanation:
Sue Tony_________________________________________________
initial number of sweets | 18 | 18
| |
Sue gives Tony x sweets | 18 - x | 18 + x
| |
Sue ,eats 5 of her sweets. and | 18 - x - 5 = | (18 + x)/2 =
Tony ,eats half of his sweets | 13 - x | 9 + x/2
If one student is chosen at random, Find the probability that the student was NOT a female that got a "C"
--------- A // B // C // Total
Male: 10 // 8 // 15 // 33
Female: 7 // 9 // 17 // 33
Total: 17 // 17 // 32 //66
The probability that the student was NOT a female that got a "C" is 15 / 32.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C = 15 / 32.
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The White Russian cocktail contains vodka, Tia Maria and milk in the ratio of 5:2:3. To make the cocktail for a party the barman used 180ml of milk. What was the total volume of the cocktail? If this was served in 60ml glasses, how many glasses would it serve?
Answer:
1) 600cm^3 2) 10 glasses
Step-by-step explanation:
x = total amount in ml
(3/10)x = 180ml (MILK)
x = 600ml
(2/10)600 = 120ml (TIA MARIA)
(1/2)600 = 300ml (VODKA)
1) 600cm^3
2) 600ml : 60ml = 10 (GLASSES)
7 of 10
Work out
(1.5 × 10¹⁰) ÷ (3 × 10-4)
Give your answer in standard form.
Answer:
5 × 10¹³
Step-by-step explanation:
(1.5 × 10¹⁰) ÷ (3 × 10⁻⁴) = 50,000,000,000,000
Which sentence correctly compares the two numbers 5.395 and 5385 ?
5.395= 5385
5.385 > 5.395
5395< 5.385
5385 < 5.395
The sentence that correctly compares the two numbers is 5385 > 5.395
What is the correct sentence?Here are inequality signs and what they mean:
Note that
5385 is greater than 5.385. Thus, the correct statement is 5385 > 5.395.
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To determine how American college students feel about commuting, 100 students at a private
the university was chosen by selecting 50 men and 50 women to participate. They were asked
how far they commute each day (in minutes) to campus.
a. Is this an observational study or experiment?
b. What is the sample?
c. What is the target population?
d. What is the sampling method? (Simple random, stratified, convenient, …)
e. Is the data collected qualitative or quantitative?
f. Why is it unlikely that the results of this study will be valid?
The nature of the research is called Observational Study while the target Population is American Students.
How to find the sampling method?
1) In study, we survey members of a sample without trying to affect them while in experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive treatment. Thus, this is an observational study.
2) The sample is the 100 students made up of 50 boys and 50 girls.
3) The target Population are American College Students
4) The sampling method is; Simple random Sampling
5) The data is qualitative because it deals with description of feelings rather than dealing with numbers and figures.
6) It is unlikely that the results would be invalid because of sampling bias as it was only done in a private university.
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A music club has $187 to buy ice cream for a party. Each carton of ice cream costs $4. If the club buys as many cartons as possible, how much money will the club have left?
Answer:
They would have $3 dollars left over.
Step-by-step explanation:
If you divide 187 by 4, you get 46.75. But if you look again, you can see that the remainder is 3 and it can confirm that it is the left over money that the club has now after buying as many ice cream cartons as possible.
Are these numbers rational or irrational? -7 √10 (square root of 10) √16 (square root of 16) 52% 1.235 > > > > 1. Rational 2. Irrational please answer quickly
Answer:
hope you can understand
11 12 13
18
A local charity holds a carnival to raise money. In one
activity, participants make a $3 donation for a chance
to spin a wheel that has 10 spaces with the values, 0,
1, 2, 5, and 10. Whatever space it lands on, the
participant wins that value. Let X represent the value of
a random spin. The distribution is given in the table.
Value of a Spin
0
1
2
5
10
Probability
0.4 0.2
0.2
0.1
0.1
20
Which of the following is the correct interpretation of
P(X<5)?
The correct interpretation of the probability P(X < 5) is; 0.8
How to Solve Probability?We are given the probability of the spin values are;
Probability of Spin Value of 0 = 0.4
Probability of Spin Value of 1 = 0.2
Probability of Spin Value of 2 = 0.2
Probability of Spin Value of 5 = 0.1
Probability of Spin Value of 10 = 0.1
P(X < 5) simply means the probability of getting a spin value less than 5. Thus;
P(X < 5) = P(0) + P(1) + P(2)
P(X < 5) = 0.4 + 0.2 + 0.2
P(X < 5) = 0.8
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Which property justifies the following if angle A is congruent to angle B and angle b is congruent to angle C then angle a is congruent to angle c
Answer: Transitive property of congruence
Determine if the following angles are congruent. What theorem proves them to be congruent. Explain your reasoning.
Answer: AAS
Step-by-step explanation:
We know that [tex]\angle TSN \cong \angle HSU[/tex] because they are vertical angles, meaning the triangles are congruent by AAS.
Evan picks up a cantaloupe that weighs 3.24 pounds. Suppose Evan
could buy 100 cantaloupes that are all this weight. Without using the
multiplication algorithm, explain how Evan could figure out the total
weight of all 100 cantaloupes.
The total weight of the 100 cantaloupe is 324 pounds
How to determine the total weight?The given parameters are:
Weight of each = 3.24 poundsNumber of cantaloupe = 100Since the number of zeros in 100 is 2;
All Evans needs to do is to move the decimal point in 3.24 two places forward.
i.e. 3.24 becomes 324 when the decimal point is moved
Hence, the total weight of the 100 cantaloupe is 324 pounds
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I need help please ASAP?!!!
Answer:
Its 43.2
I hope this helps ^^
Answer:
43.2
Step-by-step explanation:
kilometers, hectometers, decameters, meters, decimeters, centimeters, millimeters
To go right once multiply be ten
To go left once divide by ten
4.32 • 10 = 43.2
PLEASE HELP! i need done ASAP.
Answer:
m<A = 120
m<BCD = 120
m<DEC = 30
m<BFE = 90
Step-by-step explanation:
m<A is 120 cause all internal angles equal 720 added together in hexagons. 720 ÷ 6 = 120
m<BCD is 120 cause regular hexagons have eqaul angles
m<DEC is 0 cause total of the angle of triangle of triangle EDC is 180 where m<D = 120 which leaves m<E + m<C = 60 since they are equal we can combine them to m<E • 2 = 60. Divide and we get 30
m<BFE = 90 cause m<AFB = 30 and m<AFE = 120 subtract 120 and 30 to get 90
You roll a number cube. What is the probability it will land on a number greater than 5?