Which expressions are equivalent to the one below? Check all that apply.
3^x
Answers
First one isn't answer because 3^x is exponetial while x^3 is cubic function. If you draw them you will see that they are very different.
B is correct because we can divide both numerator and denominator by 6 and we get 3^x
C is not correct because x is not powering 3 so we cannot devide both by 6
D is correct because 3^(x-1) is same as 3^x*3^(-1) = 3^x/3 and when multiplied by 3 we get 3^x
E is not correct. will understand after explanation in D
F is correct. x is powering both numbers so it can be outside parethasis.
Answer:
All of the answers in the picture provided are correct
Step-by-step explanation:
Related Questions
Select all ratios equivalent to 21:14.
14:10, 8:4, 9:6, 12:21
Answers
then multiply both sides by a few different numbers on both sides each ,
for example, 3:2 is the same as
6:4 (3:2 times 2)
9:6 (3:2 times 3)
12:8 (3:2 times 4)
15:10 (3:2 times 5) and so on
the ratio of the right number I
divided by the left on all of them is 1.5
so,
14/10 equals 1.4 (nope)
8/4 equals 2 (nope)
9/6 equals 1.5 (yay)
12/21 equals 0.57 (Lol)
So your answer is 9:6
Choose the correct simplification of (7x3 − 8x − 5) + (3x3 + 7x + 1).
10x3 − x − 4
10x3 + x + 4
4x3 − 15x − 6
4x3 + 15x + 6 ...?
Answers
the correct simplification of (7x^3 − 8x − 5) + (3x^3 + 7x + 1),
Is 10x^3 − x − 4
A card is drawn from a deck of 52. Find the probability of drawing a king or a heart. Enter your answer in simplified fraction form; example: 3/20. ...?
Answers
A heart or a king: P(H or K) = P(H)+P(K)-P(H and K)
There are 13 hearts out of 52 cards, so P(H) = 13/52 = 1/4
There are 4 kings out of 52 cards, so P(K) = 4/52 = 1/13
There is 1 card which is a heart and a king (the king of hearts), so P(H and K) = 1/52, so P(H or K) = P(H)+P(K)-P(H and K) = 1/4+1/13-1/52 = 13/52+4/52-1/52 = 16/52 = 4/13
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Group A consists of X students and their total age is 221 and their average age is an integer.When group A is merged with Group B with twice the number of students (the number of students between 30 and 40) average age of B is reduced by 1.What is the original average age of B?
...?
Answers
Group A
m = 221 / c
221 = c x m
221 = 17 x 13 (as it is a whole number under 20)
Group B
m = s / 34
(221 + x) / 51 = x /34 - 1
544/ 34 = 16
16
Answer:
16 years
Step-by-step explanation:
Given,
Number of students in group A = X,
Sum of their ages = 221,
So, the average age of students in group A = [tex]\frac{\text{Sum of ages}}{\text{Total students}}[/tex]
[tex]=\frac{221}{X}[/tex]
According to the question,
[tex]\frac{221}{X}=\text{Integer}[/tex]
∴ X must be a factor of 221,
∵ 221 = 13 × 17,
Now, If X = 13,
Then the number of students in group B = 26 ( NOT POSSIBLE )
If X = 17,
Then the number of students in group B = 34
Which is between 30 and 40,
Now, Let S be the sum of ages of students in group B,
So, the average age in group B = [tex]\frac{S}{34}[/tex]
Again according to the question,
[tex]\frac{S+221}{17+34}=\frac{S}{34}-1[/tex]
[tex]\frac{S+221}{51}=\frac{S-34}{34}[/tex]
[tex]34S+7514 = 51S - 1734[/tex]
[tex]34S - 51S = -1734 - 7514[/tex]
[tex]17S = 9248[/tex]
[tex]\implies S = 544[/tex]
Therefore, the average age of B = [tex]\frac{544}{34}[/tex] = 16 years.
A scale on a blueprint is 1 inch = 5 feet. What is the length of an object that is 8 1/2 inches long on the blueprint
Answers
To find the actual length of the object, multiply the length on the blueprint by the scale factor of 5 feet/inch. The length of the object in actual size is 42 feet 6 inches.
Explanation:To find the actual length of the object represented on the blueprint, we can use the scale factor provided. The scale on the blueprint is 1 inch = 5 feet. So, if the object is 8 1/2 inches long on the blueprint, we can multiply it by the scale factor to find the actual length.
Step 1:
Convert 8 1/2 inches into a mixed number fraction by adding 1 to the whole number.
8 1/2 inches = 8 + 1/2 = 17/2 inches
Step 2:
Multiply the length on the blueprint by the scale factor:
17/2 inches * 5 feet/inch = 85/2 feet
Step 3:
Simplify the fraction if possible:
85/2 feet = 42 feet 6 inches
Therefore, the length of the object in actual size is 42 feet 6 inches.
To find the actual length of an object that is 8 1/2 inches long on a blueprint with a scale of 1 inch = 5 feet, you multiply 8.5 by 5, resulting in an actual length of 42.5 feet.
Explanation:If the scale on a blueprint is 1 inch = 5 feet, then to determine the actual length of an object that is 8 1/2 inches long on the blueprint, we simply multiply the length on the blueprint by the scale factor.
So, for every inch on the blueprint, there are 5 feet in reality. Therefore, we calculate the actual length as follows:
Multiply 8 1/2 inches by the scale factor, which is 5 feet per inch.8.5 inches * 5 feet/inch = 42.5 feet.Thus, the actual length of the object is 42.5 feet.
A machine make 24 items in 8 minutes how many can it make in 14
Answers
Convert 41,650,000 to scientific notation.
Answers
4.165 x 10⁷
Find cos theta if sin theta = 2/3. assume the terminal side of the angel falls in quadrant 2
Answers
So ø reference = 180 - ø in standard position.
Regardless, the reference angle is in quadrant 2, we need to then label the sides of the reference triangle based on the opposite and hypotenuse.
Solve for adjacent side using Pythagoras theorem.
A^2 = C^2 - B^2
A^2 = 3^2 - 2^2
A^2 = 9 - 4
A^2 =5
A = sq root of 5.
Then write the cos ratio using the new side.
Cos ø =✔️5/3. Place a negative in front of cos ø as cos is negative in second quadrant.
Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Which equation represents the average of the x-intercepts for f(x) = 4x2 – 24x + 20?
Answers
let x1 represent first x intercept and
let x2 represent second x intercept
Formula for finding average of x intercepts is logicaly:
Avg = (x1 + x2)/2
we want to find x1 and x2
4x^2 - 24x + 20 = 0
x^2 - 6x + 5 = 0
[tex]x = \frac{6 +- \sqrt{6^2 - 4*1*5} }{2*1} [/tex]
x1 = 5
x2 = 1
Avg = 3
Answer:
c
Step-by-step explanation:
What is the equation of the following graph in vertex form?
parabolic function going down from the left and turning at the point negative one comma zero and going up through the point zero comma one and continuing towards infinity
Courtesy of Texas Instruments
y = (x − 1)2
y = (x − 1)2 + 1
y = (x + 1)2 − 1
y = (x + 1)2
Answers
Graph passes through the point (-1, 0).
Therefore, x = -1 and y = 0.
[tex]y=(x+1)^2 \\0=(-1+1)^2 \\0=0^2 \\0=0 \;\; \text{T}[/tex]
This is the only equation which is true for x = -1 and y = 0.
Therefore, the solution is [tex]y=(x+1)^2[/tex]
Answer:
y = (x + 1)^2
Step-by-step explanation:
I used desmos and put each answer choice into the graphing calculator and answer choice D was the only one that matched with the image in the question.
over the course of a lifetime about how much more does a college graduate earn than someone who does not have a college degree
a. $450,000
b. $600,000
c. $750,000
d. $900,000
Answers
4n³·2n²=?
Simplify your answer.
Answers
Write a quadritic equation in standard form that has the roots of 5 and -2
Answers
Notice that if x=a or x=b the equation is true. To simplify, we'll choose A=1. In that problem, a=5 and b=-2. Hence:
[tex]1(x-5)(x-(-2))=0\iff (x-5)(x+2)=0\iff\\\\x^2-3x-10=0[/tex]
Final answer:
To find the quadratic equation with roots 5 and -2, we can use the quadratic formula. Substituting the values of the roots into the formula, we get the equation (x - 5)(x + 2) = 0.
Explanation:
A quadratic equation in standard form is written as ax² + bx + c = 0, where a, b, and c are constants. To find the equation with roots 5 and -2, we can use the fact that the solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Substituting the values of the roots into the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / (2a)
For the first root, x = 5:
5 = (-b ± √(b² - 4ac)) / (2a)
Substituting a = 1, b = -7, and c = 10, we get:
5 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))
Simplifying further:
5 = (7 ± √(49 - 40)) / 2
5 = (7 ± √9) / 2
5 = (7 ± 3) / 2
So, the first root gives us the equation:
x = 5, which translates to x - 5 = 0.
For the second root, x = -2:
-2 = (-b ± √(b² - 4ac)) / (2a)
Substituting a = 1, b = -7, and c = 10, we get:
-2 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))
Simplifying further:
-2 = (7 ± √(49 - 40)) / 2
-2 = (7 ± √9) / 2
-2 = (7 ± 3) / 2
So, the second root gives us the equation:
x = -2, which translates to x + 2 = 0.
Therefore, the quadratic equation in standard form with roots 5 and -2 is:
(x - 5)(x + 2) = 0
Please help me understand how to do this!
In ΔRST shown below, segment SU is an altitude:
What property or definition is needed to prove that ΔRUS is similar to ΔSUT?
Answers
Answer:
The correct option is 1.
Step-by-step explanation:
It is given that in ΔRST , segment SU is an altitude. It means the angle SUR and angle SUT are right angles.
It triangle RST and SUT,
[tex]\angle RST=\angle SUT=90^{\circ}[/tex] (Definition of altitude)
[tex]\angle STR=\angle UTS[/tex] (Common angle)
Two corresponding angles are equal. So by AA property of similarity,
[tex]\triangle RST\sim \triangle SUT[/tex] .... (1)
It triangle RST and RUS,
[tex]\angle RST=\angle SUR=90^{\circ}[/tex] (Definition of altitude)
[tex]\angle SRT=\angle URS[/tex] (Common angle)
Two corresponding angles are equal. So by AA property of similarity,
[tex]\triangle RST\sim \triangle RUS[/tex] .... (2)
According to transitive property of equality,
if a=b and b=c, then a=c.
From (1) and (2), we get
[tex]\triangle RUS\sim \triangle SUT[/tex] ( Transitive property of equality)
Therefore the correct option is 1.
whats 358 divided by 3 useing compatible numbers
Answers
Marcus finds that (3x^2-2y^2+5x)+(4x^2+12y-7x)= 7x^2-10y^2-2x What error did Marcus make?
A: He combined the terms 5x and –7x incorrectly.
B: He combined the terms 3x^2 and 4x^2 incorrectly.
C: He combined the terms –2y^2 and 12y^2 incorrectly.
D: He subtracted the polynomials instead of adding.
Answers
we have
[tex](3x^{2} -2y^{2}+5x)+(4 x^{2}+12y^{2}-7x)[/tex]
Combine like terms
[tex](3x^{2} -2y^{2}+5x)+(4 x^{2}+12y^{2}-7x)\\=(3x^{2}+4x^{2})+(-2y^{2}+12y^{2})+(5x-7x)\\=7x^{2} +10y^{2}-2x[/tex]
therefore
the answer is the option C
He combined the terms [tex]-2y^{2}[/tex] and [tex]12y^{2}[/tex] incorrectly
how do you do factoring the gcf out of a binomial
Answers
if you have any specific binomials you need help with, feel free to send me a message or comment on this and i'll see if i can help. if you're just asking in general, then just remember to look for what the terms have in common, then take it out.
Point M is the midpoint of segment QR. If QM = 16 + x and MR = 2(x + 2), find the length of QM.
Answers
QM+MR=QR
16+x+2(x+2)=QR
16+x+2x+4=QR
20+3x=QR
7x-5y=20 in slope intercept form
Answers
solve for y
mnus 7x both sides
-5y=-7x+20
divide both sides by -5
y=7/5x-4
make h the subject of the formula
t=gh/10
Answers
gh=10t
h=10t/g
To make 'h' the subject of the formula, multiply both sides by 10 to get the equation 10t = gh. Then divide both sides by 'g' to get h = 10t/g.
Explanation:The formula given in the question is t = gh/10. To make h the subject of the formula, we'll need to isolate it. To do this, you should start off by multiplying both sides of the equation by 10, thus removing the divide by 10 part. This will give you 10t = gh. Finally, divide both sides of the equation by g. So, your revised formula would be h = 10t/g. This formula now clearly places h as the subject.
Learn more about Rearranging formula here:
https://brainly.com/question/40333765
#SPJ2
Solve logarithm Equation: 3 log5 x-log5 4= log5 16
Answers
To solve the logarithmic equation 3 log5 x - log5 4 = log5 16, we use logarithmic properties to combine terms and then solve for x, finding that x = 4.
Explanation:To solve the logarithmic equation 3 log5 x - log5 4 = log5 16, we can use the properties of logarithms.
First, we rewrite the equation using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This gives us:
log5 x^3 - log5 4 = log5 16.
Next, we utilize the property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. So we can combine the left side of the equation into a single logarithm:
log5 (x^3 / 4) = log5 16.
Now, since the bases of the logarithms are the same, we can equate the arguments of the logarithms:
x^3 / 4 = 16
Solving for x, we multiply both sides by 4 and then take the cube root:
x^3 = 64
Therefore, x = 4, since 4 cubed equals 64.
The complete question is: Solve logarithm Equation: 3 log5 x-log5 4= log5 16 is:
To solve the logarithmic equation, apply the properties of logarithms to simplify and solve for x.
Explanation:To solve the logarithmic equation, we can use the properties of logarithms. First, let's apply the property that states the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. This gives us: 3 log5 x - log5 4 = log5 16. Next, we can apply the property that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This gives us: log5 x3 - log5 4 = log5 16. We can simplify the equation by combining the logarithms and solving for x.
x3 / 4 = 16
x3 = 64
x = 4
The box plots show student grades on the most recent exam compared to overall grades in the class.
Which of the following best describes the information about the medians?
A. The class and exam medians are almost the same.
B. The exam median is much higher than the class median.
C. The class and exam Qv3 are the same, but the exam has the lowest median.
D. The low outlier on exams pulls the median lower.
Answers
We can see that in both boxes medians are practicaly the same. Which means that the correct answer is A
Answer:
A. The class and exam medians are almost the same.
Find sin x/2, cos x/2, and tan x/2, if cos x = -12/13, 180 degrees is less than x which is less than 270 degrees
Answers
sin x = -sqrt(13^2 - 12^2) / 13 = -5/13
tan x = 5/12
tan x/2 = (1 - cos x) / sin x = 1 - (-12/13) / -5/13 = 25/13 * -13/5 = -5
2sin^2 x/2 = 1 - cos x = 1 - (-12/13) = 25/13
sin^2 x/2 = 25/13 / 2 = 25/26
sin x/2 = 5/√26
sin x/2 / cos x/2 = tan x/2
cos x/2 = sin x/2 / tan x/2 = 5/√26 / -5 = -1/√26
sin x/2 = 5/√26
cos x/2 = -1/√26
tan x/2 = -5
2x plus 4 in vertex form
Answers
Mrs. Donley's math class has a total of 25 students. On Friday, the class was given an eight question quiz on fractions. The number of incorrect answers given by the students is shown below.
Incorrect Answers Number of Students
0 5
1 7
2 4
3 6
4 2
5 1
What is the relative frequency of students that missed 1 question on the quiz?
A. 0.28
B. 0.48
C. 0.35
Answers
A. 0.28
Find the percent of tip:
Cost of meal $18.50, Tip $2.59
13%
14%
15%
16%
Answers
Cost of meal is 100%: $18.50 is 100%
Tip is x%: $2.59 is x
Make a proportion:
$18.50 : 100% = $2.59 : x
x = 100% * $2.59 : $18.50
x = 14%
Of 100 clock radios with digital tuners and / or CD players sold recently in a department store, 70 had digital; tuners and 90 and CD players. How many radios had both digital tuners and CD players? ...?
Answers
Let A be the number of radios with digital tuners and let B be the number of radios with CD players.
The total number of radios is A∪B. It consists of both A radios and B radios, but however, radios with both digital tuners and CD players (A∩B) must be excluded from that number (either way they will be counted twice):
A∪B = A + B - A∩B
A∪B = 100
A = 70
B = 90
A∩B = ?
100 = 70 + 90 - A∩B
100 = 160 - A∩B
A∩B = 160 - 100
A∩B = 60
Final answer:
To determine the number of radios with both digital tuners and CD players, we use the principle of inclusion-exclusion. With 70 radios featuring digital tuners and 90 featuring CD players out of 100, the calculation reveals that 60 radios had both features.
Explanation:
The question asks how many radios sold recently in a department store had both digital tuners and CD players, given that 70 had digital tuners and 90 had CD players out of a total of 100 clock radios. To find the number of radios that had both features, we can use the principle of inclusion-exclusion. The formula for this principle is: Total = A + B - (A and B), where A and B are the two groups, and (A and B) is the intersection of the two groups. In this case, A is the number of radios with digital tuners, and B is the number of radios with CD players.
Substituting the given values: 100 = 70 + 90 - (A and B). Solving for (A and B), which represents the radios with both features, we get: (A and B) = 70 + 90 - 100 = 160 - 100 = 60.
Therefore, 60 radios had both digital tuners and CD players.
In the figure below what is the name of the angle formed by two rays QR and QP? What is the common. endpoint,for this angle?
Answers
which equation in standard form has a graph that passes through the point (-4 , 2) and has a slope of 9/2?
A. 9x-2y=36
B. 9x-2y=26
C. 9x-2y=-40
D. 9x-2y=-10
Answers
hope that helps
because y = 9/2x +20 then 2y = 9x + 40 so 9x -2y = -40
The equation in standard form passing through (-4, 2) with a slope of 9/2 is 9x - 2y = -10.
Since the equation is in standard form, rearrange it to slope-intercept form y = mx + b.
Given slope m = 9/2 and point (-4, 2), substitute these values to find the correct equation.
After substitution, the equation is 9x - 2y = -10.
Gabriela works at a nearby electronics store. she makes a commission of 14% on everything she sells. if she sells a camera for $589 how much money does gabriel make in commission?