Which expressions are equivalent to the one below? Check all that apply.A.3xB.C.D.(21 - 7)xE.3x-7F.3
Answers
ANSWER
A, B, and C
EXPLANATION
We want to find the expressions that are equivalent to the given expression:
\(\frac{21^x}{7^x}\)First, let us simplify the given expression using the following law of exponents:
\(\frac{a^c}{b^c}=(\frac{a}{b})^c\)Therefore, we have that the expression becomes:
\(\frac{21^x}{7^x}=(\frac{21}{7})^x=3^x\)Another way of simplifying the expression is to simplify the numerator using the following law of exponents:
\((a*b)^x=a^x*b^x\)Therefore, the expression becomes:
\(\begin{gathered} \frac{21^x}{7^x}=\frac{(7*3)^x}{7^x} \\ \\ \Rightarrow\frac{7^x*3^x}{7^x} \\ \\ \Rightarrow3^x \end{gathered}\)Therefore, we see that the expressions that are equivalent to the given one are:
\(\begin{gathered} 3^x \\ \\ \frac{7^x*3^x}{7^x} \\ \\ (\frac{21}{7})^x \end{gathered}\)The correct options are A, B, and C.
Related Questions
PLEASE HELP ME SOLVE THIS QUESTION
ln(x^3 / (1 + x))
Answers
Answer:
3·ln(x) -ln(1+x)
Step-by-step explanation:
You want to "solve" the expression ln(x³/(1+x)).
Rules of logarithmsThe relevant rules of logarithms are ...
ln(a^b) = b·ln(a)
ln(a/b) = ln(a) -ln(b)
ApplicationThe given log expression can be expanded as ...
\(\ln{\left(\dfrac{x^3}{1+x}\right)}=\ln(x^3)-\ln(1+x)=\boxed{3\ln(x)-\ln(1+x)}\)
On a treasure map, a X is placed at point (9, -7). if the pirates are currently on point (9,3), how many units away are they?
Answers
Answer:
They are 10 units away from the treasure
Step-by-step explanation:
Notice that the points (9, -7) and (9, 3) are both located at the same x-value (9) while their y-values are in one case 3 units above the x-axis, and in the other 7 units BELOW the x-axis. Therefore thy differ by 3 - (-7) units , which totals 10 units.
The fraction of PKR 1 is 50 paisas
Answers
The fraction that represents the rate between PKR and Paisas is given as follows:
1/50.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:
1/50.
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What exponent is assumed is we just have the number ? For example what is the exponent for the following:80 1 0 0 0 1000 8
Answers
Answer: 1
\(\begin{gathered} \text{According to the law of indices} \\ x^1\text{ = x} \\ \text{Therefore,} \\ 8^1\text{ = 8} \\ \text{Where the exponent is 1} \end{gathered}\)Mrs Mills buys 4 packs of treats for her cats, Fluff and tigger
she gives Fluff 1/6 of a pack each day
She gives tigger 1/5 of a pack each day
for how many complete days will the 4 packs of treats last
Answers
Answer: 10 days
Step-by-step explanation:
1/6 + 1/5 = 5/30 + 6/30 = 11/30 (total for the day)
4 / (11/30) = 10.90909091 (divide the total amount of packages by the daily total)
So 10 complete days.
Fred brought a shirt and a wallet for a total of 34.26 before tax. The price of the wallet was $15 less than the price of the shirt. What was the price of the shirt?
Answers
Answer:
The price of the shirt is $24.63.
Step-by-step explanation:
Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:
x + (x - 15) = 34.26
Simplifying, we get:
2x - 15 = 34.26
Adding 15 on both sides:
2x = 49.26
Dividing by 2:
x = 24.63
Therefore, the price of the shirt is $24.63.
A fair 6-sided die is colored in the following way: The faces of 1 - 3 are colored red. The faces of 4 and 5 are colored blue. The face of 6 is colored green. What is the probability that the face comes up red OR a prime number
Answers
Answer:
There are 6 total possibilities, 3 red faces and 3 prime numbers however, 2 and 3 are prime numbers and they are red as well so total successful outcomes = 3 + 3 - 2 = 4. This means that the answer is 4 / 6 or 2 / 3.
Answer:
\(\frac{2}{3}\)
Step-by-step explanation:
\(1 \: 2\:3\) are red
\(5\) is prime.
Total of \(4\) possibilities out of \(6\)
\(\frac{4}{6}\)
in
towns
Which equation represents g(x) as a transformation of
f(x)?
O g(x) = f(x+3)
O g(x) = (x-3)
O g(x) = f(x) + 3 / 3
O g(x) = 3 /. f(x)
Answers
The base of the mountain is 6,500 feet above sea level and AB measures 230 feet across. Given that the measurements for QAP is 20° and QBP is 35°, how far above sea level is peak P ? Express your answer to the nearest foot.
Height above sea level:
Answers
Answer:
6610
Step-by-step explanation:
We have tan(X) = opposite/ adjacent
tan(QBP) = PQ/BQ
tan(35) = PQ/BQ ---eq(1)
tan(QAP) = PQ/AQ
tan(20) = \(\frac{PQ}{AB +BQ}\)
\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)
230*tan(20) + PQ*tan(20)*tan(35) = PQ
⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)
⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]
\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)
\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)
PQ = 110.4
≈110
Height above sea level = 6500 + PQ
6500 + 110
= 6610
Help quick I have 30 minutes left
Answers
Answer:
I believe B and C are correct. Maybe another but I don't think so.
Which of these is NOT a way to show that two figures are congruent?
Answers
If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.
What is Triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
What is the condition to be congruent?If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.
here, we have,
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.
In Δ PQR and ΔXYZ, as shown in figure,
we can identify that PQ = XY, PR = XZ,
and QR = YZ
and ∠P = ∠X,
∠Q = ∠Y and ∠R = ∠Z.
Then we can say that Δ PQR ≅ ΔXYZ.
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Neee help right answers please
Answers
Answer:
Step-by-step explanation:
Divided the first 2 numbers by eachother and then by four use a calculator
Answer:
1146198.07
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!!!
Answers
Answer:
D 0.89275
Step-by-step explanation:
29. What is the BEST description of a constant rate of change?
Answers
A constant rate of change occurs when the change in two variables is contant over a period of time.
In this ,
Option A;
The number of stamps in a collection when the same number of stamps is added each month
This is correct because a constant rate will be obtained when the previous number of stamps in the collection is divided by the amount added.
Answer
A.
Do 5/3 and 30/18 form a proportion?
Answers
Answer:
yes
Step-by-step explanation:
5x6=30
3x6=18
Urgent, please help
I'll mark brainliest
Answers
Answer:
Step-by-step explanation:
The function rule g(x) after the given transformations of the graph of f(x)=4x is g(x) = -1/2x
Transformation techniques
Transformation is the process of changing the position of an object on the xy-plane.
Given the parent function
f(x) = 4x
If the function is not reflected over x-axis, the resulting function will be f(x) = -4x
If the resulting function is compressed by a factors of 1/8, hence the final function rule will be;
g(x) = 1/8(-4x)
g(x) = -1/2x
Hence the function rule g(x) after the given transformations of the graph of f(x)=4x is g(x) = -1/2x
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The basic rate pay is K8.20. If the overtime is paid at time-and-a-quarter, what is the overtime rate of pay?
Answers
The overtime rate of pay is K10.25.
The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.
To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.
By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.
Therefore, the overtime rate of pay is K10.25.
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Find the slope and the coordinates of the points of intersections of the following lines with coordinate axes y= -1/4x+2
Answers
Step-by-step explanation:
y = -0.25x + 2
The slope is the coefficient of x, which is -0.25.
y-intercept is the constant term, which is 2.
When y = 0, -0.25x + 2 = 0, -0.25x = -2, x = 8.
=> x-intercept = 8.
The perimeter and area of a rectangle are 22 cm
and 30 cm² respectively. Find the length and
breadth of the rectangle
Answers
The perimeter and area of a rectangle are (5,6) and (6,5).
The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.
A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.
The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.
The perimeter of the rectangle:
P=2l+2w=22
divide 2 into both sides
l+w=11 -------------> (1)
w=11-l
Area of the rectangle:
l*w=30
l(11-l)=30
11l-l^2-30=0
l^2-11l+30=0
By factor method,
(l-5)(l-6)=0
l=5,6.
Substitute this value in w,
l=5 implies w=6
l=6 implies w=5
There we have two solutions.
The length and breadth of the rectangle is
(5,6) and (6,5).
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Mike had $800. He now has $500. What is the percent decrease?
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what is the value of x^2 - 6x + 9 when x = 2 + i?
Answers
The Expression x^2 - 6x + 9 when x = 2 + i is -2i
To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:
(2 + i)^2 - 6(2 + i) + 9
Simplifying the first term, we get:
(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2
Since i^2 = -1, we can substitute that in and simplify further:
(2 + i)^2 = 4 + 4i - 1 = 3 + 4i
Now we substitute this into the original expression:
(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9
Simplifying further, we get:
= 3 + 4i - 12 - 6i + 9
= 0 - 2i
= -2i
Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.
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What is the value of x in the figure?
Enter your answer in the box.
x=
Answers
A little square marked on angle means that the angle is 90 degrees.
By the vertical angle theorem, angles opposite each other are equal thus the angle opposite the angle with the little square is also 90 degrees.
That angle is split into two angles that is off measure 22 degrees and x degrees
-- x + 22 = 90 --> x = 68.
Hope that helps!
Answer:
68
Step-by-step explanation:
\( \hookrightarrow \: x + 22 = 90(complementary \: angles) \\ \)
\( \hookrightarrow \: x + 22 = 90 \\ \hookrightarrow \: x = 90 - 22 \\ \hookrightarrow \: x = 68\)
A construction worker earned $64 in a week. If he worked eight hours in one week, how much money did he earn per hour?
Answers
Answer:
X=8
Step-by-step explanation:
64 Divided by Eight equals Eight.
Because he worked eight hours that week and earned $64 so divide that up by eight then you got your answer.
I am very confused on this topic, it would mean the world to me if you can explain it thoroughly with understandable words for a kidPlease do number 5 and if you can number 6 so I can comprehend more. Thanks
Answers
The first step in solving the exercise is to replace the given value of b into the equation:
\(\begin{gathered} 65\div b+8\cdot4=20 \\ \frac{65}{b}+8\cdot4=20 \\ \frac{65}{5}+8\cdot4=20 \end{gathered}\)Now, we follow the PEMDAS order, that is, first multiplications and divisions and then the addition:
\(\begin{gathered} \frac{65}{5}+8\cdot4=20 \\ 13+32=20 \\ \boldsymbol{45\neq20}\text{ }\Rightarrow\text{ "}\ne\text{" reads "different"} \end{gathered}\)Finally, since 45 is different from 20, then the given value of the variable is not a solution to the equation.
Which statements contradict each other?
I. triangle ABC is a right triangle. II. m/A = 41° III. m/B = 103°
A. I and II
B. I and III
C. II and III
D. None of the statements are contradictory.
Answers
Answer: A. I and II contradict each other because in a right triangle, the measure of angle A is 90 degrees, not 41 degrees.
A wage sheet of a small business shows one employee’s details. The employee is paid $40 an hour for overtime hours where they work more than their usual 26 hours.
Answers
Answer: whats the question tho
Step-by-step explanation:
Answer:whats the question
Step-by-step explanation:
Simplify (−3)4 and −34. Show all the work
Answers
Answer:
-12
Step-by-step explanation:
(-3)4
-3*4
-12
Elaborate ur question about - 34
Please help! What is the surface area of the cylinder with height 4 m and radius 8 m? Round your answer to the nearest thousandth.
Make sure to round please.
Answers
The surface area of the cylinder is 948m²
What is surface area of cylinder?The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;
SA = 2πr(r+h)
Where r is the radius of the base and h is the height of the cylinder.
r =8m
h = 4m
SA = 2 × 3.14 × 8 (8+4)
SA = 78.96 × 12
SA = 947.52 m²
to the nearest whole number
SA = 948 m²
therefore the surface area of the cylinder is 948 m²
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50 Points!!! Solve each inequality. Then graph the solution set on a number line. Photo attached
Answers
50
Step-by-step explanation:
plot it on the number line
note: make x the subject
Answers
Answer:
Step-by-step explanation: