Which expressions are equivalent to 24-7? Choose all the correct answers. Show your work.
Answers
The equivalent expressions to \(24^{-7}\) are given as follows:
C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)
F. \((24^3 \times 24^4)^{-1}\)
What are are equivalent expressions?Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.
The exponent in the denominator can be moved to the numerator with the changed signal, hence:
\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)
Applying the power of power rule, we multiply the powers, hence:
\((24^7)^{-1} = 24^{-7}\)
When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:
\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)
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Related Questions
Which transformation will result in an image that is congruent to its pre-image? (x, y) → (2x, −2y) (x, y) → (x, y − 2) (x, y) → (−x, 2y) (x, y) → (−2x, y − 2)
Answers
(x,y) --> (x, y-2)
=======================================================
Explanation:
Choice A can be ruled out because of the jump from x to 2x, and from y to 2y. This is a dilation with a scale factor 2. Meaning the preimage enlarges to a bigger image. Specifically the larger image has side lengths twice as long as the smaller preimage. The larger image of course cannot possibly be congruent to the smaller preimage. Congruent figures must have the same corresponding side lengths.
We'll come back to choice B.
Choice C and choice D are ruled out for similar reasoning as choice A was eliminated.
-------------
To summarize the previous section: We ruled out choices A, C, and D. The only thing left is choice B.
Choice B is a translation. The jump from y to y-2 means we shift the point 2 units down. There is no left or right shifting because x stays the same.
For example, the point (5,12) moves to (5,10).
Notice that dilation is not being applied for choice B.
With any geometric translation, aka shifting, the side lengths will remain intact. Something that is 5 units long will stay 5 units long. No amount of shifting will change the distance.
Therefore, a translation preserves distances and lengths. We consider it a rigid transformation. This is why choice B will have the preimage congruent to the image.
Answer:B) (x, y) → (x, y − 2)
Step-by-step explanation:
The vertices of a triangle are A(7, 5), B(4, 2), and C(9, 2). What is m∠ ∠ A B C ?
Answers
Answer: \(45^{\circ}\)
Step-by-step explanation:
\(\angle ABC\) is formed by lines AB and BC.
The slope of AB is \(\frac{2-5}{4-7}=-1\)The slope of BC is \(\frac{2-2}{9-4}=0\).This means
\(\tan (\angle ABC)=\left|\frac{-1}{1}} \right|\\\tan(\angle ABC)=1\)
From the diagram, we can tell that angle ABC is acute, so it measures \(\boxed{45^{\circ}}\)
Aaron has a 28.7 m length of rope. He uses 6.7 m of the rope
to make a rope ladder for a playground. He cuts the remaining
rope into 2 equal pieces to make tire swings. How long is each
tire swing rope?
Answers
Answer:
first step is to minus 28.7 - 6.7=22 (I did the minus because I want to get the remaining length of the rope )
step 2 : is to divide 22 by 2 (because the question said they should divide it into two pieces )
then the answer you get from the division of 22/2 which is 11 that would be the final answer
meaning each tire swing is 11m
Find the output, y, when the input, x, is -9.
y =
Answers
Answer:
when x=-9, y=1
Step-by-step explanation:
the graph shows when the x is at -9, the y is at 1
If f(x)=x² – 4x, what is the value of 2f(a-1)?
Answers
The correct value of 2f(a-1) is 2a^2 - 12a + 10.
To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.
Given: f(x) = x^2 - 4x
Substituting (a-1) into the function:
f(a-1) = (a-1)^2 - 4(a-1)
Expanding and simplifying:
f(a-1) = (a^2 - 2a + 1) - (4a - 4)
f(a-1) = a^2 - 2a + 1 - 4a + 4
f(a-1) = a^2 - 6a + 5
Now, we multiply the result by 2:
2f(a-1) = 2(a^2 - 6a + 5)
Expanding:
2f(a-1) = 2a^2 - 12a + 10
Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.
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The simplified Euler equation that relates the number of Edges, Faces, and Vertices is:
O F - E + V = 2 O V - F + E = 2
O E - V + F = 2
Answers
F - E + = 2, the simplified Euler equation that relates the number of Edges, Faces, and Vertices.
Define Equation.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.Euler equation
F - E + v = 2
Where F is the number of faces
V the number of vertices
E the number of edges
A cube, for example, has 6 faces, 8 vertices, and 12 edges and satisfies this formula.
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Solve 6 x 3/4.
please answer i’ll give you brainliest
Answers
Answer:
\(\frac{9}{2}\) or \(4\frac{1}{2}\)
Step-by-step explanation:
\(\frac{6}{1} * \frac{3}{4}\) multiply the numerators by each other, and the denominators by each other. You will get \(\frac{18}{4}\), if you simplify \(\frac{18}{4}\), you will get \(\frac{9}{2}\) as an improper fraction, or \(4\frac{1}{2}\) as a mixed number
Answer:
9/2 or 4 1/2
Step-by
dont mind this question
Answers
Answer:
hello, there.
Step-by-step explanation:
General kanobi
Find the smallest whole number by which 16087 should be multiplied or divided to get a perfect square
Answers
There is no whole number by which you can multiply or divide 16087 to make it a perfect square.
To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.
In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.
To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.
A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.
Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.
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URGENT, LAST 2 QUESTION!! WILL GIVE BRANLIEST!!! AT LEAST TAKE A LOOK!!
What is the missing side in the proportion below?
FIRST IMAGE
A) MN
B) LM
C) NO
2. Given the two similar triangles below, which proportion is true?
SECOND PIC
A) 10/12 = 15/22.5
B) 10/15= 15/22.5
C) 12/10=15/18
D)12/15=22.5/18
Answers
Answer:
its actually: B.) LM, and B.) 10/15= 15/22.5
Step-by-step explanation:
−2.2⋅(−2)÷(−
4
1
)⋅5
Answers
Step-by-step explanation:
la respuesta no es correcta porque es falsa
PLEASE ITS EASY I FOGOT HOW TO DO IT
Answers
Answer:
x> -1
Step-by-step explanation:
Open circle means > or <
Our class can rent a bus that will cost $35 for a service fee plus $2 for every travel. We have a total of $150 we can spend on the rental. Write an equation and solve it to find out the greatest distance we could travel. Equation:
Answers
Answer: 4
Step-by-step explanation:
add 35 with 2 = 37 and then divide 150 divided by 37 = 4
Fill in the table using this function rule.
y=-3x-3
X
-2
-1
0
1
y
0
0
0
X
Ś
Answers
Answer:
X | y
---------------
-2 | 3
-1 | 0
0 | -3
1 | -6
write the following in standard form: 8/-36
Answers
Answer:
Step-by-step explanation:
8/-36
-0.222222...
Determine the axis of symmetry of the graph of the following parabola. f(x)=3(x−5)2+1 Give your answer in the form x=h.
Answers
The axis of symmetry of the parabola, having the equation, f(x) = 3·(x - 5)² + 1 is the line x = h = 5
What is a parabola?A parabola is the locus of a point that moves such that the distance of the point from a fixed point is the same as the distance of the moving point from a fixed line.
The graph of a parabola has the shape of an open umbrella
The given equation for the parabola is; f(x) = 3·(x - 5)² + 1
The equation is given in the vertex form, f(x) = a·(x - h)² + k, where;
(h, k) = The vertex of the parabola
The axis of symmetry of a parabola, which is the line that divides the parabola in two, passes through the vertex of the parabola
Comparing the equation, f(x) = 3·(x - 5)² + 1, to the vertex form of a parabola, gives;
a = 3
(h, k) = (5, 1) (The vertex of the parabola)
Which gives; h = 5
The equation of the axis of symmetry is therefore the line, x = h = 5
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Which of the following best describes the lines y-3x=4x and 6-2y=8x
○perpendicular
○parallel
○skew
○intersecting
Answers
Answer:
Intersecting (fourth answer choice)
Step-by-step explanation:
If the lines are perpendicular, parallel, or intersecting, they are not skew. Thus, we need to check if the lines can be classified as either perpendicular, parallel, or intersecting first. If the lines are classified as neither, then they are skew.First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-intercept.Converting y - 3x = 4x to slope-intercept form:
(y - 3x = 4x) + 3x
y = 7x
Thus, the slope of this line is 7 and the y-intercept is 0.
Converting 6 - 2y = 8x to slope-intercept form:
(6 - 2y = 8x) - 6
(-2y = 8x - 6) / -2
y = -4x + 3
Thus, the slope of this line is -4 and the y-intercept is 3.
Checking if y = 7x and y = -4x + 3 are perpendicular lines:
The slopes of perpendicular lines are negative reciprocals of each other.We can show this in the following formula:
m2 = -1 / m1, where
m1 is the slope of one line,and m2 is the slope of the other line.Thus, we only have to plug in one of the slopes for m1. Let's do -4.
m2 = -1 / -4
m2 = 1/4
Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.
Checking if y = 7x and y = -4x + 3 are parallel lines:
The slopes of parallel lines are equal to each other.
Because 7 and -4 are not equal, the two lines are not parallel.
Checking if the lines intersect:
The intersection point of two lines have the same x and y coordinate. To determine if the two lines intersect, we treat them like a system of equations.Method to solve the system: Elimination:
We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:
add the two equations, eliminate the ys, and solve for x:-1 (y = 7x)
-y = -7x
----------------------------------------------------------------------------------------------------------
-y = -7x
+
y = -4x + 3
----------------------------------------------------------------------------------------------------------
(0 = -11x + 3) - 3
(-3 = -11x) / 11
3/11 = x
Now we can plug in 3/11 for x in y = 7x to find y:
y = 7(3/11)
y = 21/11
Thus, x = 3/11 and y = 21/11
We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3. If we get the same answer on both sides of the equation for both equations, the lines intersect:
Checking solutions (x = 3/11 and y = 21/11) for y = 7x:
21/11 = 7(3/11)
21/11 = 21/11
Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:
21/11 = -4(3/11) + 3
21/11 = -12/11 + (3 * 11/11)
21/11 = -12/11 + 33/11
21/11 = 21/11
Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).
This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.
Factor 9t–3u.
Write your answer as a product with a whole number greater than 1.
Answers
The factor of the expression 9t – 3u will be 3 and 3t – u.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of numbers and symbols and the procedures for using these symbols in formulae.
The expression is given below.
⇒ 9t – 3u
Simplify the expression, then we have
⇒ 3·3t – 3u
⇒ 3(3t – u)
The factor of the expression 9t – 3u will be 3 and 3t – u.
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The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 65% pure fruit juice?
PLEASE HELP
Answers
24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.
According to the question,
We have the following information:
The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice.
Now, let's take x pints of 55% pure fruit juice and y pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.
So, we have:
x+y = 40
x = 40-y ...(1)
55x/100+80y/100 = 40*65/100
55x+80y = 40*65
Putting the value of x from equation 1:
55(40-y)+80y = 2600
2200-55y+80y = 2600
2200+25y = 2600
25y = 2600-2200
25y = 400
y = 400/25
y = 16 pints
Putting this value in equation 1:
x = 40-y
x = 40-16
x = 24 pints
Hence, 24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.
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If anna's test grades 66, 90, and 99, what is her test average?
Answers
Answer:
85
Step-by-step explanation:
Average calculator
How much would $200 invested at 4% interest compounded continuously be worth after 5 years ?
Answers
200 x 1.04^5 = 243.33058048
rounded to 243.33
A local congressman must decide whether or not to vote for a bill to reduce the speed limit.
Supporters of the bill claim that the gas mileage improves at lower speeds! The congressman was given the data about the Toyota Camry gas usage - presented in the table below. (Picture Attached.)
Note: MPG stands for miles per gallon of gas.
IDENTIFY THE INDEPENDENT VARIABLE FIR THIS DATA AND WHY.
Answers
The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.
How to explain the variablesThe dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.
The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.
The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.
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Asgard Middle School plans to collect more than 2,000 cans of food in a food drive. So far, 668 cans have been collected. Write and solve an inequality to find numbers of cans the school can collect on each of the final 7 days of the drive to meet this goal.
Answers
Answer:
Let x be the unknown number.
7x + 668 < 2000 => 7x plus 668 is less than 2000
where:
7x => x represents the number of cans to be collected in 7 days
668 is the number of cans already collected.
2000 is the target number of cans.
7x + 668 < 2000
- 668 -668
7x < 1332
÷7 ÷7
x < 190.30
or
x < 190
To check:
7x + 668 < 2000
7(190) + 668 < 2000
1330 + 668 < 2000
1998 < 2000
Step-by-step explanation:
This has so far not been considered in most of the European discussions about ... lance and epidemiologic capacity for collecting and analyzing information
What is the volume of the cylinder below?
Answers
Answer:
C. 2160π units³
Step-by-step explanation:
Volume of a cylinder is given by the formula :
V = πr²h
Substituting values given gives us :
V = π(12)²(15)
V = π(144)(15)
V = 2160π units³ (since it is volume)
Answer:
\(\boxed{\sf{C. \quad 2160\pi \quad units^3}}\)
Step-by-step explanation:
It is necessary to use their formula to solve this problem with the volume of the cylinder.
Volume of the cylinder formula:
\(\Longrightarrow: \sf{V=\pi r^2h}}\)
\(\sf{12^2(15)}\)
Solve.
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAdd SubtractFirst, solve with exponents.
\(\sf{12^2=12*12=144}\)
Then, rewrite the problem down.
144(15)
Multiply.
\(\sf{144*15=\boxed{\sf{2160}}}\)
Therefore, the correct answer is C. 2160π units³.(a) The number of terms in an arithmetic progression is 40 and the last is -54. Given that the sum of the 15 terms added to the sum of the first 30 terms is zero. Calculate (1) The first term and common difference, (ii) the sum of the progression.
Answers
(i) The first term (a) is 24 and the common difference (d) is -2.
(ii) The sum of the progression is 2520.
i) Finding the first term and common difference:
Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).
The nth term formula is: An = a + (n-1)d
Using the given information, we can substitute the values:
-54 = a + (40-1)d
-54 = a + 39d
We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:
S15 + S30 = 0
The sum of the first n terms of an arithmetic progression can be calculated using the formula:
Sn = (n/2)(2a + (n-1)d)
Substituting the values for S15 and S30:
[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0
Simplifying the equation:
15(2a + 14d) + 30(2a + 29d) = 0
30a + 210d + 60a + 870d = 0
90a + 1080d = 0
a + 12d = 0
a = -12d
Substituting this value into the equation -54 = a + 39d:
-54 = -12d + 39d
-54 = 27d
d = -2
Now we can find the value of a by substituting d = -2 into the equation a = -12d:
a = -12(-2)
a = 24
Therefore, the first term (a) is 24 and the common difference (d) is -2.
ii) Finding the sum of the progression:
The sum of the first n terms of an arithmetic progression can be calculated using the formula:
Sn = (n/2)(2a + (n-1)d)
Substituting the values:
S40 = (40/2)(2(24) + (40-1)(-2))
S40 = 20(48 - 39(-2))
S40 = 20(48 + 78)
S40 = 20(126)
S40 = 2520
Therefore, the sum of the arithmetic progression is 2520.
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Laura creates a rectangular prism with wooden cubes. Each cube has an edge length of 3/4 inch. she uses a total of 240 cubes. the cubes are stacked 8 cubes high. What are the possible measurements for the length and width of the rectangular prism in inches.
Enter each measurement on a separate line.
Answers
Answer:00.24
explanation:
Just add the decimal form and multiply the 240 with the decimal of the 3/4
4.Sarah wants to give her friend a fish tank for her birthday.
The tank is a cylinder that measures 10 inches high and has a
diameter of 8 inches.
a. What is the minimum amount of wrapping paper Sarah will
need to cover the present? (Please show your work for credit)
|
b.Sarah also needs to know how much filtered water to bring.
She currently has 1 gallon. Will one gallon of filtered water be
enough to fill the tank? Why or why not?
(*hint: assume 1 gallon is equal to 231 cubic inches)
Please show your work for credit
please help me
Answers
The minimum amount of wrapping paper Sarah will need to cover the present is 351.68 square inches and one gallon of filtered water is not enough because the capacity of fish tank is 2.17 gallons.
Given that, the dimensions of cylindrical fish tank are height=10 inches and radius = 8/2 = 4 inches.
We know that, the total surface area of a cylinder is 2πr(r + h).
Here, the required wrapping paper = 2×3.14×4(4+10)
= 2×3.14×4×14
= 351.68 square inches
We know that, the volume of cylinder = πr²h
= 3.14×4²×10
= 502.4 cubic inches
Here, 1 gallon is equal to 231 cubic inches
Number of gallons of filtered water required = 502.4/231
= 2.17 gallons
Therefore, the minimum amount of wrapping paper Sarah will need to cover the present is 351.68 square inches and one gallon of filtered water is not enough because the capacity of fish tank is 2.17 gallons.
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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 23.5 for a sample of size 775 and standard deviation 12.2. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
Answers
The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:
\(22.6 < \mu < 24.4\)
How to obtain the confidence interval?The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:
\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)
Looking at the z-table, the critical value for a 95% confidence interval is given as follows:
z = 1.96.
The lower bound of the interval is then given as follows:
\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)
The upper bound of the interval is then given as follows:
\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)
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If (x + 4) is a factor of f(x), which of the following must be true?
Group of answer choices
f(-4) = 0
Neither x = -4 nor x = 4 are roots of f(x).
Both x = -4 and x = 4 are roots of f(x).
f(4) = 0
Answers
Here, we replace x with -4. In doing so, we see that (-4+4) is indeed 0, making this the correct answer.
The next two choices are incorrect since only -4 is a root of f(x), as explained above (a root occurs when the function equals zero when plugging in that “root”).
The last answer is incorrect since plugging in 4 will get f(4)=8.
a gas tank which can hold a total of 41 liters contains only 5 liters of gas when the driver stops to refuel. If it takes 3 minutes to fill up the tank, what is the rate in liters per minute
Answers
Answer:
12 liters per minute.
Step-by-step explanation:
41litres-5litres=36
If 36litres are filled up within 3 min,how many litres will be filled within 1 min
1/3×36=12
=12 litres per min