Write as the sum and/or difference of logarithms. Express powers as factors.
log 7 ³√10/ y²x A. 3 log₇10 - 2log 7y - log₇3 B. log₇10 - log₇ y - log₇x C. (log₇10 - 2log₇y - 2log₇x)/3 D. (log₇10 - 2log₇y - log₇ x)/3
The correct answer is D. (log₇10 - 2log₇y - log₇x)/3.
To express the given logarithm as a sum and/or difference of logarithms, we can use the properties of logarithms.
First, let's break down the given expression: log 7 ³√(10/(y²x)).
Using the property logₐ(b/c) = logₐ(b) - logₐ(c), we can rewrite the expression as:
log 7 (10) - log 7 (y²x)^(1/3)
Next, using the property logₐ(b^c) = c * logₐ(b), we can simplify further:
log 7 (10) - (1/3) * log 7 (y²x)
Now, let's separate the terms using the property logₐ(b) + logₐ(c) = logₐ(b * c):
log 7 (10) - (1/3) * (log 7 (y²) + log 7 (x))
Finally, applying the property logₐ(b^c) = c * logₐ(b) again, we have:
log 7 (10) - (1/3) * (2 * log 7 (y) + log 7 (x))
Simplifying further, we get:
(log 7 (10) - 2 * log 7 (y) - log 7 (x))/3
Therefore, the answer is D. (log₇10 - 2log₇y - log₇x)/3.
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A scale drawing of a rectangular park had a scale of 1 cm = 90m. What is the actual perimeter of the park in meters?
The actual perimeter is 2934. The perimeter of a rectangle is calculated as P = length + breadth + length + breadth. Alternatively, P = 2(length + breadth).
What is the actual perimeter of the park in meters?Perimeter=2(l + b)
=2[6.3cm +10cm) = 2x16.3 cm 32.6cm
Scale 1 cm = Actual 90m.
32.6cm 32.6x90m
= 2934 m
We sum the lengths of all four sides to determine the perimeter of a rectangle. Because opposing sides of a rectangle are always equal, we must obtain the length and breadth measurements to calculate the perimeter of a rectangle. The perimeter of a rectangle is equal to double the sum of its length and breadth.
To calculate the perimeter, or distance around the rectangle, sum all four side lengths. This may be done quickly by adding the length and breadth and then multiplying the total by two because each side length has two lengths. The perimeter formula is perimeter = (length + width)2.
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AHHHHHHHHHHHH I HATE THIS PLS HELP ME
Answer:
y = 2/3x - 13/3
Step-by-step explanation:
Implying the x and y coordinates, you get this.
bem bpight a box pf ;aundry detergent that contains 195 scoops. each load pf laundry use 1/2 2 scoops. how many loads of laundry can ben do with one box of laundry detergent
Therefore, Ben can do 390 loads of laundry with one box of laundry detergent.
Ben bought a box of laundry detergent that contains 195 scoops. Each load of laundry uses 1/2 scoop.
To determine how many loads of laundry Ben can do with one box of detergent, we divide the total number of scoops by the scoops used per load:
Number of loads = Total scoops / Scoops per load
Number of loads = 195 scoops / (1/2 scoop per load)
Number of loads = 195 scoops * (2/1) = 390 loads
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lowest common multiple of 18 and 42 x
Answer:
I'm assuming you inserting the variable x was a mistake.
Step-by-step explanation:
The least common multiple of 18 and 42 is 126.
\(\bold{Step-by-step}\)
\(\mathrm{"LCM"}\)
\(18 \times 7 = 126\\42 \times 3 = 126\)
Any concerns, let me know, have a great day!
The height of the ball (y) depending on time (x) is given by the following nonlinear function: y = -2x^2 + 7x. How high is the ball 1.5s after being kicked?
Answer:
height = 6
Step-by-step explanation:
substitute x = 1.5 into the function
y = - 2(1.5)² + 7(1.5) = - 2(2.25) + 10.5 = - 4.5 + 10.5 = 6
Find the distance between the points (-2,-10) and (-9,-5) on a coordinate plane.
How many terms are in 12x - 3 = 18
Answer: 1.75
Step-by-step explanation:
12x-3=18
+3 +3
12x=21
12 12
x=1.75
Students are going to conduct an experiment to study the effect of a net force applied to an object on the object’s motion. In each trial of the experiment, the students will apply a net force on the object. They also need to take two other measurements. What are the other quantities they should measure in each trial of the experiment?.
For conducting experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.
As given in the question,
To conduct a experiment based on the effect of net force applied to an object the dependable quantities are as follow:
Force = mass × acceleration
As object remain same ⇒ mass is constant as object remain same.
And there is change in the acceleration.
Acceleration depends change in velocity over total time taken.
Acceleration depends on velocity and time.
Net force also depends on velocity and time.
Two measurements need to know while conducting trail experiments are velocity and time.
Therefore, to conduct experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.
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Describe the effect of each transformation on the parent function. Graph the parent function and its transformation. Then determine the domain, range, and y-intercept of each function. 2. f(x)=2x and g(x)=−5(2x)
The domain of g(x) = -5(2x) is all real numbers since there are no restrictions on x. The range of g(x) = -5(2x) is also all real numbers since the function covers all possible y-values. The y-intercept is (0, 0).
The parent function for this problem is f(x) = x, which is a linear function with a slope of 1 and a y-intercept of 0.
Transformation for f(x) = 2x:
The transformation 2x indicates that the function is stretched vertically by a factor of 2 compared to the parent function. This means that for every input x, the corresponding output y is doubled. The slope of the transformed function remains the same, which is 2, and the y-intercept remains at 0.
Graph of f(x) = 2x:
The graph of f(x) = 2x is a straight line passing through the origin (0, 0) with a slope of 2. It starts at (0, 0) and continues to the positive x and y directions.
Domain, range, and y-intercept of f(x) = 2x:
The domain of f(x) = 2x is all real numbers since there are no restrictions on x. The range of f(x) = 2x is also all real numbers since the function covers all possible y-values. The y-intercept is (0, 0).
Transformation for g(x) = -5(2x):
The transformation -5(2x) indicates that the function is compressed horizontally by a factor of 2 compared to the parent function. This means that for every input x, the corresponding x-value is halved. Additionally, the function is reflected across the x-axis and vertically stretched by a factor of 5. The slope of the transformed function remains the same, which is -10, and the y-intercept remains at 0.
Graph of g(x) = -5(2x):
The graph of g(x) = -5(2x) is a straight line passing through the origin (0, 0) with a slope of -10. It starts at (0, 0) and continues to the negative x and positive y directions.
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how does sunlight cause cracks in the street
Answer: when it heats up the molecules expand and get bigger, then when it gets cold the molecules contract or get smaller and then after it happens so many times it causes cracks.
Step-by-step explanation:
for a posttest following anova, there are four different treatment groups. how many pairwise comparisons must be made to gain a complete understanding of which treatment effects differ significantly from others? a. 4 b. 6 c. 12 d. 24
There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.
In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.
To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:
A vs B
A vs C
A vs D
B vs C
B vs D
C vs D
Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.
It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.
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The radius of a dartboard is 9 inches What is the area of the dartboard in square inches?
the area of the dartboard is approximately 254.34 square inches.
The area of a dartboard can be calculated using the formula for the area of a circle, which is given by:
Area = π * \(radius^2\)
Given that the radius of the dartboard is 9 inches, we can substitute this value into the formula:
Area = π * \(9^2\)
Area = π * 81
To calculate the area, we need to use the value of π (pi). Pi is an irrational number and is commonly approximated as 3.14. Using this approximation, we can calculate the area:
Area ≈ 3.14 * 81
Area ≈ 254.34 square inches
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The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100pi square inches, what is the rate of increase, in cubic inches per second, in the volume V?
The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.
What is volume?
Volume refers to the amount of three-dimensional space occupied by an object or a substance.
To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.
The surface area S of a sphere is given by the formula:
\(S = 4\pi r^2,\)
where r is the radius of the sphere.
The volume V of a sphere is given by the formula:
\(V = (4/3)\pi r^3.\)
To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.
Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:
dr/dt = 0.3 inches per second.
Now, let's differentiate the volume formula with respect to time:
\(dV/dt = d/dt [(4/3)\pi r^3].\)
Using the power rule of differentiation, we get:
\(dV/dt = (4/3)\pi * 3r^2 * (dr/dt).\)
Simplifying further, we have:
\(dV/dt = 4\pi r^2 * (dr/dt).\)
Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.
Substituting the value of the surface area S = 100π square inches into the surface area formula:
\(100\pi = 4\pi r^2.\)
Dividing both sides by 4π, we get:
\(r^2 = 25.\)
Taking the square root of both sides, we find:
r = 5.
Now, we can substitute the value of r into the rate of increase formula:
\(dV/dt = 4\pi(5^2) * (0.3).\)
Simplifying the expression:
dV/dt = 4π(25) * 0.3.
dV/dt = 30π cubic inches per second.
Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.
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If angle B measure 135 degrees find measure of Angle Q
A.180
B.45
C.60
D.135
Answer:
D. 135
here are some extra words for fun (and to fill the necessary 20 characters)
Solve each equation. Check your answer. 15-g=23-2 g
The solution to the equation is g = -4. To check the answer, substitute g = -4 back into the original equation and verify if both sides are equal.
To solve the equation 15 - g = 23 - 2g, we'll start by simplifying both sides of the equation.
First, let's combine like terms on each side. On the left side, 15 - g cannot be simplified further. On the right side, 23 - 2g simplifies to 23 - 2g.
Next, we'll isolate the variable g. To do this, we'll move the terms involving g to one side of the equation. Subtracting -2g from both sides, we get 15 - g + 2g = 23 - 2g + 2g. Simplifying this, we have 15 + g = 23.
To isolate g, we'll subtract 15 from both sides of the equation. This gives us 15 + g - 15 = 23 - 15, which simplifies to g = 8.
Now, to check our solution, we substitute g = 8 back into the original equation: 15 - g = 23 - 2g. Plugging in g = 8, we have 15 - 8 = 23 - 2(8), which simplifies to 7 = 7. Since both sides of the equation are equal, we can conclude that g = 8 is indeed the solution to the equation.
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y - (-2) = 2/3( x - 1) divide each side by 3/3
first simplify the equation and then divide by 3/3 it will give you the correct answer.
hope it helps...
Step-by-step explanation:
\(y - ( - 2) = \frac{2}{3} (x - 1) \\ \\ y + 2 = \frac{2}{3} (x - 1) \\ dividing \: each \: side \: by \: \frac{3}{3} \\ \\ \frac{3}{3} (y + 2) = \frac{2}{3} \times \frac{3}{3} (x - 1) \\ \\ y + 2 = 2 \times 3(x - 1) \\ y + 2 = 6(x - 1) \\ y + 2 = 6x - 6 \\ y = 6x - 6 - 2 \\ y = 6x - 8\)
Help me solve this please?
Answer:
x = − 1 ± √6, so A + D I believe
Step-by-step explanation:
can someone please help me find out what LN and KN is
Answer:
LN= 3,9
KN=-2,9
Step-by-step explanation:
its that answer because on the number lime L is 3 and N is 9 and K is -2
Which of the following fractions would convert to a repeating decimal? a) 7/8. b) 5/2. c) 3/5. d) 2/9. .
Answer:
D.2/9
Step-by-step explanation:
0.222222222
PLZ HELP!
find the value of f(-2) for the function f(x)=4x+10
Show work please
Answer:
f(-2) = +2
Step-by-step explanation:
Let x = -2
So,
f(x) = 4x + 10
Substituting the value of x gives ,
f(-2) = 4 × (-2) + 10 = 10 - 8 = 2
Given f (x) = 1/x+11, find the average rate of change of f (x) on the interval [3, 3+h]. Your answer will be an expression involving h.
The average rate of change of the function in the interval is of:
\(A = -\frac{1}{14(14 + h)}\)
What is the average rate of change?The average rate of change of a function f(x) over an interval [a,b] is given by:
\(A = \frac{f(b) - f(a)}{b - a}\)
In this problem:
The interval is [3, 3 + h], hence \(a = 3, b = 3 + h\).\(f(3) = \frac{1}{3 + 11} = \frac{1}{14}\)\(f(3 + h) = \frac{1}{3 + h + 11} = \frac{1}{14 + h}\)Then:
\(f(b) - f(a) = \frac{1}{14 + h} - \frac{1}{14} = \frac{14 - 14 - h}{14(14 + h)} = -\frac{h}{14(14 + h)}\)
\(A = \frac{-\frac{h}{14(14 + h)}}{3 + h - 3} = -\frac{-\frac{h}{14(14 + h)}}{h} = -\frac{1}{14(14 + h)}\)
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Sally went to the farmers market to buy 300 watermelons. While she is loading the watermelons into her truck, the owner of the parking lot is charging her by the hour. The cost after x hours is shown in the table below.
Write a function, f(x), to model this data.
Type your answer with no spaces. If you need to type an exponent, use the ^ symbol.
Answer:
f(x)=1.25x
Step-by-step explanation:
It goes up at a constant rate of 1.25, meaning it's a linear equation. The formula for a linear equation is:
f(x)=mx+b
M = The average rate of change
B = The initial value
And since the initial value of this data starts at 0 on the x intercept, if you subtract 1.25 from 1.25 you get 0. The average rate of change is 1.25 so you would format the equation as:
f(x)=1.25x
And there is no need to add +0, which means instead of the equation being f(x)=1.25x+0, it is much simpler as f(x)=1.25x.
I hope this was helpful!
The required function to model this data is,
f(x)=1.25x.
What is a Function?A mathematical expression, rule, or law that specifies the relation between an independent variable and a dependent variable (the dependent variable).
The property that every input is related to exactly one output defines a function as a relation between a set of inputs and a set of permissible outputs.
It goes up at a constant rate of 1.25, meaning it's a linear equation. A linear equation is written as:
f(x)=mx+b
M = The average rate of change
B = The initial value
And since the initial value of this data starts at 0 on the x intercept, if you subtract 1.25 from 1.25 you get 0. The average rate of change is 1.25 so you would format the equation as:
f(x)=1.25x
Additionally, there is no need to include 0,
which means instead of the equation being f(x)=1.25x+0,
it is much simpler as f(x)=1.25x.
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what is the sum of the polynomials
(8x^2-9y^2-4x) + (x^2-3y^2-7x)
Answer:
\(9x^{2} - 12y^{2} - 11x\)
Step-by-step explanation:
\((8x^{2} - 9y^{2} - 4x) + (x^{2} - 3y^{2} -7x)\\(8x^{2} + x^{2} ) + (-9y^{2} - 3y^{2} ) + (-4x - 7x)\\9x^{2} - 12y^{2} - 11x\)
In the first step, I rearranged the equation and put like terms together.
Then I just combined the like terms.
I hope this helps!
A cellular phone tower services a 15 mile radius. On a hiking trip, you are 9 miles east and 11 miles north of the cell tower. Are you in the region served by the tower?
The calculated distance is approximately 14.21 miles, which is less than the 15-mile radius of the cell tower. Therefore, you are within the region served by the tower.
To determine if you are within the region served by the cell tower, we can calculate the distance between your location and the tower using the Pythagorean theorem. According to the given information, you are 9 miles east and 11 miles north of the cell tower.
Using the Pythagorean theorem, the distance from your location to the cell tower can be calculated as follows:
Distance = √((east distance)^2 + (north distance)^2)
= √((9 miles)^2 + (11 miles)^2)
= √(81 + 121)
= √202
≈ 14.21 miles
The calculated distance is approximately 14.21 miles, which is less than the 15-mile radius of the cell tower. Therefore, you are within the region served by the tower.
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Evaluate -5 + k - n, when k = -3, m = -6, and n = 9 (you need to write a minimum of 2 sentences explaining your strategies and/or specific integer rules that you used.)
According to the question a minimum of 2 sentences explaining your strategies The value of the expression -5 + k - n, when k = -3, m = -6, and n = 9, is -17.
To evaluate the expression -5 + k - n, we substitute the given values of k, m, and n into the expression.
First, we substitute k = -3, m = -6, and n = 9 into the expression:
-5 + (-3) - 9
Next, we apply the rules of integer addition. The negative sign in front of a number indicates subtraction. So, -3 - 9 is equal to -12. Finally, we add -5 and -12 to get the result:
-5 + (-3) - 9 = -5 - 12 = -17.
Therefore, the value of the expression -5 + k - n, when k = -3, m = -6, and n = 9, is -17.
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what is the value of x in the equation 2(6×+4)-6+2×=3(×+3)+1
We are given the equation;
\(2(6x+4)-6+2x=3(x+3)+1\)Firstly, let's expand the brackets.
\(undefined\)Find gff(x)= fgg(x) given f(x)= 3x+4 g(x) =9x+7
g∘f(x) or g(f(x)) is equal to 27x + 43.
To find g∘f(x) or g(f(x)), we need to substitute the function f(x) into the function g(x).
Given:
f(x) = 3x + 4
g(x) = 9x + 7
To find g∘f(x), we substitute f(x) into g(x) as follows:
g(f(x)) = g(3x + 4)
Now, we substitute 3x + 4 for x in the function g(x):
g(f(x)) = 9(3x + 4) + 7
Expanding and simplifying:
g(f(x)) = 27x + 36 + 7
g(f(x)) = 27x + 43
Therefore, g∘f(x) or g(f(x)) is equal to 27x + 43.
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It took researchers three weeks to analyze a large amount of data using a supercomputer. How many minutes did it take them to analyze the data?
1,440 minutes
4,320 minutes
10,080 minutes
30,240 minutes It took researchers three weeks to analyze a large amount of data using a supercomputer. How many minutes did it take them to analyze the data?
1,440 minutes
4,320 minutes
10,080 minutes
30,240 minutes
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The factor theorem can help use determine if a factor is a [blank] of a polynomial
If and only if f(a) = 0, a polynomial f(x) has a factor (x-a). It's one of the techniques for factoring a polynomial.
A polynomial is an equation made up of coefficients and in determinates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.
The factor theorem can help us determine if a factor is a "root" or "zero" of a polynomial. In other words, if we have a polynomial function, the factor theorem allows us to check if a particular value (usually represented by the variable x) is a solution to the polynomial equation, which means that when we plug in that value for x, the resulting output of the polynomial function will be zero. If it is, then we know that (x - a) is a factor of the polynomial, where "a" is the solution we found.
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