Answer:
The correct option is: c. Prime
Step-by-step explanation:
The given expression is: [tex]x^2 -8x-12[/tex]
First we will take each given option and simplify them using FOIL method to see if we get the original given expression. So.....
[tex]a.\ \ \ (x-6)(x+2)\\ \\ =x^2+2x-6x-12\\ \\ =x^2-4x-12\\ \\ \\ b.\ \ \ (x+3)(x-4)\\ \\ =x^2-4x+3x-12\\ \\ =x^2-x-12\\ \\ \\ d.\ \ \ (x+6)(x-2)\\ \\ =x^2-2x+6x-12\\ \\ =x^2+4x-12[/tex]
We can see that options [tex]a, b\ and\ d[/tex] doesn't give the original given expression.
So, the expression [tex]x^2 -8x-12[/tex] is Prime.
Which answer represents the range of the logarithmic function given below? F(x) = log7 x
A. x>=0
B. x<0
C. x>0
D. All real numbers
Range of the logarithmic function F(x) = log7 x is C. x > 0.
What is a logarithm?The logarithm is exponentiation's opposite function in mathematics.
This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 100 = 10², the logarithm of 100 in base 10 is 2, or log10 = 2.
In the given question, F(x) = log7 x.
Assuming log7 x = y.
Therefore, x is the value equal to [tex]7^y[/tex], hence it can not be zero and negative.
Even if y is equal to zero [tex]7^y[/tex] would be 1.
∴ The range of the logarithmic function F(x) = log7 x is x > 0.
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Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkbook shows a balance of $487.38 as of January 29. The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28. How much did Eliza deposit in her account between January 18 and January 29?
Given the function f(x) = 0.5(3)x, what is the value of f−1(7)? 1) 0.565 2) 1.140 3) 1.771 4) 2.402
Answer:7=0.5 |x-4| -3
+3 +3
10=0.5 |x-4|
10/0.5=0.5/0.5 |x-4|
20=|x-4|
^
-20=x-4 20=x-4
+4 +4 +4 +4
-16=x 24=x
The answers are -16=x and 24=x
Hope this helps, an if it pleases you put as the brainliest answer!
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Step-by-step explanation:
Line AB has endpoints A(-4,5) and B(3,5). What is the x-coordinate of a point C such that B is the midpoint of line AC
The measures of an exterior angle and the adjacent interior angle add up to 360 because they form a linear pair
A.True
B.False
Answer: false
Step-by-step explanation:
The table shows the mean daily temperature in North Dakota during a week in February. Which statement about the data is true?
A.The Lowest mean temperature was on wednesday
B.The lowest temperature was on friday
C.The highest mean temperature was on friday
D.The highest mean temperature was on monday
The correct option is 2nd option i.e., the lowest mean temperature is on Friday.
The mean temperature in North Dakota during a week in February.
We have to find which statement is true.
What is the method to find mean ?
The mean can be calculated by adding all the given numbers and then dividing by the total no. of numbers.
As per the question ;
Mean daily temperature is given in a table.
Let's arrange these temperatures day wise from highest mean temperature to lowest mean temperature.
i.e.,
Tuesday - 1.3°F > Monday - 1°F > Wednesday - 0°F > Thursday > -1.2°F > Sunday - -1.4°F > Saturday > - 1.5°F > Friday - -1.7°F
So ;
The highest mean temperature is on Tuesday of 1.3°F.
The lowest mean temperature is on Friday of -1.7°F.
Thus , the correct option is 2nd option i.e., the lowest mean temperature is on Friday.
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How to find 0.36 repeating in a equivalent fraction form?
To convert 0.36 repeating into a fraction, we get [tex]\frac{4}{11}[/tex].
To convert the repeating decimal 0.36 repeating (written as 0.363636...) into a fraction, follow these steps:
Let x = 0.363636...Multiply both sides of the equation by 100 (since the repeating part is two digits long):⇒ 100x = 36.363636...
Subtract the original equation from this new equation:⇒ 100x - x = 36.363636... - 0.363636...
⇒ 99x = 36
Solve for x:⇒ x = [tex]\frac{36}{99}[/tex]
Simplify the fraction by finding the greatest common divisor (GCD) of 36 and 99, which is 9:⇒ x = ([tex]\frac{36}{99}[/tex]) / ([tex]\frac{99}{9}[/tex]) = [tex]\frac{4}{11}[/tex]
Therefore, the fraction equivalent of 0.36 repeating is [tex]\frac{4}{11}[/tex].
PLEASE HELP NEED ASAP! WILL GIVE THE BRAINLIEST TO THE FIRST PERSON WHO ANSWERS!
Write the slope intercept form of the equation of the line through the given point with the given slope.
1. through: (2,-1), slope = 2
2. through: (-2,-3), slope= -1/2
Thank you!!
How many combinations with 3 numbers 0-9?
1st number can be 0-9 = 10 numbers
2nd number can be 0-9 = 10 numbers
3rd number can be 0-9 = 10 numbers
10 * 10 * 10 = 1000 combinations
The line with m = -1 /2 and b = 1
A company sells boxes of cow bells (b) for $20 and boxes of air horns (h) for $30. They can make a batch of cow bells that fills 8 boxes or a batch of air horns that fills 9 boxes. The company only has 53 boxes. Which system of equations helps the company plan to make $275?
Solving a system of equations to help a company plan revenue and production constraints.
The system of equations:
20b + 30h = 275 (total revenue equation)
8b + 9h = 53 (total boxes equation)
By solving these equations simultaneously, the company can determine the number of cow bells and air horns to produce to make $275 while satisfying the box constraint.
Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which Ben agreed to pay $215 per month. Which of the following statements best gives the reasons that Ben’s rent payment is an essential (fixed) expense? a. It cannot be eliminated in a later budget, in order to save money. b. Living expenses have a higher priority than any other type of expense. c. The spender controls the amount of the rent by choice of apartment. d. He agreed to pay the same amount every month.
Solution:
Cost of apartment(Ben + Housemates) = $ 563 per month
Amount paid by Ben per month = $ 215
Yes, Accommodation provided by someone for fixed amount is an essential Expense.
All the three statements regarding Ben who pays $ 215 per month are true.
a. It cannot be eliminated in a later budget, in order to save money.
b. Living expenses have a higher priority than any other type of expense.
c. The spender controls the amount of the rent by choice of apartment.
Help please! I will give Brainliest to most detailed answer:)
The figure shows three right triangles. Triangles JKM, KLM, and JLK are similar.
Theorem: If two triangles are similar, the corresponding sides are in proportion.
Using the given theorem, which two statements help to prove that if segment JL is x, then x^2 = 100?
1.) Segment JL • segment JM = 64
Segment JL • segment LM = 48
2.)Segment JL • segment JM = 48
Segment JL • segment LM = 36
3.)Segment JL • segment JM = 64
Segment JL • segment LM = 36
4.)Segment JL • segment JM = 36
Segment JL • segment LM = 64
*If you can, could you please give an explanation? Thanks.
Let $abcd$ be a parallelogram. extend $\overline{bc}$ past $b$ to $f$, and let $e$ be the intersection of $\overline{ab}$ and $\overline{df}$. if the areas of triangles $bef$ and $ade$ are 1 and 9, respectively, find the area of parallelogram $abcd$.
Triangles ade and bef are similar due to equal angles. The ratio of their areas (9:1) means their sides have a ratio of 3:1. Using the properties of parallelograms, the parallelogram's area will be double the area of triangle ade, or 18 square units.
Explanation:In the given problem, we have a parallelogram abcd and we're asked to find its area. Given the properties of a parallelogram, we know that angle bad equals angle bef. This leads to the conclusion that triangle ade is similar to triangle bef since their angles are the same. As the ratio of their areas is 9:1, it's clear the ratio of their sides is 3:1, since the ratio of the areas of similar figures is the square of the ratio of their corresponding sides.
The parallelogram's area will be double the area of triangle ade, thanks to the properties of a parallelogram (it's made up of two congruent triangles). Therefore, the area of the parallelogram is 18 square units. The important steps here were recognizing the similar triangles and knowing how to calculate a parallelogram's area.
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In the diagram, AC=BD=17 and BC=3. The length of segment AD is
Read the following statement: 3x = 3x. This statement demonstrates:
the substitution property.
the reflexive property.
the symmetric property.
the transitive property.
Use the given line(s) from a random number table to select numbers to use in each problem. Select 2 contestants for a game show out of a pool of 50 46547 17395 25765 11325 14071 61688
A. 39, 25 B. 46, 47 C. 4, 6 D. 46, 25
The solution would be like this for this specific problem:
Given:
46547 17395 25765 11325 14071 61688
You want two-digit numbers between 01 and 50, so break it up into chunks of two and eliminate any string that is not between 01 and 50.
So, the numbers from the string are:
46 54 71 73 95 25 76 51 13 25 14 07 16 16 88
Eliminated numbers:
54 71 73 95 25 76 51 88
Numbers remaining:
46 25 13 14 07 16
So, the 2 contestants from a game show out of a pool of 50 would be 46 and 25 (since these are the possible contestants based from the given).
What is the degree of this polynomial? 5y^4+y^3+2/3y^2+y+1
A. 5
B. 2
C. 1
D. 4
Answer: 4
Step-by-step explanation:
Determine the equation of the graph and select the correct answer below.
parabolic function going down from the left and turning at the point negative three comma two and going up through the point zero comma twelve and continuing towards infinity
y = (x + 3)2 − 2
y = (x − 3)2 − 2
y = (x + 3)2 + 2
y = (x − 3)2 + 2
Answer:
The correct answer is [tex]y = \frac{10}{9}(x+3)^2+2[/tex]
Step-by-step explanation:
The correct answer to the question is not provided in the options listed below.
In order to find the equation of the quadratic function that you're looking for, you should identify the two points the parabola passes through: the vertex (that is point (-3,2)) and the y-intercept (the point (0,12)).
As we are given the vertex of the quadratic function, we can use the completed square form: [tex]y=a(x-h)^2+k[/tex], where h and k are, respectively, the x and y coordinates of the vertex.
As (-3,2) is the vertex, we have:
[tex]y=a(x+3)^2+2[/tex]
Now, as the graph passes through the point (0,12), we can replace x=0 and y=12 in the formula above in order to find the value of a. Then, we make a the subject of the equation:
[tex]12=a(0+3)^2+2[/tex]
[tex]12=9a+2[/tex]
[tex] 10=9a[/tex]
[tex] \frac{10}{9}=a[/tex]
So, the equation of the parabola is [tex]y=\frac{10}{9}(x+3)^2+2[/tex].
Sarah drove 3 hours more than michael on their trip to texas. if the trip took 37 hours, how long did sarah and michael each drive?
37-3 = 34
34/2 = 17
Michael drove 17 hours
Sarah drove 20 hours (17+3)
Please help!
A company has a $150 budget to provide lunch for its 20 employees. The options are to provide either roast beef sandwiches, which cost $5 apiece, or tuna sandwiches, which also cost $5 apiece. The company also wants to use the entire budget. Suppose r represents the number of roast beef sandwiches it provides and t represents the number of tuna sandwiches. Which statement is correct?
A. The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r-t=20 and 5r+5t=150.
B. The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r+t=20 and 5r+5t=150.
C. The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r-t=20 and 5r-5t=150.
D. The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150.
Answer: D. The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150.
Step-by-step explanation:
Let 'r' represents the number of roast beef sandwiches it provides and 't' represents the number of tuna sandwiches.
Then, the total number of roast beef sandwiches and tuna sandwiches is equal to the number of employees :
[tex]r+t=20[/tex]....................(1)
Also, the cost of each roast beef sandwich and cost of each tuna sandwich is same as $5.
If company wants to use the entire budget of $150, then we have another equation :-
[tex]5r+5t=150\\\5(r+t)=150[/tex]
If we divide 5 on both sides we get
[tex]r+t=30[/tex].............................(2)
When we compare equation (1) and (2) we get 20=30 but it is not possible therefore the system has no solution.
Therefore, the correct statement is "The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150."
5x2−320 factored completely?
what are the discontinuities of the function f(x)= (x^2 - 36)/(4x - 24)
The function f(x) = (x² - 36)/(4x - 24) has a removable discontinuity at x = 6, due to the fact that at this value the original function's denominator becomes zero.
The function given is f(x) = (x² - 36)/(4x - 24). To find the discontinuities of this function, we must identify values of x that cause the denominator to be zero, as the function would be undefined at those points. Factor the numerator and the denominator to simplify the expression. (x² - 36) can be factored as (x + 6)(x - 6), and (4x - 24) can be factored as 4(x - 6). So, the simplified function is f(x) = (x + 6)/4, but we must exclude the value x = 6 from the domain due to it making the original denominator zero. Therefore, the function is discontinuous at x = 6, which is also known as a point of removable discontinuity because the factor (x - 6) is canceled out in the simplification.
A dress calls for 1 1/3 yards of material for a dress.if you have 21 3/4 yards of material,how many dresses can be made?
divide 21 3/4 by 1 1/3 = 16 5/16
she can make 16 dresses
The equation y = ax describes the graph of a line. If the value of a is negative, the line
The equation y = ax represents a straight line with slope a. If a is negative, the line slopes downward to the right, not down and to the left.
The equation y = ax describes the graph of a line. The & in the equation appears to be a typo and should likely refer to a. The constant a represents the slope of the line. When the slope a is negative, the line slopes downward as it moves to the right on a coordinate plane. This is because a negative slope indicates that as the independent variable (usually the x-axis) increases, the dependent variable (y-axis) decreases. A line with a negative slope is straight, and its steepness depends on the absolute value of the slope a. Thus, the line goes down and to the left.
3x + 3 − x + (−7) > 6 what is x
3x+3-x+(-7)>6
combine like terms on left side
2x-4>6
add 4 to both sides 2x>10
x=10/2 = 5
x>5
How many radians are contained in the angle AOT in the figure? Round your answer to three decimal places
Answer:
1 radien = 57.3 degrees
Step-by-step explanation:
1 radien = 57.3 degrees
Find the product. (7 - 10x)2
Complete the series: 3760, 1880, 360, 180, 45,?
Simplify the expression
9−8b+6b
9−8b+6b
.
9−8b+6b=??
haha last one XD