The value of ac for the quadratic expression 9x^2 - 16 is -144. The value of b is 0, as it represents the coefficient of x, which is absent in the expression. Therefore, we do not need two numbers that multiply to ac and add to b; the expression is factored using the difference of squares as (3x + 4)(3x - 4).
Explanation:The polynomial 9x2 − 16 is a quadratic expression that can be factored using the difference of squares method. To answer the questions:
The value of ac is the product of the coefficient of x2 and the constant term, which in this case is 9 × (− 16) = − 144.The value of b in the standard form ax2 + bx + c is the coefficient of x, which is 0 since there is no x term in the original expression.To factor, we need two numbers that multiply to ac (which is − 144) and add up to b (which is 0). However, this step is not applicable as the polynomial is already in the form a2 − b2 and will be factored as a difference of squares.The factored form of the polynomial is (3x + 4)(3x − 4).Each week, Christian earns $x fixing bicycles and receives $10 as his allowance. To find how much he will earn in total over 2 weeks, Christian calculates: x + 10 + x + 10. What is another way Christian can calculate how much he will earn in total over the 2 weeks?
A. x + 10
B. 2x + 10
C. x + 20
D. 2(x + 10)
Christian can calculate his total earnings over 2 weeks by simplifying the expression x + 10 + x + 10 to 2(x + 10). This method combines his earnings from fixing bicycles and his allowance for each week. Therefore, the correct answer is D. 2(x + 10).
To calculate how much Christian will earn in total over 2 weeks, you can simplify the expression x + 10 + x + 10:
First, combine like terms for the amount he earns from fixing bicycles: x + x = 2x.Next, combine the constants for his allowance: 10 + 10 = 20.This gives us the total expression: 2x + 20.Rewriting this, you get 2(x + 10). Therefore, the correct answer is D. 2(x + 10).
A man drives from home to the store, shops, and then drives back home. Click on the graph until the graph that best represents the given statement appears.
Click the third graph (check the picture attached)
ExplanationRemember that [tex]speed=\frac{distance}{time}[/tex], so the line in the first part of the graph means that the man is driving his car at certain speed (different form zero) from home to the store. The horizontal graph in the middle of the graph means that he man is sopping at the store; therefore his driving speed is 0. The third part of the graph means that the man is driving again from the store to home.
Check the picture bellow to visualize it more easily.
The length of a rectangle is 3 inches more than the width. the perimeter is 30 inches. find the length and width.
Which is bigger 30% or 1/3
Please help me out!! ☮✌
180 = 93 +3x +18
180 =111 +3x
3x = 180-111
3x = 69
x = 69/3
x = 23
I need help with the following problem
Mr Webster is buying carpet for an exercise room in his basement the room will have an art of 230 square feet the width of the room is 12 1/2 what is the length
The length of Mr. Webster's exercise room is 18.4 feet, calculated by dividing the area (230 sq ft) by the width (12.5 ft).
To find the length of the room, we can use the formula for the area of a rectangle:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
Given that the area is 230 square feet and the width is 12 1/2 feet, we can plug these values into the formula:
[tex]\[ 230 = \text{Length} \times 12 \frac{1}{2} \][/tex]
To solve for the length, divide both sides by 12.5:
[tex]\[ \text{Length} = \frac{230}{12 \frac{1}{2}} \]\[ \text{Length} = \frac{230}{\frac{25}{2}} \]\[ \text{Length} = 230 \times \frac{2}{25} \]\[ \text{Length} = 18.4 \][/tex]
So, the length of the room is [tex]\( \boxed{18.4} \)[/tex] feet.
Match the following items.
1.) 2x + x + 4 = -17
2.) 3x + 4 = -17
3.) 3x = -21
4.) x = -7
Given
subtraction
combine like terms
division
The correct explanation for each expression are;
1. 2x + x + 4 = -17 Given
2. 3x + 4 = - 17 Combine like term.
3. 3x = - 21 Subtraction.
4. x = -7 Division.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2x + x + 4 = -17
Now, Solve the expression for x by using suitable property as;
⇒ 2x + x + 4 = -17
Combine like term;
⇒ 3x + 4 = - 17
Subtract 4 both side;
⇒ 3x + 4 - 4 = -17 - 4
⇒ 3x = - 21
Divide by 3;
⇒ x = - 7
Thus, The correct explanation for each expression are;
1. 2x + x + 4 = -17 Given
2. 3x + 4 = - 17 Combine like term.
3. 3x = - 21 Subtraction.
4. x = -7 Division.
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Jo is flipping a fair coin. If the coin is truly fair, how many times should it land on heads if he flips the coin 200 times
a coin has a 1/2 probability of landing on heads
so it should land on heads 1/2 of the time
1/2 of 200 = 100
Final answer:
With a fair coin, theoretical probability suggests that Jo should expect to land on heads roughly 100 times out of 200 flips. Actual results may vary slightly due to random chance, but should approximate 50 percent heads over a large number of trials.
Explanation:
If Jo is flipping a fair coin, on average, we would expect the coin to land on heads 100 times out of 200 flips. This expectation is based on the theoretical probability of getting heads, which is 0.5 or 50% for a fair coin. Therefore, if Jo flips the coin 200 times, the expected number of heads is calculated by multiplying the total number of flips by the probability of getting heads (0.5), which is 200 * 0.5 = 100.
However, it's important to note that while the theoretical probability suggests that Jo should get heads approximately 100 times, the actual result might be slightly more or slightly less due to random chance. The larger the number of flips, the closer the actual results are likely to get to the expected 50 percent heads, as demonstrated by the law of large numbers. But for any finite number of flips, there is always potential for some variation from the expected value.
If x2 + kx + 18 is factorable, what are the possible values of k?
Final answer:
The possible values of k in the factorable quadratic expression x^2 + kx + 18 can be determined by finding the factors of 18 that can be multiplied to obtain the constant term.
Explanation:
If the quadratic expression x^2 + kx + 18 is factorable, the possible values of k can be determined by finding the factors of 18 that can be multiplied to obtain the constant term.
The factors of 18 are:
1 and 18
2 and 9
3 and 6
Therefore, the possible values of k are -19, -10, -3, 3, 10, and 19.
The first aircraft has 73 more seats than the second aircraft. The third aircraft has 57 fewer seats than the second aircraft. If their total number of seats is 427 find the number of seats for each aircraft.
9/10 and -9/10 determine if parallel, perpendicular, or neither
A broken faucet leaks 1 gallon of water every 1 and1/3 months the amount of months that pass m varies directly with the amount of gallons leaked g. Find the equation that models this direct variation. How many months will it take for the faucet to leak 7 gallons of water?
Answer:
m = [tex]\frac{4}{3}[/tex]g, k= 9[tex]\frac{1}{3}[/tex] months
Step-by-step explanation:
Find an equation of the line with the given slope and containing the given point. express your answer in slope-intercept form.
chance to get brainliest What are the lower bound estimate and the upper bound estimate found by rounding to the greatest place? 764 – 241 A. lower bound 400 upper bound 600 B. lower bound 400 upper bound 500 C. lower bound 500 upper bound 600 D. lower bound 200 upper bound 800
The lower bound estimate and upper bound estimate are found by rounding 764 to 700 and 241 to 200, then subtracting to get 500. However, the mistake in the options seems that both the lower and upper bound estimates are 500. Based on the given options, the right answer should be option C with lower bound 500 and upper bound 600, albeit the upper bound estimate is not correctly represented.
Explanation:The lower bound and upper bound estimate of a calculation are found by rounding each number involved to the greatest place value then performing the calculation. In the case of the subtraction 764 - 241, the lower bound estimate will be calculated by underestimating both figures, and the upper bound will be calculated by overestimating.
Round down 764 to 700 and 241 to 200, then subtract: 700 - 200 = 500.Round up 764 to 800 and 241 to 300, then subtract: 800 - 300 = 500.Therefore, both the lower bound estimate and the upper bound estimate are 500 and the correct option is C. lower bound 500 upper bound 600
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Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 2 inches, and the larger gear has a radius of 8 inches.
What it looks like: two circles touching at one point. Larger circle has radius of 8 inches. Smaller circle has radius of 2 inches.
Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation? Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear? Show all work.
if a quadrilaterals diagonals bisect its vertices, what kind of quadrilateral must it be?
A - Rhombus
B - trapezoid
C - rectangle
D - parallelogram
Consider points R, S, and T. Which statement is true about the geometric figure that can contain these points? No line can be drawn through any pair of the points. One line can be drawn through all three points. One plane can be drawn so it contains all three points. Two planes can be drawn so that each one contains all three points.
Answer: The answer is (c) One plane can be drawn so that it contains all three points.
Step-by-step explanation: We are given three points R, S and T in a coordinate plane. Considering all these three points to be distinct and non-collinear, we can draw the following conclusions.
(i) Since each pairs of points. i.e., (R,S), (S,T) and (T,R) give rise to a straight line when joined, so option (a) is incorrect.
(ii) Through any two given points, we can always draw a line. If we consider a third point and since we are dealing with non-collinear points, so one line cannot be drawn through three points.
(iii)We can always draw a line by joining two points and when we join the two ends of the line to a third point which does not lie on the line, it will give rise to a plane. So, option (c) is correct.
(iv) We cannot draw two different planes through three given points. If we do so, the new plane will coincide with the previous one. This proves that option (d) is not correct.
Please see the attached figure, where P, Q and R are three non-collinear points. They give rise to a plane.
Thus, the correct option is (c).
A runner wants to run 10.0 km. she knows that her running pace is 7.5 miles per hour. how many minutes must she run?
A runner must run for 50 minutes to cover the distance of 10 kilometers.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
here,
A runner wants to run 10.0 km. she knows that her running pace is 7.5 miles per hour.
7.5 miles = 12 kilometers
Speed = 12 kilometers/hours
1 hour = 60 minutes
Speed = 12 / 60 kilometers per minute
Speed = 0.2 kilometers per minute
Time = distance/speed
Time = 10 / 0.2
Time = 50 minutes
Thus, A runner must run for 50 minutes to cover the distance of 10 kilometers.
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5x^2+-8x^2 how to simplify
Describe how to derive the quadratic formula from a quadratic equation in standard form. edginuity
Answer:
The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.
Step-by-step explanation:
LeAnn wants to giftwrap a present she got for her little brother. How many square inches of giftwrap will be needed to cover a box that is 4in x 6in x 2in? In your final answer, include all of your calculations.
there are 6 sides to a cube
2 are 4*6 = 24*2 =48
2 are 4*2 = 8*2 = 16
2 are 6*2 = 12*2 =24
48 +16 +24 = 88 square inches total
Is the number of bottles of juice sold at lunch continuous or discrete?
The equation of a line is x + 4y = 15.
What is the y-intercept of the line?
415
15
−15
154
Answer:
Option D.
Step-by-step explanation:
Y-intercept form of the equation of a line is given by y = mx + c
Where m = slope of the line
c = y-intercept
Given equation of a line is x + 4y = 15
We will transform this equation into the y intercept form first.
x + 4y = 15
4y = 15 - x
y = [tex]-\frac{x}{4}+\frac{15}{4}[/tex]
Therefore, y - intercept of this equation will be c = [tex]\frac{15}{4}[/tex]
Option D will be the answer.
1.3 divided by 0.0338 step by step please
What is the algebraic expression for the quotient of a number and nine
Let f(x) = 3x + 5 and g(x) = x2. Find g(x)/f(x) and state its domain.
the product of 15 and 7 added to 8
Final answer:
To calculate the requested expression, multiply 15 by 7 to get 105, and then add 8 to this product to find the sum, which is 113.
Explanation:
The question asks to calculate the result of the mathematical expression where a product is first found by multiplying 15 and 7 and then that product is added to 8. To solve this, you need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, calculate the product of 15 and 7 to get 105.
Next, add this product to 8 to find the final result.
So, 105 + 8 equals 113.
The correct answer to the question is 113, which is the sum of the product of 15 and 7, with 8 added.
Fill in 2 to 10 so every row and column adds up to 18
It is predicted that the population of a particular state will double every 25 years. a) Determine the annual and monthly growth rates. Express your answers as percents. b) Determine the continuous growth rate per year. Express your answer as a percent.
The annual growth rate is 41.4% and the monthly growth rate is 3.45%. The continuous growth rate per year is 2.77%.
Explanation:To determine the annual growth rate, we need to find the growth factor by taking the square root of the doubling factor. Since the population is predicted to double every 25 years, the annual growth rate would be the square root of 2, which is approximately 1.414. To express it as a percentage, we can subtract 1 from the growth factor and multiply by 100, resulting in an annual growth rate of 41.4%.
The monthly growth rate can be calculated by dividing the annual growth rate by 12. In this case, the monthly growth rate would be approximately 3.45%.
To determine the continuous growth rate per year, we use the formula: r = ln(2)/t, where r is the continuous growth rate and t is the doubling time in years. In this case, the continuous growth rate would be ln(2)/25, which is approximately 0.0277. Multiplying this by 100, we get a continuous growth rate per year of 2.77%.
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