Answer: The correct option is (D) (x - 3).
Step-by-step explanation: Given that a polynomial function has a zero at x = 3.
We are to select the correct expression that must be a factor of the polynomial.
FACTOR THEOREM : The theorem states that if x = a is a zero of a polynomial p(x), then (x - a) will be a factor of the polynomial p(x).
In case of our given polynomial, since x = 3 is a zero of the polynomial, so by factor theorem, we can say that
(x - 3) is a factor of the given polynomial.
Thus, the required factor is (x - 3).
Option (D) is CORRECT.
what is 475.53 minus 67.37
Using CPCTC, name the congruent parts of ΔABC & ΔQRS that are not labeled as congruent in the diagram.
A. AB=QR,BC=RS,
B.AC=QS,
C.AC=QS,BC=RS,
D. AB=QR,BC=RS,
Answer: A. AB=QR,BC=RS
Step-by-step explanation:
The congruence property of congruence triangle CPCTC says that the corresponding parts of congruent triangles are congruent.
From the given figure, we have
[tex]\angle{A}\cong\angle{Q}\\\angle{C}\cong\angle{S}[/tex]
[tex]\overline{AC}=\overline{QS}[/tex]
The other congruent parts in the triangle.
[tex]\overlien{AB}\cong\overlien{QR}[/tex] [∵ AB corresponds QR]
[tex]\\\\\overlien{BC}\cong\overlien{RS}[/tex] [∵BC corresponds RS]
Robert makes $3.50 per hour working at a convenience store. If he gets a bonus of $25 of this week how many hours must he work to make at least $165?
Choose the equation below that represents the line that passes through the point (2, 4) and has a slope of 3.
Answer
y - 4 = 3(x - 2)
y + 2 = 3(x + 4)
y + 4 = 3(x + 2)
y - 2 = 3(x - 4)
...?
The correct equation for the line that passes through the point (2, 4) with a slope of 3 is 'y - 4 = 3(x - 2)' using the point-slope form of a linear equation.
The equation that represents the line passing through the point (2, 4) with a slope of 3 is y - 4 = 3(x - 2). To find the equation of a line given a point and a slope, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.
Since the line must pass through (2, 4) and the slope (m) is 3, we plug these values into the point-slope form to get the correct equation.
richerds checkbook awnsers as of 02/19
Eight people, female and male, were surveyed about their choice of car color, green or blue. The table shows the choices they made.
Which two-way table correctly compares the categorical data?
Person Gender
(male or female) Car color
(green or blue)
1 female green
2 female green
3 female blue
4 male blue
5 male green
6 female blue
7 male blue
8 male blue
A.
Green Blue
Female 4 5
Male 4 3
B.
Green Blue
Female 2 1
Male 2 3
C.
Green Blue
Female 4 4
Male 3 1
D.
Green Blue
Female 2 2
Male 1 3
The correct two-way table for comparing the car color choices of eight surveyed individuals by gender is Option D, which shows 2 females choosing green and 2 blue, while 1 male chose green and 3 chose blue.
The question is about analyzing a two-way table that compares categorical data: gender and car color preferences. To find the correct table, we need to tally the choices made by each person based on the information given and compare it to the options provided in the answer choices. By counting the number of times each gender chose each color, we can determine the accurate representation of the data.
For females, 2 chose green and 2 chose blue.
For males, 1 chose green and 3 chose blue.
Given this information, the correct two-way table that compares the categorical data is:
Option D.
Green Blue
Female 2 2
Male 1 3
This table correctly captures the car color preferences by gender among the eight people surveyed.
Write three ratios equal to 7/35? A 1/7, 2/14, 3/21 B 5/7, 10/7, 15/7 C 7/35, 7/40, 7/45 D 1/5, 2/10, 3/15 I think it is C or D.
Answer:
[tex]\frac{1}{5} ;\frac{2}{10} ;\frac{3}{15}[/tex]
Step-by-step explanation:
To find the three ratios we only have to find the most simple ratio of [tex]\frac{7}{35}[/tex], and then find the other ratios that are equal to it.
So, [tex]\frac{7}{35} = \frac{1}{5}[/tex]
Also, [tex]\frac{1}{5} =\frac{2}{10}[/tex], by multiplying by two each part of the fraction.
Similarly, [tex]\frac{3}{15} = \frac{1}{5}[/tex], by multiplying by three.
Therefore, comparing all these ratios, all are the same, they are equal to [tex]\frac{1}{5}[/tex]. So, the option that correctly has these choices is D.
2x+y=3, 5x-2y=12 how to solve this
The slope of a line is 0, and the y-intercept is 6. the equation, written as y = 6, represents a horizontal line. true false
The answer is: true.
Here's why:
A slope of 0 indicates a horizontal line, meaning there's no change in y-value as x changes.
A y-intercept of 6 means the line intersects the y-axis at the point (0, 6).
The equation y = 6 represents a constant y-value for any x, which indeed depicts a horizontal line that intersects the y-axis at (0, 6).
Therefore, both the slope and the equation confirm that the line is horizontal.
10x+2y=10 in slope intercept form
What has the sum of 20 but the difference is 8?
At which angle will the hexagon rotate onto itself?
Answer:
The correct answer is: 60°
Step-by-step explanation:
Rotational symmetry is a type of symmetry, in which an object returns back to its original shape after rotation at an angle of 360°/n about a fixed point.
A hexagon is a regular polygon that has six edges and vertices. It has six internal angles, 120° each.
Since there are 6 equal edges, therefore, the hexagon will rotate onto itself after every rotation at an angle of: 360°/n = 360°/6 = 60°
At a local University 54.3% of incoming first-year students have computers. If 3 students are selected at random, find the following probability. A) At least one has a computer
B) None have computers
Which of the following expressions is this one equivalent to?
(x^4+2x^3-x-2)÷(x^3-1)
A. 2x-5- (3/x^3-1)
B. x^2+x+1
C. x+2
D. x^2+3x+2
...?
Answer: x+2. The answer is C.
Step-by-step explanation:
A candy store keeps track of its sales during the month of October. Below is the number of sales for the first, second, third and fourth week of the month.
Week 1 ; 2 ; 3 ; 4
Candy Sales 97 ; 168 ; 259 ; 375
Which graph could represent the data shown below?
From the attached diagram you can see that regression that best fits given data is quadratic (not linear).
option 1 is false, because it gives linear regression;option 2 is true, it gives graph, similar to quadratic parabola;options 3 and 4 are false, because graphs are decreasing.Answer: correct choice is B.
The graph of the given values is required.
Option B is correct.
The points are
[tex](1,97)[tex]
[tex](2,168)[/tex]
[tex](3,259)[/tex]
[tex](4,375)[/tex]
Let us find if the points are in the form of a line by finding the slope.
[tex]\dfrac{168-97}{2-1}=71[/tex]
[tex]\dfrac{259-168}{3-2}=91[/tex]
[tex]71\neq 91[/tex]
So, the function is not linear.
Therefore, A and C are incorrect.
Also the function is not decreasing so option D is also eliminated.
Hence, option B is correct.
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Simplify i³⁸. [i=√(-1)]
The 38th power, [tex]i^{38[/tex] simplifies to -1.
To simplify [tex]\( i^{38 \),[/tex] you can start by recognizing the pattern that powers of i repeat every four terms. This means that [tex]\( i^{4\),[/tex] equals 1, [tex]\( i^{8 \),[/tex] also equals 1, and so on. Therefore, [tex]\( i^{38 \),[/tex]can be simplified as follows:
[tex]\[ i^{38} = i^{4 \cdot 9 + 2} \][/tex]
Since [tex]\( i^4 \)[/tex] is equal to 1, we have:
[tex]\[ i^{38} = (i^4)^9 \cdot i^2 = 1^9 \cdot (-1) = -1 \][/tex]
So,[tex]\( i^{38} \)[/tex] simplifies to -1.
Complete question is:
Simplify i³⁸. [i=√(-1)]
The price of a pair of shoes is $52. The price is 15% lower than last week. What was the price of the shoes last week? Round your answer to the nearest cent. Enter your answer in the box. $
The original price of the shoes can be found by dividing the current price, $52, by 0.85, which yields an original price of approximately $61.18.
The current price of a pair of shoes is $52, which is 15% lower than it was last week. To find the original price, you can set up an equation where the original price minus 15% of the original price equals the current price of $52.
Let x represent the original price. The equation is then x - 0.15x = $52. Simplify this to 0.85x = $52. Divide both sides by 0.85 to solve for x.
x = $52 / 0.85
x = $61.18
Therefore, the price of the shoes last week was approximately $61.18.
A cyclist rides his bike at a rate of 8 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 2 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
B is between A and C, AB = 13.7 and BC = 8.3. Find AC.
10: A bin of bolts at the hardware store contains 7-dozen bolts when full. The stock clerk is supposed to reorder bolts when the bin is 1⁄6 full. How many bolts are in the bin when it’s time to reorder?
Solve: 3x-3y=3
y=-5x-17
The simultaneous equations 3x-3y=3 and y=-5x-17 can be solved using substitution, resulting in the solution x = -8/3 and y = -11/3.
To solve the simultaneous equations 3x-3y=3 and y=-5x-17, we can use substitution or elimination. Substitution is straightforward since we already have y expressed in terms of x in the second equation. We can substitute y=-5x-17 into the first equation:
3x - 3(-5x - 17) = 33x + 15x + 51 = 318x = -48x = -48 / 18x = -8/3Now, plug x back into y=-5x-17 to find y:
y = -5(-8/3) - 17y = 40/3 - 17y = 40/3 - 51/3y = -11/3The solution to the system of equations is x = -8/3 and y = -11/3.
Solve the equation sin theta = 0.3 to the nearest tenth. Use the restrictions 90degrees < theta < 180degrees.
A)
θ=107.5
B)
θ=162.5
C)
θ=197.5
D)
θ=17.5
You buy 40 of your favorite songs from a Web site that charges $0.97 for each song. What is the cost of 40 songs?
Parallelogram ABCD is dilated to form parallelogram EFGH. Side BC is proportional to side CD.
What corresponding side is proportional to segment FG?
A new game is being constructed where the game board is going to have 8 rows with 10 spaces in each row. What is the smallest game board that can be made?
Answer: There can be made 40 smallest game boards.
Step-by-step explanation:
Since we have given that
Number of rows = 8
Number of spaces in each row = 10
we need to find the smallest game board that can be made.
As we know that For Smallest we always find "L.C.M" because L.C.M. stands for least common multiple.
So, L.C.M. of 8 and 10 = 40
Hence, there can be made 40 smallest game boards.
miguel is making smoothies out of yogurt and juice to serve his friends, and he needs to make 12 cups. the ratio of yogurt to juice is 2 cups to 1 cup. how much yogurt will he use
Answer:
Eight cups of yogurt will be used.
Step-by-step explanation:
Let cups of yogurt used in 12 cups of smoothies be x
Cups of juice used in 12 cups of smoothies = 12- x
The ratio of yogurt to juice is 2 cups to 1 cup that is:
[tex]\frac{Yogurt}{Juice}=\frac{2}{1}[/tex]
Ratio will be maintained through out 12 cups of smoothies:
[tex]\frac{Yogurt}{Juice}=\frac{2}{1}=\frac{x}{12-x}[/tex]
[tex]2(12-x)=1(x)[/tex]
[tex]24-2x=x[/tex]
[tex]24=3x[/tex]
x = 8
Eight cups of yogurt will be used.
If f(x) and f^-1(x) are inverse functions of each other and f(x)=2x+5, what is f^-1(8)
Answer:
[tex]\text{The value of }f^{-1}(8)\text{ is }\frac{3}{2}[/tex]
Step-by-step explanation:
Given the function
[tex]f(x)=2x+5[/tex]
[tex]\text{we have to find the value of }f^{-1}(8)[/tex]
First we have to find the inverse
Step 1: Put f(x)=y, the equation becomes
[tex]y=2x+5[/tex]
Step 2: Replace x to y and y to x, we get
[tex]x=2y+5[/tex]
Step 3: Solve for y and then replace it with [tex]f^{-1}x[/tex]
[tex]x-5=2y[/tex]
[tex]y=\frac{x-5}{2}[/tex]
[tex]f^{-1}(x)=\frac{x-5}{2}[/tex]
Now substitute x=8, we get
[tex]f^{-1}(8)=\frac{8-5}{2}=\frac{3}{2}[/tex]
[tex]\text{hence, the value of }f^{-1}(8)\text{ is }\frac{3}{2}[/tex]
The polynomial x3 + 8 is equal to
(x + 2)(x2 – 2x + 4).
(x – 2)(x2 + 2x + 4).
(x + 2)(x2 – 2x + 8).
(x – 2)(x2 + 2x + 8)
Answer:
A
Step-by-step explanation:
other guy said it and I got it right.
y is directly proportional to x^2. It is known that y=10 for a particular value of x. Find the value of y when the value of x is halved
...?
If y is directly proportional to x^2, when x is halved, y becomes 0.25 times its original value. Given the original value of y is 10, when x is halved, the new y is 2.5.
Explanation:When we say that y is directly proportional to x^2, it means there exists a constant of proportionality (let's call this 'k') such that the equation y = k*(x^2) always holds. From the problem, we know that y=10 for a certain x, let's square this x sometimes referred as x2 (we could say [tex]x2 = (x^1.5)^2).[/tex]
If x is halved, the new x which we can call [tex]x1 = 0.5*x2[/tex], then substitute x1 in the equation of direct proportion we get [tex]y1 = k*(0.5 *2)^2 = y*0.25[/tex], this is because (0.5)^2 is 0.25. So, the new y when x is halved (y1) will be 0.25 as much as the original y. Therefore, if your initial y was 10, your new y would be y1 = 10*0.25 which equals 2.5.
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whats 3.428571429 into fraction ...?