Answer: x = {-1, -3, 2}
Step-by-step explanation:
x³ + 2x² - 5x - 6 = 0
Use the rational root theorem to find the possible roots: ±1, ±2, ±3, ±6
Use Long division, Synthetic division, or plug them into the equation to see which root(s) work (result in a remainder of zero).
I will use Synthetic division. Let's try x = 1
1 | 1 2 -5 -6
| ↓ 1 3 -2
1 3 -2 -8 ← remainder ≠ 0 so x = 1 is NOT a root
Let's try x = -1
- 1 | 1 2 -5 -6
| ↓ -1 -1 6
1 1 -6 0 ← remainder = 0 so x = -1 is a root!
The coefficients of the reduced polynomial are: 1, 1, -6 --> x² + x - 6
Factor: x² + x - 6
(x + 3)(x - 2)
Set those factors equal to zero to solve for x:
x + 3 = 0 --> x = -3
x - 2 = 0 --> x = 2
Using Synthetic Division and Factoring the reduced polynomial, we found
x = -1, -3, and 2
Identify each of the following variables as qualitative or quantitative. a. Favorite baby name b. Color of car c. Storage space on a computer drive d. Electrical current a. Is the variable qualitative or quantitative? Why? A. Favorite baby name is a qualitative variable. Its values are numerical. B. Favorite baby name is a quantitative variable. Its values are numerical. C. Favorite baby name is a qualitative variable. Its values are not numerical. D. Favorite baby name is a quantitative variable. Its values are not numerical.
Answer:
C. Favorite baby name is a qualitative variable. Its values are not numerical.
Color of car is a qualitative variable. Its values are not numerical.
Storage space on a computer drive is a quantitative variable. Its values are numerical.
Electrical current is a quantitative variable. Its values are numerical.
Step-by-step explanation:
A qualitative variable is a variable that is categorical and isn't numerical.
For example, your favourite baby names and colours are categorical, they cannot be measured on a numerical scale
Quantitative Variable are variables that can be measured on a numeric scale. Ordinal, interval and ratio scales are quantitative scales.
Storage space can be measured on a numeric scale e.g. the storage space has 400 GB
Electric current can be measured on a numeric scale e.g. eclectic current is 50 volts
Consider the following exam question and student solution. Determine whether the solution is correct. If it is not correct, write a note to the student explaining why it is wrong and give a correct solution. Exam question: You can buy a 56 pound bag of flour for $9 or you can buy a 1-pound bag for .39 cents. Compare the per pound cost for the large and small bags. Student solution: The large bag price is 56 divided by 9=6.22 per pound, which is much more than the 39 cent per pound price of the small bag.
Answer:
actually a 56 pound bag cost =9
so one pound bag cost =9/56=0.16 cents
Step-by-step explanation:
Hotel manager salary and 61,410 which is a 15 increase over the previous year salary what was the previous year salary
1. What does the slope represent of a graph? (Definition
of Slope)
help!
Answer:
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.
Step-by-step explanation:
Choose the rate of change (slope) to match the line.
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B
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Review prog
Math plzzzzz help
Answer:
B. [tex] -\frac{3}{2} [/tex]
Step-by-step explanation:
Rate of change/slope is given as [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use the coordinate pairs of any two points on the slope/line.
Let's use the following coordinates pairs:
[tex] (-2, 4) = (x_1, y_1) [/tex]
[tex] (0, 1) = (x_2, y_2)
Plug in the values into the formula, [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]:
[tex] m = \frac{1 - 4}{0 - (-2)} [/tex]
[tex] m = \frac{-3}{0 + 2} [/tex]
[tex] m = \frac{-3}{2} [/tex]
[tex] m = -\frac{3}{2} [/tex]
What is non-collinear?
Answer:
Non-colinear means that three given points do not have a single line connecting all 3 of the points.
the radius of a circular playground is 77 metre.Calculate the distance covered by a runner in 5 complete rounds around the ground.
Answer:
2419.0265 meters
Step-by-step explanation:
To find the answer you must first find the circumference of the circle. The circumference formula is C = 2 \pi r. So if you plug in 77 you get 483.8053. Then multiply that by 5 and you will have your final answer.
Polygon Q is a scaled copy of polygon P using a scale factor of 1/2. Polygon Q's area is what fraction of Polygon P's area.
Answer: Polygon Q's area is 1/4 of Polygon P's area
======================================================
Explanation:
Imagine we had a square with side length 8. The area of this square is 8*8 = 64.
Now let's reduce each side of the square by the scale factor 1/2. So each new side is 8*(1/2) = 4. The area of this smaller square is 4*4 = 16.
Comparing the new area (16) to the old one (64), we see that the new area is 16/64 = 1/4 of the old area.
In other words,
new smaller area = (1/4)*(old larger area)
So this is one example to see why (1/2)*(1/2) = 1/4 is the area scale factor based on the linear scale factor of 1/2. In short, (1/2)^2 = 1/4. Whatever the original scale factor is, square it and you'll get the area scale factor.
please help me guys im lost
Answer:
D. BC ≅ EF
Step-by-step explanation:
ASA means you're trying to show congruence by showing two angles A..A and the segment between them ..S.. are congruent. The figure shows two congruent angles. What remains is to show the segments between are congruent.
__
In ∆ABC, the marked angles are B and C, so the segment between them is BC.
In ∆DEF, the marked angles are E and F, so the segment between them is EF.
These are the segments that need to be shown congruent if you're using ASA.
BC ≅ EF
If f(x)=3x+19 find f (-3a-2)
Answer: f(-3a-2)=-9a+13
Step-by-step explanation:
To find f(-3a-2), we plug in -3a-2 into f(x).
f(-3a-2)=3(-3a-2)+19 [distribute]
f(-3a-2)=-9a-6+19 [combine like terms]
f(-3a-2)=-9a+13
Now, we know that f(-3a-2)=-9a+13.
537²×15.90²=74²
I know this looks like pythagorean theorem. But how do they teach this to high schooler?
Answer:
It looks like this question is not solvable. So, if this is absolutely correct, write "no solution".
Step-by-step explanation:
Below is the first step to attempt solving the equation.
The little twos at the top of each number are called exponents. This means a number times itself.
So,
537*537=288,369
15.9*15.9=252.81
74*74=5476
Now, take the 288,369*252.81 to get a total of 72,902,566.89 .
Since this answer is (obviously) not equal to the 5476 on the other side, the two are not equal.
Here's how you'd work it out on paper to show it isn't solvable.
(537*537)*(15.9*15.9)= (74*74)
(288,369)*(252.81)= 5476
72,902,566.89 ≠5476
So the answer would be:
Not solvable.
I NEED HELP ASAP!!!!!!!!
Answer:
you can say how u shop a discount stores like shein and shop for clearance. You can also say that u used to spend money to keep up with the trends but u realized u needed the money for other important things, so u stopped
Step-by-step explanation:
Describe the difference between the variance between samples MSB and the variance within samples MSW
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
Generally
[tex]MS_B[/tex] stand for Mean Square Between which the mean calculated based on the difference between the sample means
While
[tex]MS_W[/tex] stands for Mean Square Within which the mean calculated based on the difference between the elements within the set(group)
Thus
The [tex]MS_B[/tex] measures the differences related to the treatment given to each sample. The [tex]MS_W[/tex] measures the differences related to entries within the same sample.
Factor the given polynomial.
9z^2 +15z +4
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. 9z^2 +15z +4=
B.The polynomial is prime.
Answer:
(3z + 1)(3z + 4)
Step-by-step explanation:
[tex]9 {z}^{2} + 15z + 4 \\ = 9 {z}^{2} + 3z + 12z+ 4 \\ = 3z(3z + 1) + 4(3z + 1) \\ = (3z + 1)(3z + 4)[/tex]
What is the value of y?
Answer:
y = 40
Step-by-step explanation:
The sum of the angles of a triangle are 180 degrees
y+10 + 2y +50 = 180
3y+60 = 180
Subtract 60 from each side
3y+60-60 = 180-60
3y = 120
Divide each side by 3
3y/3 = 120/3
y = 40
3
Which expression is closest in value to 5.66?
Let's consider the standard and usually used value of irrational numbers given in the question.
It is asked to see which is closed to 5.66So, let's see the options:
A) GiveN:
[tex] \dfrac{\pi}{2} + \pi[/tex]
Let consider π = 3.14
[tex] \dfrac{3.14}{2} + 3.14[/tex]
[tex]1.57 + 3.14[/tex]
[tex]4.71 \: (approx.)[/tex]
B) GiveN:
[tex]2\pi - 1[/tex]
Here also, let's consider the value be 3.14
[tex]2 \times 3.14 - 1[/tex]
[tex]6.28 - 1[/tex]
[tex]5.28 \: (approx.)[/tex]
C) GiveN:
[tex]4 \sqrt{2} [/tex]
Let's consider the value of √2 be 1.414
[tex]4 \times 1.414[/tex]
[tex]5.6516 \: (approx.)[/tex]
D) GiveN:
[tex]8 - \sqrt{3} [/tex]
Let's consider the value of √3 be 1.732
[tex]8 - 1.732[/tex]
[tex]6.268 \: (approx.)[/tex]
So, we can see that we have got the approximate value of all the numericals, and the closest to 5.66 is 5.6516 which is the answer of Option C.
So, Correct answer is C
#CarryOnLearning
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Isaac is making soft pretzel nuggets. His recipe says that, after he makes the dough, he should divide it into 8 equal pieces. Then, he needs to roll each piece into a 2-foot-long rope and cut it into nuggets. If he decides to make each pretzel nugget 1 inch long, how many can he make in all?
Answer:
The answer to your question is 192 pretzels
Step-by-step explanation:
Data
number of pieces = 8
length of each piece = 2 ft
length of each pretzel = 1 in
number of pretzels = x
Process
1.- Convert ft to in
1 ft --------------- 12 in
2 ft --------------- x
x = (2 x 12) / 1
x = 24 ft
2.- Divide the length of each piece by the length of each pretzel
24/1 = 24 pretzels per piece
3.- Multiply the number of pretzels per the number of pieces
24 x 8 = 192 pretzels
Could I get some help on these please? Will give points.
Answer:
X=-4, Y=22, idk about the CBD
Step-by-step explanation:
4y+2=90 degrees
subtract 2 on both sides you would get
4y=88 divide 4 with 88 and get 22
solve both X's so 5x+6=3x-2
i would subtract 3x first so i can get
2x+6=-2
then subtract 6 on both sides so you would have
2x=-8 divide -8 with 2 and get -4
Chance left the park traveling 10 mph. Then, 2 hours later, Malik left traveling the same direction at
14 mph. How long until Malik catches up with Chance?
Answer:
8 hours
Step-by-step explanation:
after 8 hours chance will have traveled 100 miles and malik will have traveled 102 miles.
10 POINTS : What is the solution to the equation 3/5x-6=-1/6x+7, rounded to three decimal places?
Answer:
x = 16.957
Step-by-step explanation:
(3/5)x - 6 = (-1/6)x + 7
Add (1/6)x to both sides. Add 6 to both sides.
(3/5)x + (1/6)x = 7 + 6
(18/30)x + (5/30)x = 13
(23/30)x = 13
Multiply both sides by 30/23.
x = 13/1 * 30/23
x = 390/13
x = 16.957
5% of what number is 90?
Hey there!
ANSWER: [tex]4.5 \text { and }1800[/tex]
EXPLANATION:5% of what is 90?
If you want to find 5% of what is 90, you can try doing 90/5%.
[tex]90/5[/tex]%[tex]=1800(ANSWER)[/tex]
To get the decimal form, you can do 90*5%.
[tex]90*5[/tex]%[tex]=4.5(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
[tex] \sqrt{2k ^{2} + 17 } - x = 0[/tex]
If k>0 and x=7 in the equation, what is the value of k?
Answer:
[tex]k=4[/tex]
Step-by-step explanation:
So we have the equation:
[tex]\sqrt{2k^2+17}-x=0[/tex]
Where:
[tex]k>0\text{ and } x=7[/tex]
And we want to find k.
Firstly, let's substitute 7 for x. So:
[tex]\sqrt{2k^2+17}-7=0[/tex]
Now, we can solve for k. Add 7 to both sides:
[tex]\sqrt{2k^2+17}=7[/tex]
Square both sides:
[tex]2k^2+17=49[/tex]
Subtract 17 from both sides:
[tex]2k^2=32[/tex]
Divide both sides by 2:
[tex]k^2=16[/tex]
Take the square root of both sides:
[tex]k=\pm\sqrt{16}[/tex]
Evaluate:
[tex]k=\pm 4[/tex]
Remember that we are told k>0. In other words, k must be positive. So, we can ignore the negative answer, giving us:
[tex]k=4[/tex]
So, the value of k is 4.
And we're done!
10 + (-4) Show Example
Answer:
6
Step-by-step explanation:
10
-6
=6
Adding a negative number is simply subtraction.
10-4=6
The sum of three consecutive natural numbers is 540, find the numbers.
Answer:
179, 180, 181
Step-by-step explanation:
a +a +1 +a +2 =540
3a +3 =540
3a =540 - 3
3a=537
a=537 :3
a=179 (the first number
b=179 +1 =180 (the second number
c=179 +2 =181 (the third number
115% of what number is 138?
Answer:
120
Step-by-step explanation:
120 * 1.15 = 138
Answer:
120
Step-by-step explanation:
115% of the number 120 is 138
please help me it is easy,
Answer:
i think id say it is 10.5 i might be wrong though
Step-by-step explanation:
Answer:
14 lemonade serving
Step-by-step explanation:
1½+3=4½
In 4 liters we get 12 ⅓serving of lemonade
In ½ we get 1 serving of lemonade from the ½ we remain with to ⅙liters so we still add that as a serving
Total =12+1+1=14
how to solve |-6y|-9>-1
Answer:
y < -4/3 or y > 4/3
Step-by-step explanation:
|-6y| -9 > -1Since this is an absolute value inequality, we need two equations to set up to solve for y1st equation:-6y - 9 > -12nd equation:6y - 9 > -1Solve both equations:-6y-9>-1-6y > 8y < -4/36y -9 > -16y > 8y > 4/3
Martha has 90 red tiles and 72 yellow tiles. She wants to place the tiles in rows using one color for each row without having any tiles left
over. Each row must have the same number of tiles. What is the greatest number of tiles Martha can use for each row?
Answer:
18 tiles
Step-by-step explanation:
If she wants to find the greatest number of tiles for each row, she will want to use up all the tiles. This means we are looking for the highest common factor between the numbers 90 and 72, so all the tiles can be used up in the rows. In order to find the highest common factor we multiply together all the common prime factors between the two:
90 has the prime factors 2x3x3x5
72 has the prime factors 2x2x2x3x3
The prime factors that are common to both are 2, 3 and 3 which multiply together to get:
2x3x3 = 18
The greatest number of tiles Martha can use for each row is 18 and would result in 5 rows of red tiles and 4 rows of yellow tiles.
Hope this helped!
1. Given a right triangle the first angle is ten degrees more than three times the degree measure of the second angle and the third angle is the right angle. What is the angle measurement of the first angle? Doint)
Answer:
The first angle is [tex]70^{o}[/tex].
Step-by-step explanation:
Let the measure of the second angle be represented by [tex]x^{o}[/tex].
Thus, the first angle = [tex](3x+10)^{o}[/tex]
Third angle = [tex]90^{o}[/tex]
Sum of angles in a triangle = [tex]180^{o}[/tex]
So that;
[tex]x^{o}[/tex] + [tex](3x+10)^{o}[/tex] + 90 = [tex]180^{o}[/tex]
[tex]x^{o}[/tex] + [tex]3x^{o}[/tex] + [tex]100^{o}[/tex] = [tex]180^{o}[/tex]
[tex]4x^{o}[/tex] = [tex]180^{o}[/tex] - [tex]100^{o}[/tex]
[tex]4x^{o}[/tex] = [tex]80^{o}[/tex]
divide both sides by 4 to have;
[tex]x^{o}[/tex] = [tex]20^{o}[/tex]
The first angle = [tex](3x+10)^{o}[/tex]
= ( 3 x 20 + 10)
= 60 + 10
= [tex]70^{o}[/tex]
Therefore, the first angle is [tex]70^{o}[/tex].
Suppose that the overall probability of living to age 70 is 0.62 and that the overall probability of living to age 80 is 0.23. If a person reaches their 70th birthday, what is the probability that they will live to age 80?
Given :
P( X = 70 ) = 0.62 .
P( X = 80 ) = 0.23 .
To Find :
We need to find If a person reaches their 70th birthday, what is the probability that they will live to age 80 .
Solution :
We need to find :
[tex]P(X=70 | X=80 )[/tex]
We know ,
[tex]P(x,y ) = \dfrac{P(x)}{P(y)}[/tex]
So ,
[tex]P(X=70 | X=80 )=\dfrac{P(X=80)}{P(X=70)}\\\\=\dfrac{0.62}{0.23}=0.371[/tex]
Hence , this is the required solution .