Solution:
Given that equation is:
[tex]x^2 - kx + 28 = 0[/tex]
Roots are:
[tex]\alpha\\\\\alpha + 3[/tex]
To find: value of x
The general quadratic equation is:
[tex]ax^2 + bx + c = 0[/tex]
[tex]\text{ Product of roots } = \frac{c}{a}\\\\\text{ Sum of roots } = \frac{-b}{a}[/tex]
From given,
[tex]x^2 - kx + 28 = 0[/tex]
a = 1
b = -k
c = 28
Therefore,
[tex]Product\ of\ roots = \frac{28}{1} = 28[/tex]
[tex]Sum\ of\ roots = \frac{-k}{1} = -k[/tex]
Given roots are:
[tex]\alpha\\\\\alpha + 3[/tex]
Therefore,
The two roots are two numbers whose difference is 3 and whose product is 28
Those two roots are 4 and 7 or -4 and -7
Then, sum of roots are:
4 + 7 = 11
-4 - 7 = -11
Therefore, the possible values of k are -11 and 11
What is 2 plus 2????
Answer:
4
Step-by-step explanation:
Add 2 And 2, quite Simple
2 + 2 = 4
Hope this helps >.>
Answer:
4
Step-by-step explanation:
[tex]2+2\\Check:4-2=2\\[/tex]
Assessment started: undefined. Item 1 Rosa buys a bag of cat food for $6.75 and a pack of cat treats for $1.89. How much money does Rosa spend altogether? Enter your answer in the box
Answer:
8.68?
Step-by-step explanation:
adding them together just like that she buys cat food 6.75+ 1.89 for cat treats wouldn't thw be right? unless your needing tax as well and that's typically 10cents to ever dollar you spend
Answer:
The answer is 8.64
Step-by-step explanation:
It is decimals not actually cash so there is no tax, Plus I took the K-12 test and got it right!
If x^3 - 5x - 4x + 20 is going to factor, then one of these combinations is going to “work”, that is, the polynomial will divide evenly and give f(k) = 0 according to the Factor Theorem. So the best thing to do is employ a little trail and error. Let’s start with the smaller numbers, they will be easier to evaluate.
1. Substitute for x: 1, -1, 2, -2, 4, -4 ...20, -20.
Step-by-step explanation:
x^3 - 5x^2 - 4x + 20 (I'm assuming this is what you meant)
(1)^3 - 5(1)^2 - 4(1) + 20 = 1 - 5 - 4 + 20 = 12
(-1)^3 - 5(-1)^2 - 4(-1) + 20 = -1 - 5 + 4 + 20 = 18
(2)^3 - 5(2)^2 - 4(2) + 20 = 8 - 20 - 8 + 20 = 0
Now I know (x-2) is a factor of the polynomial.
Synthetic division
2 | 1. -5. -4. 20
| 2. -6. -20
-----------------------------
1. -3. -10. 0
x^2 -3x -10
Factor -> (x-5)(x+2)
So the factors of the original polynomial are (x-5), (x+2), and (x-2)
f(x) = 0 when x = -2,2,or 5
1 1/4 pints how many ounces
Answer:
20 oz
Step-by-step explanation:
Answer:
Your answer would be 20. Just multiply the volume value by 20.
rady White weighed 197 1/2 pounds when he decided to join a gym to lose some weight. At the end of the first month, he weighed 191 3/8 pounds. (Enter your answers as simplified mixed number
Brady White lost 4 pounds in the first month, leaving him at 193 pounds. To reach his goal weight of 184 pounds, he needs to lose an additional 9 pounds.
(a) To find out how much weight Brady White lost in the first month, we subtract his weight at the end of the month from his initial weight.
Initial weight = 197 pounds
Weight at the end of the first month = 193 pounds
So, the weight lost = Initial weight - Weight at the end of the first month
= 197 pounds - 193 pounds
= 4 pounds
Therefore, Brady White lost 4 pounds in the first month.
(b) To determine how much more weight Brady needs to lose to reach his goal of 184 pounds, we need to find the difference between his current weight and his goal weight.
Current weight = 193 pounds
Goal weight = 184 pounds
So, the amount of weight Brady needs to lose = Current weight - Goal weight
= 193 pounds - 184 pounds
= 9 pounds
Therefore, Brady needs to lose 9 more pounds to reach his goal weight of 184 pounds.
Complete question :- Brady White weighed 197 pounds when he decided to join a gym to lose some weight. At the end of the first month, he weighed 193 pounds. (Enter your answers as 2 simplified mixed numbers.)
(a) How much (in pounds) did he lose that month?
3 (b) If his goal is 184 pounds, how much more (in pounds) does he have to lose?
On average, Ainsley and her friends could complete 44 sit-ups in one minute. The number of sit-ups done by each of her friends is listed below. How many did Ainsley complete? *
47, 46, 38, 45, 41
Answer:
47
Step-by-step explanation:
The numbers given as 47, 46, 38, 45, 41 represent 5 people and adding Ainsley, they are 6 people.
The sum of individual sit ups by the 5 will be
47+46+38+45+41=217
Since the mean for 6 people is 44, it means their sum is 6*44=264
Getting the difference between the sum for 6 people and the sum for five people we get that
264-217=47
This is the number of sit-ups for the sixth person who is Ansley
A car travels 20 1/2 miles in 2/3 of an hour. What is the average speed, in miles per hour, of thr car?
Average speed of the car is 29.85 miles/hr
Step-by-step explanation:
Step 1: Calculate speed when distance = 20 1/2 = 20.5 miles and time = 2/3 hr = 0.67 hrs.Speed = Distance/Time
= 20.5/0.67
= 29.85 miles/hr
Find the exact area of the region bounded by two concentric circles with radli 10 inches and 6 Inches.
16pi
64pi
88pi
For this case we have that by definition, the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
r: It is the radius of the circle
Circle 1:
[tex]A_ {1} = \pi * (10) ^ 2 = 100 \pi \ in ^ 2[/tex]
Circle 2:
[tex]A_ {2} = \pi * (6)^2 = 36 \pi \ in ^ 2[/tex]
Thus, the area of the region bounded is given by:
[tex]A = 100 \pi-36 \pi = 64 \pi \ in ^ 2[/tex]
Answer:
[tex]64 \pi \ in ^ 2[/tex]
Option B
What is the area of 8/9ft and 2ft
Which represents the solution(s) of the equation x2 = 289?
A) x =
17
B) x = ±
17
C) x = −
289
D) x = ±
289
Answer:
B) x = +/- 17
Step-by-step explanation:
Answer:
it D
Step-by-step explanation:
I took the usatestprep
Two angles are vertical angles. One angle
measure is 68. What is the measure of
the other angle?
A. 22°
B. 68°
C. 90°
D. 112
In the context of geometry, vertical angles are always congruent, which means they have the same measure. If one of the vertical angles measures 68°, the measure of the other angle is also 68°. Therefore, the correct answer is B. 68°.
Explanation:The question is asking for the measure of the second angle, given that two angles are vertical angles and one of them measures 68°. In terms of geometry, vertical angles are the angles that are opposite each other when two lines intersect. An important property of vertical angles is that they are always congruent, which means they have the same measure. So, if one of the vertical angles is 68°, the other angle is also 68°. Hence, the correct answer is B. 68°.
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Since vertical angles are always congruent, the measure of the other angle is also 68°.
The question involves identifying the measure of the other angle when two angles are vertical angles. Vertical angles are angles that are opposite each other when two lines intersect. They are always equal to each other in measure.
Given that one angle measures 68°, the other angle, being a vertical angle, will also measure 68°.
Therefore, the correct answer is: B. 68°
What is the equation of m and n???
Answer:
m=47° n=52°
Step-by-step explanation:
38°,43°,m and n are all on the same line therefore they are all supplementary angles, or equal to 180°. 43° and m are also commplmentary angles or equal to 90°. This information will help with my work above.
1. Determine the total cost of the automobile after down payment and finance cost. Round your answer to the nearest penny; do not use commas in your answer.
price of car: $24.800.00, percent down: 18%, finance cost: 36 months at $760.00 per month
answer: ?
Answer:
24.800.000=100000
Step-by-step explanation:
gooogglleeeee PeRiOd
The cost of the car is $31824
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Price of the car =$24,800 down payment % =18 and monthly installment of $760
Thus Total cost= $24,80×0.18+36×760
= $31824
Hence, The cost of the car is $31824
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Which statements are true when verifying the solution set of |6-x/3|>18 as x <-36 or x > 72?
Since, you have not mentioned the statements, but I am solving the expression as well as verifying which anyways may be able to make you understand the concept.
Answer:
Both [tex]x<-36\quad \mathrm{or}\quad \:x>72[/tex] are the True solutions.
Step-by-step explanation:
Considering the expression
[tex]\left|6-\frac{x}{3}\right|>18[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex]
[tex]6-\frac{x}{3}<-18\quad \mathrm{or}\quad \:6-\frac{x}{3}>18[/tex]
solving
[tex]6-\frac{x}{3}<-18[/tex]
[tex]6-\frac{x}{3}-6<-18-6[/tex]
[tex]-\frac{x}{3}<-24[/tex]
[tex]3\left(-\frac{x}{3}\right)<3\left(-24\right)[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
[tex]\left(-x\right)\left(-1\right)>\left(-72\right)\left(-1\right)[/tex]
[tex]x>72[/tex]
also solving
[tex]6-\frac{x}{3}>18[/tex]
[tex]6-\frac{x}{3}-6>18-6[/tex]
[tex]-\frac{x}{3}>12[/tex]
[tex]-x>36[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
[tex]\left(-x\right)\left(-1\right)<36\left(-1\right)[/tex]
[tex]x<-36[/tex]
[tex]\mathrm{Combine\:the\:intervals}[/tex]
[tex]x<-36\quad \mathrm{or}\quad \:x>72[/tex]
Verifying the solution:
Putting the value x < -36 in [tex]\left|6-\frac{x}{3}\right|>18[/tex]
let suppose x = -37 which is < -36
[tex]\left|6-\frac{x}{3}\right|>18[/tex]
[tex]\left|6-\frac{\left(-37\right)}{3}\right|>18[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]=\left|6+\frac{37}{3}\right|[/tex]
[tex]=\left|\frac{55}{3}\right|[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0[/tex]
[tex]\frac{55}{3}>18[/tex]
[tex]\mathrm{Therefore,\:the\:solution\:is}[/tex]
[tex]\mathrm{True}[/tex]
also putting the value x > 72
let suppose x = 73 which is > 72
[tex]|6-\frac{\left(73\right)}{3}|>\:18[/tex]
[tex]=\left|-\frac{55}{3}\right|[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a[/tex]
[tex]=\frac{55}{3}[/tex]
[tex]\frac{55}{3}>18[/tex]
[tex]\mathrm{Therefore,\:the\:solution\:is}[/tex]
[tex]\mathrm{True}[/tex]
So, both [tex]x<-36\quad \mathrm{or}\quad \:x>72[/tex] are the True solutions.
Answer: 2, 3, 4, & 6.
Step-by-step explanation: edge 2021
Suppose a die is rolled twice and let P(A) = 1/2 P(B) = 1/3 find the requested probability
Answer:
Step-by-step explanation:
P(AUB)=P(A)+P(B)+P(A∧B),P(A∧B)=0 as both the events are independent.
P(AUB)=1/2+1/3=(3+2)/6=5/6
The probability value of P(A u B) is 2/3
How to determine the probability?The probability values are given as:
P(A) = 1/2
P(B) = 1/3
The required probability is then calculated using:
P(A u B) = P(A) + P(B) - P(A) * P(B)
This gives
P(A u B) = 1/2 + 1/3 - 1/2 * 1/3
Evaluate the product
P(A u B) = 1/2 + 1/3 - 1/6
Take the LCM
P(A u B) = (3 + 2 - 1)/6
Evaluate
P(A u B) = 2/3
Hence, the probability value of P(A u B) is 2/3
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Need help on my last one
1 1/4 cups to make 1 pie
So,
1 1/4 = 5/4 * 4 pies
=20/4 = 5 cups of sugar.
She has 1/2 cups of sugar so she will need 4 1/2 cups more
Area of circles
Susan designed a circular pool with a diameter of 25 meters. what is the area of the bottom of the pool? round to rhe nearest tenth.
Answer:
Area is 491.07m to the nearest tenth
Step-by-step explanation:
Find the equation of the line that is perpendicular to y = –3x + 1 and passes though the point (6, 3).
Answer:
y = [tex]\frac{1}{3}[/tex] x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 1 ← is in slope- intercept form
with slope m = - 3
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex], thus
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (6, 3) into the partial equation
3 = 2 + c ⇒ c = 3 - 2 = 1
y = [tex]\frac{1}{3}[/tex] x + 1 ← equation of perpendicular line
The equation of the line that is perpendicular to y = -3x + 1 and passes through the point (6, 3) is y = 1/3x + 1
Explanation:To find the equation of the line that is perpendicular to y = -3x + 1 and passes through the point (6, 3), we first need to find the slope of our new line. The slope of a line perpendicular to another is the negative reciprocal of the original slope. Since the slope of the original line is -3, the slope of the new, perpendicular line will be 1/3.
The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept. We already have the slope, m = 1/3, and a point through which the line passes (6, 3). Substituting these values into the equation gives us 3 = 1/3 * 6 + b. Solving for b gives us b = 1.
Therefore, the equation of the line that is perpendicular to y = -3x + 1 and passes through the point (6, 3) is y = 1/3x + 1.
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The coordinates of point H are (512, −1). Which statement tells how to locate point H on the coordinate plane?
Answer:
512 units towards the right of the y-axis, and 1 unit below the x-axis.
Four groups of students are doing a probability experiment with a standard number cube to see how many times they roll a 4 out of 500 trails. The theoretical probability of rolling a 4 is 16 or approximately 0.17 and one group came close to this probability with an experimental probability of 0.175. This MOST LIKELY came from which group?A)Group AB)Group BC)Group CD)Group D
Answer:
Group a, I did it
Step-by-step explanation:
The solution is Group A. As the number of trials get larger, experimental probability approaches theoretical probability. With a probability of 0.175 group A rolled a 4 14 out of 80 times.
PLEASE MARK BRAINLIEST
Answer:
The answer is Group A
Step-by-step explanation: I got it correct
Which expression represents x2−12x+36 in factored form?
The factored form of given is:
[tex]x^2 - 12x + 36 = (x-6)(x-6)[/tex]
Solution:
Given that,
[tex]x^2 - 12x + 36[/tex]
We have to find the factored form
From given,
[tex]x^2-12x+36\\\\\mathrm{Rewrite\:}36\mathrm{\:as\:}6^2\\\\x^2-12x+6^2\\\\\mathrm{Rewrite\:}12x\mathrm{\:as\:}2x\cdot \:6\\\\x^2-2x\cdot \:6+6^2\\\\\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2\\\\a=x,\:b=6\\\\Therefore,\\\\x^2-12x+36 = \left(x-6\right)^2\\\\Which\ is\\\\x^2-12x+36 = (x - 6)(x - 6)[/tex]
Thus the given expression is factored
Final answer:
The expression x²−12x+36 is factored as (x-6)(x-6) or (x-6)².
Explanation:
The expression x²−12x+36 represents a quadratic equation. To factor this expression, we look for two numbers that both add to the middle term, -12, and multiply to the constant term, 36. The numbers that fit this requirement are -6 and -6, since (-6) + (-6) = -12 and (-6) × (-6) = 36. Therefore, the expression in factored form is (x-6)(x-6), which can also be written as (x-6)².
15 (a) Work out
4.36 + 2.89
6.8 - 5.42
Give your answer as a decimal
Answer:
The answers are as given
4.36 + 2.89 is equal 7.25 and 6.8 - 5.42 is equal 1.38
Step-by-step explanation:
4.36 + 2.89 = 7.25
6.8 - 5.42 = 1.38
Answer:
7.25
1.38
Step-by-step explanation:
a) For first addition
4.36 + 2.89
Start adding from the right side. Take the last number and add them together.
9+6 = 15.................. write 5 and keep 1
Bring forward the kept "1"
3+8 + 1 = 12............. write 2 and keep 1
Bring forward the kept "1"
4+2 + 1 = 7...............write 7
∴ 7.25
b) For second subtraction
6.8 - 5.42 = 1.38
Start from the right side of each number
0 - 2 requires that you borrow "1" from "8" now turning "0" to "10" and "8" to "7".
now, 10 - 2 = 8...........write 8
7 - 4 = 3.............write 3
6 - 5 = 1..............write 1
∴ 1.38
Solve for x.
A. 4
B. 5
C. 6
D. 7
Step-by-step explanation:
see.... l is a perpendicular bisector of m.... so line l makes an angle 90° with m
so equation becomes
6(2x+1)= 90
12x + 6 = 90
12x = 90 - 6
12x = 84
x = 7
Hope it helps you
Thank you
in a equation like 81x^3 +9x^2+3x what would I do to the exponents. And also please solve.
Answer:
3x(27x^2+3x+1)
Step-by-step explanation:
ayou take out the GCF-greatest common factor and then factor it
Answer:
(3x + 1)2 • (3x - 1)2
Step-by-step explanation:
jasmine sells beaded jewelry. she calculates the price at which she sells the jewelry by adding a percent markup to the amount it costs her to make the jewelry
Jasmine calculates the selling price of her jewelry by adding a markup percentage to the cost price. The sale price is equivalent to the cost price plus the percentage markup applied to this cost. For example, if the jewelry cost is $10 with a markup of 20%, the selling price will become $12.
Explanation:Jasmine's method of pricing involves costs and percentage markup into consideration. To determine the selling price, she first calculates the cost to make the jewelry. This could include the cost of beads, thread, and her time. Afterwards, she determines the percentage markup. This is the additional amount on top of the cost price to generate profit. The equation can be written as: Selling price = Cost price + (Percent markup/100 * Cost Price).
For example, if it costs her $10 to make a piece of jewelry and she uses a markup of 20%, the amount of markup added would be $2 (20/100 x $10). Therefore, she would sell the jewelry for $12 ($10 + $2).
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Please help!! (100 points)
Clarissa has a sink that is shaped like a half-sphere. The sink has a value of 660tt in^3. One day her sink clogged, she has to use one conical cup to scoop the water out of the sink. The sink is completely full when Clarissa begins scooping.
(a) The conical cup (shaped like a cone) has a diameter of 5 in and a height of 8 in. How many cups of water must Clarissa scoop out of the sink with this cup to empty it?
(ROUND THE NUMBER OF SCOOPS TO THE NEAREST WHOLE NUMBER)
Answer:
13 scoops
Step-by-step explanation:
PART 1) 2.5*2.5*8/3*3.14
52.36
PART 2) 660/52.36
13 scoops
Answer:
40 scoops
Step-by-step explanation:
Volume of the sink is 660pi in³
Volume of the cone/scoop is:
⅓ × pi × 2.5² × 8 = 50pi/3 in³
No. of scoops required:
660pi ÷ 50pi/3
660 ÷ 50/3 = 39.6
Leah and Christopher work at a dry cleaners ironing shirts. Leah can iron 25 shirts per hour, and Christopher can iron 15 shirts per hour. Leah and Christopher worked a combined 13 hours and ironed 265 shirts. Write a system of equations that could be used to determine the number of hours Leah worked and the number of hours Christopher worked. Define the variables that you use to write the system.
25x + 15y = 265
x+y = 13
Step-by-step explanation:
Step 1:
Given
Number of shirts Leah can iron in an hour = 25 shirts
Number of shirts Christopher can iron in an hour = 15 shirts
Total number of hours worked by both = 13 hours
Total number of shirts ironed by them = 265 shirts
Step 2 :
Let x represent the number of hours Leah works and y represent the number of hours Christopher works
Leah irons 25 shirts in one hour, so in x hours he would iron 25x shirts
Christopher irons 15 shirts in one hour, so in y hours he would iron 15y shirts
Given total shirts ironed by them together is 265 , we have
25x + 15y = 265
They worked a combined of 13 hours, so
x+y = 13
Step 3:
The system of equations that could be used to determine the number of hours Leah worked and the number of hours Christopher worked are ,
25x + 15y = 265
x+y = 13
Answer:
System of Equations:
x + y = 13
25x + 15y = 265
x = number of hours Leah works
y = the number of hours Christopher works
can someone help with 9-14
Answer:
5
Step-by-step explanation:
Subtraciting
Answer:
If your asking what 9 - 14 is, than you would get a negative number.
9 - 14 = -5
Step-by-step explanation:
If you have any questions, please let me know.
Find the slope of the line that passes through the points (-1,-2) and (-9,-2)
Answer:
The slope is 0/-8 zero
Step-by-step explanation:
To find the slope you use the equation m=Y2-Y1 m= -2-(-2) = 0
X2-X1 -9- (-1) -8
Mike is painting a backdrop for the school play. The rectangular backdrop is 60 inches by 48 inches. If his container of paint can cover 250 square feet, does he have enough paint to cover the backdrop?
Answer:
Yes 240sq ft is only required.
Step-by-step explanation:
60 x 48 =2880 inch square
We convert to feet 1 ft = 12 inches
2880/12 = 240sq ft