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If (x + 1) is a factor of 2x - kx²-8x + 5, find the value of k.
[ Using Factor Theorem ]
Answer:
k = 11
Step-by-step explanation:
What the factor theorem is telling us is that if x + 1 is a factor of 2x - kx²-8x + 5 then when x = - 1 is put into the equation, the result will be 0. That's because x +1 = 0 when x = - 1
f(-1) = 2(-1) - k(-1)^2 - 8(-1) + 5
f(-1) = -2 - k(1) + 8 + 5 = 0
-k*(1) + 11 = 0
-k = -11
k = 11
9) Assume that the random variable X is normally distributed, with mean = 90 and standard deviation o = 12. Compute the probability P(57 < X < 105).
A) 0.7888 B) 0.8944 C) 0.8914 D) 0.8819
Answer:
Step-by-step explanation:
The mean, [tex]\bar{x}[/tex], is 90 and the standard deviation, [tex]\sigma[/tex], is 12. We are looking for the probability that the variable X will fall between 57 and 105. We use the z-score table for this, AFTER we find the z scores. The formula to find the z-scores for us is:
[tex]P(\frac{57-\bar{x}}{\sigma}\leq z\leq \frac{105-\bar{x}}{\sigma})[/tex] and we fill in accordingly:
[tex]P(\frac{57-90}{12}\leq z\leq \frac{105-90}{12})[/tex] which simplifies to
[tex]P(-2.75\leq z\leq 1.25)[/tex] and we will break them up into 2 different sets as follows:
P(-2.75 ≤ z ≤ 0) + P(0 ≤ z ≤ 1.25)
and based on the fact that z scores are given from 0 on up, we are going to convert the first one by using the logic that if z is greater than -2.75 but less than 0, by symmetry, z is greater than 0 but less than 2.75:
P(0 ≤ z ≤ 2.75) + P(0 ≤ z ≤ 1.25) and we go to the z-score table.
Locate 2.7 down along the left side and move over til you're under the .05; that gives us the z-score for 2.75 which is .4970. Do the same for 1.25 to get a z-score of .3944. Add them together to get a final z-score that covers the range of values for X:
.4970 + .3944 = 0.8914
3.3 Is it possible that a vehicle could travel so fast that the trip could be done in no time at all? Give a reason for your answer.
Answer:
No.
Step-by-step explanation:
No matter how fast something is going it still takes a moment in time, even if it's only 1/10000 of a second.
use the prime factors of 3136 and 2744 to evaluate:✓3136/3✓2744
Answer:
3136 = 2^6 × 7^2
2744 = 2^3 x 7^3
✓3136/3✓2744 = ✓(2^6 × 7^2)/3✓(2^3 x 7^3) = (2^3 x 7)/3 x 14(✓14) = 56/42✓14 =4/3✓14
The skateboard Rita would like to buy costs $ 6 less than 3 times the amount she saved. The skateboard costs $ 69. How much money has Rita saved? Choose the steps that show how to solve this problem using arithmetic
Given:
The skateboard Rita would like to buy costs $ 6 less than 3 times the amount she saved.
The skateboard costs $69.
To find:
The saved amount.
Solution:
Let x be the saved amount.
The skateboard Rita would like to buy costs $ 6 less than 3 times the amount she saved. So, the cost of the skateboard is [tex]3x-6[/tex].
The skateboard costs $69.
[tex]3x-6=69[/tex]
[tex]3x=69+6[/tex]
[tex]3x=75[/tex]
Divide both sides by 3.
[tex]x=\dfrac{75}{3}[/tex]
[tex]x=25[/tex]
Therefore, Rita saved $25.
Find the interior angle sum for the following polygon
Find the measure of the missing arc KN labeled on the graph. Show ll your work that leads the final answer. *
Answer:
Arc KN = 201°
Step-by-step explanation:
Recall: According to the tangent-secant exterior angle theorem, the measure of the vertex angle formed at an external point where a tangent and a secant meet outside a circle is ½ of the difference between the intercepted major and minor arcs.
Applying this to the problem given, we have:
m<L = ½(Arc KN - Arc KM)
m<L = 70° (given)
Arc KN = ?
Arc KM = 61°
Substitute
70° = ½(Arc KN - 61°)
2*70° = Arc KN - 61°
140° = Arc KN - 61°
140° + 61° = Arc KN
201° = Arc KN
Arc KN = 201°
If the city bus through Austin travels at 40 miles per hour, how many miles
will it travel in 4.5 hours.
2.1: Solve the one step equation
9. 70 = -5x
10. x4 = 36
11. 7x = -54
Answer:
-14, 9 and - 54/7
Step-by-step explanation:
70=-5x, x=-144x=36, x=97x=-54, x=-54/7Can someone help me out
Answer:
75.7
Step-by-step explanation:
Area of the sector,
17²×π×30/360
= 289π/12
= 75.7 (rounded to the nearest tenth)
Answered by GAUTHMATH
a) (x3 – 7x + 3 – x2) : (x – 3);
b) (2x4 – 3x3 – 3x2 – 2 + 6x) : (x2 – 2)
Answer:
Step-by-step explanation:
X^2+2x-1
2X^2-3x+1
1 point
Andrea and Barry are sharing a bag of popcorn at the movies. By himself,
Barry can eat the whole bag of popcorn in 30 minutes. Andrea takes 20
minutes to eat the whole bag. If they both eat popcorn at their usual rates,
approximately how long will it take them to finish the bag of popcorn?
Answer:
12 minutes
Step-by-step explanation:
We can use the formula
1/a+ 1/b = 1/c where a and b are the times alone and c is the time together
1/20 + 1/30 = 1/c
Multiply by the common denominator to clear the fractions
60c(1/20 + 1/30 = 1/c)
3c +2c = 60)
5c = 60
Divide by 5
5c/5 = 60/5
c = 12
12 minutes
Answer: 12 minutes
Step-by-step explanation: To solve this kind of a problem, which is called a work problem, it's important to understand the following idea:
Since Barry can eat a bag of popcorn in 30 minutes, we know that in 1 minute, Barry can eat 1/30 of the bag of popcorn and in 2 minutes, Barry can eat 2/30 of the bag of popcorn. Therefore, in t minutes, Barry can eat t/30 of the bag of popcorn. The same thing applies for Andrea. In t minutes, Andrea can eat t/20 of the bag of popcorn.
Now to solve the problem, we use the following formula:
Part of Job done by Barry + Part of Job done by Andrea = 1 job done
The part of job done by Barry is t/30 and the part
of the job done by Andrea is t/20.
So we have t/30 + t/20 = 1.
To solve for t, multiply both sides by the common denominator of 60.
So we get 2t + 3t = 60 or 5t = 60 so t = 12.
So Barry and Andrea can eat 1 bag together in 12 minutes.
Find the third term of (x^2 + 2)^4.
Answer:
Step-by-step explanation:
[tex]in~the~expansion~of~(x+a)^n\\T_{r+1}=ncr x^{n-r}a^r\\r+1=3\\r=3-1=2\\n=4\\4c2=\frac{4 \times 3}{2 \times 1} =6\\T_{2}=4(x^2)^{4-2}(2)^2\\=16(x^2)^2\\=16x^4[/tex]
the third term is: 24*x^4
We want to find the third term of the equation:
(x^2 + 2)^4
So we need to expand that.
Remember the rule:
(a + b)^2 = a^2 + 2*a*b + b^2
(a + b + c)^2 = a^2 + b^2 + c^2 + 2*a*b + 2*b*c + 2*c*a
Then we can write:
(x^2 + 2)^4 = (x^2 + 2)^2*(x^2 + 2)^2
and we have:
(x^2 + 2)^2 = (x^4 + 2*2*x^2 + 2^2) = (x^4 + 4*x^2 + 4)
Then we have:
(x^2 + 2)^4 = (x^2 + 2)^2*(x^2 + 2)^2
(x^2 + 2)^4 = (x^4 + 4*x^2 + 4)^2
And we can expand this as:
(x^4)^2 + (4*x^2)^2 + 4^2 + 2*(x^4)*(4*x^2) + 2*(4*x^2)*(4) + 2*(x^4)*(4)
now we have this expanded, so we need to simplify this:
x^8 + 16*x^4 + 16 + 8*x^6 + 32*x^2 + 8*x^4
Putting the terms in order (larger degrees go in the left) we get:
x^8 + 8*x^6 + 16*x^4 + 8*x^4 + 32*x^2 + 16
x^8 + 8*x^6 + (16 + 8)*x^4 + 32*x^2 + 16
x^8 + 8*x^6 + 24*x^4 + 32*x^2 + 16
So the third term would be the third counting from the left, which is:
24*x^4
If you want to learn more, you can read:
https://brainly.com/question/12556222
amy bill and cara each played a game . amy’s scored was ten times bill’s scored . cara’s down the ratio of amy’s scored to bill’s scored to cara’s score. give your answer in its simplest form
Answer:
10:1:5
Step-by-step explanation:
Given that,
A game was played by Amy, Bill, and Cara.
Let Amy's score be x. Then,
Bill's score would be x/10
Cara's score = x/2
Now,
The ratio of their scores;
x: x/10: x/2
= 1 : 1/10 : 1/2
To equalize the scores, multiply all of them by 10
= (1 * 10): (1/10 * 10) : (1/2 * 10)
= 10 : 1 : 5
Thus, the simplest ratio form would be 10:1:5
Answer:
Step-by-step explanation:
10:1:5
Mar-Vell Studios' blockbuster movie Gray Widow: It's About Time She Got a Movie premiered last weekend simultaneously in theaters and on streaming video. On opening weekend, the total revenue from the movie was $127,265,468, with the movie making 75% more revenue in theaters than it did via streaming video. How much money did Gray Widow make in theaters on opening weekend
Answer:
Gray Widow made $111,357,284.5 in theaters on opening weekend.
Step-by-step explanation:
75% more revenue in theaters than it did via streaming video.
The sum of the revenues is 100%.
So the theaters were responsible for the following percentage:
[tex]P = 50 + \frac{75}{2} = 50 + 37.5 = 87.5[/tex]
How much money did Gray Widow make in theaters on opening weekend?
87.5% of the total revenue, that is, 0.875 out of $127,265,468.
0.875*127,265,468 = $111,357,284.5
Gray Widow made $111,357,284.5 in theaters on opening weekend.
Two walls of a canyon form the walls of a steady flowing river. From a point on the shorter wall, the angle of elevation to the top of the opposing wall is 20° and the angle of depression to the bottom of the opposing wall is 320 feet. Using the appropriate right triangle solving strategies, solve for the following: (Do not round intermediate calculated values. Only the final answer should be rounded to one decimal place.)
Answer:
x is approximately 226.3 feet
y is approximately 308.6 feet
z is approximately 226.3 feet
Step-by-step explanation:
The given parameters of the walls are;
The angle of elevation from the top of the shorter wall to the top of the opposing wall, θ₁ = 20°
From the diagram, the angle of depression from the top of the shorter wall to the bottom of the opposing wall, θ₂ = 45°
The distance from the bottom of the shorter wall to the base of the opposing wall, l = 320 feet
x = The height of the shorter wall = l × sin(θ₂)
∴ x = 320 feet × sin(45°) = 320 feet × (√2)/2 = 160·√2 feet ≈ 226.3 feet
∴ x ≈ 226.3 feet
By observation, we have;
y = x + z × tan(θ₁)
Where;
z = l × cos(θ₂)
∴ y = 160·√2 + 320 × cos(45°) × tan(20°) ≈ 308.6
y ≈ 308.6 feet
z = l × cos(θ₂)
∴ z = 320 × cos(45°) = 160·√2 ≈ 226.3
z ≈ 226.3 feet.
help please I'll give brainliest
Answer:
35
Step-by-step explanation:
6:5
We need to get the first number to 43
6*7 = 42
Multiply each term by 7
6*7 : 5*7
42 : 35
State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.
ΔTUV
~ ____
Show working please
Answer:
Step-by-step explanation:
1.159 R (remainder) 42
| ------------------------
73 | 84.649
-73
116 (brought 6 down)
-73
434 (brought 4 down)
-365
699 (brought 9 down)
-657
42 is the remainder
↪[tex] \: \: \: \: \: \: \: \: \: \: \huge \rm{answer:} \boxed{ \purple{42}}[/tex]
[tex] \huge \red {\boxed{\sf{armed \: account}}}[/tex]
[tex] \huge\frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm1159r42}{ \: 73) \: \:84649} \\ \huge \frac{ - 73}{ \: \: \: \: \: \: 116} \\ \huge \frac{ \: \: \: \: - 73}{ \: \: \: \: \: \: \: \: \: 434} \\ \huge \frac{ \: \: \: \: \: \: - 365}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 699} \\ \huge\frac{ \: \: \: \: \: \: \: \: \: \: - 657}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{42} }[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
And that's it! Hope it wasn't too hard to understand✏
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Step-by-step explanation:
[tex] \huge \rm{Hope \: this \: helps}[/tex]
Find SP where MP=Rs875 and discount =Rs75
Answer:
SP is Rs 800.
Step-by-step explanation:
MP = Rs 875
Discount = Rs 75
so
SP = MP - discount
= Rs 875 - Rs 75
= Rs 800
A national caterer determined that 37% of the people who sampled their food said that it was delicious. If the 144 people at the Valley Ridge Nursing Home are given the same food, and asked by tables what the deliciousness of the food, what is the mean of the sampling distribution of p-hat (the population proportion)
Answer:
Hence the mean of the sampling distribution of proportion is,
[tex]\mu\hat p = p = 0.37[/tex].
Step-by-step explanation:
Here the given details are,
p = 0.37
1 - p = 1 - 0.37 = 0.63
n = 144
The mean of the sampling distribution of proportion is,
[tex]\mu\hat p = p = 0.37[/tex]
A car travels 32 km due north and then 46 km in a direction 40° west of north. Find the direction of the car's resultant vector. [?] Round to the nearest hundredth.
Answer:
Step-by-step explanation:
This requires some serious work before we even begin. First off, we will convert the km to meters:
32 km = .032 m
46 km = .046 m
And then we have to deal with the angle given as 40 degrees west of north. An angle 40 degrees west of north "starts" at the north end of the compass and moves towards the west (towards the left in a counterclockwise manner) 40 degrees. That means that the angle that is made with the negative x axis is a 50 degree angle. BUT the way angles are measured in standard form are from the positive x-axis, therefore:
40 degrees west of north = 50 degrees with the negative x axis = 130 degrees with the positive x axis. 130 is the angle measure we use. Phew! Now we're ready to start. Adding vectors requires us to use the x and y components of vectors in order to add them.
[tex]A_x=.032cos90.0[/tex] so
[tex]A_x=0[/tex] (the 90 degrees comes from "due north")
[tex]B_x=.046cos130[/tex] so
[tex]B_x=-.030[/tex] and if we add those to get the x component of the resultant vector, C:
[tex]C_x=-.030[/tex] And onto the y components:
[tex]A_y=.032sin90.0[/tex] so
[tex]A_y=.032[/tex]
[tex]B_y=.046sin130[/tex] so
[tex]B_y=.035[/tex] and if we add those together to get the y component of the resultant vector, C:
[tex]C_y=.067[/tex] Note that since [tex]C_x[/tex] is negative and [tex]C_y[/tex] is positive, the resultant angle (the direction) will put us into QII.
We find the magnitude of C:
[tex]C_{mag}=\sqrt{(-.030)^2+(.067)^2}[/tex]
We will round this after we take the square root to the thousandths place.
[tex]C_{mag}=.073m[/tex] and now for the angle:
[tex]\theta=tan^{-1}(\frac{.067}{-.030})[/tex] which gives us an angle measure of -67, but since we are in QII, we add 180 to that to get that, in sum:
The magnitude of the resultant vector is .073 m at 113°
Please help me solve this
Answer:
43
78
56
Step-by-step explanation:
Find the measure of each angle supplementary angles with measures 2X +3 and 3X +2
supplementary angles = the sum of those angles will equal to 180 degrees
so,
2x + 3 + 3x + 2 = 180
5x + 5 = 180
5x = 175
x = 35
angle 1 -> 2x + 3 = 70 + 3 = 73
angle 2 -> 3x + 2 = 105 + 2 = 107
if you want to check, 107 + 73 = 180
hope it helps :)
What is the solution, if any, to the inequality |3x|20?
all real numbers
solution
no
x>0
x
Answer:
20×2=40bnmcsshjvghjpiutewqadgjlmbcz
Answer: all real numbers
Step-by-step explanation:
Annabeth has $29.00 to spend at the sporting goods store.
She buys a T-shirt that costs $15.32. She spends all of her
money. She also wants to buy a soccer ball for $13.68, a
baseball cap for $8.39, a set of shin guards for $14.98, or a
water bottle for $5.93.
*Need asap* (might give brainiest if I can)
Hi there!
»»————- ★ ————-««
I believe your answer is:
The soccer ball.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'c'...}}\\\\15.32 + c = 29.00\\-----------\\\rightarrow 15.32 - 15.32 = 29.00 - 15.32\\\\\rightarrow \boxed{13.68}[/tex]
⸻⸻⸻⸻
She would have $13.68 dollars left. Her second item should be the soccer ball.
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
HELP ME pleaseeee help help
Step-by-step explanation:
a. x+10.
b. (5)(x)(x+10)=V
c. 5×8×18=720
d. 5,8,18
e. Yes, the dimensions all stay the same so the volume should be the same.
SOMEONE PLEASE HELP ME
Sandra is choosing an Internet service provider.
• Smart Dot Company costs $12 per month plus $0.50 for each hour of Internet used.
• Communication Plus costs $2.50 for every hour of Internet used.
a. Create an equation to represent the cost of using the internet with each company. (2 marks) Let C represent the cost of using internet in any month.
Let t represent the number of hours used
Smart Dot, multiply the cost per hour by number of hours (t) and add to the monthly fee:
C = 0.50t + 12
Communication plus: Multiply the cost per hour by number of hours (t)
C = 2.50t
a two digit number divided by another two digit number,we get 3.675 what are the numbers?
Answer:
Step-by-step explanation:
I can't get the exact answer you've given, but I can tell you some things about it. The largest number in the denominator is 30 or 31. That's because 31 * 3 is 93 exactly. However the fraction is a problem and will likely push you over 100.
3.675 * 31 = 113 something. So 31 is too big.
The closes I came was 98 / 26 which is 3.769
Guys please help me solve this I’m struggling
Answer:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
Step-by-step explanation:
Given
[tex]z = 4x + 5y[/tex]
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
Required
The maximum and minimum of z
To do this, we make use of the graphical method
See attachment for graphs of
[tex]x \ge -1[/tex]
[tex]y \le 2x +3[/tex]
[tex]y \le -1[/tex]
The corner points of the function are:
[tex](x,y) = (-1,1)[/tex]
[tex](x,y) = (-1,0)[/tex]
[tex](x,y) = (-1,-1)[/tex]
We have:
[tex]z = 4x + 5y[/tex]
Calculate z with the above values
[tex]z = 4(-1) + 5(1) = 1[/tex]
[tex]z = 4(-1) + 5(0) = -4[/tex]
[tex]z = 4(-1) + 5(-1) = -9[/tex]
So, we have:
[tex]Max\ z = 1[/tex]
[tex]Min\ z = -9[/tex]
