1. Solve 2(x + 1)^2 = 18. What are the x-intercepts?
Answer:
The x-intercepts are [tex](2,0)[/tex] and [tex](-4,0)[/tex].
Step-by-step explanation:
We are given the equation
[tex]2(x+1)^2=18[/tex]
Begin by dividing both sides of the equation by 2:
[tex](x+1)^2=9[/tex]
Next, take the square root of both sides. Remember that there are two solutions to a square root, the positive and the negative root:
[tex]x+1=\pm3[/tex]
Split the equation into two based on the two solutions:
[tex]x+1=-3[/tex]
[tex]x+1=3[/tex]
Solve each equation by subtracting 1 from both sides:
[tex]x=-4\\ x=2[/tex]
Since the x-intercepts are the solutions to a quadratic, we know the solutions are (2,0) and (-4,0).
What is the solution to the following system?
(3x+2y+z = 20
X-4y-Z=-10
2x+y + 2z = 15
Answer:
x = 4; y = 3; z = 2
Step-by-step explanation:
3x + 2y + z = 20
x - 4y - z = -10
2x + y + 2z = 15
6x + 4y + 2z = 40
x - 4y - z = -10
-------------------------
7x + z = 30
x - 4y - z = -10
8x + 4y + 8z = 60
----------------------------
9x + 7z = 50
z = 30 - 7x
9x + 7(30 - 7x) = 50
9x + 210 - 49x = 50
-40x = -160
x = 4
z = 30 - 7(4)
z = 2
2x + y + 2z = 15
2(4) + y + 2(2) = 15
y = 3
x = 4; y = 3; z = 2
Consider the sequence below:
-4, 2, 8, 14, 20, …
What explicit expression can be used to find the term x of this sequence?
Answer:
n+6=x
Step-by-step explanation:
Each number is six more than the previous number. Adding six to the previous number, n, gets us the next term in the sequence, x.
three times the number of books that you have
Step-by-step explanation:
let b represent the number of books
b×b×b
b3
If you deposit `\$300` in an account and it grows by `6\%` each year, how much money will be in your account after `1` year?
Answer:
$318
Step-by-step explanation:
6% x 300 = 18
300 + 18 = 318
Pasang fixed the marked price of a watch Rs. 4000 and he sold it allowing a discount of 10%. Then he made a profit of Rs 400. Find the cost orice of the watch.
Answer:
Cost Price = Marked Price -Discount - Profit
CP = 4000-400-400
Cost price = 3200
Rs. 3200
The answer iis in the above picture hope you like it. Pls mark brainliest
If made $90.00 how much was paid hourly?
Answer:
Made in how long of a workshift?
Step-by-step explanation:
probably extremely easy but would like a little explanation on doing this when it comes to this specific subject
Answer:
look at each pair. examine each notice exponents so you find the hidden gcf
Step-by-step explanation:
The volume of a cylinder is 1,0297 cubic
centimeters. The height of the cylinder is
21 centimeters. What is the radius, to the
nearest centimeter, of the cylinder?
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=10297\\ h=21 \end{cases}\implies 10297=\pi r^2(21)\implies \cfrac{10297}{21\pi }=r^2 \\\\\\ \cfrac{1471}{3\pi }=r^2\implies \sqrt{\cfrac{1471}{3\pi }}=r\implies 12\approx r[/tex]
What is the value of z?
Enter your answer in the box
Answer:
23 degrees
Step-by-step explanation:
The sum of the interior angles of a triangle = 180
z + 62 + 95 = 180
z = 23 degrees
Help picture below problem 16
Answer:
c²=a²+b². 13²=12²+b² 169=144+b². b² =√25=5
Step-by-step explanation:
13² = ?² + 12²
169 - 144 = ?²
√25 = ?
5 yards = ?
NO LINKS!! Explain your answers (show the support by showing the changes in x and y on your table). If the relationship is linear, inverse, or exponential, write the equation.
#5 and #6
Answer:
Linear relationship: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.
Inverse relationship: the value of one variable decreases as the value of the other variable increases.
Exponential relationship: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)
Question 5
As the x-value increases (by one unit), the y-value decreases.
Therefore, this is an inverse relationship.
The y-values are calculated by dividing 35 by the x-value.
[tex]\sf y=\dfrac{35}{x}[/tex]
**I believe there is a typing error in the table and that the y-value of x = 3 should be 11.67**
Question 6
As the x-value increases, the y-value increases. The y-value increases by a factor of 5 for each x-value increase of 1 unit.
Therefore, this is an exponential relationship.
[tex]\sf y=5^x[/tex]
Differentiate cosec5x
[tex]\dfrac{d}{dx} \csc(5x)\\\\=-\csc(5x) \cdot \cot (5x) \cdot \dfrac{d}{dx} (5x)\\\\=-5\csc(5x) \cdot \cot(5x)[/tex]
How do you write 9 1/10 as a decimal?) *
Answer:
Convert 9 1/10 to an improper fraction.
Decimal form
=9.1
Answer:
9.1
Convert [tex]9\frac{1}{10}[/tex] to [tex]9 + 1/10[/tex][tex]\frac{1}{10}[/tex] is the same as 1 divided by 10, which is 10, for this case 0.10Therefore, [tex]9 + 0.1 = 9.1[/tex]There are other, more complicated ways to do this, but we must start with an easier, understandable way first.
__________________________________________________________
Questions?Ask in the comments box.
hey, can I have some help with this? I don't get it so let me know if you have an explentation. Thanks :)
Answer: 250
Step-by-step explanation:
This problem is attempting to explain the distributive property to you.
The distributive property states that if you have the numbers a, b, and c:
[tex](a*c) + (b*c) = c * (a+b)[/tex]
In your specific case, this would look like this:
[tex](23+37) * 4\frac{1}{6}[/tex]
[tex]60 * \frac{(4*6)+1}{6}[/tex]
[tex]60*\frac{25}{6}[/tex]
To simplify, we factor a 6 out of the equation:
[tex]10*25 = 250[/tex]
Yes Or No
Mr. Rainey is a new depositor at your institution. He complains that charges for funds transfers are too
expensive
Should his complaint be logged and handled by the Reg E Department?
O Yes
Ο Νο
Answer:Yes
Step-by-step explanation:His complaint is valid.
please help me in this mathematics questionplease help me in this mathematics questionplease help me in this mathematics question
The twenty units of potatoes illustrates the measure of central tendency and probability
The modal weight, mean, and medianStart by sorting the dataset:
0.19; 0.28; 0.55;
0.62; 0.68; 0.77;
0.88; 0.89; 0.98;
0.99; 1.11; 1.22;
1.22; 1.22; 1.33;
1.44; 1.48; 1.68;
1.77; 1.99
The highest occuring element is 1.22 with a frequency of 3
The two middle elements are 0.99 and 1.11.
The mean of these two middle elements is: 0.5 * (0.99 + 1.11) = 1.05
The mean of the whole dataset is:
Mean = (0.19+ 0.28+ 0.55+ 0.62+ 0.68+ 0.77+ 0.88+ 0.89+ 0.98+ 0.99+ 1.11+ 1.22+1.22+ 1.22+ 1.33+ 1.44+ 1.48+ 1.68+1.77+1.99)/20
Mean = 1.06
Hence, the modal weight is 1.22, the mean is 1.06, and the median is 1.05
The probabilities(a) at least 1.1 kg
There are 10 potatoes that weigh at least 1.1 kg.
So, the probability is:
P = 10/20
P = 0.5
(b) more than 3.5kg
There are 0 potatoes that weigh more than 3.5 kg.
So, the probability is:
P = 0/20
P = 0
(c) below 0.50kg
There are 2 potatoes that weigh below 0.50 kg.
So, the probability is:
P = 2/20
P = 0.1
The Variance of the weight.
This is calculated as:
Var = [tex]\sum[/tex](x - mean)^2/n
This gives
Var = [(0.19 - 1.06)^2 + (0.28 - 1.06)^2 + (0.55 - 1.06)^2 + (0.62 - 1.06)^2 + (0.68 - 1.06)^2 + (0.77 - 1.06)^2 + (0.88 - 1.06)^2 + (0.89 - 1.06)^2 + (0.98 - 1.06)^2 + (0.99 - 1.06)^2 + (1.11 - 1.06)^2 + (1.22 - 1.06)^2 + (1.22 - 1.06)^2 + (1.22 - 1.06)^2 + (1.33 - 1.06)^2 + (1.44 - 1.06)^2 + (1.48 - 1.06)^2 + (1.68 - 1.06)^2 + (1.77 - 1.06)^2 + (1.99 - 1.06)^2]/20
Evaluate
Var = 0.22
This means that:
The expectation of the squared deviation of the random variable from the mean is 0.22 kg
Read more about measure of central tendency at:
https://brainly.com/question/17631693
Answer:
0.22 kg
Step-by-step explanation:
a triangle banner is to be made according to the specifications in the figure shown with dimensions given in inches. WOODEN STICKS WILL BE USED TO OUTLINE THE PERIMETER of the banner in order to attach the interior material. How many inches of wooden sticks will be required?
Applying the Pythagorean theorem, the amount of inches of wood required = Perimeter of triangle = 15 + 13 + 9 = 37 inches.
What is the Pythagroean Theorem?The Pythagorean theorem is used to find a side of a right triangle, and it states that if c is the hypotenuse and a and b are the other legs, therefore: c² = a² + b².
Find the altitude/height of the triangle using the Pythagorean theorem:
height = √(13² - 5²)
height = 12
Also, use the Pythagorean theorem to find the missing side (part of the longest side of the main triangle):
missing side = √(15² - 12²) = 9
Amount of inches of wood required = Perimeter of triangle = 15 + 13 + 9 = 37 inches.
Learn more about the Pythagorean theorem on:
https://brainly.com/question/16176867
Please help i will give brainliest to the right answer
Step-by-step explanation:
Jacinta is completely right while Tess made a mistake on the 3rd step.
she mistakenly plugged in the y value as X, and plugged in the X value as y.
so Tess is incorrect
Select all of the equivalencies
1/4=5/10
8/5=8/5
9/8=7/8
1/2=6/12
7/3=7/3
9/10=10/9
Answer:
8/5 = 8/5
1/2 = 6/12
7/3 = 7/3
Step-by-step explanation:
1/4=5/10
5/10 = 1/2
False
8/5=8/5
True
9/8=7/8
False
1/2=6/12
6/12 = =1/2
True
7/3=7/3
True
9/10=10/9
False
what is the slope of the line that passes through -14, 13 and 7, 0
Slope = change in y / change in x
slope = (0 - 13) / (7 - -14)
slope = -13/28
You invest $30,000 for 6 years, in an account that earns 14% interest. How much money is in your account at the end of 6 years?
A
$69,153.95
B
$95,848.50
C
$35,849.18
D
$65,849.18
Factor out the greatest common factor 45d^3-18d^2
Answer:
9d^2(5d−2)
Step-by-step explanation:
A polynomial function has – 5+ 3t as a root. Which of the following must also be a root of the function?
a
Radical roots occur as conjugate pairs
Given - 5 + t is a root , then
- 5 - t is also a root → a
If a tennis ball has a diameter of 14, What is the volume of the tennis ball? Round to the nearest hundreth Use
3.14 for it pi
if its diameter is 14, then its radius is half that or 7.
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=7 \end{cases}\implies \begin{array}{llll} V=\cfrac{4\pi (7)^3}{3}\implies V=\cfrac{1372\pi }{3} \\\\\\ \stackrel{using~\pi =3.14}{V\approx 1436.03} \end{array}[/tex]
Answer:
[tex]1436.76... units^3[/tex]
Step-by-step explanation:
Recall the formula for the volume of a sphere.
[tex]V = \frac{4}{3} \pi r^3[/tex]
The question gives you diameter. As you know, diameter is twice the radius. Therefore, to convert diameter into radius, you divide the diameter by 2.
[tex]r = 14/2[/tex] [tex]= 7[/tex]
Now that you have the radius, all you need to do is plug it into the volume formula.
[tex]V = \frac{4}{3}\pi 7^3[/tex] = [tex]1436.76... units^3[/tex]
Makayla leans a 18-foot ladder against a wall so that it forms an angle of 64 degrees with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary.
Please help me, I don’t understand the problem!
The ladder and the outside wall form a right triangle
The distance from the base of the ladder is 7.89 feet
How to determine the distance to the base of the ladder?The given parameters are:
Length (L) = 18 feet
Angle of elevation (θ) = 64 degrees
The distance (D) from the base of the ladder is calculated using the following cosine ratio
cos(θ) = D/L
So, we have:
cos(64) = D/18
Make L the subject
D = 18 * cos(64)
Evaluate the product
D = 7.89
Hence, the distance from the base of the ladder is 7.89 feet
Read more about right triangles at:
https://brainly.com/question/2437195
The height of 14-year-old boys in the United States is normally distributed with a mean of 64.5 in, and a standard deviation of 3.1 in.
Label the normal curve by entering the value at each standard deviation in the box.
Answer:
61.4-67.6 - 68.37% likely to fall within this range.
58.3-70.7 - 95.45% likely to fall within this range.
55.2-73.8 - 99.73% likely to fall within this range.
Step-by-step explanation:
You buy apple chips and banana chips in the ratio of 2 : 7. How many ounces of banana chips do you buy when you buy n ounces of apple chips?
Answer:
7/2 n ounces of banana
Step-by-step explanation:
a / b = 2/7
re-arrange to
7/2 a = b
n ounces of apple would result in
7/2 n = banana chip ounces
the total deposist made over a time of periode
bro what.... finish the question...
how would the equation be written with an amplitude of 3 maximum of 4 minimum of -2 period of 4 and midline of 1 (Will report scams)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here we go ~
The required equation is :
[tex] \qquad \sf \dashrightarrow\: y = asin(bx) +k [/tex]
Now, let's find the required values :
period (p) = 4
[distance between any successive Crest or trough]
a = - 3 (flipped)
b = 2π/p = 2π/4 = π/2
k = 1
Distance of starting position from origin = k
Now, plug in the values ~
[tex] \qquad\dashrightarrow \sf\: y = -3sin(\frac{\pi}{2}x)+1 [/tex]