x - 25 = (√x)^2 - 5^2 = (√x - 5)(√x + 5)
Then
(x - 25)/(√x - 5) = √x + 5
and as x approaches 25, we get a limit of √25 + 5 = 5 + 5 = 10.
Find the area of the triangle
Answer:
84mm
Step-by-step explanation:
Formula of a triangle:
A =bh/2
A=14(12)/2
A=168/2
A=84mm
Michael has a substantial student debt, but he recently got a new job, which came with a signing bonus. He calculates that with his new
job, he can put aside a fixed amount of money every month to pay off his debt. He also puts the entirety of his bonus towards paying off
his debt. He constructs the expression 36, 700 - (5,000+ 500m)to represent the size of his debt after m months. Which number
describes the value of his signing bonus?
I need help plz
Answer:
Michael needs to save $63.40, approximately.Step-by-step explanation:
The given expression is
[tex]36,700 - (5,000 + 500m)=0[/tex]
Where [tex]m[/tex] is months.
We need to solve for the variable.
[tex]36,700-5,000-500m=0\\31,700=500m\\m=\frac{31700}{500} \approx 63.4[/tex]
Therefore, Michael needs to save $63.40, approximately.
Answer:
The number representing describing the value of his signing bonus = 5,000.
Step-by-step explanation:
Total debt = $36,700
He pays $500 every month from his monthly salaries, since m = months.
The $5,000 is the amount of his signing bonus, which puts entirely towards paying off his debt.
It is like the fixed payment. While the 500m is the variable payment per month.
So, at the end of any number of months, you can easily calculate the remaining debt using the expression, 36,700 - (5,000 + 500m)
1. Terry made $53
washing cars. She made
some money selling
cookies. In total she has
$67. How much money
did she make selling
cookies?
Answer:
Terry made $14 selling cookies.
Step-by-step explanation:
[tex]67-53=14[/tex]
Answer:
$14
Step-by-step explanation:
She made $14 selling cookies.
$67-$53=$14
g(x) = - 3x - 8
g (____) =10
The approximate length of side XY is units. The approximate length of side YZ is units. The approximate length of side ZX is units. The approximate perimeter of triangle XYZ is units.
Answer:
ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units
Step-by-step explanation:
1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units
2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX = √18 units = 3√2.
3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.
4. YZ is visualized to have a length of 4 units.
5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answer:
(x - 5) (x - 7)
Step-by-step explanation:
To factor this trinomial, you must split the middle term (-12x) into two terms that can be added to get -12x, and multiplied to get 35:
[tex]x^2[/tex] - 12x + 35
[tex]x^2[/tex] -7x - 5x + 35
Group:
([tex]x^2[/tex] -7x) (-5x + 35)
Take out the GCF (Greatest Common Factor):
x(x - 7) -5(x - 7)
(x - 5) (x - 7)
Answer:
the answer is D
Step-by-step explanation:
x^2-12x+35=x^2-7x-5x+35=x*(x-7)-5(x-7)=(x-7)(x-5)
Which shows the decimal 0.16 expressed as a fraction in the simplest form?
Answer:
.16 = 16/100= 8/50= 4/25
Step-by-step explanation:
Answer:
decimal: 0.16
fraction: 4/25
percentage: 16%
Step-by-step explanation:
In 2008, data from the Center for Disease Control revealed that 28.5% of all male teenagers, aged 18-19 and attending U.S. colleges were overweight. The definition of overweight is a body mass index (BMI) of over 25.
In 2019, a professor in public health at a major university wanted to determine whether that proportion had decreased since 2008. So, he sampled 800 randomly selected incoming male freshman at universities around the country. Using the BMI measurements, he found that 210 of them were overweight. Test the professor’s claim at an α = 0.05 level of significance, the proportion of obese male teenagers in American colleges decreased. Make sure that any necessary assumptions for conducting the hypothesis test are satisfied.
A) State the null and alternative hypothesis.
H0:
Ha:
B) Determine the critical value(s) for the test.
C) Compute the test statistic (show your work).
D) Make your decision.
E) State your conclusion in terms of the professor’s claim.
Answer:
a) H0 : u = 28.5%
H1 : u < 28.5%
b) critical value = - 1.645
c) test statistic Z= - 1.41
d) Fail to reject H0
e) There is not enough evidence to support the professor's claim.
Step-by-step explanation:
Given:
P = 28.5% ≈ 0.285
X = 210
n = 800
[tex] p' = \frac{X}{n} = \frac{210}{800} = 0.2625 [/tex]
Level of significance = 0.05
a) The null and alternative hypotheses are:
H0 : u = 28.5%
H1 : u < 28.5%
b) Given a 0.05 significance level.
This is a left tailed test.
The critical value =
[tex] -Z_0.05 = -1.645 [/tex]
The critical value = -1.645
c) Calculating the test statistic, we have:
[tex]Z = \frac{p' - P}{\sqrt{\frac{P(1-P)}{n}}}[/tex]
[tex]Z = \frac{0.2625 - 0.285}{\sqrt{\frac{28.5(1-28.5)}{800}}}[/tex]
Z = -1.41
d) Decision:
We fail to reject null hypothesis H0, since Z = -1.41 is not in the rejection region, <1.645
e) There is not enough evidence to support the professor's claim that the proportion of obese male teenagers decreased.
The formula A=12(b+c)h. Write the equation in term of c?
Answer:
[tex]c = \frac{A}{12h} - b[/tex]
Step-by-step explanation:
Okay, so the goal is to isolate c on one side with all the other terms on the other side. So, let's start by dividing both sides with 12h. After we do that, we will be left with [tex]\frac{A}{12h} = b+c[/tex]. Now, we can subtract both sides by b, and we will be left with [tex]\frac{A}{12h} - b = c[/tex]. Yay! We've now isolated c and that is our final answer!
Hope this helped! :)
Marco bought gifts for his family at the school gift shop for the holidays. Marco bought 10gifts and spent $11.50. How many of each item did he buy if friendship bracelets cost $1.50 and stickers cost $1?
Step-by-step explanation:
Marco bought 10 gifts = 11. 50
If 5 bracelets = 1.50 x 5 = 7.5
4 stickers = 4 x 1 = 4
So total cost = 7.5 + 4 = 11.5
Look at recent question
Answer:
ok was it college math if so the I don't know
One brand of coffee is packaged in cylinders where the height is equal to the radius, r. The volume of the package, in cubic centimeters, can be found using the function V(r) = πr3. The number of ounces of coffee in the cylinder depends on the volume of the cylinder, V, in cubic centimeters. This can be modeled by the function C(V) = 3.2V. Which function can be used to find the number of ounces of coffee in the can based on its radius? C(V(r)) = 32.768πr3 C(V(r)) = 3.2πr3
Answer:
C(V(r)) = 3.2πr3Step-by-step explanation:
This problem is a composition of function defined by C(V(r)), now we have the functions [tex]V(r)= \pi r^{3}[/tex] and [tex]C(V)=3.2V[/tex], where the first depends on the radius, and the second dependes on the volume, that means, to find the number of ounce of coffe, we need to determine the volume of the cylinder, that's why we have to replace the volume function inside the ounces function,
[tex]C(V(r))=3.2(\pi r^{3} )[/tex]
Therefore, the right answer is the last choice.
Complete the five-number summary for the data set: 5, 2, 1, 3, 3, 6, 4, 2, 7.
you type in the answer
Answer:
NOOO OYU TYPE INTHE ANSWER
Step-by-step explanation:
A rectangular prism has dimensions of 2 ft, 4 ft, and 6 ft. If the dimensions are doubled, what would happen to the volume?
Answer:
Volume is increased in a factor of 8. The volume is increased from [tex]48\,ft^{3}[/tex] to [tex]384\,ft^{3}[/tex].
Step-by-step explanation:
The formula for the volume of the rectangular prism is:
[tex]V = w\cdot h \cdot l[/tex]
Where:
[tex]w[/tex] - Width
[tex]h[/tex] - Height
[tex]l[/tex] - Length
If dimensions are doubled, then volume is increased in a factor of 8:
[tex]V_{f} = (2\cdot w)\cdot (2\cdot h)\cdot (2\cdot l)[/tex]
[tex]V_{f} = 8\cdot w \cdot h \cdot l[/tex]
[tex]V_{f} = 8 \cdot V_{o}[/tex]
The volume is increased from [tex]48\,ft^{3}[/tex] to [tex]384\,ft^{3}[/tex].
A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.
Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.
Hey there! I'm happy to help out!
As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.
However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:
[tex]2^0, 2^1, 2^2, 2^3,2^4,... etc.[/tex]
So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!
[tex]2^9=[/tex] 2×2×2×2×2×2×2×2×2= 512
However, we want to find how much he has done in total! So, let's find how much he did on the other squares!
[tex]2^8[/tex]= 256
[tex]2^7[/tex]=128
[tex]2^6[/tex]=64
[tex]2^5[/tex]=32
[tex]2^4[/tex]=16
2³=8
2²=4
[tex]2^1[/tex]=2
[tex]2^0[/tex]=1
Now, we add these all up to find the total grains of rice!
512+256+64+32+16+8+4+2+1=895
Therefore, George has placed a total of 895 grains of rice on the chess board.
I hope that this helps! Have a wonderful day!
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We have,
On the first square, George placed 1 grain of rice.
On the second square, he placed 2 grains.
On the third square, he placed 4 grains.
On the fourth square, he placed 8 grains.
In general, on the nth square, he places [tex]2^{n-1}[/tex] grains.
So,
On the first 10 squares,
1 + 2 + 4 + 8 + ... + [tex]2^9[/tex]
This is a geometric series with a first term of 1 and a common ratio of 2.
The sum of the first n terms of a geometric series.
[tex]S_n[/tex] =[tex]a(1 - r^n) / (1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
Substituting the values,
[tex]S_{10}[/tex] = 1(1 - 2^10) / (1 - 2)
= 1(1 - 1024) / (-1)
= 1023
Therefore,
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
Learn more about geometric sequence here:
https://brainly.com/question/2321576
#SPJ7
6 to the power of 3 +7 times 4
Answer:
892
Step-by-step explanation:
1.] What is the probability of choosing a king
from a standard deck of playing cards?
Answer:
1/13
Step-by-step explanation:
there are 4 kings in a deck of 52 cards.
4/52 = 1/13
If V = 15 cm, W = 20 cm, X = 25 cm, Y = 7 cm, and Z = 22 cm, what is the perimeter of the object?
A.
53 cm
B.
64 cm
C.
118 cm
D.
78 cm
Answer:
Sum of all the sides.
Step-by-step explanation:
Perimeter is the sum of the distance in length or width, or height or circumference of all the sides of an object.
Therefore the sum total of the given sides V, W, x ,Y, Z are;
15 +20 + 25 + 7 + 22 = 89cm
Since a picture isn't available to know which sides of the objects can be added.
The sum of five consecutive integers is 70. What are the numbers?
Answer: The numbers are 12, 13, 14, 15, and 16.
Step-by-step explanation:
Write an algebraic equation.
x + (x+1) + (x+2) + (x+3) + (x+4) = 70
5x + 10 = 70
subtract 10 from both sides
5x = 60
divide each side by 5
x = 12
The numbers are 12, 13, 14, 15, and 16.
Answer:
12 to 16 :) hope it helped
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 2x − 4x3, a = −1 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 − 10(x + 1) + 12(x + 1)2 − 4(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 − 10(x + 1) + 4(x + 1)2 − 12(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 + 10(x + 1) + 12(x + 1)2 + 4(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 − 12(x + 1) + 10(x + 1)2 − 4(x + 1)3 [infinity] f n(−1) n! (x + 1)n n = 0 = 2 + 10(x + 1) + 4(x + 1)2 + 12(x + 1)3
Answer:
f(x) = 2 - 10 (1 + x) + 12 (1 + x)^2 - 4 (1 + x)^3
Step-by-step explanation:
The general form of the series is shown in the attachment. For the purpose here, we need to evaluate f(-1), f'(-1), f''(-1) and so on.
f(x) = 2x -4x^3; f(-1) = 2(-1)(1 -2(-1)^2) = (-2)(-1) = 2
f'(x) = 2 -12x^2; f'(-1) = 2 -12(-1)^2 = -10
f''(x) = -24x; f''(-1) = -24(-1) = 24
f'''(x) = -24; f'''(-1) = -24
So, the series is ...
f(x) = 2 -10(x +1)/1! +24(x +1)^2/2! -24(x +1)^3/3!
f(x) = 2 -10(x +1) +12(x +1)^2 -4(x +1)^3 . . . . . . . matches the first choice
Which description matches finding the volume of the solid ?
Answer:
As shown in the picture, the volume of solid is
V = Rectangular prism - half cylinder
Hope this helps!
:)
Answer:
Last option
Step-by-step explanation:
It's a cuboid/rectangular prism
The curve on top is due to half a cylinder being removed
Distance between (-1,0) and (8,6)
Answer:
3 √ 13
Step-by-step explanation:
Answer:
3√13
Step-by-step explanation:
We want to find the distance between these two points. To do so, we need to use the distance formula which states that the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is:
d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Here, [tex]x_1=-1,x_2=8,y_1=0[/tex], and [tex]y_2=6[/tex]. So:
d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
d = [tex]\sqrt{(-1-8)^2+(0-6)^2}=\sqrt{(-9)^2+(-6)^2} =\sqrt{81+36} =\sqrt{117} =3\sqrt{13}[/tex]
Thus, the answer is 3√13.
~ an aesthetics lover
In the phrase “rise over sun” shat does “rise” indicate?
How do you determine similarities in shapes?
Answer:
Step-by-step explanation:
. if every corresponding internal angles in both shapes are equal
. if all corresponding sides are equal or have same ratio.
more rules but depends on the shape also ( triangle, rectangle, hexagon,...)
Maggie is rock climbing. After reaching the summit, she descends 14 feet in 2 1/3 minutes. If she continues at this rate, where will Maggie be in relation to the summit after 8 minutes?
Answer:
about 27.42
Step-by-step explanation:
Classify each representation shown below as either linear or exponential.
x y
0 5
1 7.5
2 11.25
y = 2x + 4
One person sends an email to 2 people. Those 2 people send it to 4 people, and those 4 send it to 8 people.
1. Exponential
2. Linear
3. Exponential
arc length of a half of a circle with radius of 9
Answer:28.26
Step-by-step explanation:
Φ=180 since it's in a straight line
Radius=r=9
π=3.14
Length of arc=Φ/360 x 2 x π x r
Length of arc=180/360 x 2 x 3.14 x 9
Length of arc=0.5 x 2 x 3.14 x 9
Length of arc=28.26
Micheal buys a basket of mangoes on sale for 4 dollars before tax. The sales tax is 12%. What is the total price Micheal pays for the basket of mangoes?
Answer:
$[tex]4.48[/tex] is the total price.
Step-by-step explanation:
Mulitply the total by the percentage.
[tex]4 * .12 = .48[/tex]
Add those together.
[tex]4 + .48 = 4.48[/tex]
Total price of mangoes: $[tex]4.48[/tex]
Solve for x - y = -3
Answer:
0-3=-3
Step-by-step explanation:
If a sample mean is 37,which of the following is most likely the range of possible values that best describes an estimate for the population mean?
Answer:
(32, 42)
Step-by-step explanation:
Answer:
(32,42)
Step-by-step explanation:
