remember the pythagorean theorem:
a² + b² = c²
where c is the hypotenuse.
so:
[tex] {a}^{2} + {b}^{2} = { ( \sqrt{26)}}^{2} [/tex]
the square and the square root cancel each other out, so...
a² + b² = 26
we know that a and b are of equal length given the angles.
so it's
[tex] { \sqrt{13} }^{2} + { \sqrt{13} }^{2} = 26[/tex]
here the squares and square roots also cancel, but to keep the equation from the formula true we need to write them. that makes the difference between optional and B
Option A is correct,
[tex] \sqrt{13} inches[/tex]
Which statement is true about the equations
-3x + 4y = 12 and 1/4x-1/3y = 1
O The system of the equations has exactly one solution at (-8, 3).
O The system of the equations has exactly one solution at (-4, 3).
O The system of the equations has no solution; the two lines are parallel.
O The system of the equations has an infinite number of solutions represented by either equation.
Gemma recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 16 miles per hour faster than on her way home. If Gemma spent a total of 1 hour bicycle, find the two rates.
first speed --- x mph
return speed -- x+16 mph
6/x + 6/(x+16) = 1
times each term by x(x+16)
6(x+16) + 6x = x(x+16)
x^2 + 4x - 96 = 0
(x-8)(x+12) = 0
x = 8 or x is a negative
her first speed was 8 mph
her return speed was 24 mph
check:
6/8 + 6/24 = 1 , that's good!
Mary Katherine has a bag of 3 red apples , 5 yellow apples and 4 green apples , Mary takes a red apples out of the bag and does not replace it. What is the probability that the next apple she takes out is yellow
Answer:
5/11.... you put the 5 which is yellow over the others which is 12 but remember she removed 1 so it would be equal to 11
Answer:
ok so if she takes a red apple out that means
2 red
5 yellow
4 green
11 in total
so 5/11
The answer is D
Hope This Helps!!!
Need help ASAP
HELP PLEASEE
Lim x>0 (x(e^3x - 1)/(2 - 2cosx))
Evaluating the limand directly at x = 0 yields the indeterminate form 0/0. If L'Hopital's rule is known to you, you can compute the limit by applying it twice:
[tex]\displaystyle\lim_{x\to0}\frac{x\left(e^{3x}-1\right)}{2-2\cos(x)} = \lim_{x\to0}\frac{3xe^{3x}+e^{3x}-1}{2\sin(x)} \\\\\\ = \lim_{x\to0}\frac{9xe^{3x}+6e^{3x}}{2\cos(x)} = \frac62=\boxed{3}[/tex]
Is the collection og rall " student in set ? why ? class7
Answer:
in secret
Step-by-step explanation:
correct answer is in a secret
Find the distance between the two points in simplest radical form. (-6,1) and (−8,−4)
Answer: 5
Step-by-step explanation: I think it is 5
Find the mean of the following data set.
8, 5, 15, 12, 10
A. 12.5
B. 10
C. 14
D. 50
Answer:
10
Step-by-step explanation:
the sum of 8,5,15,12,10 is 50 and there are 5 numbers so 50 divided by 5 is 10 and it's mean is also 10
hope this helps !
\int (x+1)\sqrt(2x-1)dx
Answer:
[tex]\int (x+ 1) \sqrt{2x-1} dx = \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C[/tex]
Step-by-step explanation:
[tex]\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}[/tex]
[tex]\int (x+1)\sqrt(2x-1)dx\\\\ = uv - \int v du[/tex]
[tex]= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ u = x + 1 => du = dx \ ][/tex]
[tex]= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\[/tex]
If 5x = 3x+12 then x = …..
↦ [tex]\huge\underline{ \underline{Answer:-}}[/tex]
[tex]5x = 3x + 12 \\ 5x - 3x = 12 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Step-by-step explanation:
Explanation is in the attachmenthope it is h helpful to you
f(x) = -16x^2 + 22x + 3
Answer:
factor???
Factored Form: y= (-1)(8x+1)(2x-3)
Step-by-step explanation:
Please look at the included picture, show me your work and please include a good explanation. It would really help me out here.
These are indeed equivalent, and this identity is one of DeMorgan's laws.
The 6th column is the negation of the 5th column. For example, the first row says
not p or q
is true (T), so the negation would be false (F). The 5th column reads {T, F, T, T}, so the next column should be {F, T, F, F}.
Then in the 7th/last column, you are checking the truth value of the statement
p and not q
For example, in the first row, both p and q are true (T). This means (not q) is false, so (p and not q) is false (F). The last column should end up reading {F, T, F, F}, same as the previous column.
Find the length of arc AB
Step 1: Find the circumference of the circle
Formula for circumference: C = 2 * pi * r
C = 2 * pi * 27
C = 54pi
Step 2: Find the length of the desired arc
We are only looking for 20 degrees out of 360 degrees, therefore we can multiply our circumference by 20/360.
20/360 * 54pi = 3pi units
Hope this helps!
You’re making 40 servings of English custard. Each serving is 250 ml. The following recipe yields 2 L.
Calculate how much of each ingredient you will need to make enough servings of the custard.
Milk 2 L
Vanilla essence 4 ml
Sugar 200 g
Egg yolks 20
Answer:
Milk 10 L
Vanilla essence = 20 ml
Sugar = 1kg
Egg yolks 100 yolks
Step-by-step explanation:
2l/250ml = 8 servings per recipe ,
40 servings/8 = 5 "batches"
Milk 2 L * 5 = 10 L
Vanilla essence 4 ml * 5 = 20 ml
Sugar 200 g * 5 = 1000g = 1kg
Egg yolks 20 * 5 = 100 yolks
2) There are 40 boys and 60 girls in a class of students. What is the ratio of girls to students
Answer:
60:100, 6/10, 3/5, 6 to 10, etc.
Step-by-step explanation:
You take the number of girls over total students which is boys + girls. Since there's 40 boys and 60 girls, it's 60 girls to 100 students which can be written in several ways.
Answer:
60:100 / 3:5
Step-by-step explanation:
You first add the total number of students which is (40boys + 60girls) which gives us 100 students.
Then arrange the ratio of girls to students as per the question that is 60:100, reduce it to its lowest term that is dividing the ratio by 20, and finally got 3:5
The probability that a 38-year-old white male will live another year is .99813. What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy
Answer:
The insurance company should charge $1,873.5.
Step-by-step explanation:
Expected earnings:
1 - 0.99813 = 0.00187 probability of the company losing $1 million(if the client dies).
0.99813 probability of the company earning x(price of the insurance).
What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy?
Break even means that the earnings are 0, so:
[tex]0.99813x - 0.00187(1000000) = 0[/tex]
[tex]0.99813x = 0.00187(1000000)[/tex]
[tex]x = \frac{0.00187(1000000)}{0.99813}[/tex]
[tex]x = 1873.5[/tex]
The insurance company should charge $1,873.5.
which of the following function shows the absolute value parent function FX=lxl shifted up
Answer:
The answer is C.
as for C . the value of f(x) increases by 7 and so the graph goes up by units 7.
OR
g(x) = |x| + 7
we know that |x| is f(x), so :-
g(x) = f(x) + 7
and since f(x) is plot on y- axis the graph climbs the y axis by 7 units
*The graph shifts right or left for the other functions*
Please help:
Given: ∠4 is congruent to ∠2
Prove: ∠3 and ∠1 are supplementary
Statements and Reasons
Answer:
See Below.
Step-by-step explanation:
We can write a two-column proof.
Statements: Reasons:
[tex]\displaystyle 1)\, \angle 4\cong \angle 2[/tex] Given
[tex]\displaystyle 2)\, \angle 3 \cong \angle 4[/tex] Vertical Angles are Congruent
[tex]\displaystyle 3) \, \angle 1 + \angle 2 = 180[/tex] Linear Pair
[tex]\displaystyle 4)\, \angle 1 + \angle 4 = 180[/tex] Substitution
[tex]\displaystyle 5) \, \angle 1 + \angle 3 = 180[/tex] Substitution
[tex]\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}[/tex] Definition of Supplementary Angles
What is the gradient of the blue line?
5
4
3
2
1
-5 -4 -3 -2 - 1 0 1. 2. 3. 4. 5
- 1
- 2
- 3
- 4
- 5
The line starts at (-5,3) and finishes (5,0.5)
Answer:
The gradient is -0.25
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-5,3)[/tex]
[tex](x_2,y_2) = (5,0.5)[/tex]
Required
The gradient (m)
This is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{0.5-3}{5--5}[/tex]
[tex]m = \frac{-2.5}{10}[/tex]
[tex]m = -0.25[/tex]
The greatest number of elements possible in
Answer:
4
9
Step-by-step explanation:
If X has 5 elements, and Y has 4 elements, and all 4 of Y's elements are the same as 4 of X's elements, then the intersection of the sets has 4 elements.
If X has 5 elements and Y has 4 elements, and they are all different, then the union of the sets has 9 elements.
Answer:
4
9
What is the value of 3 minus (negative 2)?
A number line going from negative 5 to positive 5.
Answer:
5
Step-by-step explanation:
3-(-2) will become positive 5. so number line will go towards positive 5.
A group of 40 bowlers showed that their average score was 192. Assume the population standard deviation is 8. Find the 95% confidence interval of the mean score of all bowlers.
Answer:
[tex]CI=189.5,194.5[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=40[/tex]
Mean [tex]\=x =192[/tex]
Standard deviation[tex]\sigma=8[/tex]
Significance Level [tex]\alpha=0.05[/tex]
From table
Critical Value of [tex]Z=1.96[/tex]
Generally the equation for momentum is mathematically given by
[tex]CI =\=x \pm z_(a/2) \frac{\sigma}{\sqrt{n}}[/tex]
[tex]CI =192 \pm 1.96 \frac{8}{\sqrt{40}}[/tex]
[tex]CI=192 \pm 2.479[/tex]
[tex]CI=189.5,194.5[/tex]
The cone and the cylinder below have equal surface area. O A. True O B. False
Answer:
the answer is false
Step-by-step explanation:
comment if you want explanation
Answer:
True
Step-by-step explanation:
When using the formulas to find the surface area, both have equal surface area
Identify the effect on the graph of replacing f(x) by A f(x)
Answer:
See explanation
Step-by-step explanation:
Required
Effect of replacing [tex]f(x)[/tex] with [tex]f(x - h)[/tex]
f(x) is represented as: (x,y)
While
f(x - h) is represented as (x - h, y)
Notice the difference in both is that, the x value in f(x - h) is reduced by a constant h while the y value remain unchanged.
This means that the graph of f(x) will shift horizontally (i.e. along the x-axis) to the left by h units
if you subtract 1/2 from a number and multiply the result by 1/2 you get 1/8. What is the no.
Step-by-step explanation:
1/6
1/6- 1/2 = 1/4
1/4*1/2= 1/8
Suppose you buy a home and finance $275,000 at $2,223.17 per month for 30 years. What is the amount of interest paid? (Round your answer to the nearest cent.)
Explanation:
30 years = 30*12 = 360 months
If the monthly payment is $2,223.17 for 360 months, then you'll pay back a total of 2223.17*360 = 800,341.20 dollars overall.
Subtract off the amount financed, or amount loaned, to get the total interest.
800,341.20 - 275,000 = 525,341.20 is the amount of interest paid (in dollars).
This works because effectively, the total amount paid back consists of principal + interest. The principal is the amount the bank loans you.
So we could rephrase that last equation into saying
principal + interest = 275,000 + 525,341.20 = 800,341.20 = total amount paid back.
2/9 divided by 5/6
help pleaseee
Hey there!
[tex]\mathsf{\dfrac{2}{9}\div\dfrac{5}{6}}[/tex]
[tex]\mathsf{= \dfrac{2\times6}{9\times5}}[/tex]
[tex]\mathsf{2\times 6 = \bf 12}[/tex]
[tex]\mathsf{9\times5 = \bf 45}[/tex]
[tex]\boxed{\mathsf{=\bf \dfrac{12}{45}}}[/tex]
[tex]\large\textsf{BOTH NUMBERS has the Greatest Common Factor (GCF) of 3}[/tex]
[tex]\mathsf{= \dfrac{12\div3}{45\div3}}[/tex]
[tex]\mathsf{12\div3=\bf 4}[/tex]
[tex]\mathsf{45\div3=\bf 15}[/tex]
[tex]\boxed{\mathsf{=\bf \dfrac{4}{15}}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{4}{15}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\~\frak{Amphitrite1040:)}}[/tex]
Two linear equations are shown in the graph.
#Brainliest award
What are the coordinates of the point where the two lines intersect?
A. (–2, 3)
B. (3, 3)
C. (3, 0)
D. (–3, 3)
Answer:
I am taking this graph because this question looked similar to this one.
Step-by-step explanation:
Answer should be B.
The intersection point is (3,3)
Help meeee plzzzzzz!!!!
OPTION B is the correct answer.
A table is on sale for $247, which is 76% of the regular price.
What is the regular price?
Answer:
$325
Step-by-step explanation:
Find the regular price by dividing 247 by 0.76:
247/0.76:
= 325
So, the regular price was $325
