Answers
Answer:
C
Step-by-step explanation:
The right triangle on the right side of the figure has a height of 6 (two same sides lengths) and a base of 3.
x is the hypotenuse (side opposite of 90 degree angle).
We can use the pythagorean theorem to find x. The pythagorean theorem tells us to square each leg (height and base) of the triangle and add it. It should be equal to the hypotenuse square.
For this triangle it means, we square 6 and 3 and add it. It should be equal to x squared. Then we can solve. Shown below:
[tex]6^2 + 3^2 = x^2\\36 + 9 = x^2\\45 = x^2\\x=\sqrt{45}[/tex]
Now we can use property of radical [tex]\sqrt{x}\sqrt{y} =\sqrt{x*y}[/tex] to simplify:
[tex]x=\sqrt{45} \\x=\sqrt{5*9} \\x=\sqrt{5} \sqrt{9} \\x=3\sqrt{5}[/tex]
Correct answer is C
Answer:
The correct answer is option C. 3√5
Step-by-step explanation:
Points to remember
For a right angled triangle
Hypotenuse ² = Base² + Height²
From the attached figure we can see a square and a right angled triangle associated with the square.
Sides of square = 6
To find the value of x
Base = 3 and height = 6
Hypotenuse = x
x² = 3² + 6²
= 9 + 36 = 45
x = √45 = 3√5
Therefore the correct answer is option C. 3√5
Related Questions
An online ticket seller charges $44 for each ticket ton concert, plus a fixed handling fee of $12. Define the unknown variables and write an equation to model the situation.
Answers
Answer:
x= number of tickets bought
y= total
44x+12=y
3y + 15x = - 15
(a) y = 5x - - 5
(b) y = -5x - 5
(c) y = -5x + 5
(d) y = 5x + 5
Answers
Answer:
b
Step-by-step explanation:
Given
3y + 15x = - 15
Isolate 3y by subtracting 15x from both sides
3y = - 15x - 15 ( divide all terms by 3 )
y = - 5x - 5 → b
Answer:
B
Step-by-step explanation:
So, my buddy is new to doing Calculus and needs help understanding this equation, it would be very appeciated for some help
Answers
To evaluate the integral, rewrite the integrand as
[tex]x^{-x}=e^{\ln x^{-x}}=e^{-x\ln x}[/tex]
Recall that
[tex]e^x=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}\implies x^{-x}=\sum_{n=0}^\infty\frac{(-x\ln x)^n}{n!}[/tex]
The leftmost sum is the well-known power series expansion for the function [tex]f(x)=e^x[/tex]. In the rightmost sum, we just replace [tex]x[/tex] with [tex]-x\ln x[/tex].
This particular power series has a property called "uniform convergence". Roughly speaking, it's a property that says a sequence of functions [tex]f_n(x)[/tex] converges to some limiting function [tex]f(x)[/tex] in the sense that [tex]f_n(x)[/tex] and [tex]f_{n+1}(x)[/tex] get arbitrarily close to one another. If you have an idea of what "convergence" alone means, then you can think of "uniform convergence" as a more powerful form of convergence.
Long story short, this property allows us to interchange the order of summation/integration to write
[tex]\displaystyle\int_0^1x^{-x}\,\mathrm dx=\int_0^1\sum_{n=0}^\infty\frac{(-x\ln x)^n}{n!}\,\mathrm dx=\sum_{n=0}^\infty\frac{(-1)^n}{n!}\int_0^1(x\ln x)^n\,\mathrm dx[/tex]
The integral can be tackled with a substitution,
[tex]x=e^{-u/(n+1)}\implies-(n+1)\ln x=u\implies\mathrm dx=-\dfrac1{n+1}e^{-u/(n+1)}\,\mathrm du[/tex]
so that the integral is equivalent to
[tex]\displaystyle\int_0^1(x\ln x)^n\,\mathrm dx=\int_\infty^0\left(e^{-u/(n+1)}\right)^n\left(-\frac u{n+1}\right)^n\left(-\frac1{n+1}e^{-u/(n+1)}\right)\,\mathrm du[/tex]
[tex]=\displaystyle\frac{(-1)^n}{(n+1)^{n+1}}\int_0^\infty e^{-u}u^n\,\mathrm du[/tex]
The remaining integral reduces to [tex]n![/tex], which you can derive for yourself via integration by parts/power reduction.
So we have
[tex]\displaystyle\int_0^1x^{-x}\,\mathrm dx=\sum_{n=0}^\infty\frac{(-1)^n}{n!}\cdot\frac{(-1)^nn!}{(n+1)^{n+1}}=\sum_{n=0}^\infty\frac1{(n+1)^{n+1}}[/tex]
which is the same as
[tex]\displaystyle\sum_{n=1}^\infty\frac1{n^n}=\sum_{n=1}^\infty n^{-n}[/tex]
and hence the identity.
Please help me! Thank you!!
Answers
Answer:
x = 113
Step-by-step explanation:
The corresponding angles in both triangles are congruent
Hence x = 113
ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
It would be similar.
Which expression is a factor of both x^2 − 9 and x^2 + 8 x + 15
Answers
Answer:
x+3
Step-by-step explanation:
1. Use formula for the difference of squares:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
to factor
[tex]x^2-9=(x-3)(x+3).[/tex]
2. Factor [tex]x^2+8x+15:[/tex]
[tex]x^2+8x+15=x^2+3x+5x+15=x(x+3)+5(x+3)=(x+3)(x+5).[/tex]
Now you can see that [tex]x+3[/tex] is the common factor.
Answer:
x + 3
Step-by-step explanation:
x² - 9 ← is a difference of squares and factors as
x² - 9 = (x - 3)(x + 3)
To factor x² + 8x + 15
Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)
The factors are + 5 and + 3, since
5 × 3 = 15 and 5 + 3 = 8, thus
x² + 8x + 15 = (x + 5)(x + 3)
Thus the factor (x + 3) is common to both
Which expression is equivalent to the following complex fraction?
Answers
Answer:
Second Option: = 2(y-2x)/(3y-5x)
Step-by-step explanation:
The expression is:
=(2/x-4/y)/((-5)/y+3/x)
Taking LCM in both, numerator and denominator
= ((2y-4x)/xy)/((-5x+3y)/xy)
Since we know,
(a/b)/(c/d)=ad/bc
Applying the rule to the given fraction:
=(2y-4x)(xy)/(-5x+3y)(xy)
xy will be cancelled and we will be left with:
=(2y-4x)/(-5x+3y)
Taking 2 as common:
= 2(y-2x)/(3y-5x)
So the second option is the correct answer. ..
If m = 4 in and n = 6 in, what is the surface area of the geometric shape formed by this net?
A. 52 sq in
B. 56 sq in
C. 40 sq in
D. 64 sq in
Answers
Answer:
the answer is 64 sq. in
Step-by-step explanation:
first you need to find the area of the triangle
a =1/2 bh
= 1/2 (4 in) (6 in)
= 12 sq. in
then find the area of the square
area = lw
=(4 in) (4 in)
= 16 sq in.
then add
Surface area = 4 (12 sq in.) + 16 sq. in
= 64 sq. in
point A has an x coordinate of -2 and lies in a circle with a center at (0,0) and a radius of 5 . to the nearest tenth , what is the y-coordinate for point a ?
Answers
Answer:
the y-coordinate is ±√21
Step-by-step explanation:
Aren't you saying that the point lies ON the circle?
If so:
(x - h)^2 + (y - k)^2 = r^2
This becomes
x^2 + y^2 = r^2 because the center is at (0, 0).
This becomes x^2 + y^2 = 25 because the radius is 5.
Let's substitute -2 for x and find y:
4 + y^2 = 25, or y^2 = 21
Then the y-coordinate is ±√21
Answer:
The answer is B 4.6
Step-by-step explanation:
Its on edgen 2022
Iterations question 12 :) just need some help
Answers
Answer:
A
Step-by-step explanation:
The function is f(x) = [tex]6^x[/tex]
we need to find the value of the function when x = 3. We simply plug in 3 into x and solve.
f (3) = [tex]6^3[/tex]
This means 6 multiplied by itself 3 times. So
6 * 6 * 6 = 216
correct answer is A
Which point is a solution to the inequality shown in this graph? (0,-3)(5,0)
Answers
ANSWER
(0,-3)
EXPLANATION
The point which is a solution to the inequality must lie in the solution region ( the shaded region)
Also the boundary line is solid. This means that any point on the boundary line is a solution.
(6,0) zero falls outside the shaded region.
(5,-5) is also not in the shaded region.
(0,-5) is also not in the shaded region.
(0,-3) lies on the boundary line therefore it is a solution.
Answer: is 0,-3
Step-by-step explanation:
Isaac and William, in the mall parking lot, have found 11 quarters, 3 fifty-cent pieces, 36 dimes, 40 nickels, and 134 pennies. What is the experimental probability that the next coin they find is worth more than ten cents?
Answers
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
The experimental probability is based on what already happened.
So we see that both of them found a total of 11 + 3 + 36 + 40 + 134 = 224 coins.
The coins that are worth MORE THAN 10 cents are 11 quarters and 3 fifty-cent pieces (we exclude dimes because we want MORE THAN 10 cents, NOT 10 cents exactly).
So 11 + 3 = 14 coins are worth MORE THAN 10.
So the probability of finding one worth more than 10 cents next is 14/224 = 1/16
!!!please help!!!
The diagram below shows the dimensions of Tessa’s garden.
A) What is the perimeter, in feet, of Tessa’s garden? Show or explain all your work.
B) What is the area, in square feet, of Tessa’s garden? Show it explain all your work.
C) Tessa decoded that she liked the shape of her garden but wanted to have 2 times the area. She drew a design for a garden with every dimension multiplied by 2. Explain the error in Tessa’s design.
Answers
Perimeter =525.66 ft
Area = 10913.27 ft2
See photo
a spinner is divided into 6 equal sections numbered from 1 to 6 if the arrow is spun once what is the probability that it will land on a section numbered 4 or 5
Answers
Answer:
1/3
Step-by-step explanation:
4 and 5 are two terms
two out of 6 terms is one third
therefore it has a probability of one out of three
Answer:
the answer is 2/6 i just did this test
a cell phone is 84 mm long and 46 mm wide. what is the ratio of the width to the length
Answers
46:84, it can be simplified to 23:42
A ratio can be written in three different forms and then at that point will you simplify it. 46 width to 84 length, 46:84, 46/84. You can divide 46/84 by 2/2 which will then give you 23/42 or 23:42 or 23 mm wide to 42 mm long. Depends how you choose to express this ratio! Hope that helps
Lisa bought a computer on sale for 30 percent off of 599 dollars. What is the discount
Answers
Answer:
The discount is 179.70
Answer:
$419.30
Step-by-step explanation:
599*.30=179.7
599-179.7
=$419.30
A 9-meter piece of wire costs $8.64. What is the unit price?
Answers
Answer:
$0.96
Step-by-step explanation:
To find the unit price is to find the price of 1 meter.
9m = $8.64
1 m = 8.64 ÷ 9 = $0.96
Find the volume of the square pyramid shown. Round to the nearest whole number. The diagrams are not drawn to scale. Pleaseeee help
Answers
The answer is 392
Volume (for pyramid) = Length(width) Hight/3
Answer:
392 cm³
Step-by-step explanation:
The volume of a pyramid is one third the height times the area of the base.
V = ⅓ h A
The base is a square, so the area is the width times length.
V = ⅓ h wl
Given that h = 6 cm, w = 14 cm, and l = 14 cm:
V = ⅓ (6 cm)(14 cm)(14 cm)
V = 392 cm³
Based on the side lengths alone, could the triangles be similar?
No, the sides are not proportional.
Yes, the sides are in the ratio 2:5.
Yes, the sides are in the ratio 4:5.
Yes, the sides are in the ratio 1:5.
Answers
Answer:
Yes, the sides are in the ratio 2:5.
Can you mark me as the brainliest??
Answer: The correct option is
(B) Yes, the sides are in the ratio 2:5.
Step-by-step explanation: We are given to check whether the triangles can be similar based on the side lengths alone.
From the figure, we note that
the sides lengths of the triangle RST are
RS = 3.0 cm, ST = 6.0 cm and RT = 6.4 cm.
and the corresponding side lengths of triangle XUW are
XU = 7.5 cm, UW = 15.0 cm and XW = 16.0 cm.
So, the ratio of the corresponding sides of the two triangles are as follows :
[tex]\dfrac{RS}{XU}=\dfrac{3}{7.5}=\dfrac{30}{75}=\dfrac{2}{5},\\\\\\\dfrac{ST}{UW}=\dfrac{6}{15}=\dfrac{2}{5},\\\\\\\dfrac{RT}{XW}=\dfrac{6.4}{16}=\dfrac{64}{160}=\dfrac{2}{5}.[/tex]
Therefore, we get
[tex]\dfrac{RS}{XU}=\dfrac{ST}{UW}=\dfrac{RT}{XW}=\dfrac{2}{5}=2:5.[/tex]
Hence, the corresponding sides are proportional and they are in the ratio 2 : 5.
Thus, (B) is the correct option.
Plot three points that solve the equation -x-2y=-10
Answers
Answer:
See the attachment for a plot
Step-by-step explanation:
I find it convenient to plot lines using their x- and y-intercepts, when those are integers. To find the intercepts, we can divide the equation by the constant on the right:
x/10 +y/5 = 1
This is "intercept form". The denominator in each term is the corresponding intercept:
the x-intercept is 10, point (10, 0)
the y-intercept is 5, point (0, 5)
We can choose another value of y to find a third solution. Let y=2. Then we have ...
-x -2(2) = -10 . . . . . put 2 for y in the original equation
-x = -6 . . . . . . . . . . add 4
x = 6 . . . . . . . . . . . . multiply by -1
A third point is (6, 2)
Multiply 6x^2-4x-5(2x^2+3x)
Answers
Answer:
[tex]\large\boxed{6x^2-4x-5(2x^2+3x)=-4x^2-19x}[/tex]
Step-by-step explanation:
[tex]6x^2-4x-5(2x^2+3x)\qquad\text{use the distributive property}\\\\=6x^2-4x+(-5)(2x^2)+(-5)(3x)\\\\=6x^2-4x-10x^2-15x\qquad\text{combine like terms}\\\\=(6x^2-10x^2)+(-4x-15x)\\\\=-4x^2-19x[/tex]
Answer:
Step-by-step explanation:
I learned to solve these with a box method.
6x^2 -4x -5
2x^2
3x
with this method you add the matching terms
6x^2 -4x -5
2x^2 | 1 | 2 | 3
3x | 2 | 3 | 4
6x^2 -4x -5
2x^2 | 12x^4 | -8x^3 | -10x^2
3x | 18x^3 | -12x^2 | -15x
12x^4 + 10x^3 - 22x^2 - 15x
Tim’s height is 1m 20cm and Erica’s height is 1m. What is the simplified ratio of Tim’s height to Erica’s height?
Answers
Tim is 20 cm higher on height
Tim's height is 1m 20cm (120cm) and Erica's height is 1m (100cm). The simplified ratio of their heights is 6:5.
To find the simplified ratio of Tim's height to Erica's height, we need to convert both heights to the same unit of measurement (centimeters) before calculating the ratio.
Tim's height = 1m 20cm = 100cm + 20cm = 120cm
Erica's height = 1m = 100cm
Now, we can calculate the ratio of Tim's height to Erica's height:
Ratio = Tim's height / Erica's height
Ratio = 120cm / 100cm
Ratio = 6/5
The simplified ratio of Tim's height to Erica's height is 6:5.
To know more about ratio:
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Will give 30 points
The parks department has started building a new playground at Canyonside Park. The shape of the playground with wood chips?
The supervisor needs to purchase wood chips to cover the ground in the playground area. If wood chips are sold in bags containing enough to cover 4 square feet and these bags cost $8.00 apiece, how much will it cost to cover the entire area of the playground with wood chips?
a. $612.00
b. $1,224.00
c. $1,728.00
d. $4,896.00
Answers
Answer:
Option B. [tex]\$1,224[/tex]
Step-by-step explanation:
step 1
Find the area of the playground
The area of the playground is equal to the area of a rectangle plus the area of a triangle
[tex]A=(10)(36)+\frac{1}{2}(36)(24-10)=612\ ft^{2}[/tex]
step 2
Find the number of bags of wood chips needed
by proportion
[tex]\frac{1}{4}=\frac{x}{612} \\ \\x=612/4\\ \\ x=153\ bags[/tex]
step 3
Find the cost
[tex]\$8.00*(153)=\$1,224[/tex]
Answer:
ANSWER IS B
Step-by-step explanation:
YOUR WELCOME ENDGEUNITY STUDENTS
How do I find the percentages of things on a two way frequency table?
Answers
To find the percentages of things on a two-way frequency table, calculate the relative frequencies by dividing each frequency value by the total number of observations and multiplying by 100. This will give you the proportion of each category expressed as a percentage.
Explanation:To find the percentages of things on a two-way frequency table, you need to calculate the relative frequencies. The relative frequency is the fraction or decimal value that represents the proportion of each category. You can obtain the relative frequencies by dividing each frequency value by the total number of observations and then multiplying by 100 to convert it into a percentage.
For example, if you have a frequency of 5 in a certain category out of 100 total observations, the relative frequency would be -
= 5/100
= 0.05 or 5%.
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Finding percentages in a two-way frequency table involves understanding joint, marginal, and conditional distributions. Relative frequencies are calculated row by row, and expected frequencies are calculated based on population size and expected percentages. Marginal and conditional distributions focus on one variable or a subpopulation, respectively.
Explanation:To find the percentages of things on a two-way frequency table, you first need to understand what the contents of the table represent. The numbers in the body of the table are called joint frequencies. For example, if you have a value of 20 signifying the count of women who prefer football, and the total sample size is 50, then the percentage of relative frequency is (20/50)*100 = 40%.
Expected frequencies are calculated by multiplying the expected percentages by the total population size. For example, with an expected percentage of 0.15 and 600 as the total population, you'd calculate 0.15*600=90 as the expected frequency.
Relative frequencies are calculated by dividing each frequency by the total frequency. For example, if in one row the frequency is .25, and the total cumulative frequency so far is .15, then the cumulative relative frequency for that row would be .15 + .25 = .40. Repeat this process for each row to fill out the rest of the table.
A marginal distribution involves focusing on only one of the variables in the table. The reason why 20 (in the ratio 20/50) is a marginal frequency is because it represents the margin or part of the total population that is women.
A conditional distribution goes a step further by focusing on a particular subset of the population, not just one variable. For example, if we focus only on the subset of women who prefer football, we'd calculate the conditional distributions differently.
To find statistical measures such as the median, you can use the cumulative relative frequencies. In this case, you would look for the value corresponding to the 50th percentile in the cumulative relative frequency column.
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10(10-x) how do you distribute with this equation and what would you get?
Answers
Answer:
[tex]\boxed{100 - 10x}[/tex]
Step-by-step explanation:
The distributive property states that
a(b + c) = a·b + a·c
We can use this property solve your equation.
10(10 – x)
Distribute the 10
10×10 – 10×x
Do the multiplications
[tex]\boxed{100 - 10x}[/tex]
Use a calculator to find ln 0.0006. Round answer to 2 d.p.
Pls help, I'll give you 10 points!!!!!
Answers
ln(.0006) = -7.42
Any questions please just ask.
if F(x) = x+6 and G(x) = x^4, what is G(F(x))?
Answers
Answer:
c because f(x) is x+6 and the bracket means multiply
A tree casts a shadow of 23 meters. At the end of the shadow, the angle of elevation to the top of the tree is 37 degrees. Find the height of the tree
Answers
The best answer would give the hight of the shadow without the angle of elevation, not knowing the time of the day the shadow was measured
Answer:
17.33 meters
Step-by-step explanation:
Which function has a vertex at (2,6)
Answers
Answer:
B, f(x) = 2|x - 2| + 6
Step-by-step explanation:
the functions shown have vertical stretches, horizontal shifts, and vertical shifts as a transformation
we do not need to focus on the stretch, and moreso the shifts
the horizontal shift takes place on the x-axis and it is written with the parent function (in this case the parent function is |x|). when the shift is negative (ex: x -2), this means that the x-coordinate would be positive. if the shift is positive (ex: x + 2) the x-coordinate would be negative
the vertical shift takes place on the y-axis and unlike the horizontal shift, is written on the outside of the parent function, like the +6 and -6 in each of the functions we are given. when a shift is positive (ex: +6), the y-coordinate is positive and when a shift is negative (ex: -6) the y coordinate is negative
using this information, we can see that 2|x - 2| + 6 fits this criteria, as we have a positive vertex
therefore the answer is B, f(x) = 2|x - 2| + 6
The function that has a vertex at (2, 6) is:
f(x) = 2|x-2| + 6
To find the function with a vertex at (2, 6), we need to examine the general form of the absolute value function and how it affects the position of the vertex.
The general form of the absolute value function is f(x) = a |x - h| + k, where (h, k) represents the vertex of the absolute value function.
Given the vertex (2, 6), we have h = 2 and k = 6.
Now, let's analyze each given function:
1. f(x) = 2|x-2| - 6
This function has a vertex at (2, -6), not (2, 6). So, it's not the correct function.
2. f(x) = 2|x-2| + 6
This function has a vertex at (2, 6), which matches our given vertex. So, it could be the correct function.
3. f(x) = 2|x + 2| + 6
This function has a vertex at (-2, 6), not (2, 6). So, it's not the correct function.
4. f(x) = 2|x + 2| - 6
This function has a vertex at (-2, -6), not (2, 6). So, it's not the correct function.
Therefore, the function that has a vertex at (2, 6) is:
f(x) = 2|x-2| + 6
A=2.5
B=12
3a+9b=?
Please Help!
Answers
(3x2.5)+(9x12)
7.5+108
115.5
Answer:
3(2.5)+ 9(12)=
Multiply
7.5 + 108= 115.5
Step-by-step explanation:
Plzzz brainlist !!!