Answer:
O -x+y=-2
Step-by-step explanation:
-x + y = -5
⇔ y = x - 5
a line parallel to y = x - 5 must have the same slope as the line y = x - 5
Then
The equation of the parallel line is of the form : y = x + p
Finding p :
the point (-6,-8) lies on the parallel line means :
-8 = -6 + p
Then
p = -8 + 6 = -2
Finally :
y = x - 2 ⇔ -x + y = -2
question 12. write the product using exponents
Part 2: Approximately what value of will give her a box with the greatest volume? Explain your reasoning.
( only need part 2 already have part one thx)
The value of x that gives the box the greatest volume is approximately 2.08
How to determine the value that gives the greatest volume?The equation of the volume of the box is given as:
V(x) = x(12 - 2x)(13 - 2x)
Expand
V(x) = (12x - 2x^2)(13 - 2x)
V(x) = 156x - 24x^2 - 26x^2 + 4x^3
V(x) = 156x - 50x^2 + 4x^3
Differentiate the function
V'(x) = 156 - 100x + 12x^2
Set to 0
156 - 100x + 12x^2 = 0
Rewrite as:
12x^2 - 100x + 156 =0
Divide through by 4
3x^2 - 25x + 39 =0
Using a graphing calculator, the values of x are:
x = 2.08 and x = 6.26
Substitute these values of x in V(x)
V(2.08) = 2.08 * (12 - 2 * 2.08)(13 - 2 * 2.08) = 144.16
V(6.26) = 6.26 * (12 - 2 * 6.26)(13 - 2 * 6.26) = -1.56
The volume cannot be negative.
So, we have:
V(2.08) = 144.16
Hence, the value of x that gives the box the greatest volume is approximately 2.08
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evaluate the equation of 3 x 10^-2
Answer:
0.03
Step-by-step explanation:
the first thing you would do in this equation is to deal with the exponent
a negative exponent puts the number under 1
1/10^2
10^2 is also 100
1/100
3 * 1/100 is 3/100 so that is your answer
3/100 is also 0.03
Answer: [tex]\frac{3}{100}[/tex] or 0.03
Step-by-step explanation:
3×[tex]10^{-2}[/tex]
3 × [tex]\frac{1}{100}[/tex]
⇒ [tex]\frac{3}{100}[/tex]
⇒ 0.03
i need help on this please
Find the measures of the interior angles of the triangle.
I really need help with this, it is due 10 pm tonight, if you can help thanks so much :)
Answer:
∠ A = 140° , ∠ B = 30° , ∠ C = 10°
Step-by-step explanation:
the sum of the 3 interior angles = 180°
sum the given angles and equate to 180
x - 5 + 2x + 140 = 180
3x + 135 = 180 ( subtract 135 from both sides )
3x = 45 ( divide both sides by 3 )
x = 15
then
∠ A = 140°
∠ B = 2x = 2 × 15 = 30°
∠ C = x - 5 = 15 - 5 = 10°
Answer:
Angle A = 140°Angle B = 30°Angle C = 10°Step-by-step explanation:
Find the measures of the interior angles of the triangle.
The sum of the interior angles of a triangle is 180°180 = 140 + 2x + x - 5
40 + 5 = 3x
45 = 3x
x = 45 : 3
x = 15°
-----------------------
check
180 = 140 + 2 * 15 + 15 - 5
180 = 180
the answer is good
---------------------------
Find the angles
140° = angle A
2x = 15 * 2
2x = 30° (angle B)
x - 5 = 15 - 5
x = 10° ( angle C)
-----------------------
check
140 + 30 + 10 = 180°
the answer is good
If f(x) = x² — 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?
4
-2
2
04
Answer:
-2
Step-by-step explanation:
Given that;
f(x) = x² -2x
and g(x) = 6x + 4
(f + g)(x) = x²-2x+6x+4
:- x² +4x + 4 = 0
x² +2x +2x + 4 = 0
x(x + 2)+2(x + 2) = 0
(x + 2)(x + 2) = 0
:- x = -2
A triangle has sides with lengths of 55 feet, 65 feet, and 81 feet. Is it a right triangle?
yes
no
I am a bit confused on how to solve it so please explain
Answer:
Step-by-step explanation:
You could do it either way, but I have attached an image with one way to do it.
Then, using the exterior angle theorem, you can do:
(180-4x) + 100 = 3x
280 - 4x = 3x
280 = 7x
x = 40
From there, don't forget to plug in the numbers if you need to do so :)
What is the arc length of ACB?
Answer:
C. 82.43
Step-by-step explanation:
acb's angle is 315 degrees because
360 - 45 = 315
arc length is in radians
arc length is radius times (angle times (pi÷180))
arc length is 15 times (315 times (pi÷180))
arc length is 82.43
cuemathcomgeometry
Make sure your answer is in
degrees. You should be able to
find this without a calculator.
-
cos ¹(cos 43°) = [? ]°
Answer:
[tex]\cos^{-1}( \cos 43^{\circ}) = 43^{\circ}[/tex]
Step-by-step explanation:
The correct answer of the given function [tex]cos^{-1}[/tex] (cos 43°) will be 43°.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
It will be possible to comprehend the graphs, domains, differentiation, and integration of the four quadrants' trigonometric functions.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
We know that the inverse trigonometric function of any function will vanish.
[tex]cos^{-1}[/tex] (cos 43°) = 43° cos inverse has vanished with cos and thus 43° is coming out to be the answer.
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IF a universal set U = {x:x belongs to N , x less or equal to 10} , A ={y:y = 2n , n belongs to N , n less than 5} and B ={z:z = 3n , n belongs to N , n less than 4}
Answer:
your answer is N = {xxx: =9n
question 16. You sent an email to 8 friends. They each forwarded the email to 8 friends, and those friends each forwarded the email to 8 friends. The chain of emails is represented by the expression 8+8²+8³. How many people were sent your email.
Answer:
584
Step-by-step explanation:
8 + 8 squared + 8 cubed is 8 plus 64 plus 512 which is 584
this net can be folded to make a square pyramid. what is the surface area of the pyramid
Answer:
[tex]85in^2[/tex]
Step-by-step explanation:
to find the surface area we need to find the followng areas:
area of the square area of a triangle and multiply it by 4 (because there are 4 triangles)And once we have those areas, we add them to find the surface area.
Area of the square:
the formula to find the area of a square is:
[tex]a_{square}=l^2[/tex]
where [tex]l[/tex] is the length of the side: [tex]l=5in[/tex]
thus the area of the square is:
[tex]a_{square}=(5in)^2[/tex]
[tex]a_{square}=25in^2[/tex]
Area of the triangles:
the are of 1 triangle is given by
[tex]a_{triangle} =\frac{b*h}{2}[/tex]
where [tex]b[/tex] is the base of the triangle: [tex]b=5in[/tex] (the base of the triangle is the side of the square)
and [tex]h[/tex] is the height of the triangle: [tex]h=6in[/tex]
thus, the area of 1 triangle is:
[tex]a_{triangle} =\frac{(5in)*(6in)}{2}[/tex]
[tex]a_{triangle} =\frac{30in^2}{2}[/tex]
[tex]a_{triangle} =15in^2[/tex]
the area of the 4 triangles is (we multiply by 4):
[tex]a_{4-triangles}=4(15in^2)[/tex]
[tex]a_{4-triangles}=60in^2[/tex]
finally we add the area of the square and the area of the 4 triangles to find the total surface area:
[tex]Surface=25in^2+60in^2[/tex]
[tex]Surface=85in^2[/tex]
A doctoral student wants to determine the relationship between steps per minute and the time it takes to walk 100 feet in
minutes. Thirty trials are completed and the correlation coefficient between steps per minute and time in minutes is determined
to be -0.543. Therefore, fewer steps per minute were related to longer time spans. How is the correlation affected if the units for
time are changed from minutes to seconds? (3 points)
The correlation and time measurement would change proportionally to one another.
The correlation would increase because changing the units for time would result in an increase in time values.
It is impossible to determine the amount of change experienced by the correlation.
The correlation would decrease because only the units for one of the variables changed.
The correlation would stay the same because the change in units for time would have no effect on it.
Using correlation coefficients, it is found that that the correct option is given as follows:
The correlation would stay the same because the change in units for time would have no effect on it.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.The correlation coefficient does not have units, hence if the units of the measures is changed, the coefficient remains constant, which means that the correct option is given by:
The correlation would stay the same because the change in units for time would have no effect on it.
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(2/3 - 3/4 × 1/8) ÷ (2/3 - 3/4 + 5/8)
[tex]( \frac{2}{3} - \frac{3}{4} \times \frac{1}{8} ) \div ( \frac{2}{3} - \frac{3}{4} + \frac{5}{8} )[/tex]
Solution:First, solve the brackets.
First bracket:
[tex]( \frac{2}{3} - \frac{3}{4} \times \frac{1}{8} )[/tex]
[tex] = \frac{55}{96} [/tex]
Second bracket:
[tex]( \frac{2}{3} - \frac{3}{4} + \frac{5}{8} )[/tex]
[tex] = \frac{13}{24} [/tex]
Then divide.
[tex] \frac{55}{96} \div \frac{13}{24} [/tex]
[tex] = \frac{55}{52} \: or \: 1\frac{3}{52} [/tex]
answer:
as improper fraction= 55/52
as mixed fraction= 1 3/52
hope this helps
Find the slope of the line that passes through (6,9) and (9,5)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]
Find the slope of the line that passes through (6, 9) and (9, 5).
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond[/tex]
[tex]\boxed{\\\begin{minipage}{3cm}\xrightarrow {slope\:formula\:below} \\ $\displaystyle\frac{y_2-y_1}{x_2-x_1}$ \\ \end{minipage}}}[/tex]
Substitute 5 for y₂, 9 for y₁, 9 for x₂ and 6 for x₁:-
[tex]\boxed{\frac{5-9}{9-6}}[/tex]
On simplification,
↬ [tex]\boxed{\frac{-4}{3}}[/tex]
►So we conclude that the slope of the line is
►[tex]\boxed{-\frac{4}{3}}[/tex] ◀︎
Good luck.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Find the measure of all sides. Round to the nearest tenth.
Answer:
the value of x=9 and AB(h)=9.396
The battery life of a fully charged cell phone is normally distributed, with a mean of 14 hours and a standard deviation of 2 hours. What is the probability that a randomly selected cell phone will have a battery life of at least 8 hours
Answer:
.0013
Step-by-step explanation:
8 hours is 3 standard deviations BELOW the mean z-score = -3
from z scor table , tis corresponds to .0013
The graph of which equation is shown below?
Please answer quickly!!!
What does each line on the protractor stand for?
one-half of a degree
ten degrees
one degree
five degrees
Answer: I'm a fourth grader Here's my answer One degree
I hope This helps and yes It will make sense because Each on line is one degree and I got A test And it was right Any questions just type In the comments
A spinner with a yellow, blue, red, and green section is shown. The arrow is pointing at the yellow section. The fair spinner shown is spun 2 times. The set of possible outcomes are: S = {RR, BB, YY, GG, RB, BR, RY, YR, RG, GR, BY, YB, BG, GB, YG, GY} The number of yellows in the outcome is summarized in the table on the right. A 2-column table has 3 rows. The first column is labeled Yellow with entries 0, 1, 2. The second column is labeled Frequency with entries 9, 6, 1. Using the data from the theoretical probability table, what is the probability of the spinner landing only once on yellow in two spins? 0.0625 0.5625 0.375 1
The probability of the spinner landing only once on yellow in two spins is P = 0.375
How to get the probability?All the possible outcomes have the same probability, so, the probability that in two spins the spinner land only once in yellow is given by the quotient between the number of outcomes that have only one yellow and the total number of outcomes.
All the outcomes are:
{RR, BB, YY, GG, RB, BR, RY, YR, RG, GR, BY, YB, BG, GB, YG, GY}
16 in total.
The ones where the spinner lands only once on yellow are:
{RY, BY, YB, YG, GY, YR}
6 outcomes.
So the probability is:
P = 6/16 = 0.375
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Answer:C
Step-by-step explanation:
find (a) the arc length and (b) the area of a sector.
Answer:
a) 23.56 ft (2 dp)
b) 58.90 ft² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=r \theta[/tex]
[tex]\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}[/tex]
Calculation
Given:
[tex]\theta=\dfrac{3 \pi}{2}[/tex] r = 5 ft[tex]\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 5\left(\dfrac{3 \pi}{2}\right)\\& = \dfrac{15}{2} \pi \\& = 23.56\: \sf ft\:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(5^2) \left(\dfrac{3 \pi}{2}\right)\\\\& = \dfrac{25}{2}\left(\dfrac{3 \pi}{2}\right)\\\\ & = \dfrac{75}{4} \pi \\\\& = 58.90 \: \sf ft^2\:(2\:dp)\end{aligned}[/tex]
There are 7 seniors on the high school soccer team. Two of them will be
chosen to be co-captains. How many ways are there to choose the co-
captains?
Decide if this is a permutation or a combination, and then find the number of
ways to choose the co-captains.
The two co-captians can be chosen in 21 different ways.
How many ways are there to choose the co-captains?
If the two co-capitans are equivalent, then we need to find combinations.
So we want to find how many combinations of 2 elements we can make out of a set of 7 elements.
This is given by:
[tex]C(7, 2) = \frac{7!}{(7 - 2)!*2!} = \frac{7*6}{2} = 21[/tex]
So the two co-captians can be chosen in 21 different ways.
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what is the volume of a cylinder with a radius of 5
and a height of 12
Answer:
300pi
Step-by-step explanation:
the formula for volume of a cylinder is pi3^2h
So pi * (25) * 12
300 pi.
If you forget the formula, remember circle area is pir^2 and multiplying that by the height will raise the circle's area, giving us volume.
pls help with this question asap
Answer:
30 ft
Step-by-step explanation:
Perimeter
= 3 + 4 + 4 + 7 + 4 + 4 + 4
= 30 ft.
For Which distributions is the median the best measure of center?
Select each correct answer
Answer: 6, 6, 9 and 25
Step-by-step explanation:
bbringingbbringingout the data's from the graph and arrangementsarrangingarrangingarrangementsarrangingarranging them serially that's from smallest to biggest biggest, then selecting the middle number if the number of entire entries is an odd number but if it's an even number you take the average of the two middle number
HELP ASAP PLEASEE
Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown. Circles X and Y are shown. Circle X has a radius of 6 units and circle Y has a radius of 2 units. Which steps would prove the circles similar?
-Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 4.
- Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 4.
-Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
-Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3.
Answer & step-by-step explanation:
to arrive at the similarity, the transformation must be as follow:
the small circle will be dilated for a specific scale factor,
the radius of X circle is R= 6, and the radius of the small circle is r = 2
besides, two circles are similar if and only if R = r, (their radius ar equal)
therefore r = 2*k = 6, and from where k = 6 / 2 = 3 units
the answer is
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
Answer:
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
Step-by-step explanation:
To prove circles are similar:
Translate the circles so that they share a common center point. (The circles are now concentric as they have the same center).
Dilate the smaller circle to increase its size to coincide with the larger circle. The amount that the circle needs to be dilated by is the scale factor.
As the radius of circle Y is 2 and the radius of circle X is 6, determine the scale factor by dividing the larger radius by the smaller radius:
scale factor = 6 ÷ 2 = 3
Solution:
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
By the way, you forgot to give us the image:
According to a survey, 15% of city workers take the bus to work. donatella randomly surveys 10 workers. what is the probability that exactly 6 workers take the bus to work? round the answer to the nearest thousandth.
The probability that exactly 6 workers take the bus to work is 0.001
How to determine the probability?The given parameters are:
Sample size, n = 10Required sample = exactly 6Probability of success, p = 15%The probability that exactly 6 workers take the bus to work is calculated using the following binomial expression
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x{[/tex]
So, we have:
[tex]P(6) = ^{10}C_6 * (15\%)^6 * (1 - 15\%)^4[/tex]
Evaluate the expression
P(6) = 0.001
Hence, the probability that exactly 6 workers take the bus to work is 0.001
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5 The diagram shows three identical shapes. į of
shape A is shaded and of shape C is shaded.
What fraction of shape B is shaded? ......
Answer:
7/24
Step-by-step explanation:
The total amount of unshaded area of shape B is the sum of the areas of the unshaded regions of shapes A and B.
Unshaded area in A: 1 - 2/3 = 1/3
Unshaded area in C: 1 - 5/8 = 3/8
Sum of unshaded areas of A and B: 1/3 + 3/8 = 8/24 + 9/24 = 17/24
Shaded area of B: 1 - 17/24 = 24/24 - 17/24 = 7/24
8. Between what two consecutive integers must the value of log, 7342 lie? Justify your answer.
9. Between what two consecutive integers must the value of log, (500) lie? Justify your answer.
Can someone help me with these questions? I don’t understand what the question is asking or how to solve. Only 8 and 9
The two consecutive integers that the value of log₄7342 lie between are 6 and 7
The two consecutive integers that the value of log₅(1/500) lie between are -4 and -3
What are consecutive integers?Consecutive integers are whole numbers that follow each other without gaps. For example, 1 and 2; 6 and 7; 5 and 6; 18 and 19 etc.
From the question, we are to determine between what two consecutive integers must the value of log₄7342 lie
The value of log₄7342 = 6.42
On the number line, 6.42 is between 6 and 7.
Hence, the two consecutive integers that the value of log₄7342 lie between are 6 and 7
For log₅(1/500)
The value of log₅(1/500) = -3.861
On the number line, -3.861 is between -4 and -3
Hence, the two consecutive integers that the value of log₅(1/500) lie between are -4 and -3
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