Step-by-step explanation:
45⁴⁵ 15¹⁵
(3²·5)⁴⁵ (3·5)¹⁵
(3⁹⁰ 5⁴⁵) (3¹⁵ 5¹⁵)
3¹⁰⁵ 5⁶⁰
3⁷⁵ 3³⁰ 5⁶⁰
3⁷⁵ (3·5²)³⁰
3⁷⁵ 75³⁰
a square and a triangle have equal perimeters. the square has a perimeter of 4(2p-4), and the triangle has a perimeter of 4p+36. find the perimeter value.
A. p= 72
B. p= 44
C. p= 88
D. p= 36
Answer:
C
Step-by-step explanation:
Since the figures have equal perimeters we can equate them, thus
4(2p - 4) = 4p + 36 ← distribute left side
8p - 16 = 4p + 36 ( subtract 4p from both sides )
4p - 16 = 36 ( add 16 to both sides )
4p = 52 ( divide both sides by 4 )
p = 13
Substitute p = 13 into either of the 2 expressions, then
4p + 36 = 4(13) + 36 = 52 + 38 = 88 → C
The value of perimeter is found as 88 units. The correct option is (C).
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
As per the question the perimeters are equal.
The following equation can be written as,
4(2p - 4) = 4p + 36
⇒ 8p - 16 = 4p + 36
⇒ 4p = 52
⇒ p = 13
Thus, the perimeter value can be obtained by substituting p = 13 in 4p + 36 as below,
⇒ 4 × 13 + 36 = 88
Hence, the perimeter value is 88 units.
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Last night, the two dinner specials at Ava's favorite restaurant were salmon filet and steak. The restaurant served 64 specials in all, 75% of which were salmon filets. How many salmon filets did the restaurant serve?
Answer:
48
Step-by-step explanation:
64 times 0.75 is 48
____probability is the predicted ratio of favorable outcomes to the total number of outcomes.
THEORETICAL probability is the predicted ratio of favorable outcomes to the total number of outcomes.
TRUE or FALSE
If an angle has a measure of 1 radian, then the arc intercepted by that angle has an arc length equal to the radius of the circle.
Answer: True
Step-by-step explanation: the angle subtends, s, divided by the radius of the circle, r. One radian is the central angle that subtends an arc length of one radius (s = r). Since all circles are similar, one radian is the same value for all circles.
The given statement is correct. If an angle has a measure of one radian, the arc intercepted by that angle has an arc length equal to the radius of the circle.
What is meant by radian and radius?Simply put, a Radian is a unit of measurement for angles that is based on the radius of a circle. This means that if we imagine wrapping the length of the radius around a circle, the angle formed at the center of the circle by this arc is equal to 1 Radian. Radians, like degrees, are a type of angle measurement. One radian is equal to the angle formed when the radius of the circle is equal to the arc opposite the angle. So, in the diagram above, the angle is one radian because the arc AB is the same length as the radius of the circle.Therefore,
Because the Latin word for length is spatium, arc lengths are denoted by s.
Length of an Arc = θ × r,
Where θ exists in radian.
Length of an Arc = θ × (π/180) × r,
Where θ exists in degree
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An angle, θ, is in standard position. The terminal side of the angle passes through the point (4, 5).
Find cosθ.
Answer:
cos Θ = [tex]\frac{4}{\sqrt{41} }[/tex]
Step-by-step explanation:
Given the angle passes through (4, 5 ) then the right triangle with sides 4 and 5 has hypotenuse h given by
h² = 4² + 5² = 16 + 25 = 41 ( take the square root of both sides )
h = [tex]\sqrt{41}[/tex]
In relation to Θ, 4 is adjacent and 5 is opposite, thus
cos Θ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{\sqrt{41} }[/tex]
Answer: 4√41/41
Step-by-step explanation:
The base diameter and the height of a cone are both equal to x units. A cone has a height of x and a diameter of x. Which expression represents the volume of the cone, in cubic units?
Answer:
1/12piX^3
Step-by-step explanation:
Theo wants to use a cookie recipe
that makes 36 cookies, but he wants
to increase the number of cookies to
54. If the recipe calls for 2 cups
of sugar, how much sugar should
he use?
how do you graph y = 5
Answer:
start at the origin (0,0) then move up 5 (Don't count the origin as the first move up). Now your point is (0,5)
Step-by-step explanation:
Look at the image below.
This is how you graph y=5
(4,2) in y+mx+b form
Line 1
Line 2
Graph above
Answer:
Step-by-step explanation:
Can someone help me with this question please !
Answer:
a) A triangle which the angles ratio is 1 : 2 : 3 is a 30º - 60º - 90º right triangle.
b) The shortest side is opposite to the shortest angle. So, we can calculate it using sin 30º.
[tex]$\text{sin}(30\º)=\frac{\text{Opposite side to x}}{19} $[/tex]
[tex]$\frac{1}{2} =\frac{\text{Opposite side to x}}{19} $[/tex]
[tex]$\text{Opposite side to x}= 9.5$[/tex]
Answer:
see explanation
Step-by-step explanation:
(a)
Sum the parts of the ratio, 1 + 2 + 3 = 6 parts
Divide 180° ( sum of angles in a triangle ) by 6 to find the value of one part of the ratio.
180° ÷ 6 = 30° ← value of 1 part of the ratio, thus
2 parts = 2 × 30° = 60°
3 parts = 3 × 30° = 90°
Thus the triangle is right
-----------------------------------------
(b)
The sides of a 90°- 60°- 30° triangle are in the ratio
2 - [tex]\sqrt{3}[/tex] - 1 ( where 2 represents the hypotenuse )
Thus the other 2 sides of the triangle are
19 ÷ 2 = 9.5 , and
9.5 × [tex]\sqrt{3}[/tex] ≈ 16.45
The shortest side is 9.5
Find the volume of a pyramid with a square base, where the side length of the base is 16.6\text{ m}16.6 m and the height of the pyramid is 10.1\text{ m}10.1 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
55.4 m^3
Step-by-step explanation:
The volume of a pyramid of base area A and height h is V = (1/3)(A)(h).
Here, V = (1/3)(16.6 m)^2 * 10.1 m = 55.4 m^3
Answer:
55.4 m^3
Step-by-step explanation:
I need help in this question I’ve been stuck on it for so long :)
Answer:
Linear
Step-by-step explanation:
We see that in the left column, the integers increase by one at a time and that in the right column, the integers decrease by two at a time. Therefore, the rate of the increasing and decreasing of numbers is the same throughout the table so this line is linear.
Also, you could use desmos, a graphing calculator which is free on your computer to plot these points and to see that the line is linear.
plz do this one I very appreciated if you did this question
Answer:
113.04 meters
Step-by-step explanation:
pi*r^2
3.14*6*6= 113.04
Answer:
The Answer is 113.1m²
Step-by-step explanation:
Area is πr²
Sprinkler shoots 6m
a = π6²
a = 3.14 * 36
area is 113.1m²
how to get a perimeter of 200
Answer:
You could have a square with side of 50 ft.
Step-by-step explanation:
If the odds in favor of an event happening are 3-7, what is the probability of Sant
that event happening?
Answer:
30%
Step-by-step explanation:
when a transversal cuts a pair of parallel lines, name one angle that is formed
Answer:
Angle pairs formed by parallel lines cut by a transversal When two parallel lines are given in a figure, there are two main areas: the interior and the exterior. When two parallel lines are cut by a third line, the third line is called the transversal.
Step-by-step explanation:
Answer:
Step-by-step explanation:
If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°.
Identify the slope and y-intercept of the line.
y = 6x-5
Answer:
slope = 6
y-intercept = -5
Step-by-step explanation:
The equation is in slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept
Let's find the slope:
The slope is the number being multiplied by x.
y = mx + b
y = 6x - 5
Therefore, the slope is 6.
Let's find the y-intercept:
The y-intercept is the last number in the equation.
y = mx + b
y = 6x -5
Therefore, the y-intercept is -5.
Angle θ is in standard position and terminates in quadrant II. If tanθ = -15/8, then cscθ = _____.
Answer:
csc Θ = [tex]\frac{17}{15}[/tex]
Step-by-step explanation:
Given
tan Θ = - [tex]\frac{15}{8}[/tex] = [tex]\frac{opposite}{adjacent}[/tex] ← of a right triangle , then
hypotenuse h² = 15² + 8² = 225 + 64 = 289 ( square root both sides )
h = [tex]\sqrt{289}[/tex] = 17
Using the identity
csc x = [tex]\frac{1}{sinx}[/tex]
sin Θ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{15}{17}[/tex]
Since Θ is in second quadrant then sinΘ and csc Θ > 0, thus
csc Θ = [tex]\frac{1}{\frac{15}{17} }[/tex] = [tex]\frac{17}{15}[/tex]
write 0.126126126... as a fraction
Answer:
x = 126/999
Step-by-step explanation:
Let x = .126126126 repeating
Multiply each side by 1000
1000x = 126.126126126 repeating
subtract the first equation from the second
1000x = 126.126126126 repeating
- x = .126126126 repeating
999x = 126
Divide each side by 999
999x/999 = 126/999
x = 126/999
QUICK ANSWER THIS!!!
j/-2+7=−12
Answer:
38
Step-by-step explanation:
j/-2=-19
j=38
Answer:
38
Step-by-step explanation:
J/-2+7=-12
-7 -7
J/-2 -19
x-2 x-2
J= 38
I was trying to edit but it kept saying "an error occured"
I'm sorry
Find the volume of a right circular cone that has a height of 4.5 ft and a base with a
diameter of 14.2 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
The volume of the cone is:
237.6 cubic feet.Step-by-step explanation:
The volume of a cone is:
Volume of a cone = (1/3) PI * r^2 * hWhere:
r = radius.
h = height.
Since the exercise provides the diameter but not the radius, you simply have to divide the diameter in two:
Radius = diameter / 2 Radius = 14.2 ft / 2 Radius = 7.1 ft / 2Now we proceed to replace in the formula:
Cone volume = (1/3) PI * (7.1 ft)^2 * 4.5 ft Cone volume = 237.5515285 ft^3 Cone volume = 237.6 ft^3What are the coordinates of the vertices of a triangle A'B'C' that results from a translation of triangle ABC two units
down?
A’ (0,1) B’(4,0)C’(-3,-2)
A’(-2,1) B’(2,0)C’(-5,-6)
A’(-4,3) B’(0,2)C’(-7,-4)
A’(-2,5) B’(2,4)C’(-5,-2)
i need help will give brainliest!!!
Answer:
A
Step-by-step explanation:
Answer:
The answer is B.
Step-by-step explanation:
Because you have your slope (4.20) it doesn't matter what it is just as long as it is there.
A set of sofa prices are normally distributed with a mean of 2500 dollars and a standard deviation of 200 dollars.
A leather sofa has a price of 2410 dollars.
What proportion of sofa prices are higher than the price of the leather sofa?
You may round your answer to four decimal places.
We have been given that a of sofa prices are normally distributed with a mean of 2500 dollars and a standard deviation of 200 dollars. A leather sofa has a price of 2410 dollars. We are asked to find the proportion of sofa prices that are higher than the price of the leather sofa.
First of all, we will find the z-score corresponding to sample score 2410.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{2410-2500}{200}[/tex]
[tex]z=\frac{-90}{200}[/tex]
[tex]z=-0.45[/tex]
Now we need to find area under normal curve that is greater than z-score of [tex]-0.45[/tex] that is [tex]P(z>-0.45)[/tex].
Using formula [tex]P(z>a)=1-P(z<a)[/tex], we will get:
[tex]P(z>-0.45)=1-P(z<-0.45)[/tex]
Now we will find area under curve using normal distribution table.
[tex]P(z>-0.45)=1-0.32636[/tex]
[tex]P(z>-0.45)=0.67364[/tex]
Upon rounding to 4 decimal places, we will get:
[tex]P(z>-0.45)\approx 0.6736[/tex]
Therefore, approximately 0.6736 of sofa prices are higher than the price of the leather sofa.
Answer:
0.6736
Step-by-step explanation:
khan academy
How many meters are 60 km equal to?
A. 60,000 m
B. 600 m
C. 6,000 m
D. 6 m
Answer:
1km = 1000m
=> 60km = 60 x 1000 = 60000m
=> Option A is correct.
Hope this helps!
:)
Match the relational or logical operations to their corresponding output.
Answer:
try and put them do in order
Step-by-step explanation:
Thanks for coming to us with your question. I know this answer is quite late, but hopefully it'll be helpful to others.
Answer:
False --> 1011 > 1100
True --> 110 + 111 == 1101
50 --> 1010 x 101
13 --> 110 + 111
17 --> 1010101 / 101
Step-by-step explanation:
This solution is achieved by calculating the binary operations, then finding either their values or the validity of their statements.
1011 > 1100 is the same as 11 > 12, which is false.
110 + 111 == 1101 is the same as 6 + 7 = 13, which is true.
1010 x 101 is the same as 10 x 5, which is 50.
110 + 111 is the same as 6 + 7, which is 13.
1010101 / 101 is the same as 85 / 5, which is 17.
Need help with this pls!!
(Show work pls)
Answer:
length of each side is 17cm
Answer: length of each side is 17cm
Step-by-step explanation:hoped this helped
Need help with the photo above no work needed just explain and the answer the the question thank you
Answer:
Step-by-step explanation:
If you think money, a question like this won't confuse you.
Which would you rather owe your parents
13 dollars or
10 dollars
The answer is obvious, isn't it? Most people would rather owe 10 dollars rather than 13.
The minus sign is the same as debt. - 13 is less than - 10. You are further and further in the hole when you owe 13 dollars than 10.
So the inequality is not correct. The answer is no.
So still with money
-13<- 11
13 > 11
you would rather have 13 dollars in your pocket than 10.
You would rather owe -10 dollars than - 13
Potatoes cost $4 for every 5 pounds Letr represent the number of pounds of potatoes purchased and y represent the cost of the
Create an equation to represent the relationship between the cost and number of potends of potatoes Enter a number in the
the equation
Answer:
$20
Step-by-step explanation:
Solve the equation -10X +1 + 7X = 37
Answer:
X = -12
Step-by-step explanation:
-10X + 1 +7X = 37
-10X + 7X + 1 = 37 {Add the like terms}
-3X + 1 = 37 {Subtract 1 form both sides}
-3X + 1 -1 = 37 -1
-3X = 36 {Divide both sides by (-3)}
[tex]\frac{-3x}{-3}=\frac{36}{-3}\\\\[/tex]
X = -12
Answer:
-12
Step-by-step explanation: