1. First, you must apply the formula for calculate the sum of the interior angles of a regular polygon, which is shown below:
(n-2) × 180°
"n" is the number of sides of the polygon (n=5).
2. Then, the sum of the interior angles of the pentagon, is:
(5-2)x180°=540°
3. The problem says that the measure of each of the other interior angles is equal to the sum of the measures of the two acute angles and now you know that the sum of all the angles is 540°, then, you have:
α+α+2α+2α+2α=540°
8α=540°
α=540°/8
α=67.5°
4. Finally, the larger angle is:
2α=2(67.5°)=135°
5. Therefore, the answer is: 135°
If x is the measure in degrees of each of the acute angles, then each of the larger angles measures 2x degrees. Since the number of degrees in the sum of the interior angles of an n-gon is 180(n-2), we have
x+x+2x+2x+2x=540 ⇒ 8x = 540 ⇒ x=135/2.
The large angles each measure 2x=135 degrees.
Convert 5x + 6y = -5 to slope-intercept form. Simplify your answer
The shampoo you like to use is on sale. But you only get the lower price if you buy 3 bottles. You want to know how much you'll save.
Write a formula that will help you determine how much you'll save by buying 3 bottles
on sale.
Let's let
s = sale price per bottle
r = regular price per bottle
c = cost savings
In the figure the horizontal lines are parallel and AB=CB=CD, if LM=5 find JM
Each shape is 1 whole. What fraction is represented by the shaded part of the model?
Fraction is a way to describe a part of a whole. The fraction is represented by the shaded part of the model is [tex]\dfrac{2}{1}[/tex].
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25
If we look at each of the shapes, we can observe that the whole of the shape is shaded therefore, the shaded part of the shape is equal to the shape which is represented by 1.
Now, in the image, there are two shapes given each of which is completely shaded, and the whole shape is represented by 1. therefore, these two shapes will be represented by 2.
The shaded shape can be written as,
[tex]2 = \dfrac{2}{1}[/tex]
Hence, the fraction is represented by the shaded part of the model is [tex]\dfrac{2}{1}[/tex].
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A parabola has a vertex at (0,0). The focus of the parabola is located on the positive x-axis. Which part of the graph will the directrix pass through? the origin the negative part of the x-axis the positive part of the x-axis the negative part of the y-axis
Answer with explanation:
→→Information given about Parabola
Vertex of the Parabola = (0,0)
Focus is located on the positive x- axis.
Definition of Parabola: A parabola is locus of all the points such that distance from a fixed point known as focus to distance from a fixed line called, Directrix is always constant.
Let focus of the parabola be (k,0), where , k>0.
Distance between vertex (0,0) and focus(k,0) = Distance between vertex (0,0) and point on negative x-axis (-k,0).
Directrix will pass through point (-k,0).
So, equation of Directrix will be, x= -k
Directrix will pass through
Option B: The Negative part of the x -axis.
Evaluate the dot product of (6,-3) and (8,5).
If all terms of a series are positive, the series sums to a positive number?
A.
The statement is false because the series could converge to a negative number.
B.
The statement is true because the series will converge to a positive number because the series contains no negative terms.
C.
The statement is true because the series cannot diverge since all the terms are positive.
D.
The statement is false because the series could diverge.
A geometric series is the sum of an unlimited number of terms with a fixed ratio between them. The correct option is B.
What is geometrical series?A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.
The given statement "If all terms of a series are positive, then the series sums to a positive number" is true because the series will converge to a positive number because the series contains no negative terms.
Hence, the correct option is B.
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Finn bought 2 packs of stickers. Each pack had the same number of stickers. A friend gave him 4 more stickers. Now he has 24 stickers in all. How many stickers were in each pack. Explain how you solved it.
Let the number of stickers in each pack be 'x'
Finn bought 2 packs of stickers.
Number of stickers in 2 packs = [tex] 2 \times x [/tex] = 2x
According to the question, a friend gave him 4 more stickers and now he has 24 stickers in all.
Therefore, [tex] 2x+4=24 [/tex]
[tex] 2x=24-4 [/tex]
[tex] 2x=20 [/tex]
x = 10
Therefore, number of stickers in each pack are 10.
Jamie is making treat bags with 1/3 cups of M&M's in each bag how many cups of M&M's will she need to make 20 bags
A(n)___ schedule is a table that gives the details of loan payments.
a local post office sells stamps in packs of 4, 6 and 7. andy bought several packs of 4. erin bought several packs of 6. jarred bought several packs of 7. each of the three friends ended up with the same number of stamps that each person could have purchased?
The number of stamps each could have purchased is 84
How to determine the number of stamps each purchased
From the question, we have the following parameters that can be used in our computation:
Andy = packs of 4
Erin = packs of 6
Jarred = packs of 7
Expand 4, 6 and 7
So, we have
4 = 2 * 2
6 = 2 * 3
7 = 7
The LCM of 4, 6 and 7 is then calculated as
LCM = 2 * 2 * 3 * 7
Evaluate
LCM = 84
Hence, the number of stamps each could have purchased is 84
name AND define the two ways to classify polynomials
Rita rode her bicycle out into the country at a speed of 20 miles per hour and returned along the same route at 15 miles per hour. If the round trip took 5 hours and 50 minutes, how far out did she ride?
find the product of 3 and 3/4 and 1 1/10 how do you find the product and how did you come up with it could you show your work
In the neighborhood park there is a circular grassy picnic area, but half of the grass has died. The city wants to replant the grads, but needs to know the square footage of the damaged area. If the circular picnic are is 150 feet across what is the square footage of the damaged area
Answer: The damaged area is equal to 8831.25ft^2
Step-by-step explanation:
We know that we have a circular area, where half of the grass has died. We know that the circular picnic is "150 feet across" I guess this means that if you walk in a straight line from the edge of the circular area, through the middle, and to the next edge, the distance is 150ft.
This would mean that the diameter is equal to 150ft.
With this we can calculate the total area of the circle; this is:
A = pi*r^2
where r is the radius, that is half the diameter, so we have r = 150ft/2 = 75ft
and pi = 3.14
so we have:
A = 3.14*(75ft^)^2 = 17662.5ft^2
And we know that half of that area has the grass damaged, so the amount of square feet of grass needed is equal to A/2 = (17662.5ft^2)/2 = 8831.25ft^2
Solve the inequality and graph on a number line. 7x + 4 ≤ x – 2
solve this equation for x. round to the nearest hundredth. 0.8=logx
A single card is drawn from a deck. find the probability of selecting a heart or a 8.
Answer with Step-by-step explanation:
Let
A:selecting a heart
Total cards=52
number of hearts=13
P(A)=13/52
B:selecting a 8
number of 8=4
P(B)=4/52
A∩B:selecting a heart with 8 on it
number of hearts with 8 on it=1
P(A∩B)=1/52
A∪B:selecting a heart or a 8
We have to find P(A∪B)
P(A∪B)=P(A)+P(B)-P(A∩B)
= [tex]\dfrac{13}{52}+\dfrac{4}{52}-\dfrac{1}{52}[/tex]
=[tex]\dfrac{13+4-1}{52}[/tex]
= 16/52
= 4/13
Hence, the probability of selecting a heart or a 8 is:
4/13
Work out: 2/3 x 2 =
the floor plan of a kitchen is shown at the right. if the entire floor is to be tiled, how many square feet of tile are needed
Can every even number be written as a sum of two primes?
Final answer:
No, not every even number can be written as a sum of two primes. This is known as the Goldbach Conjecture, which states that every even number greater than 2 can be expressed as the sum of two prime numbers.
Explanation:
No, not every even number can be written as a sum of two primes. This is known as the Goldbach Conjecture, which states that every even number greater than 2 can be expressed as the sum of two prime numbers. So far, this conjecture has been tested for even numbers up to at least 4, and no counterexamples have been found. However, it has not been proven to be true for all even numbers.
For example, the number 4 can be expressed as the sum of two primes (2 + 2), but the number 6 cannot be expressed as the sum of two primes. On the other hand, the number 8 can be expressed as the sum of two primes (3 + 5). This pattern continues, with some even numbers being expressible as the sum of two primes and others not.
find the value of r so that the line passes through (1,2) and (5,r) has a slope of -8
Bill needs to find the area of the ground covered by a conical tent. The tent is 12 feet tall and makes a 70° angle with the ground. Which expression can be used to find the area?
a) π · (12 · tan 70°)2
b) 36 · π
c) π · (12tan 70°12tan 70°)2
d) π · (tan 70°12tan 70°12)2
a) π · (12 · tan 70°)2. To find the area of the ground covered by the conical tent, use the formula for the surface area of a cone, A = πr(r+√(r^2+h^2)).
Explanation:To find the area of the ground covered by the conical tent, we can use the formula for the surface area of a cone. The formula is A = πr(r+√(r^2+h^2)), where r is the radius and h is the height of the cone.
In this case, the height of the cone is 12 feet and the angle it makes with the ground is 70°. To find the radius, we can use trigonometry. The radius is given by r = h tanθ, where θ is the angle with the ground. Plugging in the values, we get r = 12 tan(70°).
Now, substituting the value of r into the formula for the surface area of the cone, we get A = π(12 tan(70°))(12 tan(70°)+√((12 tan(70°))^2 + 12^2)). This simplifies to option a) π · (12 · tan 70°)2.
x+y= -9
x+2y= -25
According to the system of equations above, what is the value of y?
62, 52, 52, 52, 64, 69, 69, 76 for the given sample data, find
What is the radius of a circle circumscribed about a rectangle with a length of 8 centimeters and a width of 6 centimeters?
Answer:
I think its 5
Step-by-step explanation:
I may be wrong
A baker has 34 cup of sprinkles to spread on cupcakes. Each cupcake needs 18 cup of sprinkles.
The baker uses the fraction model that is partially shown to find the number of cupcakes that will have sprinkles.
mediaIMG7358611486128321.jpg34=6
Which is the correct division equation that describes the model?
A. 18 ÷
B. 34÷18=8
C. 34÷18=6
D. 18÷34=332
Five coins are tossed. let x be the number of heads and y be the number of tails. find the expectation
which of the following statements are true? Select all that apply.
a) The image of the point (-3,-5) under a reflection across the x-axis is (3,-5).
b) The image of the point (1,9) under a reflection across the y-axis is (1,-9).
c) The image of the point (8,7) under a reflection across the line y=-x is (-7,-8).
d) The image of the point (-6,-6) under a reflection across the y=x is (-6,-6).
e) The image of the point (2,4) under a reflection across the y-axis followed by a reflection across y=xis (-2,-2).
f) Point K (3,-1)is reflected across the x-axis to creak point K'.The line x+3y=6 passes through point K'.
Answer: The answer in order are false, false, true, true, false and (3,1)
Step-by-step explanation:
We know that image of a point (x,y) under the y-axis
is (-x,y) i.e. the sign of x coordinate changes
Similarly in case of x-axis sign of y coordinate changes
i.e (x,y) is reflected to (x,-y)
Also the reflection of (x,y) under the line y=x is (y,x)
and the reflection of (x,y) under the line y=-x is(-y,-x)
So
a) Given image of (-3,-5) under x-axis is (3,-5).
Hence statement is false
b) Given image of (1,9) under y-axis is (1,-9)
Hence the statement is false
c) Given image of (8,7) under y=-x is (-7,-8)
i.e. the statement is true
d) Given image of (-6,-6) under y=x is (-6,-6)
i.e the statement is true
e) Given image of (2,4) under y axis followed by x-axis is (-2,-2)
Hence the statement is false
f) (3,-1) is reflected in x-axis to (3,1)
Hence the point k is (3,1)
Answer:
a
b
e
g
Step-by-step explanation:
I just did the assignment lol-
If x = 3 inches, y = 10 inches, w = 5 inches, and z = 5 inches, what is the area of the object?
A.33 square inches
B.40 square inches
C.20 square inches
D.60 square inches
If x = 3 inches, y = 10 inches, w = 5 inches, and z = 5 inches. Then the area of the given figure is 40 inches.
What is area?"The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc."
What is the area of the square ?The area of the square is side times side i.e., a^2.
What is area of the rectangle ?The area of the rectangle is length times width i.e., l*b.
Here,
x = 3 inches, y = 10 inches, w = 5 inches, z = 5,
In the given figure:
Area of the square BCDE is a^2 = 5^2 = 25
Area of the rectangle ABFG is l*b = 5*3 = 15
Total area of the figure is = area of the square + area of the rectangle = 25+15 = 40.
Hence, the answer is option B.
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