The goalposts are 6.92m tall.
Angle of incidence Equals Angle of reflection, according to the physics principle of reflection.
Both angles ( θ) are equal, as seen in the attached image.
m<ABC = mADC = 90° - θ
m<ACB = mECD = 90°
detailed explanation?
Angle of incidence Equals Angle of reflection, according to the physics principle of reflection.
Both angles ( θ) are equal, as seen in the attached image.
m<ABC = mADC = 90° - θ
m<ACB = mECD = 90°
Thus, the ABC triangle and the EDC triangle will both be similar.
Their corresponding sides will also be proportionate due to the property of comparable triangles
AB/BD = CB/CD.
1.15/ED = 2.0/12.5
ED = 1.15 * 12.05 /2.0
ED= 6.92
ED = ED = 6.92 m
The goalposts are 6.92m tall.
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find the sum of 6 terms in the sequence 3,6,12, ...
A group of friends decided to buy bulk chocolate from a candy store. If some friends
each want 1/7 of a kilogram of chocolate of the 10 kilograms of chocolate
purchased, then how many people can get a share of chocolate?
70 people can get share from the chocolate.
What is share?Real estate investment trusts, limited partnerships, and mutual funds all employ shares as a sort of unit. A share is an immovable unit of capital that symbolizes the ownership connection between the company and the shareholder. The denominated value of a share is its face value, which could not be the same as the share's market value.
The capital of a firm consists of the whole face value of its issued shares.
Total amount of chocolate purchased = 10 kg
Amount of chocolate each friend want =1/7 kg
So, number of people who can get share = 10 / (1/7)
= (10×7)/1
= 70 people
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19. the sum of twelve and sixteen divided by the sum of three and four
20.the difference of twenty-two and six divided by the sum of five and three
21.the sum of thirty-six and fourteen divided by the product of two and five
22.the quotient of thirty-two and four divided by the sum of one and three
23.the sum of six and fifteen divided by 24.the difference of thirteen and nine
25.the difference of thirty-one and seventeen divided by the product of ten
Answer:
they require the use of fractions.
Step-by-step explanation:
sum means to add both numbers
difference means to subtract the small number from the big number
quotient means to divide
product means to multiply
24. 13-9= 4
not sure what you meant by q23 and q25.
19. the sum of twelve and sixteen divided by the sum of three and four = 4
20. the difference of twenty-two and six divided by the sum of five and three = 2
21. the sum of thirty-six and fourteen divided by the product of two and five = 4
22. the quotient of thirty-two and four divided by the sum of one and three = 2
23. the sum of six and fifteen divided by 24 = 21/24
24. the difference of thirteen and nine = 4
25. the difference of thirty-one and seventeen divided by the product of ten = 7/5 = 1.4
HELP! EZ MATH!! ANSWER QUICK PLEASE!!!
Answer:
The correct answer is 57. 4^3 was misidentified as 4×3.
Step-by-step explanation:
[tex] {4}^{3} - 7 = 64 - 7 = 57[/tex]
Please answer asap please and thank you
Answer:
Step-by-step explanation:
A carpenter has a 15 foot ladder. For safety, the bottom of his ladder must be placed 5 feet from the wall. In order to complete his work, the ladder must reach 14.5 feet up the wall. Under these conditions, can the carpenter complete his work? Rounded to the nearest tenth, how far up the wall does the ladder reach?
The carpenter will not be able to complete his work because the ladder reach 14.1 ft up the wall.
In this question, we have been given a carpenter has a 15 foot ladder. For safety, the bottom of his ladder must be placed 5 feet from the wall.
Consider the following diagram.
In right triangle ABC, AC represents the length of the ladder, CB is the distance between wall and the bottom of the ladder.
Using Pythagoras theorem,
AC² = AB² + BC²
15² = 5² + AB²
225 - 25 = AB²
AB = √200
AB = 14.1 ft ............(1)
We have been given that in order to complete his work, the ladder must reach 14.5 feet up the wall.
From (1), we can see that the ladder will reach 14.1 ft up the wall.
This means, under these conditions, the carpenter will not be able to complete his work.
Therefore, the carpenter will not be able to complete his work because the ladder reach 14.1 ft up the wall.
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Whats 6% of 583! Because its very confusing and if you can help that would be great
Answer:
34.98is the answer ............ .............
Answer: 34.98
Step-by-step explanation:
'Percent (%)' means 'out of one hundred':
6% = 6 'out of one hundred',
p% is read p 'percent',
6% = 6/100 = 6 ÷ 100
What does it mean to calculate the percentage of a number?
6% of 583 = ?
... is equivalent to multiplying them:
6% × 583 = ?
6% of 583 =
6% × 583 =
6/100 × 583 =
(6 ÷ 100) × 583 =
6 × 583 ÷ 100 =
3,498 ÷ 100 =
34.98
Maran is selling candy apples at a fund-raiser for a charity. She made 160 candy apples and spent $120 on ingredients and supplies. She sold all the candy apples for $480.
Select TWO statements that are true.
A.Maran spent $3 on each candy apple.
B.Maran spent $0.75 on each candy apple.
C.Maran sold each candy apple for $4.
D.Maran earned a profit of $3 on each candy apple sold.
E.Maran sold each candy apple for $3.
If Maran made 160 candy apples, spending $120 on ingredients and supplies while selling all the candy apples for $480, then the two statements that are true are:
B. Maran spent $0.75 on each candy apple (Cost Price), and
E. Maran sold each candy apple for $3 (Selling Price).
As per the question statement, Maran made 160 candy apples, spending $120 on ingredients and supplies while selling all the candy apples for $480.
We are required to identify the two true statements from a the set of 5 statements, provided in the question itself, related to the per candy cost price, sell price and profit of Maran.
Since he made 160 candy apples, spending $120 on ingredients and supplies, therefore, the cost price of per candy will be $(120/160) = $0.75, i.e., Statement B that Maran spent $0.75 on each candy apple is True.
Also, he sold all 160 candies for a total of $480, therefore, the sell price of each candy is $(480/160) = $3. Hence, Statement E that Maran sold each candy apple for $3., is also true.
Now, since the cost price of each candy is $0.75 and the sell price of the same is $3, then Maran made a profit of $(3 - 0.75) = $2.25 per candy. But statement D mentions that Maran earned a profit of $3 on each candy sold, which is false.
Cost Price: It is the price at which, an object or commodity is manufactured or bought at, by the retailer.Selling Price: It is the price at which, the commodity is sold by the retailer, and if the selling price is higher than the cost price, the retailer is said to earn a profit, while in the opposite case, the retailer is said to incur a loss.To learn more about Cost Prices & Selling Prices, click on the link below.
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plsssss help meeeeeeeeeeeeeee
Answer:
136 ,24 ,180 ,34
Step-by-step explanation:
Please explain!!
A DVD has a diameter of 12 centimeters. What is the area of the dvd? Round your answer to the nearest hundredth.
Answer:
Given diameter (D) = 12Radius = D = 26Circumference = πD= 12π= 37.699111843078Area = π(D)22= 36π= 113.09733552923
Mary paid $16 for her 12 month subscription to Word Up magazine. How much did Mary pay per magazine?
Answer: 1.3333333333....
Step-by-step explanation: 16 divided by 12 is 1.3333333333333333333333333333333333333333333333333333333333333333333333333333..................................................................
If Mary spent 16 dollars for 12 magazines, it would be $1.33 for each.
x y
7 11
8 13
9 15
10 17
27
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
The correct answer is that y does not vary directly with x.
If y and x are directly related, then the equation y=kx would be true for each point in the set.
What is the explanation:
If y is directly related to x, then every point in the set would fit the equation y=kx.
For the first point, we would have 11=7k, which would imply that k=11/7.
For the second point, we would have 13=8k, which would imply that k=13/8.
By utilizing proportions to check, we can see that 11/7 does not equal 13/8.
Cross multiplying yields 11*8=7*13, or 88=91
Since this is untrue, k is not a constant and y does not change in accordance with x.
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Show the relationship between -5/6 and -7/10. Use an inequality symbol
[repost]
From the inequality concept ( -7 / 10) > ( -5 / 6).
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Given fractional numbers are -5/6 and -7/10. The numbers in the form of inequality will be calculated as:-
-7 / 10 = -0.7
-5 / 6 = -0.84
-0.7 > -0.84
-7 / 10 > -5 / 6
Therefore, from the inequality concept ( -7 / 10) > ( -5 / 6).
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Factorise the following:
a) x^2 + 10x + 16
b) x^2 + 7x + 12
c) x^2 + 13x + 12
Answer:
Step-by-step explanation:
a)
[tex]x^2+10x+16=\\x^2+2x+8x+16=\\x(x+2)+8(x+2)=\\(x+2)(x+8)[/tex]
b)
[tex]x^2+7x+12=\\x^2+3x+4x+12=\\x(x+3)+4(x+3)=\\(x+3)(x+4)\\[/tex]
c)
[tex]x^2+13x+12=\\x^2+x+12x+12=\\x(x+1)+12(x+1)=\\(x+1)(x+12)[/tex]
Answer:
[tex]\textsf{(a)} \quad (x+8)(x+2)[/tex]
[tex]\textsf{(b)} \quad (x+4)(x+3)[/tex]
[tex]\textsf{(c)} \quad (x+12)(x+1)[/tex]
Step-by-step explanation:
Factoring quadratics
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].Rewrite [tex]b[/tex] as the sum of these two numbers.Factor the first two terms and the last two terms separately.Factor out the common term.Part (a)[tex]\textsf{Given}: \quad x^2+10x+16[/tex]
Two numbers that multiply to 16 and sum to 10 are: 2 and 8.
[tex]\implies x^2+2x+8x+16[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+2)+8(x+2)[/tex]
Factor out the common term (x + 2):
[tex]\implies (x+8)(x+2)[/tex]
Part (b)[tex]\textsf{Given}: \quad x^2+7x+12[/tex]
Two numbers that multiply to 12 and sum to 7 are: 3 and 4.
[tex]\implies x^2+3x+4x+12[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+3)+4(x+3)[/tex]
Factor out the common term (x + 3):
[tex]\implies (x+4)(x+3)[/tex]
Part (c)[tex]\textsf{Given}: \quad x^2+13x+12[/tex]
Two numbers that multiply to 12 and sum to 13 are: 1 and 12.
[tex]\implies x^2+x+12x+12[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+1)+12(x+1)[/tex]
Factor out the common term (x + 1):
[tex]\implies (x+12)(x+1)[/tex]
5. Which of the following functions has a graph with the largest positive x-intercept?
A. f(x) = 2(x+5)-1
B. f(x) = 8(x+8)
c. f(x) = 2(x-8) +1
D. f(x)=13(x-3)
The function which has a graph with the largest positive x-intercept is C. f(x) = 2(x-8) +1
What is a x-intercept?The value of the x coordinate at the point where the graph crosses the x-axis is known as the x-intercept for any curve. Alternatively, we can say that the x-intercept is the value of the x coordinate at the point where the value of the y coordinate equals zero.
Let y be 0, so lets find the x-intercept of
A. 2(x+5)-1 = 0
⇒ 2(x+5) = 1
⇒ 2x + 10 = 1
⇒ 2x = -9
⇒ x = -9/2
B. 8(x+8) = 0
⇒ x+8 = 0
⇒ x = 0 −8
⇒ x = −8
C. 2(x-8) +1 = 0
⇒ 2x − 15 = 0
⇒ 2x = 15
⇒ x = 15/2
⇒ x = 7.5
D. 13(x-3) = 0
⇒ x − 3 = 0/13
⇒ x − 3 = 0
⇒ x = 0 + 3
⇒ x = 3
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The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?
The dimensions are 24 by 13.5 cm
How to determine the dimensions of the rectangle?The given parameters are
Length = 3 cm less than twice the width
This means that
L = 2W - 3
Where
L represents Length and W represents Width
The perimeter is given as
P = 75 cm
The perimeter is calculated as
P = 2*(L + W)
So, we have
2*(L + W) = 75
This gives
2*(2W - 3 + W) = 75
Evaluate
2*(3W - 3) = 75
Divide by 2
3W - 3 = 37.5
So, we have
3W = 40.5
Divide by 3
W = 13.5
Recall that
L = 2W - 3
So, we have
L = 2 * 13.5 - 3
Evaluate
L = 24
Hence, the dimensions of the rectangle are 24 by 13.5 cm
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Margie has 15 feet of ribbon. It takes 7/8 of a foot of ribbon to make a bow for a bouquet. How many bows can Margie make with her ribbon?
Margie can make 13 bows with her ribbon.
In the US, a foot is used to measure length or distance. "Feet" is the plural form of the single unit of measurement known as "foot." Foot or feet are denoted by the letter ft.
Margie has 15 feet of ribbon.
To make a bow for a bouquet, it takes 7/8 of a foot of ribbon for a bouquet.
1 bow = 7/8 × 1 foot
Therefore, the number of bows Margie can make with the ribbon will be:
Number of bows = 7/8 × 15 feet
Number of bows = 13.125 ≈ 13
Hence, Margie can make 13 bows with her ribbon.
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What is the relationship between translations, reflections, and ridgid motion?
The relationship between translations, reflections, and rigid motion is that they are all types of rigid motions, which means their size does not change.
What exactly is rigid motion?Rigid motion is the movement of a set in which the distance between points remains constant.
What is translation?Translation is a type of rigid motion in which an object simply slides while maintaining its direction.
What do you mean by reflection?A reflection, like a mirror, causes an image to flip to another location.
We must establish a connection between translations, reflections, and rigid motion.
We can conclude from the above definitions that the size of the object remains constant, but it is undergoing different transitions.
Therefore, Translations, reflections, and rigid motion all belong to the category of transformations that are rigid motions, which means that their sizes don't change.
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Will plays a game at a theme park.
There are 20 cards numbered from 1 to 20.
Will takes a card at random.
He wins if the card he chooses shows a prime number.
Work out the probability that Will wins.
Give your answer as a fraction in its simplest form.
Answer:
find prime numbers between 1-20:
= 2,3,5,7,11,13,17,19
=8 prime numbers
probability of winning = 8/20=2/5
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which equation represents the lines through (2, -4) and (0, 4)?
The equation that represents the lines through (2, -4) and (0, 4) is y = -4x + 4
How to determine the equation of the lineIt is crucial to note that the equation of a line is expressed as;
y = mx+ c
Where;
y is a point of the distance on the y-axisx is a point of the distance on the x-axism is the slope or gradient of the linec is the intercept of the line on the y-axisFrom the information given, we have the point as;
(2, -4) and (0, 4)
Now, let's determine the slope
The formula for determining the slope or gradient of a line is expressed as;
Slope, m = y2 - y1/x2 - y1
Now, substitute the values into the formula
Slope, m = 4 -(-4)/0 -2
expand the bracket
Slope, m = 4 + 4/-2
Add the values
Slope, m = 8/-2
Slope, m = -4
To determine the intercept, use the points of x and y
-4 = -4(2) + c
expand the bracket
-4 = -8 + c
c = -4 + 8
c = 8
The equation of the line is;
y = -4x + 4
Thus, the equation of the line is y = -4x + 4
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HELP thanks and 5 stars to the best answer. Enter the value of the smiley face?
The value of the smiley face given the values of the rectangle, triangle and star is 908.
What is the value of the smiley face ?In order to solve this question, take note of the BODMAS rule. The BODMAS rule gives the order in which mathematical operations should be solved.
B - bracket O - of D - division M - multiplication A - addition S - subtractionThe value of the rectangle would be determined first using the third equation provided in the question. let a represent the value of a rectangle.
(4 x a) + (2 x a) - (3 x a) = 15
4a + 2a - 3a = 15
3a = 15
a = 15 / 3
a = 5
The next step is to determine the value of the triangle. The second equation would be used. Let b represent the value of the triangle.
(3 x 5) + (4 x b) = 47
15 + 4b = 47
4b = 47 - 15
4b = 32
b = 32 / 4
b= 8
Now, determine the value of the star using the first equation. Let the value of the star be represented with c.
5 + (3 x 8) - c = 17
5 + 24 - c = 17
29 - c = 17
c = 29 - 17
c = 12
Now, the value of the smiley face can be determined using the last equation:
12 x (8 + 12 - 5) + 8(8 . 12 - 5)
12 x (15) + 8(91)
180 + 728 = 908
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Simplify.
Rewrite the expression in the form z^n
z^7/z^-14
In the form exponent function zⁿ, the above equation z⁷/z⁻¹⁴ would equal z²¹.
What are exponential functions?The term "exponential function" refers to a function whose expression calls for the input to exist as an exponent (power) of some constant. The following describes their typical form. There are numerous equivalent forms in which they are written.
Briefing:The negative exponent rule instructs us to place a number with a negative exponent in the denominator and the opposite is also true.
State product of power property of exponents.
Keep the bases the same when multiplying two bases with the same value, and then add the exponents to find the answer.
[tex]\frac{z^7}{z^{-14}}[/tex]
[tex]\frac{z^7}{z^{-14}}[/tex]
[tex]z^{7-(-14)}[/tex]
z²¹.
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identify 5/6 as irational number
PLEASE HELP NOW!!!!!!!!!!! (03.04 MC)
Two exponential functions, f(x) and g(x), are graphed on the same coordinate plane.
Graph of f of x equals 2 to the x power going through points 0 comma 1 and 1 comma 2 and graph of g of x equals 2 to the x power minus 1 going through points 0 comma 0 and 1 comma 1.
What effect does subtracting 1 from the parent function have on the transformed function?
a
Subtracting 1 from the parent function shifts the function up one unit.
b
Subtracting 1 from the parent function shifts the function down one unit.
c
Subtracting 1 from the parent function shifts the function right one unit.
d
Subtracting 1 from the parent function shifts the function left one unit.
Subtracting 1 from the parent function will transform the function in the following way: b Subtracting 1 from the parent function shifts the function down one unit
what is transformation?This refers to as movement of object in an organized way such that the movement can always be calculated from the initial position.
The movement involved in transformation on images is ordered and there are some terms used to classify such movements. some of the terms are:
ReflectionDilationTranslation and so onThe movement done in the question is a translation. This is a linear movement towards a particular direction. the movement is translation is usually:
Up: adding numbers to the y directiondown: subtracting number in the y directionRight: adding number to the x directionLeft: subtracting number or value from the x directionSubtracting 1 from the parent function. the parent function as used refers to the y direction hence option b is the correct answer
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a binomial experiment consists of trials. the probability of success for each trial is . what is the probability of obtaining - successes? approximate the probability using a normal distribution. (this binomial experiment easily passes the rule-of-thumb test for approximating a binomial distribution using a normal distribution, as you can check. when computing the probability, adjust the given interval by extending the range by 0.5 on each side.)
The trials in a binomial experiment are the steps. the likelihood of each trial being successful is. What is the likelihood of success? The probability of success is P=1.42.
What in mathematics is a binomial?The binomial distribution is used to summarise the number of trials or observations where each trial has the same probability of attaining a certain value.. When flipping a coin, the probability of witnessing a certain number of successful outcomes in a specified number of trials is determined by the binomial distribution; as there are only two possible outcomes, the likelihood of flipping a coin is 12 or 0.5 for each trial we do.
based on the facts provided;
here ,
n=500 ,p=0.4,q=0.6, X=number of successes
when n*p and n*q>5 then we can use normal approximations
here n*p=500*0.4=200 >5 ,n*q=500*0.6=300>5
so we can use normal approximation
mean =200
variance =200*0.6=120,
std. deviation=120^1/2
we need to find
P(185<=X<=220), applying continuity correction factor
P(184.5<=X<=220.5)
Z=(X-mean)/std. dev~N(0,1)
P((184.5–200)/10.95<=Z<=(220.5–200)/10.95)
=P(-1.42<=Z<=1.87)
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Complete the statements below to explain two ways to convert miles to kilometers.
1 mile ≈1.61 kilometers
1 kilometer ≈0.62 mile
CLEARCHECK
Kilometers are ____
miles.
That means the number of kilometers in a distance will always be
_____ the number of miles in that distance.
We can convert miles to kilometers by ______
by 1.61.
We can convert kilometers to miles by ______
by 0.62.
The statements below to explain two ways to convert miles to kilometers is
Kilometers are 0.62 miles , That means the number of kilometers in a distance will always be 0.62 the number of miles in that distance.We can convert miles to kilometers by multiply by 1.61.We can convert kilometers to miles by multiply by 0.62.What is unit conversion?Unit conversion can be described as the conversion that can be made to convert an item in a particular unit to another unit.
From above the conversion rate for the conversion of miles to kilometer and there conversion of kilometer was given , which can be used in making the conversion.
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assuming the ocean’s level is currently rising at about 1.6 millimeters per year, create an application that displays the number of millimeters that the ocean will have risen each year for the next 25 years.
40 millimeters; the ocean will have risen each year for the next 25 years.
ocean’s level is currently rising at about 1.6 millimeters per year.
create an application that displays the number of millimeters that the ocean will have risen each year for the next 25 years.
IN, 1 year —> 1.6 millimeters;
25 years —> 25*1.6 millimeters;
= 40 millimeters;
40 millimeters; the ocean will have risen each year for the next 25 years.
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What is the product of the common prime factors 24 and 32?
Answer:
2*2*2
That's the prime product of their common factors
6. A solid wooden cylinder of height 8 cm and radius 3 cm is cut in two along a vertical axis of symmetry. Calculate the total surface area of the two pieces.
Total surface area of cylinder is 303.34 [tex]cm^{2}[/tex]
What is cylinder ?A cylinder is a 3D solid shape made up of two bases that are parallel and identical and are connected by a curved surface. These bases resemble spherical disks. The axis of the cylinder shape is a line drawn through the center or connecting the centers of two circular bases.
The surface area of a cylinder is
SA = [tex]2\pi r^{2}[/tex] + 2πrh
where:
r = radius
h = height
This formula comes from adding the areas of the surfaces of the cylinder. It has two flat circular faces and a rounded face.
If we cut the cylinder from the circular face symmetrically, the surface area for one piece will be
SA = 2[[tex]\frac{\pi r^{2} }{2}[/tex]] + ([tex]\frac{2\pi r}{2}[/tex])h + 2rh
We will have 2-half flat circular faces, a flat rectangular surface, and half of the rounded surface.
Simplify the SA formula.
SA = [tex]\pi r^{2}[/tex] + πrh + 2rh
SA = r(πr + πh + 2h)
Substitute the values into this formula.
SA = 3(3π + 8π + (2×8))
SA = 3(11π + 16)
SA = 33π + 48
SA = 151.67[tex]cm^{2}[/tex]
Since we have 2 pieces, multiply this result by 2.
2(151.67[tex]cm^{2}[/tex]) = 303.34[tex]cm^{2}[/tex]
Total surface area is 303.34[tex]cm^{2}[/tex]
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write the mixed expression as a rational expression: 2+9/g
mixed expression as a rational expression will be [tex]\frac{2g+9}{g}[/tex]
WHAT IS FRACTION ?In mathematics, a fraction is a number that is expressed as a quotient in which the numerator and denominator are divided. In a simple fraction, both are integers. A complicated fraction contains a fraction in either the numerator or denominator. Any fraction that is right has a numerator that is less than its denominator.
CALCULATIONto convert mixed fraction into rational fraction
we multiply denominator with whole number and add it with numerator and the result of this gives numerator . and the denominator is same as mixed fraction .
so for the given expression ,
2 * g + 9 is numerator
and g is denominator .
= [tex]\frac{2g+9}{g}[/tex]
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