Answers
Using relations in a right triangle, we have that:
1 - a) x = 54.28º.
1 - b) y = 57.794º.
1 - c) z = 31.056º.
2) The angle is of 62.8º.
3) The angle is of x = 53.017º.
4) The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.
5) The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For item 1a, we have that the sides, hence:
tan x = 8.9/6.4
x = arctan(8.9/6.4)
x = 54.28º.
For item 1b, we have the adjacent side and the hypotenuse, hence:
cos y = 9.7/18.2
y = cos^-1 (9.7/18.2)
y = 57.794º.
For item 1c, we have the opposite side and the hypotenuse, hence:
sin z = 6.5/12.6
z = sin^-1(6.5/12.6)
z = 31.056º.
For item 2, we have the sides, given at the graph at the end of the answer, hence:
tan x = 7.2/3.7
x = tan^-1(7.2/3.7)
x = 62.8º.
The angle is of 62.8º.
For item 3, first we find the hypotenuse of the bottom triangle, by the Pythagorean Theorem, as follows:
h² = 7.9² + 18.6²
h = sqrt(7.9² + 18.6²)
h = 20.21.
Then:
sin x = 20.21/25.3
x = sin^-1(20.21/25.3)
x = 53.017º.
For item 4, we have the adjacent side and the hypotenuse, hence:
cos(x) = 3/3.2
x = cos^-1 (3/3.2)
x = 20.364º.
The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.
For item 5, we have the opposite side and the hypotenuse, hence:
sin y = 1.8/2.9
y = sin^-1 (1.8/2.9)
y = 38.37º.
The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.
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Related Questions
3 charles can type 675 words in 9 minutes how many words can charles type in 3 minutes
Answers
In one minute, Charles can type in 3-minute 225 words.
How many words can Charles type in 3 minutesIn one minute, Charles can type
675/9 = 75 words.
Hence, in 3 minutes Charles can tape [tex]75\times3[/tex] = 225 words (if works with the same rate).
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a company makes widgets from three machines. machine m1 makes 3000/hour, and 80% are good. machine m2 makes 4000/hour, and 90% are good. machine m3 makes 3000/hour, and 60% are good. all widgets are mixed together. what is the probability that a widget drawn at random is good
Answers
If all the widgets from the three machines are mixed together, then the probability that a good widget will be drawn at random is 0.78 or 78%.
Probability is defined as how likely an event is to occur, or how likely it is that a proposition is true.
If machine 1 makes 3000/hour and 80% are good, then the chances of it being good is 80% also or, 2400 out of 3000.
80% of 3000 is 2400
If machine 2 makes 4000/hour and 90% are good, then the chances of it being good is 90% also or, 3600 out of 4000.
90% of 4000 is 3600
If machine 3 makes 3000/hour and 60% are good, then the chances of it being good is 60% also or, 1800 out of 3000.
60% of 3000 is 1800
Mixing together the widgets from the three machines, use the formula to calculate the probability of an event which is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Probability(good) = (2400 + 3600 + 1800)/(3000 + 4000 + 3000)
Probability(good) = 7800/10000
Probability(good) = 0.78 or 78%
Hence, the probability that a good widget drawn at random is 0.78 or 78%.
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if the length of a rectangle is increased by 30 percentage and the width of the same rectangle is decreased by 30 what is the affect on the area
Answers
Answer:
The area will decrease by 9%.
Step-by-step explanation:
The area of a rectange is given by the formula below.
[tex]\boxed{\text{Area of rectangle}= \text{length}×\text{width}}[/tex]
Let the original length and width of the rectangle be L and W respectively.
Start by finding the original area:
Original dimensions
Length= L= 100%L
Width= W= 100%W
Original area= LW
Let's find the dimensions of the new rectangle in terms of L and W.
New dimensions
Length= (100% +30%)L= 130%L
Width= (100%-30%)W= 70%W
New area
[tex] = \frac{130}{100} L \times \frac{70}{100} W[/tex]
[tex] = \frac{91}{100} LW[/tex]
= 91% LW
Comparing the new area with the original area:
100% LW- 91% LW= 9% LW
∴ The area will decrease by 9%.
*Note that percentage is equivalent to dividing a number by 100.
5| c + 7 | = -45
Absolute Volume
Answers
Answer:c=16
Step-by-step explanation:5c+35=-45=5c=-45-35=5c=-80. C=16
janice wants to put a fire at the mid point between two of her trees in her backyard. the coordinates of tree A are (3, 5) and the coordinates of tree b are (-3,-3). How far is the fire from tree b?
Answers
Answer:
janice wants to put a fire at the mid point between two of her trees in her backyard. the coordinates of tree A are (3, 5) and the coordinates of tree b are (-3,-3). step by step thinking we want tree A is coordinat at 35. three b coordinate is -3-3 .janice stand between centre that from A mark 6feet so At B is 3
A restaurant earns $1073 on friday and $1108 on saturday. Write and solve an equation to find the amount x(in dollars) the restaurant needs to earn in Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day
Answers
The amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.
What is average ?
The average is the ratio of the sum of the number of a given set of values to the total number of values present in the set.
It is given that restaurant earns $1073 on Friday and $1108 on Saturday.
The amount which restaurant needs to earn on Sunday to average $1000 per day over the three-day period can be calculated by finding the average.
The average is given by ratio of sum of amount on each day from Friday to Sunday and divide it by number of days.
Let's assume amount earn on Sunday is $x.
So ,
[tex]\frac{1073 + 1108 + x}{3}[/tex] = 1000
1073 + 1108 + x = (1000 × 3)
2181 + x = 3000
Let's solve this equation to get the value of x.
x = 3000 - 2181
x = $819
So , amount earn by restaurant is $819.
Therefore , the amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.
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Help please!
The area of a square is 9 square feet. What is the length of one side of the square?
Answers
Answer:
the length of one side of square is 3
Area = side^2
9 = x^2
3 = x
Check: 3 x 3 aka 3^2 equals 9
Evaluate the expression if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2 . − | 10 − 7 r + 8 m + 2 p |
Answers
Answer:
-53
Step-by-step explanation:
if m = − 4 , n = 1 , p = 2 , q = − 6 , r = 5 , and t = − 2
-| 10 - 7r + 8m + 2p |
Substitute the given values into the equation.
-| 10 - 7(5) + 8(-4) + 2(2) |
Simplify
-| 10 - 35 + -32 + 4) |
-| -53 |
= -53
Absolute value of -53 is 53 however there is a negative sign outside of it, so the answer is -53
what is the diffrence between irregular and irrational numbers?
Answers
Answer:
Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number. Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.
Step-by-step explanation:
please make my answer as brainelist
work out the volume of cylinder B
Answers
Answer:
720cm³
Step-by-step explanation:
Volume of a cylinder is given by Base Area (A) x Height (h)
or V = Ah
Volume of cylinder A = 18 x 5 = 90 cm³
Base Area A = πr² where r is the radius of the base
For cylinder A, if radius = rₐ
Area = π x (rₐ)² = 18
We can see that cylinder B has twice the height of cylinder A. That means cylinder B radius is twice the radius of cylinder A
So radius of cylinder B = 2 x rₐ = 2rₐ
Base Area of Cylinder B = π x (2rₐ)² = 4π(rₐ)² = 4 x Base Area of cylinder A = 4 x 18 = 72
So while the heights are in the ration 1:2, the base areas are in the ratio 1:4 because the areas are directly proportional to the square of the radius
Hence Volume of Cylinder B = 72 x 10 = 720 cm³
Another way to look at this is that the volume of cylinder B = 8 (2 x 2 x2) times the volume of cylinder A = 8 x 90 = 720cm³
Simplify. 5/4+4(3/4−12)2
Answers
Answer:-355/4
Step-by-step explanation:
Answer:
= -355/4
Step-by-step explanation:
= 5/4 + 4(3/4 - 12)(2)
= 5/4 + (-45)(2)
= 5/4 + -90
= -355/3
a survey indicated that the vast majority of college students own their own personal computers what information would you want to know before you accepted the results of this survye
Answers
The required information is (B), (C), (D), and (I).
What is a survey?A survey in human subjects research is a set of questions designed to elicit specific information from a specific group of people. Surveys can be conducted over the phone, by mail, on the internet, or even on street corners or in shopping malls. In fields such as social research and demography, surveys are used to gather or gain knowledge.Survey research is frequently used to assess people's thoughts, opinions, and feelings.So,
A. Who paid for the survey? It is not required.
B. Who made up the population from which the sample was drawn? Needed.
We need to know if the sample is representative of the "college students" population, on which we are basing our conclusions.
C. What sampling strategy was used? Needed.
We want to know if the sample was chosen at random.
D. How large was the sample size? Needed.
This information is required to determine the accuracy of the results.
E. What are the colleges represented in the sample?
It's not necessary if we already know "B."
F. How many survey questions were there? It is not required.
G. How many people participated in the survey? It is not required.
H. What were the questions? It is not required.
I. Is the language in the questions clear, accurate, unbiased, and valid? Needed.
We want to know if the answer was unbiased and clear so that we can determine if the conclusions are also unbiased.
J. What day of the week was the survey held? It is not required.
Therefore, the required information is B, C, D, and I.
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The correct question is given below:
A survey indicates that the vast majority of college students own their own personal computers. What information would you want to know before you accepted the results of this survey? Select all that apply. A. Who funded the survey? B. What was the population from which the sample was selected? C. What sampling design was used? D. What was the sample size? E. What are the names of the colleges included in the sample? F. How many questions were asked in the survey? G. How many people conducted the survey? H. What questions were asked? I. Were the questions clear, accurate, unbiased, and valid? J. On what day of the week was the survey conducted? g
help needed ASAP. high school geometry
Answers
Answer:
9 u^2
Step-by-step explanation:
there's 2 ways to solve this problem
easy way
plot every coordinate and youll see it's a square
square area = side^2
3^2 = 9 answer
and this method
working with 3 points (triangle)
W - X - Y
0 0
0 3
-3 3
0 0
--------------
2
--------------------------------------
0 0
0 -9
0 0
-----------
l-9/2l
4.5
since a square is made of 2 triangles
4.5 * 2 = 9 u^2
On a map with a scale of 1 inch to 12 feet, the area of a restaurant is 60 in². Han says that the actual area of the restaurant is 720 ft²
O True
O False
Answers
Answer:
False
Step-by-step explanation:
The scale is for length only, when converting to area scale, you have to square both sides of the scale.
1 in² = 144 ft²
Solve for x. 7x - 3 = 2x - 18
Answers
Answer:
x = -3Step-by-step explanation:
7x - 3 = 2x - 18
5x = -15
x = -15 : 5
x = -3
-----------------------------
check
7 * (-3) - 3 = 2 * (-3) - 18
-24 = -24
the answer is good
1) 2 + x = 22 3) -6 + p = -18 5) -29 = -20 + n 7) -5 + r = -23 9) 11 = x + 13 11) 101 = n +55 2) -15 = -18 + n 4) -18 + v = -9 6) -19 = n - 13 8) -12 = k +5 10) 11 = -1 + x 12) x - 36 = -68
Answers
Answer:
1)x=20
3)p=−12
5)n=−9
7)r=−18
9)x=−2
11)n=46
2)n = 3
4)v=9
6)n=−6
8)k=−17
10)x=12
12)x=−32
Step-by-step explanation:
Let's solve your equation step-by-step.
1) 2+x=22
Step 1: Simplify both sides of the equation.
x+2=22
Step 2: Subtract 2 from both sides.
x+2−2=22−2
x=20
3) −6+p=−18
Step 1: Simplify both sides of the equation.
p−6=−18
Step 2: Add 6 to both sides.
p−6+6=−18+6
p=−12
5) −29=−20+n
Step 1: Simplify both sides of the equation.
−29=n−20
Step 2: Flip the equation.
n−20=−29
Step 3: Add 20 to both sides.
n−20+20=−29+20
n=−9
7) −5+r=−23
Step 1: Simplify both sides of the equation.
r−5=−23
Step 2: Add 5 to both sides.
r−5+5=−23+5
r=−18
9) 11=x+13
Step 1: Flip the equation.
x+13=11
Step 2: Subtract 13 from both sides.
x+13−13=11−13
x=−2
11) 101=n+55
Step 1: Flip the equation.
n+55=101
Step 2: Subtract 55 from both sides.
n+55−55=101−55
n=46
2) −15=−18+n
Step 1: Simplify both sides of the equation.
−15=n−18
Step 2: Flip the equation.
n−18=−15
Step 3: Add 18 to both sides.
n−18+18=−15+18
n=3
4) −18+v=−9
Step 1: Simplify both sides of the equation.
v−18=−9
Step 2: Add 18 to both sides.
v−18+18=−9+18
v=9
6) −19=n−13
Step 1: Flip the equation.
n−13=−19
Step 2: Add 13 to both sides.
n−13+13=−19+13
n=−6
8) −12=k+5
Step 1: Flip the equation.
k+5=−12
Step 2: Subtract 5 from both sides.
k+5−5=−12−5
k=−17
10) 11=−1+x
Step 1: Simplify both sides of the equation.
11=x−1
Step 2: Flip the equation.
x−1=11
Step 3: Add 1 to both sides.
x−1+1=11+1
x=12
12) x−36=−68
Step 1: Add 36 to both sides.
x−36+36=−68+36
x=−32
3/11 x 3/4 x 4 Please help I have no idea how to do this
Answers
Answer:
[tex]\bold{\dfrac{9}{11}}[/tex]
Step-by-step explanation:
I will use the dot notation for multiplication
We have
[tex]\dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \:4[/tex]
Convert 4 to a fraction:
[tex]4=\dfrac{4}{1}[/tex]
Therefore
[tex]\dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \:4 \\\\= \dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \dfrac{\cancel {4}}{1}\\\\[/tex]
Cross-cancel common factor 4
[tex]=\dfrac{3}{11}\cdot \dfrac{3}{1}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{a}{b}\cdot \dfrac{c}{d}=\dfrac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]=\dfrac{3\cdot \:3}{11\cdot \:1}[/tex]
[tex]=\bold{\dfrac{9}{11}}[/tex]
Although it is much larger in reality, when we
see Saturn from Earth, it looks like it has a
diameter of 20 μm. Through a telescope, the
diameter looks 9,000 um long. What
magnification scale was used?
Answers
The magnification scale used was 450:1
Saturn from Earth, it looks like it has a diameter of 20 μm.
d₁=20μm
Through a telescope, the diameter looks 9,000 μm long.
d₂= 9,000 μm
magnification scale = d₂/d₁
= 9,000 μm/20μm
= 450/1
magnification scale used was 450:1
A scale factor is a number that can be used to adjust the size of any geometrical figure or object in relation to its original size. It's used to draw the enlarged or reduced shape of any given figure, as well as to calculate the missing length, area, or volume of an enlarged or reduced figure. It should be noted that the scale factor only affects the figure's size and not its shape.
A scale factor is a number or conversion factor used to adjust the size of a figure without changing its shape. It is used to enlarge or reduce the size of an object. If the dimensions of the original figure and the dimensions of the dilated (increased or lowered) figure are known, the scale factor can be determined. A rectangle, for example, has a length of 5 units and a width of 2 units. If we raise the size of this rectangle by a factor of two, the sides will become 10 and 4, respectively. As a result, we can use the scale factor to determine the dimensions of the altered figures.
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a real-valued function f (x) is said to be increasing on the closed interval [a, b] if for all x1, x2 ∈ [a, b], if x1 < x2, then f (x1) < f (x2) write the negation of this definition
Answers
A real valued function f(x) is said to be decreasing on the interval [a,b] for all x1,x2 if x1 < x2, And f(x1) > f(x2)
What are increasing and decreasing function ?A function is said to be increasing if we increase the value of the independent variable the function also increases and a function is said to be decreasing if we increase the value of the independent variable the function decreases.
According to the given question real-valued function f (x) is said to be increasing on the closed interval [a, b] if for all x1, x2 ∈ [a, b], if x1 < x2, then f (x1) < f (x2).
A real valued function f(x) is said to be increasing on the interval [a,b] if a < b, And f(a) < f(b).
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To win the annual read-a-thon at his school, Ronald has to read more books than any of his
classmates over winter break. He starts by reading a lot of sports books. Then, he reads 7
mystery books. In all, Ronald reads 25 books for the read-a-thon.
Which equation can you use to find the number of sports books n Ronald reads?
n+ 7 = 25
n - 7 = 25
Submit
7n = 25
7
= 25
Solve this equation for n to find the number of sports books Ronald reads.
sports books
Answers
Answer:
The equation for this question should be n+7=25
where n=18
Step-by-step explanation:
among cbc students, 50% of students are enrolled in less than three courses and 33% of students are taking a math class. if 71% of students are either enrolled in less than three courses or taking a math course, what percentage of students are enrolled in less than three courses and taking a math course? group of answer choices 38% 35.5% 17% 83% 12%
Answers
12% of students are enrolled in less than three courses and taking a math course
For given question,
50% of students are enrolled in less than three courses and 33% of students are taking a math class.
The probability that the students are enrolled in less than three courses is 0.5
P(A) = 0.5
The probability that the students are taking a math class is 0.33
P(B) = 0.33
if 71% of students are either enrolled in less than three courses or taking a math course.
P(A ∪ B) = 0.71
We need to find the percentage of students that are enrolled in less than three courses and taking a math course.
i.e., we need to find P(A ∩ B)
We know that, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∩ B) = 0.5 + 0.33 - 0.71
P(A ∩ B) = 0.12
So, 12% of students are enrolled in less than three courses and taking a math course.
Therefore, 12% of students are enrolled in less than three courses and taking a math course.
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Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched. What is the change in elevation?
Answers
The change in elevation will be 0.
What is the change in elevation?It should be noted that from the information, Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched.
Therefore, when it flew, the expression will be +168.
When it came down, the expression will be -168.
Therefore, the change in elevation will be:
= +168 - 168.
= 0
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Find the value of k if the line y = kx +4 goes through the point (2, -2). Thank you
Answers
The answer is in the screenshot.
which row of pascal’s triangle would you use to expand (2x 10y)15? row 10 row 12 row 15 row 25 how many terms are in this expansion? 3 terms
Answers
15th row of the Pascal's Triangle is used to expand [tex](2x+10y)^{15}[/tex]. There will be 16 terms in the expansion.
Pascal's Triangle is used to find the co-efficient for binomial expansions.
The nth row of the Pascal's Triangle gives the coefficients in the expansion of binomial expressions of degree n. For example, in the expansion of [tex](x+y)^2[/tex] , the binomial coefficients are 1,2,1 which is given in the 2nd row of Pascal's Triangle. Also the expansion has three terms, therefore. The Pascal triangle starts with 0th row consisting of only 1.
Here the given expression is [tex](2x+10y)^{15}[/tex] of degree 15. So its binomial coefficient is given in the 15th row of Pascal's triangle.
The number of terms in the binomial expansion of degree n will be n+1 because the coefficients in nth row will n+1 in number.
Hence there will be 16 terms in the expansion of [tex](2x+10y)^{15}[/tex].
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Answer:
The person above helped, and below I've attached a ss with all of the parts of this question answered - Hope it helps!
Step-by-step explanation:
Brainliest would be very much appreciated :) - hope you have a good day!
(Adding and Subtracting Rational Numbers MC)
Solve negative four minus one and three fifths.
five and three fifths
one and three fifths
four fifths
negative five and three fifths
Answers
Answer:
negative 5 and 3/5
Step-by-step explanation:
-4-1&3/5
-5&3/5
negative 5 and 3/5(three fifths)
don't forget to mark as brainliest
Answer:
negative 5 and 3/5
Step-by-step explanation:
-4-1&3/5
-5&3/5
negative 5 and 3/5(three fifths)
don't forget to mark as brainliest
Step-by-step explanation:
Simplify.
[tex]\sqrt{20+5}[/tex]
Answers
Answer: 5
Step-by-step explanation:
[tex]\sqrt{20+5}[/tex]=
[tex]\sqrt{25}[/tex]=5
Answer:
√(20 + 5) = 5
Step-by-step explanation:
Let's solve the problem,
→ x = √(20 + 5)
→ x = √25
→ [ x = 5 ]
Hence, the answer is 5.
What is this 6/x-5/-7=11
Answers
X=7/12
Explanation
Na
Which equation represents the line with slope −2/3 that passes through (3, 0)?
Answers
The following equation [tex]y=\frac{-2x}{3}+2[/tex] represents the given line.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=3x+1. Where:
a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex].
b= the constant term that represents the y-intercept.
For solving linear equations, you should organize variables on one side of the equation and the numbers on the other side. When a number or variables change side, its signal also is changed.
For the given example: a=3 and b=1
The question gives:
the value of the slope (a) = -2/3the coordinates of a point = (3,0)Thus, you can write from the question information :
y=ax+b
0= -2/3*(3)+b
0= -2 + b
b=2
Now, you know the value of the slope and the constant term.
Therefore, the standard form for the linear equation is:
[tex]y=\frac{-2x}{3}+2[/tex]
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how do you find the y-intercept from vertex form
Answers
It is found that the intercepts can be found from vertex form, if the graph is hovering above the x axis (k<0).
What is y-intercept of a function?The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.
Assume that we've got: y = f(x) At y-axis, we've got x = 0, so putting it will give us the y-intercept. Thus, y-intercept of y = f(x) is y = f(0)
If a quadratic equation is written in the form y=a(x-h)² + k
therefore it is called to be in vertex form. It is called so because when you plot this equation's graph, we will see vertex point(peak point) is on (h,k)
To convert the given equation to vertex form, We will take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.
To find the intercepts, if the graph is hovering above the x axis (k<0) then there will be no real solutions for the x intercept.
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If point A (–1, 0) is the midpoint of segment CT, and T is located at (1, 2), what are the coordinates of point C?
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad T(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +x}{2}~~~ ,~~~ \cfrac{ 2 +y}{2} \right) ~~ = ~~ \stackrel{\textit{\LARGE A}}{(-1~~,~~0)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1+x}{2}=-1\implies 1+x=-2\implies \boxed{x=-3} \\\\\\ \cfrac{2+y}{2}=0\implies 2+y=0\implies \boxed{y=-2}[/tex]