The lengths of two sides of a triangle are 5 inches and 8 inches. Which of the following lengths could be the length of the third side of the triangle? Select all that apply.
By using the triangular inequality, we conclude that the other side must measure more than 3 inches and less than 13 inches.
Which values could the length of the third side take?
Remember that the triangular inequality says that the sum of any two sides on a triangle is larger than the other side of the triangle.
If we define the missing side of the triangle as x, then we must have:
5 + x > 8
8 + x > 5
8 + 5 > x
From the third inequality we get the upper bound:
13 > x.
From the first inequality we get the lower bound:
x > 8 - 5 = 3
Then:
3 < x < 13
This means that the other side of the triangle must measure more than 3 inches and less than 13 inches.
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A cell phone tower that is 70 meters tall is built on level ground
and casts a shadow 230 meters long at a particular moment.
find the angle of elevation of the sun relative to an observer
standing at the tip of the shadow.
The angle of elevation of the sun relative to an observer standing at the tip of the shadow is 16.9°.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
Given that:-
A cell phone tower that is 70 meters tall is built on level ground and casts a shadow 230 meters long at a particular moment.The angle of elevation will be calculated by applying trigonometric property in the triangle given below;-
[tex]tan\theta=\dfrac{P}{B}[/tex]
[tex]tan\theta=\dfrac{70}{230}[/tex]
[tex]\theta=tan^{-1} (\dfrac{70}{230})[/tex]
[tex]\theta[/tex] = tan[tex].^{-1}[/tex](0.3043)
[tex]\theta[/tex] = 16.9
Therefore angle of elevation of the sun relative to an observer standing at the tip of the shadow is 16.9°.
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In the triangle below, what is the measure of B?
A. 18°
B. 56°
C. 90°
D. 28°
The measure of the angle B from the isosceles triangle is equal to 28°. (Correct choice: D)
What is the measure of the missing angle?
In this problem we have the case of an isosceles triangle, that is, a triangle with two sides of equal length and two angles of same measure. By properties from isosceles triangles, we know that the measures of sides AC and BC are the same and angles B and C are the same.
Then, if we know that AC = AB = 10 and m ∠C = 28°, then the measure of the angle B is equal to 28°.
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please help will give brainlest
Answer:
18
Step-by-step explanation:
Here,
given,
a=3 and b=6
Then
4a+b=?
Put respective values on 4a+b
4*3+6
=12+6
=18
Answer:
18
Step-by-step explanation:
step 1:4a+b=
step 2:(4x3)+6=
step 3:12+6=
answer=18
hope this helps
The ratio of the ages of Mandy and Sandy is 2:5. After 8 years, their ages will be in the ratio 1:2. What is the difference between their present ages?
Caitlin says the difference in their ages is 24 years. In two or more complete sentences, explain whether or not Caitlin is correct. In your explanation, include the equations and calculations necessary to support or contradict Caitlin's answer.
A ratio shows us the number of times a number contains another number. Caitlin is right.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of the ages of Mandy and Sandy is 2:5. Therefore, the ratio will be,
M/S = 2/5
M = 2S/5
After 8 years, their ages will be in the ratio 1:2, therefore,
(M+8)/(S+8) = 1/2
2M + 16 = S + 8
2M - S = -16 + 8
Substitute the value of M,
2(2S/5) - S = -8
-0.2S = -8
S = 40
Now, if we substitute the value of S in the first ratio,
M/S = 2/5
M/40 = 2/5
M = 16
Now, if we take the difference in their ages the difference will be 24(40-16).
Since the difference is 24, we can conclude that Caitlin is right.
Hence, Caitlin is right.
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please answer this !!
uhm i dont know sorry but i can't help you
If set A contains four distinct numbers and set B contains seven distinct letters, how many elements are in (A U B)?
There are 11 elements are in (A U B)
How to determine the number of elements?The given parameters are:
n(A) = 4
n(B) = 7
The number of elements in (A U B) is calculated using:
n(A U B) = n(A) +n(B) - n(A U B)
Given that the sets have distincts elements, we have:
n(A U B) = 4 + 7 - 0
Evaluate
n(A U B) = 11
Hence, there are 11 elements are in (A U B)
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Answer: There are 11 elements are in (A U B)
Step-by-step explanation:
A quart of stain covers 100 square feet. How many quarts should you buy to stain the wheelchair ramp? (Assume you do not have to stain the bottom of the ramp.)
This shows that the number of quarts she should you buy to stain the wheelchair ramp is 9 quart
Surface area of a pyramidThis the sum of all the area of the surfaces. The given figures is made of 3 rectangles and 2 triangles
Determine the surface area
TSA = (25*25) + (2 * 5*301/12) + (5*2.08333)
TSa = 625 + 258.33333 + 10.41665
TSA = 893.74995
If a quart of stain covers 100 square feet, the total nuber to buy is given as:
Number to buy = 894/100 = 8.94
This shows that the number of quarts she should you buy to stain the wheelchair ramp is 9 quart
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1 euro = $1.09 $1= 62 rupees Change 400 euros into rupees using these exchange rates.
Answer:
27,032 Rupees
Step-by-step explanation:
$1.09 x 400 = $436
$436 x 62 = 27,032
(Hope this helps and that it's not wrong ^-^)
The marked price of a watch is 30% above the cost price. When it is sold allowing 20% discount on it, there is a gain of Rs 150. Find the marked price and the cost price of them.
Answer:
Marked price: Rs. 4875
Cost price: Rs. 3750
Explanation:
(i) Cost price: 100%
(ii) Marked price: (100% + 30%) = 130%
(i) Let the cost price be p
(ii) Marked price: 130% × p = 1.3p
Given, 20% discount then sold at 80%
Discount price: (130% × 80%) × p = 1.04p - discounted price
Gain price: 1.04p - p = 0.04p
Cost price:
0.04p = 150
p = 150/0.04 = 3750 ← This is the cost price.
Marked price:
1.3p = 1.3(3750) = Rs. 4875
What conclusions can be drawn about finding the quotient in scientific notation? Check all that apply. Start Fraction (9.6 times 10 Superscript negative 8 Baseline) Over (3.2 times 10 Superscript 4 Baseline) End Fraction A.The coefficient of the solution is 6.4, the difference of the original coefficients. B.The exponent of the solution is –12, the difference of the original exponents. C.The coefficient of the solution must be greater than or equal to one but less than 10. D.The quotient is 3.0 × 10-12 E.The solution is a very large number
The quotient of the expressions (9.6 x 10⁻⁸) and (3.2 x 10⁴) is 3.0 × 10⁻¹². Then the correct option is D.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
The expressions are given below.
(9.6 x 10⁻⁸) and (3.2 x 10⁴)
Then the quotient of the expressions will be
⇒ (9.6 x 10⁻⁸) / (3.2 x 10⁴)
⇒ (3 x 10⁻⁸) / (10⁴)
⇒ 3 x 10⁻⁸ x 10⁻⁴
⇒ 3 x 10⁻⁸⁻⁴
⇒ 3 x 10⁻¹²
Then the correct option is D.
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If you roll a standard number cube 95 times, how many times do you expect the cube to show a one or a three?
Answer:
32 times
Step-by-step explanation:
the probability in getting a certain number is you first find out the chance of rolling one side on a die. There are six sides, and there is two numbers on it you want a 3 and a 1. so you would get 2/6 would be the fraction of what you what most likely get, so you would multiply 95 by 2/6 you get the correct answer
factorize
2x²-x²-x
Please help me fast to solve this problem.
Answer: x (x - 1)
Step-by-step explanation:
[tex]2x^{2} - x^{2} -x[/tex]
[tex]x^{2} -x[/tex]
x (x - 1)
A number x is at least 5 and is at most 8
Answer:
[tex]5 \leqslant x \leqslant 8[/tex]
The production supervisor at a particular office products company finds that it takes 3 hours to manufacture each table for one of its special dining room sets. Each
chair
takes 8 hours to manufacture. A total of 6000 hours is available to produce tables and chairs of this style. The linear equation that models this situation is
3x+8y=6000, where x represents the number of tables produced and y the number of chairs produced.
a. Complete the ordered pair solution (0.) of this equation. Describe the manufacturing situation that corresponds to this solution.
The ordered pair is (0…)
The ordered pairs of the equation are
0 tables, 750 chairs2000 tables. 0 chairsHow to find the ordered pairs of the equationThe equation is given as
3x + 8y = 6000
We have x = number of tables
y = number of chairs
When x = 0
3(0) + 8y = 6000
8y = 6000
y = 750
When y = 0
3x + 8(0) = 6000
3x = 6000
x = 2000
The ordered pairs of the products are:
0 table 750 chairs
200 tables, 0 chairs.
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Work out the area of this circle.
Take pi to be 3.142 and give your answer in 2 decimal places.
Answer: 63.63 m²
Explanation:
Area of circle:
π(radius)²Here given:
radius: (diameter/2) = (9/2) = 4.5 m
π should be taken as 3.142
So area of circle:
3.142(4.5)² = 63.6255 ≈ 63.63 (rounded to two decimal place)Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the area of this circle.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
→ [tex]\bf{Area_{circle}=\pi r^{2}}[/tex]
Notice that we are asked to use 3.142 for [tex]\pi[/tex] (pi).
The radius isn't given to us; what we have instead is...the diameter.
To find the radius, we divide the diameter by 2.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{\bf{To\;find\;the\;radius,\;we\;divide\;the\;diameter\;by\;2}}[/tex]
Thus, the radius is
[tex]\bf{9\div2=4.5}[/tex]
Now substitute the values (3.142 for pi and 4.5 for r):
[tex]\bf{A=3.142\times4.5^{2} }[/tex]
Simplifying,
[tex]\bf{A=3.142\times20.25}[/tex]
Simplifying,
[tex]\bf{A=63.6255\:m}[/tex]
Rounding to 2 decimal places (D.P.):
[tex]\bf{A=63.63\:m}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
~Just a smiley person helping fellow students :)
if the sine ratio is given, then how can sin 0/2 be determined?
Step-by-step explanation:
If you know, the sine. You must find the cos ratio, using the Pythagorean trig theorem.
Next, you use the half angle identity for sin
[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos(a) }{2} } [/tex]
Example.
[tex] \sin( \alpha ) = \frac{ \sqrt{3} }{2} [/tex]
We must find
[tex] \sin( \frac{ \alpha }{2} ) [/tex]
First, use the Pythagorean identity
[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]
[tex]( \frac{ \sqrt{3} }{2} ) {}^{2} + \cos {}^{2} (a) = 1[/tex]
[tex] \frac{3}{4} + \cos {}^{2} (a) = 1[/tex]
[tex] \cos {}^{2} (a) = \frac{1}{4} [/tex]
[tex] \cos( \alpha ) = \frac{1}{2} [/tex]
Now use the half angle identiy
[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]
[tex] = \frac{ \sqrt{1 - \frac{1}{2} } }{ \sqrt{2} } [/tex]
[tex] = \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} } [/tex]
[tex] = \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ \sqrt{1} }{ \sqrt{4} } = \frac{1}{2} [/tex]
So the answer for our example is 1/2
Mo buys a house for £120 000 He sells the house for £150 000 Work out the percentage profit that Mo makes.
Step-by-step explanation:
profit amount=150000-120000
profit amount=30000
profit %= profit amount/cost price*100
therefore profit percent=30000/120000*100
there for profit %=25%
The percentage of profit will be equal to 25%
What is the percentage?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
The profit percentage will be calculated as:-
Profit amount = 150000-120000
Profit amount = 30000
Profit %= profit amount/cost price*100
Profit percent=30000/120000*100
Profit percentage = 25%
Therefore the percentage of profit will be equal to 25%
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Over the last 3 months, Janet exercised a total of 101 hours. She exercised 4 hours more during the second month than the first month. In the third month, she exercised 3 hours less than the second month.
Create an equation that represents this situation, where h represents the number of hours Janet exercised during the first month.
In 1st month let she exercised h hours
in second month she exercised h+4 hours
in third month she exercised h+4-3=h+1 hours
Now
h+h+4+h+1=1013h+5=1013h=96h=32hoursAnswer:
Let's say the unknown variable is h
In 1st month let she exercised h hours
in the 2nd month she exercised h+4 hours
in the 3rd month she exercised h+4-3=h+1 hours
Now, to display the sequence:
h+h+4+h+1=101
3h+5=101
3h=96
h=32hours
Find the value of x and the measure of angleMNQ.
3x − 11°62°
The value of x is
90
° and the measure of angleMNQ is
180
°.
Answer:
180
Step-by-step explanation:
Find the value of x and the measure of angleMNQ.
3x − 11°62°
The value of x is
90
° and the measure of angleMNQ is
180
°.
Which of these is a recurring cost of car ownership?
A. Windshield replacement
B. Driver's license application fee
C. Gas
O D. Bumper replacement
which of the following is located over the center of the base of a regular pyramid
A vertex
B slant height
C face
D edge
Answer:
vertex
Step-by-step explanation:
(Refer to the attached image)
[tex]\sf Sine \ Rue : \ \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
Given following:
A = 56°B = 77°a = 38 mb = ? mSolve for b (distance between school and mall):
[tex]\dashrightarrow \sf \dfrac{\sin 56}{38} = \dfrac{\sin 77}{b}[/tex]
[tex]\dashrightarrow \sf b= \dfrac{38\sin 77}{\sin 56}[/tex]
[tex]\dashrightarrow \sf b= 44.6615 \quad \approx \quad 45[/tex]
The ratio of adults to children at a party is 3:5
What fraction of the party are adults?
There are 72 people at the party.
Work out the number of children at the party.
The ratio of adults to children at a party is 3:5. There are 72 people at the party. Find out number of children.
✭ Explanation -:In this question we are provided with the ratio of adult and children 3 : 5 respectively. It is given that 72 people are there at the party. We are asked to calculate number of children.
We are asked to calculate number of children
Let us assume number of adults and children as 3x and 5x
It is given that total number of people are 72.
According To Question
3x + 5x = 72
→ 8x = 72
→ x = 72/8 = 9
x = 9
Adults = 3x = 3 × 9 = 27 people
Children = 5x = 5 × 9 = 45 people
Hence, there are 45 children in the party.In the following exercises, translate into an equation and solve
Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?
Answer: 6 children
Step-by-step explanation:
Given:
Children - 24
Groups - 4
Number of children per group - x
Solve:
24 ÷ 4 = x
x = 6
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Which set of ordered pairs has point symmetry with respect to the origin (0, 0)? (5, 4), (-5, -4) (5, 4), (5, -4) (5, 4), (4, 5) (5, 4), (-5, 4)
The set of ordered pair that has point symmetry in respect to origin is (5, 4), (-5, -4).
What is the point of symmetry?
This is a term that is used to refer to the points that are on the same distance from the origin but are on opposite sides.
The line that connects the points are known to move through the origin such that when measured on the graph, the distances between these points but they are opposite because they are in negatives and positives on the two sides.
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Answer:
the answer is (5,4),(-5,4)
Step-by-step explanation:
About how many students do not prefer non- fiction?
x
A. 60
B. 75
C. 100
D. 150
E. 180
Help
Answer:
B. 75%
Step-by-step explanation:
If about a quarter ( 25% ) do like non-fiction, then we know that the rest do not prefer it ( 75% )
75 + 25 = 100
Aisha has a piece of string that she cuts into smaller pieces. This line plot shows the length of each piece. Juan has a piece of string that is 12 as long as Aisha's seventh-longest piece. (Note: The problem states the seventh-longest piece, not the seventh-longest length.)
How long is Juan's piece of string?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
2 5/8 inches
Step-by-step explanation:
There are 2 pieces 5 3/4 inches long.
There is 1 piece 5 1/2 inches long.
There are 4 pieces 5 1/4 inches long.
The seventh longest piece is one of the pieces measuring 5 1/4 inches.
Juan's piece is 1/2 as long as 5 1/4 inches.
1/2 × 5 1/4 inches = 1/2 × 21/4 = 21/8 inches = (16/8 + 5/8) = 2 5/8 inches
Solve for x.
(x−2)^2+2=38
x= ___ or x= ___
Answer:
[tex]x \: = \: \boxed{ \bold{ - 4 }}\: \: \text{or} \: \: x \: = \: \boxed{ \bold{ 8}}[/tex]
Step-by-step explanation:
[tex](x \: - \: 2 {)}^{2} \: + \: 2 \: = \: 38[/tex]
[tex] {x}^{2} \: - \: 4x \: + \: 4 \: + \: 2 \: = \: 38[/tex]
[tex] {x}^{2} \: - \: 4x \: + \: 6 \: = \: 38[/tex]
[tex] {x}^{2} \: - \: 4x \: + \: 6 \: - \: 38 \: = \: 0[/tex]
[tex] {x}^{2} \: + \: 4x \: - \: 8x \: - \: 32 \: = \: 0[/tex]
[tex]x \: \times \: (x \: + \: 4) \: - \: 8(x \: + \: 4) \: = \: 0[/tex]
[tex](x \: + \: 4) \: \times \: (x \: - \: 8) \: = \: 0[/tex]
When it happens that the product of the factors is the same as zero. It is divided into two possible cases.[tex]x \: + \: 4 \: = \: 0 \\ x \: - \: 8 \: = \: 0[/tex]
We solve the two equations:[tex]x \: = \: - 4 \\ x \: = \: 8[/tex]
Answer:[tex]x \: = \: - 4 \\ x \: = \: 8[/tex]
MissSpanishThe graph of y=cosx is translated by (30,-1). What is the equation of the translated graph?
The equation on the graph is shown (I really hope this helps)
Equation of the translated graph is;
⇒y = cos(x - 30) - 1
What is equation of translated graph?
Equation of the translated graph is solved as;
g(x) = f(x + k) + C
Where, k and C are points.
Given that;
The equation is;
y = cos x
Since, Graph of function y = cosx is translated by (30, -1).
So, Equation of translated graph will be;
y = cos(x - 30) - 1
Hence, The equation of the translated graph will be;
⇒ y = cos(x - 30) - 1
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