The fraction of hour that remained is 1/2 hour.
It is given in the question that three students were scheduled to give book reports in 1 hour.
After the first report, 2/3 hour remained. The next report took 1/6 hour.
We have to find the fraction of hour that remained.
We know that,
Total time for reports = time taken for first report + time taken for second report + time remained for third report
Hence, we can write,
Time taken for first report = 1-2/3 = 1/3 hour
Time taken for second report = 1/6 hour
1 = 1/3 + 1/6 + time remained for third report
1 = 2/6 + 1/6 + time remained for third report
1 = 3/6 + time remained for third report
1-3/6 = time remained for third report
3/6 = 1/2 = time remained for third report
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any ideas??
Thank you
Answer:
x-0.5,1,2,3,4,5,6
y-12,6,3,2,1.5,1
Step-by-step explanation:
Substitute the x value inside the formula. E.g. y=6 over 0.5, then solve.
Plot the points on the graph and join the up.
Answer:
Step-by-step explanation:
An 18 meters ladder is resting against a wall and makes an angle of 30° with the ground.
If the ladder is pushed vertically along the wall by a distance of x meters, the angle is
changed to 60° with the ground. The value of x is
A)9(√3 −1)
B) 2√3
c) ³(√3-1)
D) 9-√3
Answer:
A
Step-by-step explanation:
using the sine ratio and the exact values
sin30° = [tex]\frac{1}{2}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
calculate the height of the wall below x , call it h
the hypotenuse is the length of the ladder
using the sine ratio in the lower right triangle.
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{18}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2h = 18 ( divide both sides by 2 )
h = 9
lower part of the wall is 9 meters
using the sine ratio in the right triangle on the right
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9+x}{18}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2(9 + x) = 18[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
9 + x = 9[tex]\sqrt{3}[/tex] ( subtract 9 from both sides )
x = 9[tex]\sqrt{3}[/tex] - 9 = 9([tex]\sqrt{3}[/tex] - 1)
Answer:
[tex]\textsf{A)} \quad x=9(\sqrt{3}-1)[/tex]
Step-by-step explanation:
Interior angles of a triangle sum to 180°. Therefore, if the ladder makes an angle of 30° with the ground, the angle it makes with the wall is 60°.
Therefore, the two triangles are congruent as their corresponding angles are the same and the length of their longest side (hypotenuse) is the same.
30-60-90 Triangle Theorem
A 30-60-90 triangle is a special right triangle where the measures of its angles are in the ratio 1 : 2 : 3 and the measure of its sides are in the ratio 1 : √3 : 2.
The formula for the sides is b : b√3 : 2b where:
b = the side opposite the 30° angle (shortest leg).b√3 = the side opposite the 60° angle.2b = the side opposite the right angle (hypotenuse).Therefore, as the length of the hypotenuse is 18:
[tex]\implies 2b=18[/tex]
[tex]\implies b=9[/tex]
[tex]\implies b\sqrt{3}=9\sqrt{3}[/tex]
To find x, subtract the length of the shortest leg of the right triangle from the length of the other leg of the right triangle:
[tex]\implies x=9\sqrt{3}-9[/tex]
[tex]\implies x=9(\sqrt{3}-1)[/tex]
The volume of a cuboid is 54cm³. The length is 2cm and the width is 3cm. Work out the height of the cuboid.
Step-by-step explanation:
divide volume by product of length and width
54cm³= 3cm x 2cm
54/6= 9cm
Solve the equation for y. Leave your answer in terms of π.
π=7x−2y
answer-x=π/7+y/7
Step-by-step explanation:
yes
the convex polygon below has 7 sides. find the value of x
Answer:
x = 147
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 7 , then
sum = 180° × 5 = 900°
sum the interior angles and equate to 900
x + 141 + 112 + 129 + 106 + 139 + 126 = 900
x + 753 = 900 ( subtract 753 from both sides )
x = 147
Jordan has a points card for a movie theater.
.
• He receives 85 rewards points just for signing up.
• He earns 10.5 points for each visit to the movie theater.
• He needs at least 240 points for a free movie ticket.
What is the least number of visits he needs to make in order to earn a free movie
ticket?
The least number of visits he needs to make in order to earn a free movie ticket is approximately 15 visits.
What is the least number of visits needed?Points received for signing up = 85 rewards points
Points received for each visit to the movie theater = 10.5 points
Points needed for a free movie ticket = 240 points
Number of visits = x
85 + 10.5x ≤ 240
10.5x ≤ 240 - 85
10.5x ≤ 155
x ≤ 155 / 10.5
x ≤ 14.761
Approximately,
x ≤ 15 visits
Therefore, Jordan needs at least 15 visits to earn a free movie ticket.
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Write the following linear equation in slope intercept form. 3x + 4y=64
Answer:
[tex]\sf y =\dfrac{-3}{4}x+16[/tex]
Step-by-step explanation:
Slope intercept form: y = mx +bWhere m is the slope and b is the y-intercept.
3x + 4y = 64
Subtract 3x from both sides,
4y = -3x + 64
Now, divide both sides by 4,
[tex]\sf \dfrac{4y}{4}=\dfrac{-3x}{4}+\dfrac{64}{4}\\\\y = \dfrac{-3}{4}x + 16[/tex]
solve for angle 1
pls hurry
Answer:
Step-by-step explanation:
246 degrees
Answer:61.5
Step-by-step explanation:
123/2=61.5
61.5+57=118.5
180-118.5=61.5
Please help me. Yall are so smart
The product of negative four and a number is at most
negative sixty-two. Choose al possible values of the number.
The possible values of the number will be -62/4 or -31/2.
Multiplication of numbers may be defined as the tool or arithmetic operation which can be used to increase the count of a number. For example, if there is a number 4, then in order to increase the number it will be multiplied with some other number like 9. Now, the number will be 4×9 = 36. We are given that the product of -4 with a number gives the answer as 62. Let us assume the number as x and form the equation in accordance with the data given in the question.
-4×(x) = 62
Now, to find x we divide -4 on both the sides and we get
x = -62/4
This number can also be simplified by dividing both numerator and denominator with 2 and we get
x = -31/2.
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Select all equations that are Equivalent to 4x + 8y = 12
a. 4x + 8y + 3 = 15
b. 4x + 8y = 10
c. 5 (4x + 8y) = 60
d. x + 2y = 6
c.(4x+8y)=60
it is equivalent
Answer:
A and C
Step-by-step explanation:
Substitute 4x + 8y = 12
A:
12+3=15
15=15 ✓
B:
12=10 ×
C:
5(12)=60
60=60 ✓
D:
Multiply 4 to x+2y=6 to make it 4x+8y=12
x+2y=6
4x+8y=24
12=24 ×
There are 25 students in the class, 40% of them are girls. How many boys are there in the class?
Answer:
15
Step-by-step explanation:
40/100×25
=10
25-10=15
PLS HELP I'LL GIVE BRAINIEST TO WHOEVER ANSWERS ALL AND IS CORRECT
What is the justification for each step in the solution of the equation?
54+2x=5x−3(2+6x)
Select from the drop-down menus to correctly justify each step.
1)54+2x=5x−6−18x
a. addition to property of equality
b.distributive property
c.multiplication property of equality
2)60=−15x
a. addition to property of equality
b.division property of equality
c.multiplication property of equality
3)−4=x
a. addition to property of equality
b.division property of equality
c.subtraction property of equality
Answer:
1) 54+2x=5x−6−18x Distributive Property
2) 60=−15x Division Property of Equality
3) −4=x Division Property of Equality
Explanation:
1.) This answer is Distributive Property because the parenthesis in the original equation were removed through the process of distributing.
3(–2 – 6x) was distributed by multiplying 3 • –2 and 3 • –6x to get –6 – 18x
2.) This answer is Division Property of Equality because for all real numbers x, y, and z, if x = y and z ≠ 0, then x/z = y/z. This is true in this equation because of 60/–15 = −15x/–15.
3.) Division is used to get the value of x, which is –4.
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write 6400kg in grams giving your answer in standard form
Answer: 6400kg=6.4*10⁶ g
Step-by-step explanation:
6400 kg=
6.4*10³ kg=
6.4*10³*10³ g=
6.4*10³⁺³ g=
6,4*10⁶ g
Answer - 6.4 × 10^6
Step by step Explaination-
6400 kg=
6.4*10³ kg=
6.4*10³*10³ g=
6.4*10³⁺³ g=
6,4*10⁶ g
Firstly, we'll discuss the units of digits -
1. We'll convert 6400 kilograms into grams. Multiply the value in kilograms by the factor '1000'.
2. Standard form may be a means of writing variety thus it's easier to browse. it's typically used for terribly large or small numbers.
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?:7 =8:14 and 32:? =12:24
Answer:
First question mark is 4, second question mark is 64
Step-by-step explanation:
For the first question mark, 7 is half of 14, and half of 8 is 4, so they would be the same ratio, and then for the second, 12 to 24 is just one half, meaning you would need to find double 32, which is just 64
I'm stuck pls help me
2/4
Answer:
its the 3rd option
Step-by-step explanation:
you solve parenthesis then multiply then had to minus which gave you the total
Solve for w.
ρ = m / ℓ⋅w⋅h
What is w equal to?
The / means it's a fraction, the M is on top, and the rest is on the bottom, 20 points, please help, no links.
Point B is on line segment AC
Given: AB = 4x - 6, AC = 2x + 10, and BC=4, determine the numerical length of AC.
Answer:
22
Step-by-step explanation:
AB + BC = AC
4x -6 + 4 = 2x + 10 Combine like terms
4x -2 = 2x + 10 Subtract 2s from both sides of the equation
2x -2 = 10 Add 2 to both sides
2x = 12 Divide both sides by 2
x = 6
Plug in 6 for x in AC
2x + 10
2(6) + 10
12 + 10
22
what is decimal? i dont understand it at al
Answer: irelating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten:
Step-by-step explanation:
10. What is m/ABD in the figure shown?
The measure of m∠ABD in the figure shown is 19°.
Given:
∠BCD = 71°
In the figure, ΔABC is an isosceles triangle where AB = BC.
According to the Isosceles Triangle Theorem, an isosceles triangle has equal angles on either side of its equal sides.
So, ∠BAD = ∠BCD = 71°
The sum of angles in a triangle sums to 180°.
∠ABC + ∠BAD + ∠BCD = 180°
∠ABC + 71° + 71° = 180°
∠ABC + 142° = 180°
∠ABC = 180° - 142° = 38°
DB is the angle bisector of ∠ABC.
Now, ∠ABD = ∠CBD = 38°/2 = 19°
The measure of ∠ABD is 19°.
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Solve for the long leg and for the hypotenuse of the 30-60-90 triangle.
By using the properties of the 30-60-90 right triangles, the lengths of the long leg and the hypotenuse are √3 · L and 2 · L, respectively.
What are the lengths of the hypotenuse and the long leg of the 30-60-90 right triangle?
Right triangles are triangles where one of its internal angles is a right angle, that is, has a measure of 90°. 30-60-90 triangles are right triangles whose internal angles have measures of 30°, 60° and 90°, respectively.
This kind of right triangles have the following features:
The long leg is adjacent to the least angle of the triangle, that is, the angle whose measure is 30°.The short leg is opposite to the least angle of the triangle, that is, the angle whose measure is 30°.The length of the long leg is √3 times the length of the short leg.The length of the hypotenuse is 2 times the length of the short leg.If we know that the short leg has a length of L, then the lengths of the long leg and the hypotenuse are √3 · L and 2 · L, respectively.
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if F(x)=x (power of 2) +3x-2 find F (5)
SHOW WORK
Find the slope ………..
10/ 6 2/3 please asap
Answer:
what is the symbol between the 2 fractions?
n + n+1 = 2n+1 = 2n+2-1 = 2(n+1) -1
2 = factor so must be even.
even number -1 is always odd
The value of n is 1/2 and it is not an even number or odd number
How to determine the solution to the equation?From the question, the steps are given as
n + n + 1 = 2n + 1
n + n + 1 = 2n+2-1
n + n + 1 = 2(n+1) -1
Also, from the question, we have the result of the expression to be
2
This means that
n + n + 1 = 2
Substitute n + n + 1 = 2(n+1) -1 in the equation n + n + 1 = 2
So, we have
2(n + 1) - 1 = 2
Add 1 to all sides of the equation
So, we have
2(n + 1) = 3
Divide both sides of the equation by 2
So, we have
n + 1 = 3/2
Subtract 1 from all sides
n = 1/2
The above implies that the number n is neither an even number, nor an odd number
This is so because the result is a fraction
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find the missing side length, and round to the nearest tenth if necessary.
Answer:
3.2
Step-by-step explanation:
→ State Pythagoras theorem
x² + y² = z²
→ Substitute in
3² + 1²
→ Simplify
10 = z²
→ Evaluate
√10 = 3.2
Answer:
3.2
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
a = 3
b = 1
[tex]3^{2}[/tex] + [tex]1^{2}[/tex] = 9 + 1 = 10
[tex]c^{2}[/tex] = 10
c = [tex]\sqrt{10}[/tex]
c = 3.16227766017
Round to the nearest tenth
c = 3.2
At the beginning of the year, Josue had $70 in savings and saved an additional $9
each week thereafter. Arianna started the year with $30 and saved $19 every week.
Let J represent the amount of money Josue has saved t weeks after the beginning of
the year and let A represent the amount of money Arianna has saved t weeks after
the beginning of the year. Write an equation for each situation, in terms of t, and
determine the interval of time when Josue has more in savings than Arianna.
There will be no interval of time when Josue has more in savings than Arianna, they have same savings is after 4 weeks
How to calculate the above question?Step one:
For Josue
initial savings balance= $70
weekly savings = $9
Let J represent amount of money Josue has saved and t the number of weeks after the beginning of the year
The total amount in the savings after t weeks is
J=9t+70-------1
For Arianna
initial savings balance= $30
weekly savings = $19
Let A represent the amount of money Arianna has saved and t the number of weeks after the beginning of the year
The total amount in the savings after t weeks is
J=19t+30---------2
Step two
equation 1 and 2 to find t
9t+70=19t+30
9t-19t=30-70
-10t=-40
divide both sides by 10
t=4
t=4 weeks
so after 4 weeks Josue and Arianna will have the same amount of money
For Josue t=4
J=9(4)+70-------1
J=36+70
J=$106
For Arianna t=4
A=19(4)+30---------2
A=76+30
A=$106
The two equations above shows that after 5 weeks their savings will be $106.
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The surface area of the solid shown is 12 in. 6 in. 8 in. I square inches and its volume is cubic inches.
The surface area and the volume of solid prism are 432in² and 576in³ respectively.
What is the surface area and volume of the rectangular prism?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles
The surface area of a rectangular prism is expressed as;
A = 2( wl + hl + hw )
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length.
Given the data in the question;
Length l = 12inWidth w = 8inHeight h = 6inSurface area A = ?Volume V = ?The surface area of the solid is;
A = 2( wl + hl + hw )
A = 2( (8in × 12in) + (6in × 12in) + (6in × 8in) )
A = 2( 96in² + 72in² + 48in² )
A = 2( 216in² )
A = 432in²
Therefore, surface area of the rectangular prism is 432in²
The volume of the solid is;
V = w × h × l
V = 8in × 6in × 12in
V = 576in³
Therefore, volume of the rectangular prism is 576in³
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Please help I need to do it step by step and I can’t add or subject or divide or multiply fractions on this website
Answer:
x = 9
Step-by-step explanation:
To solve for x, you must isolate the variable.
First, start by adding 2 to BOTH sides to eliminate the 2.
3=1/3x. then divide each side by 1/3
3÷1/3 = x
3/1 × 3/1 = x
9 = x
on a recent diet nina lost 43lb more than leila. their total weight loss was 95 lbs. how many pounds did nina lose
L = lbs lost by Leila
N = lbs lost by Nina
since we know that Leila lost "L" lbs and Nina lost 43lbs more than that, so Nina lost then "L + 43", and we also know their total weight was 95lbs hmmmm so
[tex]\stackrel{Leila's}{L}~~ + ~~\stackrel{Nina's}{(L+43)}~~ = ~~\stackrel{total}{95}\implies 2L+43=95\implies 2L=52 \\\\\\ L=\cfrac{52}{2}\implies L=26\hspace{15em}\underset{Nina~lost}{\stackrel{26~~ + ~~43}{\text{\LARGE 69}~lbs}}[/tex]