The rational numbers - 5 / 6 and - 7 / 10 are equivalent to - 25 / 30 and - 21 / 30, respectively. Then, the relationship is that - 5 / 6 is the less than - 7 / 10 as - 25 < - 21.
What is the relationship between two rational numbers?
Rational numbers are real numbers of the form m / n, where m and n are integers and n is not zero. In this problem we need to determine the relationship between two rational numbers, this can be done by amplifying the two rational numbers to a form with the same denominator and then compare the two numerators.
First, find the least common multiple of the two denominators:
6 = 2 × 3
10 = 2 × 5
L.C.M. = 2 × 3 × 5 = 30
Second, amplify each rational number:
- (5 × 5) / (6 × 5) = - 25 / 30
- (7 × 3) / (10 × 3) = - 21 / 30
Third, compare the numerators of the fraction found in the previous step:
Since - 25 < - 21, then - 5 / 6 < - 7 / 10.
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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 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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?: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
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]
Pleaseee help, it's urgent! Just (i)
I'll give whoever is right the brainliest answer.
Answer:
(i) 7 + 4√2 cm^2.
(ii) 50 - 8√2 cm^2.
Step-by-step explanation:
(i)
Area = (3 + √8)(5 - 4/√2)
= 3(5 - 4/√2) + √8(5 - 4/√2)
= 15 - 12/√2 + 5√8 - 4√4
= 15 - 8 -( 12√2)/2 + 5*(2√2)
= 7 - 6√2 + 10√2
= 7 + 4√2.
(ii)
Area of the square
= AC^2
= (3 + √8)^2 + (5 - 4/√2)^2 (By Pythagoras)
= 9 + 6√8 + 8 + 25 - 40/√2 + 16/2
= 9 + 8 + 8 + 25 + 12√2 - 20√2
= 50 - 8√2.
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:
A store sells 2 1/4 pounds of tomatoes in a package for $4.45. The expression 4.45p represents the cost of the tomatoes for a number of packages. What does the variable p represent?
Based on the given, the variable p from the expression 4.45p represent pounds of tomatoes sold.
What the variable p represent?Algebra is a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
Pounds of tomatoes sold = 2 1/4 poundsCost of the tomatoes = $4.45The cost of the tomatoes for a number of packages = 4.45p
If the store sold 2 1/4 pounds of tomatoes
The cost of the tomatoes for a number of packages = 4.45p
= 4.45(2 1/4)
= 4.45(9/4)
= 4.45(2.25)
= $10.0125
In conclusion, the variable p represent pounds of tomatoes sold in the store.
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if F(x)=x (power of 2) +3x-2 find F (5)
SHOW WORK
10/ 6 2/3 please asap
Answer:
what is the symbol between the 2 fractions?
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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Find the slope ………..
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
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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On subtracting 20 from twice a number we get 50, then the number is
On subtracting 20 from twice a number we get 50, then the number is 35 in this context.
What is Subtraction?This is referred to as a type of mathematical operation in which one number is taken or deducted from the other and the sign is ( - ). this expression is used in every facet of life for their daily activities.
We were told that 20 was subtracted from twice a number to give 50 which means that twice the number is 70. The exact number will therefore be 70/2 which will then result in 35 and is therefore the most appropriate choice.
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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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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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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
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
A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of finished products and computes the sample mean product weight. If test results over a long period of time show that of the values are over pounds and are under pounds, what are the mean and the standard deviation for the population of products produced with this process?.
Standard deviation of population mean is 0.33.
Why is there a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.it is shown that 5% values are over 2.1 pounds and 5% are under 1.9 pounds
so stastically that means
P( X > 2.1, μ; σ) = 0.05 and P( X 1.9; μ; σ) = 0.05
where μ is mean of the sample and σis the standard deviation of the sample.
so mean can be calculated easily μ = (2.1 + 1.9)/2 = 2.0
and as we can interpret P(1.9 <x < 2.1; 2.0; σ) = 0.90 by normal distribution the Z value for 90% confidence interval is 1.65
so σ = (2.1 -2) /1.65 = 0.06
standard deviation of the sample mean= 0.06
and by that standard deviation of population mean = 0.06 * (30) 0.5 = 0.33
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The complete question is -
A production process is checked periodically by a quality control inspector. the inspector selects simple random samples of 30 finished products and computes the sample mean product weight. If test results over a long period of time show that 5% of the values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process? What is the population mean? (to 1 decimal) What is the population standard deviation (to 2 decimals)?
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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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:
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
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
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
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
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.
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
FIRST ANSWER GETS BRAINLIEST
What is the distance between the points (2,−3) and (−5,−3) ?
0 units
3 units
6 units
7 units
Answer: 7 units
Step-by-step explanation:
Estimate the quotient of 41 ÷ 7.94.
4
5
6
7
Answer:
5
Step-by-step explanation:
Since 7 into 42 is six we know the answer can't be 7 because it's too high. We can also rule out 6 because 6 times 7.94 is more than 41. The first answer choice is wrong because if you take away the .94, 7 times 4 is 28 which is pretty far from 41. If you multiply 5 and 7, it comes out to 35. That's significantly closer than four.
Hope this helps! :)
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 ×