When you add two rational numbers, each number can be written as a
✔ fraction .
Step-by-step explanation:
When you add two rational numbers, each number can be written as a fraction.
What is a rational number?A Rational number can be defined as any number which can be represented in the form of p/q where q ≠ 0. It can be made by dividing an integer by an integer.
For the given situation,
The sum of two rational numbers is rational.
The closure property of addition of rational number states that if we add two rational number, then the sum of these two rational number will also be a rational number.
Adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication.
Hence we can conclude that when you add two rational numbers, each number can be written as a fraction.
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Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?
Answer:
-12 and 2
Step-by-step explanation:
[tex]x^2+10x=24\\[/tex]
[tex]x^2+2*5*x=24[/tex]
[tex]x^2+2*5*x+5^2-5^2=24[/tex]
[tex](x^2+2*5*x+5^2)-5^2=24[/tex]
Using the identity
[tex]a^2+2*a*b+b^2 = (a+b)^2[/tex]
we get
[tex](x+5)^2-5^2=24[/tex]
[tex](x+5)^2-25=24\\[/tex]
[tex](x+5)^2=24+25\\(x+5)^2=49\\(x+5)=+7 \\or (x+5)=-7\\[/tex]
Solving both of them we get
x=-12 or x=2
Jared is in charge production in a factory that makes lightbulbs. The factory made 2648 lightbulbs over the weekend. Jared wants to pull a sample of these bulbs for testing. Which sample would give Jared the most -accurate test readings ? —a sample consisting every 20th lightbulb- a sample consisting every 40th light bulb- a sample consisting every 50th lightbulb- a sample consisting every 100th light bulb?
Answer:
A
Step-by-step explanation:
someone pleaseeeeeeeeee help me!
1. Displacement vectors of 5 km north, 3 km east, 2 km south, and 3 km west combine to a total displacement of
3 km north.
13 km west.
0 km.
2 km south.
Continue the following pattern; describe the eighth figure in this pattern
Answer:
The Eighth Figure would be an 8 by 8 square with 64 small squares
Step-by-step explanation:
The Figures shown in the picture are following a fairly simple pattern. Each variation is adding 1 row and 1 column of squares. Variation 4 has a 4 by 4 square with 16 small square (4*4 = 16). If we continue with pattern then variation 8 will be an 8 by 8 square with 64 smaller squares inside it (8*8 = 64)
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3500 calories for 6 servings of pie how many calories per serving
PLEASE MATH HELP!!
The area of this circle is 96π m².
What is the area of a 30º sector of this circle?
4π m²
8π m²
9π m²
16π m²
30 degrees / 360 degrees = 0.0833
0.0833 * 96 = 8
answer is 8π m²
The area of a [tex]30^{\circ}[/tex] sector of this circle is [tex]8\pi \ m^2[/tex]. The correct option is B. [tex]8\pi \ m^2[/tex].
Given,The area of circle is [tex]96 \pi \ m^2[/tex].
We have to calculate the area of [tex]30^{\circ}[/tex] sector of this circle.
Area of circle:We know that, Area of circle is,
[tex]A=\pi r^{2}[/tex]
Here, [tex]96\pi =\pi r^{2}[/tex]
Or,
[tex]r^{2} =96[/tex]
[tex]r=\sqrt{96}[/tex]
[tex]r=4\sqrt{6}[/tex]
So, radius of the circle,
[tex]r=4\sqrt{6}[/tex] [tex]m[/tex].
Now we know that Area of a Sector of Circle
Say [tex]A_{1}[/tex],
[tex]A_{1} = \frac{\Theta}{360} \pi r^{2}[/tex]
where [tex]\Theta[/tex] is the angle subtended at the center, given in degrees, and '[tex]r[/tex]' is the radius of the circle.
So,
[tex]A_{1} =\frac{30}{360} \pi (4\sqrt{6} )^{2}[/tex]
[tex]A_{1} =\frac{1}{12} \pi \times96[/tex]
[tex]A_{1} =8\pi \ m^2[/tex].
Hence the area of a [tex]30^{\circ}[/tex] sector of this circle is [tex]8\pi \ m^2[/tex]. the correct option is B [tex]8\pi \ m^2[/tex].
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What is the slope of any line parallel to y = 4x + 17
Need a smart person fast!
Quadrilateral JPRA is similar to quadrilateral KDEW . PR=27 mm , DE=15 mm , and WE=25 mm .
What is AR ?
Final answer:
To find AR in quadrilateral JPRA similar to quadrilateral KDEW, use the concept of similar triangles to determine AR = 45 mm.
Explanation:
To find AR in quadrilateral JPRA that is similar to quadrilateral KDEW, we can use the concept of similar triangles.
Calculate the scale factor between the two quadrilaterals: PR/DE = AR/WE
Substitute the known values: 27/15 = AR/25 and solve for AR which gives AR = 45 mm.
Prism A is similar to Prism B. The volume of Prism A is 2080 cm³.
What is the volume of Prism B?
260 cm³
520 cm³
1040 cm³
16,640 cm³
The volume of prism B is [tex]\rm 260 \; cm^3[/tex] and this can be determined by taking the ratio of the volume of both the prism.
Given :
Prism A is similar to Prism B. The volume of Prism A is 2080 cm³.To determine the volume of prism B, first determine the ratio of the volume of prism A to the volume of prism B that is:
[tex]\rm \dfrac{V_A}{V_B}=\dfrac{8^3}{4^3}[/tex]
[tex]\rm \dfrac{V_A}{V_B}=8[/tex]
Now, put the value of the volume of prism A in the above expression.
[tex]\rm \dfrac{2080}{V_B} = 8[/tex]
Divide 2080 by 8 in the above equation.
[tex]\rm V_B = \dfrac{2080}{8}[/tex]
[tex]\rm V_B = 260\;cm^3[/tex]
So, the volume of prism B is [tex]\rm 260 \; cm^3[/tex].
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In 10 minutes, the top three finishers in a hot dog eating contest consumed a total of 130 hot dogs. the winner, person a, ate 8 more hot dogs than the runner-up, person
b. person c finished a distant third, 10 hot dogs behind person
b. how many hot dogs did each person eat?
Final answer:
The winner, Person A, ate 52 hot dogs, the runner-up, Person B, ate 44 hot dogs, and Person C finished third with 34 hot dogs.
Explanation:
The question involves solving a system of linear equations to find out how many hot dogs each participant in a hot dog eating contest ate. Let's assign variables to each person: A for the winner, B for the runner-up, and C for the third-place finisher. According to the problem, A ate 8 more hot dogs than B, and C ate 10 fewer hot dogs than B.
Here are the equations based on the information provided:
A = B + 8 (Person A ate 8 more than person B)C = B - 10 (Person C ate 10 less than person B)A + B + C = 130 (Together they ate 130 hot dogs)Now we substitute the expressions for A and C in terms of B into the third equation:
(B + 8) + B + (B - 10) = 1303B - 2 = 1303B = 132B = 44Using the value of B, we find out A and C:A = 44 + 8 = 52C = 44 - 10 = 34Therefore, Person A ate 52 hot dogs, Person B ate 44 hot dogs, and Person C ate 34 hot dogs.
I need help!!!! Please if you get it right i will mark you brainliest!
Verify the identity.
tan x plus pi divided by two = -cot x
Can someone help me with this problem?
I NEED HELP ASAP Use the Law of Detachment or the Law of Syllogism to draw a conclusion. 3. If Shauna is early for her meeting, she will gain a promotion. If Shauna wakes up early, she will be early for her meeting. Shauna wakes up early.
Roger counted the kids in the cafeteria on Monday. There were 9 tables of 10 kids at the start of lunch. In the middle of lunch, 4 kids came in and sat down. How many kids were in the cafeteria then?
Each person in a ticket line gets either one or two tickets. You are the 51st person in line. Forty percent of the people in front of you get one ticket each, and the rest of the people in front of you get two tickets each. How many tickets will have been given out when you reach the ticket booth?
Write the expression-3x2+2y2+5xy-2y+5x2-3y2 in simplest form A how many terms are in the simplified expression? B how many terms in the simplified expression negative
A) There are 3 terms in the simplified expression. B) There are 2 terms in the simplified expression that are negative.
First, let's combine the terms that are alike. We can combine the [tex]x^2[/tex] terms and the [tex]y^2[/tex] terms:
(-3 [tex]x^2[/tex] + 5 [tex]x^2[/tex] ) + (2 [tex]y^2[/tex]- 3 [tex]y^2[/tex]) + 5xy - 2y
This gives us:
2 [tex]x^2[/tex] - [tex]y^2[/tex]+ 5xy - 2y
We can then combine the xy and y terms:
2 [tex]x^2[/tex] - ( [tex]y^2[/tex]+ 2y)
This gives us:
2 [tex]x^2[/tex] - [tex]y^2[/tex]- 2y
So, the simplified expression is 2 [tex]x^2[/tex] - [tex]y^2[/tex]- 2y.
There are 3 terms in the simplified expression.
There are 2 terms in the simplified expression that are negative.
Here is a breakdown of the steps involved in simplifying the expression:
Combine the [tex]x^2[/tex] terms and the [tex]y^2[/tex] terms.
Combine the xy and y terms.
Check to make sure that there are no common factors that can be canceled.
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You have a camera with a 16 mp resolution. how many pixels are represented by that resolution?
Which expressions is not a polynomial
A. z + 1
B. 2x^4 - y
C. 6 + w
D. y^2 - ^3√y + 4
Bob is building a wooden cabin. The cabin is 303030 meters wide. He obtained a bunch of 171717 meters long wooden beams for the roof of the cabin. Naturally, he wants to place the roof beams in such an angle that each pair of opposite beams would meet exactly in the middle. What is the angle of elevation, in degrees, of the roof beams
Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
The width of the room is 30 meters.
If two beams will be making an angle, they will half the width.
There will be a right triangle made, so using SOH CAH TOA,
[tex]cos x=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos x=\frac{15}{17}[/tex]
taking cos inverse
x = [tex]cos^{-1} (\frac{15}{17} )[/tex]
x = 28.07° : Answer
Hope it will help :)
Answer:
28.07
Step-by-step explanation:
Credit to first said it
Ashley walks 1/3 of a mile each day. After 10 days, how many miles has she walked? 2 1/33 1/39 1/310 1/3
Find the dimensions of a rectangle whose perimeter is 24 feet and whose area is 27 square feet.
99 POINTS! NEED HELP ASAP! WILL GIVE BRAINLIEST ANSWER!
Jenny is baking three dozen cookie sandwiches for her friend’s birthday party. She plans to transport the cookie sandwiches in the same food storage container but is not sure if all 36 will fit inside of the container.
Part A: Calculate the volume of one cookie sandwich to the nearest cubic unit. Use 3.14 for
Part B: Calculate the total capacity of the food storage container to the nearest cubic unit. Use 3.14 for [tex] use 3.14 for \pi
use this equation for Parts B and A[/tex]
Part C: Given your calculations regarding the volumes in Parts A and B, do you anticipate that Jenny will be able to transport all of the cookie sandwiches in one food storage container? In two or more complete sentences, explain your reasoning.
Alright to solve it
Part A)
C = 1.5
F =1
You will need to solve it for volume= length times width and times height
3.14 x 1^2 x 1.5
The answer you will get is 5 in^3
Part B) Just do the same proccess as i did on the first one
CV= 192 in^3
Part C)
C=36x5in^3
So this is going to be 180 in^3 because is the less volume.
Hope this helps
Tobey
Find the 11th term from the end in the AP 56, 63, 70,..., 329
How can I find the measurements for this questions?
The area of a triangle is 36 square meters. The base is 1 meter less than the height. What is the height of the triangle?
Arthur buys a zero coupon bond with a face value of $5000 for $4000. The bond has five years until it matures. How much would Arthur earn if he holds this bond to maturity?
x = y−4, 2x−5y = 3
Which one-variable linear equation represents the system of equations?
2(y-4)-5y = 3
2x-5(y-4) = 3
2x-5y = y-4
2x-5(x-4) = 3
The solution is Option A.
The value of the equation is 2( y - 4 ) - 5y = 3
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the value of x = y - 4 be equation (1)
Let the value of the equation 2x - 5y = 3 be equation (2)
Now ,
We know the value of the equation x = y -4
Substituting the value of equation (1) in equation (2) , we get
2 ( y - 4 ) - 5y = 3
So , the equation has now become ,
2 ( y - 4 ) - 5y = 3
Hence , the value of the equation is 2 ( y - 4 ) - 5y = 3
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Solve 5kx + 6 = 7kx for x
Zaira spent 55 hours in 2 weeks working on a science project. she worked 32 hours the first week. Write and solve an addition equation to find the amount of time she spent working the second week.