Question 7: Choose the correct simplification of the expression (3x − 6)(2x2 − 4x − 5)
Answer:
C) 6x³ - 24x² + 9x + 30
Step-by-step explanation:
(3x - 6)(2x² - 4x - 5)
3x • 2x² = 6x³
3x • -4x = -12x²
3x • -5 = -15x
-6 • 2x² = -12x²
-6 • -4x = 24x
-6 • -5 = 30
Combine terms.
6x³ - 12x² - 15x - 12x² + 24x + 30
Combine like terms.
6x³ - 24x² + 9x + 30
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12. Write 0.8 as a fraction,
Pls explain in full detail.
Answer:
8/10
Step-by-step explanation:
10x10 is 100 8x10 would be 80 so 80/100=8/10
Answer:
8/10 = 4/5
Step-by-step explanation:
0.8 is 8-10th which means 8 divided by 10
reducing 8/10 to its lowest term since 8 and 10 has 2 as common factor, then
(8=2*4)/(10=2*5)
if 2 cancels out, then you are left with 4/5
MAKE EXAMPLES WHERE YOU USE THE DISCOUNT AND THE INCREASE OF PERCENTAGES
Answer:
once upon a time a dude went to a store. there was a dude jacket for 20% off.
Step-by-step explanation:
Now do the opposite. for exapmle, the price increased by 20 %.
5000 X 10 X 10 X 50
Answer:
25000000
5000 X 10 is 50000
50000 X 10 is 500000
500000 X 50 is 25000000
Step-by-step explanation:
Answer:
25000000
Step-by-step explanation:
A way to tackle this is to split all the numbers up into a digit and a power of 10.
5000 = 5*1000, and 1000 can be written as 10^3
10 = 1*10, and obviously 10 is 10^1
50 = 5*10, where 10 is 10^1
Now we have (5*10^3) * (1 * 10) *(1 *10)*(5 *10)
Gathering all the digits, we have 5*1*1*5, giving us 25
Gathering all the powers of 10, we have 10^3*10*10*10 = 10^6
expanding and multiplying gives us the final answer of 25000000
What is the image point of (-5,9) after a translation left 1 unit and down 1 unit?
Answer: (-6,8)
Step-by-step explanation:
Translation is a rigid motion inn which every point of the figure moved in the same direction and for the same distanceTranslation rules are
Left c units : [tex](x,y)\to(x-c,y)[/tex]
Down c units : [tex](x,y)\to(x,y-c)[/tex]
The image point of (-5,9) after a translation left 1 unit and down 1 unit will be:
[tex](-5,9)\to(-5-1,9-1)=(-6,8)[/tex]
Hence, the image point is (-6,8).
PLEASE HELP ASAP! If t is a real number, what is the maximum possible value of the expression -t^2 + 8t -4?
Answer:
12
Step-by-step explanation:
Hello, as the coefficient of the leading term is negative we know that the vertex of the parabola is a maximum. So we need to find the vertex.
This expression is maximum for
[tex]t=-\dfrac{b}{2a} \text{ where the parabola equation is}\\\\ax^2+bx+c=0[/tex]
So, here, it gives t = 8/2=4, and then, the maximum is
[tex]-4^2+8*4-4=-16+32-4=32-20=12[/tex]
So the answer is 12.
Thanks
Nikki gathered data about the length of time she spent listening to the radio and the number of commercials she heard. She organized the data in a scatter plot, where x represents the minutes spent listening and y represents the number of commercials. Then she used the graphing tool to find the equation of the line of best fit: y = 0.338x − 1.387. Based on the line of best fit, for approximately how many minutes will Nikki need to listen to the radio to hear 20 commercials?
Answer:
The number of minutes Nikki needs to listen to the radio to hear 20 commercials is 63.275 minutes
Step-by-step explanation:
The given dependent and independent variables are;
The number of minutes spent by Nikki listening = x
The number of commercials aired = y
The relationship between the independent variable, x ans the dependent variable, y, was given by the Nikki's graphing tool line of best fit as follows;
y = 0.338·x - 1.387
Therefore, the number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y is given as follows;
20 = 0.338·x - 1.387
20 + 1.387 = 0.338·x
0.338·x =20 + 1.387 = 21.387
x = 21.387/0.338 = 63.275 minutes
The number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y = 63.275 minutes.
Answer:
C. 63 minutes
Step-by-step explanation:
Answer ASAP, will give brainliest
Answer:
Step-by-step explanation:
1) Diagonal bisect the angles of Rhombus
∠CAB = ∠CAD
∠CAB = 71
2) ∠DAB = ∠CAB + ∠CAD
∠DAB = 71 + 71 = 142
In Rhombus, adjacent angles are supplementary
∠DAB + ∠ABC = 180
142 + ∠ABC = 180
∠ABC = 180 - 142
∠ABC = 38
3) In rhombus, opposite angles are congruent
∠ADC = ∠ABC
∠ABC = 38
In rhombus, diagonal bisect angles
∠BDC = (1/2)*∠ADC
∠BDC= 38/2
∠BDC = 19
4) Diagonals bisect each other at 90
∠DEC = 90
5) Diagonals bisect each other
BE = DE
BE + DE = DB
7x -2 +7x -2 =24 {add like terms}
14x - 4 =24
14x = 24+4
14x = 28
x = 28/14
x = 2 m
6) AB = 13m
BE = 7x - 2 = 7*2 -2 = 14 -2 = 12 m
In right angle ΔAEB, {use Pythagorean theorem}
AE² + BE² = AB²
AE² + 12² = 13²
AE² + 144 = 169
AE² = 169 - 144
AE² = 25
AE = √25
AE = 5 m
Diagonals bisect each other
AE = EC
AC = 2*5
AC = 10 m
7)Side = 13 m
Perimeter = 4*side
= 4*13
Perimeter = 52 m
8) d1 = AC = 10 m
d2 = DB = 24 m
Area = [tex]\frac{d_{1}*d_{2}}{2}[/tex]
[tex]=\frac{10*24}{2}\\[/tex]
= 10 *12
= 120 m²
A batch of hot chocolate is made with 24 teasoons of cocoa and 12 cups of milk. How many teaspoons of cocoa are needed for every cup of milk?
Answer:
2 teaspoons
Step-by-step explanation:
24 tsp/12 cups = x tsp /1 cup
Cross multiplying, we have:
12x = 24
x = 2
The solution is 2 teaspoons of cocoa
Number of teaspoons of cocoa is given by the equation A = 2 teaspoons
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 number of teaspoons of cocoa be represented as A
Now , the equation will be
A batch of hot chocolate is made with 24 teaspoons of cocoa and 12 cups of milk
So , for 12 cups of milk = 24 teaspoons of cocoa is required
And , for 1 cup of milk A = 24 teaspoons of cocoa is required / 12
Substituting the values in the equation , we get
Number of teaspoons of cocoa A = 24 teaspoons / 12
Number of teaspoons of cocoa A = 2 teaspoons
Therefore , the value of A is 2 teaspoons
Hence , the number of teaspoons is 2
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Consider the equation: x 2 − 6 = 2 − 18 x x 2 −6=2−18xx, squared, minus, 6, equals, 2, minus, 18, x 1) Rewrite the equation by completing the square. Your equation should look like ( x + c ) 2 = d (x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or ( x − c ) 2 = d (x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation? Choose 1 answer: Choose 1 answer: (Choice A) A x = 9 ± 89 x=9±89x, equals, 9, plus minus, 89 (Choice B) B x = − 9 ± 89 x=−9±89x, equals, minus, 9, plus minus, 89 (Choice C) C x = 9 ± 89 x=9± 89 x, equals, 9, plus minus, square root of, 89, end square root (Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
Answer:
1. (x+9)^2 = 89
2. (Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
Step-by-step explanation:
x^2 - 6 = 2 - 18x
1) rewrite the equation by completing the square
x^2 - 6 = 2 - 18x
x^2 + 18x = 2+6
x^2 + 18x = 8
Find the half of the coefficient of x and square it
18x
Half=9
Square half=(9)^2
=81
Add 81 to both sides
x^2 + 18x = 8
x^2 + 18x + 81 = 8 + 81
x^2 + 18x + 81 = 89
(x+9)^2 = 89
Check:
(x+9)(x+9)=89
x^2 + 9x + 9x + 81=89
x^2 + 18x +81 =89
2) (x+9)^2 = 89
√(x+9)^2 = √89
x+9=√89
x=√89 - 9
It can be rewritten as
x= -9 ± √89
(Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
HELP ILL MARK YOU BRANLIEST!!!! 40POINTS!! What is the sign of the product (3)(−25)(7)(−24)? Positive, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is positive Positive, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is positive Negative, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is negative Negative, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is negative
Answer:
the sign is positive
Step-by-step explanation:
to negatives make a positive.
and that last point you added is wrong two positives equals a positive.
different signs= negative
same signs=positive
The formula for the area (A) of a circle is A = π • r2, where r is the radius of the circle. Ronisha wants to find the area of a sector of a circle that has a central angle of π6 radians. Enter the number that Ronisha should multiply by to find the area of the sector of the circle. Round your answer to the nearest hundredth.
Greetings from Brasil...
Here we will apply rule of 3...
This formula, A = πR², its for the whole circle, that is, 360° (2π)
We want the area of only a part, that is, a circular sector whose angle π/6
sector area
2π ----- πR²
π/6 ----- X
2πX = (π/6).πR²
2πX = π²R²/6
X = π²R²/12π
X = πR²/12If Ronisha multiply the area by 1/12 she will get the area of sector with angle of π/6
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. The height (in feet) of a rocket launched from the ground is given by the function f(t) = -16t2 + 160t. Match each value of time elapsed (in seconds) after the rocket’s launch to the rocket's corresponding instantaneous velocity (in feet/second).
Answer:
The pairs are;
t, v
2, 96
4, 32
5, 0
6, -32
7, -64
9, -128
Step-by-step explanation:
The given equation is f(t) = -16·t² + 160·t
We have, the velocity, v = d(f(t))/dt = d(-16·t² + 160·t)/dt = -32·t + 160
Which gives;
t, v
0, -32×(0) + 160 = 160
1, -32×(1) + 160 = 128
2, -32×(2) + 160 = 96
3, -32×(3) + 160 = 64
4, -32×(4) + 160 = 32
5, -32×(5) + 160 = 0
6, -32×(6) + 160 = -32
7, -32×(7) + 160 = -64
8, -32×(8) + 160 = -96
9, -32×(9) + 160 = -128
The given velocity values are;
96, -64, 32, 0, -128, -32 which correspond to 2, 7, 4, 5, 9, 6
The pairs are;
t, v
2, 96
4, 32
5, 0
6, -32
7, -64
9, -128
(x-1)(x+2)(x-3)(x+7)(x-5)/2x-2
=0
What can x be?
Answer:
see below
Step-by-step explanation:
Multiplying the equation by 2x - 2 on both sides to cancel out the denominator gives us (x - 1)(x + 2)(x - 3)(x + 7)(x - 5) = 0. Using Zero Product Property and setting each factor to 0, we get:
x - 1 = 0 or x + 2 = 0 or x - 3 = 0 or x + 7 = 0 or x - 5 = 0
x = 1, x = -2, x = 3, x = -7, x = 5
Unfortunately, x cannot be 1 as the numerator would become 0 and then the expression on the left side would become undefined so the final answer is x = -2, x = 3, x = 7, x = 5.
What were Malcolm's and Ravi's maximum speeds?
Answer:
Malcom's maximum speed = 200 km/h
Ravi's maximum speed = 320 km/h
Step-by-step explanation:
Let m = Malcom's maximum speed
Let r = Ravi's maximum speed
Average of their maximum speed would be represented as [tex] \frac{m + r}{2} = 260 [/tex]
[tex] m + r = 520 [/tex].
Make m the subject of the formula by subtracting r from both sides:
[tex] m = 520 - r [/tex]. Let this be equation 1.
Given that Malcom's speed (m), when doubled is 80 km/h more than that of Ravi (r). This can be expressed as: [tex] 2m = r + 80 [/tex]. This is equation 2.
Plug in (520 - r) into equation 2 to replace m:
[tex] 2(520 - r) = r + 80 [/tex]
[tex] 1040 - 2r = r + 80 [/tex]
Solve for r. Subtract 1040 from both sides:
[tex] 1040 - 2r - 1040 = r + 80 - 1040 [/tex]
[tex] - 2r = r - 960 [/tex]
Subtract r from both sides
[tex] - 2r - r = r - 960 - r [/tex]
[tex] - 3r = - 960 [/tex]
Divide both sides by -3
[tex] \frac{-3r}{-3} = \frac{-960}{-3} [/tex]
[tex] r = 320 [/tex]
To find m, plug in the value of r into equation 1.
[tex] m = 520 - r [/tex]. =>Equation 1
[tex] m = 520 - 320 [/tex]
[tex] m = 200 [/tex].
Malcom's maximum speed = m = 200 km/h
Ravi's maximum speed = r = 320 km/h
is 1 whole 1 by 3 considered as an integer??
Answer:
No it's not.
Step-by-step explanation:
[tex]1 \frac{1}{3} = \frac{4}{3} = 1.333333[/tex]
Integers are set of numbers consisting
Whole numberNatural numberNegative numbersIt doesn't consist
Fractions &DecimalsHope this helps ;) ❤❤❤
Answer:
[tex]\boxed{\sf No}[/tex]
Step-by-step explanation:
[tex]\displaystyle 1 \frac{1}{3} =1.3333333...[/tex]
Integers are whole numbers that can be positive or negative. Integers do not include fractions and decimals.
Sylvia burns 6 calories per minute when she runs, How many calories does she burn when
she runs for 15 minutes?
The circle shown above has a radius of 5 units, and the central angle of the sector that is shaded is 25π radians. Determine the area of the shaded sector, in terms of π. Enter the area of the sector.
Answer:
The answer is below
Step-by-step explanation:
Given that:
The radius of the circle (r) = 5 units
The central angle (θ) = 25π
A sector of a circle is the portion of a circle made up of two of its radii and an arc. The area of a sector that subtends with a central angle (θ) and a radius (r) is given by the formula:
[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2[/tex]
Substituting the radius of the circle and the central angle:
[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2\\\\Area\ of\ sector=\frac{25\pi}{360} *\pi (5)^2\\\\Area\ of\ sector=\frac{125\pi^2}{72}[/tex]
Type the correct answer in the box. Use numerals instead of words. Use the order of operations to evaluate this expression: 7 + (5 – 9)2 + 3(16 ÷ 8).
By using PEDMAS rule, 7 + (5 – 9)2 + 3(16 ÷ 8) is 5.
What is PEDMAS Rule?PEDMAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, D- Division, M- Multiplication, A- Addition, and S- Subtraction.
Given
7 + (5 – 9)2 + 3(16 ÷ 8)
By using PEDMAS rule,
= 7 + (-4)2 + 3(2)
= 7 + (-8) + 6
= 7 - 8 + 6
= -1 + 6
= 5
By using PEDMAS rule, 7 + (5 – 9)2 + 3(16 ÷ 8) is 5.
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The solution of equation, 7 + (5 – 9)2 + 3(16 ÷ 8) is,
⇒ 29
Since, We knw that,
PEMDAS stands for P- Parentheses, E- Exponents, D- Division, M- Multiplication, A- Addition, and S- Subtraction.
We have to given that,
Expression is,
7 + (5 - 9)² + 3(16 ÷ 8)
Now, Simplify By using PEDMAS rule,
= 7 + (5 - 9)² + 3(16 ÷ 8)
= 7 + (-4)² + 3(2)
= 7 + 16 + 6
= 23 + 6
= 29
Thus, By using PEDMAS rule, 7 + (5 – 9)2 + 3(16 ÷ 8) is, 29
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Given that ΔABC is a right triangle with the right angle at C, which of the following is true?
1. tan A = 1/(tan B)
2. tan A = sin B
3. cos A = 1/(cos B)
4. sin B = 1/(sin A)
Answer:
1. tan A = 1/(tan B)
Step-by-step explanation:
By definition,
tangent A = opposite / adjacent = a / b
and
tangent B = opposite / adjacent = b / a
Therefore tangent A = a/b = 1/tan(B)
Answer: Tan a=tan b
I belive
Step-by-step explanation:
Solve: 3a^2-4b a= -6 b= -5 If you could also leave an explanation that would be great! Thank you for your time!
Answer:
128
Step-by-step explanation:
3a² - 4b
plug in values
3(-6)² - 4(-5)
use PEMDAS and simplify (-6)² first
3(36) -4(-5)
multiply
108 + 20
add
128
hope this helps :)
Fachorise completely
x^2y^2-1
Answer:
[tex](xy+1)(xy-1)[/tex]
Step-by-step explanation:
x²y²-1
=(xy)²-(1)²
=(xy+1)(xy-1)
Your car gets 15 miles per gallon and your friend's car averages 25 mpg. You decide
head off to St. George Island on vacation, 361 miles away. If gas costs $2.79/gallon and you decide to split the
gas costs, how much money will you save by driving your friend's car?
Answer:
the answer is $27.90
Step-by-step explanation:
if you do 15 times 2.79 you will get $41.85
then do 25 times 2.79 and you will get $69.75
then subtract 69.75 from 41.85 and your answer will be $27.90
i hope this helps this is the only way i could find the answer!
$29.4864 money will you save by driving your friend's car.
Given that, your car gets 15 miles per gallon and your friend's car averages 25 mpg.
You decide to go on a road trip to St. George Island, which is 361 miles away.
What are Gallons?A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters exactly.
Gallons needed for your car =361/15=24.06 gallons
Cost of 24.06 gallons of gas=24.06×2.79=$69.774
Gallons needed for friends car =361/25=14.44 gallons
Cost of 4.44 gallons of gas=14.44×2.79=$40.2876
Hence, while driving a friend's car you will save 69.774-40.2876=$29.4864
Therefore, $29.4864 money will you save by driving your friend's car.
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Nina is training for a marathon. She can run 4 1/2 kilometers in 1/3 of an hour. At this pace, how many kilometers can Nina run in 1 hour?
Answer:
Nina can run:
13 1/2 km in 1 hour
Step-by-step explanation:
4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2
proportions:
9/2 hours ⇔ 1/3 hour
N hours ⇔ 1 hour
N = (9/2)*1 / (1/3)
N = (9/2) / (1/3)
N = (9*3) / (2*1)
N = 27/2
27/2 = 26/2 + 1/2 = 13 + 1/2 = 13 1/2
Nina can run:
13 1/2 km/h
13 1/2 km in 1 hour
Nina can run [tex]13\frac{1}{2}[/tex] km in an hour
The distance Nina can run in an hour can be determined by dividing the distance she can run in 1/3 of an hour by 1/3
Distance Nina can run in an hour = distance run ÷ [tex]\frac{1}{3}[/tex]
[tex]4\frac{1}{2}[/tex] ÷ [tex]\frac{1}{3}[/tex]
Convert the mixed fraction to an improper fraction [tex]\frac{9}{2}[/tex] × 3 = [tex]\frac{27}{2}[/tex]
Convert the improper fraction back to an mixed fraction = [tex]13\frac{1}{2}[/tex] km
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15 Points and Brainliest :)
Answer:
Step-by-step explanation:
Hello, please consider the following.
Option A. First week we got $200.
Week 2, we got $200+$50=$250
Week 3, we got $250+$50=$300
Week 4, we got $300+$50=$350
Week 5, we got $350+$50=$400
Week 6, we got $400+$50=$450
[tex]\begin{array}{c |c |c |c |c |c |c|}Week & 1 & 2 & 3 & 4 & 5 & 6\\----&---&---&---&---&---&---\\Amount &200 &250 &300 &350 & 400 &450\end{array}[/tex]
Option B. First week we got $200.
Week 2, we got $200+$200*10%=$200+$20=$220
Week 3, we got $220(1+10%)=$220(1.10)=$242
Week 4, we got $242(1.10)=$266.2
Week 5, we got $266.2(1.10)=$292.82
Week 6, we got $292.82(1.10)=$322.102
[tex]\begin{array}{c |c |c |c |c |c |c|}Week & 1 & 2 & 3 & 4 & 5 & 6\\----&---&---&---&---&---&---\\Amount &200 &220 &242 &266.2 & 292.82 &322.102\end{array}[/tex]
Thank you.
Ernesto solves the equation below by first squaring both sides of the equation. \sqrt{\dfrac{1}{2}w+8}=-2 2 1 w+8 =−2square root of, start fraction, 1, divided by, 2, end fraction, w, plus, 8, end square root, equals, minus, 2 What extraneous solution does Ernesto obtain?
Answer:
w = -8Step-by-step explanation:
Given the equation solved by Ernesto expressed as [tex]\sqrt{\dfrac{1}{2}w+8}=-2[/tex], the extraneous solution obtained by Ernesto is shown below;
[tex]\sqrt{\dfrac{1}{2}w+8}=-2\\\\square\ both \ sides \ of \ the \ equation\\(\sqrt{\dfrac{1}{2}w+8})^2=(-2)^2\\\\\dfrac{1}{2}w+8 = 4\\\\Subtract \ 8 \ from \ both \ sides\\\\\dfrac{1}{2}w+8 - 8= 4- 8\\\\\dfrac{1}{2}w= -4\\\\multiply \ both \ sides \ by \ 2\\\\\dfrac{1}{2}w*2= -4*2\\\\w = -8[/tex]
Hence, the extraneous solution that Ernesto obtained is w = -8
What is 4,331,507 expressed in scientific notation? A. 4.331507 x 10 B. 4.331507 x 10 C. 4.331507 x 10 D. 4.331507 x 10
Answer:
4.331507 x 10⁶
Step-by-step explanation:
you move the decimal place 6 times to the right, so 10⁶
Answer:
Step-by-step explanation:
4,331,507=4.331507×10^6
if a is an even natural number such that a|208 and (a,b)=1, then find the value of b
this is gauss theroeam
Answer:
b=13
Step-by-step explanation:
2|208
2|104
2|52
2|26
|13
208=2^4×13=16×13
now (16,13)=1
as a is an even number so a=16
b=13
∵g.c.d of 16 and 13=1
or (16,13)=1
The diagram below is divided into equal parts. Which ratio correctly compares the number of shaded sections to the total number of sections? A diagram is divided into 4 shaded parts and 4 white parts. One-half 4 to 4 2:1 StartFraction 8 Over 4 EndFraction
Answer: 1/2 is correct.
Step-by-step explanation:
There are 8 total parts, and 4 of them are shaded. 4 is half of 8, therefore, your answer is 1/2.
Hope this helps!
Answer:
The answer is A
Step-by-step explanation:
because there are 4 shaded parts and 8 parts in total.
4/8=1/2
It's A
Write an absolute value equation to satisfy the given solution set shown on a number line.
Answer:
Step-by-step explanation:
|x-a|≤b
-b≤x-a≤b
add a
a-b≤x≤a+b
put a-b=-8
a+b=-4
add
2a=-12
a=-12/2=-6
-6+b=-4
b=-4+6=2
so |x+6|≤2
Given TS¯¯¯¯¯¯¯ and TU¯¯¯¯¯¯¯ are midsegments, PR=18.2, TS=6.5. Find QU . A. 9.1 B. 3.25 C. 13 D. 6.5
Answer:
The correct option is;
D. 6,5
Step-by-step explanation:
TS and TU are midsegments
Segment PR = 18.2
Segment TS = 6.5
Given that TS is the midsegment of PR and PQ, therefore, TS = 1/2×QR
Which gives;
Segment QR = 2×TS = 2 × 6.5 = 13
Segment QR = 13
Given that TU is a midsegment to PQ and QR, we have that QU = UR
Segment QR = QU + UR (segment addition postulate)
Therefore, QR = QU + QU (substitute property of equality)
Which gives;
QR = 2×QU
13 = 2×QU
Segment QU = 13/2 = 6.5
The length of segment QU is 6.5.
