Answers
Answer:
x = 9, GH = 21, CD = 17
Step-by-step explanation:
Quadrilateral CDEF is a trapezoid in which G and H are mid points of the sides CF and DE respectively.
In a trapezoid, segment joining the mid points is equal to the half of the sum of the parallel sides.
[tex] \therefore \: GH = \frac{1}{2} (CD + FE) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x - 1 + 25) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x + 24) \\ \\ \therefore \:3x - 6 =\frac{1}{2} \times 2 (x + 12) \\ \\ \therefore \:3x - 6 = x + 12 \\ \\ \therefore \:3x - x = 12 + 6 \\ \\ \therefore \:2x = 18 \\ \\ \therefore \:x = \frac{18}{2} \\ \\ \huge\red{ \boxed{\therefore \:x = 9}} \\\\ \because \overline{GH} = 3x - 6 \\ \\\therefore \:\overline{GH} =3 \times 9 - 6 \\ \\ \therefore \:\overline{GH} =27 - 6 \\ \\ \huge\purple{ \boxed{\therefore \:\overline{GH} =21}} \\ \\ \because\overline{CD} = 2x - 1 \\\\ \therefore \:\overline{CD} =2 \times 9 - 1 \\ \\ \therefore \:\overline{CD} =18 - 1 \\ \\ \huge\pink{ \boxed{\therefore \:\overline{CD} =17}} \\ \\ [/tex]
Related Questions
Evaluate
1/3 ÷ 2/5 =
Give your answer as a fraction in its simplest form.
Answers
Answer:
5/6
Step-by-step explanation:
Since 1/3÷2/5 can also be written as 1/3/2/5
So the ÷ can then be converted to × and 2/5 will change to 5/2
So let's solve
1/3×5/2
5/6
Since there is no common number that can divide the two
So the final answer is 5/6
Answer:
5/6
Step-by-step explanation:
1/3 divided by 2/5 is 2 1/2
this is because when you do this you use KCF
Keep Change Flip
you keep 1/3
change the sign to times
and flip the last fraction around to 5/2
*
(3) Sing Lu jogs around a park near her house 3 times a week. The
distance around the park is 0.8 mile. How many laps around the
park are necessary to run 6 miles?
**
*
Answers
Answer:
7.5 laps.
6 ÷ 0.8 = 7.5
I might be wrong.
Write two numbers that are opposites and each more than 6 units away from 0.
Answers
Answer:
6 and - 6
Step-by-step explanation:
Two numbers that are opposites and each more than 6 units away from 0 is (8, -8).
What is coordinate plane?A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
Given that, two numbers that are opposites and each more than 6 units away from 0.
Opposites are basically two numbers that are at different sides of the number line. For example, -2 and 2 are opposites because they are the same distance away from 0 on a number line making them opposites. To make an opposite just take a positive number, and then add a negative to it (8, -8).
Therefore, two numbers that are opposites and each more than 6 units away from 0 is (8, -8).
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20 POINTS, PLS HELP!!! BOGO (buy one, get one free) is an example of _____.
(Select all that apply.)
a sale
an incentive
a discount
income
Answers
I hope this helped! Mark me Brainliest! :) -Raven❤️
A line passes through the points (-3, -10) and (0, -5). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
Y = mx + b
Step-by-step explanation:
Vanessa is a caterer. she made several batches of appetizers last weekend for an event. this weekend, vanessa made 4 times as many batches. she made a total of 25 batches of appetizers for the two weekends. determine the number of batches vanessa made last weekend and the number of batches she made this weekend. let b= the number of batches of appetizers vanessa made last weekend.
Answers
Answer:
100 x 13/16 x 25b =4
18 3/4 = 25b/4
b=25/4
b= 6.25
Step-by-step explanation:
25/4 = 6 1/4 last weekend and 18 3/4 this weekend.
What is the range of h(x)?
Answers
Answer:
multiply
Step-by-step explanation:
In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=54°, and RS = 26 feet. Find the length of QR to the nearest tenth of a foot.
Answers
You may use the law of sines, that states that in every triangle the ratio between a side and the sine of the opposite angle is constant.
So, in your case, we have
[tex]\dfrac{QR}{\sin(\hat{S})}=\dfrac{RS}{\sin(\hat{Q})}[/tex]
We know that [tex]\hat{S}[/tex] is 90 degrees, so its sine is 1. Also, we know that RS=26. So, the equation becomes
[tex]QR=\dfrac{26}{\sin(54)}[/tex]
Answer:
32.1 FT
Step-by-step explanation:
the sum of the digits 2014 is 7. How many whole numbers between 100 and 999 have 9 as the sum of their digits?
Answers
Answer:
45
Step-by-step explanation:
this should be correct :)
There are 9 in the 100's
108
117
126
135
144
153
162
171
180
There are 8 in the 200's (starting to see a pattern?)
207
216
225
234
243
252
261
270
There are 7 in the 300's
306
315
324
333
342
351
360
9+8+7+6+5+4+3+2+1 = 45
To find the number of whole numbers between 100 and 999 with a sum of 9 as their digits, we can use combinations. By selecting the digits using the given steps, we find that there are 50 such numbers.
Explanation:To find how many whole numbers between 100 and 999 have 9 as the sum of their digits, we can use the concept of combinations. We can select 3 digits (from 0 to 9) to form a number, and there are 10 choices for each digit. However, we need to consider the constraint that the sum of the digits should be 9. So, we can select the digits such that the first digit and second digit will have a sum of 9, and the third digit will also be 9. This can be done in the following steps:
Select a number from 0 to 9 for the first digit.Select a number from 0 to the remaining digits to get a sum of 9 (e.g., if the first digit is 5, then we can choose the second digit from 0 to 4).The third digit should always be 9 to satisfy the condition.Applying these steps, we have 10 choices for the first digit, 5 choices for the second digit (since the second digit cannot be greater than the first digit to achieve a sum of 9), and only 1 choice for the third digit. Therefore, the total number of whole numbers between 100 and 999 with a sum of 9 as their digits is 10 * 5 * 1 = 50.
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Jen uses 8.6 gallons of gasoline to drive 164.7 miles. Which is the best estimate for thenumber of miles per gallon of gasoline her vehicle gets?
A. 10 miles per gallon
B. 16 miles per gallon
C. 20 miles per gallon
D. 30 miles per gallon
Answers
Answer:
C
Step-by-step explanation:
164.7/8.6 = 19.15
about 20 miles per gallon
The best estimate of the rate of fuel consumption is C, 20 mi/gal
Which is the best estimate for thenumber of miles per gallon of gasoline her vehicle gets?To estimate the rate between miles and gallons, we just need to take the quotient between the given distance and the volume of gasoline consumed. Then we will get the rate:
R = 164.7mi/8.6 gal
R = 19.4 mi/gal
The closest value is the one at option C, which is 20 miles per galon.
Learn more about rates at:
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Which function is a translation of the parent absolute value function?
f(x) = 2lx|
f(x) = lX+6l
f(x) = |x|
f(x) = -4lxl
Answers
Answer:
Answer is B on Edge 2021
Step-by-step explanation:
need math help asap:)
Answers
Answer:
12
Step-by-step explanation:
8/6 = 1.333333333
That is the scale factor
then you mulitply by 9
9*1.3333333333=12
plz mark brainliest
what is the distance between (0,-1), (5,1)
Answers
Answer:
square root of 29 or approximately 5.38
Which shows the image of quadrilateral ABCD after the transformation R0 90?
Answers
Answer:
second picture
Step-by-step explanation:
The rule to rotate a point counterclockwise about the origin is:
Or in words, we switch the coordinates of the point and change the sign of the y-coordinate.
We know from the first picture that the coordinates of our quadrilateral ABCD are A = (-1, 0), B = (0, -1), C = (-2, -3), and D = (-3 , -2), so let's apply the rotation rule to each one of those points:
Now we know that the coordinates of the quadrilateral after a rotation of 90° are A' = (0, 1), B' = (1, 0), C' = (3, -2), and D' = (2, -3), which corresponds to the second picture
Answer:
b.
Step-by-step explanation:
You are looking at two area rugs for your bedroom. One is a square with a side length of 6.3 feet. The other is a rectangle that is 4.8 feet by 8.2 feet. Which rug will cover the greater area? How much more area will it cover? Justify your response with mathematics.
Answers
Answer:
The square rug. The area of the rug is 39.69 ft² and is 0.33 ft² bigger than the rectangle rug.
Step-by-step explanation:
The find the area of a square, you multiply the length or the width (they all have the same length in a square) by the width (or the length), which would be the same exact number. So in that case—
The square has a side length of 6.3. To find the area of the square, we simply multiply 6.3 · 6.3 =39.69.
So, the area of the square is 30.69 ft²
————————————————————————————————————————
To find the area of a rectangle, you have to multiply the width by the length. (Or vise versa) This is showed by the following formula.
L·W=A
Where L=length, W=width, and A=area.
If the length is 8.2 and the width is 4.8, we can do the multiplicant equation that follows.
8.2·4.8= 39.36 ft².
Now that we have the area of both figures, we can compare them.
The square rug— 39.69
The rectangular rug— 39.36
Of we subtract the areas
39.69 and 39.36, we get the answer that the square rug is bigger by 0.33 ft².
MATH!!! I HAVE NO IDEA HOW TO DO THIS PLEASE SHOW ME THE WORK I WANNA KNOW HOW TO DO THIS FOR THE NEXT QUESTION!!!!
Answers
PLEASE MARK BRAINLIEST!
Answer:
Sorry I'm late!
Step-by-step explanation:
Formula ⇒ [tex]A = \frac{1}{2}bh[/tex]
[tex]A = \frac{1}{2}bh[/tex]
[tex]A = \frac{1}{2}(5)(7)[/tex]
[tex]A = \frac{1}{2}(35)[/tex]
[tex]A = 17.5[/tex]
The Area of the face of the triangle is 17.5 in²I hope this helps!
- sincerelynini
Simplify the expression to a single numerical value. 3x2^3 x 2x3^2.
A.144
B.432
C.900
D.5,184
Answers
Answer:
The answer is B.432
Step-by-step explanation:
When you use a calculator but i used a app and simplified the question
URGENT DUE TODAY!!! PLEASE HELP!!! i will give brainliest
Answers
Answer:
180 centimeters
Step-by-step explanation:
First, you have to make these into 2 different shapes. Two different prisms. You can see all the dimensions on the right shape, but not the left. How do you know the width? Well, since the width is the same for the WHOLE figure, the width for both shapes is the same. To find the volume of a rectangular prism, you need to multiply the length, width, and height.
Length * height * width
Shape 1: [tex]8 * 3 * 5 = 120[/tex] cm
Shape 2: [tex]2*6*5=60[/tex] cm
Then, you add the volumes of the 2 shapes to get the final volume.
120 + 60 = 180 cm
Create a table of values for the equation Y= 2/7x + 3
Answers
here this is the answer
In the triangle, x = 3. Find y.
Answers
Answer:
y = 3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Assuming what you're talking about is a right triangle and the two sides are x, y= [tex]\sqrt{18} = \sqrt{9(2)} =\sqrt{9}[/tex] x [tex]\sqrt{2} = \sqrt[3]{2}[/tex]
The length of a rectangular block is 20 inches. Its width is half its length.
Its height is half its width. What is the surface area of the block?
Answers
Answer:
width is 10 and the height is 5
Step-by-step explanation:
when divide 20 by 2 it gives you 10 and if you divide 10 by 2 it gives you 5 hope i helped
write (2y)^3 without exponents
Answers
EXPLANATION:
because if it is to the third power it is multiplied three times. If it is (5c)^3 it would be 5c•5c•5c
David swan, biked, and ran in the Camp Race. She biked twice as long as she ran, and swam 15 minutes more than she ran. Her total time for all parts of the race was 1 hour and 35 minutes. How many minutes did David spend on each part of the race?
Answers
Answer:
She biked 40 minutes.She ran 20 minutes.She swam 35 min.
Step-by-step explanation:
since you have 95 minutes for all parts first subtracted 15 from what she swam the you have four equal parts left the time she ram then twice she ran she biked and then the she swam 15 minutes More that she ran so you dived 95-15 which is 80 80/4 is 20 so she ran 20 min so 20 x 2 is 40 for she bike 40 then 20+15 is 35 so 40+20+35=95 an hour an 35 minutes
A 270-mile highway has a toll booth at the beginning, a toll booth every 45 miles, and then a final toll booth at the end. A
passenger vehicle must pay a $2.75 toll each time that it passes by a toll booth. There are no additional tolls when exiting
the highway.
Josh entered the turnpike at its beginning and exited after driving 120 miles. How much in toll fees did Josh have to pay?
Answers
Answer:
$8.25
Step-by-step explanation:
270 sectioned out by 45s is 7 toll booths on the highway. That means theres a toll booth at 0 mi, 45, 90, 135, 180, 225 and 270 mi. If Josh exits after 120 mi, he only hits the booth at the beginning and then the last one at 90 mi because he doesn't reach the next one at 135 mi. $2.75 per toll booth and if he passed 3, then 2.75 x 3 = $8.25.
This should be correct, hope it helps. :)
A square rug has an inner square in the center. The side length of the inner square is x inches and the width of the outer region is 4 in. What is the area of the outer part of the rug?
Answers
To find the area of the outer part of the square rug, calculate the total area using the length of the entire square (x + 8)² and subtract the area of the inner square (x²), yielding (x + 8)² - x² square inches.
Explanation:The subject of this question is geometry - specifically area calculations in mathematics. The student is asking for the area of an outer part of a square rug. The main rug is comprised of a square within another square, with the side length of the smaller square being x inches and the distance in between the small and large square (representing the outer region) being 4 inches.
To calculate the area of the outer region, first, we need to calculate the side length of the outer (entire) square. This would be x + 2*4 = x + 8 inches (4 inches from each side). The total area of the rug would be squared side length of the outer square, which is (x + 8)² square inches.
Subsequently, the area of the inner part of the rug can be calculated as x² square inches (since it's a square). Therefore, the area of the outer part of the rug would be obtained by subtracting the area of the inner square from the total area of the rug, yielding: (x + 8)² - x² square inches.
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To find the area of the outer part of the rug, we first need to find the area of the entire rug and then subtract the area of the inner square.
Let s be the side length of the outer square.
The area of the entire rug is the area of the outer square:
Area of outer square = [tex]s^2[/tex]
Since the width of the outer region is 4 inches, we know that the side length of the outer square is [tex]\( s = x + (2 \times 4) = x + 8 \).[/tex]
So, the area of the outer square is:
Area of outer square = [tex](x + 8)^2[/tex]
Now, let's find the area of the inner square:
Area of inner square = [tex]x^2[/tex]
The area of the outer part of the rug is the difference between the area of the outer square and the area of the inner square:
Area of outer part = Area of outer square - Area of inner square
[tex]\[ = (x + 8)^2 - x^2 \][/tex]
Now, let's expand and simplify:
[tex]\[ = x^2 + 16x + 64 - x^2 \][/tex]
= 16x + 64
So, the area of the outer part of the rug is 16x + 64 square inches.
God bless whoever soul that answers this
Answers
Answer:
Step-by-step explanation:
Write the series in expanded form.
Š (n − 3)(n+ 2)
7
=0
-6-6-2+0
-6-6-4 +0
-6-4-4-2
6- 4 – 4 +0
Answers
Answer:
It's B
Step-by-step explanation:
Just took this
Answer: B
Step-by-step explanation:
What is the Circumference of this circle? Hint: Use the formula A = 2 x pi x r. *
A. 31.4 ft
B. 10 ft
C. 78.5 ft
D. 17.7 ft
Answers
What is 8/10 x 1/2= ??
Answers
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Step 1: Multiply
[tex]\frac{8}{10} * \frac{1}{2}[/tex]
[tex]\frac{8*1}{10*2}[/tex]
[tex]\frac{8}{20}[/tex]
[tex]\frac{8/4}{20/4}[/tex]
[tex]\frac{2}{5}[/tex]
Answer: [tex]\frac{2}{5}[/tex]
Answer:
[tex]\frac{4}{10}[/tex]
Step-by-step explanation:
[tex]\frac{8}{10}[/tex] x [tex]\frac{1}{2}=\frac{4}{10}[/tex]
[tex]\frac{8(1)}{10(2)}=\frac{4}{10}[/tex]
[tex](0.8)0.5=0.4[/tex]
One half of 0.8 is 0.4.
What is the range for this set of data?
7, 15, 12
Answers
Answer:
8.
Step-by-step explanation:
To find the range, take your largest number and subtract it to
your smallest number. 15-7 is 8. Therefore, your range is 8.
Answer:
8 is the range
Step-by-step explanation:
Step 1: Find the range
To find the range, subtract the lowest number from the highest number.
Example: 5, 9, 15
What is the highest number → 15
What is the lowest number → 5
What is the range 15 - 5 = 10 is the range
Problem: 7, 15, 12
What is the highest number → 15
What is the lowest number → 7
What is the range 15 - 7 = 8 is the range
Answer: 8 is the range