Mrs. Katz is planning to create a flower
garden in the shape of a trapezoid.
She started by creating a blueprint.
What is the value of x?
Answers
The value of x can be found by using the formula for the area of a trapezoid. The value of [tex]$x$[/tex] is [tex]$4$[/tex] inches.
What is area?Area is a two-dimensional measurement that is used to measure the size of a shape or surface. It is measured in square units, such as square centimeters, square meters, square kilometers, and so on. The formula for the area of a trapezoid is: [tex](a+b)/2 *h[/tex], where a and b are the lengths of the parallel sides, and h is the height. Mrs. Katz needs to calculate the value of x by plugging in the lengths of the parallel sides and the height into the formula.
We know that the opposite sides of a trapezoid are parallel, so we have [tex]AB \parallel DC.[/tex]
Using the given information, we can set up an equation in terms of [tex]$x$[/tex] and solve for it. We know that the height of the trapezoid is [tex]$8$[/tex] inches, and we know that the bases are [tex]$x$[/tex] inches and [tex]$16$[/tex] inches.
Using the formula for the area of a trapezoid, we have:
[tex]\text{Area} = \frac{1}{2}(AB+DC)(\text{height})[/tex]
Plugging in the values we know, we get:
[tex]\text{Area} = \frac{1}{2}(x+16)(8)[/tex]
We are also given that the area of the trapezoid is [tex]$100$[/tex] square inches, so we can set up an equation:
[tex]100 = \frac{1}{2}(x+16)(8)[/tex]
Simplifying and solving for [tex]$x$[/tex], we get:
[tex]100 &= \frac{1}{2}(x+16)(8)\20 &= (x+16)\x &= 4[/tex]
Therefore, the value of [tex]$x$[/tex] is [tex]$4$[/tex] inches.
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Related Questions
The angles in a triangle are in the ratio 1:2:3.
a) Show that the triangle is a right-angled triangle.
Answers
Answer:
Step-by-step explanation:
Remark
The angles can measure
x + 2x + 3x
The total must be 180 degrees because all triangles have 180 degrees
Equation
x + 2x + 3x = 180 Combine
6x = 180 Divide by 6
6x/6 = 180/6
x = 30
1x = 30
2x = 60
3x = 3*30 = 90
A right angle triangle has 90 degrees.
If x = 8 and y = -3, evaluate the following expression: 20 - 5y + 2x
Answers
Answer:
51
Step-by-step explanation:
Given the following question:
[tex]20-5y+2x[/tex]
[tex]x=8[/tex]
[tex]y=-3[/tex]
Substitute and solve using PEMDAS:
[tex]20-5y+2x[/tex]
[tex]20-5(-3)+2(8)[/tex]
[tex]5\times-3=-15[/tex]
[tex]20--15+2(8)[/tex]
[tex]2\times8=16[/tex]
[tex]20-(-15)+16[/tex]
[tex]20--15=35[/tex]
[tex]35+16=51[/tex]
[tex]=51[/tex]
Your answer is "51."
Hope this helps.
Josephine is constructing a circle circumscribed about triangle XYZ. She uses the following sequence of steps to construct the circle.
1. She constructs the perpendicular bisectors of two sides.
2. She finds their point of intersection, P.
3. She uses a compass, with the fixed end on X, to draw a circle passing through point P.
Did Josephine make any errors while constructing the circle?
OA. Yes, she should have placed the compass with the fixed end on P and drawn a circle through point x.
OB. No, she did not make any errors.
OC.
Yes, she should have constructed the angle bisectors.
ज
OD.
Yes, she should have found the perpendicular bisectors of all 3 sides.
Answers
Answer:
A
Step-by-step explanation:
there is not much more to say.
the point where actually all 3 line bisectors intersect, is also called the "circumcenter". I guess you understand what that means : it is the center of the circle circumscribing the whole triangle (passing through all 3 corners/vertices).
once you find that point with 2 line bisectors, there is no need to construct the third - it WILL intersect the others at the same point.
Answer:
A
Step-by-step explanation:
A parabola can be drawn given a focus of (0, –9) and a directrix of
y=-5. What can be said about the parabola?
Answers
Answer:
Step-by-step explanation:
x2+(y-9)2=(y-5)2distance from point on curve to focus [squared]
Find the area of trapezoid ABCD by decomposing it into a rectangle and triangle.
A)80 cm^2
B)96 cm^2
C)104 cm^2
D)112 cm^2
Answers
Area of right triangle: 1/2 x 6 x 8 =24
Area of rectangle: 8 x 10 = 80
Add both areas get = 104cm
Answer:
c) 104
Step-by-step explanation:
e
Which describes the horizontal cross section of
the given right rectangular prism?
A. A rectangle with dimensions of 15 inches and 16
inches.
B. A rectangle with dimensions of 15 inches and 7
inches.
C. A rectangle with dimensions of 9 inches and 15
inches.
D. A rectangle with dimensions of 9 inches and 7
inches.
Answers
The horizontal cross section of a rectangular prism would have the same shape and size as the rectangular base.
What is a prism?A prism is a three dimensional shape with two parallel bases of the same shape and the other faces which are quadrilateral.
A rectangular prism has the shape of a cuboid. The horizontal cross section of a rectangular prism would have the same shape and size as the rectangular base.
Find out more on prism at: https://brainly.com/question/23963432
A deck of cards have suits spade, diamonds, clubs, and hearts. There are 13 of each suit Ace, 2,3,4,5,6,7,8,9,10, jack, queen, and king. What is the probabililty of choosing a King from a standard deck?
Answers
Answer:
1 out of 13
Step-by-step explanation:
A box contains 5 red, 3 white, and 2 blue marbles. A sample of six marbles is drawn with replacement; that is, each marble is replaced before the next marble is drawn. Find the probability that: (a) 3 are red, 2 are white, 1 is blue, (b) 2 are red, 3 are white, 1 is blue, (e) 2 of each color appear
Answers
Answer:
i dont know but i'll try
Step-by-step explanation:
10-6=4
2 each color
i think because if you divide 4 divided by 2 is 2.
SO i thought wait oh no dont copy this rate it as bad as you want but im just a ---- grader
Please help if you can!!
Answers
Answer:
47x+10
Step-by-step explanation:
I am trying Find the surface area of a prism or cube and it only has 3.5
Answers
Therefore, (3.5)^2 * 6 =
73.5 [whatever units]^2
if danielle still drove 24 miles on the eight day how many miles would tim need to drive to make the median amount of miles that tim and danielle drove the same?
Answers
Answer:
the answer would be she would drive 192 miles
please help find the point of intersection (ordered pair)
x + 2y=3
2x - 4y = -20
Answers
Answer:
Check out Tiger algebra
it gave me
Slope=-2.000/2.000=-1.000
x - intercept = 3/1 = 3.00000
y - intercept = 3/2 = 1.50000
and
Slope=1.000/2.000=0.500
x - intercept = 10/1 = 10.00000
y - intercept = 10/2 = 5
It requires nothing.
I just need help with this pls
Answers
Answer:
Option D
Step-by-step explanation:
Hello!
Recall the quadratic equation: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Remember that a quadratic equation is written in the form [tex]ax^2 + bx + c\\[/tex]
So:
a = 2b = 5c = -1Plug the values in and solve:
[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-5\pm\sqrt{5^2 - 4(2)(-1)}}{2(2)}$\\\\x = $\frac{-5\pm\sqrt{25 +8}}{2(2)}$\\\\x = $\frac{-5\pm\sqrt{33}}{4}[/tex]
This would be [tex]\boxed{\text{Option D}}[/tex]
Three sisters, whose average age is 10, all have different ages. When they get together in pairs, the average ages of two such pairs are 11 and 12. What is the age of the eldest sister?
Answers
The age of the eldest sister is 16 years.
What is an equation?An equation is used to show the relationship between two or more variables and numbers.
Let x represent the age of the older sister and y, z represent the other sisters ages.
Three sisters, whose average age is 10, all have different ages. Hence:
(x + y + z)/3 = 10 (1)
Also, When they get together in pairs, the average ages of two such pairs are 11 and 12, hence:
(x + y)/2 = 11 (2)
(x + z)/2 = 12 (3)
From equation 1, 2 and 3:
x = 16, y = 6, z = 8
The age of the eldest sister is 16 years.
Find out more on equation at: https://brainly.com/question/18176080
Solve the following:
(i)20 ÷7
(ii) 22÷7
Answers
Answer: i) 2.85714285714, ii) 3.14285714286
Step-by-step explanation:
i) 20/7 = 2.85714285714
ii) 22/7 : This is an approximation for pi. it comes to: 3.14285714286
Which expression shows a sum of five terms? (3 points)
5(x + 5)
5x
x5
5 + x + 5 + x + x
5.
Answers
Answer:
5 + x + 5 + x + x
Step-by-step explanation:
We are given 4 expressions and we have to determine which expressions shows a sum of five terms.
We use the process of elimination:
5(x + 5)
=5x+25 (distributing 5)
This contains sum of only two terms, eliminate.
5x
It contains only 1 term, eliminate.
5 + x + 5 + x + x
It contains 5 terms 5,x,5,x and x, KEEP!
5.
Only contains 1 term, eliminate.
With this said, were left with:
5 + x + 5 + x + x
Which is the correct answer! :)
What is the value of m in the equation {m-in
-n = 16, whеn n = 8?
o20
032
оооо
44
48
Answers
Answer:
m = 24
Step-by-step explanation:
if i'm wrong sorry not that good with math
[tex]\frac{x^{2} -1}{16x} X \frac{4x^{2} }{5x + 5}[/tex]
Answers
Answer:
x^2-x / 20
Step-by-step explanation:
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{x^{2} -1}{16x} \times \frac{4x^{2} }{5x + 5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{\cancel{(x+1)}(x-1)}{16x} \times \frac{4x^{2} }{5\cancel{(x + 1)}} \quad\quad(a^2-b^2 = (a+b)(a-b))\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{x-1}{\cancel{16x}} \times \frac{\cancel4x^{\cancel2} }{5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{(x -1)(x)}{4\times 5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{x^2-x}{20} \\\end{gathered} [/tex]
More Identities:-[tex]\begin{gathered}\boxed{\sf{ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf{ {(a - b)}^{2} = {a}^{2} + {b}^{2} -2ab \: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf{ {x}^{2} - {y}^{2} = (x + y)(x - y) \: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf {(a + b)² = (a - b)² + 4ab\: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf {(a - b)² = (a + b)² - 4ab\: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf {(a + b)² + (a - b)² = 2(a² + b²)\: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf{ (a + b)³ = a³ + b³ + 3ab(a + b)\: }} \\ \end{gathered}[/tex]
[tex]\begin{gathered}\boxed{\sf {(a - b)³ = a³ - b³ - 3ab(a - b)\: }} \\ \end{gathered}[/tex]
PLEASE HELP ASAP
What is 7/8 expressed as a percent? Enter your answer as a decimal in the box.
Answers
Answer:
87.5
Step-by-step explanation:
Please help with this question (I will mark brainliest) Thank u >u<
A turtle population that started at 368 has begun to decrease by 7 percent each month. Which equation below could be used to model this situation?
Answers
Answer:
Im Not 100% but, I will give you the best answer.
I think it might be Option 3
If not, (give me 1 star)
I tried
Step-by-step explanation:
6. If the mean of A and B is 20, the mean of B and C is 24 and the mean of A, B and C is 18. What is the mean of A and c?
Answers
Answer:
10
Step-by-step explanation
[tex]\frac{a+b}{2}=20\\\frac{b+c}{2}=24\\ \frac{a+b+c}3}=18\\[/tex]
20x2 = 40 -> a+b=40
24x2 = 48 -> b+c=48
18x3 = 54 -> a+b+c=54
solve the equations...
a=6
b=34
c=14
a+c/2 = 6+14/2 = 10
Which number is not in scientific notation? (1 point)
0.2 • 10^3
3 • 10^28
1.03 • 10^–2
1.5 • 10^–6
Answers
Answer:
Hi I'm always here to help!!!
_______________________
Ah welp that was wrong it was A
Sorry that I was wrong
_______________________
Have a great day!!!!
Answer:
Your answer would be:
A.) 0.2 x 10^3
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS
Answers
Answer:
b
Step-by-step explanation:
Answer:
(-1, -1)
explanation:
The value of y will be negative and x value shall be same.
Here the original coordinates of A: (-1, 1)
So new coordinates: (-1, (-)1) = (-1, - 1)need help on this graph
Answers
The length and the breadth of a rectangle are 40 m and 30 m respectively. If its perimeter = perimeter of a square. Find the side of the square
Answers
Answer:
above is the solution to the question
Calculate the simple interest earned as a amount R1400 at an annual interest rate 6.5% over 3 years?
Answers
Answer:
principle (p)=Rs1400
Rate(R)=6.5
time(T)=3
we know that
I=P×I×T/100
=1400×6.5×3/100
=273
therefore the simple interest earned is Rs273
Judy and Amna are on a safari. They are standing 20 feet apart when they spot a snake. Judy and Amna run in opposite directions at speeds of 180 feet per minute and 120 feet per minute, respectively. In how many minutes will they be 2420 ft apart?
Answers
The solution is in the pic
Using proportions, it is found that Judy and Amna will be 2420 ft apart after 8 minutes.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
They run in opposite directions, at speeds of 180 feet per minute and 120 feet per minute, respectively, hence each minute they get 180 + 120 = 300 feet apart.
They already are 20 feet apart, so they will need to get more 2420 - 20 = 2400 ft apart. Hence:
1 minute - 300 ft apart.
x minutes - 2400 ft apart.
Applying cross multiplication:
300x = 2400
x = 8.
Judy and Amna will be 2420 ft apart after 8 minutes.
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Worth 10 points please help me
Answers
Answer:
x = 100°
Step-by-step explanation:
40 + 40, the bottom two angles, = 80. a triangle has 180 degrees in total. 180 - 80 = 100. the missing angle of the bottom triangle is 100. since the bottom 100 is a vertical angle to the x, x must equal 100 degrees
Yolanda is driving on a highway. She uses one gallon of gas every 20 miles she drives. The distance, D (in miles), she travels on g gallons of gas is given by the
following
D=20g
How far does Yolanda drive if she uses 5 gallons of gas?
Answers
Answer:
1g=20d so 5g=100d
Step-by-step explanation:
If it is 20 MPG, then, to find it for 5 gallons of gas, we have to multiply 20 by it. So, we have to do - 20x5
20x5=100
So hence, Yolanda drives 100 miles on the highway using 5 gallons of gas.
Thanks!
Alex simplified the expression 7+(3x 1.4)+5+2+(5x 14) to find the area of the figure on the grid.
What error did Alex make?
O He found the perimeter of the figure instead of the area.
O He added the lengths of the lines creating the indentation instead of subtracting them.
O He used 5x1.4 and 3x 1.4 as the length of each diagonal line instead of 5 and 3.
O He added the five lengths together instead of multiplying them.
Answers
The error Alex made is that he found the perimeter of the figure instead of the area.
Area and perimeter of shapesGiven the expressions
7+(3x 1.4)+5+2+(5x 14)
He used the expression to simplify the grid
The expression simplified shows that Alex added all the measures of the sides of the grid instead of taking the product of the length and width
Note that the operation Alex performed is the perimeter of the figure instead of the area hence the error Alex made is that he found the perimeter of the figure instead of the area.
Learn more on area and perimeter of figure here: https://brainly.com/question/443376
Answer:
A - He found the perimeter of the figure instead of the area.
Step-by-step explanation: