FIGURE ABCD BELOW IS A QUADRILATERAL. WHAT IS THE VALUE OF X ?
A. 15
B. 40
C. 45
D. 65
Answers
Answer:
x = 45
Step-by-step explanation:
Note that:
The sum of the interior angles of a quadrilateral is 360°.
Angle: ADC+BAD+ABC+BCD = 360°
Thus, Substitute ∠ABC = 3x, ∠BAD = (2x-5) , ∠ ADC = (x+15), ∠ BCD = 80 turn into ADC+BAD+ABC+BCD = 360° :
Also known as :
(x+15) +(2x-5) + 3x+80=360
Solving for x
Add the numbers
x + 90+2x+3x=360
Combine like terms
6x + 90=360
subtract 90 from both sides
6x = 270
x = 45
Hence the value of x = 45
Kavinsky
Answer:
C. 45
Step-by-step explanation:
1) Sum of the interior angles of any shape:
(n - 2) x 180, where n is the number of vertices of a shape. In this case, we have 4 vertices.
= (4 - 2) x 180
= 2 x 180
= 360°
2) Add all the given values equating to 360.
2x - 5 + 3x + 80 + x + 15 = 360
6x + 90 = 360
6x = 360 - 90
6x = 270
x = 270/6
x = 45
Related Questions
=
15. Given a rectangle ABCD with AD 12. The diagonals AC and BD intersect at point O such that
mZDOC = 30°. Find the area of the rectangle.
Answers
Answer:
To find the area, we need to find the side length AB (and DC).
The easiest way to approach this is to draw a sketch with all the given information (see attached).
As point O is the center point of the rectangle, we can draw a horizontal line from point O to the center point of BC (point M on the diagram) and create a right triangle. We can then use the Sine rule to find the shortest leg of the triangle (marked as x on the diagram). This will be half of the side length AB, and so to find the side length, simply multiply it by 2.
To find the missing angles of the right triangle:
m∠COM = (180° - 30°) ÷ 2 = 75°
m∠OCM = 180° - 90° - m∠COM = 90° - 75° = 15°
Sine rule
[tex]\sf \dfrac{a}{sinA}=\dfrac{b}{sinB}=\dfrac{c}{sinB}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \dfrac{x}{\sin(15)}=\dfrac{6}{\sin(75)}[/tex]
[tex]\implies x=\sin(15)\cdot \dfrac{6}{\sin(75)}[/tex]
[tex]\implies x=12-6\sqrt{3}[/tex]
As AB = [tex]2x[/tex]
[tex]\begin{aligned} \implies AB & =2x\\ & =2(12-6\sqrt{3})\\ & =24-12\sqrt{3}\end{aligned}[/tex]
Now we have both side lengths of the rectangle, we can easily calculate the area.
Area of a rectangle = width × length
= (24 - 12√3) × 12
= 288 - 144√3
= 38.5846837...
= 38.585 units² (nearest thousandth)
Calculate the magnitude of :
1.1.
[tex] \alpha [/tex]
Answers
Answer:
135°
have a nice day
hope it helps
15<96–q
what is the value of q
Answers
Answer: q < 81
Step-by-step explanation:
isolate q
15 < 96 - q
-81 < -q
divide by negative 1 but flip inequality because you are dividing by a negative
81 > q so
q < 81
Which statement(s) are true?
No event can be impossible.
No event can be certain.
The more unlikely an event, the closer it is to impossible.
The more likely an event, the closer it is to certain.
Answers
Answer:
no event can be impossible
Answer: no event can be impossible
Step-by-step explanation:
Find the volume . Round to the nearest tenth
Answers
volume: 1740 ft³
[tex]\sf volume\ of \ the \ prism = volume \ of \ rectangle \ + \ volume \ of \ triangular\ prism[/tex]
[tex]\sf volume\ of \ the \ prism =length * width * height+ \ \dfrac{1}{2} * base * height * length[/tex]
[tex]\sf volume\ of \ the \ prism =15* 10* 8+ \ \dfrac{1}{2} * 9* 12* 10[/tex]
[tex]\sf volume\ of \ the \ prism =1200+ 540[/tex]
[tex]\sf volume\ of \ the \ prism =1740[/tex]
Answer:
1740 ft³
Step-by-step explanation:
Volume
= Volume of right triangular prism (upper) + Volume of cuboid (below)
= 1/2L₁B₁H₁ + L₂B₂H₂
= 1/2 x 12 x 10 x 9 + 15 x 10 x 8
= 5 x 108 + 120 x 10
= 540 + 1200
= 1740 ft³
help, I’m terrible with percentages
Bob has a 1% chance of getting a prize from a cereal box, while the other prizes have a 99% chance for him to get. How many cereal boxes does Bob have to buy in order to get the prize? Show your work.
I’m pretty sure you’re supposed to find out something like “one in a million chance!”
Answers
Answer:
99 boxes im sure
if a sum of money increased by 1/5 of itself every year and in 5 years amounts to Rs.8546,find the sum
Answers
Answer:
Answer :
Given : If a sum of money amounts to Rs 2200 in 5 years
Let sum of money = x
And as given : The interest is 3838 of the principal . So we get
x ( 3838 ) = 2200 - x
3x = 17600 - 8x
11x = 17600
x = 1600
So, Sum of money = Rs . 1600
Then interest = 2200 - 1600 = Rs . 600
Let Rate of interest = r %
And we know Simple interest = P × r × t100P × r × t100 , So we get
⇒1600 × r × 5100 = 600⇒16× r × 5100 = 6⇒80r = 600⇒r = 60080 = 152 = 712%⇒1600 × r × 5100 = 600⇒16× r × 5100 = 6⇒80r = 600⇒r = 60080 = 152 = 712%
So
Step-by-step explanation:
Solve the equation for x. Assume a≠0. 4=ax−14
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve for x ~
[tex]\qquad \tt \dashrightarrow \:4 = ax - 14[/tex]
[tex]\qquad \tt \dashrightarrow \:ax = 4 + 14[/tex]
[tex]\qquad \tt \dashrightarrow \:ax = 18[/tex]
[tex]\qquad \tt \dashrightarrow \:x = \dfrac{18}{a}[/tex]
Please help. You get imaginary money if you help
Answers
Answer:
perimeter: 73.81 inarea: 284.955 in²Step-by-step explanation:
You want to find the perimeter and area of a sector that is 3/4 of the circle. The perimeter will be the sum of twice the radius and the length of the arc. The area will be 3/4 of the area of the full circle.
__
PerimeterThe length of a circular arc is ...
s = rθ . . . . . where θ is the central angle in radians
s = (11 in)(3/2π) . . . . . . . a 3/4 circle has a central angle of 3/2 radians
s = (11 in)(3/2)(3.14) = 51.81 in
When we add the two radii to this, we get a total perimeter of ...
P = 2r +s = 2(11 in) +51.81 in = 73.81 in . . . . perimeter of the figure
__
AreaThe area of a sector is given by the formula ...
A = 1/2r²θ . . . . . where r and θ are the radius and central angle (in radians)
A = 1/2(11 in)²(3/2π) = (1/2)(121 in²)(3/2)(3.14)
A = 284.955 in² . . . . area of the figure
A chemist has three different acid solutions.
The first solution contains 15 % acid, the second contains 30 % acid, and the third contains 50 %
acid,
She created 78 liters of a 35 % acid mixture, using all three solutions. The number of liters of 50 %
solution used is 3 times the number of liters of 30 % solution used.
How many liters of each solution was used?
Answers
Answer:
Its 50 and it can reach 60
A factory produces 72 pairs of
legging 6 minutes. At the same rate,how many pairs of leggings will the factory produce in 8 minutes?
Answers
Answer:
96 pairs
Step-by-step explanation:
72 pairs / 6 minutes will simplify to 12 pairs per minute.
Then (12 pairs / minute)(8 minutes) =
96 pairs
Can someone tell me what I did wrong here
Answers
Answer:
should have divided it directly ........ maybe or it's just messy........ maybe
Step-by-step explanation:
..........
...........
8x + 16 = 36
8x = 36 - 16
8x = 20
x = 20 / 8
x = 2.5
Write an equation of the line with a slope of -3 and y -intercept of 0 .
y=
Answers
Answer:
y=-3x
Step-by-step explanation:
4 Alfie did a survey to find which soup was most popular.
The choices were:
tomato
c
chicken
mushroom
A quarter of the children chose chicken soup.
Four times as many children chose tomato soup as chose mushroom soup.
Alfie makes a pie chart to show this information.
What angle should he use for the children who chose tomato soup?
Answers
The angle that would be used to show the number of children that chose tomato soup on a pie chart is 200°.
What angle reprsents the children that chose tomato soup?
A pie chart displays data in a circle. The sum of angles in a pie chart is 360 degrees
The first step is to determine the angle that would be used for children that chose chicken soup: 1/4 x 360 = 90
Remaining angle = 360 - 90 = 250 degrees.
Angle that can be used to represent the children that chose tomato soup: 4x + x = 250
5x = 250
x = 50
50 x 4 = 200 degrees
To learn more about pie charts, please check: https://brainly.com/question/26250795
the day before yesterday is 2 days after Sunday what day is today
Answers
Thursday
Explanation:
Two days after Sunday is Tuesday
Tuesday would be the day before yesterday (Wednesday)
So today is Thursday
Answer:
The Day before the day before yesterday was two days after the day before my birthday. Today is Thursday. The following steps can be used in order to determine the day on birthday: Step 1 - Remember today is Thursday according to the given data. Step 2 - Now, the Day before the day before yesterday is Monday. Step 3 - The two days before Monday is Saturday. Step 4 - And the day of the birthday is after Saturday that is Sunday
Step-by-step explanation:
Find the surface area of the right triangular prism (above) using its net (below).
Answers
Answer:
96 units²
Rectangles
A = bh
4 x 7 = 28
5 x 7 = 35
3 x 7 = 21
Triangles
A = bh/2
(4 x 3)/2 = 6
(4 x 3)/2 = 6
Total SA
28 + 35 + 21 + 6 + 6
96 units²
BRAINLIEST please if this helped!
A spinner with 10 equally sized slices has 2 blue slices, 4 yellow slices, and 4 red slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a blue slice? Write your answer as a fraction in simplest form.
Answers
Answer:
1/5
Step-by-step explanation:
the number of all slices is 10.. and you got 2 blue ones
so you get 2/10 and if you simplify it you get 1/5
PLEASE HELP!!!! ILL MARK BRAINLIEST WITH 10O POINTS!!!!!!! WITH EXLANATION!!
Use the diagram below to create a paragraph proof for the statement: "The sine and cosine of complementary angles are equal"
Answers
Answer:
Complemenraty angles are two angles with sum of 90°. In the given triangle ∠A and ∠B are complementary.
Now, the sine and cosine
sine = opposite side/hypotenusecosine = adjacent side/hypotenuseFind the sine of ∠A and cosine of ∠B
sin A = BC/ABcos B = BC/ABSince right sides are equal, left sides are equal too
sin A = cos BSimilarly, we can show that
sin B = cos AProved
You would use a back-to-back stem-and-leaf plot when you want to analyze the heights of the boys on the basketball team.
False
True
Answers
Answer:
true because there are going to be many heights already
Step-by-step explanation:
i it's true
this is because already there will be
so many heights
Which equations are true for x = –2 and x = 2? Select two options
x2 – 4 = 0
x2 = –4
3x2 + 12 = 0
4x2 = 16
2(x – 2)2 = 0
Answers
So. The first one 4th one are true
what is the value expression of the expression
2(x + 4) - (y•8)
when x=1/8 any y= 3/16
.A) 11/4
.B) 65/2
.C) 21/4
.D) 27/4
HELP ASAP
Answers
Answer:
D - 27/4
Step-by-step explanation:
2(1/8 + 4) - (3/16 × 8)
= 27/4
Gifts are packaged in cylinders.
Each cylinder is 12 cm high with a diameter of 8 cm.
Calculate the volume of each cylinder.
Use 3 as a value for at
Give your answer using the correct units.
Answers
Answer:
Step-by-step explanation:
V = [tex]\pi r^{2} h[/tex]
V = (3.14)(16)(12)
V = 50.24 cm³
2x +5 > -1 on the number line
Answers
Answer:
Below
Step-by-step explanation:
2x + 5 > -1
Treat the equality sign (ex. < >) as the costumary equal sign (=).
2x + 5 + (-5) > -1 + (-5) ---- -5 will cancel out the 5 on the left
2x/2 > -6/2 ------ divide by 2 to single out the x
x > -3
Remember to draw an open dot. Draw an arrow from -3 to the extreme right.
3.) Given the graph of the line represented by the equation f(x) = -3x + b,
if b is decreased by 5 units, the graph of the new line would be shifted 5 units
1) right
2) up
3) left
4)down
Answers
Answer: (4)
Step-by-step explanation:
Which decimal is greater: 7.09 or 7.1?
Answers
Answer: 7.1
Step-by-step explanation:
7.09<7.10
7.10=7.1
sometimes adding a zero helps
a=[4 -7 3 -2] find the determinant
Answers
Answer:
13
Step-by-step explanation:
[tex]\text{determinant of A} =\begin{vmatrix}4&-7\\ 3&-2\end{vmatrix}[/tex]
[tex]\text{determinant of A} =\left( 4\times \left( -2\right) \right) -\left( 3\times \left( -7\right) \right)[/tex]
[tex]\text{determinant of A} =-8+21=13[/tex]
What is the length of a rectangle formed from the lateral surface of a cylinder?
Answers
Answer:
B. 2[tex]\pi[/tex]r
Step-by-step explanation:
Which of the
following graphs
satisfies these
inequalities?
x- y< 2.
x + 2y > 8
y<4
A
B
2
f
Answers
B
is the answer. Good luck!!
june uses 12eggs to make cupcakes she uses 4eggs for each batch of cupcake
Answers
Answer:
12/4=3
Step-by-step explanation:
12/4
Answer:
3 batches
Step-by-step explanation:
Assuming that you are asking for how many batches she can make, we can divide 12 by 4 to find the number of batches.
Find the probability of the following event
You roll a prime number
Answers
Answer:
4/6
Step-by-step explanation:
A die can roll out six numbers from 1 to 6.
Prime numbers from 1 to 6 are: 1,2,3,5
4 out of 6 are prime