Answer:
∠1 = 36°
∠2 = 72°
∠3 = 72°
∠4 = 72°
∠5 = 36°
Step-by-step explanation:
The angles of rhombus are ∠1 = 36°, ∠2 = 72°, ∠3 = 72°, ∠4 = 72°, ∠5 = 36°.
What is a rhombus?
A rhombus is a quadrilateral with four equal sides and opposite equal angles. It has two diagonals that bisect each other at right angles. It also has opposite sides parallel and the sum of all the four interior angles is 360 degrees.
For the given situation,
From the diagram of rhombus,
The angle is 72°.
In rhombus,
Opposite angles are equal.
So, [tex]\angle2 = \angle3 = \angle4[/tex] are equal to [tex]\angle72[/tex].
Diagonals bisect the angles and the sum of two adjacent angles is equal to 180 degrees.
⇒ [tex]\angle D + \angle E = 180[/tex]
Here, [tex]\angle D = \angle 72 + \angle 72[/tex]
⇒ [tex]\angle D = \angle 144[/tex]
Thus, [tex]\angle E = \angle 180 -\angle 144[/tex]
⇒ [tex]\angle 1 = \angle 36[/tex]
we know that, [tex]\angle E = \angle G[/tex]
⇒ [tex]\angle 5 = \angle 36[/tex]
Hence we can conclude that the angles of rhombus are ∠1 = 36°, ∠2 = 72°, ∠3 = 72°, ∠4 = 72°, ∠5 = 36°.
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Can someone help me on this plzzz
Answer:
6
Step-by-step explanation:
z = 2
4z^2- 3z - 4
4(2)^2 - 3(2) - 4
4(4) - 3(2) - 4
16 - 6 - 4
6
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What is the common ratio of the sequence?
-2, 6, -18, 54,...
a. −3
b. −2
c. 3
d. 8
Answer:
A -3
Step-by-step explanation:
-2 x -3 = 6
6 x -3 = -18
-18x -3 = 54
How would you write 12-^3 using a positive exponent?
12^3
12^0
12^3/1
1/12^3
Answer:
[tex] \frac{1}{ {12}^{3} }[/tex]
Step-by-step explanation:
[tex] {12}^{ - 3} = \frac{1}{ {12}^{3} } \\ [/tex]
can you figure out the missing number in this sequence?
2, 5, 9, 14, 27
Answer:
The missing number in the sequence is 20
Step-by-step explanation:
The difference between the numbers are as follows: 3,4,5,6,7
The missing number of the given sequence is 13.
The given sequence is,
2, 5, 9, 14, 27
We can see that the difference between each consecutive number is increasing.
The difference between 2 and 5 is 3,
The difference between 5 and 9 is 4,
The difference between 9 and 14 is 5,
And the difference between 14 and 27 is 13.
Therefore, it's possible that the next number in the sequence could have a difference of 14 or more.
So,
To determine the missing number,
We can look at the pattern of the differences between the numbers in the sequence.
Since the difference between 14 and 27 is 13,
We can assume that the difference between the missing number and 27 is at least 14.
Therefore, we can subtract 14 from 27 to get our missing number, which is 13.
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What is the slope of the line below?
Answer:
A) -4/5
Step-by-step explanation:
( -8, 10) and ( -3, 6)
Slope:
m=(y2-y1)/(x2-x1)
m=(6-10)/(-3+8)
m= (-4)/5
m = -4/5
What is the spread of the data?
A. 15 to 30 years
B. 18 to 25 years
C. 21 to 25 years
D. 18 to 21 years
HELP PLEASE!!! I really dont understand this!
If 10% of a number is 12 and 45% of the same number is 54, find 35% of that number.
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Answer: 42
Explanation:
120 x .35 = 42
I hope this helped!
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42 is your answer
Answer:
let no be x
10% of x=12
x=1200/10=120
again
45% of x=54
x=5400/45=120
here
35% of 120=35/100×120=42
select the values that make the inequality w<-4 true
Answer:
w=-5
Step-by-step explanation:
Find the areas of the sectors formed by ∠DFE. Round your answers to the nearest hundredth.
Answer:
Area of sector DFE = 177.79cm²
Area of sector DGE = 437.65cm²
Step-by-step explanation:
Find the diagram attached;
Area of the sector is expressed according to the formula;
Area of the sector = theta/360 * πr²
theta is the central angle = 360 - 256
theta = 104°
r is the radius = 14cm
Substitute into the formula as shown;
Area of the sector = theta/360 * πr²
Area of the sector DFE = 104/360 * 3.14(14)²
Area of the sector DFE = 0.289 * 615.44
Area of the sector DFE = 177.79cm²
Hence the area of the sector <DFE to the nearest hundredth is 177.79cm²
For sector DGE:
Area of the sector DGE = 256/360 * 3.14(14)²
Area of the sector DGE = 0.7111 * 615.44
Area of the sector DGE = 437.65cm²
Hence the area of the sector <DGE to the nearest hundredth is 437.65cm²
someone please help ??? :,(
Answer:
32/40 = 24/x
x=30
Answer:
30
Step-by-step explanation:
32x= 40•24
32=960
X=30
A tennis court is surrounded by a fence so that the distance from each boundary (edge) of the tennis court to the fence is
the same. If the tennis court is 78 feet long and 36 feet wide, what is the area of the entire surface inside the fence?
Answer:
the answer is 2,808
Step-by-step explanation:
you have to multiply 78 by 36 because it is area
What is the approximate area of Nevada?
205 mi
309 mi
Reno
Carson City
511 mi
Las
Vegas
o 221,244 mi?
110,622 mi?
163,295 mi?
O 200,948 mi?
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Areas,
Let's divide the above map in to 2 parts , that is a rectangle and a triangle, and add both thier areas to get the area of the Nevada.
so we get as,
Area of triangle = 1/2*b*h
Area of triangle ==> 1/2*309*306 ==> 47277 mi^2
Area of rectangle = l*b = 205*309 ==> 63345 mi^2
Area of NEVADA = 47277 + 63345 = 110622 mi^2
hence the area = 110622 mi^2
Answer:
the approximate area of Nevada is 110,567 mi²
Some one help me solve for x
Answer:
x = 10
Step-by-step explanation:
The sum of the interior angles of a quadrilateral = 360°
Sum the angles and equate to 360
9x + 15 + 85 + 90 + 80 = 360, that is
9x + 270 = 360 ( subtract 270 from both sides )
9x = 90 ( divide both sides by 9 )
x = 10
Write each equation in slope-intercept form by following the steps below.
1. y = 2 + 4(x - 3)
a. Distribute 4 through the parentheses.
y=2 +
b. Simplify by combining like terms.
c. Is the equation in the form y = mx + b?
If not, rewrite it.
Given:
The equation is
[tex]y=2+4(x-3)[/tex]
To find:
The slope intercept form of the given equation.
Solution:
We have,
[tex]y=2+4(x-3)[/tex]
Step a: Distribute 4 through the parentheses.
[tex]y=2+4(x)+4(-3)[/tex]
[tex]y=2+4x-12[/tex]
Step b: Simplify by combining like terms.
[tex]y=4x+(2-12)[/tex]
[tex]y=4x-10[/tex]
Step c: Is the equation in the form [tex]y = mx + b[/tex]? If not, rewrite it.
The equation [tex]y=4x-10[/tex] in the form of [tex]y = mx + b[/tex].
Therefore, the slope intercept form of the given equation is [tex]y=4x-10[/tex].
i need help please this is quite hard for me
WORTH 21 POINTS!!! Find the area of the shaded regions
Answer:
84.823005
Step-by-step explanation:
π6^2=113.09734
(360-90)/360=3/4
3/4* 113.09734=84.823005
Step-by-step explanation:
area of circle=
[tex]\pi \: r ^{2} [/tex]
22/7×6×6=113.14
=3/4of 113.14
=84.55cm²
Find the final hourly wage if a $10.50 starting wage is increased by 6% each year for 7 years.
Answer:
In seven years the hourly rate will be $15.79.
Step-by-step explanation:
Giving the following information:
Hourly rate= $10.5
Number of periods= 7 years
Increase rate (i)= 6%
To calculate the hourly rate in 7 years, we need to use the following formula:
FV= PV*(1 + i)^n
FV= 10.5*(1.06^7)
FV= $15.79
In seven years the hourly rate will be $15.79.
Please! Someone help:((
Answer:
n = √75
Step-by-step explanation:
n is the altitude of the right triangle.
Thus:
n = √(15*5) (right triangle altitude theorem/geometric mean theorem)
n = √75
3. There are 25 students in the debate
club. Of those students, 15 are girls.
What percent of the students in the
debate club are girls?
ANSWER Quick PLEASE
Answer:
60%
Step-by-step explanation:
To make a percent, it needs to be out of 100. So, the fraction would be 15/25. To make it 100, multiply each by 4 to get 100 since 25 times 4 equals 100. 15 times 4 is 60, so its 60 percent.
Answer:
In the debate club, 60% of the students are girls.
Step-by-step explanation:
(15) girls divide by total students(25)
15/25 = .6
.6*100 = 60%
if Alex and Mpho have to share R20 in the ratio 2:3,how much will Mpho get?
A R4
B R8
C R10
D R12
Answer:
D
Step-by-step explanation:
sum of ratio=2+3=5
Mpho gets=3/5×20=12
Solve for d. the question
Answer:
d = A or 49
Step-by-step explanation:
25^2 =625
24^2 = 576
625-576= 49 or 7^2
What is the initial value of the linear function through
Questions 7 and 8 please. Really need help thank you!!
Answer:
7) sin 60° = 25√3/Z
0.8660 = 25√3/Z
Z = 50
8) using the Pythagorean theorem:
50² = (25√3)² + y²
2500 = 1875 + y²
y² = 625
y = 25
Answer:
z = 50
y = 25
Step-by-step explanation:
Using the 30, 60, 90 triangle rule
you can figure this out.
The rule says
With a 30, 60, 90 triangle
Given the shorter leg, (side across the 30 degree angle,
To find longer leg (side across the 60 degree angle):
Multiple shorter leg by radical 3.
To find hypotenuse (side across the 90 degree angle):
Multiple shorter leg by 2.
Thus
Shorter leg (side opposite 30 degree): 25
Longer leg (side opposite 60 degree):
25 radical 3
Hypotenuse(side opposite 90 degree): 50
2.
х
у
First
Differences
-2
12
Second
Differences
s
-1
3
0
0
1
3
2.
12
Answer:
I um need the question to answer.
Step-by-step explanation:
The sum of-3 and four times a number is no more than -11." Whats the inequality
Answer:
-3+4x<=-11
No more than is <=
The inequality for the sum of-3 and four times a number is no more than -11 is -3 + 4x ≤ -1.
The relationship between two expressions or values which are not equal is called inequality. It shows how many times one expression is less than or equal, or greater than another expression.
Let the unknown variable is [tex]x[/tex].
According to the question,
The sum of -3 and four times of number be [tex]4x - 3\\[/tex] is less than -11.
So, the equation will be,
[tex]- 3 + 4 x < -11[/tex].
Thus, the inequality will be [tex]- 3 + 4 x < -11[/tex] .
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2x - 4y = -2
2x + 3y = -16
What is the solution
Answer:
x=-5
y=-2
Step-by-step explanation:
equation 1 - equation 2
(2x-4y=-2) - (2x+3y=-16) = (-7y=14)
y=14/-7=-2
then substitute y=-2 into any equation
2x-4(-2)=-2
2x+8=-2
2x=-10
x=-10/2=-5
Toby found a $52 wallet on the clearance
rack for 60% off. If sales tax is 6.25%, how
much will he pay in total?
A.$22.10
B.$23.75
C.$28.50
D.$33.15
Answer:
A. $22.10
Step-by-step explanation:
52 x 0.4 = 20.8
20.8 x 1.0625 = 22.1
Which function will translate f(x) = x right 5 units and
up 1 unit?
A.f (x) = (x – 5)2 + 1
B.f(x) = (x + 5)2 + 1
C.f(x) = (x - 5)2 - 1
D.f(x) = (x + 1)2 – 5
a3 = 18 and a6 = -486
Find a10
Answer:
The value of a₁₀ is -1158
Step-by-step explanation:
a₃ = 18
a₆ = - 486
Now,
a₃ = 18 can be written as
a + 2d = 18 ...(1) and
a₆ = - 486 can be written as
a + 5d = - 486 ...(2)
Now, from equation (2) we get,
a + 5d = - 486
a + 2d + 3d = - 486
18 + 3d = - 486 (.°. a + 2d = 18)
3d = - 486 - 18
3d = - 504
d = - 504 ÷ 3
d = - 168
Now, for the value of a put the value of d = -168 in equation (1)
a + 2d = 18
a + 2(-168) = 18
a - 336 = 18
a = 18 + 336
a = 354
Now, For a₁₀
a₁₀ = a + 9d
a₁₀ = 354 + 9(-168)
a₁₀ = 354 - 1512
a₁₀ = -1158
Thus, The value of a₁₀ is -1158
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