Answer:
13. (a) 120°, 120°, (b) 8.94 cm14. (a) 17.9 cm, (b) 22.4 cmStep-by-step explanation:
Refer to the attached sketch (not to scale)Question 13(a) The center of the circle is also the circumcenter of the triangle PQR.
Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:
∠POQ ≅ ∠QOR ≅ PORSum of the three angles is 360° as cover the full circle.
Each angle measure is:
∠POQ = ∠QOR = ∠POR = 360°/3 = 120°(b) Each side is 16 cm and the radius is 12 cm.
The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.
The segment MO is:
MO² = PO² - PM² = PO² - (PQ/2)²MO² = 12² - (16/2)² = 80MO = √80 = 8.94 cm (rounded)Question 14ΔXYZ is isosceles with:
XY = XZ = 20 cmYZ = 18 cm(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude
Find h:
h² = XZ² - ZM² = XZ² - (ZY/2)²h² = 20² - (18/2)² = 319h = √319h = 17.9 cm (rounded)(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.
Find ∠ZXM:
sin ∠ZXM = ZM/ZX = 9 / 20m∠ZXM = arcsin (9/20) = 26.7° (rounded)Find ∠ZOM:
m∠ZOM = 2*m∠ZXM = 2*26.7 = 53.4°Find the measure of the radius:
sin ∠ZOM = ZM/rsin 53.4° = 9/rr = 9 / sin 53.4°r = 11.2 cm (rounded)Find the measure of the diameter:
d = 2r = 2*11.2 cm = 22.4 cmYou have an annual salary of $85,063. Your monthly expenses include a $1,555 mortgage payment, a $274 car lease payment, $139 in minimum credit card payments, and a $179 payment on your student loan. Calculate your DTI (debt-to-income) ratio as a PERCENTAGE
Answer:
DTI ratio in percentage = 30.29%
Step-by-step explanation:
Annual salary = $85,063
This means that gross monthly pay = 85063/12 = $7088.58
Now,
Total monthly debt payments = 1555 + 274 + 139 + 179 = $2147
Debt to income ratio = (2147/7088.58) × 100% = 30.29%
Hey I know this is kind of a lot but can someone pls help.
Answer:
J) x = 6; slope is undefined
Step-by-step explanation:
Choice F is incorrect because the equation and slope. Choice G is incorrect because the slope. And, Choice H is incorrect because the equation and the slope.
Which of the following is an example of a physical property?(55 points)
A. nail rusting
B. camp fire burning
C. Table salt melting
D. silver spoon tarnishing
x-4.88=-5.78
solve for x
Answer:
-0.9
Step-by-step explanation:
Answer:
x =-.9
Step-by-step explanation:
x-4.88=-5.78
Add 4.88 to each side
x-4.88+4.88=-5.78+4.88
x =-.9
Drew needs to air up his teams 8 soccer balls. Each ball has a diameter of 70cm. In terms of pi, what is the total volume of air in all 8 soccer balls?
Answer:
1.44m^3
Step-by-step explanation:
Given data
Number of balls= 8
Diameter of ball = 70cm = 0.7m
Radius= 35cm= 0.35m
We know that a ball has a spherical shape
The volume of a sphere is
V= 4/3πr^3
substitute
V= 4/3*3.142*0.35^3
V= 0.18m^3
Hence if 1 ball has a volume of 0.18m^3
Then 8 balls will have a volume of
=0.18*8
=1.44m^3
Please please please help me with this pleasseee!!!
[tex]\Large\boxed{\tt Answer:~A:~y=-3x+5}[/tex]
All we have to do in order to find the equation that is equivalent to 6x + 2y = 10 is to solve for y.
Step 1: Keep y on one side of the equation and move the rest to the other.
[tex]\tt 6x + 2y = 10\\2y = -6x + 10[/tex]
Step 2: Divide all terms by 2 to isolate y.
[tex]\tt 2y \div 2=y\\-6x \div 2 = -3x\\10 \div 2 =5\\\\y=-3x+5[/tex]
I need help on this math problem fast with work shown and answer thx
Answer:
angle 1 = 124
angle 2 = 56
angle 3 = 124
angle 4 = 56
Step-by-step explanation:
This problem is a bit like a puzzle. To make notation easier I'm going to do this:
angle 1 = a
angle 2 = b
angle 3 = c
angle 4 = d
Now, let's start with what we know from the image.
All angles added together form a circle or 360 degrees
a + b + c + d = 360
In the same regard a + d = 180, and b + c = 180
Also,
a = c
and
b = d
It also tells us angle 4 is 25 degrees greater than one fourth of angle 1. Which is written as.
d = 1/4(a) + 25
If we look at all the equations we have, we can see that two of the equations have two of the same variables:
a + d = 180
and
d = 1/4(a) + 25
Using substitution we can take the second equation substitute it for d in the first equation giving us:
a + (1/4(a) + 25) = 180
Now we just solve for a
[tex]\frac{4}{4} a+ \frac{1}{4} a + 25 = 180\\\\\frac{5}{4}a + 25 = 180 \\\\(\frac{5}{4}a + 25) - 25 = (180) -25\\\\\frac{5}{4} a = 155\\\\\frac{5}{4} a * \frac{4}{5} = 155 * \frac{4}{5}\\\\a = 124[/tex]
Therefore a, or angle 1, is 124
Since a = c, then c, or angle 3, is also 124
Since a + d = 180 and a = 124 then
d = 180 -124
d = 56
So, d, or angle 4, is 56
And because b = d then b, or angle 2, is also 56
a = 124
b = 56
c = 124
d = 56
For extra measure, we can check our work by using the first equation
a + b + c + d = 360
124 + 56 + 124 + 56 = 360
question in the pic
helpppp plsssss(I’ll give 80 pointssss
Answer:
-4 + -6 = -10
Step-by-step explanation:
From the line at negative 4 it goes to negative 10 you need to add six to four to make ten. Though since it is negative numbers we add a negative 6
A pyramid with a rectangular base has a volume of 60 cubic feet and a height of 6 feet. The width of the rectangular base is 4 feet. Find the length of the rectangular base.
Answer:
length=2.5feet
Step-by-step explanation:
Volume =Base area * height
6/60=(4*length) * 6/6
10=4length
length=10÷4
=2.5feet
The length of the pyramid is 7.5 feet.
What is a pyramid with rectangular base?'A rectangular pyramid is a type of pyramid with the base shaped like a rectangle but the sides are shaped like a triangle. A pyramid usually has triangular sides but with different bases.'
According to the given problem,
Volume = 60 cubic feet
Height = 6 feet
Width of rectangular base = 4 feet
Let the length be x,
Volume =[tex]\frac{L * W * H}{3}[/tex]
⇒ 60 = [tex]\frac{x*6*4}{3}[/tex]
⇒ 180 = 24x
⇒ x = [tex]\frac{180}{24}[/tex]
⇒ x =[tex]\frac{45}{6}[/tex] = 7.5
Hence, we can conclude that the value of the length of the rectangular base is 7.5 feet.
Learn more about rectangular pyramid here: https://brainly.com/question/16602334
#SPJ2
Which expression is equivalent to
[tex](3 {u}^{3} {v}^{4}) ^{2} [/tex]
A.
[tex]3 {u}^{5} {v}^{6} [/tex]
B.
[tex]3 {u}^{6} {v}^{8} [/tex]
C.
[tex]9 {u}^{6} {v}^{8} [/tex]
D.
[tex]9 {u}^{5} {v}^{6} [/tex]
Answer:
C
Step-by-step explanation:
When 3 is squared, it becomes 9. That means that both A and B are incorrect.
The powers on u and v are doubled not added to become u^6 and v^8 so that makes C the only possible answer.
Find the area of the following
triangle:
5 cm
10 cm
A= [?] cm?
Answer:
25
Step-by-step explanation:
A=1/2×b×h
A=1/2×5cm×10cm
A=25cm
PLEASE HELP AND ILL GIVE BRAINLIEST
Answer:
2
Step-by-step explanation:
Subtract the number with the term both sides ( which is 9)
[tex] {x}^{2} + {y}^{2} - 6x + 4y = - 9[/tex]
Complete the square for the x terms and y terms.
( To complete the square divide the coefficient term by 2 and square it, then add that product to both sides.)
[tex] {x}^{2} - 6x + 9 + {y}^{2} +4y + 4 = - 9 + 9 + 4[/tex]
[tex] (x - 3) {}^{2} + (y + 2) {}^{2} = 4[/tex]
Take the square root of the right side to find the radius
[tex] \sqrt{4} = 2[/tex]
Find the least common multiple of 18, 24, 42
Answer: 504. Multiple for : 18, 24 and 42. Factorize of the above numbers : 18 = 2 • 32 24 = 23 • 3. 42 = 2 • 3 • 7
What is the equation of the horizontal line?
Answer: y = 1
y = 2x+7 x = -3
y = 2(-3) + 7
y = 1
Need help with this question thank you!
Answer:
Step-by-step explanation:
(5,3) should be your slope. Start from the bottom of the line and go up. Use the X axis slope 1st because of the x1 y1 coordinates.
Answer:
(5,-1)
(-4,0)
Step-by-step explanation:
5 is in the X axis
-1 is in the Y axis
-4 is in the Y axis
0 is in the X axis
A rectangular prism has a base perimeter of 28 inches and a height of 6 inches. What is the lateral surface area of the prism?
Answer:
uhuhuhuhuhuhuhuhuhuhuh oh yeah
Step-by-step explanation:
what is the area of a trapezoid
Answer:
28 in² = 28
Step-by-step explanation:
[tex]a = \frac{a + b}{2}h[/tex]
[tex]a = 6[/tex]
[tex]b = 8[/tex]
[tex]h = 4[/tex]
[tex]a = \frac{6 + 8}{2}4[/tex]
[tex] \frac{14}{2} 4[/tex]
[tex]7 \times 4[/tex]
[tex] = 28[/tex]
Answer = 28 _
The diameter of a circle is 4 feet. What is the circumference?
d=4 ft
Give the exact answer in simplest form.
I need the answers
Answer: 4π
Step-by-step explanation: C= 2πr; 2r=d; C=dπ; C=4π!
Answer:
4π ft
Step-by-step explanation:
C = 2πr (Circumference formula for a circle)
diamater = 4, so diamter = 2 x radius, 4 = 2 x r , so r = 2
Use formula:
C = 2π(2) = 4π
4π ft (Exact answer)
please solve for x!!!!
Answer:
-14
Step-by-step explanation:
Hello,
Let's have a look at this figure and think about how are these two angles related to each other. These two angles are vertically opposite angles, and any two vertically opposite angles should be equal to each other.
Because the two angles should be equal to each other, we can equate the two equations together and solve for x.
9x + 184 = 7x + 156
9x - 7x = 156 - 184
2x = -28
x = -14
Principal = $47,300 Rate = 3% Time = 4 months What will the total payment plus interest be?
Answer:
Simple Interest (I) = Principle * Rate * Time
so I = PRT
P = $47300
R = 3% = 0.03
T = 4months = 0.33years
so
Assuming its per year after 4month
I = (47300)(0.03)(0.333333)
I = 472.999527
I = $473
Now we'd add the interest(I) to the Principle
$47300 + $473 = $47773.00
Assuming it is per month, after 4months
I = PRT
I = (47300)(0.03)(4)
I = $5676.00
Now add the interest to the principle
$47300 + $5676 = $52976.00
Step-by-step explanation:
there you go hope this help
AAAAAA help me pls
(I need help on number 5)
Answer:
1620!
Step-by-step explanation:
Answer:
1620
Step-by-step explanation:
For every six dollars that Jamal saves in his account, his brother saves eight dollars in his account.
If Jamal has $24.00 dollars in his account, how much money does his brother have in his account?
Answer:
jamel brother has 48.00 dollors
Step-by-step explanation:
Answer: He has 32$ 24 divided by 6 is 4 multiply 4 by 8 and you get 32
Write the Recursive form and next of the following sequence
8,10,12,14,16...
Answer:
Step-by-step explanation:
The recursive form is a(n + 1) = a(n) + 2, with a(1) = 8.
The next term is a(6) = a(5) + 2, which heere is a(6) = 16 + 2 = 18
Solve 5/4=x/12.
x=
Please help!
Answer: x=15
Step-by-step explanation:Step 1: Cross-multiply.
5
4
=
x
12
(5)*(12)=x*(4)
60=4x
Step 2: Flip the equation.
4x=60
Step 3: Divide both sides by 4.
4x
4
=
60
4
x=15
Answer:
x=15
NO LINKS!! NO ONE WANT TO HELP ME PLEASE IM WASTING ALL MY POINTS PLSSS HELPPPP :((( Which of the following equations describe the line shown below? Check all
that apply MULTI CHOICE MORE THAN OND
(1,6) (-3,-6)
Answer:
Option E
Step-by-step explanation:
The two points are (1,6) and (-3,-6) . We can find the Equation of the line using two point form , as ,
[tex]\implies y - y_1 =\dfrac{y_2-y_1}{x_2-x_1}(x - x_1) \\\\\implies y - 6 = \dfrac{-6-6}{-3-1}(x-1) \\\\\implies y-6 = \dfrac{-12}{-4}(x-1) \\\\\implies \boxed{\boxed{y -6 = 3(x-1)}} [/tex]
On looking at options we see that option E is correct .
Hence the correct option is E.hi so... im horrible at math and can't figure this out so can someone pls answer this? and in the most simplified way possible because my tiny brain can't handle too many steps aha. WILL GIVE BRAINLIEST... just so u guys know l mao
Can someone help with this question? I’m stuck.
Answer:
2
Step-by-step explanation:
2+2 is 4 so therefore the answer is 2.00.
Math help me out this is tricky man hurry solve both
Answer:
1) a , b , c , e are ans....
2) a.F b.T c.F d.T
PLEASE ANSWER!! Write the equation of a line that passes through the points (-2,-9) and (2,-9).
Answer:
Step-by-step explanation:
the equation in the point slope form is
and reducing the equation (slope-intercept form)
Step-by-step explanation:
first we calculate the slope of the line with the formula:
where is a point where the line passes, and is another point where the line passes.
Since we have the following points:
(8, -2)
(5,5)
we conclude that
now we substitute this values to find the slope:
to find the equation now that we know the slope we use the point-slope equation:
and we subtitute the slope and the values of and :
we reduce this equation:
the equation in the point slope form is
and reducing the equation (slope-intercept form)