Answer:
[tex]\sf \theta=\dfrac34 \ radians=42.97 \textdegree \ (nearest \ hundredth)[/tex]
Step-by-step explanation:
Formulae
[tex]\sf radius (r)=\dfrac12 d[/tex]
(where d is the diameter of a circle)
[tex]\sf arc \ length =r\theta[/tex]
(where r is the radius and [tex]\theta[/tex] is measured in radians)
Calculation
Given:
[tex]\sf radius (r)=\dfrac12 \cdot 8=4 \ mi[/tex]arc length = 3 miSubstituting these values into the formula for arc length:
[tex]\implies \sf 3 =4\theta[/tex]
[tex]\implies \sf \theta=\dfrac34 \ radians[/tex]
To convert radians to degrees use
[tex]\sf 1 \ rad \cdot \dfrac{180\texrdegree}{\pi}[/tex]
[tex]\implies \sf \dfrac34 \cdot \dfrac{180\texrdegree}{\pi}=42.97183463...\textdegree[/tex]
Now
[tex]\\ \rm\rightarrowtail \theta=\dfrac{l}{r}[/tex]
[tex]\\ \rm\rightarrowtail l=r\theta[/tex]
[tex]\\ \rm\rightarrowtail 3=4\theta[/tex]
[tex]\\ \rm\rightarrowtail \theta=\dfrac{3}{4}^c[/tex]
The sum of three consecutive even integers is 108. What is the largest number?
34
35
37
38
Answer:
38
Step-by-step explanation:38 because 108. x = 17. 2x + 4 = 34 + 4 = 38
A triangle has side lengths of 18 in., 22 in., and 29 in. Is the triangle acute, obtuse, or right?
Acute
Obtuse
Right
None of the above
========================================================
Explanation:
We have a triangle with these side lengths
a = 18b = 22c = 29Computing a^2+b^2 gets us
a^2+b^2 = 18^2+22^2 = 808
Compare this to c^2
c^2 = 29^2 = 841
Because 808 < 841, this means a^2+b^2 < c^2
-------------------
We have three cases:
If a^2+b^2 > c^2, then the triangle is acuteIf a^2+b^2 = c^2, then we have a right triangleIf a^2+b^2 < c^2, then the triangle is obtuseFor more information, check out the converse of the Pythagorean Theorem.
4 3/5 - 4/5 = ?
please explain it
ixl
Answer:
[tex] \frac{19}{3 } \: or \: 3 \frac{4}{5} [/tex]
Step-by-step explanation:
Change the mixed number into a regular fraction.
[tex] \frac{23}{5} - \frac{4}{5} [/tex]
Subtract the numerator.
[tex] \frac{19}{5} [/tex]
As a mixed number:
[tex]3 \frac{4}{5} [/tex]
the question is attached
What part of the expression below should be calculated first 8 x {22 x [15 + (14 x 2)]} A 8+22. B 22×15. C 14x2. D 15+14.
Answer:
14*2
Step-by-step explanation:
8 x {22 x [15 + (14 x 2)]}
With multiple parentheses work from the inside out
The inner most parentheses are
14*2
The number 3 is a common factor of _________.
A) 9 and 15
B) 6 and 10
C) 8 and 12
Answer:
A) 9 and 15.
Step-by-step explanation:
First, let's see what each number's factor is:
A)
9 : 1, 3 & 9
15 : 1, 3, 5 & 15
B)
6 : 1, 2, 3 & 6
10 : 1, 2, 5 & 10
C)
8 : 1, 2, 4 & 8
12 : 1, 2, 3, 4, 6 & 12
Therefore, The number 3 is a common factor of A) 9 and 15.
___
Find the center and the radius of the circle.
(x-4)^2 + (y + 3)^2 = 74
Answer:
radius = [tex] \sqrt{74} [/tex]center = [tex](4,-3)[/tex]Step-by-step explanation:
We would like to calculate the centre and the radius of the circle . The given equation is ,
[tex]\longrightarrow (x - 4)^2+(y+3)^2=74 [/tex]
As we know that the Standard equation of circle is given by ,
[tex]\longrightarrow (x - h)^2+(y-k)^2=r^2[/tex]
where ,
[tex](x,y)[/tex] is a point on circle .[tex](h,k)[/tex] is the centre of circle .[tex]r[/tex] is the radius of the circle .We can rewrite the equation as ,
[tex]\longrightarrow (x-4)^2+\{ y -(-3)\}^2=(\sqrt{74})^2\\ [/tex]
Now on comparing to the standard form , we have ;
radius = [tex]r[/tex] = [tex]\sqrt{74}[/tex]center = [tex](h,k)[/tex] =[tex](4,-3)[/tex]Graph :-
[tex] \setlength{\unitlength}{7mm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\circle*{0.2}}\put(0.2, - .1){(4,-3)}\put(-1.2,0){\vector(0,1){5}}\put(-1.2,0){\vector(0, - 1){5}}\put(-1,0.7){\vector(1,0){5}}\put(-1,0.7){\vector( - 1,0){5}}\put(0,0){\line(-1,0){2.3}}\put( - 1.2,-0.7){$\sf \sqrt{74}$}\put(2,6){$\boxed{\sf \textcopyright \: RISH4BH }$}\end{picture} [/tex]
And we are done !
We are given the equation of circle (x - 4)² + (y + 3)² = 74 , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;
So, consider the equation of circle ;
[tex]{:\implies \quad \sf (x-4)^{2}+(y+3)^{2}=74}[/tex]
Can be further written as ;
[tex]{:\implies \quad \sf (x-4)^{2}+\{y-(-3)\}^{2}=({\sqrt{74}})^{2}}[/tex]
On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows
Centre = (4, -3)Radius = √74 unitsFactor the equation k^2 + 25
Answer:
k^2+25
Step-by-step explanation:
Factor k^2+25
=k^2+25
Doesn't factor
Parallelogram P Q S R is shown. The length of P Q is (4 x minus 1) centimeters and the length of R S is (3 x + 7) centimeters.
The perimeter of parallelogram PQSR is 74 cm. What is QS?
4 cm
6 cm
8 cm
12 cm
The opposite sides PQ and RS of the parallelogram PQRS are congruent
The value of the length QS is 6 cm
How to determine the length QS?The given parameters are:
PQ = 4x - 1
RS = 3x + 7
Opposite sides are congruent.
So, we have:
4x - 1 = 3x + 7
Collect like terms
4x - 3x = 1 + 7
Evaluate the expressions
x = 8
The perimeter is calculated using:
Perimeter = 2(QS + RS)
This gives
2(QS + RS) = 74
Divide by 2
QS + RS = 37
Substiute RS = 3x + 7
QS + 3x + 7 = 37
Substitute 8 for x
QS + 3*8 + 7 = 37
This gives
QS + 31 = 37
Subtract 31 from both sides
QS = 6
Hence, the value of the length QS is 6 cm
Read more about parallelograms at:
https://brainly.com/question/2844650
Answer:
6cm or b
Step-by-step explanation:
Your first six-month auto insurance premium was $629.00. Based on your driving record, your renewal premium is $786.25. What percent increase did you see in your premium?
8%
20%
оооо
25%
32%
Hello!
Answer:
[tex]\Large \boxed{\sf 20\%}[/tex]
Step-by-step explanation:
→ We want to calculate the percentage increase we saw in our premium.
→ To calculate the percentage increase we saw in our premium, let's calculate the difference between our first six-month car insurance premium and our renewal premium:
[tex]\sf 786.25 - 629.00 = 157.25[/tex]
→ Calculate the percentage:
→ The formula used to calculate the percentage is:
[tex]\sf \dfrac{value}{total ~value} \times 100\%[/tex]
→ Apply this formula with value = 157.25 and total value = 786.25:
[tex]\sf \dfrac{157.25}{786.25} \times100\%[/tex]
→ Simplify the expression:
[tex]\sf \dfrac{157.25}{786.25} \times100\%\\\\\\= 0.2 \times100\%\\\\\\= 0.2 \times \dfrac{100}{100} \\\\\\= 0.2 \times 1\\\\\\= 0.2\\\\\\= \dfrac{20}{100} \\\\\\\boxed{\sf= 20\%}[/tex]
So the percentage increase we saw in our premium is 20%.
Which equation represents the graphed function?
-3x + 2 = y
-2/3x+2=y
3/2x-3=y
2x-3 = y
The linear equation that represents the graph is 3/2x - 3 = y
Data;
-3 + 2 = y-2/3x + 2 = y3/2x - 3 = y2x - 3 = yLinear EquationFrom the given graph, we can see at the x-axis that the line touches at point 2 and at the y-axis, the line touches at point 3.
If we decide to multiply through by 3 to eliminate the fraction, the equation would look like this.
[tex]\frac{3x}{2} -3 = y\\2(\frac{3x}{2}) -3(2) = 2(y)\\3x - 6 = 2y[/tex]
Kindly find the attached image of the graph.
Learn more on linear equation here;
https://brainly.com/question/14323743
Convert to vertex form: f(x) = x2 + 16x + 64
Answer:
Step-by-step explanation:
hello :
note : the vertex form is :
ax²+bx+c = a(x+(b)/(2a))²- delta/4a² and delta = b²- 4ac
in this exercice you have : a =1 b = 16 and c=64
continu ..........
I have attached the questions below please help me
Answer:
point A is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Find the area of the parallelogram shown below.
Answer:
144√3 square feet
Step-by-step explanation:
There is a 30°-60°-90° triangle. In this triangle, the longer leg, which is the height of this parallelogram, is √3 times the length of the shorter leg (8 feet). Multiplying base times height, we have
18 * 8√3, which is 144√3 square feet.
please it’s not hardHow many points are contained on a line?
infinitely many
20.000
none
Answer:
Infinitely many
Step-by-step explanation:
Infinitely many points are contained on a line.
Answer:
infinitely many
Step-by-step explanation:
A line consists of infinitely many points.
hope this helps!! p.s. i really need brainliest :)
For the function f(x)=−7x2+8x−8, find f(4).
Answer:
- 88
Step-by-step explanation:
[tex]f(x ) = - 7 {x}^{2} + 8x - 8 \\ plug \: x = 4 \\ \\ \implies \: f(4 ) = - 7 {(4)}^{2} + 8(4) - 8 \\\\ \implies \: f(4 ) = - 7 \times 16 + 32 - 8 \\\\ \implies \: f(4 ) = - 112+ 32 - 8 \\ \\ \implies \: f(4 ) = - 120+ 32 \\\\ \implies \: f(4 ) = - 88 \\[/tex]
An American roulette wheel has 38 spaces, labeled using the numerals 1 through 36, 0, and 00. In a random spin of the wheel, what is the probability that the ball will land on 2?
This is because there's one space labeled "2" out of 38 spaces total.
This fraction is approximately equal to 1/38 = 0.0263 meaning there's roughly a 2.63% chance of landing on this space.
The probability is 0.0263 that the ball will land on 2 in a random spin of the wheel.
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.
Assuming an unbiased wheel.
The probability of an event = number of favourable outcomes/ number of total outcomes.
The total number of outcomes is 38
The number of favourable outcomes is one because there's one space labeled "2" out of 38 spaces total.
The probability of an event = 1/38 = 0.0263
Hence, the probability is 0.0263 that the ball will land on 2 in a random spin of the wheel.
Learn more about probability
brainly.com/question/11234923
#SPJ2
Write an equation in standard form of an ellipse that has a vertex at (0, 6), a co-vertex at (1, 0), and a center at the origin.
Answer:
The standard form of the equation of the ellipse is x² + y²/36 = 1
Step-by-step explanation:
* Lets revise the standard equation of the ellipse
- The standard form of the equation of an ellipse with
center (0 , 0) is x²/b² + y²/a² = 1
where,
* the length of the major axis is 2a
* the coordinates of the vertices are (0 , ±a)
* the length of the minor axis is 2b
* the coordinates of the co-vertices are (±b , 0)
* the coordinates of the foci are (0 , ± c), where c² = a² - b²
* Now lets solve the problem
∵ The vertex of the ellipse is (0 , 6)
∴ a = 6
∵ The co-vertex is (1 , 0)
∴ b = 1
∵ the center is the origin (0 , 0)
∵ The standard form equation is x²/b² + y²/a² = 1
∴ x²/(1)² + y²/(6)² = 1 ⇒ simplify
∴ x² + y²/36 = 1
* The standard form of the equation of the ellipse is x² + y²/36 = 1
9×4 - 10 fours - ? fours
Answer:
9×4 - 10 fours - 26 fours
Step-by-step explanation:
9×4 - 10 fours - 26 fours
Does anyone mind giving me a hand answering this question?
Answer:
A. x = 4
B. ∠C = 80°
Step-by-step explanation:
A.The sum of interior angles in a pentagon is 540°. We can write an equation for the sum of angles using this fact. Clockwise from lower left, we have ...
140° +(20x)° +100° +(16x +16)° +(160 -5x)° = 540°
31x +416° = 540° . . . . . . collect terms
31x = 124° . . . . . . . . . . subtract 416°
x = 4
__
B.The measure of angle C is found by substituting the value of x into the given expression for angle C.
(16x +16)° = (16(4) +16)° = 80°
Angle C is 80°.
_____
Additional comment
It can be useful to remember that the sum of interior angles of an n-gon is ...
(180°)(n -2)
This can be derived from the fact that the sum of exterior angles is always 360°.
These relations apply to convex polygons. YMMV when there are reflex angles or when sides cross each other.
Choose the correct graph of the function y=√x+2 .
Answer:
[D]
Step-by-step explanation:
Graph using the end point and a few selected points.
x y
0 2
1 3
2 3.41
Graph is below:
[RevyBreeze]
Miko has 3 cakes.
She cuts each cake into 4 equal pieces.
How many pieces of cake does Miko have?
Answer:
12 pieces of cake
Step-by-step explanation:
4 pieces for each cake
there is a total of three cakes
needed to find total pieces of cakes
multiply 4 by 3 and you will get 12 pieces of cake.
Answer:
Miko has 12 pieces of cake
The diameter of a circle is 12 ft. Find its area to the nearest whole number. Answer: A =
Answer:
113 ft²
Step-by-step explanation:
π = 3.14
r = 6
Use the formula for the area of a circle:
A = πr²
A = 3.14*6²
A = 3.14*36
A = 113.04
A = 113
Hope this helps :)
Answer:
Area = 113 ft²
Step-by-step explanation:
The formula to find the area of a circle is:
Area = π × r²
r is the radius that can be found by taking half of the diameter.
r = [tex]\frac{12}{2}[/tex] = 6
Area = π × 6²
Area = π × 36
Area = 113.09 = 113 [ to the nearest whole number ]
A 22° B 54° С What is the measure of AD? O 108° 0 27° 126 54°
Answer:
A. 108
sorry if im wrong but if u am I'm so sorry
Please help me ASAP
I will mark brainliest!
Answer:
please report my answer
Step-by-step explanation:
I want my account deleted
Answer:
17
Step-by-step explanation:
16+17+18=51
I knew the highest number had to be lower than 20. So I did 17+18+19. That didn't work but noticed it was close to 51. Tried 16+17+18 and it equals 51 :)
Jemima was arranging 400 packets of biscuits for a sale. She put 52 packets into a basket and displayed 25% of the remaining packets on the shelves. What percentage of all the packets of biscuits did Jemima display on the shelves?
Answer:
87% of all the packets of biscuits Jemima displayed on the shelves.
Step-by-step explanation:
400-52=348
so, 348*25%
348*25/100
87
Each of students reported the number of movies they saw in the past year. Here is what they reported.
11,6 ,9 ,16 ,12 ,18 ,14
Find the mean number of movies that the students saw.
If necessary, round your answer to the nearest tenth.
Answer:
18+16+14+12+11+9+6=8686÷7=12.2812.28=13Answer:
12.3
Step-by-step explanation:
11+6 +9 +16 +12 +18 +14 =86
86/7 = 12.28571
Tenths is the place value of the digit that appears after the decimal. It represents the 1/10 position of the digit
(12.3) rounded to the nearest tenth.
An 18 ft. tree casts a 15 ft. long shadow as shown in the following figure.
Which of the following is the angle formed by the sun's rays and the ground?
A.30
B.40
C.50
D.60
Answer:
The answer should be C=50
Step-by-step explanation:
WARNING: For this high pointed question, we clearly state that if you do not achieve the goal of the inquirer, you will instantly be banned and will NOT be allowed to access our page anymore. Our team must ensure the quality of every answer.)
Question: The time is 1 o'clock. What are the next two times at which the hour and minute hands will be perpendicular?
The next two times at which the hands of the clock will be perpendicular are at 1:20 and at 1:50.
When will the hands be perpendicular?The two hands will be perpendicular when the angle between them is 90°. Remember that every 5 minutes that the minute clock moves, there is an angle of 30°.
Each hour that the hour hand moves, there is an angle of 30°.
The first time that we will have an angle of 90° between the hands is at:
1:20
Because the minute hand is at an angle of -30° with respect to the x-axis at 20 minutes, and the hour hand is at an angle of 60° at 01.
The next time will be when the minute clock moves another 30 minutes (half the circle) and this will be at 01:50.
If you want to learn more about angles, you can read:
https://brainly.com/question/17972372
Find the Perimeter
Length - 152 cm
Breadth- 120 cm
Step-by-step explanation:
Perimeter=2(l+b)
=2(152+120)
=544 cm