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Ugo [173]
3 years ago
12

In circle O, SU is a diameter. Circle O is shown. Line segment S U is a diameter. Line segments R O and T O are radii. Points R

and T are between points S and U. Angles S O R and T O U are congruent. Angle R O T is (13 x + 15) degrees and angle T O U is (9 x + 5) degrees. What is mArc S T? 100° 108° 130° 160°

Mathematics
2 answers:
Finger [1]3 years ago
8 0

Answer:

130°

Step-by-step explanation:

See the attached diagram.

Given that ∠ ROS = ∠ TOU = 9x + 5

Again, ∠ ROT = 13x + 15.

Therefore, 13x + 15 + 2 (9x + 5) = 180

⇒ 31x + 25 = 180

⇒ 31x = 155

⇒ x = 5

Hence, ∠ SOT = ∠ SOR + ∠ ROY = 9x + 5 + 13x + 15 = 22x + 20 = 130°  

(Answer)

shusha [124]3 years ago
5 0

Answer:

130 on edge

Step-by-step explanation:

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A carton of 24 bottles of sports drink costs $16. How many bottles of sports drink can you get
MrRa [10]

Answer:

8

Step-by-step explanation:

24 bottles = 16 dollars!

? bottles = 12 dollars

Note:

In these type of Questions, find out  any dollars you could get with 1 bottle

or in simple terms, (first find the unit Rate)

<em>24/16 = 1.5</em>

1 bottle = 1.5 dollars

? bottles = 12 Dollars?

12/1.5

= 8

<h2>I hope that helps! </h2><h3>Have a wonderful day! </h3>
8 0
3 years ago
Find the vertex of the graph of the function.
lapo4ka [179]

Answer: The correct options are  (1) (5,10), (2) (3,-3), (3) x = -1, (4) y=(x+2)^2+3, (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

f(x)=a(x-h)^2+k        .....(1)

Where,  (h,k) is the vertex of the parabola.

(1)

The given equation is,

f(x)=(x-5)^2+10

Comparing this equation with equation (1),we get,

h=5 and k=10

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

f(x)=3x^2-18x+24

f(x)=3(x^2-6x)+24

To make perfect square add (\frac{b}{2a})^2, i.e., 9. Since there is factor 3 outside the parentheses, so subtract three times of 9.

f(x)=3(x^2-6x+9)+24-3\times 9

f(x)=3(x-3)^2-3

Comparing this equation with equation (1),we get,

h=3 and k=-3

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

f(x)=4x^2+8x+7

f(x)=4(x^2+2x)+7

To make perfect square add (\frac{b}{2a})^2, i.e., 1. Since there is factor 4 outside the parentheses, so subtract three times of 1.

f(x)=4(x^2+2x+1)+7-4

f(x)=4(x+1)^2+3

Comparing this equation with equation (1),we get,

h=-1 and k=3

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

y=x^2+4x+7

To make perfect square add (\frac{b}{2a})^2, i.e., 2^2.

f(x)=x^2+4x+4+7-4

f(x)=x^2+4x+4+7-4

f(x)=(x+2)^2+3

Therefore, the correct option is  4.

(5)

The given equation is,

h=-16t^2+672t

It can be written as,

h=-16(t^2-42t)

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

x=\frac{b}{2a}

x=\frac{42}{2}

x=21

Therefore,  after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

f(x)=3x^3-12x^2-15x

f(x)=3x(x^2-4x-5)

Use factoring method to find the factors of the equation.

f(x)=3x(x^2-5x+x-5)

f(x)=3x(x(x-5)+1(x-5))

f(x)=3x(x-5)(x+1)

Equate each factor equal to 0.

x=0,-1,5

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0
3 years ago
An engineer on the ground is looking at the top of a building. The angle of elevation to the top of the building is 22°. The eng
Pavlova-9 [17]
Let the distance from the engineer to the base of the building be x, then
tan 22 = 450/x
x = 450/tan 22 = 1,113.79

Therefore the distance from the engineer to the base of the building to the nearest foot = 1,114 feet
5 0
3 years ago
Please answer !!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!!!!!
xxTIMURxx [149]
Since it is a right angle you would subtract 57 from 90 because both angles added together are 90°. 90-57= 33°
8 0
3 years ago
(3x^3)^2 <br><br> A. 3x^6 <br> B. 9x^5 <br> C. 6x^6<br> D. 9x^6 <br><br> (PLEASE HELPP!!!)
Savatey [412]

Question: Simplify:     (3x^3)^2    

Step by Step:

STEP 1 : Equation at the end of step 1

(3x³)²

STEP2:

2.1    x³ raised to the 2 nd power = x( 3 * 2 ) = x⁶

Answer: 3²x⁶

Hope it Helps.

4 0
3 years ago
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