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3 years ago

What is the measure of angle R?

Mathematics

2 answers:

luda_lava [24]3 years ago

7 0

The answer to the question is A

lakkis [162]3 years ago

6 0

A 68 since it is an = triangle

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Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ

In-s [12.5K]

PART A

The equation of the parabola in vertex form is given by the formula,

$y - k = a {(x - h)}^{2}$

where

$(h,k)=(1,-2)$

is the vertex of the parabola.

We substitute these values to obtain,

$y + 2 = a {(x - 1)}^{2}$

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.

$6 + 2 = a {(3 - 1)}^{2}$

$8= a {(2)}^{2}$

$8=4a$

$a = 2$
Hence the equation of the parabola in vertex form is

$y + 2 = 2 {(x - 1)}^{2}$

PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

$y + 2 = 2{(x - 1)}^{2}$

This implies that

$y + 2 = 2(x - 1)(x - 1)$

We expand to obtain,

$y + 2 = 2( {x}^{2} - 2x + 1)$

This will give us,

$y + 2 = 2 {x}^{2} - 4x + 2$

$y = {x}^{2} - 4x$

This equation is now in the form,

$y = a {x}^{2} + bx + c$
where

$a=1,b=-4,c=0$

This is the standard form

7 0

3 years ago

John’s mathematics teacher drew a triangle that had a 70° angle and a 20° angle. What is the measure of the third angle in the t

kari74 [83]

All triangles interior angles equal 180
So these 3 angles = 180

7 0

3 years ago

A parking lot covers 32,420 square feet. What is its area to the nearest thousand feet

alexira [117]

Number in the thousands place: 2
Number in the hundreds place: 4

Since 4<5, the number rounds down.
Final answer: 32,000

5 0

2 years ago

Caitlin makes candles and sells them in her online shop. Tall candles cost $8 each and short candles cost $5 each. last month, s

snow_tiger [21]

Answer:

tall candles = 39

Short candles = 52

Step-by-step explanation:

let tall candles be x

and short candles be y

No. Of candles sold = x + y =91

Money made from candles will be equal to = 8x + 5y = $572

These both are simultaneous linear equations.

x + y =91 ( multiply by 5)

5x + 5y = 455

8x + 5y = $572

Subtract them:

-3x = -117

x = -117/3

x = 39

put value of x in

x + y = 91

39 + y = 91

y = 91 - 39

y = 52

x shows tall candles so they are 39

y shows short candles so they are 52

3 0

2 years ago

Mrs Johnson has $110 to spend on parking will cost $12 and admission tickets will cost $140 per person including tax

Vaselesa [24]

The answer is Ms Hernandez can bring up to 6 people to the zoo.

x - the number of people that she can bring to the zoo

The parking will cost $7: a = 7

Admission tickets will cost $15.50 per person: b = 15.50x

She can spend on parking and admission tickets $100:

a + b ≤ 100

a = 7

b = 15.50x

7 + 15.50x ≤ 100

15.50x ≤ 100 - 7

15.50x ≤ 93

x ≤ 93 / 15.50

x ≤ 6

5 0

3 years ago