Solve for r. Round to the nearest tenth of a degree, if necessary. P 5 3.1 Q R​

Answer:

(4,1);(1,4)

Step-by-step explanation:

The point on the parabolic equation y = -x² + 4x + 1 and line y = -x + 5 intersect is P ( 4 , 1 ) and Q ( 6 , -1)

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the parabolic equation be y = -x² + 4x + 1

Let the equation of line be y = -x + 5

Now , To find the points of intersection between the parabola y = -x² + 4x + 1 and the line y = -x + 5, we need to set the two equations equal to each other and solve for x and y simultaneously.

Setting y = -x² + 4x + 1 equal to y = -x + 5, we get:

-x² + 4x + 1 = -x + 5

Rearranging the equation, we get a quadratic equation in standard form:

-x² + 4x + x - 1 - 5 = 0

-x² + 5x - 6 = 0

Factoring the quadratic equation, we get:

-(x - 1)(x - 6) = 0

Setting each factor equal to zero and solving for x, we get two potential values for x:

x - 1 = 0 or x - 6 = 0

x = 1 or x = 6

Now, substituting the values of x back into the equation y = -x + 5 to find the corresponding y-values, we get:

For x = 1:

y = -1 + 5

y = 4

So, one point of intersection is (1, 4)

For x = 6:

y = -6 + 5

y = -1

So, the other point of intersection is (6, -1).

Hence , the point of intersection is P ( 4 , 1 ) and Q ( 6 , -1)

To learn more about parabola click :

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Answer:

Step-by-step explanation:

it does not show the problem

Answer:

5/12 x 2/3 = 10/36 = 5/18 foot2

Answer:

0.7 repeating is 7/9

0.04 repeating is 4/99

4.45 repeating 4 4/11

2.19191919...... is 2 19/99

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

x^2-11x=-24

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is a classic proof of the Pythagorean Theorem!

Pythagorean theorem is a^2 + b^2 = c^2. With a square, its area is its side length squared. Therefore, if we think about this as squares, then the sum of the area of square X and square Y will be equal to the sum of square Z.

Looking at your answer choices, the best option is C - The number of tiles needed to cover Region Z is the same number of tiles needed to cover both Region X and Region Y.

Hope this helps!! :)

Answer:

A

Step-by-step explanation:

Answer:

403100 is the answer.Hope this helps

Answer:

SOLUTION:  

The volume V of a prism is V = Bh, where B is the

area of a base and h is the height of the prism.  

The volume is ====  108 cm3

.

Step-by-step explanation:

Answer:

if one of the angles is 90°

Step-by-step explanation:

when it has an angle that is 90° that means that it is a right triangle

let me know if you need more b/c I wasn't sure whether to make it more advanced for middle school lol

Hope this helps! :)

Answer: 2 ounces

Step-by-step explanation:

Since Juan and Bill share a 12-ounce bucket of clay and Juan used 1/6 of the bucket, the quantity used by Juan will be:

= 1/6 × 12

= 2 ounce bucket of clay.

On the other hand, Bill used 2/3 of the bucket of clay. The quantity used will be:

= 2/3 × 12

= 8 ounce

Therefore, the quantity they both used will be:

= 2 ounce + 8 ounce

= 10 ounces.

The ounces left in the bucket will be:

= 12 ounces - 10 ounces

= 2 ounces

Answer:

1/3 n - 3 > 6; n = 9

Step-by-step explanation:

1/3(9) - 3 > 6

3 - 3 > 6

0 > 6

Answer:

£40

Step-by-step explanation:

3+5=8

160÷8= 20

20× 5=100

20×3=60

100-60=40

Answer:

£40

Step-by-step explanation:

160 shared between 3:5

3 + 5 = 8 (parts)

160 ÷ 8 = 20

20 = 1 part

Sue has 3 parts; (20 x 3) = £60

Oliver has 5 parts; (20 x 5) = £100

Work out how much more oliver get conpared to sue

oliver has £100, sue has £60

£100 - £60 = £40

oliver has £40 compared to sue

Answer: 40%

Step-by-step explanation:

I took the k12 test lol

Answer:

Step-by-step explanation:

missing angle is 113 degree because the relation between 113 degree and missing angle is that they are alternate interior angle and alternate interior are always equal.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the number line is not given. The general explanation is as follows;

First, record the time she hung up (say, time = x)

To rewind 15 minutes back means, x - 15

So, point on the number line will be x - 15

Take for instance

[tex]x = 45[/tex]

The point on the number line will be:

[tex]x - 15 = 45 - 15[/tex]

[tex]x - 15 = 30[/tex]

See attachment for illustration

Answer:

Option 1

Flood

Step-by-step explanation:

As she lives next to the river heavy rains can cause the water to overflow

Answer:

Step-by-step explanation:

The line crosses with y-axis when x = 0:

The y-intercept is the required point and its coordinates are (0, 7)

-12u+168b is the answer

Answer:

90° angle

Step-by-step explanation:

Every time you see an angle that has a box, it measures 90°

Answer:

d . 9 ^ 2

Step-by-step explanation:

9 ^ 3 *  9 ^ 4    /  9 ^ 5

=   81

= 9 ^  2

so the answer is D

Mark brainliest

[tex]d. \: {9}^{2} [/tex] ✅

Step-by-step explanation:

[tex] \frac{ {9}^{3} \times {9}^{4} }{ {9}^{5} } \\ = \frac{ {9}^{3 + 4} }{ {9}^{5} } \\ = \frac{ {9}^{7} }{ {9}^{5} } \\ = {9}^{7 - 5} \\ = {9}^{2} [/tex]

Note:-

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

B is correct

Step-by-step explanation:

Answer:

29 in.²

Step-by-step explanation:

2 in. × 2 in. = 4 in.²

3 in. × 5 in. = 15 in.²

2 in. × 5 in. = 10 in.²

4 in.² + 15 in.² + 10 in.²

29 in.²

Answer:

You can use the definite integral to find the volume of a solid with specific cross sections on an interval, provided you know a formula for the region determined by each cross section. If the cross sections generated are perpendicular to the x‐axis, then their areas will be functions of x, denoted by A(x). The volume ( V) of the solid on the interval [ a, b] is

Answer:

No

Step-by-step explanation:

0.002 has one extra zero making it smaller than 0.02

Answer:

Step-by-step explanation:

.02 is the same thing as [tex]\frac{2}{100}=\frac{1}{50}[/tex]

.002 is the same thing as [tex]\frac{2}{1000}=\frac{1}{500}[/tex]

so, no, they are not equivalent.

Answer:

x = 16

Step-by-step explanation:

The given angles are alternate angles and are congruent , then]

10x - 23 = 137 ( add 23 to both sides )

10x = 160 ( divide both sides by 10 )

x = 16

Answer:

Area

4 and width 8 equals 32

Perimeter

length 4 and width 8 equals 24

Area

length 20 and width 22 equals 440

Perimeter

length 20 and width 22 equals 88

Area

length 12 and width 8 equals 96

Perimeter

length 12 and width 8 equals 40

Area

length 15 and width 20 equals 300

Perimeter

length 15 and width 20 equals 70

Isn't this what you are asking for or is it something else. I hope this helps, If I did the answer wrong tell me and I will change it

Answer:

x = 61

Step-by-step explanation:

These 2 angles are supplementary which means they add up to 180:

2x - 6 + x + 3 = 180

3x - 3 = 180

3x = 183

x = 61