Rectangular garden measures 31 feet by 41 feet. surrounding the garden is a path 4 feet wide find the area of this path

Answer:

Step-by-step explanation:

Let Kayla made number of 2 points shots = x

and the number of 3 points shots = y

Since she made total nine shots so the equation will be

x + y = 9 --------(1)

She scores a total of 22 points so the equation will be

2x + 3y = 22 --------(2)

Now we multiply equation (1) by 2 and subtract it from equation (2)

(2x + 3y) - 2(x + y) = 22 - 18

2x + 3y - 2x - 2y = 4

y = 4

from equation (1)

x + 4 = 9

x = 5

Therefore, number of 2 shots are 5 and number of 3 shots are 4.

The annual rate of decay is r = 0.87

We know that if a quantity has a half-life of T, then the rate of decay must be such that:

r^T = 0.5

This means that when a time T passes, the original quantity becomes half of what it originally was.

In this case we know that the half-life is T = 5 years, then we have:

r^5 = 0.5

r = 0.5^(1/5) = 0.87

Then the annual rate of decay is r = 0.87, and if the initial quantity is 18 grams, we can write the exponential decay as:

f(t) = 18g*(0.87)^t

If you want to learn more about exponential decays, you can read:

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Answer:

13%

Step-by-step explanation:

I took the test on edge and got it right

Answer:

Step-by-step explanation:

1/2 * 8 * 15 * x=3360 c^3

x = 56 units

Answer:

52%

Step-by-step explanation:

There are 25 filled in squares in the first image, and 13 filled in squares in the second image.

To find the percentage we can divide the part of the base (a) by the base (b).

a = 13

b = 25

13/25 = 0.52

Move the decimal two places over to the right.

We have: 7 = 2 × 3 + 1

Answer: 3

Ok done. Thank to me :>

Answer:

9

Step-by-step explanation:

5+4=9

Answer:

D

Step-by-step explanation:

(7+8)*3

Answer:

Yes, the statement is true

Btw, it's an angle not angel

Please mark as brainliest

Answer:

that is True.

Answer:

[tex]\large{\boxed{\sf Chord = 8cm }}[/tex]

Step-by-step explanation:

First see figure in attachment . As we know that ,Perpendicular from centre of the circle bisects the chord . Hence here ,

[tex]\sf\qquad\longrightarrow AB = 2AC = 2x [/tex]

Now in ∆OAC , by Pythagoras Theorem , we have ;

[tex]\sf\qquad\longrightarrow (5cm)^2= x^2+(3cm)^2\\ [/tex]

[tex]\sf\qquad\longrightarrow 25cm^2=x^2+9cm^2\\[/tex]

[tex]\sf\qquad\longrightarrow x^2=25cm^2-9cm^2\\[/tex]

[tex]\sf\qquad\longrightarrow x^2=16cm^2\\ [/tex]

[tex]\sf\qquad\longrightarrow \pink{ x = 4cm } [/tex]

Therefore , the length of chord will be ,

[tex]\sf\qquad\longrightarrow AB = 2x \\ [/tex]

[tex]\sf\qquad\longrightarrow AB = 2(4cm)\\[/tex]

[tex]\sf\qquad\longrightarrow \pink{ AB = 8cm } [/tex]

Hence the length of chord is 8cm .

Answer:

A.600

B.980

C.350

D.210

Step-by-step explanation:

just see what the arrow

Answer:

C) 3.5 hours

Step-by-step explanation:

30 minutes is a half of an hour.

So that would be seven halves of an hour.

If we multiply the amount of halves by the amount of day late we get our answer.

0.5 x 7 = 3.5

Or we could simply add 0.5 seven times.

Answer:

2 2/3

Step-by-step explanation:

Since we only know how much milk we have we will disregard the flour. That leaves us with 4 cups of milk total and 1 1/2 cups of milk per serving. Simply divide 4 by 1 1/2 to get your answer of 2 2/3. Now, if they only want full servings, then the answer would be 2.

Solution:

Given:

Let's represent the number of oranges and grapefruits by the letters o and g.

This means that...

Now, let's solve the expression to find out how much does Dion has to pay.

Substituting o and g with the given values:

We also know that Dion gave a $20. To find the change, subtract the money Dion gave with the money required to pay for the fruits.

Thus, Dion got $13.85 as change.

The factors of the polynomial equation by complete the statements about factoring by grouping are,

[tex](2x-1)\\(7x+3)[/tex]

The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.

To find the factor of a polynomial, make the groups of the equation, and equate them equal to zero.

The provided polynomial equation is,

[tex]14x^2+ 6x - 7x - 3[/tex]

Rearrange the equation,

[tex]14x^2- 7x + 6x - 3[/tex]

Take out the common terms 7x from the first two terms and 3 from the last two terms.

[tex]7x(2x- 1) + 3(2x - 1)\\(2x-1)(7x+3)[/tex]

Thus, the factors of the polynomial equation by complete the statements about factoring by grouping are,

[tex](2x-1)\\(7x+3)[/tex]

Learn more about factor of polynomial here;

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Answer:

True, 52-2 equals 50, 50 is greater than 6.

Step-by-step explanation:

i hope my answers are ✅.......

Answer:

2 time greater

Step-by-step explanation:

5x20=100

10x20=200

100x2=200

so its 2 times greater

Answer:

  x = 1 +√5

Step-by-step explanation:

There are different formulas for the area of a triangle available, depending on the given information.

When two sides and the angle between them are given, the relevant area formula is ...

  Area = 1/2(ab)sin(C)

When the base and height of a triangle are given, the relevant area formula is ...

  Area = 1/2bh

The problem statement tells us the two triangles shown have equal areas. That means the two formulas will give the same result.

  Area from angle = Area from base/height

  1/2(x·x)sin(30°) = 1/2(x-2)(x+1)

  x² = 2(x² -x -2) . . . . . . . . . . . use sin(30°) = 1/2, multiply by 4

  x² -2x -4 = 0 . . . . . . . . subtract x², eliminate parentheses

  (x -1)² = 5 . . . . . . . . . add 4+1 to complete the square

  x = 1 ± √5 . . . . . . take the square root, add 1

The value of x must be greater than 2 in order for the triangle side lengths to be positive. (x-2 > 0) This means x = 1-√5 is an extraneous solution.

The value of x is 1 +√5.

Answer:

Step-by-step explanation:

Here it's given that a 6m ladder is leaned against a house, and the base of ladder is 2m away from the foot of the house. Here I am assuming x to be the height of the house.

Diagram :-

[tex] \begin{picture}(3,3)\setlength{\unitlength}{1cm} \linethickness{.6mm}\put(0,0){\line(1,0){4}}\put(0.01,0){\line(4,3){4}}\put(4,0){\line(0,1){3}}\put(4.3,1){$\bf x $} \put(2,-0.5){$\bf 2m$}\put(1,1.5){$\bf 6m$}\put(.9,0.2){$\bf\theta $}\put(2,4){$\boxed{\sf - RISH4BH }$}\end{picture} [/tex]

Using, Pythagoras theorem ,

[tex]\longrightarrow h^2=p^2+b^2 [/tex]

Substitute,

[tex]\longrightarrow (6m)^2=x^2+(2m)^2[/tex]

Simplify,

[tex]\longrightarrow 36m^2= x^2+4m^2 [/tex]

Subtracting 4m² on both sides,

[tex]\longrightarrow x^2 = 36m^2 -4m^2=32m^2 [/tex]

Put square root on both sides,

[tex]\longrightarrow x =\sqrt{32m^2}[/tex]

Simplify,

[tex]\longrightarrow \underline{\underline{ x = 5.65\ m}}[/tex]

Again in order to find out the angle of elevation,

[tex]\longrightarrow cos\theta =\dfrac{b}{h} [/tex]

Substitute,

[tex]\longrightarrow cos\theta =\dfrac{2m}{6m}[/tex]

Simplify,

[tex]\longrightarrow cos\theta =\dfrac{1}{3} [/tex]

Take cos inverse both sides,

[tex]\longrightarrow \underline{\underline{\theta =cos^{-1}\bigg(\dfrac{1}{3}\bigg)}}[/tex]

The length of the wall is 5.66m and the angle of elevation is 70.56°

Data;

To calculate the length of the wall or side of the house, we have to use Pythagorean theorem which is given as

[tex]x^2 = y^2 + z^2[/tex]

Let's substitute the values and solve for the length of the wall

[tex]x^2 = y^2 + z^2 \\6^2 = 2^2 + z^2 \\36 = 4 - z^2\\z^2 = 36 - 4\\z^2 = 32\\z = \sqrt{32} \\z = 5.66m[/tex]

The length of the wall is 5.66m.

To calculate the angle of elevation, we can use trigonometric ratio SOHCAHTOA

since we have the value of all the sides, we can decide to use any of the ratios.

I will use sine angle to solve for the angle of elevation.

[tex]sin \theta = \frac{opposite}{hypothenuse} \\sin \theta = \frac{5.66}{6} \\sin \theta = 0.943\\\theta = sin^-^1 (0.943)\\\theta = 70.56^0[/tex]

The angle of elevation is 70.56°

Learn more on Pythagorean theorem and trigonometric ratio here;

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Answer:

The area of the circular park is about 1017.88

Step-by-step explanation:

First, we recall the area of a circle.

A=  πr^2

Next, we plug in the radius

A=  π*18^2

A=  π*324

A= 1017.88

To conclude, that is how you find the area of a circular park.

x is 9

Okay bye  bye

:9 :O)

Answer:

y = 4

Step-by-step explanation:

======================================================

Explanation:

Use the distance formula to calculate the distance from R to S. This is identical to the length of segment RS.

[tex]R = (x_1,y_1) = (-3,-1) \text{ and } S = (x_2, y_2) = (0,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-0)^2 + (-1-3)^2}\\\\d = \sqrt{(-3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

Segment RS is exactly 5 units long.

-----------------------

Repeat similar steps to find the length of segment ST

[tex]S = (x_1,y_1) = (0,3) \text{ and } T = (x_2, y_2) = (3,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-3)^2 + (3-0)^2}\\\\d = \sqrt{(-3)^2 + (3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d \approx 4.2426\\\\[/tex]

ST is roughly 4.2426 units long.

------------------------

Lastly, let's calculate the length of segment TR.

[tex]T = (x_1,y_1) = (3,0) \text{ and } R = (x_2, y_2) = (-3,-1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-3))^2 + (0-(-1))^2}\\\\d = \sqrt{(3+3)^2 + (0+1)^2}\\\\d = \sqrt{(6)^2 + (1)^2}\\\\d = \sqrt{36 + 1}\\\\d = \sqrt{37}\\\\d \approx 6.0828\\\\[/tex]

TR is about 6.0828 units long.

------------------------

Summary of the segment lengths:

The three sides are different lengths.

Therefore, the triangle is scalene.

Answer: D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Which fractions

Step-by-step explanation:

Answer:

1+1/4

Step-by-step explanation:

Subtract 7/8 from both sides of the equation

so 2-3/4=5/4