Find the equation of the line

Alex has five cups of strawberries and wants to use 1 3/4 cups of strawberries for a fruit salad and 3 1/2 cups for jam. Alex has enough strawberries to make both recipes.

To check if Alex has enough strawberries, we add the amount of strawberries needed for the fruit salad (1 3/4 cups) and the amount needed for the jam (3 1/2 cups)

1 3/4 cups + 3 1/5 cups

= 1 + 3/4 + 3 + 1/5

Multiplying 3/4 with 5/5 and 1/5 with 4/4 to make denominator equal

= 1 + 15/20 + 3 + 4/20

= 4 + 19/20

= 4 19/20 cups

4 19/20 is less than 5 cups. So Alex has enough strawberries for both recipes.

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The distance and bearing of the boat from its original location are about 183.33 miles, N71.97°E

A bearing is a description of the amount by which a north or south headed line is deflected in the eastern or western direction.

The initial direction in which the boat is traveling = Due east

The distance the boat travels in the direction due east = 130 miles

The distance the boat travels in the direction N38°E = 72 miles

Therefore;

The distance the boat has traveled from its original location is found using the law of cosines as follows;

The included angle between the 130 miles distance the boat travels east and the 72 miles distance the boat travels N38°E = 90° + 38° = 128°

Let d represent the distance of the boat from its original location, we get;

d² = 130² + 72² - 2 × 130 × 72 × cos(128°) ≈ 33609.1828181

d ≈ √(33609.1828181) ≈ 183.33

The distance of the boat from its original location is about 183.33 miles

Let the angle formed by the direction of the boat to its destination and the path the boat travels east, according to the law of sines, we get;

183.33/(sin(128°) ≈ 72/(sin(B))

(sin(B)) ≈ 72 × (sin(128°))/183.33

m∠B ≈ arcsin(72 × (sin(128°))/183.33) ≈ 18.03°

The bearing of the boat from its original location is; N(90° - 18.03°)E = N71.97°E

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Answer:

B, because dividing is the same thing as multiplying by the reciprocal

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

Two angles a, b are complentary if a+b = 90.

Therefore, 4x + (2x+6) = 90

6x + 6 = 90

6x = 84

x = 84/6 = 14.

Answer:

x=14°

Step-by-step explanation:

Complementary angles are angles that add to 90°.

4x+2x+6=90

add like terms

6x+6=90

subtract 6 on both sides

6x=84

divide 6 on both sides

x=14

x is 14°.

Answer:

[tex] - 4x > - 10 \\ x < 2.5[/tex]

Answer:

x=5

hope it helps

if u want to check use Pythagoras theorem

The phrase b2 - 4ac is referred to as the discriminant for the quadratic equation ax2 + bx + c = 0.

The phrase b2 - 4ac is known as the discriminant for the quadratic equation ax2 + bx + c = 0. How many roots f(x) has is shown by the discriminant's value: - The quadratic function has two unique real roots if b2 - 4ac > 0 A repeated real root exists in the quadratic function if b2 - 4ac = 0.

D=b2 - 4ac, discriminatory

The constant term c.

In mathematics, a discriminant is a parameter of an object or system that is calculated to help with its classification or solution. For the cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc 4b3 4a3c 27c2, while the discriminant for the quadratic equation ax2 + bx + c = 0 is b2 4ac.

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The required length of the side AC of the given right triangle is 32 units.

A right triangle is a triangle with one right angle or two perpendicular sides.

It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle.

The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.

A triangle is referred to be a right triangle when one of the interior angles is 90 degrees or a right angle.

So, using the hypotenuse AC as the point of convergence for the right triangle ABC,

AB is 8 and AD is 2.

Verify whether the triangle ΔABD resembles ΔACB.

∠ BCA = ∠ DBA (90 - ∠ DBC)

∠ A = ∠ A

As a result, ΔABD and ΔACB share an AAS resemblance.

Utilize the similarity property to determine the length of AC.

AC/AB = AB/AD

x / 8 = 8 / 2

x = 32

Therefore, the required length of the side AC of the given right triangle is 32 units.

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Correct question:

Given a right triangle, ABC with altitude BD drawn to hypotenuse AC. If AB = 8 and AD = 2, what is the length of AC?

(a) x² + 2xy - y² must be added to x² + xy + y² to get 2x² + 3xy. (b)  5a + b -6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16.

a)

Here we are given the expression x² + xy + y²

Now we need to add something so that this expression becomes x² + 3xy

Let the expression to be added be p.

Hence we get

x² + xy + y² + p = 2x² + 3xy

or, p = 2x² + 3xy - (x² + xy + y²)

or, p = 2x² + 3xy - x² - xy - y²

or, p = x² + 2xy - y²

Hence, x² + 2xy - y² must be added.

b)

Here we are given the expression 2a + 8b + 10

We need to subtract another expression to get -3a + 7b + 16

Let the expression be t. Hence we get

2a + 8b + 10 - t = -3a + 7b + 16

or, t = 2a + 8b + 10 - (-3a + 7b + 16)

or, t = 2a + 8b + 10 + 3a - 7b - 16

or, t = 5a + b - 6

Hence 5a + b - 6 must be subtracted,

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Correct Question

(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?

(b) What should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16?

Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.

What is an Algebraic expression ?

Algebraic expression can be defined as combination of variables , constants and exponents.

Radical expression, in which if the expression contains square root than it called as the radical expression.

Examples are  : - [tex]\sqrt{7}[/tex] , [tex]\sqrt{x}[/tex] and etc .

Rational exponent , in which it is in the form of p/q is called as the rational exponent .

Examples are :- 5/8 , 6/9,8/7 and etc .

Hence, Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.

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Answer:

19/24m-1/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Isolate the term of y from one side of the equation.

Add by 9.2 from both sides of an equation.

[tex]\sf{y-9.2+9.2=8.78+9.2}[/tex]

Solve.

Add.

8.78+9.2=17.98

[tex]\large\boxed{y=17.98}[/tex]

Therefore, the correct answer is y=17.98.

The measure of  angle B is m ∠B = 107°.

What is similar triangles?

Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects include all equilateral triangles and squares with any side length. To put it another way, if two triangles are similar, then their corresponding angles and sides are congruent and equal in size.

Given:   Δ NPZ ~ Δ HBZ

As the triangles NPZ and triangle HBZ are similar that means the corresponding angles are congruent.

⇒ ∠N = ∠H,  ∠P = ∠B,  ∠Z = ∠Z

Since,

∠P = (8x - 37)°,  ∠Z = 42°,  ∠H = (2x - 5)°

⇒ 2x - 5 = ∠H,  ∠B = 8x - 37,  Z = 42°

Since, the sum of three angles of triangle is 180°.

⇒              ∠H + ∠B + ∠Z = 180°

(2x - 5)° + (8x - 37)° + 42° = 180°

                10x - 42° + 42° = 180°

                                  10x = 180°

                                     x = 18°

So,

∠B = (8x - 37)° = 8(18) - 37 = 144 - 37 = 107°.

Hence, the measure of  angle B is m ∠B = 107°.

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Answer:

D

Step-by-step explanation:

It is exponential decay if it was growth then it would say 1+0.12 not 1-0.12

Answer:

your asking what is 9+x÷2? do you know what x is?

Step-by-step explanation:

I think it would be 4.5+x I'm a little confused. sorry I hope this helped!

Answer:

35/20 and 36/20

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

[tex]\frac{3x}{x-1}[/tex] + [tex]\frac{8}{x-1}[/tex]

These fractions have a common denominator and so do not require to be altered.

The numerators can be added to simplify, that is

= [tex]\frac{3x+8}{x-1}[/tex]

The remaining fractions have different denominators and would require to be altered before they could be added.

Answer:

(2P + G) feet/min

Step-by-step explanation:

Speed of the panda = P

Speed of the giraffe = P + G

Thus,

Speed of Panda + Speed of Giraffe = approaching time

= P + P + G

= 2P + G

Thus, The panda and the giraffe are approaching each other at a rate

of (2P + G) ft/min

Hope it helps :)

Answer:2p+g

Step-by-step explanation:

2+p+g=

2p+g

Answer:

Hi! Your answer is going to be the one with -1 (x) , 15 (y).

Step-by-step explanation:

This is a quadratic function, not a linear function. Hope this helps!

To graph the equation y = 1x / 2 + (-5), you will need to plot several points that satisfy the equation and then connect them with a line.

To do this, you can pick a few values of x, substitute them into the equation to find the corresponding values of y, and then plot these points on the coordinate plane.

For example, if you choose x = -2, the corresponding value of y is (-2) * (1 / 2) + (-5) = -5.5. If you choose x = 0, the corresponding value of y is (0) * (1 / 2) + (-5) = -5. And if you choose x = 2, the corresponding value of y is (2) * (1 / 2) + (-5) = -4.

You can then plot these points on the coordinate plane and connect them with a line to graph the equation.

Im really sorry that I was unable to provide a picture.  I hope this helped!

Answer:

Graph the line using the slope and y-intercept, or two points.

Slope:

1/2

y-intercept: (0,−5)

x   y

0 −5

2 −4

Step-by-step explanation:

Answer:

Find the distance of each segment

Step-by-step explanation:

Use the distance formula :

https://tutors.com/math-tutors/geometry-help/distance-formula#:~:text=The%20Distance%20Formula%20squares%20the%20differences%20between%20the,-%20y%201%29%20is%20the%20change%20in%20y.

add the lengths together

Hope this helps!!

x² + y² + 6x - 6y - 207 = 0 is the equation for the circle whose circumference has endpoints at (12, 3), and (-18, 3).

We are aware that a circle's general equation is (x - h)2 + (y - k)2 = r2, where (h, k) is its center and r is its radius.

Therefore, to bring the constant term to the righthand side of the equation, add 21 to both sides.

So, the midpoints of the diameter are determined by the coordinates of the circle's center since the endpoints of the diameter are (x1, y1) = (12,3) and (x2, y2) = (-18,3).

The midpoints are so:

x = (x₁ + x₂)/2 = (12 + (-18))/2 = (12 - 18)/2 = -6/2 = -3 and

y = (y₁ + y₂)/2 = (3 + 3)/2 = 6/2 = 3.

Consequently, the circle's center's coordinates are (-3, 3)

The circle's diameter:

The circle's radius is [(x1 - h)2 + (y1 - k)2], where:

(x₁, y₁) = coordinates of end of diameter = (12, 3) and

(h, k) = coordinates of center of circle = (-3, 3)

As a result, when we enter the values of the variables into r, we get:

r = √[(x₁ - h)² + (y₁ - k)²]

r = √[(12 - (-3))² + (3 - 3)²]

r = √[(12 + 3)² + 0²]

r = √[15² + 0²]

r = √15²

r = 15

The formula for the circle:

The formula for a circle with a center (h,k) is: (x - h)² + (y - k)² = r²

By changing the variables' values in the equation, we arrive at:

(x - h)² + (y - k)² = r²

(x - (-3))² + (y - 3)² = 15²

(x + 3)² + (y - 3)² = 15²

x² + 6x + 9 + y² - 6y + 9 = 225

x² + 6x + y² - 6y + 9 + 9 - 225 = 0

x² + y² + 6x - 6y - 207 = 0

Therefore, x² + y² + 6x - 6y - 207 = 0 is the equation for the circle whose circumference has endpoints at (12, 3), and (-18, 3).

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[tex] \huge\mathrm{Answer࿐}[/tex]

diameter of the semi - circle = 10 ft

Measure of curved segment = π r

Perimeter :

_____________________________

[tex]\mathrm{ \#TeeNForeveR}[/tex]

Answer:

5/3

Step-by-step explanation:

4 4/9 * 3/8 = 40/9 * 3/8 = 120/72 = 10/6 = 5/3

Answer:

18b^6

Step-by-step explanation:

3b⁴ x 6b²