Solve the following system of equations.
5x - 4y= -16
2x+9y=-17

(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?

Answer:

A

Step-by-step explanation:

[tex]y = \frac{9}{4}x - 8 \\\\y = \frac{9}{4}x +\frac{9}{4} \\\\\frac{9}{4}x - 8 = \frac{9}{4}x +\frac{9}{4}\\\\-8 = \frac{9}{4}\\[/tex]

This equation is incorrect, therefore there are no solutions.

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:

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

Answer:

Step-by-step explanation:

In ratio and proportion , when we compare two ratios or we can say two fractions then they are said to be equivalent when both of them are same.

Answer:

19/24m-1/3

Step-by-step explanation:

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:

F. side-angle-side

Step-by-step explanation:

the answer is F because side AB is congruent to CB (side)

the angle is given that m<ABD is 90 degrees which also means m<CBD is also 90 degrees. (angle)

segment BD is a reflexive property (side)

Answer:

x=5

hope it helps

if u want to check use Pythagoras theorem

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:

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:

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:

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:

15 nickels

Step-by-step explanation:

Choose variables:  n = number of nickels,  d = number of dimes.

There are two pieces of information given:

There are 45 coins, so  n + d = 45.

The total value is $3.75 (let's use cents in order to avoid decimals), so

5n + 10d = 375

Solve the first equation for d by subtracting n from both sides.

d = 45 - d

Substitute this expression for d in the value equation:

5n + 10(45 - n) = 375  See? The only variable is now  n!

Distribute the 10 (multiply).

5n + 450 - 10n = 375

450 - 5n = 375

-5n = -75

n = 15

There are 15 nickels.

Answer:

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

Step-by-step explanation:

[tex] \huge\mathrm{Answer࿐}[/tex]

diameter of the semi - circle = 10 ft

Measure of curved segment = π r

Perimeter :

_____________________________

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

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.

Answer:

5/3

Step-by-step explanation:

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

Answer: 45

Step-by-step explanation:

Answer:

One way is to make a factor tree. She below for examples.

Step-by-step explanation:

Answer:

You basically just count jumps of that number

Answer:

Step-by-step explanation:

The vote goes half and half:  7 draw, 7 other activities.

Half and half of 20 students works out to 10 draw, 10 engage in other activities.

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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Answer: 24

Step-by-step explanation:

2/5 times 60 = 24

of means to multiply.

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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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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Answer and Step-by-step explanation:

Yes, this is a statistical question.

Because it is asking the amount of hours of television people in a town watches every day, so it would be a ratio of hours per day for tv.

#teamtrees #PAW (Plant And Water)

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