Find an equation of the line passing through each of the following pairs of points (−3, 1), (0, 3)

Answer:

0.01x+45>0.05x+10

Step-by-step explanation:

Let g represent the number of gloves purchased and h represent the number of hats purchased.

The gloves cost $12 and a hat costs $8

We need to write an inequality that represents this situation.

Cost of gloves = $12g

Cost of hats = $8h

No more than $56 means [tex]\le 56[/tex].

We can write the inequality as follows :

[tex]12g+8h\le 56[/tex]

Hence, this is the required solution.

Answer:

330

Step-by-step explanation:

heart = 110, and the problem is asking the value of 3 hearts. 3 x 110 = 330

Answer:

d: 330

Step-by-step explanation:

spade  = heart*2

spade-heart = 110

substitute spade into spade:

2*heart-heart = 110

heart = 110

So,

heart = 110

and,

spade = 2*heart = 2*110 = 220

so spade+heart = 220 + 110 = 330

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Area:-

Answer:

[tex]A=\boxed{10.5}\; \;\rm sq. \; un.[/tex]

Step-by-step explanation:

Area of a Trapezoid

[tex]\boxed{A=\dfrac{1}{2}(a+b)h}[/tex]

where:

From inspection of the given diagram:

Substitute the found values into the formula and solve for A:

[tex]\implies A=\dfrac{1}{2}(2+5)(3)[/tex]

[tex]\implies A=\dfrac{1}{2}(7)(3)[/tex]

[tex]\implies A=\dfrac{7}{2}(3)[/tex]

[tex]\implies A=\dfrac{21}{2}[/tex]

[tex]\implies A=10.5\; \;\rm sq. \; un.[/tex]

The volume of the resulting cone is equal to 50 [tex]m^3[/tex].

Given the following data:

Mathematically, the volume of a cone is given by this formula:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where:

Applying the dilation factor, we have:

[tex]V =(\frac{1}{3} )^3 \times 1350\\\\V=0.037037037 \times 1350[/tex]

V = 50 [tex]m^3[/tex].

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(a) ∠ORP and ∠ORN are a linear pair .

Let us prove that option a , is the correct option by finding the value of x .

Angle ORP and angle ORN are a linear , which means their sum will be equal to 180° .

So :-

[tex]80 + 3x + 10 = 180[/tex]

[tex]3x + 80 + 10 = 180[/tex]

[tex]3x + 90 = 180[/tex]

[tex]3x = 180 - 90[/tex]

[tex]3x = 90[/tex]

[tex]x = \frac{90}{3} [/tex]

[tex]x = 30°[/tex]

As we were able to find put the value of x only after we cam to know that ∠ORP and ∠ORN are a linear pair , we say that option a is the correct statement .

Therefore , the correct answer is :-

(a) ∠ORP and ∠ORN are a linear pair .

The value of x is equal to 30°. Hence, proved.

Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line. Angles on a straight line add to 180°.

Given that, m∠ORP=80° and m∠ORN=(3x+10)°.

Here, m∠ORP+m∠ORN=180° (Angles on straight line adds upto 180°)

80°+(3x+10)°=180°

90°+3x=180°

3x=90°

x=90°/3

x=30°

Hence, proved.

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Answer:

y = 6x - 2

Step-by-step explanation:

y = mx + b

y = 6x + (-2)

Applying the definition of a parallelogram, the value of x in the length of the sides of the given parallelogram is: x = 3.

A parallelogram is a quadrilateral that has two pairs of opposite sides that are congruent to each other.

Given the following:

Find x by creating an equation:

PQ = RS (congruent sides)

Substitute

9x + 1 = 13x - 11

Combine like terms

9x - 13x = -1 - 11

-4x = - 12

x = 3

Therefore, applying the definition of a parallelogram, the value of x in the length of the sides of the given parallelogram is: x = 3.

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Answer:

It would be 6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

5x + 2 - 7x = -10

Combine the two x's:

-2x + 2 = -10

Subtract 2 from both sides:

-2x = -12

Divide both sides by -2:

x = 6

Answer:

Step-by-step explanation:

Answer:

I believe you just subtract 845.67ml - 243.36 which is equal to 602.31

Step-by-step explanation:

Answer:

2.6x

Step-by-step explanation:

Answer:

2.6

Step-by-step explanation:

Answer:  5

Step-by-step explanation:

The x-coordinate of the midpoint of the segment is the average of the x-coordinates of the two endpoints.

Therefore, the x-coordinate of the midpoint of AB is the average of the x-coordinate of A and the x-coordinate of B.

We are given that the x-coordinate of A is 62 and of B is -42.

The average of 62 and -42 = (62-42)/2 = 10/2 = 5

Answer:

b. {(2, 1), (3, 1) (4, 3), (5, 3)}

The required solution to the given inequality is x > 16, as shown in the graph.

In mathematics, an inequality is a statement that two values or expressions are not equal. An inequality uses one of the comparison symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to). For example, "x + 3 < 10" is an inequality that states that the value of x plus 3 is less than 10.

Here,
As mentioned in the question,
To graph, the solution of the inequality (x+8) > 2 (2.0 + 10).

Simplifying the given inequality:
(x+8) > 2 (2.0 + 10)

x+ 8 > 2(12)
x > 24 - 8
x > 16

Thus, the required solution to the given inequality is x > 16.

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answer: 2, 3, 5, 7

Answer:

8

Step-by-step explanation:

There are several groups so there can't be just one. And the lowest number needed for a group is 4. So the minimum amount of people to participate would have to be 8.

Answer:

16.67

Step-by-step explanation:

5/30 = 1/6

1/6 x 100 = 100/6

100/6 simplified is 16.67

Answer:

Use PEMDAS

Step-by-step explanation:

P-parenthesis ( )

E-Exponent

M-Multiplication *

D-Division /

A- Addition+

S-Subtraction -

so, first you would do 30 * 100= 3000

Then, you would do 5/3000=???

Answer:

4,500

Step-by-step explanation:

Answer:

..

Step-by-step explanation:

Answer:

3;8

Step-by-step explanation:

Answer: ss*$7.50 + aa*$11 ≥ $990.

Step-by-step explanation:

We have two variables:

aa = # of adult tickets sold.

ss = # of student tickets sold.

The total profit is:

P = ss*$7.50 + aa*$11

And we want P ≥ $990.

Then we can write the inequality:

ss*$7.50 + aa*$11 ≥ $990.

Now, we have only one equation and two variables, so there are a lot of possible solutions for this system.

Answer:

c

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

When converting radical expressions to rational exponents the exponent on the radicand (1) becomes the numerator of the rational exponent, and the index/root of the radical (4) becomes the denominator of the rational exponent. (1/4)

Answer: (x,y)→(−x,−y)

Step-by-step explanation: The rule for a rotation by 180° about the origin is (x,y)→(−x,−y)

Answer:

C. Natural Numbers

Step-by-step explanation:

Before we determine what groups [tex]\sqrt{100}[/tex] fits into, we must simplify it.  We get the number 10, which is much easier to categorize.  Out of the four options, the natural numbers are the smallest group, containing only the numbers we use to count (i.e. 1, 2, 3, 4 ...).  We know that 10 fits into this category because 10 is a non-zero whole number.  Since the natural numbers contain 10 and are the smallest subset, the answer is C.

As a note: 10 will also fit into the whole numbers and rational numbers since all natural numbers are parts of these two groups as well.  These groups contain more numbers, however, making them larger than the natural number set so we can eliminate them.  10 is also not an irrational number since we can accurately define it with a fraction.

Answer:

A) x = -1

Step-by-step explanation:

[tex]f(-1)=3^{-1}=\dfrac13\\\\g(-1)=2(-1)+5=3\\\\\implies f(x) < g(x)[/tex]

[tex]f(2)=3^{2}=9\\\\g(2)=2(2)+5=9\\\\\implies f(x)=g(x)[/tex]

[tex]f(-3)=3^{-3}=\dfrac{1}{27}\\\\g(-3)=2(-3)+5=-1\\\\\implies f(x) > g(x)[/tex]

[tex]f(-4)=3^{-4}=\dfrac{1}{81}\\\\g(-4)=2(-4)+5=-3\\\\\implies f(x) > g(x)[/tex]

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π                →      A + B = π - C

                                                         A + C = π - B

                                                         B + C = π - A

Cofunction Identities:       sin [(π/2) - A] = cos A

                                          cos [(π/2) - A] = sin A

Sum to Product Identity:   sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]

Pythagorean Identity:       cos²A + sin²A = 1    →   cos²A = 1 - sin²A

Even/Odd Identity:           cos (-A) = -cos(A)

Double Angle Identity:     cos (2A) = 2 cos²A - 1

Proof LHS → RHS:

LHS:                      cos [(B + C) - A] - cos [(A + C) - B] + cos [(A + B) + C]

Given:                   cos [(π - A) - A] - cos [(π - B) - B]  + cos [(π - C) - C]

                         =  cos (π -2A) - cos (π -2B) + cos (π -2C)

Cofunction:          cos (-2A)  - cos (-2B) + cos (-2C)

Even/Odd:            -cos (2A) + cos (2B) - cos (2C)

Double Angle:     -(2cos²A - 1) + cos (2B) - cos (2C)

                           = 1 - 2cos²A + cos (2B) - cos (2C)

Sum to Product:    1 - 2cos²A - 2sin(B+C) · sin (B-C)

Given:                     1 - 2cos²A - 2sin (π - A) · sin (B - C)

Cofunction:             1 - 2cos²A - 2sin A · sin (B - C)

Pythagorean:         1 - 2(1 - sin²A) - 2sin A · sin (B - C)

                            = 1 - 2 + 2sin²A - 2sin A · sin (B - C)

                            =     -1 + 2sin²A - 2sin A · sin (B - C)

Factor:                        -1 + 2sin A (sin A - sin (B - C))

Given:                     -1 + 2sin A [sin (π - (B + C)) - sin (B - C)]    

Cofunction:             -1 + 2sin A [sin (B + C) - sin (B - C)]  

Sum to Product:      -1 + 2sin A [2 cos B · sin C]  

                               = -1 + 4sin A · cos B · sin C

LHS = RHS  [tex]\checkmark[/tex]