Find an equation for the line with the given properties. Express the equation in slope-intercept form.
Containing the points P = (-3,1) and Q = (-1,0). What is the equation of the line?
y =

Answer:

What was the average temperature change per hour -3 degrees per hour​

Step-by-step explanation:

Take the temperature drop and divide by the time

-13 1/5 ÷ 4 2/5

Change to improper fractions

-(13 *5+1)/5 ÷ (4*5+2)/5

-66/5 ÷22/5

Copy dot flip

-66/5 * 5/22

Rewrite

-66/22 * 5/5

-3 degrees per hour

Since we are looking for a drop

3 degrees per hour

Answer:

[tex] \implies \rm Volume_{(Hemisphere)} = \dfrac{2}{3}\pi {r}^{3} \\ [/tex]

[tex]\implies \rm Volume_{(Hemisphere)} = \dfrac{2}{3} \times \dfrac{22}{7} \times 8 \times 8 \times 8 \\ [/tex]

[tex]\implies \rm Volume_{(Hemisphere)} = \dfrac{2}{3} \times \dfrac{22}{7} \times 512 \\ [/tex]

[tex]\implies \rm Volume_{(Hemisphere)} = \dfrac{22528}{21} \\ [/tex]

[tex]\implies \rm Volume_{(Hemisphere)} = 1072.8\: {cm}^{3} \\ [/tex]

Answer:

[tex]18n - 24[/tex]

Step-by-step explanation:

[tex]6(3n - 4) = 18n - 24[/tex]

Answer:

18n-24

Step-by-step explanation:

6(3n-4)

Open the brackets .......

(6×3n)-(6×4)

=18n_24

Answer:

[tex]{ \tt{3 {y}^{2}(y + 4) - 7(y + 4) }} \\ = { \tt{(y + 4)( {3y}^{2} - 7) }}[/tex]

Answer:

See attachment for graph

Step-by-step explanation:

See comment for correct question

Given

[tex]y = \log_bx[/tex]

Required

The corresponding points on [tex]y =b^x[/tex]

On the graph, we have:

[tex](x_1,y_1) \to (1,0)[/tex]

[tex](x_2,y_2) \to (2,1)[/tex]

[tex](x_3,y_3) \to (4,2)[/tex]

[tex](x_4,y_4) \to (8,3)[/tex]

[tex](x_5,y_5) \to (16,4)[/tex]

First, we solve for b in [tex]y = \log_bx[/tex]

Using laws of logarithm, the equivalent of the above is:

[tex]x = b^y[/tex]

[tex](x_2,y_2) \to (2,1)[/tex] implies that:

[tex]2 = b^1[/tex]

[tex]2 = b[/tex]

Rewrite as:

[tex]b =2[/tex]

So, the equation [tex]y =b^x[/tex] becomes:

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

Using the same values of x, we have:

[tex](x_1,y_1) = (1,2)[/tex]

[tex](x_2,y_2) = (2,4)[/tex]

[tex](x_3,y_3) = (4,16)[/tex]

[tex](x_4,y_4) = (8,256)[/tex]

[tex](x_5,y_5) = (16,65536)[/tex]

See attachment for graph

The points (1,2), (2,4), and (4,16) are plotted on the graph attached below and this can be determined by using the given data.

Given :

Logarithmic Function  --  [tex]\rm y = log_b(x)[/tex]    --- (1)

The following steps can be used in order to determine the corresponding points that must be on the graph [tex]\rm x = b^y[/tex]:

Step 1 - Now, substitute the value of x and y that is (2,1) in the expression [tex]\rm x = b^y[/tex].

[tex]\rm 2 = b^1[/tex]

b = 2

Step 2 - Now, substitute the value of b in the equation [tex]\rm y=b^x[/tex].

[tex]\rm y = 2^x[/tex]    --- (2)

Step 3 - At (x = 1) the above expression becomes:

y = 2

Step 4 - At (x = 2) the expression (2) becomes:

y = 4

Step 5 - At (x = 4) the expression (2) becomes:

y = 16

The graph of [tex]\rm y = 2^x[/tex] is attached below.

For more information, refer to the link given below:

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Answer:

x ≈ 40.0°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{WX}{VW}[/tex] = [tex]\frac{57}{68}[/tex] , then

x = [tex]tan^{-1}[/tex] ([tex]\frac{57}{68}[/tex] ) ≈ 40.0° ( to the nearest tenth )

[tex] \Huge \underline {\mathcal {{{\color{orange}{108 \degree}}}}} [/tex]

Option ( A ) is the correct answer.

Put the data set in order:

12, 14, 24, 31, 41, 46, 49

In order to find a value of x using the range, x has to be on either end of the data set. Meaning:

x, 12, 14, 24, 31, 41, 46, 49 or 12, 14, 24, 31, 41, 46, 49, x

Since the range is the highest value minus the lower value, you can set two equations for x:

x - 12 = 63

x = 75

49 - x = 63

x = -14

Thus, x = 75, -14

Two values of x are -14 & 75

The difference between highest and lowest numbers of the set of numbers is called the range of numbers.

The given values are 12, 46, 31, 49, 24, 41, 14

Arranging all the values in ascending order we get,

12, 14, 24, 31, 41, 46, 49

If x will be included, then x is in the 1st position or in the last position.

Then the values are x, 12, 14, 24, 31, 41, 46, 49 or 12, 14, 24, 31, 41, 46, 49, x

The range of the number is 63

So, we get two equations from it.

1 ) 49-x = 63

2 ) x-12 = 63

Solving eq. (1) we get, x = 49-63 = -14

Solving eq. (2) we get, x = 63+12 = 75

So the values of x are -14 & 75

Learn more about range of number here :

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Answer:

3

Step-by-step explanation:

Given the polynomial : p(x)=1−2x2−3x3+4x

Rearranging : p(x) = -3x³ - 2x² + 4x + 1

Looking at the polynomial Given, we can see that it is a univariate polynomial, that is it has only one variable which is x. Thus for polynomials of this sort, the order of the polynomial is the highest exponent occurring in the polynomial equation. Therefore, the order of the polynomial above is 3, because the highest power of the function is 3.

This means that those with 4 as their highest exponent are of order 4 and those with highest exponent as 2 are of order 2.

Answer:

Area of label = 100 inch² (Approx.)

Step-by-step explanation:

Given:

Height of label = 8 inches

Diameter of label = 4 inches

Find:

Area of label

Computation:

Design of label = Rectangle

So,

Width of label = 2πr

Width of label = 2(3.14)(4/2)

Width of label = 2(3.14)(2)

Width of label = 12.56 inches

Area of label = Height of label x Width of label

Area of label = 12.56 x 8

Area of label = 100.48

Area of label = 100 inch² (Approx.)

Answer:

y =2/3x -2

Step-by-step explanation:

The y intercept is -2

The slope is

m = (y2-y1)/ (x2-x1)

Using the points (0,-2) and  (3,0)

m = ( 0 - -2)/(3 -0)

    = (0+2)/(3-0)

   = 2/3

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y =2/3x -2

Given:

In a quadrilateral ABCD, diagonals AC and BD intersect at point E.

[tex]AE\cong EC[/tex]

[tex]BE\cong DE[/tex]

To prove:

The figure is a parallelogram.

Solution:

We know that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

In a quadrilateral ABCD, diagonals AC and BD intersect at point E.

[tex]AE\cong EC[/tex]

[tex]BE\cong DE[/tex]

Since the diagonals AC and BD of a quadrilateral ABCD bisect each other, therefore the quadrilateral ABCD is a parallelogram.

Hence proved.

Answer:

the answer is C.

Step-by-step explanation:

in this situation as time passes, the number of quarts picked decreases.

hope it helps!

Step-by-step explanation:

HELIUM: To fill air balloon

ARGON: Used for filling incandescent metal filament electric bulbs

Given:

Dividing a number by 2 always results in a smaller number.

To find:

The counterexample to the given claim.

Solution:

If 0 is divided by is divided by any non-zero real number [tex]a[/tex], then

[tex]\dfrac{0}{a}=0[/tex]

Let us consider the unknown number be 0. Then dividing a number by 2, we get

[tex]\dfrac{0}{2}=0[/tex]

Here, the result is not a smaller number because [tex]0=0[/tex].

Therefore, the counterexample to the given claim is "Dividing 0 by 2".

Answer:

-1

Step-by-step explanation:

Answer:

31 square units

Step-by-step explanation:

See the picture below.

Each full or almost full square was counted first. There are 24 of them.

Then parts of squares of counted together to add to 1 square. They are color coded in the figure below. After adding them all up, the total was 31.

The area of the irregular shape is,

⇒ 27.5 square units

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The irregular shape is very similar to a trapezium with coordinates are,

(-3,3), (2, 2), (2, -2) and (-3, -4).

Now, We know that;

Area of a trapezium is,

⇒ [(a + b)/2] × h

where, a and b refer to the two parallel sides and h is the distance between them.

Hence,  From the above coordinates:

a = 7 length units,

b = 4 length units and

h = 5 length units.

Therefore, We get;

The approximate area = [(7 + 4)/2]5

                                   = 27.5 square units

Thus, The area of the irregular shape is,

⇒ 27.5 square units

Learn more about the multiplication visit:

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Step-by-step explanation:

A you see here, we have 3 different shapes. a Triangle, a big and small rectangle. Lets start with the triangle.

between the 8 in's, theres a gap. 5+4=9,

9+8+8=25. we have the length of the triangle.

9*25 divided by 2= 112.5. thats are area of the triangle.

for the bigger rectangle, 20*9=180, the area of the rectangle, and the smaller rectangle at the bottom is 16.

Now we add:

112.5+180+16=308.5  

hope this helps!

Answer: [tex]37.4\ m[/tex]

Step-by-step explanation:

Given length of shadow [tex]l=55\ m[/tex]

Hill inclination [tex]21.4^{\circ}[/tex]

Angle of elevation for sun [tex]48.3^{\circ}[/tex]

Suppose the length of the pole is [tex]h[/tex]

from the figure, and using sine rule. It can written

[tex]\Rightarrow \dfrac{55}{\sin 41.7^{\circ}}=\dfrac{h}{\sin 26.9^{\circ}}\\\\\Rightarrow h=55\cdot\dfrac{\sin 26.9^{\circ}}{\sin 41.7^{\circ}}\\\\\Rightarrow h=55\cdot 0.68011\\\Rightarrow h=37.40\ m[/tex]

Answer:

x = - 3

Step-by-step explanation:

The axis of symmetry passes through the vertex ( turning point ) of the graph and is a vertical line with equation

x = c ( c is the value of the x- coordinate of the vertex )

The vertex is (- 3, - 1 ) with x- coordinate - 3 , then

equation of axis of symmetry is x = - 3

Answer:

look at the png below

Step-by-step explanation:

Answer:

y = 4x-3

Step-by-step explanation:

First we need to determine the slope

Using two points on the line (0,-3)  (1,1)

Using the slope formula

m = (y2-y1) /(x2-x1)

   = (1- -3)/(1-0)

 (1+3)/  (1-0)

  4

We know the y intercept, -3

y = mx+b where m is the slope and b is the y intercept

y = 4x-3

The answer is: (2, 3) :)

Answer:

[tex]x + 2x + 34 + 20 = 180 [/tex]

Answer:

x=42

Step-by-step explanation:

Statement Reason

1. m∠AOB = 180° —  Def. of straight ∠

2. m∠AOE + m∠EOF + m∠FOB = m∠

AOB      —-    Parts − whole Postulate

3. x + 2x+34° + 20° = 180°  —-   Substitution

4. x = 42°.  —- Algebra

This is statement and reason! (no problem rsm people)

Answer:

( 25 x 100 )

option 1 is the answer

Step-by-step explanation:

Remaining options are not correct since they don't have 100 as a factor.

Answer:

x=5

Step-by-step explanation:

The sides have to be equal length

3x+4 = 5x-6

Subtract 3x from each side

3x+4-3x = 5x-6-3x

4 = 2x-6

Add 6 to each side

4+6 = 2x-6+6

10 = 2x

Divide by 2

10/2 =2x/2

5 =x

Two parallel sides is 3x + 4 = 5x - 6

[tex]\bf \large \longrightarrow \: \: 3x \: + \: 4 \: = \: 5 x \: - \: 6[/tex]

[tex]\bf \large \longrightarrow \: \:6 \: + \: 4 \: = \: 5x \: - \: 3x[/tex]

[tex]\bf \large \longrightarrow \: \:10 \: = \: 2x[/tex]

[tex]\bf \large \longrightarrow \: \: \frac{10}{2} \: = \: x \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \cancel\frac{10}{2} \: \large \: ^{5} \: = \: x \\ [/tex]

[tex]\bf \large \longrightarrow \: \:x \: = \: 5[/tex]

Option ( B ) is the correct answer.

Answer:

Solution given:

in 1990

cost of orange[C.P]=$0.56

in 2003

cost of orange[S.P]=$0.86

now

increased price[profit]=S.P-C.P=$0.86-$0.56=$0.3

Now

increased percent [profit%]=?

we have

profit%=profit/c.p*100%

=0.3/0.56*100=53.57℅

Therefore

the oranges appreciated by 53.57%

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

we have, 1990 oranges cost $0.56 per pound. In 2003 they cost $0.86 per pound.

so,

[tex]\sf{increase_{(profit)}=0.86-0.56=0.3 }[/tex]

we know that,

[tex]\bold{ profit\%=\dfrac{profit}{C.P}×100 }[/tex]

According to the question,

Answer:

x = -1

Step-by-step explanation:

3x - 1/9 (27) = 18

3x - 3

Divide both sides be 3

x = -1

Answer:

x = 7

Step-by-step explanation:

to solve this equation we are given the value of y which 27. just substitute 27 for y in the equation :

3x - 1/9(27) = 18

3x - 3 = 18

3x = 21

x= 7

Answer:

8^1/3

Step-by-step explanation:

(8^5/3)^1/5

8^5/3×1/5

8^5/15

8^1/3

Answer:

Step-by-step explanation:

Exponent Rule: [tex](a^{m})^{n}=a^{m*n}[/tex]

[tex](8^{\frac{5}{3}})^{\frac{1}{5}}= 8^{\frac{5}{3}}*{\frac{1}{5}}\\\\\\=8^{\frac{1}{3}}\\\\= \sqrt[3]{8} \\\\= \sqrt[3]{2*2*2}\\\\= 2[/tex]