find the distance between the points (-16,11) and (16,4)

Answer:

(f+g)(x) = x - 7

Step-by-step explanation:

(f+g)(x) tells you to add the functions together. It means

f(x) + g(x)

= -3x - 5 + 4x - 2

combine like terms.

= 4x-3x - 5 - 2

= x - 5 - 2

simplify.

= x - 7

(f+g)(x) means

f(x) + g(x)

= x - 7

Jimmy will take 24 hours to do the given job alone.

What is the teamwork equation for problem solving?
Problems with teamwork are resolved using this technique. If the first person completes a task in 'A' units of time and a second person completes a task in 'B' units of time, they can complete a task in 'T' units of time together (total).
The teamwork equation can be applied, that is: (1/A) + (1/B) = (1/T)

Given, time taken by Britney to do the job individually = B = 12 hours
Also, time taken by Britney and Jimmy to do the job together = A = 8 hours
Let the time taken by Jimmy to do the job individually = A hours
Thus, using the equation established in the literature above and substituting the given values, we have:
(1/A) + (1/B) = (1/T) ⇒ (1/A) + (1/12) = 1/8 ⇒ 1/A = (1/8) - (1/12)
⇒ 1/A = (3/24) - (2/24) ⇒ 1/A = 1/24 ⇒ A = 24
Thus, Jimmy will take 24 hours to do the given job alone.

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The statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."

What is a regular hexagon?

It is a regular hexagon when the lengths of all the sides and the measures of all the angles are equal. In a regular hexagon, each inside angle is 120 degrees. The characteristics of a regular hexagon. The lengths of each side are equal.

Here, we let

P = it has exactly four sides.

Q = it is not an hexagon.

The negation is like this;

If it is a hexagon, then it does not have exactly four sides.

Thus, we concluded that “it is a hexagon” is your hypothesis (p) and “it has exactly 6 congruent sides” is your conclusion (q).

Hence, the statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."

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The graph of the coordinate points of the vertices of ABCD indicates;

Part A The perimeter of ABCD ia approximately 61.2 units

Part B. The area of ABCD is 199.5 square units

The perimeter of a figure is length of the line that goes round the figure.

A. The perimeter of the polygon is the sum of the length of the sides of the polygon, which is found as follows;

AB = √((21-11)²+(11-(-1))²) ≈ 15.6

BC = √((21-26)²+(11-(-1))²) = 13

CD = √((26-2)²+(-1-(-8))²) = 25

AD = √((2-5)²+(-8-(-1))²) ≈ 7.6

The perimeter of the polygon = 15.6 + 13 + 25 + 7.6 = 61.2

B. Plotting the figure indicates that the figure consists of two triangles, ΔABC and ΔACD

The base length of triangle ΔABC = 26 - 5 = 21

The height of triangle ΔABC = 11 - (-1) = 12

The area of triangle ΔABC = 0.5 × 21 × 12 = 126

Base length of triangle ΔADC = 21

Height of triangle ΔADC = -1 - (-8) = 7

Area of triangle ΔADC = 0.5 × 21 × 7 = 73.5

Area of the composite figure is therefore;

A = 126 + 73.5 = 199.5

The area of the figure is therefore; 199.5 square units

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The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)

Given equation y = 3x + a / 2x - 5

= y(2x - 5) = 3x + a

= 2xy - 5y = 3x + a

= 2xy - 3x = a - 5y

= x(2y-3) = a - 5y

Hence, x = (a - 5y) / (2y - 3)

First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).

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At 2:20 pm they finish the paint of wall.

Given, Al took 6 hours to paint a wall.

Bob took 4 hours and Chuck took 3 hours for same.

Let the work of painting wall is = LCM(6,4,3) = 12 Units

So in 1 hour Al works = 12/6 = 2 units

In 1 hour Bob works = 12/4 = 3 units

In 1 hour Chuck works = 12/3 = 4 units

In 1 hour, Al and Bob together do = 2+3 = 5 units

In 1 hour, all three together do = 2+3+4 = 9 units

Now from noon i.e. 12 to 1.00 pm Al works alone.

So 2 units of work is done.

From 1 pm to 1.30 pm, Al and Bob work together.

In 30 minutes i.e. ½ hour Al and Bob did = (1/2)*5 = 5/2 units

From 1.30 pm they all three work together.

Now the remaining work is = 12-(2+5/2) = 12-9/2 = 15/2 units

So they complete rest in = (15/2)/9 = 5/6 hours = 50 minutes

Hence the time of finishing the work = 1.30 + 50 minutes = 2.20 pm.

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Answer:plot the point (2,5)

Step-by-step explanation:

Answer:

1. 384 cm square

2. m

3. -3 and 4

4.   1

Answer:

1) B

2) B

3) C

4) A

Step-by-step explanation:

     [tex]\sf \boxed{\text{Area of cube = $6a^2$}}[/tex]

Here, a is the side of the cube.

     Area of cube = 6 * 8 * 8

                            = 384 square cm  

Option B

2) y = mx + c.

Here, m is the slope or gradient and c is the y-intercept.

Option B

3) y = -3x + 4

Compare with y =mx + c,

         where m is the gradient and c is the y-intercept.

m = -3 and  = 4

Option C

4)

[tex]\sf Slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\[/tex]

         [tex]\sf =\dfrac{-3-[-2]}{2-3}\\\\=\dfrac{-3+2}{-1}\\\\=\dfrac{-1}{-1}\\\\=1[/tex]

Option A

Answer:

Step-by-step explanation:

Hi Mia,  are you aware that the last name Hamilton is a famous math person?  :)    anyway,  

The triangle in the picture is an isosceles triangle,  we know that b/c the angle of the one is 45° meaning the other side must also be a 45° angle.  So we know the two sides are the same length.

side n = 7 [tex]\sqrt{2}[/tex] / 2

then use Pythagoras to find m

[tex]c^{2}[/tex] = ( 7 [tex]\sqrt{2}[/tex] / 2)^2  + ( 7 [tex]\sqrt{2}[/tex] / 2)^2

[tex]c^{2}[/tex] = 49*2/4  + 49*2/4

[tex]c^{2}[/tex] = 49/2  + 49/2

[tex]c^{2}[/tex] = 98/2

[tex]c^{2}[/tex] = 49

c = 7

side m = 7   :)  nice, huh ?

a) Sin X = O/H

Sin 45 = [tex]7\sqrt{2}[/tex]/2/H

H= [tex]7\sqrt{2}[/tex]/2/ Sin 45

m= 7

b) cos X = A/H

   cos 45= A/7

A= cos45*7

n= 4.95

Answer:

113 people (112.5 if you don't round but you can't have half a person)

Step-by-step explanation:

45 men plus the number of women (x) is how many people there are

so you would do 3/x=2/45 since x is the number of women

do some basic algebra, and you get 67.5 women so round if you want to to 68 (i will round because you can't have half a person)

68+45=113 people

Answer: 9/2

Step-by-step explanation: Hope this helps.

The density of this sand is 1600 kg/m³.

What is the meaning of density?

The amount of something per unit of length, area, or volume: as. : the substance's mass per unit volume. In grams per cubic centimeter, density.

Given that the dimension of a cuboid is length 45 cm, width 30 cm and height 42 cm.

The volume of the cuboid is (45 × 30 × 42) cm³

                                              = 56,700 cm³

                                              = (56,700/100³) m³

                                              = 0.0567 m³

The mass of the sand is 90.72 kg.

The density of the sand is

= mass /volume

=90.72 kg / 0.0567 m³

= 1600 kg/m³

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All the improper fractions in mixed or whole numbers are as follows:

So, the given improper fractions in the mixed or whole numbers are:

Therefore, all the improper fractions in mixed or whole numbers are as follows:

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The sample size necessary for a 90% confidence interval about the mean height of a shrub with a margin of error of 0.5 inches and a population standard deviation of 1.3 inches is 18.

Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.

MOE = z x (SD / √n)

where MOE = margin of error = 0.5 inches

z = found by using a z-score table

SD = sample standard deviation = 1.3 inches

n = sample size

At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.

(100 - 90) / 2 = 5

100 - 5 = 95

Find 0.95 in the z-table to get the value of z.

At p = 0.95, z = 1.647

Plug in the values to the formula and solve for the sample size, n.

MOE = z x (SD / √n)

0.5 = 1.647 x (1.3 / √n)

√n = 1.647(1.3) / 0.5

n = 18.34

n = 18

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Equation of the line which passes through the given points (-p ,-q) and

(p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.

As given in the question,

Given condition is :

p ≠ q ≠ 0

Equation of the line which passes through the given points (-p ,-q) and

(p, q) is given by:

(x₁ , y₁) = (-p ,-q)

(x₂ , y₂) = (p, q)

(y -y₁)/ (x -x₁) = (y₂ -y₁)/ (x₂ -x₁)

⇒(y +q)/(x+ p) = (q +q)/(p +p)

⇒(y +q)/ (x +p) = 2q /2p

⇒p(y+ q) =q( x +p)

⇒yp + pq = qx +pq

⇒yp = xq

⇒y = (q /p)x

Therefore, equation of the line which passes through the given points (-p ,-q) and (p, q) where p ≠ q ≠ 0 is given by y = (q/p)x.

The complete question is :

Given p ≠ q ≠ 0, what is the equation of the line that passes through the points (–p, –q) and (p, q)?

A. y = –x

B. y = q/px

C. y = q

D. y = 2x + (2p – q)

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Answer:

b

Step-by-step explanation:

just did it

The equation 2.5x + 2y = 225 represents the total cost and 2.5x  represents the cost of dried fruit when its quantity is x.

A health food business prepares trail mixes out of dried fruit and nuts. The dried fruit costs $2.50 per pound, while the nuts cost $2.00 per pound. The overall cost of making the trail mix is $225.

Let the quantity of the dried fruit is x,

And the quantity of nuts is y,

As per the given question, the equation would be as:

2.5x + 2y = 225

The above equation represents the total cost and 2.5x  represents the cost of dried fruit when its quantity is x.

Thus, 2.5x  represents the cost of dried fruit when its quantity is x.

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New current if the voltage is increased to 4 volts. = 0.1 A or 100 mA

What is a current simple definition?

amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit.

=> I  ∝  V

=> I  = V/R    

R is a constant

and R  is resistance

When 3 volts are applied to a circuit, 75 milliamperes of current flow through the circuit.

=> 75 x 10⁻³  = 3 /R

=> R = 3 x 10³/75

=> R =  10³/25

=> R = 40

I  = V/R    

V = 4

R = 40

=> I  = 4/40

=> I  = 1/10

=> I = 0.1 A

or 100 mA

new current if the voltage is increased to 4 volts. = 0.1 A or 100 mA

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Answer:

[tex] - 8(9 - ( - 33 - 15) \div 12[/tex]

[tex] - 8(9 - ( - 48) \div 12[/tex]

[tex] - 8(9 + 4)[/tex]

[tex] - 8(13)[/tex]

[tex] - 104[/tex]

Answer:

-104

Step-by-step explanation:

Divide 108 by 12

Calculate -3 × 11 - 15 which is 48

Remove the parentheses

Divide 48 by 12 which is 4

9 + 4 is 13

-8 × 13 = -104

The table of solutions for the given equation (y = -2x²) include the following:

x                    y_

-2                  -8

-1                   -2

0                   -0

1                    -2

2                   -8

Also, a graph of the solution of this equation (y = -2x²) has been plotted in the image attached below.

In order to determine the valid and true solutions to the given quadratic equation, we would have to substitute the values of contained in the table into the quadratic equations as follows;

At x = -2, the value of point y is as follows:

y = -2x²

y = -2(-2)²

y = -2 × 4

y = -8

At x = -1, the value of point y is as follows:

y = -2x²

y = -2(-1)²

y = -2 × 1

y = -2

At x = 0, the value of point y is as follows:

y = -2x²

y = -2(0)²

y = -2 × 0

y = 0

At x = 1, the value of point y is as follows:

y = -2x²

y = -2(1)²

y = -2 × 1

y = -2

At x = 2, the value of point y is as follows:

y = -2x²

y = -2(2)²

y = -2 × 4

y = -8

In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.

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A stratified sample in this case can be selected as follows:

The rooms are divided by whether they overlook the ocean or the street, and 25 of each are selected.

The five most common classifications for sampling are listed as follows:

In this problem, the groups are given as follows:

50 rooms will be sampled, hence the number that is sampled from each group is given as follows:

50/2 = 25 rooms from each group.

The problem asks to describe a stratified sample for this situation.

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From the figure, the lines parallel to AE are DH, CG, and EF.

Geometry is heavily reliant on parallel and perpendicular lines, and they can be easily distinguished thanks to a few unique qualities. If two lines never cross each other, are in the same plane, and are at the same distance from one another, then they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees.

If two straight lines are in the same plane and never intersect, they are said to be parallel lines.

So from the figure, we can see that the lines parallel to AE are DH, CG, and EF, as the lines are in the same plane.

As equidistant lines, they are always the same distance apart.

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The inequality that can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget is 26.03d + 0.13m ≤ 350.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, the rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven

Let the number of days be d.

Let the number of miles be m.

The appropriate inequality to illustrate this is 26.03d + 0.13m ≤ 350.

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The width of pool deck is 7 ft and new dimensions of pool and deck are 21 ft and 35 ft .

In the given question we have,

Area of whole background ( pool + deck) = 1176 ft²------(1)

Area is a two dimensions quantity . so, we work here in 2-D.

length of pool = 28 ft , width of pool= 14 ft

let the width of deck be x ft . Now, the new dimensions are following

length of pool and deck = 28 + x + x = (28+2x ) ft

width of pool and deck = 14 + x + x = (14+ 2x) ft

here, 2x include in lenth and width for surronding deck.

total area of pool and deck ( backyard ) = lenth × width = 1176 ft² ( from (1) )

(28+2x) ( 14+2x) = 1176 ----(2)

Now, we shall solve above equation (2) and find out value of x

28×14 + 56x + 28x + 4x^2 = 1176

=> 4x²+ 84x + 392 - 1176 = 0

=> 4x² + 84x - 784=0 => x² + 21x - 196 = 0

=> x²+ 28x - 7x - 196 = 0 => x(x+ 28) - 7(x+28)=0

=> (x+28) (x-7) = 0

either x + 28= 0 or x - 7 = 0 =>either x= -28 or x= 7

but width can't be negative value so, discard

x= -28.

Hence, the width of pool deck is 7 ft.

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Answer: -3/8 or -0.375

Step-by-step explanation:

you have to get similar denominators to simplify

so times 1/4 by 2 to get 2/8

and then just do 2/8 - 5/8 and you get the answer

Answer:

51.3

Step-by-step explanation:

Since it's telling us that (x=7) then that means 8.2x is going to be multiplied

8.2(7) or 8.2 x 7.

Then you end up getting an answer of 57.4

But you are not finished yet and need to subtract 6.1

so 57.4 - 6.1 = 51.3

And your result will be (51.3)

I hope this helps you understand this problem!

Joe, for the most part, tipped 20% of his bill, compared to 10% for Mike, which is particularly noteworthy. The actually difference between their invoices in dollars was approximately 10.

Let  be Mike's bill and   be Joe's bill.

(10/100) *m = 2

M = 20

(20/200 )*j = 2

J = 10

So the desired difference is

m-j = 20 – 10

= 10

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The slope of the line perpendicular to the line 2x - 12y = 120 will be -6.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following equation -

2x - 12y = - 120

Rearranging the equation, we get -

2x - 12y = 120

12y = 2x - 120

6y = x - 60

y = (1/6)x - 10

The slope of the line perpendicular to the line 2x - 12y = 120 will be -

m[2] = -1 / (1/6) = - 6

m[2] = - 6

Therefore, the slope of the line perpendicular to the line 2x - 12y = 120 will be -6.

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Step-by-step explanation:

these intercepts are the points where the graph intersects with the coordinate axes (x and y).

the x-intercept is a point on the x-axis, meaning when y = 0.

the y-intercept is a point on the y-axis, meaning when x = 0.

so, the x-intercept here is 14 at the point (14, 0).

the y- intercept is 7 at the point (0, 7).

that means the object started falling from a height of 7 meters and hit the ground after 14 seconds.

the falling speed was then

7 meters / 14 seconds = 0.5 meters / second

what are we talking about ? an asteroid with very little gravity ?

The value of j based on the equation d = j + 3.16 if d = 158 is 154.84 meters.

d = j + 3.16

substitute the value of d into the equation

d = j + 3.16

158 = j + 3.16

substract 3.16 from both sides

158 - 3.16 = j

j = 154.84

So therefore, based on the given equation d = j + 3.16, j = 154.84

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The value of j in the equation = 154.84

Distance

Distance is the length of space covered by the car when it moves from one location to another

Given;

Equation d=j+3.16 represent the situation

distance travelled by the car= 3.16meters

d=158

Step 1: Substituting the value of d into the equation d=j+3.16

158= j +3.16

Step 2: Subtract 3.16 from both sides

158-3.16 = j + 3.16 -3.16

Step 3: Add the equation

j= 154.84

Therefore, the value of j in the equation = 154.84

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