)) Find the slope of the line that passes through (10, 1) and (1, 3).

Answer:

The y intercept is when x=0

When x=0,

y+3= 5(-3)

y+3= -15

y=-18

the y intercept is thus -18.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Good evening ,

Answer:

D : y = -6

Step-by-step explanation:

A line D has a slope of 0 shouled be parallel to the x-axis then

it’s equation in slope intercept form should be y=a

And since, It passes through the point (-1,-6) then a=-6

finally:

the equation of D is y=-6.

:)

Answer:

A

Step-by-step explanation:

1)The mole is a unit of measure that contains as many elementary entities as in atoms of 12 grams of Carbon  (12 AMU). The Carbon mass is the reference.

2)We have to specify which particle we are using when dealing with mole unit:

particle, atoms, molecules, ions, electrons, etc.

[tex]1\:mol \:C=6*10^{23} \:particles[/tex]

3) So If I have 6 moles of a substance, I am going to have six times the number of particles that are in 12 grams of carbon-12.

[tex]36*10^{23} \:particles[/tex]

There are 4 queens in a deck of cards.

You have 4 chances out of 52 total cards to get a queen.

The probability is 4 queens / 52 cards = 4/52, which can be reduced to 1/13

Answer:

A = 110.25

Step-by-step explanation:

add all the equations and equal it to 180 because all triangle angles add to 180:

4x+1 + 3x + 3x-1 = 180

10x =70

/10   /10

x = 7

Insert x into each equation and solve:

3(7)-1 = 20

4(7)-1 = 27

3(7) = 21

and then use A = 1/2 base*height formula:

A= 1/2 21* 20

A= 210

Area of triangle A is 210 cm²

Given that;

Perimeter of the triangle = 70cm

Sides of triangle = 3x, 4x + 1, 3x - 1

Find:

Area of triangle A

Computation:

3x + (4x + 1) + (3x - 1) = 70

3x + 4x + 3x = 70

10x = 70

x = 7

So,

Perpendicular = 3x - 1 = 21 - 1 = 20 cm

Hypotenuse = 4x + 1 =28 + 1 = 29 cm

base = 3x = 21 cm

Area of triangle A = (1/2)(b)(h)

Area of triangle A = (1/2)(21)(20)

Area of triangle A = (21)(10)

Area of triangle A = 210 cm²

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Answer:

The answer is: B, C, and F.

Step-by-step explanation:

A. No.

3 1/3 - 1 5/6 =

10/3 - 11/6 =

20/6 - 11/6 =

9/6 = 2/3

B. Yes.

1 1/4 + 1/4 = 1 1/2

C. Yes.

6 1/2 - 8 = 1 1/2

D. No.

4 1/4 - 1 3/4 =

17/4 - 7/4 =

10/4 =

5/2 =

2 1/2

E. No

5/8 + 7/8 =

13/8 =

1 5/8

F. Yes.

2 1/4 - 3/4 =

9/4 - 3/4 =

6/4 =

3/2 =

1 1/2

The following situations result in a sum of 3/2 B, C, and F.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

A.

[tex]3\frac{ 1}{3} - 1 \frac{5}{6}[/tex]

10/3 - 11/6

20/6 - 11/6

9/6 = 2/3

No, the following situations don't result in a sum of 3/2.

B.

5/4 + 1/4 = 1 1/2

Yes, the following situations result in a sum of 3/2.

C.

11/2 - 8 = 1 1/2

Yes, the following situations result in a sum of 3/2.

D.

17/4 - 7/4 =

10/4 = 5/2

No, the following situations don't result in a sum of 3/2.

E.

5/8 + 7/8 = 13/8

No, the following situations don't result in a sum of 3/2.

F.

9/4 - 3/4

6/4 = 3/2

Yes, the following situations result in a sum of 3/2.

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Answer:

[tex]EF=61\ units[/tex]

Step-by-step explanation:

we know that

In this problem, the length of the mid-segment EF is the sum of the two bases divided by 2

so

[tex]EF=\frac{1}{2}(BC+AD)[/tex]

substitute the given values

[tex]3x+7=\frac{1}{2}(2x+7+5x-11)[/tex]

Solve for x

[tex]6x+14=(7x-4)[/tex]

[tex]7x-6x=14+4[/tex]

[tex]x=18[/tex]

Find the length of EF

[tex]EF=3x+7[/tex]

substitute the value of x

[tex]EF=3(18)+7[/tex]

[tex]EF=61\ units[/tex]

Answer:

measure of angle K is 48° or m∠K = 48°

Step-by-step explanation:

Given:

ΔJKL= ΔPQR

m∠P = 52°

m∠Q = 48°

m∠R = 80°

When 2 triangles are equal or congruent to each other then their corresponding angles are equal or congruent by congruence property.

Hence ,

m∠P = m∠J

m∠Q = m∠K

m∠R = m∠L

But m∠Q = 48° hence m∠K = 48°

Hence measure of angle K is 48°

Answer:

16/15 or 1 1/15

Step-by-step explanation:

2/6/8=8/3

1/5/8=8/5

----------------

8/3-8/5=40/15-24/15=16/15=1 1/15

Using the blueprint scale of 5 inches to 25 feet, the width of the door on the blueprint at 1.5 inches translates to an actual width of 7.5 feet.

To find the actual width of the door in feet using a given scale, we use proportional relationships.

The scale provided is 5 inches : 25 feet.

This means that every 5 inches on the blueprint correspond to 25 feet in actual size.

To find the actual door's width, we calculate it using the following proportion:

5 inches / 25 feet = 1.5 inches / x feet

Now, we solve for 'x' to find the actual width:

5/25 = 1.5/x

Now, cross-multiply and divide to find 'x':

5x = 25 * 1.5

x = (25 * 1.5) / 5

x = 37.5 / 5

x = 7.5 feet

So the actual door's width is 7.5 feet.

Answer:

19 ft, 24 ft and 38 ft are the lengths of triangle.

Step-by-step explanation:

Let the length of second side be x.

Now given:

Given: Length of first side is 2 times length of second side = 2x

Given:Length of third side is 5 ft longer than the second side = 5+x

Perimeter of triangle = 81 ft.

Need to Calculate length of each side.

Now we know that sum of all three sides of triangle is equal to perimeter of triangle.

Hence,

[tex]x+2x+5+x =81\\4x= 81-5\\4x=76\\x=19 ft[/tex]

Also,

2x= 2×19 =38 ft.

5+x = 5+19 =24 ft.

Hence,

Length of first side  = 38 ft.

Length of second side = 19 ft.

Length of third side =24 ft.

Answer:

30,000 x (4 x 3)  =  100 times  300 x (4 x 3)  

Step-by-step explanation:

Here, the given expressions are:

Expression 1 :     30,000 x (4 x 3)

Expression 2 :     300 x (4 x 3)

Now, simplifying both the expressions, we get

30,000 x (4 x 3)  = 30,000 x (12)   = 3,60,000

300 x (4 x 3)  = 300 x (12) = 3,600

Now, dividing both the expressions, we get:

[tex]\frac{3,60,000}{3,600}  = 100[/tex]

or, [tex]\frac{\textrm{Expression 1}}{\textrm{Expression 2}}  = 100\\[/tex]

or, {Expression 1}  = {Expression 2} x 100

⇒The expression 1 is 100 times the expression 2

Hence,  30,000 x (4 x 3)  =  100 times  300 x (4 x 3)  

Answer:

The product of the perimeter of the triangle and the height of the prism

Step-by-step explanation:

The options of the question are

The product of the perimeter of the triangle and the height of the prism

The product of the perimeter of the side times the height of the triangle

The product of the perimeter of the triangle and the height of the triangle

The product of the perimeter of the side times the height of the prism

we know that

The surface area of a triangular prism is

[tex]SA=2B+Ph[/tex]

where

B is the area of the triangular base

P is the perimeter of the triangular base

h is the height of the triangular prism

The term 2B represent the area of the top and the bottom of the triangular prism

The term Ph represent the lateral area of the triangular prism (The product of the perimeter of the triangle and the height of the prism)

Answer:

B is the volume of the base

Step-by-step explanation:

Slope intercept form of line passing through midpoint of CD and perpendicular to CD is [tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]

Need to find the slope intercept form for the line perpendicular to C(-4,-5) and D(4,9)

And passing through the midpoints of the line CD.

Lets first calculate slope of CD  

Let say slope of CD be represented by [tex]m_1[/tex]

General formula of slope of line passing through points [tex]\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)[/tex] is as follows:

[tex]m=\frac{\left(y_{2}-y_{1}\right)}{\left(x_{2}-x_{1}\right)}[/tex]

[tex]\text { In case of line } \mathrm{CD} , x_{1}=-4, \quad y_{1}=-5 \text { and } x_{2}=4, y_{2}=9[/tex]

[tex]\text {So slope of line } \mathrm{CD} \text { that is } m_{1}=\frac{(9-(-5))}{(4-(-4))}=\frac{14}{8}=\frac{7}{4}[/tex]

Let’s say slope of required line which is perpendicular to CD be [tex]m_2[/tex]

As product of slope of the lines perpendicular to each other is -1

=> slope of line CD [tex]\times[/tex] slope of line perpendicular to CD = -1

[tex]\begin{array}{l}{=>m_{1} \times m_{2}=-1} \\\\ {\Rightarrow \frac{7}{4} \times m_{2}=-1} \\\\ {\Rightarrow m_{2}=-\frac{4}{7}}\end{array}[/tex]

Now let’s find midpoint of CD

[tex]\text { Midpoint }(x, y) \text { of two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { is given by }[/tex]

[tex]x=\frac{x_{2}+x_{1}}{2} \text { and } y=\frac{y_{2}+y_{1}}{2}[/tex]

[tex]\text { So in case of line } \mathrm{CD} , x_{1}=-4, y_{1}=-5 \text { and } x_{2}=4, y_{2}=9[/tex]

And midpoint of CD will be as follows

[tex]x=\frac{x_{2}+x_{1}}{2}=\frac{4+(-4)}{2}=0 \text { and } y=\frac{y_{2}+y_{1}}{2}=\frac{9-5}{2}=2[/tex]

So midpoint of CD is ( 0 , 2 )

As it is given that line whose slope intercept form is required is perpendicular to CD and passing through midpoint of CD , we need equation of line passing through ( 0 , 2 ) and having slope as [tex]m_{2}=-\frac{4}{7}[/tex]

Generic equation of line passing through [tex]\left(x_{1}, y_{1}\right)[/tex] and having slope of m is given by

[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]

[tex]\text { In our case } x_{1}=0 \text { and } y_{1}=2 \text { and } m=-\frac{4}{7}[/tex]

Substituting the values in generic equation of line we get

[tex](y-2)=-\frac{4}{7}(x-0)[/tex]

As we required final equation in slope intercept form which is y = mx + c, lets rearrange our equation is required form:

[tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]

Hence can conclude that slope intercept form of line passing through midpoint of CD and perpendicular to CD is [tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]

To find the equation of the line perpendicular to the line passing through points C(-4,-5) and D(4,9) and passing through the midpoint (0, 2), follow these steps: 1) Find the slope of the given line. 2) Find the midpoint of the line. 3) Find the negative reciprocal of the slope. 4) Use the slope and midpoint to write the equation of the perpendicular line in slope-intercept form.

To find the equation of a line perpendicular to the line passing through points C(-4,-5) and D(4,9) and passing through the midpoint of the line, we need to follow these steps:

Let's go through these steps:

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, the points are C(-4,-5) and D(4,9). So, we can substitute the values into the formula:

slope = (9 - (-5)) / (4 - (-4))

slope = 14 / 8

slope = 7 / 4

The midpoint of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

In this case, the points are C(-4,-5) and D(4,9). So, we can substitute the values into the formula:

midpoint = ((-4 + 4) / 2, (-5 + 9) / 2)

midpoint = (0 / 2, 4 / 2)

midpoint = (0, 2)

The negative reciprocal of a slope is found by changing the sign of the slope and taking its reciprocal.

In this case, the slope is 7 / 4. So, the negative reciprocal is -4 / 7.

Now that we have the slope (-4 / 7) and the midpoint (0, 2), we can use the slope-intercept form of a line to write the equation:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting the values, we have:

y = (-4 / 7)x + b

To find the value of b, we can substitute the coordinates of the midpoint (0, 2) into the equation:

2 = (-4 / 7)(0) + b

2 = 0 + b

b = 2

So, the equation of the line perpendicular to the line passing through C(-4,-5) and D(4,9) and passing through the midpoint (0, 2) is:

y = (-4 / 7)x + 2

Answer:

A. [tex]g(x)=-2x+1[/tex]

Step-by-step explanation:

Given:

[tex]f(x)=-2x+7[/tex]

The function [tex]f(x)[/tex] is shifted 6 units below which forms the function [tex]g(x)[/tex]

To find the function [tex]g(x)[/tex], we apply the following translation rules:

[tex]f(x)\rightarrow f(x)+c[/tex]

If [tex]c>0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units up.

If [tex]c<0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units down.

Since the function [tex]f(x)[/tex] is shifting 6 units below, thus value of [tex]c<0[/tex] which is taken as  -6.

The translation occurring here is given by:

[tex]f(x)\rightarrow f(x)-6[/tex]

Thus,

[tex]g(x)=f(x)-6[/tex]

Substituting [tex]f(x)=-2x+7[/tex]

[tex]g(x)=-2x+7-6[/tex]

∴ [tex]g(x)=-2x+1[/tex]

The question is missing important data. The quadrilateral having vertices A, B, C and D is a cyclic quadrilateral.

Answer:

B) 85°

Step-by-step explanation:

Given:

A cyclic quadrilateral with ∠A is 95° and ∠B is 105°.

For a cyclic quadrilateral, the sum of the opposite interior angles is equal to 180°

Therefore, sum of angles A and C is 180°.

[tex]\angle A + \angle C=180\°\\95\°+\angle C=180\°\\\angle C=180-95\\\angle C =85\°[/tex]

Therefore, the correct option is option B) 85°

Answer:

A)75

Step-by-step explanation:

Opposite angles in an inscribed quadrilateral are supplementary.

∠B + ∠D = 180°

105° + ∠D = 180°

∠D = 75°

It will take John 2800 steps to walk from his house to James' house

Step-by-step explanation:

First of all we have to convert all the measurements in same unit.

Distance = 0.7 km

As 1 km = 1000 m

0.7*100 = 700m

And

1 m = 100 cm

700*100 = 70000cm

Now,

25 cm = 1 step

[tex]So,\\70000cm = \frac{70000}{25}\\=2800\ steps[/tex]

It will take John 2800 steps to walk from his house to James' house

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Answer:

m=-23/10

Step-by-step explanation:

-2 67/90=-247/90

m-4/9=-247/90

m=-247/90+4/9

m=-247/90+40/90

m=-207/90

m=-23/10

Answer:

19 more female sheep.

Step-by-step explanation:

Answer:

66 more female sheep.

Step-by-step explanation:

What you do is subtract 113 subtract 47 which is 66 and if you want to make sure add,66+47.

The question is incomplete. Here is the complete question:

A 20-foot ladder is leaning against a wall. The foot of the ladder makes an angle of 58 degrees with the ground. Find, to the nearest foot, the vertical distance from the top of the ladder to the ground.

Answer:

17 ft

Step-by-step explanation:

Let the height from the top of the ladder to the ground be 'x' feet.

Given:

The triangle for the given situation is shown below.

Now, from the triangle ABC, AB is the length of the ladder, A is the top of ladder, B is the foot of the ladder and AC is 'x'.

The length of the ladder is, [tex]AB=20\ ft[/tex]

The angle made by the foot of the ladder with the ground is, [tex]\angle ABC=58[/tex]°

Now, using the sine ratio for the angle ∠ABC, we have:

[tex]\sin(\angle ABC)=\frac{AC}{AB}\\\sin(58)=\frac{x}{20}\\x=20\times \sin(58)\\x=20\times 0.8480\\x=16.96\approx 17\textrm{ ft (Nearest foot})[/tex]

Therefore, the vertical distance from the top of the ladder to the ground is 17 feet.

The acceleration of the object will be 10 m/s²

Step-by-step explanation:

Direct variation is a relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other

For a moving object, the force acting on the object varies directly with the object's acceleration.

Assume that the force is F and the acceleration is a

∵ F ∝ a

∴ F = k a

∵ F = 20 newtons

∵ a = 4 m/s²

- Substitute these values in the equation above to find k

∵ 20 = k (4)

∴ 20 = 4 k

- Divide both sides by 4

∴ k = 5

- Substitute the value of k in the equation

∴ F = 5 a ⇒ equation of variation

∵ F = 50 Newtons

∵ F = 5 a

∴ 50 = 5 a

- Divide both sides by 5

∴ 10 = a

∴ a = 10 m/s²

The acceleration of the object will be 10 m/s²

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Answer:

x = - g - c + y or g+c-y=x

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]g=x-c+y\qquad\text{add}\ c\ \text{to both sides}\\\\g+c=x-c+c+y\\\\g+c=x+y\qquad\text{subtract}\ y\ \text{from both sides}\\\\g+c-y=x+y-y\\\\g+c-y=x\to x=g+c-y[/tex]

Answer:

The solution for the given expression is 0 ,  2

Step-by-step explanation:

Given expression as :

- x² + [tex]\frac{4}{2}[/tex] x = 0

or, - 2 x² + 4 x = 0

or, 2 x ( -x + 2 ) = 0

or, ( - x + 2 ) ( 2 x ) = 0

or, 2 x = 0

∴  x = 0

and ( - x + 2 ) = 0

Or, - x = - 2

∴   x = 2

Hence The solution for the given expression is 0 ,  2  Answer

Answer:

1 function {(2,2),(4,4),(6,6),(8,8)} written is a function the other following coordinates are not functions due to it not being a straight line as a 'proper' function should be.

Answer:

The answer is:

{(2,2),(4,4),(6,6),(8,8)} is a function

{(0,3),(3,5),(5,6),(8,4)} is a function

{(1,2),(3,3),(4,8),(6,3)} is a function

{(3,4),(5,2),(5,6),(7,3)} is not a function

Step-by-step explanation:

Sorry I don't have an explanation, but I know these are correct because I took the test and got this correct. ;)

Answer:

5/16

Step-by-step explanation:

1/4 x 5/4=  5/16

(just multiply it, straight across.)

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

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

We have two points A(4, 3) and B(-1, 3).

Substitute:

[tex]m=\dfrac{3-3}{-1-4}=\dfrac{0}{-5}=0[/tex]

The slope m = 0, therefore it's a horizontal line.

The equation of a horizontal line:

[tex]y=a[/tex] where a is any real number

The line passes through points A and B, where ordinates are equal 3.

Therefore the equation is

[tex]y=3[/tex]

The amount of money he earns in 6 weeks is equal to $1512.

Given the following data:

To find the amount of money he earns in 6 weeks:

First of all, we would determine the amount of money he earns each week:

[tex]Weekly\;salary = Salary \times Number \;of \;hours \;worked\\\\Weekly\;salary =9\times 28[/tex]

Weekly salary = $252

In 6 weeks:

Total salary = [tex]252\times6[/tex]

Total salary = $1512

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