What is the equation in point slope form of the line that is parallel to the given line and passes through the point (4,1)?


A Y-1=-2(x-4)
B y-1=-1/2(x-4)
C y-1=1/2(x-4)
D y-1=2(x-4)

Answer:

x = ± 6

Step-by-step explanation:

Hello!

The value of x is 6 or -6.

Hi...

[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]

[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]

Divide both sides by 5

[tex]\hookrightarrow{\mathtt{\frac{5x^2}{5}} = {\mathtt{\frac{180}{5}}[/tex]

Simplify:

[tex]\hookrightarrow{\mathtt{x^2 = 36}[/tex]

[tex]\hookrightarrow{\mathtt{For \: x^2 \: = f(a) \: the \: solutions \: are \: x = \sqrt{f(a)}}[/tex] , [tex]\mathtt{- \sqrt{f(a)}}[/tex]

[tex]\hookrightarrow{\mathtt{x = \sqrt{36}}[/tex] , [tex]\mathtt{x = -\sqrt{36}}[/tex]

Factor the number: 36 = 6²

[tex]\mathtt{= \sqrt{6^2}}[/tex]

Apply radical rule: [tex]\mathtt{\sqrt[n]{a^n} \: = a}[/tex]

[tex]\mathtt{\sqrt{6^2} = 6} \\\mathtt{= 6}[/tex]

- [tex]\sqrt{36} = -6[/tex]

[tex]\boxed{\fbox{\bf{x = 6 , x = -6}}}[/tex]

Hope It Helps You...

A graphic logo that depicts the meaning of any warning or sign through pictorial illustrations is called a pictogram. It can be used in chemicals, laboratories, geography or tourism. The label should have: Flammable and Health Hazard!

The pictogram can be explained as: According to the above description, the label sign should have a warning sign of flammable as it can catch and cause fire, a health hazard as it can cause corrosion, carcinogenic and irritation followed by an exclamation mark.

The flammable sign depicts that the substance can cause and catch fires also it can contain pyrophoric. It is cancer-causing, respiratory irritant and toxic hence is hazardous to health.

The exclamation mark is used at the end of the sentence for showing awareness and to convey the meaning of the sign.

Therefore, Flammable and Health Hazard! the sign should be used.

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The missing probability from the line in the diagram attached is 0.5.

The number line is a graduated straight line system showing the value of each real number from (-∞, +∞).

The probability of a number line in the diagram below is halfway (middle) between the impossible event and a certain event.

Thus,

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Answer:

7/6

Step-by-step explanation:

To find the slope you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

so doing that i get 7/6

Hope This Helped

Answer:

4/5

Step-by-step explanation:

Given,

Area of the triangle = 1/4 square meters

From the diagram,

Height = 2/5 m

To find : Length of the base

Formula : -

A = bh/2

Here,

A denotes Area

b denotes Base

h denotes Height

A = 1/4

h = 2/5

A = bh/2

Cross multiply,

A * 2 = bh

2A = bh

2 * (1/4) = b * (2/5)

(1 * 2)/4 = (b * 2)/5

2/4 = 2b/5

1/2 = 2b/5

Cross multiply,

1 * 5 = 2 * 2b

5 = 4b

b = 4/5 meters

Hence,

The length of the base is 4/5 meters.

The length of the base of the triangle is 5/4 meters.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

The formula to find the area of the triangle is,

Area = [tex]\frac{1}{2}[/tex] × base × height

Given,

Area of the given triangle = 1/4 square meters

Height = 2/5 meters

Substituting in to the formula,

[tex]\frac{1}{2}[/tex] × base × 2/5 = 1/4

1/5 × base = 1/4

Base = 5/4 meters

Hence the base of the triangle is 5/4 meters.

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Answer:

Answer Option C

Step-by-step explanation:

They make a big plus sign, PLUS=PERPENDICULAR

Answer:

West North West

Step-by-step explanation:

West North West would be the bottom half of North West after you split the compass heading into 2 again.

Answer:

north of west = 290 degrees

north of east = 70

Step-by-step explanation:

Answer:

No, because both of them will never be able to match; become equivalent. You would have to multiply 2 different numbers to make them match, meaning they would not be proportional. For a comparison to be proportional, the ratio you are trying to simplify to must be achieved by multiplying 2 numbers from the previous ratio by one LCD.

[tex]\frac{3\cdot 4}{7 \cdot 3} = \frac{12}{21}[/tex]

They are able to make 12/21, but that does not mean they are proportional.

The inequality that is correctly graphed is the one in option B.

Remember that if we have symbols like ≤ or ≥, we graph a solid circle, while if we use symbols like > or <, we need to use an open circle.

If we write:

x < -3

Then we must have an orange line to the left of x < -3

Finally, the option that you marked is wrong.

Why?

There it says that:

"x < -3 and x > 1"

The "and" means that x meets both properties at the same time, which is impossible.

The correct option is the one that says:

"x < -3 or x > 1".

The "or" means that x needs to meet only one of the two conditions, not both at the same time.

Then the correct option is B.

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Answer:

Hi! The answer is x=16

The regular polygon that has a rotation of 240 degrees to carry the polygon onto itself is the equilateral triangle.

Options

Equilateral triangle

Octagon

Rectangle

Pentagon

A polygon that can carry itself onto itself after a rotation of 240 degrees must obey the following rule:

Angle of rotation = 360/Sides

Next, we test the options:

Option (a) equilateral triangle

Angle of rotation = 360/3

Evaluate

Angle of rotation = 120

Next, we list the multiples of 120

120, 240, 360.....

See that 120 is a factor of 240.

This means that the equilateral triangle would be rotated onto itself when rotated by 240 degrees.

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Answer: 9.42 cu. meters

Step-by-step explanation:

V= 1/3 x TT x r^2 x height

TT (pi) =  3.14

r^2 is 1/2 diameter = 1.5

height = 4

V = 1/3 x 3.14 x 1.5^2 x 4

V= 1/3 x 3.14 x 2.25 x 4

V = 9.42 cu. meters

t=2/61

1 Rearrange terms

2

Multiply the numbers

3

Combine like terms

4

Add

10

to both sides

5

Simplify

6

Add

303t

to both sides

7

Simplify

8

Divide both sides by the same factor

9

Simplify

Answer: 2. 5. f(x)=x²-5; vertically stretched by a factor of 4, followed by a translation 3 units to the right. 4(x²-5). 4((x-3)²-5) g(x)= 4(x-3)²-20.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

y goes up by 4, so the each step is by 4, so that is the slope, which is the number before x, and then you subtract 4 to find the y-intercept, and 3-4=-1

The equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".

Equate Cole's age

t - 3 = 18

t = 18 + 3

t = 21

Therefore, the equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".

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Answer:

V=lwh

3

Step-by-step explanation:

The angle of triangle are ∠A = 86, ∠B = 55, ∠C = 39. The side of the triangles are a = 0.99, b = 0.81, c = 0.62.

Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.

[tex]\dfrac{sin A}{a} = \dfrac{sin B}{b} = \dfrac{sin C}{c}[/tex]

We have given angles of the triangle as

∠A = 86

∠B = 55

∠C = 39

So,

[tex]\dfrac{sin 86}{a} = \dfrac{sin 55}{b} = \dfrac{sin 39}{c}[/tex]

Now,

a = 0.99

b = 0.81

c = 0.62

The side of the triangles are a = 0.99, b = 0.81, c = 0.62.

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Answer:

c; 6

Step-by-step explanation:

to find the rate of change from x = 2 to x = 4 you use the (y2 - y1) / (x2 - x1) formula

so

(21 - 9) / (4 - 2)

12 / 2

6

the average rate of change is 6

Step-by-step explanation:

this looks totally like

f(x) = 1/3 x - 3

to me.

because

f(0) = -3

f(3) = -2

f(6) = -1

so, f(9) = 1/3 × 9 - 3 = 3 - 3 = 0

f(9) = 0

you did not list that as answer option, but that is the correct answer.

Volume of a right cone with base radius r cm and height h cm :

V = 1/3 π r² h cm³

Surface area :

A = (π r² + π r √(h² + r²)) cm²

Volume of a sphere with radius r cm :

V = 4/3 π r³ cm³

Surface area :

A = 4 π r² cm²

Volume of a cuboid with dimensions r cm × r cm × h cm :

V = r² h cm³

Surface area :

A = 2 r² + 4 r h

a. If the cone and sphere have the same volume, then

1/3 π r² h = 4/3 π r³   ⇒   h = 4r

b. If the area of the cuboid is 98 cm², then

2 r² + 4 r h = 98   ⇒   r (r + 2 h) = 49

c. Since h = 4r, substituting this into the equation from (b) gives

r (r + 8 r) = 9 r² = 49   ⇒   r² = 49/9   ⇒   r = 7/3

d. With r = 7/3, we have

h = 4 × 7/3 = 28/3

and so the volume of the cuboid is

V = (7/3 cm)² (28/3 cm) = 1372/27 cm³

Answer:

Step 1: area is base × height

Step 2: 36cm2

Step-by-step explanation:

Base × height is 9 and 4 and 9×4 = 36cm2

Hope this helps :)

Answer:

V=whl=3·5·8=120

Step-by-step explanation:

Just use l x w x h and there you go.

Answer:

A and B

Step-by-step explanation:

In both of these relations, each input corresponds to one and only output.

Answer:

7. 630

8. I'm not sure on this one-

9. 1331

Step-by-step explanation:

So for a rectangular prism the formula is l x w x h (length times width times height) Which would be 14 * 5 * 9 which equals 630

For the triangular prism, I forgot the formula

For the cube, you are given 1 number, 11, since it's a cube all lengths are the same so you do 11 to the power of 3 = 1331

Answer:

5 4/5 or 5.8

Step-by-step explanation:

convert 29/5 to 5 4/5

or

divide 29/5 is 5.8

The probability that the ball we remove at the 11th round is blue will be 0.6.

From the information given, we remove a random ball and replace it with a new red ball. for example, after the first round we have 9 blue balls and one red ball.

Since we have 9 blue balls and remove one every round. Let's assume that the number of blue and red balls will be 6 and 4 respectively in the 11 the round

Therefore, the probability that the ball we remove at the 11th round is blue will be:

= 6/(6 + 4)

= 6/10

= 0.6

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The 2 equations are classified as Identities because both sides remain the same for all values of z.

1) We are given the equation;

23z + 19 = 3(5z - 9) + 8z + 46

Let us try z = 0

23(0) + 19 = 3(5(0) - 9) + 8(0) + 46

19 = -27 + 46

19 = 19

Let us try z = 5;

23(5) + 19 = 3(5(5) - 9) + 8(5) + 46

134 = 48 + 40 + 46

134 = 134

Thus, this is an identity as both sides remaining the same for all values of z.

2) We are given the equation;

15y + 32 = 2(10y - 7) - 5y + 46

At y = 0, we have;

15(0) + 32 = 2(10(0) - 7) - 5(0) + 46

32 = -14 + 46

32 = 32

Let us try y = 2;

15(2) + 32 = 2(10(2) - 7) - 5(2) + 46

62 = 26 - 10 + 46

62 = 62

This is an identity as both sides remaining the same for all values of z.

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Step-by-step explanation:

0.777... is rational since it can be put in fraction form which is 7/9

note: if something can be put as an integer/integer its rational