Factorise fully 3m+12

Hello!

miles driven = x

the initial cost = 29

f(x) = 29 + 0.35x

Answer:

y = 4x + 1

Step-by-step explanation:

y = mx + b

b = y-intercept

From the graph we see that b = 1

m = slope

Start at (0, 1). Go up 8 units. Rise = 8. Go right 2 units. Run = 2.

slope = rise/run = 8/2 = 4

y = 4x + 1

Answer: 2

8/4

4/2

2/1

2

Step-by-step explanation:

8/4

4/2

2/1

2

Answer:

5x

= 5(8)

= 40

I hope I've helped

Since the sum of angles of a triangle is 180 degrees

Since the measures of the 3 angles of the 1st triangle are

Add them and equate the sum by 180 degrees

Add the like terms on the left side

Subtract 87 from both sides

Since the measures of the 3 angles of the other triangles are

Add them and equate the sum by 180 degrees

Add the like terms on the left side

Subtract 126 from both sides

Substitute the value of x in equation (1) to find y

Subtract 54 from both sides

The answers are:

x = 54

y = 39

Answer:

Approximately 2 days.

Step-by-step explanation:

The frog can only jump 3 lily pads each day.

24 hours = 1 day

\(\frac{24}{3}\) = 8 hours

Thus, it would take the frog 8 hours to cover a lily pad.

To get to the edge of the pond, the frog would jump through 6.5 lily pads (since he is at the middle of a lily pad at the center of the pond).

So that;

Total time required to get to the edge of the pond can be determined by;

6.5 × 8 hours = 52 hours

Number of days to get to the edge of the pond = \(\frac{52}{24}\)

                                                                    = 2.2

It would take him approximately 2 days to get to the edge of the pond.

Answer:

The function is increasing during the interval 0 < x < 5.

Step-by-step explanation:

“The domain on which the function is increasing” is just a fancy way of saying, over what X values is the f(x), or y, of the function increasing! When looking at a graph, whenever the function line is going up, that is when the function is increasing. All you need to to is find the X values over this time. Then, just format them in the [lowest x] < x < [highest x] format.

With this function, we can see that the f(x), or y, is increasing between X = 0 and X = 5. We would write 0 < x < 5. This shows that x is more than 0, but is less than 5 over the interval where it is increasing.

Let me know if you have any questions!

Answer: Standard Deviation, σ: 0.23979157616564

Count, N: 8

Sum, Σx: 33.6

Mean, μ: 4.2

Variance, σ2:  0.0575

Steps

σ2 =  

Σ(xi - μ)2

N

=  

(4.5 - 4.2)2 + ... + (4.1 - 4.2)2

8

=  

0.46

8

=  0.0575

σ =  √0.0575

=  0.23979157616564

Step-by-step explanation: but here

it isnt letting me do the fraction or the other things so yeah it will look wrong but its write for the entire graph

According to the angles between intersecting secant and tangent, the value of

angle DF is 52 degrees

angle PQR = 49 degrees

The value of angle DF is solved using the angles of intersecting secant out side the circle

The theorem give the formula in the form

44 = 1/2 (140 - DF)

88 = 140 - DF

DF = 140 - 88

DF = 52 degrees

Using intersection of tangents, for the second figure

exterior angle = 1/2 (major arc - minor arc)

major arc = 360 - 131 = 229

PQR = 1/2 (229 - 131)

PQR = 49 degrees

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Answer:

E

Step-by-step explanation:

using the Sine rule in Δ ABC

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

where a is the side opposite ∠ A , b opposite ∠ B , c opposite ∠ C

we require to calculate ∠ C

∠ C = 180° - (64 + 85)° = 180° - 149° = 31°

then to find a , using

\(\frac{a}{sinA}\) = \(\frac{c}{sinC}\)

\(\frac{a}{sin64}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

a × sin31° = 9.3 × sin64° ( divide both sides by sin31° )

a = \(\frac{9.3sin64}{sin31}\) ≈ 16.23 ( to 2 decimal places )

then to find b , using

\(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

\(\frac{b}{sin85}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

b × sin31° = 9.3 × sin85° ( divide both sides by sin31° )

b = \(\frac{9.3sin85}{sin31}\) ≈ 17.99 ( to 2 decimal places )

The study of data collection, analysis, presentation, and interpretation is known as statistics.

Given,

What is statistics?

Data collection, analysis, presentation, and interpretation are all part of the science of statistics. Much of the early motivation for the subject of statistics came from governmental needs for information on a variety of economic activity and census data.

Types of statistics;

Based on the characteristics, the various statistical kinds are divided: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as using pie charts, bar graphs, or tables.

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Answer:

The function is:

\(f(x) = x - 0.15x\)

Can also be written as:

\(Sale = Original - 0.15(Original)\)

Step-by-step explanation:

Given that the sale percentage is 15%

In general, the sale price is calculated by finding the discount according to discount percentage and then subtracting the discount from original price.

Given that x is the original price

Then the discount will be:

\(Discount = Original Price * 0.15\\Discount = 0.15x\)

The sale price will be:

\(Sale Price = Original\ Price - 0.15(Original\ Price)\\\)

As x is the original price

\(f(x) = x - 0.15x\)

Can also be written as:

\(Sale = Original - 0.15(Original)\)

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Answer:

  2.5%

Step-by-step explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

The z-score of 335 is ...

  Z = (X -µ)/σ

  Z = (335 -555)/110 = -220/110 = -2

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

  P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

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Answer:

17.5 ft

Step-by-step explanation:

Draw a picture as shown in the attached image. From the image, you can see that a proportion can be set up comparing the height of the flagpole and student to their respective shadows. Once you set up the proportion, solve to get the height of the flagpole.

Answer:

x^2+12x=-11

Step-by-step explanation:

Answer:

(-1, 12) and (-11, 132)

Step-by-step explanation:

The logarithmic function that models the data is given as follows:

y = 1.0994 + 5.6403 ln(x).

The logarithmic function is used as from the table, the data has a initial fast increase and then the rate of the increase decreases, as the graph reaches it's horizontal asymptote.

The function is defined using a logarithmic regression calculator, inserting the points of the data-set.

From the table, the points are given as follows:

(0, 0.5), (1, 1.4), (2, 4.1), (3, 7.6), (4, 9.1), (5, 10).

(as x represents the number of years after 2005).

Inserting these points into the logarithmic regression calculator, the equation is given as follows:

y = 1.0994 + 5.6403 ln(x).

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According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

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The slope of a line

Given two points through which a line passes A(x1,y1), B(x2,y2), the slope of the line can be calculated with the formula:

We are given the point A(-4,-8) and the (incomplete) point B(?,1). Knowing the slope is m=2, we can calculate the missing value at point B. Let's call it x: B(x,1).

Substituting all the values in the formula of the slope, we get:

Operating:

Solving for x:

The missing value is 1/2, thus point B is B( 1/2 , 1 )

Answer:

A=3

B=4

C=81

Step-by-step explanation:

Just did it

Answer:

a =

✔ 3

b =

✔ 4

c =

✔ 81

Answer:

1-23.5

2-2

3-5.59

4-0.278

Answer: 12

Step-by-step explanation:

       1 2  

   5 ⟌ 6 0  

     - 5    

       1 0  

     - 1 0  

         0  

The zeroes of the polynomial are x=3, x=-5 and x=3/5

The locations where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero . The highest power of the variable x is referred to as a polynomial's degree. A linear polynomial is a polynomial with degree 1.

Given:

f(x)=5x³+7x²−81x+45.

let us take x= 3

5(27)+7(9)-81(3)+45

=135+63-243+45

= 243-243

=0

So, 3 is a root of polynomial and x-3 is factor of Polynomial.

Now, divide 5x³+7x²−81x+45 by x-3 we get 5x²+22x-15

Now, factorise 5x²+22x-15.

= 5x²+25x-3x-15

= 5x( x+ 5) - 3(x+ 5)

= (5x - 3)( x+ 5)

Then, x= 3/5 and 5

Hence, the zeroes of the polynomial are x=3, x=-5 and x=3/5

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Answer:

6

Step-by-step explanation:

15/5=3

30/5=6

Answer:

6

Step-by-step explanation:

Answer:

the answer to the problem is 35.

Answer:

he horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa"

Step-by-step explanation:

Answer:

Volume of rectangular prism = 1 1/3 x 5/6 x 2/3 = 4/3 x 5/6 x 2/3 = 20/27

Volume of cube = 1/6 x 1/6 x 1/6 = 1/216

Number of cubes that will pack the rectangular prism = 20/27 / 1/216 = 160

eddibear3a and 47 more users found this answer helpful

Step-by-step explanation:

Volume of prism = l x w x h

Volume of right rectangular prism = 1 1/4 x 5/8 x 3/4 = 75/128

Volume of cube = s^3

= 1/8^3 = 1/512

Total cubes = volume of prism / volume of cube

Total cubes = 75/128 / 1/512

Total cubes = 300

The answer is 300

The requried volume of the pedestal is 135 cubic inches.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The volume of a triangular prism is given by the formula V =base x h, where the base is the area of the base and h is the height of the prism.

In this case, the area of the base is given as 9 in², and the height of the prism is given as 15 inches.

Therefore, the volume of the pedestal is:

V = base x h

V = 9 in² x 15 inches

V = 135 cubic inches

So the volume of the pedestal is 135 cubic inches.

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