Factor Completely: 3x2 + 9x - 30

Answer:

The correct option is:

x+y = 2

Step-by-step explanation:

Street 1 is given.

If Street 2 is parallel to Street 1, then they will have the same slope.

Find slope of Street 1:

Take any 2 points on Street 1. Consider (-2,3) and (1,0)

Slope is given by:

m = (y₂ - y₁) / (x₂ - x₁)

m = 0-3 / 1-(-2)

m = -3/3

m = -1

For Street 2:

y = mx + c

y = -1x +c

As it passes through (-2,4), substitute the point in the above equation:

4 = -1(-2) + c

c = 2

So substitute m = -1 and c =2 into general form of equation:

y = mx + c

y = -x + 2

or

x+y = 2

Answer:

x = 25.

Step-by-step explanation:

Since the side of the triangle that is labeled as 60 units bisects the right angle of the largest triangle, we can say that the smallest triangle, medium triangle, and largest triangle are all similar.

Since the smaller length of the middle triangle corresponds to x, and the longer length of the middle triangle (144) corresponds to the longer length of the smaller triangle (60), we can set up a proportion!

[tex]\frac{x}{60} =\frac{60}{144}[/tex]

144 * x = 60 * 60

144x = 3600

2x = 50

x = 25

Hope this helps!

Answer:

(1, 2)

Step-by-step explanation:

The function m(x) has the point (5, 2) on its graph is equivalent to say that m(x) evaluated at x = 5 gives 2 as result, that is, m(5) = 2.

f(kx) transforms point (x, y) into (x/k, y). Therefore: m(5x) transforms point (5, 2) into (5/5, 2) or (1, 2).

Answer:

  78π m²

Step-by-step explanation:

The lateral area of the cylinder is ...

  LA = 2πrh

  LA = 2π(3 m)(8 m) = 48π m²

The lateral area of one cone is ...

  LA = πrh . . . . where h is the slant height

  LA = π(3 m)(5 m) = 15π m²

Then the total surface area of the figure is the area of the two cones plus that of the cylinder:

  S = 2(cone area) + cylinder area

  S = 2(15π m²) +(48π m²)

  S = 78π m²

Corrected Question

The solution to an inequality is represented by the number line. How can this same solution be written using set-builder notation? {x | x > }

Answer:

[tex]\{x | x >3 \}[/tex]

Step-by-step explanation:

Given an inequality whose solution is represented by the number line attached below.

We observe the following from the number line

There is an open circle at 3, therefore the solution set does not include 3. (We make use of > or < in cases like that)

The arrow is pointed towards the right. All points to the right of 3 are greater than 3, therefore:

The solution in the number line can be written using set-builder notation as:

[tex]\{x | x >3 \}[/tex]

Answer: 2 1/10, 3.122, 3.19, 61/10

Step-by-step explanation:

Let's first turn each number into decimal form: (1/10=.1, 2/10=.2,etc.)

2.1, 6.1, 3.122, 3.19.  Obviously, the smallest number is 2.1, because it has a 2 in the ones place.  Next, we see a tie in the ones place between 3.122 and 3.19.  Then we look at the tenths place and see another tie.  Then, at the hundredths place, we see that 3.19 is greater that 3.122.  Thus, the order of the numbers is 2.1,3.122,3.19,6.1.

Hope it helps <3

Answer:

A

Step-by-step explanation:

Edge 2020

Answer:

19 : 25

Step-by-step explanation:

Answer:

Table 2

Step-by-step explanation:

The question is to identify the table where the relative frequency of orders for blue pants is half the relative frequency of their orders for black shorts.

We are interested in the number of blue pants and black shorts.

If we name them as p and b respectively, then we are looking for a table where s/p=2

Let's verify relevant data in all tables:

Table 1:

Table 2:

Table 3:

Table 4:

So only one of tables- the second one from top represents the required data.

Answer:

The second table

Step-by-step explanation:

I did the test.

Answer:

2,435

Step-by-step explanation:

find two even and two odd

Answer: 3.5 pi.

Step-by-step explanation: Since we know the circumference formula of a circle is 2*pi*radius, we just have to substitute 7 in there, and divide by 4. So here ya go, 3.5 pi.

Answer:

A is the correct answer

Step-by-step explanation:

Graph (A) represents the system of equations 4x + y = 3 and 2x - 3y = 3 option (A) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

The system of equations

4x + y = 3 and

2x - 3y = 3

In the first line, the slope is -4, and the y-intercept at (0,3)

In  the second line, the slope is 2/3, and the y-intercept at (0,-1)

Thus, graph (A) represents the system of equations 4x + y = 3 and 2x - 3y = 3 option (A) is correct.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

Answer:

The perimeter of given figure  = 56.56 ft

Step-by-step explanation:

Step(i):-

From diagram

      The length of the rectangle = 10 ft

     The width of the rectangle = 8 ft

     Perimeter of the rectangle

                      = 2 ( l+w)

                     =  2 ( 10 + 8)

                     = 2 × 18

                     = 36

Step(ii):-

The semi circle is included in the given diagram

Now we will find the perimeter of semicircle

We know that

        perimeter  of the circle

          p = 2πr + d

        perimeter of the semicircle

        [tex]P = \frac{1}{2} 2\pi r + d[/tex]

       P = πr + 2 r    (∵ d = 2 r)

Step(iii):-

From diagram the diameter of semicircle is equal to the width of the rectangle

      d = 8

     d = 2 r = 8

The radius of the circle 'r' = 4  

    perimeter of the semicircle

       P = πr + 2 r  

      P = 3.14 ( 4) + 8

     P= 20.56

Conclusion:-

The perimeter of given figure

                    = perimeter of rectangle + perimeter of semicircle

                    = 36 + 20.56

                   =56.56 ft

Hey there! :)

Answer:

C. (0, 5)

Step-by-step explanation:

Where the equation crosses the y axis is known as the y-intercept.

In the equation y = mx + b, the b  value represents the y-intercept where x = 0. Therefore:

Rearrange the equation pictured:

y = 5 - 3x --> y = -3x + 5

The b value in this equation is 5, so

The y-intercept of this equation is (0, 5).

Answer:

Option C is the correct option.

Here,

When X=0

y= 5-3*0

= 5-0

=5

x=0

y=5

Hope this helps...

Good luck on your assignment..

Answer:

See explanation below for further details.

Step-by-step explanation:

A rational consist of two real numbers such that:

[tex]\frac{a}{b} =c[/tex]

If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.

If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example:

If [tex]a = x^{2}[/tex] and [tex]b = x[/tex], then:

[tex]c = \frac{x^{2}}{x}[/tex]

[tex]c = x[/tex]

If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example

If [tex]a = 3\cdot x^{3}[/tex] and [tex]b = x[/tex], then:

[tex]c = \frac{3\cdot x^{3}}{x}[/tex]

[tex]c = 3\cdot x^{2}[/tex]

But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.

Example

If [tex]a = 10^{2x}[/tex] and [tex]b = 3\cdot 10^x[/tex], then:

[tex]c = \frac{10^{2\cdot x}}{3\cdot 10^{x}}[/tex]

[tex]c = \frac{1}{3}\cdot 10^{2\cdot x -x}[/tex]

[tex]c = \frac{1}{3}\cdot 10^x[/tex]

Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.

If [tex]a = 5\cdot e^{x}[/tex] and [tex]b = -3\cdot e^{x}[/tex], then:

Example

[tex]c = \frac{5\cdot e^{x}}{-3\cdot e^{x}}[/tex]

[tex]c = -\frac{5}{3}[/tex]

It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.

Example

[tex]5\cdot a^2\cdot x -9[/tex]

Answer:

D

Step-by-step explanation:

The formula of a circle is [tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex] where the vertex is (h,k).

The vertex is (4,-2) and the radius is 5, so substitute the numbers in and you get the solution.

Answer:

D

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

15+2x> 31

Subtract 15 from each side

2x > 16

Divide by 2

2x/2 > 16/2

x > 8

There is an open circle at 8

The line goes to the right

Answer:

25

Step-by-step explanation:

The Side Splitter Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally. Therefore:

6/15 = 10/?

6*? = 10*15

? = 10*15/6

? = 25

Answer:

Solution,

Finding the value of X,

[tex]11x + 2 = 68[/tex]

( being vertically opposite angles)

[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]

Value of X is 6

Now, finding the value of z

[tex]z + 68 = 180[/tex]

(sum of angle in linear pair)

[tex]z = 180 - 68 \\ z = 112[/tex]

Value of z is 112.

Hope this helps....

Good luck on your assignment...

Answer: The correct answer is 94 cm.

Step-by-step explanation:

wingspan         length

60 meters        70.5 m

----------------- = ----------------

80 cm                   x

Cross multiply

(60 m)x = (70.5 m)(80 cm)

Solve for x by dividing both sides of equation by 60 m:

x = (70.5 m)(80 cm) / (60 m) = 94 cm

The length of the model is 94 cm.

Answer:

94 cm

Step-by-step explanation:

Write and solve an equation of ratios:

70.5 m       60 m

----------- = -----------

    L           80 cm

Cross multiplying, we get:

(70.5 m)(80 cm) = (60 m)L

                                                                     (70.5 m)(80 cm)

Then the model length, L, should be  L = -------------------------

                                                                              60 m

or

L = 94 cm

Answer:

answer is (0,1)

Step-by-step explanation:

check

by substituting x=0 and y=1 in the equation above

- 2(0)+1> -4

1> -4

Thereby (0,1) is the required solution to the inequality

Answer:

No

Step-by-step explanation:

We have to check if 3/5 = 6/25. If we convert 3/5 into a fraction with denominator of 25 so that we can compare the two we get 15/25 and this is clearly not equal to 6/25. Therefore, the answer is no.

Answer:

157+364= 521 square mm

Step-by-step explanation:

Area of 1/2 circle = 1/2 pi r-squared = 1/2x10x10x3.14 = 157 square mm

Area of trapezoid = (a+b)/2xh = (20+32)/2 x 14 = 364 square mm

157+364= 521 square mm

Answer:

The factors of the polynomial are 5,  ( 3x - 2y), and  (3x + 2y)

Step-by-step explanation:

The given polynomial is 45x² - 20y²

45x² - 20y² = 5 (9x² - 4y²)

45x² - 20y² = 5 [ (3x)² - (2y)² ]

Using difference of two squares,  (3x)² - (2y)² = ( 3x - 2y)(3x + 2y)

45x² - 20y² = 5 ( 3x - 2y) (3x + 2y)

The factors of the polynomial are 5,  ( 3x - 2y), and  (3x + 2y)

Answer:

5(3x - 2)(3x + 2)

Step-by-step explanation:

Please indicate exponentiation with " ^ " :  45 x^2 - 20 y^2​.

Identify the GCF and factor it out:  5(9x^2 - 4y^2)

Recognize that (9x^2 - 4y^2) is the difference of two squares, which factors into (3x - 2y)(3x + 2y)

Then   45 x^2 - 20 y^2 = 5(3x - 2)(3x + 2)

Answer:

All real numbers

Step-by-step explanation:

The equation F(x)=x is an identity function. If you plot this on a graph, you notice that it is a diagonal line that always passes through (0,0), making the domain all real numbers.

Answer:

The won percentage is 24 / 29 ≈ 83% (24 + 5 = 29 games total) and the loss percentage is 5 / 29 ≈ 17%.

Answer:

The slope of a linear function. The steepness of a hill is called a slope. The same goes for the steepness of a line. The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run

Step-by-step explanation:

:)

Answer:

117,600 ways

Step-by-step explanation:

This problem can be solved using fundamental principle of counting , according to which , if there are m different things and n different things,

then there m*n ways to combine.

Example: if there 5 shirts and 3 ties,

then number of ways in which different combination shirt and tie can be worn is

5*3 = 15 ways.

____________________________________

In the problem,\

number of states is 50,

let those states be

A1, A2, A3, A4 ......A50

in each state there are 2 senate

Condition

3-Senator committee in which no two members are from the same state.

then

first member can be chosen from any of the 50 state,

hence first member can be chosen in 50 ways

for simplicity lets take state A1, you can choose any one you wish

second member cannot be from state A1, then number of state left = 49

second member can be chosen from  any of 49 state left

hence second member can be chosen in 49 ways

for simplicity lets take state A2,

Third member cannot be from state A1 and A2, then number of state left = 48

Third member can be chosen from  any of 48 state left

hence Third member can be chosen in 48 ways

for simplicity lets take state A3,

Hence no. of ways of choosing  3-Senator committee be formed such that no two Senators are from the same state = 50*49*48 = 117,600 ways

Answer:

y = (x - 2)² + 1

Step-by-step explanation:

Gnerela equation of a parabola in vertex form:

y = a(x - h)² + k

where (h, k) is the vertex

From the description of the graph:

Replacing into the general equation:

y = a(x - 2)² + 1

5 = a(0 - 2)² + 1

5 - 1 = a*4

4/4 = a

1 = a

Then, the equation is: y = (x - 2)² + 1

Answer:

The correct answer is A, "y = (x - 2)² + 1"

Step-by-step explanation:

I just completed the test and got full credit using this option.