12x+10y=2
-x+4y= -5

Without actually solving, explain whether substitution or elimination would be a better method for solving the system.

The probability that the 2-digit number is prime is 3/8

The sets are given as:

First digit = {1, 2}.

Second digit = {1, 2, 3, 4}

When the 2-digit is formed, we have:

Numbers = {11, 12, 13, 14, 21, 22, 23, 24}

In the above set, there are 3 prime numbers out of the 8 numbers.

Hence, the probability that the 2-digit number is prime is 3/8

Read more about probability at:

https://brainly.com/question/11234923

#SPJ1

The solutions to the quadratic equations are:

a) [tex]x = \frac{3 \pm \sqrt{19}}{5}[/tex]

b) x = -8, x = 5.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

Item a:

The coefficients are a = 5, b = -6, c = -2, hence:

Item b:

The equation is:

x² + 3x = 40

x² + 3x - 40 = 0.

It can be simplified as follows:

(x - 5)(x + 8) = 0.

Hence the solutions are:

More can be learned about quadratic equations at https://brainly.com/question/24737967

#SPJ1

It will take approx. 22 minutes and 30 seconds for the speeches.

It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Here, Time duration of each learner = 1 minutes 30 seconds

                                                            = 3/2 minutes.

        Total number of learners = 15

Time taken by all the speech category = 15 X 3/2

                                                                 = 45/2

                                                                = 22 minutes 30 seconds

Thus, It will take approx. 22 minutes and 30 seconds for the speeches.

Learn more about Division from:

https://brainly.com/question/1575906

#SPJ1

Answer:

the chance is 1.5 out of 5

Answer:

The required linear equation satisfying the given conditions f(-5)=-4 and f(5)=2 is

[tex]$$y=\frac{3}{5} x-1$$[/tex]

Step-by-step explanation:

It is given that f(-5)=-4 and f(5)=2. It is required to find out a linear equation satisfying the conditions f(-5)=-4 and f(5)=2. To find it out, first, represent the given conditions in the form of points and then find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the form [tex]$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$[/tex]

Step 1 of 4

Observe, f(-5)=-4 gives the point (5,-4)

And f(5)=2 gives the point (5,2)

This means that the function f(x) satisfies the points (-5,-4) and (5,2).

Step 2 of 4

Now find out the slope of a line passing through the points (-5,-4) and (5,2).

[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{2-(-4)}{5-(-5)} \\m &=\frac{2+4}{5+5} \\m &=\frac{6}{10} \\m &=\frac{3}{5}\end{aligned}$$[/tex]

Step 3 of 4

Now use the slope [tex]$m=\frac{3}{5}$[/tex] and use one of the two given points and write the equation in point-slope form:

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-2)=\frac{3}{5}(x-5)$$[/tex]

Distribute [tex]$\frac{3}{5}$[/tex],

[tex]$$\begin{aligned}&y-2=\frac{3}{5} x-\frac{3}{5} \times 5 \\&y-2=\frac{3}{5} x-3\end{aligned}$$[/tex]

Step 4 of 4

This linear function can be written in the slope-intercept form by adding 2 on both sides, [tex]$y-2+2=\frac{3}{5} x-3+2$[/tex]

[tex]$$y=\frac{3}{5} x-1$$[/tex]

So, this is the required linear equation.

Answer:

18+62=80x

12+18=30x

x=80÷30=2

x>2

Answer:

try 4

Step-by-step explanation:

8x4= 32

32-7=25

Answer:

this question is not clear i have read it twice an still dont understand it. Sorry

Option (A) :  least: 10 hours; greatest: 14 hours

The function f(x) = sin x has all real numbers in its domain, but its range is

−1 ≤ sin x ≤ 1.

How to solve such range questions?

Such questions in which every term is in addition and its range is asked is simplest ones to solve if we know the range of each of term. This can be seen from this question

Given: d(t) = 2sin(xt) + 12

=  −1 ≤ sin (xt) ≤ 1.

=  −2≤ 2 sin (xt) ≤ 2.

=  10 ≤ 2sin (xt) + 12 ≤ 14

=   10 ≤d(t) ≤ 14

Thus  least: 10 hours; greatest: 14 hours

Learn more about range of trigonometric ratios here :

https://brainly.com/question/14304883

#SPJ4

Answer:

==============

Let the cost price is x.

We have:

Solve it for x:

The cost is 22500, find selling price with 20% profit:

Answer:

The LCM is 20

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the LCM of 4, 10

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The lcm stands for the least common multiple.

Using our times tables, let's find the lcm of 4 and 10.

[tex]\bf{Which\;is\;20}[/tex]. 40 is indeed a common multiple of 4 and 10, but it's not the least common multiple. The lcm is 20.

We can also list some multiples of 4 and 10 and find the lcm.

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40...

10: 10, 20, 30, 40, 50, 60...

As you can see, we end up with the same answer: the lcm of 4 and 10 is indeed 20.

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{=Lcm=20}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]

The data is modeling a geometric sequence because they have a common ratio of 2.

The recursive formula to determine the time she will complete station 5

Part C:

The explicit formula to find the time she will complete the 9th station.

Read more about recursive formula here:

https://brainly.com/question/1275192

#SPJ1

We now have three equations, so we can solve them.

Let's define the length of the 3 boards in terms of x:

F=x

S=2x-3

T=2

F+S+T =26

x+2x-3+2 =26

3x =26+1=27

x =27/3 = 9 feet for First section

2x-3 =18-3 = 16 feet = Second

2 = Third

9+16+2 = 27

27 is the length of the shortest piece.

Learn more about the length at

https://brainly.com/question/2217700

#SPJ4

Answer:

2 parts

Step-by-step explanation:

The rectangle has a 1/2 ratio, because there are 4 parts of the circle, you will shade 2. This is because 2/4 ratio is simplified to 1/2.

Answer:

Step-by-step explanation:

I'm going to assume you want it to be a perfect triangle, so then we would have the equation 4x=24. So we can divide each side by 4 to get rid of the 4 and get x by itself. So 24/4= 5. So x=5

Answer:

my ans will be wrong also and right also 50%5$chances it is an opposite angle so it is in out manner so iys sum is 180 so we have to subbtract

Step-by-step explanation:

65०to 180०(180०-65०=115०) i think ans is 115०the missing angle measurement is 115०in my opinion

There's no "whole" number that gets exactly to 2230 (but the question that you are asking is the square root of 2230 I believe) but the answer would essentially be about 47.22.

The true statements about the pool are

The given parameters are:

To measure the drain, we simply calculate the perimeter of the edge of the pool.

This means that (a) is correct

When the volume is calculated, the unit is cubic yard or yd³.

This means that (b) is wrong

The area of the cover is:

Area = Length * Width

This gives

Area = 25 yards * 10 yards

Evaluate

Area = 250 square yards

This means that (c) is correct

The length of the drain is calculated as:

Perimeter = 2 *(Length + Width)

This gives

Perimeter = 2 * (25 + 10)

Evaluate

Perimeter = 70

This means that (d) is wrong

Lastly (e) is correct, because the width of pool is 10 yards

Read more about perimeter and volume at:

https://brainly.com/question/15465114

#SPJ1

Answer:

b is not a polynomial

Step-by-step explanation:

b is not a polynomial because in y-3/y the y in denomination means y to the power -1 when it is taken to numerator and if power is negative then it is not a polynomial

Answer:

(x+5)² + (y+5)² = 18

Step-by-step explanation:

Since the outline of the circle intersects with the point (-8,2), you can substitute to find the equation of the circle in the form (x-h)² + (y-k)² = r². First the center of the circle is given in the form (h,k). So (-5, -5) → (x – (-5))² + (y – (-5))² = r² → (x + 5)² + (y + 5)² = r².

Then to find r², substitute the given point with x and y.

((-8) + 5)² + ((-2) + 5)² = r²

(-3)² + (3)² = r²

18 = r²

r² = 18.

For the given experiments there are following outcomes.
A) Independent
b) Dependent
C) Dependent
D) Dependent
E) Independent

Probability can be defined as the ration of favorable outcomes to the total number of events.

For A)
A coin is tossed and a dice is flip. Both the event are independent of each other.

For B)
Choosing of clips have same total number of events that why both the events are dependent to each other.

For C)
It also have same number of total samples cause both cherries and nuts contained chocolate belongs to the same box. That's why its also dependent.

For D)
It is also dependent because the total number of sample is same for both the marbles.

For E)
It is independent, because for every box that picked reduces the size of sample and probability of picking new box wont depends on previous box.

Thus, this is how events are dependent and independent

Learn more about probability here:

brainly.com/question/14290572

#SPJ1

Answer:

The given lines are perpendicular.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (1,7) and (5,5). Whereas, line 2 passes through (-1,-3) and (1,1).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}m_{1} &=\frac{5-7}{5-1} \\m_{1} &=\frac{-2}{4} \\m_{1} &=-\frac{1}{2}\end{aligned}$$[/tex]

Step 2 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{2}=\frac{1-(-3)}{1-(-1)} \\&m_{2}=\frac{4}{2} \\&m_{2}=2\end{aligned}$$[/tex]

And

[tex]$$\begin{aligned}&m_{1} m_{2}=-\frac{1}{2}(2) \\&m_{1} m_{2}=-1\end{aligned}$$[/tex]

Since, both slopes are reciprocal of each other.

Therefore, the lines are perpendicular.

Original function involved multiplication by 4 and then subtraction of 2.

Inverse function involves addition of 2 and then division by 4.

So the inverse represents the reverse of the given process.

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

According to the function,

Let the function be represented by f(x).

Step 1- Multiplying the number x by 4 results in 4x.

Step 2 - Subtracting 2 from results give 4x - 2.

So the function becomes:

f(x) = 4x - 2

We will find the inverse function by Replacing f(x) by y, and isolate x on one side of the equation and find the inverse:

[tex]y=4x-2\\\\ < br/ > y+2=4x\\ < br/ > x =\frac{1}{4} (y+2)\\ < br/ > f^-^1(y) = \frac{1}{4} (y+2)\\ < br/ > f^-^1(x) = \frac{1}{4} (x+2)[/tex]

Here,

The inverse function represents the reverse process.

Here, Original function involved multiplication by 4 and then subtraction of 2.

Inverse function involves addition of 2 and then division by 4.

So the inverse represents the reverse of the given process.

Learn more about Function here:https://brainly.com/question/12431044

#SPJ1

Answer: C

Step-by-step explanation:

[tex]\sin x=\frac{13}{18}\\\\x=\sin^{-1} \left(\frac{13}{18} \right) \approx \boxed{46.24^{\circ}}[/tex]

The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.

An equation is an expression that shows the relationship between two or more variables and numbers.

The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

[tex]\bf{\dfrac{1}{2}(27+6)10 }[/tex]

Add 27 and 6 to get 33.

[tex]\bf{\dfrac{1}{2}(33)(10) }[/tex]

Multiply 1/2 by 3 to get 33/2.

[tex]\bf{\dfrac{33}{2}(10) }[/tex]

Express 33/2 (10) as a single fraction.

[tex]\bf{\dfrac{(33)(10)}{2} }[/tex]

Multiply 33 and 10 to get 330.

[tex]\bf{\dfrac{330}{2} }[/tex]

Divide 330 by 2 to get 165.

[tex]\bf{165 \ \ \to \ \ \ Answer}[/tex]

h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.

In the question, we are given that during a local high school football game, the height of h feet of a football after t seconds can be represented by the quadratic function h(t) = -16t² + 58t + 2.

We are asked to find h(2.5) and explain its meaning.

To find h(2.5), we substitute t = 2.5, in the quadratic function h(t) = -16t² + 58t + 2.

Thus,

h(2.5) = - 16(2.5)² + 58(2.5) + 2,

or, h(2.5) = - 16(6.25) + 145 + 2,

or, h(2.5) = -100 + 147,

or, h(2.5) = 47.

Hence, h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.

Learn more about quadratic functions at

https://brainly.com/question/1063981

#SPJ1