Determine whether each triangle is isosceles, equilateral, or can not be determined.

Given:

b) To find:

We know that,

Thus, the answer is,

a) To find:

We know that,

Thus, the answer is,

Solve first for the slope intercept form for the equation x + 3y = 24.

Since they are parallel, then they should have the same slope m. We now solve for b using the point (-2,-3)

After solving for b, complete the equation.

SOLUTION:

We want to find the inverse of f(x);

We solve for x;

Thus the answer is OPTION A

The simplest form of 7 × (-2/-5) × (7/-6) is - 49/15.

A whole number or another fraction is produced when one fraction is multiplied by another fraction. We all know that a fraction has two components: a numerator and a denominator. In order to multiply any two fractions, we must multiply the numerators and denominators, respectively.    

Here we have

=> [tex]7. \frac{-2}{-5} .\frac{7}{-6}[/tex]

Can be multiplied as given below

=> [tex]7 \times\frac{-2}{-5} \times\frac{7}{-6}[/tex]  

=> [tex]7 \times\frac{1}{5} \times\frac{7}{-3}[/tex]  

=> [tex]-\frac{49}{15}[/tex]  

Therefore,

The simplest form of 7 × (-2/-5) × (7/-6) = -49/15

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m = -13

-16 = m - 3

Add 3 to both sides of the equation

-16 + 3 = m - 3 + 3

-13 = m

m = -13

Given data:

The given inequality is 3(x+5) >12.

The given inequality can be written as,

The graph of the above solution is,

Thus, the solution of the given inequality is (-1, ∞).

Answer:

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

The sum of the measures of the angles of a triangle is 180:

The sum of the measures of the second and third angles is nine times the measure of the first angle:

The third angle is 26 more than the second:

Substitute the second equation into first:

Solve for x:

Substitute the value of x into second and solve for y:

Solve the third equation for y:

Compare the last two equations and find the value of z:

Find the value of y:

Answer:

x = 18°

y = 68°

z = 94°

Step-by-step explanation:

Define the variables:

Given information:

Create three equations from the given information:

[tex]\begin{cases}x+y+z=180\\\;\;\;\;\;\:\: y+z=9x\\\;\;\;\;\;\;\;\;\;\;\;\;\: z=26+y\end{cases}[/tex]

Substitute the third equation into the second equation and solve for x:

[tex]\implies y+(26+y)=9x[/tex]

[tex]\implies 2y+26=9x[/tex]

[tex]\implies x=\dfrac{2y+26}{9}[/tex]

Substitute the expression for x and the third equation into the first equation and solve for y:

[tex]\implies \dfrac{2y+26}{9}+y+26+y=180[/tex]

[tex]\implies \dfrac{2y+26}{9}+2y=154[/tex]

[tex]\implies \dfrac{2y+26}{9}+\dfrac{18y}{9}=154[/tex]

[tex]\implies \dfrac{2y+26+18y}{9}=154[/tex]

[tex]\implies \dfrac{20y+26}{9}=154[/tex]

[tex]\implies 20y+26=1386[/tex]

[tex]\implies 20y=1360[/tex]

[tex]\implies y=68[/tex]

Substitute the found value of y into the third equation and solve for z:

[tex]\implies z=26+68[/tex]

[tex]\implies z=94[/tex]

Substitute the found values of y and z into the first equation and solve for x:

[tex]\implies x+68+94=180[/tex]

[tex]\implies x=18[/tex]

Equation in slope intercept form is written as

y = mx + b

If slope m = 1/3 and y-intecept b = 3

Equation form using the information above is

Point slope form using the point (3, 4)

simply use the formula

y - y₁ = m( x- x₁ )

You have the following expression for the function f(x):

f(x) = 2x + 3

In order to calculate the value of f(4), just replace x=4 into the function f(x) and simplify it:

f(4) = 2(4) + 3

f(4) = 8 + 3

f(4) = 11

Hence, the answer is:

A) 11

10x - 2y = -4 ==== (1)

4x + 5y = -19 ==== (2)

To solve the system we should make the coefficients of y have the same values to eliminate it, then

Multiply equation (1) by 5 and equation (2) by 2

5(10x) - 5(2y) = 5(-4)

50x - 10y = -20 ===== (3)

2(4x) + 2(5y) = 2(-19)

8x + 10y = -38 ===== (4)

Now add equations (3) and (4) to eliminate y

(50x+8x) + (-10y + 10y) = (-20 + -38)

58x + 0 = -58

58x = -58

Divide both sides by 58 to find x

x = -1

Substitute the value of x in equation (1) or (2) to find the value of y

4(-1) + 5y = -19

-4 + 5y = -19

Add 4 to both sides

-4 + 4 + 5y = -19 + 4

0 + 5y = -15

5y = -15

Divide both sides by 5 to find y

y = -3

The solution of the system is (-1, -3)

Given

Answer

height of tower is 105 ft

Solution

For this case we can conclude the following:

triangle HJK ≅ triangle QRS because one is rotation of 90º about the origin of the other

Rectangle DEFG ≅ rectangle MNLP because one is a translation of the other

triangle ABC ≅ no given figure because one is not related by rigid motions of the other

To find a solution to the equation y = 3x - 1, we have to replace a variable by a number and compute the other variable.

Assuming x = 0, then

y = 3(0) - 1

y = 0 - 1

y = -1

Then, the point (0, -1) is a solution

Assuming x = 1, then

y = 3(1) - 1

y = 3 - 1

y = 2

Then, the point (1, 2) is a solution

Assuming x = 2, then

y = 3(2) - 1

y = 6 - 1

y = 5

Then, the point (2, 5) is a solution

In the next graph, the solutions and the line are shown

The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

Replacing with points (0, -1) and (1,2) we can compute the slope, as follows:

First let's find the missing value of the hypotenuse:

we have that the hypotenuse equals sqrt(41). Now we can find the values of the trigonometric functions:

1) To solve this System of Solutions graphically, we'll need to plot those lines described by those respective equations.

2) Let's set two tables

y=-5x +4

x | y

1 -1 ( 1,-1)

2 -6 ( 2,-6)

3 -11

y=3x + 4​

x | y

1 | 7 ( 1,7)

2 |10 ( 2,10)

3 | 13

2.2 Let's plot those equations and interpret the results:

3) As these lines have point (0,4) as their common point. Therefore we can state that the solution for this consistent system is S=(0,4)

Part A

The net force is 4 N up

Part B

The net force is 3 N to the left

Solution

We have the following values:

68,84,75,82,68,90,62,88,76,93,73,79,88,73,58,93,71,59,

58,51,61,65,75,87,74,62,95,78,63,72,66,96,79,65,74,77,95,

85,78,86,71,78,78,62,80,67,69,83,76,62,71,75,82,89,67,58,

73,74,73,65,81,76,72,75,92,97,57,63,68,83,81,82,53,85,94,

52,78,88,77,71

Part a

Range = Max- Min= 97-51= 46

Part b

The mean is given by:

Part c

The median is given by:

Position 40 ordered= 75 and Position 41 ordered= 75

Then the median is:

Part d

The most is the most frequent value and for this case is:

Repeated 5 times

Mode = 78

Part e

The data within the interval 50-54 is:

51 52 53

The variance is given by:

And the deviation si:

Answer:

Explanation:

If we have a linear equation of the form

then m = slope and b = y-intercept.

Now in our case, we have

which means that slope = 2 and y-intercept = 3

Therefore, we graph a line that has a slope of 2 and a y-intercept of 3.

A slope of 2 means that for every step you take to the right on a graph, you move 2 steps up to get to a point on the line.

The y-intercept of 3 means that the line passes through the point (0, 3).

Using these two facts about the line, we draw the following line.

From the above plot, we can clearly see that the line has a slope of 2 and a y-intercept of 3 - the same line described by y = 2x + 3.

Answer:

Explanation: We have to find the vertex form of the parabola equation from the given standard form of it:

The general form of the vertex parabola equation is as follows:

Comparing the equation (2) with the original equation (1) by looking at the graph of (1) gives the following:

Therefore the vertex form of the equation is as follows:

Therefore the answer is Option(A).

We need to simply use the triangle inequality Theorem, This theorem state that the sum of the two side lengths of a triangle must always be greater than the third side.

Now let's check from the given lengths

16 + 21 = 37 and 37 is less than 39 which is the third side

Hence, it cannot form a triangle

The first step to solve the problem is to create a function that relates the number of quizzes he attends by the number of weeks that elapses. Since he alread took one quizz, then the function must start from that and must grow at a rate of 5 quizzes per week. We have:

We want to know how many weeks until he takes 31 quizzes, then we need to make the expression equal to 31 and solve for the value of w. We have:

Then we subtract both sides by 1.

Then we divide both sides by 5.

It'll take 6 weekes before he have taken a total of 31 quizzes.

Answer:

72°

Step-by-step explanation:

Origin is completely 360° and its divided into 5 sides. So,360÷5=72°

write the total costs a linear function in the form

in which:

y= total cost

x= number of months

m= charge per month

b= fixed start up fee

replace all data in the equation

Since the question is the cost for 1 month, x=1

The cost for the use of the cellphone is $250

The unit rate = 0.6 holes per hour

Number of holes dug by the team = 12

Total time taken = 20 hours

The unit rate = (Number of holes) / (Time)

The unit rate = 12/20

The unit rate = 0.6 holes per hour

The selling price as a percent of the cost is given by the ratio between the selling price and the the cost. The selling price is given, which is $119.95 the cost is given by the difference between the selling price and the Markup($25.99). Combining all those informations in an equation, we have

To write this as a percentage, we just multiply the ratio by 100.

The selling price is 128% of the cost.

The popcorn balls cost $1.00 each

Jumbo candy bars cost $1.50 each

This week they have made a total of $229 and have sold 79

popcorn balls.

First, let's make a function with includes this information.

Let's say that popcorn balls are x and Jumbo candy bars are y.

So the function would be

1.00x+ 1.50y = 229

We already have the x value which represents the total of popcorn balls sold this week, so replace this value in the function:

1.00x+ 1.50y = 229

1.00(79)+ 1.50y = 229

79.00 + 1.50y = 229

Solve the equation for y to find the total of candy bars sold.

79 + 1.50y = 229

1.50y = 229 - 79

1.50y = 150

y = 150/1.50

y = 100

So the have sold 100 candy bars this week

Let's call the numbers a, b and c.

The first statement tells us that the sum of the three numbers is 106, so:

The second statement tells us that the second number is two times the third so:

The final statement tells us that the first number is 6 more than the third, so:

This gives us a system of three equations with three variables. Let's take the value of a given by the third equation, use it in the first one and isolate another variable:

Let's take this value of b and use it in the second equation:

Now we know the exact value of c, so let's go back to the third equation:

and now we also know the exact value of a, so let's go back to the second equation:

So, the first number (a) is 31, the second (b) is 50 and the third (c) is 25.

31+50+25=106.

The volume of a rectangular prism is given by the product of its three dimensions.

Since the box dimensions are 4 cm, 5 cm and 10 cm, its volume is:

So the volume of the box is equal to 200 cm³.

Given:

Simplify the equation,

Answer: x = 56.