5t + 5 = 30 solve for t

Keywords

parallel, perpendicular, graphing, linear equation, slope, lines

we know that

If two lines are perpendicular, then the product of their slope is equal to minus one

so

[tex]m1*m2=-1[/tex]

If two lines are parallel, then their slope are equal

[tex]m1=m2[/tex]

In this problem we have

[tex]y=x+11[/tex] --------> linear equation A

the slope is [tex]m1=1[/tex]

[tex]y=-x+2[/tex]  --------> linear equation B

the slope is [tex]m2=-1[/tex]

Find the product

[tex]m1*m2=-1[/tex] ---------> the lines are perpendicular

therefore

the answer is the option B

Perpendicular

using a graphing tool

see the attached figure

Answer:

Perpendicular

Step-by-step explanation:

Given are two equations as

[tex]y=x+11\\y=-x+2[/tex]

We have to find whether these two are parallel or perpendicular or neither

For this first we have to find the slope of these two lines

I line slope = 1

II line slope =-1

Since slopes are not equal, the lines are not parallel.

Let us check product of these slopes.  IF product =-1 the lines are perpendicular

We find that product = [tex]1*-1=-1[/tex]

Hence two lines are perpendicular

Answer:

a horizontal translation and a glide reflection

Step-by-step explanation:

Answer:

center

Step-by-step explanation:

The point in the middle of a circle called, B. Center

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know, The largest chord that passes through the center of a circle is called a diameter.

All the other line segments that can be drawn with endpoints touching the circumference of a circle are called chords.

The radius is half the length of the largest chord(diameter).

A circle is defined as if we fix a point and mark points in a plane such that each point is equidistant from that fixed point a circle will be formed.

That fixed point is called the center of a circle.

learn more about circles here :

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Final answer:

The area of a square as a function of its perimeter is A = (P/4)².

Explanation:

The area of a square can be represented as a function of its perimeter. Let's say the side length of the square is a. The perimeter of the square is given by P = 4a. So, to write the area A as a function of the perimeter P, we can use the formula:
A = (P/4)²

To find the standard form equation of a hyperbola with given vertices and foci, calculate the values of a and b using distances from the origin, and then insert into the standard form equation (y²/a²) - (x²/b²) = 1. The final equation for the hyperbola with vertices at (0, ±2) and foci at (0, ±7) is 45y² - 4x² = 180.

To find the equation of a hyperbola in standard form, we need the vertices and the foci. Given that the vertices are at (0, ±2), we know that the hyperbola is vertical, and the distance between the vertex and the center, which is the origin, is 2 units, so a=2. Since the foci are at (0, ±7), the distance from the center to a focus is 7 units, which means c=7.

With these values, we can calculate b by using the relationship c² = a² + b². Plugging in the known values gives us 7² = 2² + b², so b² = 49 - 4 = 45. Therefore, b = √45.

The standard form equation of a vertical hyperbola with a center at the origin is (y²/a²) - (x²/b²) = 1. Replacing a and b with the found values, the equation becomes (y²/4) - (x²/45) = 1. Multiplying through by 180, which is the least common multiple of 4 and 45, we get the equation in standard form: 45y² - 4x² = 180.

Answer:

D) 6 1/12

Have a good day.

Answer:

D. It’s right

Step-by-step explanation:

Answer:

[tex]y-2=3(x-4)[/tex]

Step-by-step explanation:

We are given that a line has a slope (m) of 3 and passes through (4, 2). We want to write this equation in point-slope form.

Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point.

We can substitute what we know into the equation.

First, substitute 3 as m.

[tex]y-y_1=3(x-x_1)[/tex]

Now, substitute 4 as [tex]x_1[/tex] and 2 as [tex]y_1[/tex].

[tex]y-2=3(x-4)[/tex]

The local minimum values of h are -3 and 0, and occur at the points (-2,-3) and (3,0).

From the graph, we can see that:

Local minimum values of h occur at (-2,-3) and (3,0)

Local minimum values of h are -3 and 0 respectively.

To find the local minimum values of h, we look for the points on the graph where the function changes from decreasing to increasing. These points are called local minimums.

From the graph, we can see that h changes from decreasing to increasing at the points (-2,-3) and (3,0). Therefore, these are the local minimum values of h.

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The young man has a 50% chance of developing Huntington's disease, as he can inherit the HD allele from his father. Similarly, if he carries the HD allele and has a child with a woman who does not carry the HD allele, their child has a 50% risk of inheriting and developing the disease.

Huntington's disease is associated with genetics and can be passed from parents to offspring. If this young man's father suffers from the condition due to a dominant allele, HD, and his mother does not carry the HD allele, he has a 50% chance of inheriting and later developing the disease. This probability arises because the offspring inherits one allele from each parent.

If the young man has a child with a woman who does not carry the HD disease allele, the child's risk of developing the condition depends on whether the father carries the HD allele. If the father does not carry the HD allele, the probability that their first child would be affected by Huntington's disease is 0%. If the father does carry the HD allele, the risk would be 50% as the child will inherit one allele from the each parent (one from the father who might have HD and one from the mother who does not carry the HD allele).

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5x+2y >/= 5

Answer: 2 burgers and 2 fries if he has only $15

Burgers=$5 each

Fries=$2 each

5+5=10

2+2=4

which comes out to $14 so the max he can get is 2 each

To solve for x, given that the perimeter of a square is equal to the perimeter of an equilateral triangle, the equation 4x = 3(x + 1) can be used.

To find the value of x when the perimeter of a square is equal to the perimeter of an equilateral triangle, we set up an equation. Since the side of the square is given by x, and the perimeter of a square is 4 times the length of a side, the perimeter of the square is 4x. The length of a side of the equilateral triangle is given by x + 1, and since the perimeter of the equilateral triangle is 3 times the length of a side, its perimeter is 3(x + 1). Setting these two perimeters equal to each other gives us the equation 4x = 3(x + 1).

Answer:

The bar graph is given ,which shows the amount of time Latisha participated in an exercise program over a four-week period.

If amount of exercising , that is increase over time appear larger

She must use a larger range on the vertical scale.There will be no change in width of bar graph, as coloring the bar graph with different color will make no sense.

Pictorial representation of this problem is depicted below:

Option (B) is true.Use a larger range on the vertical scale.

This answer is correct in the sense that , if time of exercise increases,

Otherwise, if you increase the width between two whole numbers, the graph will appear larger.That is between if width between 0 to 1 is 1 cm than increase it by 1.5 cm or 2 cm, that will make the bar graph larger.  

Solving literal equations for a variable is beneficial for finding general solutions that apply to multiple situations, saves time by avoiding repetitive calculations, and reduces potential errors when working with complex numbers.

Why Solve Literal Equations for a Variable

Solving a literal equation for a variable is fundamental in mathematics because it allows one to find a general solution that can apply to various situations. Instead of replacing a variable with a given number each time, which can be time-consuming and error-prone especially when dealing with long decimals and complex fractions, working with no numbers—just variables—simplifies the process. Having found the values that make the equation true, one can easily convert words to an algebraic expression or equation that best models a given problem. This results in the ability to find a solution more swiftly and with less room for error.

For example, in computer programs, solutions to equations are frequently required for multiple sets of input values. Algebraically solving an equation provides a general form that can easily be reused with different inputs, saving substantial time and resources. Additionally, in complex problems involving multiple unknowns, solving for one variable in terms of others can lead to a simplified equation, making it easier to solve the problem.

Answer:

1: 720

2: [tex]\frac{1}{336}[/tex]

Step-by-step explanation:

1: There are 10 kids in a race so the number of ways such that they come first , second and third=10×9×8

                           =720

(since the first place is occupied by any one of the ten students i.e. we have ten choices after occupying first position there are only 9 students left for second position and after occupying second for the third position only 8 choices are left)

2: We have to find the probability such that there is no replacement  such that we draw 135.

for the first position we have to find the probability([tex]P_{1}[/tex]) that '1' comes out of 8 numbers=[tex]\frac{1}{8}[/tex]

similarly for second choice we could not take 1 as there is no replacement

so probability that 3 comes([tex]P_{2}[/tex]) =[tex]\frac{1}{7}[/tex]

similarly probability that 5 comes at third position([tex]P_{3}[/tex]) = [tex]\frac{1}{6}[/tex]

hence, probability that 135 is drawn= [tex]\frac{1}{8}\times\frac{1}{7}\times\frac{1}{6}=\frac{1}{336}[/tex]

Answer: 4,2 is the correct answer

Step-by-step explanation: