Mark drew two lines that form a right angle. What word describes the lines mark drew

Answer:

Step-by-step explanation:

The cable is 50 yards long, viewing post is 40 yard high , how far is the bottom cable from the base of the viewing post

B is true
D as well

we have

[tex]-p(d+z)=-2z+59[/tex]

Solve for z

[tex]-p(d+z)=-2z+59\\-pd-pz=-2z+59[/tex]

Group terms that contain the variable z, and move the other terms to the opposite side of the equation

[tex]-pz+2z=59+pd\\z(2-p)=59+pd[/tex]

Divide by [tex](2-p)[/tex] both sides

[tex]z=\frac{(59+pd)}{(2-p)}[/tex]

therefore

the answer is

[tex]z=\frac{(59+pd)}{(2-p)}[/tex]

Final answer:

The equation −p(d+z)=−2z+59 was solved for z by distributing the negative sign, combining like terms, and dividing by the coefficient of z, resulting in z = (59 + pd)/(2 - p).

Explanation:

The student asked to solve the equation −p(d+z)=−2z+59 for z. To solve for z, we need to isolate z on one side of the equation, following these steps:

Distribute the negative sign through the parentheses on the left side of the equation: −pd − pz = −2z + 59.

Move the terms containing z to one side of the equation: −pz + 2z = 59 + pd.

Combine like terms by adding pz to both sides: 2z + pz = 59 + pd or z(2 - p) = 59 + pd.

Divide both sides by (2 - p) to solve for z: z = (59 + pd)/(2 - p).

Now, z is isolated and the solution is given in terms of p and d.

3s+2=12-2s

(3s-3s)+2=12(-2s-3s)

2=12-5s

2-12=(12-12)-5s

-10=-5s

-10/-5=-5s/-5

2=s

Check

(3*2)+2=12-(2*20

6+2=12-4

8=8

S=2

Answer:

6 x $2.5 = $15

$15 + $5 = $20

The speed of boat is 7 km/h and speed of stream is 6 km/h.

What is speed ?

In unit time the distance covered by any object is called speed.

In mathematical term, Speed is express as S=D/T,

where S=speed, D=distance, T= time .

Let the speed of boat in N, and the speed of current is D,

Given that,

The speed in downward stream of a boat N+D= 13 km/h,    (1)

And the speed in upward stream of a boat N-D= 1 km/h.     (2)

To Find speed of boat in still water, add equation (1) and (2),

2N=14 ⇒ N=7 km/h

To Find speed of current, substract equation (1) and (2),

2D=12 ⇒ D=6 km/h.

The speed of boat is 7 km/h and speed of stream is 6 km/h.

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The value of a gold nugget containing 0.82 ounces of gold at $1566.80 per ounce is $1284.776.

The value of a gold nugget containing 0.82 ounces of gold, given that gold is worth $1566.80 per ounce, can be calculated through a simple multiplication. The value of the gold nugget is found by multiplying the amount of gold in the nugget by the price per ounce of gold.

To calculate:

Therefore, the gold nugget is worth $1284.776.

The average rate of change in altitude of the hiker from her starting point to her ending point is -63.5 feet per minute.

The following can be deduced based on the information provided in the question:

During the first walk, she descended 1024 feet and during the second walk, she descended 500 feet. Therefore, the total will be:

= 1024 feet + 500 feet = 1524 feet

During the first walk, the time taken was 17 minutes while for the second walk, the time taken was 7 minutes. Therefore, the total time taken will be:

= 17 minutes + 7 minutes

= 24 minutes.

Therefore, the average rate will be:

= 1524 / 24

= 63.5 feet per minute

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Answer:

Step-by-step explanation:

Dave has a 32-ounce energy drink and he drinks 10 ounces then 68.75% of the energy drink has been left by Dave.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Dave has a 32-ounce energy drink.

Dave drinks 10 ounces of energy drink.

We need to find the percentage of ounces Dave had left from his energy drink.

To find this first we have to subtract 10 from 32

32-10 = 22.

Now let us find 22 is what percentage of 32.

x/100 × 32 = 22

0.32x=22

Divide both sides by 0.32

x=22/0.32

x=68.75 %

Hence, 68.75% of the energy drink has been left by Dave.

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[tex]9\times10^{-8}[/tex] is [tex]3\times10^{4}[/tex] times larger than [tex]3\times10^{-12}[/tex].

The given number is [tex]9\times10^{-8}[/tex] and [tex]3\times10^{-12}[/tex].

We need to find how many times larger is  [tex]9\times10^{-8}[/tex] than [tex]3\times10^{-12}[/tex].

To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.

Now, [tex]\frac{9\times10^{-8}}{3\times10^{-12}}[/tex]

[tex]=3\times\frac{10^{-8}}{10^{-12}}[/tex]

[tex]=3\times10^{-8+12}[/tex]  (∵[tex]\frac{a^{m}}{a^{n}} =a^{m-n}[/tex])

[tex]=3\times10^{4}[/tex]

Therefore, [tex]9\times10^{-8}[/tex] is [tex]3\times10^{4}[/tex] times larger than [tex]3\times10^{-12}[/tex].

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The number of bus stops is 4 if the bus driver made 6 stops on his way into town option (C) 4 is correct.

A dot plot also referred to as a dot chart or stripe graph, is a sort of simple histogram-like figure used in statistics for little data sets with values falling into a number of discrete bins.

It is given that:

The bus driver made 6 stops on his way into town. No passengers exited the bus. By stop 3, there were 9 passengers on the bus

The graph is shown in the picture.

The x-axis represents the bus stops  

The y-axis represents the number of passengers

From the graph point to the 13 on the y-axis and locate the related value of x on the x-axis.

The number of bus stops corresponds to 13 = 4

Thus, the number of bus stops is 4 if the bus driver made 6 stops on his way into town option (C) 4 is correct.

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The acceleration of the wagon is 3.2 m/s².

To find the acceleration of the wagon, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force applied to it divided by its mass. In this case, the net force is 64 N (the horizontal force applied) and the mass of the wagon is 20 kg. So the acceleration can be calculated as follows:

A = F/M = 64 N / 20 kg = 3.2 m/s²

Therefore, the acceleration of the wagon is 3.2 m/s².

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1.) You plug a number into the variable x. Then you will solve the equation for h(x) to find the time it takes for the rocket to travel the path given.

Answer:

Step-by-step explanation:

Given that a rocket path is given by

[tex]h(x) = -4x^2 + 16x[/tex]

When it hits the ground h(x) =0

Hence we get

[tex]-4x^2 + 16x=0\\x=0, 4[/tex]

i.e. after 4 minutes the rocket hits the ground

2) Given that

[tex]s(t) = -16t^2 + 48t + 280.[/tex]

We have to find time t when height >280

[tex]s(t) = -16t^2 + 48t + 280>280\\\\t=0, 3[/tex]

Between 0 and 3 seconds the object would be above the building.

a. The algebraic expression that represents the length of the extended table is 6 + 2x

b. The variable 'x' represents the length added by inserting each identical table leaf.

How to write an algebraic expression

a) To write an algebraic expression representing the length of the extended table, consider the original length of the table (6 feet) and the length added by inserting two identical table leaves (each with a longest side length of 3 feet).

Let's denote the length added by inserting the table leaves as 'x'.

Since we're inserting two identical leaves, the total length added would be 2x.

The length of the extended table can be expressed as the sum of the original length (6 feet) and the length added by the table leaves (2x):

Length of the extended table = 6 + 2x

b) The variable 'x' represents the length added by inserting each identical table leaf. It quantifies the extra length that extends the original table when the leaves are inserted.