A train was traveling at a constant speed.the table below shows the distance,in miles the train traveled for the first 4 hours.Write an equation to represent the relationship between t,the time,and d,the total distance traveled by the train

Answer:

C= 2*pi*r

Step-by-step explanation:

Answer:

The vertices of the triangle after the translation are (-1 , -1) , (-4 , -5) , (-8 , 0)

The image of Δ NPQ after the translation is Δ KLM

Step-by-step explanation:

*Lets revise translation

- If point (x , y) translate to the right h units

∴ Its image is (x + h , y)

- If point (x , y) translate to left h units

∴ Its image is (x - h , y)

- If point (x , y) translate up k units

∴ Its image is (x , y + k)

- If point (x , y) translate down k units

∴ Its image is (x , y - k)

* Now lets solve the problem

- From the graph the vertices of the triangle are

 (0 , 2) , (-3 , -2) , (-7 , 3)

- The triangle will translate by the rule (x , y) ⇒ (x - 1 , y - 3)

∴ The triangle translate 1 unit to the left and 3 units down

- We will subtract each x-coordinate by 1 and each y-coordinate by 3

∴ The image of point (0 , 2) is (0 -1 , 2 - 3) = (-1 , -1)

∴ The image of point (-3 , -2) is (-3 - 1 , -2 - 3) = (-4 , -5)

∴ The image of point (-7 , 3) is (-7 - 1 , 3 - 3) = (-8 , 0)

* The vertices of the triangle after the translation are

 (-1 , -1) , (-4 , -5) , (-8 , 0)

- From the graph the vertices of the triangle NPQ are

 N (-7 , -6) , P (-4 , -3) , Q (-4 , -6)

- The triangle will translate by the rule (x , y) ⇒ (x + 8 , y + 1)

∴ The triangle translate 8 units to the right and 1 unit up

- We will add each x-coordinate by 8 and each y-coordinate by 1

∴ The image of point N (-7 , -6) is (-7 + 8 , -6 + 1) = (1 , -5)

∴ The image of point P (-4 , -3) is (-4 + 8 , - 3 + 1) = (4 , -2)

∴ The image of point Q (-4 , -6) is (-4 + 8 , -6 + 1) = (4 , -5)

* The vertices of the triangle after the translation are

 (1 , -5) , (4 , -2) , (4 , -5)

- Lets find from the graph the names of these vertices

∵ Δ KLM has the same vertices k (1 , -5) , L (4 , -2) , M (4 , -5)

* The image of Δ NPQ after the translation is Δ KLM

To remove 3 acres of contaminated soil at 24 inches deep, 346 full truckloads are needed, assuming each truck has a capacity of 28 cubic yards.

The student's question is regarding the number of truckloads required to haul away contaminated soil. We are given that 3 acres of soil need to be removed to a depth of 24 inches, and the trucks used have a hauling capacity of 28 cubic yards each.

To calculate how many full truckloads are required, we first need to convert the area and depth measurements from acres and inches into cubic yards (the unit of the truck's capacity). One acre is 43,560 square feet, so 3 acres would be 3 x 43,560 = 130,680 square feet. Depth needs to be converted from inches to feet, so 24 inches is 24 / 12 = 2 feet.

The total volume of soil to be removed in cubic feet is:

130,680 square feet x 2 feet = 261,360 cubic feet.

Since there are 27 cubic feet in one cubic yard, the total volume in cubic yards is:

261,360 cubic feet / 27 cubic feet per cubic yard = 9,680 cubic yards.

Finally, to find the number of full truckloads needed:

9,680 cubic yards / 28 cubic yards per truck = 345.71 trucks.

Since you can't have a fraction of a truck, you would need 346 full truckloads to remove all the contaminated soil. Each truck can carry exactly 28 cubic yards, and the last truck may not be full to capacity, but 346 is the number of full truckloads required for the task.

Answer:

Step-by-step explanation:

Think about it for a second.

Take log 3 (-9). 3 to what power is -9.

Let's try:

3 ^ 2 = 9. So it's not negative 9.

Maybe 3 ^ -2 = 1/9. Still not -9.

Let's try 3 ^ 1/3 = 1.4422. Still not remotely close.

So we can make a conclusion that a positive number to any real exponent can't give us a negative number.

A logarithmic equation exists as an equation that involves the logarithm of an expression including a variable. To translate exponential equations, first, see whether you can write both sides of the equation as powers of the identical number.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.

As the base of a power function, 0, 1, and every negative integer provide a possible issue. Furthermore, if those values cannot be relied upon to be the base of a power function, they cannot be relied upon to be the base of a logarithm either. For this reason, we restrict the base of the logarithm to only positive numbers other than 1.

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Answer:

y = 1

Step-by-step explanation:

This is very simple.

The mid-line of a sinusoidal function is the horizontal line that passes through the middle of the extreme values.

The midline of a sinusoid of the form  y = a Cos (bx + c) + d is going to be

y = d

The form   y = a Cos (bx + c) + d  is the transformed of the version y = Cos x. Midline is only affected by a vertical shift, which is d.

Thus, the midline of the equation given  y=2 cos (4∅+5) + 1  is y = 1

Answer: y2/10

Step-by-step explanation:

The equivalent expression for [tex]\( y^{1/5} \)[/tex] using radicals is [tex]\( \sqrt[5]{y} \).[/tex]

Sure, I can help with that! To express [tex]\( y^{1/5} \)[/tex] using radicals, we need to rewrite the exponent [tex]\( \frac{1}{5} \)[/tex] as a radical.

The expression [tex]\( y^{1/5} \)[/tex] can be written as [tex]\( \sqrt[5]{y} \)[/tex].

Here's the step-by-step calculation:

1. Start with the expression [tex]\( y^{1/5} \).[/tex]

2. Rewrite the exponent [tex]\( \frac{1}{5} \)[/tex] as a radical, giving [tex]\( \sqrt[5]{y} \)[/tex].

To understand why [tex]\( y^{1/5} \)[/tex] can be expressed as [tex]\( \sqrt[5]{y} \)[/tex], let's break it down:

The exponent [tex]\( \frac{1}{5} \)[/tex] means taking the fifth root of [tex]\( y \)[/tex]. The radical symbol [tex]\( \sqrt[5]{\;} \)[/tex] represents the fifth root. So,[tex]\( y^{1/5} \)[/tex] is equivalent to [tex]\( \sqrt[5]{y} \).[/tex]

In other words, raising [tex]\( y \)[/tex] to the power of [tex]\( \frac{1}{5} \)[/tex] is the same as finding the number which, when multiplied by itself five times, equals [tex]\( y \)[/tex]. This is precisely what the fifth root accomplishes.

Therefore, the equivalent expression for [tex]\( y^{1/5} \)[/tex] using radicals is [tex]\( \sqrt[5]{y} \).[/tex]

Complete question:

Using radicals write an equivalent expression for the expression y1/5

Answer:

3 - 3i

Step-by-step explanation:

I think you meant:

     6

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

   1 + i

To simplify this, that is, to "rationalize the denominator," multiply both numerator and denominator by the conjugate of 1 + i, which is 1 - I:

6(1 - i)

----------- = 3(1 - i)= 3 - 3i

  1 -(-1)

the correct value of the expression is 3-3i.

The value of 6/(1+i) can be found by multiplying both the numerator and the denominator by the complex conjugate of the denominator. The complex conjugate of 1 + i is 1 - i. Therefore, we have:

(6/(1+i)) × (1-i)/(1-i) = (6 × (1-i))/(1+ i)(1-i) = (6-6i)/(1-i^2) = (6-6i)/(1+1) = (6-6i)/2 = 3-3i.

Thus, the correct value of the expression is 3-3i.

For this case we have a function of the form [tex]y = f (x)[/tex]

Where:

[tex]f (x) = 5x[/tex]

We must find the value of the function when [tex]x = 2,[/tex] that is, [tex]f (2).[/tex] Then, replacing the value of x in the function:

[tex]f (2) = 5 (2)\\f (2) = 10[/tex]

Thus, when [tex]x = 2[/tex] the function has a value of 10.

Answer:

[tex]f (2) = 10[/tex]

Answer: [tex]f(2)=10[/tex]

Step-by-step explanation:

You have the following linear function:

[tex]f(x)=5x[/tex]

To evaluate this function for the given value, you need to substitute the value of the variable "x" ([tex]x=2[/tex]), which is the input value, into the linear function to obtain the output value. Then:

For [tex]x=2[/tex]

[tex]f(2)=5(2)[/tex]

Make the multiplication.

Therefore, the result is:

[tex]f(2)=10[/tex]

Answer:

4 batch

Step-by-step explanation:

1 batch = 36 cookies

? batches = 144 cookies

? batches = 144 / 36

? batches = 4

4 batch gives the number of batches that will make 144 cookies.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

Given

1 batch = 36 cookies

batches = 144 cookies

batches = 144 / 36

batches = 4

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460 miles to San Diego

460/6=76.6 repeating -12 then divided by 2

means the other slower car was going approx 32.3 MPH

I may be wrong considering i had to google how far san diego was, if there was a graph or anything telling distance lmk

Answer:

Speed of the faster car is 68 mph and speed of slower car is 40 mph.

Step-by-step explanation:

Let the faster car has the speed = x mph

and slower car has the speed = y mph

Let the distance between San Jose and San Diago = d miles

Now we will form the first equation.

"Speed of the faster car was 12 mph less than twice the speed of the slower one"

x = 2y -12 ----------(1)

Since "faster car cover the distance d in 6 hours"

so, [tex]x=\frac{d}{6}[/tex]

"By that time the slower car still was 168 miles away from the destination"

so, [tex]y=\frac{d-168}{6}[/tex]

[tex]y=\frac{d}{6}-\frac{168}{6}[/tex]

y = x - 28 {since [tex]x=\frac{d}{6}[/tex]} ---------(2)

By substitution method,

x = 2(x - 28) - 12

x = 2x - 56 - 12

x - 2x = - 68

x = 68 mph

By putting x = 68 in equation 2

y = 68 - 28

y = 40 mph

Therefore, speed of the faster car is 68 mph and speed of slower car is 40 mph

Answer:

∠B = 65°; ∠C = 115°

Step-by-step explanation:

The first thing you to do is set ∠B and ∠D equal to each other.

[tex]3n+20=6n-25[/tex]

The reason you do this is because the oppisite angles are equal to each other in a parallelogram.

Next, you want to start simplifying the equation (I personally like to start with the variables).

[tex]....3n+20=6n-25\\-3n.....-3n[/tex]

Then, you simplify again (you can combined these if you want but for example I am breaking it down more.

[tex]....20=3n-25\\+25.......+25\\....45=3n[/tex]

Then you dived by 3, and you get 15=n. Now (and people often forget this step) you have to plug it back in to solve for the equartion. ∠B=3(15)+20, ∠B=65. Now you have to subtract 65 from 180 because ∠B and ∠C are completmtry. 180-65=115=∠C

Answer:

Part a) The slope is equal to [tex]m=21.2\frac{\$}{year}[/tex]

Part b) The linear equation is equal to [tex]y=21.2x+3,090[/tex]

Part c) The tuition would be [tex]\$3,238.4[/tex] in 2,017

Step-by-step explanation:

step 1

Find the slope m

Let

x-----> the year after 2,010

y-----> the tuition

we have

For the year 2,010

[tex]x=0\ years[/tex]

For the year 2,015

[tex]x=(2,015-2,010)=5\ years[/tex]

so

[tex]A(0,3,090), B(5,3,196)[/tex]

Calculate the slope

[tex]m=\frac{(3,196-3,090)}{(5-0)}=21.2\frac{\$}{year}[/tex]

step 2

Find the linear equation

with the slope m and the point A find the linear equation

[tex]y-y1=m(x-x1)[/tex]

substitute the values

[tex]y-3,090=21.2(x-0)[/tex]

[tex]y=21.2x+3,090[/tex] -------> linear equation that would predict tuition for any year after 2010

step 3

Assuming the linear trend remained constant, what would tuition be in 2017

so

For [tex]x=(2,017-2,010)=7\ years[/tex]

substitute in the linear equation

[tex]y=21.2(7)+3,090=\$3,238.4[/tex]

The slope of the increase in Ivy Tech's tuition from 2010 to 2015 is $21.2 per year. The linear model to predict future tuition costs is: y = 3090 + 21.2*(Years after 2010). Using this model, the predicted tuition for 2017 is approximately $3227.4.

The subject of your question is the calculation of a linear model for Ivy Tech's tuition increase over the years. In 2010, the tuition was $3090, and in 2015, it increased to $3196.

To calculate the slope, we subtract the tuition of the two years, and divide it by the difference in the years. Thus, the slope is: (3196-3090) / (2015-2010) = $21.2 per year.

Your linear model would therefore be: y = 3090 + 21.2*(Years after 2010). For example, if you want to predict the tuition in 2017, you would use : y = 3090 + 21.2*(2017-2010) = $3227.4. This suggests that the tuition in 2017 would be approximately $3227.4, provided the trend remains the same.

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Answer:

If a number has infinite repeating decimals, the correct form to write repeating decimilas is by adding a line -also con vinculum- above the repeating decimals.

For example:

[tex]\frac{1}{3} = 0,3333333 =[/tex] [tex]0.\overline{3}[/tex]

Answer:

C. 17, 12, 7

Step-by-step explanation:

In a triangle, the sum of the lengths of any two sides must be greater then the length of the third side. If you can show any two segments, the sum of whose lengths is less than the length of the third segment, that cannot form a triangle.

In choices A, B, and D, there is at least one sum of the lengths of two segments that is less then the length of the third segment. That shows that choices A, B, and D cannot form triangles.

A. 8 + 7 = 15 < 16 No

B. 9 + 7 = 16 = 16 No

D. 11 + 5 = 16 < 17 No

C.

17 + 12 = 29 > 7

12 + 7 = 19 > 17

17 + 7 = 24 > 12

Yes

Answer:

C (2,2)

B (2,-2)

A (-2,-2)

Step-by-step explanation:

[tex]m < \frac{ - 185}{k} [/tex]

HOPE THIS WILL HELP YOU

For this case we must find the value of the variable "m" of the following expression:

[tex]-mk-110> 75[/tex]

We follow the steps below:

We add 110 to both sides of the inequality:

[tex]-mk> 75 + 110\\-mk> 185[/tex]

We divide between k on both sides of the inequality:

[tex]\frac {-mk} {k}> \frac {185} {k}\\-m> \frac {185} {k}[/tex]

We multiply by "-" on both sides of the inequality, remembering that the sense of inequality changes:

[tex]m <- \frac {185} {k}[/tex]

ANswer:

[tex]m <- \frac {185} {k}[/tex]

Answer: Tax= 2.275 Total= 38.275

Step-by-step explanation:

Answer:

The correct option is the first one.

Step-by-step explanation:

We know that 14 men and 24 women applied for a job. So a total of 38 persons applied for that job.

But there are 4 ways a man can be chosen. It can be the first person chosen, the second, the third of the fourth one.

So we know that the number of ways that four people can be selected out of 38 people is  38C4=73,815.

Also the number of ways 3 woman can be selected is 14*24C3 =14*2024 = 28,336.

Then, the probability of randomly selecting a group with 3 women is 28,336/73,815=0.3838

The correct option is the first one.

Answer:

The correct answer is first option, 0.384

Step-by-step explanation:

It is given that, there are 14 men and 24 women apply for job.

4 are selected random

To find the probability

total people = 14 + 24 = 38

The number people selected in 38C₄ = 38 * 37 * 36 * 35

number of ways 1 men selected in 14C₁ ways

Number of ways 3 women selected is 24C₃ ways

Total number of ways select only 1 men and 3 women = 14C₁ * 24C₃

Required probability = (14C₁ * 24C₃)/(38 * 37 * 36 * 35)

     = 0.3837 ≈ 0.384

The correct answer is first option

Answer:

25

Step-by-step explanation:

12/x = 48/100

48/100 = 0.48

12 = 0.48x

12/0.48 = 25

Answer:

b

Step-by-step explanation:

13

ANSWER

a) One Solution

b) the solution is x=2

EXPLANATION

The given equation is:

[tex]5(2x - 3) = 5[/tex]

We expand to get;

[tex]10x - 15 = 5[/tex]

Group similar terms;

[tex]10x = 15 + 5[/tex]

This implies that,

[tex]10x = 20[/tex]

Divide both sides by 10 to obtain,

[tex]x = 2[/tex]

Answer:

[tex]x_{1}=\frac{1+\sqrt{33} }{4}\\x_{2}=\frac{1-\sqrt{33} }{4}[/tex]

Step-by-step explanation:

Using quadratic formula

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

we will have two solutions.

2x^2 - x - 4 = 0

So, a=2   b=-1  c=-4, we have:

[tex]x_{1}=\frac{+1+\sqrt{-1^{2}-4*2*-4} }{2*2}\\\\x_{2}=\frac{+1-\sqrt{-1^{2}-4*2*-4} }{2*2}[/tex]

Finally, we have two solutions:

[tex]x_{1}=\frac{1+\sqrt{33} }{4}\\\\x_{2}=\frac{1-\sqrt{33} }{4}[/tex]

ANSWER

[tex]{(x - 4)}^{2} + {y}^{2} = 12[/tex]

EXPLANATION

The equation of a circle given the center (h,k) and radius r is given by:

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

The circle has center (4,0) and radius

[tex]r = 2 \sqrt{3} [/tex]

We substitute the center and radius to get,

[tex]{(x - 4)}^{2} + {(y - 0)}^{2} = {(2 \sqrt{3)} }^{2} [/tex]

[tex]{(x - 4)}^{2} + {(y - 0)}^{2} = 12[/tex]

[tex]{(x - 4)}^{2} + {y}^{2} = 12[/tex]

Making x the subject of the equation would be x = y - y or x = 0.

To make x the subject of the equation x + y = y , first isolate x on one side of the equation. To do this, subtract y from both sides of the equation:

x + y - y = y - y

This simplifies to :

x = 0

The solution is that x = 0. This means that no matter what the value of y is, x will always be 0 when the equation x + y = y holds true .

The full question is:

Make the variable in brackets the subject of the formula:
(x + y ) = y            (x)

Answer:

Below is the sequence of steps which are required to follow in order to have the expression in its simplified form.

Step 1

[tex](875x^{5}y^{9})^{\frac{1}{3}}[/tex]

Step 2

[tex](125.7)^\frac{1}{3}.x^{\frac{3}{5}}.y^{\frac{9}{3}}[/tex]

Step 3

[tex](125)^{1/3}.(7)^{1/3}.x(^{\frac{3}{3}+\frac{2}{3}}).y^{3}}[/tex]

Step 4

[tex](5^{3} )^{\frac{1}{3}}.7^\frac{1}{3}.x^{(1+\frac{2}{3})}.y^{3}[/tex]

Step 5

[tex]5^{1}.7^\frac{1}{3}.x^{1}.x^\frac{2}{3}.y^3[/tex]

Step 6

5xy³([tex]7^{\frac{1}{3} }[/tex][tex]x^{\frac{2}{3} }[/tex])

Step 7

5xy³([tex]7x^{2}[/tex])[tex]\frac{1}{3}[/tex]

Step 8

5xy³[tex]\sqrt[3]{7x^{2}}[/tex]

Answer:

x = -11.9

Step-by-step explanation:

x + 5.1 = –6.8

Subtract 5.1 from each side

x + 5.1-5.1 = –6.8-5.1

x = -11.9

-11.9

Subtract 5.1 from Both sides to get -11.9 and that’s what x equals

The given triangle has a right angle.

We use the mnemonics SOH-CAH-TOA.

1i) [tex]\sin C =\frac{Opposite}{Hypotenuse}[/tex],[tex]\implies \sin C =\frac{30}{34}[/tex],[tex]\implies \sin C =\frac{15}{17}[/tex]

ii) [tex]\cos C =\frac{Adjacent}{Hypotenuse}[/tex],[tex]\implies \cos C =\frac{16}{34}[/tex],[tex]\implies \cos C =\frac{8}{17}[/tex]

[tex]\tan C =\frac{Opposite}{Adjacent}[/tex],[tex]\implies \tan C =\frac{30}{16}[/tex],[tex]\implies \tan C =\frac{15}{8}[/tex]

2. We want to find the hypotenuse.

We know an angle to be 23 degrees.

We were also given the side opposite to this angle to be 1200km.

Therefore we use the sine ratio.

Answer:

1) sin C = 30 / 34

cos C = 16/34

tan C = 30/16

2) The value of x = 1304.34

Step-by-step explanation:

1.

In a right angled triangle, we have perpendicular, hypotenuse and base.

The hypotenuse is the longest side and opposite to the right angle. the side having 90 degree angle is perpendicular.

Applying formulas we can find the values:

the formulas are : cos (Ф) = Base / hypotenuse

sin (Ф) = Perpendicular / hypotenuse

tan (Ф) = Perpendicular / Base

Putting values in the formula from figure:

sin C = Perpendicular / Hypotenuse

sin C = 30 / 34

cos C = Base / Hypotenuse

cos C = 16/34

tan C = Perpendicular / Base

tan C = 30/16

2.

We need to find the hypotenuse of the given triangle, we are given base = 1200 m and the angle is 23°

We know, cos Ф = Base / Hypotenuse.

Solving this, We can find the value of x.

cos (23) = 1200 / x

x cos (23) = 1200

x (0.920) = 1200

x = 1200 / 0.920

x = 1304.34

The value of x = 1304.34

Answer:

M=65

Step-by-step explanation:

1=65 thus 2=65

trust me I'm right I am always right

Answer:

10.5

Step-by-step explanation:

6x +3 = 66

Subtract 3 from each side

6x+3-3 = 66-3

6x = 63

Divide each side by 6

6x/6 = 63/6

x = 10.5

the answer is X= 10.5

Answer: ARE THEIR OPTIONS TO CHOSE FROM

Step-by-step explanation:

Answer:

No options so i cant help please put below thx (:

Step-by-step explanation:

the answer is 5

u substitute -1 into x and then solve

Answer:

the answer is D: 5