A tank has 120 gallons of water and is being drained at a rate of 1/2
gallon each second. Another tank has 100 gallons of water and is being drained at a rate of 1/4
gallon each second. Which equation could be used to determine x, the number of seconds, when the two tanks have the same amount of water?

You have the following equation:

-2(x - 3) = 26

in order to solve the previous equation, proceed as follow:

-2(x - 3) = 26 use distribution property

-2(x) - 2(-3) = 26

-2x + 6 = 26 subtract 6 both sides

-2x = 26 - 6 simlify like terms right side

-2x = 20 divide by -2 both sides

x = 20/(-2)

x = -10

Hence, the solution to the given equation is x = -10

Answer:

5

Step-by-step explanation:

negetive two minus negative seven equal to five

Answer:

14.7

Step-by-step explanation:

Let's say the width is x

So volume would be 24 × 2x × x = 10368

24 × 2x² = 10368

2x² = 10368 / 24 = 432

x² = 216 , width can't be negative so

x = 14.6969... ~~ 14.7

Answer:

Explanation:

• Car 1 leaves point A at 5:30 p.m., driving due south at an average speed of 35 mph.

• Car 2 leaves point A at 6:30 p.m., driving due north at an average speed of 45 mph.

At 9:30 pm, the time taken by the cars is:

The distance covered by each car is:

Since car 1 drives due South and Car 2 due North of point A:

Therefore, the distance between the drivers at 9:30 p.m. will be:

The two drivers are 275 miles apart at 9:30 pm.

Simplify the equation 8x + 2y = 12 to obtain the equation in y = mx + b.

In equation y = mx + b, slope is m and y-intercept is b.

So on compare the equation y = -4x + 6 with standard equation the slope is m - -4.

Answer: m = -4.

The difference in the record temperatures is 58.3° Fahrenheit.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol - , or, denotes subtraction. For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

Given Data

The record high temperature on January 15 is 41.5 Fahrenheit the record low temperature on that day is -16.8.

Difference = High temperature - Low temperature

Difference = 41.5 -(-16.8)

Difference = 41.5 + 16.8

Difference = 58.3

The difference in the record temperatures is 58.3° Fahrenheit.

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Given data:

The expression for the age of the girl after two year is,

x+2

The age of girl 5 year ago is,

x-5

According to the given statement of the question.

x+2=2(x-5)

x+2=2x-10

x=12

Thus, the present age of the girls is 12 years old.

Find the missing endpoint if S is the midpoint RT. R(-9, 4) and S(2, -1); Find T.

we know that

The formula to calculate the midpoint between two points is equal to

we have

S(2,-1)

(x1,y1)=R(-9,4)

(x2,y2)=T

substitute the given values in the formula

Find the x2 coordinate

2=(-9+x2)/2

-9+x2=4

x2=4+9=13

Find the y2 coordinate

-1=(4+y2)/2

4+y2=-2

y2=-2-4

y2=-6

therefore

|u|=c is equivalent to u = c or u = -c.

Given that c > 0.

i.e., c is a positive number.

Then |u| = c. That is, absolute value of u = c, a positive number.

An absolute value function is defined by,

 |u| = { u   ; if u ≥ 0

        { -u   ; if u < 0

The absolute value of any number, Positive or negative, is always a positive number.

So here |u| = c, with c > 0.

Comparing with the definition of absolute value function, c is either u or -u.

More clearly, c = u, when u ≥ 0 or c = -u , when u < 0.

Hence the value of c depends on u.

Thus,  |u|=c is equivalent to u = c or u = -c.

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Answer:y

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Since AB = BC,

3m + 5 = 4m - 10

m = 15

We are given the following two vectors

We are asked to find the following

First, multiply the vector a with the scaler -2 to get -2a

Now, multiply the vector b with the scaler 5 to get 5b

Finally, add -2a and 5b to get -2a+5b

Therefore, the resultant vector in component form is

Arrange them in Ascending order :

-8(4/7) < -8.2 < 25/3 < √70

What is  Ascending order?

When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.

Given numbers,

√70 ,-8.2, 25/3, -8(4/7)

We have to Arrange these in ascending order

First lets get these terms to its simplest form

Value of √70 = 8.36

value of 25/3 = 8.33

Value of -8(4/7) = -8.57

Now we have the simplest value of all the following numbers

That is:

8.36, -8.22, 8.33, -8.57

The smallest of all is -8.57

Then -8.57 will be at first

-8.57, 8.36, -8.22, 8.33

now the second will be -8.22

-8.57, -8.22, 8.36, 8.33

Now the third would be 8.33

So the last would be 8.36 that is the greatest

-8.57, -8.22, 8.33, 8.36

Now, for the original value it would be:

-8(4/7) < -8.2 < 25/3 < √70

Hence, The ascending order of the number is -8(4/7) < -8.2 < 25/3 < √70

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Answer:

  6 ft

Step-by-step explanation:

You want the length of the short side of a 30°-60°-90° triangle, given the longest side is 12 ft.

A 30°-60°-90° triangle has side lengths in the ratios ...

  1 : √3 : 2

Here, the longest side is given as 12 ft, so we can multiply this set of ratios by 6 ft to find the lengths of all of the sides:

  1 : √3 : 2 = (6 ft) : (6√3 ft) : (12 ft)

The shortest side has length ...

  k = 6 ft

__

Additional comment

You can also use trig functions to find the length k:

  k/(12 ft) = cos(60°) = 1/2, or

  k/(12 ft) = sin(30°) = 1/2

  k = (1/2)(12 ft) = 6 ft

Answer:

f(1)= -3

Step-by-step explanation:

what f(1) means is when x is 1 what is y. I dont see the graph labeled so im just assuming that the graph is going by ones. So what i did was i found where x is one and then i checked at what point did the line match with the y axis which was 3 points below 0 on y axis ( disclaimer if the graph isnt going by ones then its going to be a different answer, but you can use the same process to find it.

The y-intercept of the line graphed by the equation [tex]\frac{1}{2} x+y=7[/tex] is (0,7)

Option (D) is correct.

The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.

The given equation is [tex]\frac{1}{2} x+y=7[/tex]

Converting the equation in Slope-intercept form, we get

[tex]y=-\frac{1}{2} x+7[/tex]                   ...(1)

Now, to find the y-intercept, substitute x = 0 in the equation and solve for the value of y

Putting x = 0 in equation (1), we get

[tex]y=-\frac{1}{2} (0)+7[/tex]

[tex]y=7[/tex]

Therefore, the y-intercept of the line will be (0,y) i.e., (0,7)

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To write an equation for the lines of the graph, we have to find the slope and the y-intercept of each line.

The y-intercept can be find as the value of y when the line intersects the y-axis.

For company L, that intersects at (0,10), the y-intersect is y(0)=10.

For company K, that intersects at (0,5). the y-intersect is y(0)=5.

The slope can be find using two points of the line.

For Company L we will use points (0,10) and (20,15). Then, we calculate the slope as:

For Company K, the points will be (0,5) and (20,15), and the slope will be calculated as:

With the slope and y-intercept we can write the equation of each line in slope-intercept form.

For Company L, with slope m=0.25 and y-intercept b=10 we will have:

For Company K, with slope m=0.5 and y-intercept b=5, we will have:

Answer:

The system of equations will be:

Company L: y=0.25x+10

Company K: y=0.5x+5

Answer:

The five consecutive integers whose sum is 170 are 32, 33, 34, 35, and 36

Step-by-step explanation:

hope it help

have a nice day

Answer:

x + 6.

Step-by-step explanation:

a number which is x and increased by 6 is adding 6

The cost of the the 17 feet by 23 feet Turkish cloth given the constant of variation is  TL14,467.

A variable varies jointly if the value of one variable depends on the value of two or more variables. In this question, if the length and width of the cloth increases, the cost of the cloth increases. Also,  if the length and width of the cloth decreases, the cost of the cloth decreases.

The equation that represents joint variation is:

y = kab

Where:

TL3848 = k(13 x 8)

k = TL3848 / (13 x 8)

k = $37

The cost of 17 feet by 23 feet cloth :

37 x 17 x 23 = TL14,467

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Answer:

so 50:30

=50-30=20

chocolate and 5are caramel

20:5

5can go into 20 =4

20:5

=4:1

Step-by-step explanation:

bag of candy is 50pieces 30piecesare chocolate and 5arecaramel

step 2 . you will subtract 50from30=20

step 3. 5can go into 20=4times

20:5 is equal to 4:1

a)Total different number plates will be 45697600

b) Total different number plates will be 32292000

What is permutation and combination?

In a combination, the elements of the subset can be listed in any order. In a permutation, the elements of the subset are listed in a specific order.

Arranging people, digits, numbers, alphabets, letters, and colors are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations

We are given that license plate allows 2 digits and 4 upper case letters

a) repetition is allowed

hence for 2 numbers we have 10*10=100 choices

Also letter are allowed 26*26*26*26=456976 choices

And Hence total choices are 456976*100=45697600 ways

b) Repetition is not allowed

hence for 2 numbers we have 10*9=90 choices

Also letter are not allowed 26*25*24*23= 358800 choices

And Hence total choices are 456976*100=32292000 ways

Hence

a)Total different number plates will be 45697600

b) Total different number plates will be 32292000

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A) Simplification of the given Algebraic Expression is; [-⁴³/₂₄j + (-1)]/12

B) The equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9

A) We want to simplify negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths. This would be expressed as;

-1/8j + 2/3 - (5/3j + 9/12)

= -1/8j + 2/3 - 5/3j - 9/12

= -1/8j - 5/3j + (2/3 - 9/12)

= (-3j-40j / 24 + (8-9) / 12

= [-⁴³/₂₄j + (-1)]/12

B) The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)

Expand the brackets to get;

-13.5b - 6.3 - 6b - 0.6

= -13.5b - 6b - 6.3 - 0.6

= - 19.5b - 6.9

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Using the binomial distribution, the probability of no one having done a one time fling is of 0.735 = 73.5%.

The mass density formula for the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the formula are given as follows:

In the context of this problem, the values of the parameters are as follows:

The probability that no one has done a one time fling is P(X = 0), hence the probability is calculated as follows:

P(X = 0) = (0.95)^6 = 0.735 = 73.5%.

The problem asks for the probability that no one has done a one time fling.

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We are told that

If we were given the graph of f(x), note that in this equation we add 5 to the value of f(x) to find the value of g(x). So, in terms of the graph, as we are taking the final value of f and adding 5, this means that we are moving the graph of f 5 units up. That is the graph of g(x) is the graph of f(x) shifted 5 units up

Speed of the wind for jet speed in still air 240mph and jet covers 700 miles with tailwind and same distance against the wind in total time of 6 hours is equal to 40mph.

As given in the question,

Given data:

Jet speed in still air = 240mph

Let x be the speed of the wind.

Speed with tail wind = 240 +x

Distance covered with tail wind = 700miles

Time taken by jet with tail wind

= Distance/ speed

= 700 / (240 +x)  __(1)

Speed against the wind = 240 - x

Distance covered against the wind = 700miles

Time taken by jet against the wind

= Distance/ speed

= 700 / (240 - x)  __(2)

Total time taken is 6 hours

[700 / (240 +x)] + [700 / (240 - x)] = 6

⇒ 700( 240 -x + 240 + x) = 6 (240 +x)(240 - x)

⇒ 700 ( 480) = 6 ( 240² -x²)

⇒ 700 (80) = 57600 -x²

⇒ x² = 57600 - 56000

⇒ x² = 1600

⇒ x = √1600

⇒ x= 40 mph

Therefore, speed of the wind for jet speed in still air 240mph and jet covers 700 miles with tailwind and same distance against the wind in total time of 6 hours is equal to 40mph.

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Robert will paint 310.5 square ft

The side of Robert's barn contains a triangle and a rectangle of which the dimensions are given in the diagram.

If Robert paint one side of the barn, then he needs to paint the triangle as well as the rectangle. So we need to find the area of the triangle and rectangle first.

For the triangle, base = 23 ft

height = 7 ft

Area of the triangle = 1/2 bh

                                 = 1/2 x 7 x 23

                                 = 80.5 square ft.

For the rectangle, length = 23 ft

width = 10 ft

Area of the rectangle = length x width

                                    = 23 x 10

                                    = 230 square ft.

Area Robert needs to paint = Area of the triangle + Area of the rectangel

                                              = 80.5 + 230

                                              = 310.5 square ft.

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Answer:

See below

Step-by-step explanation:

-7/8  /  (- 7/5)     =  - 7/8  *- 5/7  = 5/8  

Olivia would be able to get 11 toppings.

Steps:

8.00 / .75 = 10.6

Round~

11

You're welcome!!!