6. The table shows the volume of water in
cubic meters, V, in a tank after water has
been pumped out for a certain number of
minutes.
Which equation could represent the
volume of water in cubic meters after t
minutes of water being pumped out?
A. V = 30-2.5t
B. V = 30-0.5t
C. V = 30-0.51²
D. V = 30-0.11²

Answer:

U: (-7, 0)

S: (-7, -2)

T: (3, -2)

Step-by-step explanation:

Moving a point 6 to the left is the same as subtracting 6 from its x value. Moving a point up 1 is the same as adding 1 to its y value.

Point=(x-6, y+1) where x is the point's original x value and y is the point's original y value.

U: (-1-6, -1+1)=(-7, 0)

S: (-1-6, -3+1)=(-7, -2)

T: (9-6, -3+1)=(3, -2)

let's firstly convert the mixed fractions to improper fractions and then subtract.

[tex]\stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}} ~\hfill \stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}~~ - ~~\cfrac{14}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~ - ~~(2)14}{6}}\implies \cfrac{51~~ - ~~28}{6}\implies \cfrac{23}{6}\implies {\LARGE \begin{array}{llll} 3\frac{5}{6} \end{array}}[/tex]

Answer:

3 = x ÷ 4

Step-by-step explanation:

Given expressions:

8 = x - 2 ⇒ x = 8 + 2= 10

3 = x ÷ 4  ⇒ x = 3*4 = 12

x - 6 = 5  ⇒ x = 5 + 6 = 11

x - 3 = 9  ⇒ x = 9 + 3 = 12

3 of them involves addition, one of them - multiplication

The second expression doesn't belong

The number that can be equal to 2x² -50 =  2(x + 5)(x - 5).

For the given equation;

= 2x² -50

Take 2 common;

= 2(x² - 25)

This could be written as;

= 2(x² - 5²)

Now use per the property of (a² - b²)  = (a + b)(a - b).

= 2(x + 5)(x - 5)

Thus, the given expression 2x² -50 can be represented as 2(x + 5)(x - 5).

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The name of each midpoint and the segment it bisects include the following:

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

In this scenario, the name of each midpoint and the segment it bisects include the following:

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Complete Question:

Name each midpoint and the segment it bisects.

The domain of the function C(t) is R - { -5. -2}.

The domain of a function is the set of all values for which the range of the function is defined.

To achieve an immediate response to a particular drug's effects the concentration, C, in mg/L, of a particular medication after being injected into a patient is given by the function

C(t) = [tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex] where t represents time in hours.

We know that a function is undefined when its denominator becomes zero.

∴ We have to factor the quadratic equation t² + 7t + 10 which is,

t² + 5t + 2t + 10 = 0.

t(t+5)+2(t+5) = 0.

(t+5)(t+2) = 0.

So, t = -5 or t = -2 are the two values of this equation which makes the function c(t) undefined.

∴ The domain of the function [tex]\frac{-18t^2 + 54t}{(t+5)(t+2)}[/tex] is all real numbers except -2 and - 5 which can be written as

Domain of C(t) is R - { -5, -2}, where R represents all real numbers.

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Greetings from Brasil...

90X - 128 = 24X + 50

90X - 24X = 50 + 128

Answer:

2

Step-by-step explanation:

8-4=4

4/2=2

Answer:

so you take 2×4=8 and 2×2=4 I think that's how to do it

Answer: Everything lol

Step-by-step explanation:

Answer:

0.025

Step-by-step explanation:

Divide 4 by 139 and get the number as a decimal

Answer:

12'

Step-by-step explanation:

Pythagoras theorem = a² = b²+c²

*a² is always the hypothenuse (the longest side if the triangle)

you could use b² as the base and c² as the height

to find the height i.e., c² you transpose and substitute what we know so that'll be

13'² = 5'² + c²

you expand which will then give you

169 = 25 + c²

you then take over the 25+ which when addition goes over the equal sign becomes subtraction so that'll now give you

169 - 25 = c²

144 = c²

we want to find for c not c² so to do that we find the square root of 144 which is equal to 12.

so the height is equal to 12'

hope this helps

(12x^5 + x² + 4) /4.

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

Given equation

x²/4+3x^5+1

Find common denominator

x²/4+3x^5 . 4/4+4/4

Combine fractions with common denominator

(x²+3x^5 . 4+4)/4

Multiply the numbers

(x²+12x^5 +4)/4

Rearrange terms

(x²+12x^5 +4)/4

(12x^5 + x² + 4) /4

Thus , solution of the given polynomial is (12x^5 + x² + 4) /4. we can also write it as -

3x^5 + x² / 4 + 1.

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Answer: The answer is B. a||b and l||m

Step-by-step explanation: I hope this helps.

After solving the equation ln x = -2, x is the value of equal to  [tex]e^{-2}[/tex]

We have been asked to find x in ln x = -2

⇒ ln x = -2

⇒ x = [tex]e^{-2}[/tex]

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The equivalent expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given:

(p^3)(2p^2 - 4p)(3p^2 - 1)

Now further solving

(p^3)(2p^2 * 3p^2 - 2p^2 * 1 - 4p * 3p^2 + 4p)

=(p^3) (6p^4 - 2p^2 - 12 P^3 + 4p)

=(p3)(6p^4 - 12p^3 - 2p^2 + 4p)

Hence, the value of expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).

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By option verification,

i.e., substituting the options by given equation and verifying

Given -2x + 3y > = 1  and - 5x + 6y <= 1

Substituting option A i.e., ( x , y ) = ( 6,6)

-2x + 3y >=1 --> -2 * 6 + 3 * 6 >= 1

                   --> -12+ 18 >= 1    

                  ---> 6>=1

-5x + 6y<=1--> -5 * 6 + 6 *6 <=1

                 --> -30+ 36 <=1

                -->6<=1

False

Substituting option B i.e., (x ,  y)= (7 ,8)

-2x + 3y>=1  --> -2* 7 + 3 * 8>=1

                   --> -14 + 24>=1

                  --> 10>=1

-5x + 6y<=1 --> -5 *7 + 6* 8<=1

                  --> -35 + 48<=1

                  --> 13<=1

False

Substituting option C i.e., (x, y) = ( 8 ,7)

-2x + 3y >=1 --> -2* 8 + 3* 7>=1

                    --> -16 + 21>=1

                   --> 5>=1

-5x + 6y <=1 --> -5 * 8 +  6 * 7 <=1

                   --> -40 + 42<=1

                  --> 2<=1

False

Substituting option D i.e., (x ,y ) = (9, 7)

-2x + 3y >= 1 --> -2* 9 + 3 * 7 >=1

                    --> -18 +21>=1

                   --> 3>=1

-5x + 6y <=1 --> -5* 9 + 6 * 7 <=1

                    --> -45 + 42<=1

                   --> -3<=1

True

Therefore (x ,y ) = (9, 7) is the solution of the given equation -2x + 3y>=1 and -5x = 6y <=1

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Answer: For the people who were just as confused with the answer above, the answer is D-

Step-by-step explanation:

Using operations with functions, we have that:

a) w(t) = -3t + 5.

b) The pool will leak all the water in 1.67 hours.

c) 1.67 hours.

d) Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.

e) The domain of the function is 0 ≤ t ≤ 1.67.

The amount of water in the pool is determined by the subtraction of the amount flowing into the pool by the amount being drained out the pool.

For this problem, these following functions are given:

Hence the amount of water in the pool is given by:

w(t) = f(t) - d(t)

w(t) = t² + 8t + 9 - t² - 11t - 4

w(t) = -3t + 5.

Hence:

The function is: w(t) = -3t + 5.

The pool will have leaked all the water when:

w(t) = 0.

Hence:

-3t + 5 = 0.

3t = 5

t = 1.67.

The pool will leak all the water in 1.67 hours.

Equaling f(t) and d(t), we have that:

t² + 8t + 9 = t² + 11t + 4.

3t = 5.

t = 1.67.

Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.

The domain of a function is the set that contains all input values of the function. For this problem, the input is the time, hence:

Hence:

The domain of the function is 0 ≤ t ≤ 1.67.

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Tonya's total earnings for a month where her total sales were $80,000 is $5,450

What made up Tonya's total earnings?

Tonya's total earnings in any month comprises the basic salary of  $650 , 3% of sales as sales commission on sales revenue of up to $32,000 and 8% as commission on sales in excess of $32,000

total earnings=basic salary+(3%*sales of up to $32,000)+(8%*sales of above $80,000)

basic salary=$650

3%*sales of up to $32,000=3%*$32,000

3%*sales of up to $32,000=$960

8%*sales of above $80,000=8%*($80,000-$32,000)

8%*sales of above $80,000=8%*$48,000

8%*sales of above $80,000=$3,840

Tonya's total earnings for a month=$650+$960+$3,840

Tonya's total earnings for a month=$5,450

Note that the total earnings based on the basic salary of $650 and sales revenue of $80,000 is $5,450

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Answer:

Step-by-step explanation: 37 times 1000 equals 37000 if you times anything by 1000 just add 2 zeros to the end

150cm² is the area of matting visible.

So, the area of matting is 100 × 2.5:

Now, the area of the matting is visible:

Rounding to nearest tens: 150cm²

Therefore, the area of matting visible is 150cm².

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The numeric values of the expressions are given as follows:

3. 36.

5. 38.

7. 16/61.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

In item 3, we have that:

4|m - n|, m = -7, n = 2.

Hence the numeric value is:

4|-7 - 2| = 4|-9| = 4 x 9 = 36.

In item 5, we have that:

s²t - 10 with s = -8, t = 3/4.

Hence the numeric value is:

(-8)² x 3/4 - 10 = 48 - 10 = 38.

In item 7, we have that:

(a + b)^5/(a - 2b²), a = 6, b = -8.

Hence the numeric value is:

(-2)^5/(6 - 128)

-32/-122 (negative divided by negative is positive).

32/122 (simplify by 2).

16/61.

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Answer: 2/189

Step-by-step explanation:

The solution for y is given as :  y = (34+x)/36

According to the question we have been the linear equation in two variable as :

                       2y - x = 34 (-y + 1)

We need to solve the above equation for y. For that we will do step by step.

First we will open the brackets on the right hand side of the equation we get

                        2y - x = -34y + 34

then we will combine the terms on the left hand side of the equation.

                        2y + 34y = 34 + x

                          36y  = 34+x

dividing both the sides by 36 we get

                         36y/36 = (34+x)/36

                             y = (34+x)/36

Hence the solution for y is given as :  y = (34+x)/36

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The constant of proportionality for the paints portraits is estimated as 5.

For, the given question;

The relation between the portraits and the time for their drawing made by Drew is-

In 5 hours ----> 1 portrait

Thus, 5/1 = 5

In 10 hours ------> 2 portrait

Thus, 10/2 = 5

In 15 hours -----> 3 portrait

Thus, 15/3 = 5 .....and so on.

Therefore, the constant of proportionality is found as 5.

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The minutes when the scenes have the same amounts rendered is 14 minutes.

The expression for the kitchen is illustrated as 540 + 90t.

The expression for the garden is illustrated add 960 + 60t.

Therefore, for the same amount, this will be:

540 + 90t = 960 + 60t.

Collect like terms

90t - 60t = 960 - 540

30t = 420

Divide

t = 420 / 30

t = 14 minutes

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Step-by-step explanation:

f(x) = x² - 3x + 3

f(4) = 4² - 3.4 + 3

f(4) = 16 - 12 + 3

f(4) = 7