Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?

There are 16 cups in a gallon.

Answer: 2:3

Step-by-step explanation:

First list out the factors for 32 and 48

32- 1, 2, 4, 8, 16, 32

48- 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The greatest factor they have in common is 16. So, divide both numbers by 16 to get the simplest form of the ratio.

32/16=2

48/16=3

The simplest form is 2:3

The selling price of the article including VAT will be 1000.

The cost at which an article is sold is known as the selling price.

Let the market price will be x

Given data;

Discount=20 %

The amount of the discount is;

[tex]\rm Discount = x- x \times \frac{20}{100} =\frac{80x}{100}[/tex]

Applied tax is;

[tex]\rm \frac{80x}{100} +\frac{80x}{100} \times \frac{15}{100} =904 \\\\ \frac{8000x+1040 x}{10000} =904 \\\\ 9040 x = 904 \times 10000 \\\\\ x=\frac{904 \times 10000}{9040} \\\\ x=1000[/tex]

Hence, the selling price of the article including VAT will be 1000.

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The function g(x) gets shifted toward right by 6 units. Then the correct option is C.

The complete question is attached below.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

The function f(x) is given below.

f(x) = 10ˣ

And the function g(x) is given as

g(x) = f(x – 6)

Then the function can be written as

[tex]\rm g(x) = 10^{x - 6}[/tex]

The function g(x) gets shifted toward right by 6 units.

Then the correct option is C.

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The value of a is 14.

The branch of mathematics concerned with specific functions of angles and their application to calculations.

Given:

tan3a=cot2a​

tan 3a=  tan (90- 2a)

On comparing

3a= 90- 2a

5a= 90

a= 14

Hence, the value of a is 14.

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-243

Step-by-step explanation:

số dương nhân -3 thì đc số âm, số âm nhân với -3 để đc số dương.

vd: 1. -3 = -3 ;   -3 .-3= 9 ;..... 81 . -3= -243

Answer:

all once will product the term by mines 3

so the final will bt -3 *81 = -243

Answer:

well by using the formulae a²+b²=c² with "a" being the opposite "b" being the adjacent and "c" being hypotenuse

Answer:

BY LEARNING  Pythagorean Theorem Formula Proof using Similar Triangles

Step-by-step explanation:

In a right-angled triangle, the Pythagoras Theorem Formula is expressed as:

c2 = a2 + b2

Where,

'c' = hypotenuse of the right triangle

'a' and 'b' are the other two legs.

See below for the vocabularies and their correct definition

Match the following vocabulary

The terms are given as:

To get the inverse of a conditional, the hypothesis and the conclusion are negated, without interchanging them.

So, we have:

Inverse of a conditional ⇒ A new statement formed by negating both the hypothesis and the conclusion.

To get the contrapositive of a conditional, the hypothesis and the conclusion are negated, after interchanging them.

So, we have:

Contrapositive of a conditional ⇒ Formed by exchanging the hypothesis and the conclusion and negating both of them.

To get the converse of a conditional, we simply interchange the hypothesis and the conclusion, without negating them

So, we have:

Converse of a conditional ⇒ A statement formed by interchanging the hypothesis and the conclusion in a conditional statement.

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Answer:

The answer is Convers because it literally takes the hypothesis and the conclusion and interchanges them.

Step-by-step explanation:

The first part is half of the second part. The first part is 16 and the second part is 8.

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Let the first part is x, y os the second part, and the no of half times is z then the equation is;

x × y = z

16×(1/2) = 8

Hence,the first part is half of the second part. The first part is 16 and the second part is 8.

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Answer:

131.13

To find the area do w (width) times l (length/breadth) so the equation to find the area would be L*W=A

Answer:

$30 is the original price.

Step-by-step explanation:

Let x be the original price of the gift.  The sisters got a 10% discount, so the price paid by them is 0.90x.

The five sisters each paid $5.40, so the total they paid was:

5*($5.40) = $27.

This is equal to the 0.90x:  

0.90x = $27

x = $27/0.90

x = $30

Chocolates

The value of x in the second matrix is -1

The operation is given as:

[tex]\left[\begin{array}{ccc}2&-1&1\\1&1&1\\4&-2&2\end{array}\right] \left[\begin{array}{c}4&11&5\end{array}\right] \to \left[\begin{array}{ccc}0&-3&x\\1&1&1\\4&-2&2\end{array}\right] \left[\begin{array}{c}-18&11&5\end{array}\right][/tex]

Let the rows be represented by R1, R2 and R3.

By observation, the row operation performed is:

[tex]R1 \to R1 - 2R2[/tex]

This means that:

The new elements of row 1 are gotten by subtracting twice the elements of row 2 from row 1.

Using the above operation, we have:

x = 1 - 2 * 1

Evaluate the difference

x = -1

Hence, the value of x is -1

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The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.

The rate of change between 2 and 3 trees is given by:

R₂₃ = (180 - 120)/(3-2)

R₂₃  = 60.

Also, the rate of change between 3 and 5 trees is given by:

R₃₅ = (290 - 180)/(5-3)

R₃₅ = 110/2

R₃₅ = 55.

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Complete Question:

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?

The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

What is a nonlinear function?

A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.

The rate of change between 2 and 3 trees is given by:

R₂₃ = (180 - 120)/(3-2)

R₂₃ = 60.

Also, the rate of change between 3 and 5 trees is given by:

R₃₅ = (290 - 180)/(5-3)

R₃₅ = 110/2

R₃₅ = 55.

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Complete Question:

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?

Answer:

11

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x² - 6x - 4 +5x + 3 ← collect like terms

= x² - x - 1

then

(f + g)(- 3) = (- 3)² - (- 3) - 1 = 9 + 3 - 1 = 11

Answer:

11

Step-by-step explanation:

F(–3)=(–3)²–6(–3)–4===> 9+18–4=23

g(–3)=5(–3)+3=‐15+3=–12

23–12=11

Answer:

w = 3

Step-by-step explanation:

1/w = 1 2/3 / 5      cross multiply

1 2/3 (w) = 5

w = 5 / ( 1 2/3 ) =  5 / ( 5/3) = 15/5 = 3

Step-by-step explanation:

Since we have a vertical directrix, the equation of the parabola is

[tex](y - k) {}^{2} = 4p(x - h)[/tex]

Where p is the distance from the vertex to the directrix.

or the distance from the vertex to the focus.

Since we have a sideways parabola, let use the point for the directrix is (-6,0). So let find the midpoint of (-6,0) and (6,0). That would be our vertex.

[tex] \frac{ - 6 + 6)}{2} = 0[/tex]

[tex] \frac{0 + 0}{2} = 0[/tex]

So our vertex is (0,0).

So our equation become

[tex] {y}^{2} = 4px[/tex]

The distance from the focus and directrix is 6.

So p=6.

[tex] {y}^{2} = 24x[/tex]

So p is 6.

Since p is 6,

[tex] \frac{ {y}^{2} }{24} = x[/tex]

Answer:

DeltaMath allows teachers to create free online accounts and assign their students automatically-graded, interactive problems from a long list of modules sorted by level – from middle school Common-Core-aligned math to AP Calculus.

Step-by-step explanation:

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Answer:

y^3

Step-by-step explanation:

x^3 y^3     and    y^4  

y^3 * x^3     and y^3  * y

Answer:

d. 93 [tex]m^{2}[/tex]

Step-by-step explanation:

4×3= 12, 12/2 =6, 6×4 = 24

5×3= 15, 15×4= 60

3×3=9,

24+60+9= 93

Answer:

The equation of the line is y ≥ 1/3(x)-1

Step-by-step explanation:

Given

The line intersects y-axis at (0,-1). Therefore, the y-intercept is -1

The line passes through the points (0,-1)  and (3,0)

The slope can be obtained as follows,

m = 0-(-1)

        3-0

    = 1/3

The linear equation with slope and intercept  is given as follows.

y = mx + c

Substitute 1/3 for m, 3 for x and 0 for y  in equation  to obtain the value of

c .

0 = 1/3 *3 + c

c= -1

To check whether the equation includes origin substitute 0 for x and 0 for y in equation

Therefore, y≥ mx+c

                      = 1/3*x-1

Hence, Linear inequality represented is y ≥ 1/3(x) -1

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"Law of conservation of Mass and Energy", is the reason for which it is important to keep the two sides of an equation balanced when solving.

The other properties that we should consider while rewriting the expressions of an equation is that we should not multiply or divide the expressions by zero on both the sides.

According to the law of conservation of mass, mass is neither generated nor destroyed during a chemical process. For instance, when coal is burnt, the carbon atom in it transforms into carbon dioxide. The carbon atom transforms from a solid to a gas, yet its mass remains constant. Similar to this, according to the law of conservation of energy, energy cannot be generated or destroyed. For instance, kinetic energy is converted to potential energy when a toy vehicle is rolled down a ramp and collides with a wall.

While rewriting expressions of an equation, we should not multiply or divide them by zero, as multiplying or dividing by zero makes two non-equal expressions equal (0 and ∞ respectively.

This is the reason why is it important to keep the two sides of an equation balanced, and that the expressions should not be multiplied or divided by zero.

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The two options are R₀ 270 , R₀ 90 , Option C and D .

The complete question is attached in the image.

There are two types of transformations namely , Rigid Transformation and Non- Rigid Transformation

The rigid transformations do not change the shape and size of the preimage .

The non Rigid transformation do not change the shape but change the size of the preimage.

The rule rotating the origin , 270 degree is

(x,y) ----> (y , -x)

as (x,y) is (0,5)

Therefore after 270 degree transformation

(y,-x) is (5 , 0)

So, the clockwise rotation is 90 degree about origin

(x,y) ----> (y , -x)

as (x,y) is (0,5)

Therefore after 90 degree transformation

(y,-x) is (5 , 0)

Therefore the two options are R₀ 270 , R₀ 90 , Option C and D .

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Answer:

Given - angle X = angle A

angle Z = angle C

To find - criteria of congruence

Solution -

In triangle BAC and triangle YXZ

angle X = angle A

angle Z = angle C

we need one pair of side to be comgruent to show the following traingles congruent

if AC is congruent to XZ

then by angle side angle criteria of triangle both the triangles are congruent..

Answer:

B

Step-by-step explanation:

Answer:

[tex]\fbox {1) A}\\\fbox {2) A}[/tex]

Step-by-step explanation:

Q1

⇒ Graph A is most accurate as the situation is linear and the dots indicate per cup as you can't have any rational part (such as 0.5 cups, etc.)

Q2

⇒ A

⇒ The graph is discrete because the sellers have limited the purchaser to buy a distinct whole number of cups

If 3 ft = 1yard

?        = 16 yards?

Thats [tex]\frac{16 yards * 3ft}{1yard}[/tex]

The common values cancel each other out and you'll have 48 feet :)

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:\dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{4 + \sqrt{45} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{4}{6} + \cfrac{ \sqrt{45} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{3 \times 3 \times 5} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ 3\sqrt{5} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Step-by-step explanation:

The height of each story in a hotel is  feet. The height is measured from the ceiling to the floor. The hotel has 2 underground levels that are used as banquet halls. Stephen is a waiter who works two levels below ground. At what elevation are Stephen’s feet? Assume the ground level of the hotel is at 0 feet.

A.

feet

B.

feet

C.

D.

feet

Answer:

I don't see the equation options.  See below for a predicted equation.

y= (2/3)x + 4

Step-by-step explanation:

The points are (-3,2), (0,4), and (3,6).  I will assume they lie in a straight line.

Find an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

m, the slope, is also known as the "Rise/Run."

Pick any two points.  I'll use (0,4) and 3,6)

Rise = (6-4) = 2

Run  = (3-0) = 3

Slope = 2/3

The equation becomes y = (2/3)x + b

B is easy in this case.  Point (0,4) tells us that y = 4 when x = 0 (the definition of b).

The equation is y= (2/3)x + 4

See the attached graph.

Answer:

5.5x + 9

Step-by-step explanation:

0.3x plus 24, 5x, and 0.2x minus 15

Expression:

This means that,

0.3x + 24 + 5x + 0.2x - 15

We know the perimeter of the triangle is,

Where a , b , c refers to the sides of that triangle.

So Just add them up:

Hence,last choice is accurate.

Answer:

[tex]\sf B) \ y=-\dfrac{1}{5}x-4[/tex]

Explanation:

Equation: y = mx + b      [where "m" is slope, "b" is y-intercept]

The y-intercept (b) is -4

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here take two points: (0, -4), (5, -5)

[tex]\sf slope \ (m) : \dfrac{-5-(-4)}{5-0} = -\dfrac{1}{5}[/tex]

[tex]\sf Hence \ equation : y = -\dfrac{1}{5} x -4[/tex]