3. The equation 4x + 16y = 36 is a true equation for a particular
value of x. Explain why x + 4y = 9 is also true for the same value of x.

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Work Shown:

If cos(A) = sin(B), then A+B = 90, where A & B are both acute angles in degree form.

In this case, A = 52, so,

A+B = 90

B = 90-A

B = 90-52

B = 38

Telling us that

cos(A) = cos(52) = 0.6157

sin(B) = sin(38) = 0.6157

cos(52) = sin(38)

CS = x, and since AB = BC = CD = DA = 1cm -> SD = 1 - x

We see that angle DSP = angle APQ (because they simultaneously equal to 90 when added angle DPS)

So, triangle DSP = triangle APQ (equal hypotenuse - square side and equal angle.)

Similarly, we can prove triangle SCE and QBE in the same way

So, all 4 of the triangles are equal to each other.

-> SD = CE = BQ = AP = 1-x

Calculate the area of 4 triangles : [ x(1-x) : 2 ] x 4 = x(1-x) x 2

Area (PQRS) = 1 - [ x(1-x)] x 2 = 1 - 2x + 2x(squared) = [tex]2x^{2} -2x + 1[/tex]

ii) Half area of PQRS = [tex]x^{2} -x+1[/tex]

= [tex]x^{2} -\frac{1}{2} x-\frac{1}{2} x + \frac{1}{2} = x(x-\frac{1}{2} )- \frac{1}{2}(x-\frac{1}{2} ) + \frac{1}{4} = (x-\frac{1}{2})^{2} + \frac{1}{4}[/tex]

We have : [tex](x-\frac{1}{2}) ^{2}[/tex]

has the smallest value of 0 -> The smallest half value of PQRS = 1/4 -> The smallest value of PQRS = 1/2

Answer:

He would need 3/4 a gallon to paint the wall

Step-by-step explanation:

Answer:

Twenty-one Thousand

Step-by-step explanation:

Answer: 5/12

Step-by-step explanation:

Answer:

The coordinates (12,7) would NOT be a solution to the system of linear inequalities shown below.

Step-by-step explanation:

If you do the graphing and you look at all your options of coordinates, (12,7) is the only one that is not in the shaded areas or in the lines of the inequalities. Therefore, (12,7) should be the answer to that question. :)

The trial of stimulation that can model the probability of the gender of the kittens is tossing a coin five times and count the number of heads.

Probability simply means the chance of the occurrence of an event. It's the numerical description of how likely an event will occur.

In this case, from the complete question, the trial of stimulation that can model the probability is to toss a coin five times and count the number of heads. The gender of the kittens can be allocated to the head or tail of the coin.

This is important to determine the probability that in a litter of 5 kittens, there will be more female than male kittens.

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Answer:

3-2r + 1 - 13

Step-by-step explanation:

3-2r + 1 - 13

Answers:

=============================================

Work Shown:

3 < 2x+1 < 13

3-1 < 2x+1-1 < 13-1 .... subtract 1 from all sides

2 < 2x < 12

2/2 < 2x/2 < 12/2 ... divide both sides by 2

1 < x < 6

The value of x is between 1 and 6, excluding both endpoints.

Since we exclude both endpoints, the graph will have open holes at 1 and 6 on the number line. The shading is between the open holes. The graph is below.

Converting 1 < x <6 to interval notation leads to (1, 6)

The curved parenthesis in interval notation indicate "exclude the endpoint".

Answer:

8 unit difference x, stays the same on y

Step-by-step explanation:

5 to -3 = 8 units

Answer:

Triangles that have exactly the same size and shape are called congruent triangles. The symbol for congruent is ≅. Two triangles are congruent when the three sides and the three angles of one triangle have the same measurements as the three sides and three angles of another triangle.

Answer:

have exactly the same size and shape

Step-by-step explanation:

triangles are congruent when they have three sides

In order to develop a function that models the situation regarding the optimal parameters, the following are needed:

It should be noted that a function simply means the relation or expression that has to do with two or more variables.

In this case, to develop a function that models the situation regarding the optimal parameters, one has to introduce the variables and find an equation relating to the variable.

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Answer: [tex]3\frac{1}{3}[/tex]

Answer:

Range of the function is {7,5,2,0}

Step-by-step explanation:

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Answer:

{7, 5, 2, 0}

Step-by-step explanation:

The domain is essentially all the [tex]x[/tex] values of the function, where the range is the value of [tex]h(x)[/tex].

So in order to solve this we simply plug in each number into the equation and get:

[tex]h(x)=|-2-5| = |-7|=7[/tex]

[tex]h(x)=|0-5| = |-5|=5[/tex]

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

[tex]h(x)=|5-5|=|0|=0[/tex]

Therefore the range is: {7, 5, 2, 0}

Answer:

t > 28

Step-by-step explanation:

[tex]\dfrac{t}{4} > 7[/tex]

Multiply both sides by 4:

[tex]\implies t > 28[/tex]

Answer:

3.75 miles

Step-by-step explanation:

Displacement is the shortest distance from the initial to the final position. So to calculate you do 15 - (3/4 of 15) = 3.75

Answer:

f [ x ] = [ x - 3] [ x + 8 ] = x^2 + 5x - 24

Step-by-step explanation:

f (x)=[ x - 3] [ x + 8 ]

x [ x + 8 ] -3[ x + 8 ]

x^2 + 8x - 3x - 24

x^2 + 5x - 24

Answer:

a  c

Step-by-step explanation:

Answer:

B because based by what I'm seeing it is the same answer to the other equation. Which is -34.

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[tex]

x \: \: is \: \: all \: \: real \: \: numbers.[/tex]

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Thus the correct answer is (( C )) .

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Answer:

true

Step-by-step explanation:

y = ab^x

the coordinates of the point are x and y values.

so, we can express "a" by these values :

k = ab^h

a = k/(b^h) = k × b^-h

now we use this identity in the original equation and get

y = k × b^-h × b^x = k×b^(x-h)

and that is exactly the same as the proposed form.

Addison needs to cut $45 from Food/Clothes and $41 from Entertainment, to pay the revised monthly payment.

It is given that

Addison has a balance of $3,450 on her credit card.

APR = 18%

Current monthly payment = $86.25

She wants to choose a monthly payment for 24 months.

So for 24 months,

A revised monthly payment using formula,

[tex]M = \frac{P.\frac{R}{12}. (1+\frac{R}{12} )^N }{(1+\frac{R}{12})N -1}[/tex]

R = 0.18

P = 3450

N = 24

Revised montly payment M = $172.24

Current monthly payment = $86.25

Difference = $86

So, she needs to cut the expenses by  $86

If she cut $45 from Food/Clothes and $41 from Entertainment, she can easily pay the revised monthly payment.

Therefore, Addison needs to cut $45 from Food/Clothes and $41 from Entertainment, to pay the revised monthly payment.

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Answer:

the variable

Step-by-step explanation:

Given expression:

[tex](6x+9)^2-5[/tex]

When evaluating the expression for [tex]x=1[/tex], we need substitute 1 for the variable ([tex]x[/tex]) in the expression.

Evaluating the expression for [tex]x=1[/tex]:

[tex]\implies (6\cdot1+9)^2-5[/tex]

[tex]\implies (6+9)^2-5[/tex]

[tex]\implies (15)^2-5[/tex]

[tex]\implies 225-5[/tex]

[tex]\implies 220[/tex]

Answer:

Variable

Step-by-step explanation:

Let's find the value

[tex]\\ \rm\Rrightarrow (6x+9)^2-5[/tex]

[tex]\\ \rm\Rrightarrow (6+9)^2-5[/tex]

[tex]\\ \rm\Rrightarrow 14^2-5[/tex]

[tex]\\ \rm\Rrightarrow 196-5[/tex]

[tex]\\ \rm\Rrightarrow 191[/tex]

Answer:

3 ft

Step-by-step explanation:

(I assumed that this was a rectangular prism based on the dimensions given, but do correct me if I assumed incorrectly.)

The formula for finding the volume of a rectangular prism is: [tex]V=w*h*l[/tex]

In this case, we already know that the volume of the prism is 24, so we can plug 24 in for V:

[tex]24=w*h*l[/tex]

We also already know the height and the length because they gave it to us, so we can plug it in as follows:

[tex]24=w*2*4[/tex]

Then we can multiply 2 and 4 on the right side:

[tex]24=w*8[/tex]

Then, to get the w alone, we can divide by 8 on both sides:

[tex]3=w[/tex]

Now that gives us that the width of the rectangular prism is 3ft.

Answer:

9.42

Step-by-step explanation:

Volume of cylinder= πr^2h

Answer:

37.68 yd

Step-by-step explanation:

= [tex]\pi[/tex]r²h

= (3.14)(1)²(12)

= 3.14 x 1 x 12

= 3.14 x 12

= 37.68 yd

Answer:

here you go

Step-by-step explanation:

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number.

Then: divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

Answer:

There are two patterns to chose two different biscuits; a digestive then a chocolate or a chocolate and then a digestive.

The probability of choosing a digestive then a chocolate is as follows:

7/12 * 5/11 =0.265

The probability of choosing a chocolate then a digestive is as follows:

5/12*7/11 = 0.265

Therefore the combined probability is 0.53 or 53%

Probability of digestive and chocolate

And

Probability of digestive and ginger

And

Probability of ginger and chocolate

Answer:

Wouldn't both of the witch watch whichever watch they felt like watching?

Step-by-step explanation:

Answer:

Let us divide the circle into 4 equal parts because they have told that 1/4 th part so there are 4 equal parts because,fractions represent equal parts of a whole or a collection.

Let us take a circle with centre 'O'

Now, the 1/4th part of circle is a sector with angle 90° & radius 3.5cm

We can find the area of sector in 2 methods

Method 1 :

Formula :

Here , r is radius & θ is the angle in sector where θ is measured in degrees

Hence , area of sector = 9.6cm²

Method 2 :

Formula:

Here , r is radius & θ is angle in sector where θ is measured in radians

First we have to convert 90° into radians

We know that π radians = 180°

90 ° = π/2 radians

Substituting

Hence , area of sector = 9.6 cm²

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