A cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F. The table shows temperature readings for the cake.

a. Given a room temperature of 70⁰F , what is an exponential model for this data set?

Answer:

x = 3, y = 5.

Step-by-step explanation:

8x - 3y = 9

4x - 4y = -8

multiply the second equation by 2:

8x - 8y = -16

Subtract this from the first equation:

5y = 25

y = 5.

Substitute for y in equation 2:

4x - 4(5) = -8

4x = -8 + 20 = 12

x = 12/4 = 3.

Answer:

2

Step-by-step explanation:

1=1=2

After solving the equation, x = 19/4 Is the value of x in 4x = 19

⇒ 4x = 19

⇒ x = 19/4

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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Answer:

24

Step-by-step explanation:

A composite function exists as a function that depends on another function. A composite function exists formed when one function exists substituted into another function.

The value of f(f(f(x))) is 1/x

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

A function that depends on another function is referred to as a composite function. When one function is inserted into another, a composite function is produced. For instance, f(g(x)) is the composite function created when x in f is replaced with f(x). f(g(x)). You can interpret f(g(x)) as "f of g of x."

Let the given function be f(x) = 1/x

f(f(x)) = f(1/x) = 1/(1/x)

simplifying the above equation, we get

f(f(x)) = f(1/x) = x  

f(f(f(x))) = f(x) = 1/x

Therefore, the value of f(f(f(x))) = f(x) = 1/x

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The the vertices if the triangle is reflected over the y-axis and then dilated by a scale factor of 2 wii be A'(4, 6), B'(0, 0) and, C'(-2, 4).

According to the given question.

The vertices of a triangle ABC are A(-2, 3), B(0, 0), and C(1, 2).

As we know that,

The rule for reflecting a triangle over the y axis is to negate the value of x-coordinate of each point, but leave the y-value the same.

Therefore, the vertices of triangle ABC when it is reflected over y-axis are

A'(2,3)

B'(0, 0)

C'(-1, 2)

Also, when the triangle is dialated by a scale factor 2 then the vertices will be

A'(4, 6)

B'(0, 0)

And, C'(-2, 4)

Hence, the the vertices if the triangle is reflected over the y-axis and then dilated by a scale factor of 2 wii be A'(4, 6), B'(0, 0) and, C'(-2, 4).

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Given the perimeter, the length and width of the rectangular family portrait are 20 inches and 31 inches respectively.

The perimeter of a rectangle is expressed mathematically as;

P = 2( l + w )

Given the data in the question;

Let "x" represent the width of the rectangle.

To determine the width and length of the rectangle, plug the given values into the formula above and solve for x.

P = 2( l + w )

102 = 2( ( 2x - 9 ) + x )

102 = 2(  2x - 9 + x )

102 = 2(  3x - 9 )

Apply distributive property

102 = 2(3x) + 2(-9)

102 = 6x - 18

102 + 18 = 6x

120 = 6x

6x = 120

x = 120/6

x = 20

Now, the numerical length and with of the rectangular frame will be;

Width w = x = 20 inches

Length l = 2x - 9 = 2(20) - 9 = 40 - 9 = 31 inches.

Given the perimeter, the length and width of the rectangular family portrait are 20 inches and 31 inches respectively.

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Answer: It is a rational number.

Hence, [tex]2.738[/tex] a rational number.

What is the rationa number?

A rational number is a type of real number, which is in the form of [tex]\frac{p}{q}[/tex] where [tex]q[/tex] is not equal to zero. Any fraction with non-zero denominators is a rational number.

Here [tex]2.73[/tex] acn be written as

[tex]2.73=\frac{2.73}{1}[/tex]

Now, we multiply numerator and denominator by [tex]100[/tex].

So, it would be

[tex]\frac{2.73(100)}{1(100)}\\\\=\frac{273}{100}[/tex]

So, the fraction is written as [tex]2.73[/tex].

Hence, [tex]2.738[/tex] a rational number.

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Myron would need 7.2 hours to cook 3 kilograms of meat.

time = 12 hours

cook = 5 kilograms of meat.

i.e. For 5 kilograms of meat, it takes 12 hours to cook.

Thus, for 3 kilograms of meat,

Multiple 12  by 3 and divided by 5

= 12/5 * 3

= 12 * 3/5

= 36 / 5

= 7.2 hrs.

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Answer:  12 hours

Step-by-step explanation: 5 kilo grams of meet

The amplitude and the period of the function are 3 and 2, respectively.

Sinusoidal functions are periodic bounded functions whose form is described below:

y = A · sin (2π · t / T + Ф) + y'

Where:

The period is the horizontal distance between two consecutive peaks or two consecutive bottoms and the amplitude is equal to the half of the distance between a peak and a consecutive bottom. Hence, the amplitude and the period are, respectively:

Amplitude

A = 0.5 · [2 - (- 4)]

A = 3

Period

T = 2 · [0.75 - (- 0.25)]

T = 2

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Applying the slope formula, the slope of the line is determined as: 2.

The slope of a line  represented by a table of values can be calculated using any two set of ordered pairs form the given table, and applying the slope formula below:

Slope (m) = y2 - y1/x2 -x1

Using any two points of the line, (0, -0.25) and (1, -0.2), as represented in the table, let:

(0, -0.25) = (x1, y1)

(1, -0.2) = (x2, y2)

Plug in the values

Slope (m) = (-0.2 -(-0.25))/(1 - 0)

Slope (m) = 0.05/1

Slope (m) = 0.05

Thus, the slope of the line as represented by the table of values is calculated as: 0.05.

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After solving, the factors of equation 4x²+16=34x are:

So,

Given equation: 4x²+16=34x

Then,

Factors are: (x-8) and (4x-2)

Therefore, after solving, the factors of equation 4x²+16=34x are:

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The correct question is given below:
Solve each equation.

4x²+16=34x

Greetings from Brasil...

Answer:

6x2 + 11x

Step-by-step explanation:

First collect like terms:

8x2 - 2x2 + 3x + 8x - 10 + 10 (Ps: x2 and x are not the same!)

Combine them:

6x2 + 11x (the -10 and 10 cancel out)

and this is your polished answer!

The equation when both cards would have the same amount of money left is 30 = 5p.

An equation is an algebraic expression that has an equal to sign. A linear equation is an equation that has a single variable that is raised to the power of one. When drawn on a graph, a linear equation is a straight line

Amount left on the gift card = value of the gift card - (amount spent on pizza x number of pizzas bought)

Amount left on Jim's gift card = 100 - ($15 x p)

100 - 15p

Amount left on Yoko's gift card = 70 - (10 x p)

70 - 10p

When both cards have the same amount of money left, the two above expressions would be equal

100 - 15p = 70 - 10p

Combine similar terms:

100 - 70 = 15p - 10p

Add similar terms:

30 = 5p

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Answer:

The lines are neither

Step-by-step explanation:

A radical expression can always be rewritten using a rational exponent .

Radicals : The expressions which include a root (  [tex]\sqrt[n]{x}[/tex]  ) are called radicals . For ex . [tex]\sqrt{2}[/tex] , [tex]\sqrt[3]{3}[/tex] , [tex]\sqrt[7]{5}[/tex] , and so on .

Rational Exponent : Numbers of the form ( [tex]a^{m}[/tex] ) are called rational exponents . For ex . [tex]7^{2}[/tex] , [tex]11^{3}[/tex] , [tex]5^{5}[/tex] and so on .

A radical can be converted into a rational exponent . This can be done by keeping the no . inside root as it is and reciprocating the index and raising it to the power of exponent .

( [tex]\sqrt[n]{x}[/tex] ) = ( [tex]x^{1/n}[/tex] ) where x is the base and 1 / x is the power of the exponent .

Hence , a radical expression can always be rewritten using a rational exponent .

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Simply solve the given equation and then evaluate according to the given situations. The answer is

a) Too high

b) Too high

c) Too low

Diego evaluated 2 3/11−4/5

Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum. It is one of the essential mathematical functions we use in our everyday activities.

Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller

2 3/11 - 4/5 = 81/55 = 1.47

a) 2 3/11 + 4/5 = 169/55 = 3.07 (Too high)

b) (2 3/11 - 4/5) + 4/5 = 125/55 = 25/11 = 2.27 (Too high)

c) 2 3/11 - (2 3/11 - 4/5) = 25/11 - 81/55 = 44/55 = 4/5 = 0.8 (Too low)

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Simply answer the supplied equation, then make a judgment call based on the scenarios. The response is

a) Excessive

b) Excessive

• Too little

Diego scored a 2 3/11/4/5.

In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. It is one of the fundamental mathematical operations we employ on a daily basis.

The operation of subtraction is used to calculate the difference between two numbers. If you remove a few items from a collection of things, the group will get smaller.

2 3/11 - 4/5 = 81/55 = 1.47

a) 2 3/11 + 4/5 = 169/55 = 3.07 (Too high)

b) (2 3/11 - 4/5) + 4/5 = 125/55 = 25/11 = 2.27 (Too high)

c) 2 3/11 - (2 3/11 - 4/5) = 25/11 - 81/55 = 44/55 = 4/5 = 0.8 (Too low)

Answer:

y = 3x

Step-by-step explanation:

Slope-intercept form of an equation is a shortcut, fill-in-the-blank form you can use to write the equation of a line.

Slope-intercept eq:

y = mx + b

You fill in slope where the m is. And you fill in the y-intercept for the b.

In your problem they gave you two points. You can calculate slope with two points. Subtract the y's, 3-0, put that on top of a fraction. And subtract x's, 1-0, put that on the bottom of the fraction. The slope, m, is 3/1, which is 3.

slope:

m = 3-0 / 1-0 = 3/1 =3

The y-intercept is actually given in your problem. The y-intercept is the point where the line crosses the y-axis. The y-intercept is the point where the x is 0. They gave you the point (0,0) that is the y-intercept. So b = 0.

Fill the m and b in with the given numbers!

y = 3x + 0 Simplify.

y = 3x

Answer:

14x⁸ - 12x⁶ + 16x⁴

Step-by-step explanation:

To find the required polynomial, multiply 2x² and the quotient.

Multiply each term of (7x⁶ - 6x⁴ + 8x²) by 2x².

2x² * 7x⁶ = (2*7) *x²⁺⁶ = 14x⁸

Required polynomial =2x² *(7x⁶ - 6x⁴ + 8x²)

                                   = (2x²*7x⁶) - (2x²*6x⁴) + (2x²*8x²)

                                    = 14x⁸ - 12x⁶ + 16x⁴

The 83rd percentile contains intervals which are 50 and 100 thousand kilometers.

What is a histogram ?

A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals.

It is given that , data for most recent 23 vehicles is shown in the histogram.

On the x-axis distance driven in thousands of kilometers and on the y-axis frequency is represented in the histogram.

For 23 vehicles , we have different ranges of distance driven i.e., 0 - 50 , 50 - 100 , 150 - 200 . 200 - 250 , 250 - 300.

We know that the 83rd percentile meant the distance driven is greater than or equal to 83 %.

i.e.,

Here , 83 lies between 50 - 100 , so , 83rd percentile contains intervals which are 50 and 100 thousand kilometers.

Therefore , 83rd percentile contains intervals which are 50 and 100 thousand kilometers.

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Simplified answer to the given expression are :

a) 3/5

b) 2

c) 2.236

What is an mathematical expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

a) given expression is : [tex]\sqrt{\frac{9}{25}}[/tex]

Now, to simplify it we write the factors of 9 and 25 as 3 x 3 and 5 x5 and then take the root of them to get 3/5 as answer.

 [tex]\sqrt{\frac{9}{25}}[/tex] = √(3 x 3)/ √(5 x 5 ) = 3/5

b) given expression is :  [tex]\sqrt{\frac{12}{3}}[/tex]

Now, to simplify it we first divide 12 with 3 that is 4 and then take the root of 4 to get 2 as answer :

 [tex]\sqrt{\frac{12}{3}}[/tex] = √4 = 2

c) given expression is :  [tex]\frac{\sqrt{15}}{\sqrt{3}}[/tex]

Now, to simplify it we first divide 15 with 3 that is 5 and then take the root of 5 to get 2.236 as answer :

[tex]\frac{\sqrt{15}}{\sqrt{3}}[/tex] = √15/3 = √5 = 2.236  

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Step-by-step explanation:

what form should the equation have ?

I assume slope-intercept

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

but since we have the slope and a point, we can start with the point-slope form and transform it :

y - y1 = a(x - x1)

"a" is again the slope, (x1, y1) is the point.

so,

y - 7 = -5/3 × (x - -3) = -5/3 × (x + 3) = -5x/3 - 5

and therefore

y = -5x/3 + 2

If b^{h} < 1 then it will be a vertical stretch.

What authority possesses a power rule?

When a base is raised to a power and then the entire expression is raised to another power, the power of a power rule in exponents is used to simplify the algebraic statement.

A translation of function f is f₁ (x) = bˣ⁻h . It is equivalent to a vertical stretch or vertical compression of function f.

[tex]f_{1} (x) = b^{x - h}[/tex]

If we used the rules of powers, we know that when we have a subtraction in the power of an exponential, it can be split into a division. So the function can be rewritten as

 [tex]f_{1} (x) = \frac{b^{x} }{b^{h} }[/tex]

Remember the original function was

f(x) = bˣ

therefore

[tex]f_{1}(X) = \frac{f(x)}{b^{h} }[/tex]

this means that if [tex]b^{h} < 1[/tex] then it will be a vertical stretch.

If b^{h} < 1  then it will be a vertical stretch.

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Answer:

2x=20 i guess

Step-by-step explanation:

2x -5= 15

add 5 to both sides

you should get 20

it's 2x=20

The factored form of the equation x² + 6x + 8 is (x + 4) (x + 2), that is, option B.

Here, we are given a quadratic equation x² + 6x + 8

We can factorize this equation using the splitting the middle term method.

Here the coefficient of x is 6, hence, we need to spilt 6 in such a manner that the product of the split terms is 8.

6 can be written as 4 + 2 and we can see that 4 × 2 = 8

Hence, we can write the given equation as-

x² + 4x + 2x + 8

= x (x + 4) + 2 (x + 4)

= (x + 4) (x + 2)

Hence, the factored form of the equation x² + 6x + 8 comes out to be (x + 4) (x + 2), that is, option B.

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Answer:

A) –2 or 3∕5

Step-by-step explanation:

Two possible cases since we are dealing with absolute values:

7h + 1 = 3h - 7 ; h = -2 here

7h + 1 = -(3h - 7) ; h = 3/5 here

Answer:

4

Step-by-step explanation:

B= 1

D= -3

Distance between the two? 4 points

1 - (-3) = 4

Yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Luke gets pizza delivered from the same local pizza parlor every Thursday. This week, he ordered 3 pizzas for his family and spent $32.75.

Last week he ordered 4 pizzas and spent $41.50.

Each pizza costs when ordered 3 pizzas

= 32.75/3 = $10.91

Each pizza costs when ordered 4 pizzas

= 41.50/4 = $10.37

Yes, the pizza parlor charges a delivery fee.

= (41.50+32.75)/(3+4) = 10.60

d = 10.60p

Thus, yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.

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