On Monday, Caroline owed her Mom $350, she was able to pay back $200. Then she spent $23 for gasoline. She returned a sweater to Target and received a refund of $35. Then she spent $15 at the bookstore. Write one number sentence to show what happened on Monday. Then calculate how much money Caroline has now.

Answer:

Center (6, -3)

Radius 5

Answer:

The expression is: (225 - (32 × 4))/0.15

Steps:

first we'll calculate the rental cost of 4 days without the miles driven

32 × 4 = $128.00

now we'll calculate the money that can be spent on miles

225 - 128 = $97.00

with $97.00 they can drive: 646.66 miles

97 / 0.15 = 646.66 miles

The expression is: (225 - (32 × 4))/0.15

9514 1404 393

Explanation:

For proofs of this nature, it often works well to replace everything possible with appropriate equivalents. Here, we'll use sin² to represent sin²(A), and equivalent notation for other trig functions.

We will change the left side to the form of the right side.

  [tex]\displaystyle \frac{\tan^2-\cot^2}{1+\cot^2}=\frac{\sin^2-\cos^2}{\cos^2}\\\\=\frac{(\sec^2-1)-(\csc^2-1)}{\csc^2}\\\\=(\sin^2)(\sec^2-\csc^2)\\\\=\frac{\sin^2}{\cos^2}-1=\frac{\sin^2-\cos^2}{\cos^2}\qquad\text{Q.E.D.}[/tex]

__

The equivalents (identities) used are ...

  1+tan² = sec²

  1+cot² = csc²

  1/csc = sin

  sec = 1/cos

Answer:

[tex]\sqrt{655*655} =655[/tex]

Step-by-step explanation:

655*655 is pretty much equal to 655²

the square root of a number to the power of 2 is equal to the number without the power

so √655² would be equal to 655

Answer:

[tex]655[/tex]

Step-by-step explanation:

[tex] \sqrt{655 \times 655} \\ = 655[/tex]

Answer:

[tex]6x-6y-16=0[/tex]

Step-by-step explanation:

Consider the following system of equations:

[tex]a_1x+b_1y+c_1=0\\\\a_2x+b_2y+c_2=0[/tex]

The system of equations has infinite solutions if [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

One equation is [tex]3x-3y=8[/tex]

[tex]3x-3y-8=0[/tex]

Take another equation as [tex]6x-6y-16=0[/tex]

So, the two equations are [tex]3x-3y-8=0[/tex] and [tex]6x-6y-16=0[/tex]

[tex]a_1=3,b_1=-3,c_1=-8,a_2=6,b_2=-6,c_2=-16[/tex]

[tex]\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}\\ \frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2}\\ \frac{c_1}{c_2}=\frac{-8}{-16}=\frac{1}{2}[/tex]

So,

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

Therefore, another equation can be [tex]6x-6y-16=0[/tex]

Answer: The answer to your question is to not ask clearly you just answered your own question like yoooooooooooooooooooo.

Step-by-step explanation:

Answer:

I think the calculation answer will be 9,999,811,112

Answer:

f^−1(x)=2^x/4

Step-by-step explanation:

The inverse of the function will be;

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

A relation between a set of inputs having one output each is called a function.

Given that;

The function is,

⇒ y = log₂ (4x)

Now,

Since, The function is,

⇒ y = log₂ (4x)

Find the inverse of the function as;

⇒ y = log₂ (4x)

⇒ [tex]2^{y} = 4x[/tex]

⇒ [tex]\frac{2^{y}}{4} = x[/tex]

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

Thus, The inverse of the function y = log₂ (4x) is,

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

Learn more about the function visit:

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Answer:

A D and E

Step-by-step explanation:

The statements true about the graph of the function are

a) The axis of symmetry is the line x = 6

b) The parabola opens down

c) The vertex of the graph is at (-6, -11)

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) = -3x² + 36x - 119

And , the vertex form of the function is

f ( x ) = -3 ( x - 6 )² - 11

Now , The axis of symmetry is the line x = 6. This is true because in vertex form, the equation of the axis of symmetry is given by x = h, where (h, k) is the vertex of the parabola. In this case, the vertex is (6, -11), so the axis of symmetry is x = 6.

The parabola has a minimum. This is also true because the coefficient of the x² term in the given equation is negative (-3), which means the parabola opens downward and has a minimum at the vertex.

Hence , the graph of the polynomial is solved

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Step-by-step explanation:

I think it is a good day and the answer is 3

Answer:

Inequality to determine number of glass sets: 10x + 230 ≥ 498

Solved inequality: x ≥ 26.8 (She needs to buy at least 27 sets)

Step-by-step explanation:

In order to write an inequality to represent this situation, you must first identify the important information:

- The restaurant needs 498 glasses total at the least

- They already have 230 glasses

- Each set of glasses has 10 glasses

Now, you can write an inequality to represent this situation:

498 (needed glasses) ≤ 230 (glasses already owned) + 10x (number of glasses in one set (x))

You can rewrite it as 10x + 230 ≥ 498 so that x is on the left and it is ordered by variable exponential value. Now you have the inequality to represent the situation, so to find the number of sets of glasses Brooklyn could buy, you need to isolate x:

10x + 230 ≥ 498 (given)

10x ≥ 268 (subtract 230 from both sides)

x ≥ 26.8 (divide both sides by 10)

So, Brooklyn needs to buy at least 27 sets since she can't buy 4/5 of a set.

Answer:

10x + 230 ≥ 498

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

40°

Step-by-step explanation:

If your are reffering to a triangle the answer would be 40 since the three angles of a triangle must always add up to 180° so you would add b+d (110+30) resulting in 140 which you would then subtract from 180 getting you 40°

Answer: 20 hrs

Step-by-step explanation:

Answer:

[tex]x=49.16^{\circ}[/tex]

Step-by-step explanation:

We need to find the value of x in the given figure.

It is a right angled triangle, in which base is 19, height is 22.

We can use trigonometry to find x.

We know that,

[tex]\tan\theta=\dfrac{P}{B}[/tex]

Where

P is perpendicular and B is base

So,

[tex]\tan x=\dfrac{22}{19}\\\\x=\tan^{-1}(1.157)\\\\x=49.16^{\circ}[/tex]

So, the value of x is equal to [tex]49.16^{\circ}[/tex].

Answer:

theres no numbers?

Step-by-step explanation:

Answer:

Step-by-step explanation:

you do 10/2 for the radius, so that will be 5. then you do 3.14*5*5= 78.5

Answer:

-3+7=4 is the answer if thats what you is looking for

Step-by-step explanation:

Answer:

A/C ≅ 2

Step-by-step explanation:

diameter of circle d = 8 in

Circumference of the circle C= 25 in

Let us assume we have to find the area of the circular lid  A = [tex]\frac{\pi}{4}d^2[/tex]

⇒ A= [tex]\frac{\pi}{4}\times8^2= 50.24 in^2[/tex]

Therefore ratio of area to circumference A/C = 50.24/25 = 2.0096≅2

Answer: approximately 15

Step-by-step explanation:

Answer:

radius = 5.48ft

Step-by-step explanation:

The formula for the circumference of a circle is: C = πr² or pie times the radius squared.

Now that we know this, we can plug in the equation.

94.25 = πr²

÷π         ÷π

30 = r²

√30 = √r²

5.48 = r

So, the radius of the circle is 5.48 ft

Answer:

El reloj de Nuestra Basílica de Chiquinquirá empleará 20 segundos para indicar las 8 a.m.

Step-by-step explanation:

De acuerdo a la información proporcionada, sabes que el reloj de Nuestra Basílica de Chiquinquirá señala cada hora con igual número de campanadas, por lo que a las 8 a.m. tocará 8 campanadas y puedes usar una regla de tres para encontrar cuantos segundos empleará en hacerlo dado que conoces que las 6 campanadas se demoran 15 segundos:

6 campanadas → 15 segundos

8 campanadas →         x

x=(8*15)/6

x= 20

De acuerdo a esto, la respuesta es que el reloj de Nuestra Basílica de Chiquinquirá empleará 20 segundos para indicar las 8 a.m.

Answer:

76+76=152

Step-by-step explanation:

Answer:

x-8

......................

Step-by-step explanation:

-8x-12+9x+4

-8x+9x-12+4

x-8

x-8=0

x=8