The perimeter of a bedroom is 88 feet. The ratio of the width to the length is 5:6. What are the dimensions of the bedroom?

Final answer:

To simplify the expression 43 + 2(3 - 2), first solve inside the parentheses (3 - 2 = 1), then multiply by 2 (2 × 1 = 2), and finally add to 43 to get 45.

Explanation:

The question asks to simplify the expression 43 + 2(3 − 2). To simplify, follow the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). First, solve the expression within the parentheses, which is 3 − 2 = 1. Next, multiply the result by 2 (2 × 1 = 2). Lastly, add this result to 43 to get the final answer, 43 + 2 = 45. This process demonstrates how to approach and simplify mathematical expressions using proper order of operations.

Answer:

40

Step-by-step explanation:

Subtracting a number k from 300 looks like this 300-k.

Adding a number k to 220 looks like this 220+k.

They are saying for some number k that we have 300-k and 220+k is the same value.

That is, 300-k=220+k.

This is the equation we are going to solve for your number.

300-k=220+k

Add k on both sides:

300=220+2k

Subtract 220 on both sides;

80=2k

Divide both sides by 2:

40=k

k=40.

So the number is 40.

Check: 300-40=260 while 220+40=260.

Answer:

d. (-2, 5)

Step-by-step explanation:

Point T is reflected over the y-axis.

Therefore, the coordinates are (-2, 5).

Answer:

T' is (-2,5)

Step-by-step explanation:

To reflect a point across the y-axis, you will note the following:

1- the sign x-coordinate of the point is flipped while the value remains the same

2- both the sign and the value of the y-coordinate remain the same

We are given that:

point T is (2,5)

Applying the above:

sign of x-coordinate is flipped and value is the same :

x- coordinate of T' is -2

both sign and value of y-coordinate are the same:

y-coordinate of T' is 5

Based on the above:

T' would be (-2,5)

Hope this helps :)

Answer:

Option C (f(x) = x^2)

Step-by-step explanation:

Quadratic Function is a polynomial which has a maximum degree of 2. It is expressed in the form:

f(x) = a + bx + cx^2; where a, b, and c are real numbers.

Any function which has the highest degree of 2 (not more than that) is the quadratic function. Option A illustrates the absolute values function. Option B shows a function which does not match the characteristics of the quadratic equation. Option D shows a linear function. Therefore, Option C (i.e. f(x) = x^2) is the correct choice!!!

Answer:

x=9

Step-by-step explanation:

Since y=18

The new equation is [tex]2x+3*6=36[/tex]

Moving some terms, it stays like the following:

[tex]2x=36-18[/tex]

solving for x, give us that x=9

Answer:

[tex]\frac{x-2}{x^2-x-2}[/tex]

Step-by-step explanation:

A removable discontinuity is when there is a hole in your graph. This is usually because one X value has been canceled out. Most of the time, it takes factoring to figure out if there is a removable discontinuity when looking at an equation.

First, look at the numerator [tex]x-2[/tex] . This can't be factored any further. However, [tex]x^2-x-2[/tex] can be factored since it is a trinomial (has three terms) .

For the purposes of this example, you may want to think about it as

[tex]1x^2 -1x-2[/tex]

To factor, multiply the the outside coefficients

1 x -2 = -2

Now take the middle coefficient (-1) and ask yourself what two numbers multiply to make -2, but still add to be -1.

-2 x 1 = -2

-2 + 1 = -1

So in factored form, the equation is

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

Since you have x-2 on both top and bottom, that can be canceled out. x - 2 would be your removable discontinuity in this situation.

A removable discontinuity can occur in a function if there are common factors in both the numerator and denominator that can be canceled out.

A function has a removable discontinuity at a particular point if the function is undefined at that point but can be made continuous by redefining the value at that point. To identify the removable discontinuity, we need to factor both the numerator and denominator of the function. By factoring, we can determine if any common factors exist that can be canceled out, resulting in a removable discontinuity.

Let's consider the given functions:

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Answer:

C) f(x) = x2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

He didn't change the direction of the inequality when he divided both sides by -2.

Step-by-step explanation:

Let's go through each step and see.

First step: They distribute and they did so correctly. -4(x+8)=-4x-32.

Second step: They added 2x on both sides.  

Third step:  They added 32 on both sides.

Fourth step: The divide both sides by -2 correctly but since this is inequality you must flip the sign.

For example 3>2 but if you multiply both sides by -1 or divide both sides by -1 you get -3<-2.

You have to flip the sign whenever you multiply or divide both sides of inequality by negative number.

Option B, 1/3

Since pepper topping can be in any size pizza, it remains as a 1/3 probability, since there are three toppings per size.

Answer:

January

Step-by-step explanation:

January is a counter-example of the name of the month begins with a January then it's a winter month by a season.

The counter example is : January since it begins with the letter J and is a winter month, which is not summer.

An example that disproves a statement (shows that it is false) is called a counter example.

The counter example will be : January since January is a month that starts with J that is not a summer month

January is the only month that fits this criteria.

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Has la serie numérica

a= 34.969.385

b = 34.969.386

c = 34.969.387

[tex]a < b < c[/tex]

Answer:

sin(45°)= AC/9

cos(45°)= BC/9

Step-by-step explanation:

This is a right angle triangle:

∠ABC =∠CAB = 45°

Now

AC= CB

AB = 9 units.

We will apply sines:

sine(45°)= AC/AB

We know that AB = 9 units.

So substitute the value of side AB

sin(45°)= AC/9

Now apply cos(45°)

cos(45°)=  BC/AB

Again substitute the value of AB:

cos(45°)= BC/9

Thus the answer is

sin(45°)= AC/9

cos(45°)= BC/9  ....

Answer:

A

E

Step-by-step explanation:

Answer:

5/48

Step-by-step explanation:

1x5=5

8x6=48

which give u

5/48

Answer:

[tex]\large\boxed{\dfrac{5}{48}}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{8}\times\dfrac{5}{6}=\dfrac{1\times5}{8\times6}=\dfrac{5}{48}\leftarrow\text{this is the simplest form}[/tex]

[tex](f+g)(x)=3x-2+2x+1=5x-1[/tex]

Answer:

[tex]\sqrt{37}[/tex]

Step-by-step explanation:

Distance formula

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

[tex]d = \sqrt {\left( {1 - 2 } \right)^2 + \left( {-2 - 4 } \right)^2 }[/tex]

Simplify

[tex]d = \sqrt {\left( {-1 } \right)^2 + \left( {-6 } \right)^2 }[/tex]

Simplify

[tex]d = \sqrt {\left 1 + \left 36}[/tex]

[tex]d = \sqrt{37}[/tex]

Answer

[tex]d = \sqrt{37}[/tex]

Answer:

(- 5, - 28 )

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = (x + 5)² - 28 ← is in vertex form

with vertex (h, k) = (- 5, - 28)

Answer:

x(1 - .4)

Step-by-step explanation:

x = regular price.

1 - .4 = .6 = 60%

The sale price is equal to the full price (aka x) minus the discounted price (40% of x = 40/100 times x =  .4x)

Therefore sale price = x - .4x or x(1 - .4)

Final answer:

The expression 1(y), when y = -5/8, is calculated by multiplying 1 by -5/8, which simply yields -5/8.

Explanation:

The task is to find the value of the expression 1(y) when y is given as -5/8. The expression 1(y) can be interpreted as simply '1 times y'. Therefore, we need to multiply the number 1 by -5/8 to find the answer.

1(y) = 1 * (-5/8) = -5/8

This is a basic arithmetic operation, specifically multiplication, commonly encountered in mathematics. When we multiply any number by 1, the result is the number itself, which in this case applies to the negative fraction -5/8.

Answer:

2) y-x=2

Add x on both sides:

 y        =x+2

The slope is 1 and the y-intercept is 2.

Step-by-step explanation:

So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

Let's put all of these in that form:

1) y+x=2

Subtract x on both sides:

 y     =-x+2

The slope is -1 and the y-intercept is 2.

2) y-x=2

Add x on both sides:

 y        =x+2

The slope is 1 and the y-intercept is 2.

3) y-x+2=0

Add x on both sides:

 y     +2=x

Subtract 2 on both sides:

 y        =x-2

The slope is 1 and the y-intercept is -2.

4) y+x-2=0

Add 2 on both sides:

 y +x      =2

Subtract x on both sides:

 y           =-x+2

The slope is -1 and and the y-intercept is 2.

Answer: 7,920 feet.

Step-by-step explanation: There are 5,280 feet in a mile. To find how many feet are in 1.5 miles, multiple 1.5 by 5,280.

1.5 x 5,280 = 7,920

There are 7,920 feet in 1.5 miles.

Answer:

a. a correlation matrix

Step-by-step explanation:

The best fitting straight line for a data set of X-values plotted against y-values is  called a correlation matrix.

Answer:

You can use teh associative property to split 48 and 82 each into 2 peices

(40+8)(80+2) then you can move the parenthesis around. 40+(8+80)+2

40+(88+2)

40+90=130

[tex]\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^{log_a x}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_6(\sqrt[3]{6})\implies \log_6(6^{\frac{1}{3}})\implies \cfrac{1}{3} \\\\[-0.35em] ~\dotfill\\\\ \log_2(64)\implies \log_2(2^6)\implies 6 \\\\[-0.35em] ~\dotfill\\\\ -3\log_5(25)\implies -3\log_5(5^2)\implies -3(2)\implies -6 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \log_2(\sqrt[4]{8})\implies \log_2(\sqrt[4]{2^3})\implies \log_2(2^{\frac{3}{4}})\implies \cfrac{3}{4} \\\\[-0.35em] ~\dotfill\\\\ \log_3\left( \frac{1}{81} \right)\implies \log_3\left( \frac{1}{3^4} \right)\implies \log_3(3^{-4})\implies -4[/tex]

Answer:

3/4 goes with [tex]\log_2(8^\frac{1}{4})[/tex]

-4 goes with [tex]\log_3(\frac{1}{81})[/tex]

-6 goes with [tex]-3\log_5(25)[/tex]

1/3 goes with [tex]\log_6(6^\frac{1}{3})[/tex]

Step-by-step explanation:

[tex]\log_6(6^\frac{1}{3})=\frac{1}{3}\log_6(6)=\frac{1}{3}\cdot 1=\frac{1}{3}[/tex]

[tex]\log_2(64)=6 \text{ since } 2^6=64[/tex]

[tex]-3\log_5(25)=-3(2)=-6 \text{ since } 5^2=25[/tex]

[tex]\log_2(8^\frac{1}{4})=\frac{1}{4}\log_2(8)=\frac{1}{4}\log_2(2^3)=\frac{1}{4}\cdot (3)\log_2(2)=\frac{1}{4} \cdot 3 \cdot 1=\frac{3}{4} [/tex]

[tex] \log_3(\frac{1}{81})=\log_3(\frac{1}{3^4})=\log_3(3^{-4})=-4\log_3(3)=-4(1)=-4[/tex]

Here are few rules I used:

[tex]\log_a(b)=x \text{ means } a^x=b[/tex]

[tex]\log_a(a)=1 [/tex]

[tex]\log_a(b^r)=r \log_a(b)[/tex]

Oil added or consumed during the day equals evening oil level minus morning oil level (g - h).

To calculate how much oil was consumed or added during the day, you can use the formula:

Change in oil = g - h

If the value is positive, it means oil was added.

If the value is negative, it means oil was consumed (leaked or used).

For example, if in the morning your car had 5 liters of oil (h = 5) and in the evening it had 7 liters (g = 7):

Change in oil = 7 - 5 = 2 liters

This means 2 liters of oil were added during the day.

Answer:

x = - [tex]\sqrt{7}[/tex]

Step-by-step explanation:

Radical roots occur in pairs, that is

x = [tex]\sqrt{7}[/tex] is a root then so is x = - [tex]\sqrt{7}[/tex]

Answer:

-√7 = -2.64

Step-by-step explanation:

The polynomial function has roots. The first root is 3 and the second is √7.

When we have a square root that means that we get two roots from the same number but one is negative and the other is positive. For example, if we have:

√x² = ±x

Because we can have:

(-x)² = x², or

(x)²=x².

So a square root always gives us two answers, one negative and the other positive.

Answer:

{2, 3, √13}  

Step-by-step explanation:

In a right triangle, the sum of the squares of the two shorter sides equals the square of the third side (Pythagoras).

Let's check each set of sides in turn.

A. {2, 3, √13}

2² + 3² = 4 + 9 = 13

(√13)² = 13

This is a right triangle.

B. {5, 5, 2, √10}

This is a quadrilateral (four sides).

C. {5, 12, 15}

5² + 12² = 25 +144 = 169

15² = 225

This is not a right triangle.

Answer:

Approximately 92.51.

Not sure what the desired rounding is since it isn't listed.

Step-by-step explanation:

So the first vector G is 40.3 m long in a -35 degree direction.

Lat's find the components of G.

[tex]G_x=40.3\cos(-35)=33.0118[/tex].

[tex]G_y=40.3\sin(-35)=-23.1151[/tex].

The second vector H is 63.3 m long in a 270 degree direction.

[tex]H_x=63.3\cos(270)=0[/tex].

[tex]H_y=63.3\sin(270)=-63.3[/tex].

The resultant vector can be found by adding the corresponding components:

[tex]R_x=G_x+H_x=33.0118+0=33.0118[/tex]

[tex]R_y=G_y+H_y=-23.1151+(-63.3)=-86.4151[/tex]

Now we are asked to find the magnitude of [tex](R_x,R_y)[/tex] which is given by the formula [tex]\sqrt{R_x^2+R_y^2}[/tex].

Since [tex](R_x,R_y)=(33.0118,-86.4151)[/tex] then the magnitude is [tex]\sqrt{(33.0118)^2+(-86.4151)^2}=\sqrt{8557.34844}=92.51[/tex].

The magnitude of the sum of vector G (40.3m, -35°) and vector H (63.3m, 270°) is found by breaking each vector into its components, summing these components, and using the Pythagorean theorem. The magnitude of the sum of these vectors is approximately 92.1 m.

Given that vector G has a magnitude of 40.3 m and is in a -35.0° direction, and vector H has a magnitude of 63.3 m and is in a 270° direction, the sum of these vectors can be determined. This sum is found by breaking each vector into its component forms, adding the components together, and then using the Pythagorean theorem to find the magnitude of the result.

For vector G: Gx = 40.3m * cos(-35) = 33m and Gy = 40.3m * sin(-35) = -23.14m. For vector H: Hx = 0 (as sin(270) equals 0) and Hy = -63.3m (as sin(270) equals -1). The sum vector S = (Gx+Hx, Gy+Hy) = (33m+0 , -23.14m-63.3m) = (33m, -86.44m). Thus, to find the magnitude of the sum of the vectors, we use the Pythagorean theorem: |S| = sqrt((33m)² + (-86.44m)²) = 92.1 m (rounded to 1 decimal place).

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Answer:

12 miles per hour

Step-by-step explanation:

Let her normal rowing speed be x

Also note the formula D = RT, where d is distance, R is rate(speed) and T is time

On windy day, her speed is x + 4

On against wind return, her speed is x - 4

With wind, she can go 48 miles in same amount of time when she goes 24 miles against wind. This can be written as:

48 = (x+4)T

24 = (x-4)T

We can write each equation in terms of T and equate both. So we have:

48/x+4 = T

24/x-4 = T

Thus,

[tex]\frac{48}{x+4}=\frac{24}{x-4}\\48(x-4)=24(x+4)\\48x-192=24x+96\\24x=288\\x=\frac{288}{24}\\x=12[/tex]

Thus, Jaime's normal rowing speed is 12 miles per hour

Answer:

C. Marc

Step-by-step explanation:

to get the amount they earn in an hour divide the amount they earn by the amount of hours they worked for.

Maria: 60 divided by 8 = 7.50

Marc: 46.50 divided by 6 = 7.75