An architect is designing a new library. The library’s floor plan is a rectangle divided into a bookshelf space with bookshelves, and a reading space with a rug and chairs. Each bookshelf is x ft wide and x + 3 ft long. The bookshelves are 3 ft from each other. The walkway between the two rows of bookshelves is 2 ft wide. Write the dimensions and area as polynomials in standard form.





What are the dimensions of the bookshelf space?



length = __ x + __ ft



width = __ x + __ ft



What is the area of the bookshelf space?



area = __ x2 + __ x + __ ft2

Answer:

The last one

Step-by-step explanation:

The first one is counting by 2 so is the second one but the third doesn’t start at 4 it starts at 3 so I think the last one would be the better answer

Answer:

Step-by-step explanation:

Are the volumes equal?      No, so throw out the first and the last one.

Is the volume of the pyramid greater than the volume of prism?  

                                            No, so throw out the third one

so by inspection it must be the remaining one

or mathematically

    vol pyramid = (1/3)(base)(height)

    vol prism     =  (base)(height)

              vol pyramid   /   vol prism      

           (1/3)(base)(height) / (base)(height)   = 1/3

Answer:

f(2) = 2

Step-by-step explanation:

Given function:

f(x) = 5x - 12

To Find:

f(2)

Solution:

Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.

\(f(x) = 5x - 12\)

\(f(2) = 5(2)- 12\)

\(f(2) = 10 - 12\)

\(\boxed{f(2) = - 2}\)

Hence,f(2) is equal to -2.

Answer:

youd get 0.25 off and yes you would save 25 cents the difference would be 2.25 dollars instead of 2.50

Step-by-step explanation:

im so so sorry if im wrong so so sorry

The linear equation two variables can be solved by various methods one of the methods to solve the linear equations is the substitution method. The solution of the given equation is x=2 and y=10.

What is  linear equation in two variables ?

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.

Main body:

The given equations are :

10x+3y=50     .... (1)

-5x-y=-20      ....(2)

Multiply equation (2) by 3 and then add the equation (1) to eliminate the variable y.

10x+3y+3(-5x-y)=50+3*-20

-5x=-10

x=2

Now putting the value of x in equation (1), and solve it further.

10*2+3y=50

3y=30

y=10

Hence, the value of x is 2 and the value of y is 10.

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The unite rate of the kendra's bike ride is found as 3 blocks / min.

The given question is-

Unit rate = number of blocks/ total time

Unit rate = 30 / 10

Unit rate = 3 blocks / min

Thus, the unit rate of the kendra's bike ride is found as 3 blocks / min.

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Answer:

31 ≤ x

Step-by-step explanation:

22 ≤ x - 9;

22 + 9 ≤ x - 9 + 9;

31 ≤ x

Answer:

3 2/3

Step-by-step explanation:

7 1/6 - 3 1/2= 3 2/3

The circles with the specified angle of internal sectors, indicates that we get the following arc and radial lengths;

2. m∠ADC = 160°

m∠BDC = 160°

3. Length of \(\widehat{CB}\) ≈ 11.17 inches

4. Length of \(\widehat{ABC}\) ≈ 13.96 inches

5. a. The radius of ⊙ Q ≈ 14.324 inches

The radius is the straight line extending from the circle center to the circumference. The radius is the shortest distance from the circle center to the circumference of the circle.

Angle ∠ADC is congruent to ∠BDC in the circle with center D

∠ADC ≅ ∠BDC

2. ∠ADC ≅ ∠BDC, therefore;

m∠ADC = m∠BDC

The angle sum property of the angle at the center of a circle, indicates that we get;

40° + m∠ADC + m∠BDC = 360°

Therefore by plugging in m∠ADC = m∠BDC, we get;

40° + m∠ADC + m∠ADC = 360° (substitution property)

40° + 2 × m∠ADC = 360°

2 × m∠ADC = 360° - 40° = 320°

m∠ADC = 320° ÷ 2 = 160°

m∠ADC = 160° = m∠BDC

m∠BDC = 160°

3. The length of the arc \(\widehat{CB}\), can be obtained from the proportion of the circumference of the circle D represented by the sector BDC as follows;

Length of the arc \(\widehat{CB}\) = ((m∠BDC)/360°) × 2·π·r

Where;

r = The radius of the circle

The radius of the circle, r = 4 inches

Therefore; Length of the arc \(\widehat{CB}\) = (160°/360°) × 2 × π × 4 ≈ 11.17

4. The length of the arc \(\widehat{ABC}\) can be found as follows;

The angle at the center of the arc \(\widehat{ABC}\) = 40° + m∠BDC

Therefore; The angle at the center of the arc \(\widehat{ABC}\) = 40° + 160° = 200°

5. The length of the arc \(\widehat{AB}\) = 15 inches

The angle formed by the sides AQ and BQ of the sector AQB = 60°

Therefore, we get;

length of the arc \(\widehat{AB}\) = (60°/360°) × 2 × π × r = 15 inches

r = 15/((60°/360°) × 2 × π) ≈ 14.324

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The odds of selecting a red 9 is 1/26.

Probability of an event E is represented by P(E)  can be defined as (the number of favorable outcomes) / (Total number of outcomes).

Given the total number of cards in a standard deck = 52

there can be  only two red9 as one 9 from heart and one red from diamond.

So the number of outcome for red 9 =2

the probability of odds of selecting red 9 is \(\frac{2}{52}\) which can be further simplified into \(\frac{1}{26}\).

Therefore , The odds of selecting a red 9 is 1/26.

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The mean of the given data is 206.5.

To find the mean of the given data:

Sum of values = 211 + 226 + 186 + 221 + 181 + 228 + 207 + 215 + 203 + 203 + 204 + 196 + 226 + 212 + 212 + 201 + 219 + 191 + 191 + 185 + 193 + 231 = 4,542

Number of values = 22

Mean = 4,542 ÷ 22 = 206.5

Therefore, the mean of the given data is 206.5.

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Answer:

Step-by-step explanation:

Ur answer sir :)

1) 6⁴

2) t²

3) b⁴

4) 5²× 7³

5) 2²× a²

6)a³× c⁴× d

Answer:

No it can't be.

Step-by-step explanation:

Because 57 is not a perfect square.

Step-by-step explanation:

The 20° angle is equal to the angle next you friend.

since they are interior alternate angles

The height of the ballon is 600 feet

Let x be the missing distance we are looking for

so the missing distance is 1754 feet

Here I represented the situation to visualize the problem

Let h be L be the length of the ladder

so the ladder is 14 ft

Answer:

The value of x is 8.1

Step-by-step explanation:

We can use SOH CAH TOA to find our answer.

In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.

We can calculate the length of the string by using the COS function.

So we can say the tangent of angle \(\beta\) is the opposite side divided by the adjacent side.

\(tan( \beta)=\frac{O}{A}\)

We are given the angle and the opposite side. We are looking for the adjacent side.

Lets solve for \(A\).

Take the reciprocal of both sides.

\(\frac{1}{tan(\beta)} =\frac{A}{O}\)

Multiply both sides by \(O\).

\(\frac{1}{tan(\beta)} *O=A\)

We are given

\(\beta=56\textdegree \\O=12\)

\(\frac{1}{tan(56)} *12=A\)

\(A=8.0941022\)

Answer:

please someone answer this

Step-by-step explanation:

pls

Answer:

0.75

Step-by-step explanation:

The volume of the prism is 21 * 5 = 105 cubic feet.

To find the volume of a prism with a triangular base, you need to follow these steps:

1. Determine the area of the triangular base: Since the base is a right triangle with leg lengths of 6 feet and 7 feet, you can use the formula for the area of a right triangle: (1/2) * base * height. In this case, the area would be (1/2) * 6 * 7 = 21 square feet.

2. Multiply the area of the triangular base by the height of the prism: The prism is 5 feet tall, so the volume can be calculated by multiplying the area of the base (21 square feet) by the height (5 feet).

Thus, the volume of the prism is 21 * 5 = 105 cubic feet.

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Answer:

I think it is  22 but I might be wrong.

Step-by-step explanation:

To solve graphically this set of equations, we should first draw both lines and see the value of x at which the lines crosses

Both graphs can be drawn as follows

We can see that both graphs intersect at a negative value of x. With a more accurate graph, we can determine that both lines intersect at x=-2.

So the solution for this system of equation is x=-2.

The radius in cm of the smaller circle whose centers lie in the circumference of the central circle has 10 cm radius is 5 cm.

The smaller circles are tangent to each other, so they form an equilateral triangle. The side length of the equilateral triangle is the diameter of the smaller circle.

The diameter of the smaller circle is the same as the distance between two adjacent centers of the smaller circles. The distance between two adjacent centers of the smaller circles is half the circumference of the central circle.

Using the Pythagorean Theorem, find the radius of the smaller circle (r) as follows:

r² + r² = 10²

2r² = 100

r² = 50

r = √(50) = 5 cm

Therefore, the radius of the smaller circle is 5 cm.

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Complete question:

The Central Circle Has 10cm Radius. Six Equal Smaller Circles Are To Be Arranged So That They Are Externally Tangent To Each Other And The Centers Lie In The Circumference Of The Central Circle . What Should Be The Radius In Cm, Of The Smaller Circle?

The equation or system of equations that can be used to determine the number of cats and dogs Bea has in her pet shop is d = 2c - 5 d + 3 = c + 3. We can solve the system of equations using substitution and plug it back into either equation to find the value of d, which is 8 cats and 10 dogs.

The equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop is:

d = 2c - 5

d + 3 = c + 3

No, Bea's Pet Shop could not initially have 15 cats and 20 dogs. This is because the equation or system of equations states that the number of dogs is five less than twice the number of cats, which would mean that 15 cats would result in 25 dogs, which is not equal to 20.

To determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop, we can use the equation or system of equations that we previously created.

d = 2c - 5

d + 3 = c + 3

We can solve the system of equations using substitution:

d = 2c - 5

d + 3 = c + 3

d + 3 = c + 3

d = c + 3

2c - 5 = c + 3

2c = c + 8

c = 8

Once we determine the value of c, we can plug it back into either equation to find the value of d:

d = 2(8) - 5

d = 15 - 5

d = 10

Therefore, Bea initially had 8 cats and 10 dogs in her pet shop.

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The complete question is: At Bea's Pet Shop, the number of dogs, d, is initially five less than twice the number of cats, c. If she decides to add three more of each, the ratio of cats to dogs will be – Write an equation or system of equations that can be used to find the number of cats and dogs Bea has in her pet shop. Could Bea's Pet Shop initially have 15 cats and 20 dogs? Explain your reasoning. Determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop.​

Answer:

Step-by-step explanation:

ac=bc

The multiplication property of equality states that if a = b and c#0, then

ac = bc

When both sides of an equation are multiplied by the same number, the expressions on both sides of the equation stay equal to one another, according to the multiplication property of equality.

We have a = b and c#0.

According to multiplication property of equality we can multiply c in both side of equation a= b so that the equality remain maintains.

Thus, a= b

ac = bc

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Answer:

0.75 customers a minute

Step-by-step explanation:

6 customers in 8 mins = 0.75 customers in 1 min

Find this by dividing both values by 8

Answer:

262, 440

Step-by-step explanation:

40 x 3^8

40 x 6561

262, 440

B. Make a histogram of the data.It can also be used to detect outliers and to compare distributions of different data sets.

A histogram is a type of graph used to visualize the distribution of a given set of data. It is created by plotting the frequency of occurrence of each data point on a graph, with the x-axis representing the data points and the y-axis representing the frequency of occurrence. The height of the bar above each data point indicates how often the value appears in the data set. The shape of the histogram gives an indication of the underlying distribution of the data. By plotting the frequency of occurrence of each data point, a histogram can provide insights into the mean, median, mode, and other characteristics of the data set. It can also be used to detect outliers and to compare distributions of different data sets.

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while the presence of only one spot on a TLC plate may suggest that the compound is pure, further analysis is needed to confirm the purity of the compound, such as melting point determination, NMR spectroscopy, or HPLC (high-performance liquid chromatography).

Using UV and seeing only one spot on a TLC (thin-layer chromatography) plate is not a definitive indicator of the purity of a product.

While it is true that a pure compound will only show one spot on a TLC plate, there are several reasons why a compound may still show only one spot even if it is not pure. For example:

The impurity may have a similar Rf (retention factor) value to the compound of interest and therefore co-migrate with it on the TLC plate, making it difficult to distinguish between the two.

The impurity may be present in such a small amount that it is not visible on the TLC plate.

The compound of interest may have multiple conformers or isomers that have the same Rf value and appear as a single spot.

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Answer:

1. All numbers between, including 0 and 15.

Step-by-step explanation:

The domain is the independent variable (x), so in this case, it's be the amount of time James spent typing. James types for 15 minutes, so of course 0 and 15 have to be included, as it'll give a complete graph of what he's done so far.