The perimeter of the base of a pentagonal prism is 45 cm. what is the width of the rectangular side of that prism?

Answer:

150

Step-by-step explanation:

We can write a proportion to find the total amount in the choir using the information given. A proportion is two equivalent ratios set equal to each other.

[tex]\frac{24}{100}=\frac{36}{y}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

24y=100(36)

24y=3600

y=150.

There are 150 students in the choir.

Answer: A

Step-by-step explanation:

[tex]\stackrel\frown{XY}[/tex] ≅ [tex]\stackrel\frown{YZ}[/tex]

⇒ ∠XOY ≅ ∠ZOY

[tex]\overline{XO}[/tex] ≅ [tex]\overline{ZO}[/tex] since they are both a radius

[tex]\overline{OY}[/tex] ≅ [tex]\overline{OY}[/tex] based on reflexive property

∴ ΔXOY ≅ ΔZOY by SAS

So, [tex]\overline{XY}[/tex] ≅ [tex]\overline{ZY}[/tex] by CPCTC

ZY = 10.2 is given

so, XY = 10.2 by substitution property

Answer:

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

Step-by-step explanation:

On a standard cube there are the numbers 1, 2, 3, 4, 5, 6

Only 2 are divisible by 3, that is 3 and 6, hence

P(divisible by 3 ) = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

When the function f(x) is replaced with -1/2f(x), it results in vertical reflection over x-axis and vertical compression of the graph.

When the function f(x) is replaced with -1/2f(x), it means that the values of the original function are multiplied by -1/2. This has two effects on the graph of the function:

Therefore, the correct answer is B) vertical reflection over x-axis and vertical compression.

The point slope formula is

y-y1=m(x-x1)

M represents slope and (y1, x1) are the coordinates to your point.

From this question we know the slope is -1/7 so you plug that in to the formula which will give you

Y-y1=-1/7(x-x1)

There isn’t a point attached to this question so let’s make up a point and say it’s (1,7). You plug this into the equation to get

Y-7=-1/7(x-1)

This is your equation.

The perimeter (P∆AKL) of triangle AKL is 21.294 m, and the area is 20.25 m². Triangle AKL is a 30-60-90 triangle, with sides in the ratio 1:√3:2, allowing for straightforward calculations of the perimeter and area using the given side lengths and right triangle properties.

To find the perimeter (P∆AKL) and the area of triangle AKL (∆AKL), we can use the properties of a right triangle. Since we have one angle of 60°, and the right angle 90°, the remaining angle must be 30°. With this information, we recognize that triangle AKL is a 30-60-90 special right triangle.

For a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. Knowing one side, AK (the side opposite the 60° angle), is 9 m, we determine the side opposite the 30° angle (AL) is half that length, so AL = 9m / 2 = 4.5 m. The side opposite the 90° angle (KL) is √3 times the side opposite the 30° angle, so KL = 4.5m * √3 = 7.794 m.

Now we can find the perimeter (P) by adding all the sides:

The area (A) of a right triangle is (½)*base*height.

Answer:

S22 for the arithmetic sequence is:

First option: 15.4

Step-by-step explanation:

a12=2.4

d=3.4

S22=?

Sn=(a1+an)n/2

n=22

S22=(a1+a22)22/2

S22=(a1+a22)11

ak=aj+(k-j)d

a12=a1+(12-1)d

2.4=a1+11(3.4)

2.4=a1+37.4

Solving for a1: Subtracting 37.4 both sides of the equation:

2.4-37.4=a1+37.4-37.4

Subtracting:

-35=a1

a1=-35

a22=a12+(22-12)d

a22=2.4+10(3.4)

a22=2.4+34

a22=36.4

S22=(a1+a22)11

S22=(-35+36.4)11

S22=(1.4)11

S22=15.4

Answer:

i think Banu is 40 and Binu is 20

Step-by-step explanation:

if Banu was 35 and Binu was 15, 5 years go by Banu is 40 so still 20 years older and Binu is 20, Binu is half the age of Banu.

Answer:

Use desmos it is really helpful

[tex]The\:Answers\:Are:[/tex]

[tex]A.\:If\:\:UV=KL \:\:And\:\:KL=6,\:Then\:\:UV = 6,\:True[/tex]

[tex]C.\:Angle\:ABC\:Is\:Congruent\:To\:ABC,\:True[/tex]

[tex]\mathrm{E.\:If\:Angle\:DE F\:Is\:Congruent\:To\:Angle\:HJK,\:Then\:Angle\:HJK\:Is\:Congruent\:To\:Angle\:DE F},\:True[/tex]

[tex]The\:Questions\:B\:And\:C\:Are\:False[/tex]

[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]

[tex]\mathrm{Please\:Mark\:Brainliest!!!}[/tex]

[tex]\mathrm{-Austint1414}[/tex]

Answer:

The length of the string is 32.56 feet  (Approx) .

Step-by-step explanation:

As given

A kite is 37 feet in the air and string forms an angle of 62 degrees .

Now by using the trignometric identity.

[tex]sin\theta = \frac{Perpendicular}{Hypotenuse}[/tex]

As shown in the figure given below.

[tex]\theta = 62^{\circ}[/tex]

Perpendicular = AB

Hypotenuse = AC = 37 feet

Put in the identity .

[tex]sin\ 62^{\circ} = \frac{AB}{AC}[/tex]

[tex]sin\ 62^{\circ} = \frac{AB}{37}[/tex]

[tex]sin\ 62^{\circ} = 0.88\ (Approx)[/tex]

Put in the identity

[tex]0.88 = \frac{AB}{37}[/tex]

AB =  0.88 × 37

AB = 32.56 feet  (Approx)

Therefore the length of the string is 32.56 feet  (Approx) .

Final answer:

A total of 4 more students need to sign up for all 56 students to be placed on teams of 10 in the flag football league.

Explanation:

The question is asking how many additional students will need to sign up to ensure that all students can participate in a flag football league, with the stipulation that each team is made up of 10 students. With 56 students currently signed up, we can divide this number by the team size to see how many complete teams can be formed:

56 students ÷ 10 students per team = 5 teams with 6 students left over.

To have a complete additional team, 10 students are needed. Since there are already 6 students without a team, the number of additional students required is:

10 students needed for a complete team - 6 students already signed up but not placed on a team = 4 additional students needed.

Answer: [tex]\bold{y=\dfrac{24}{x}}[/tex] ; indirect variation ; x = 2.4

Step-by-step explanation:

direct variation is when: [tex]\dfrac{y}{x}=k[/tex]   ; where k is the constant rate

indirect variation is when: xy = k  ; where k is the constant rate

In the table provide: x * y = 24 for each coordinate provided, so this is indirect variation, with equation: [tex]y = \dfrac{24}{x}[/tex]

since k = 24, then input y = 10 and k = 24 into the equation above:

[tex]10 = \dfrac{24}{x}[/tex]

[tex]10x = 24[/tex]

[tex]x = \dfrac{24}{10}[/tex]

x = 2.4

Answer:

The Correct Answer Is A.) 25 Square Units

Step-by-step explanation:

The area of the corkboard that is not covered by the target is 25 sq. units.

(Option A).

The area of the corkboard that is not covered by the target is calculated from the difference between the area of the square and area of the target.

Area of the square is calculated as;

A = L²

A = ( 5 + 5)²

A = 100 sq units

The area of the target is 75 sq. units, so we wil use this value

The area of the corkboard that is not covered by the target is calculated as;

A = 100 - 75

A = 25 sq. units.

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See the attached explanation and diagram.

Answer:

Johnny had 5 items and Bobby had 13 items.

Step-by-step explanation:

Let us assume that Johnny has x items and Bobby has y items in their list.

Bobby had 3 more than twice as many items on it than Johnny. So,

[tex]\Rightarrow y=3+2x[/tex]  ----------1

Johnny asked for 8 fewer items than bobby. So,

[tex]\Rightarrow y-8=x[/tex]  -----------2

Putting the value of x from equation 2 in equation 1, we get

[tex]\Rightarrow y=3+2(y-8)[/tex]

[tex]\Rightarrow y=3+2y-16[/tex]

[tex]\Rightarrow 2y-y=16-3[/tex]

[tex]\Rightarrow y=13[/tex]

Putting the value of y in equation 2,

[tex]\Rightarrow 13-8=x[/tex]

[tex]\Rightarrow x=5[/tex]

So, Johnny had 5 items and Bobby had 13 items.

Answer:

25

Step-by-step explanation:

let x questions on the text, so we get:

56/100=14/x,   4/100=1/x,

x=25

Answer:-5

Step-by-step explanation:

2x+7-x+12=14

x+19=14

x=-5

Answer:

x=-5

Step-by-step explanation:

Ok so, (2x+7)+(-x+12)=14

solve the equation, by opening the parantheses.

2x+7+-x+12=14

x= -5

Answer:

The correct answer option is: [tex]a_n=\frac{5}{2} n-\frac{11}{2}, 37[/tex].

Step-by-step explanation:

We are given the following arithmetic sequence and we are to write an explicit formula for it and the find the 17th term of the sequence:

{[tex]a_n[/tex]}={[tex]-3, -\frac{1}{2} ,2,\frac{9}{2} ,7[/tex]}

From the given options, we can put in the values of n and check if it proves to be true.

For  [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex], put values of [tex]n[/tex] from 1 to 5 which the number of the term.

[tex]a_1=\frac{5}{2} (1)-\frac{11}{2}\\\\a_1=-3[/tex]

[tex]a_2=\frac{5}{2} (2)-\frac{11}{2}\\\\a_2=-\frac{1}{2}[/tex]

[tex]a_3=\frac{5}{2} (3)-\frac{11}{2}\\\\a_3=2[/tex]

[tex]a_4=\frac{5}{2} (4)-\frac{11}{2}\\\\a_4=\frac{9}{2}[/tex]

[tex]a_5=\frac{5}{2} (5)-\frac{11}{2}\\\\a_5=7[/tex]

Therefore, the formula for the given sequence is  [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex].

Also, [tex]a_{17}=\frac{5}{2} (17)-\frac{11}{2}=37[/tex]

Answer: The correct one is an=5/2n-11/2,37 so A :)

Answer:

4/5 of 450 is 360

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alicia was rock climbing. She climbed to a height of 30 ft. Next , she climbed down 18 ft. Finally she climbed up another 55 ft. Write an addition expression to describe this situation then find the sum of your addition expression to determine Alicia's elevation.

Answer :

(a) The number of rows need will be, 57 rows.

(b) The amount in pounds of food a circus horse eat each day is, 35.71 pounds.

Step-by-step explanation :

Part A:

As we are given that the there are 9 seats in each row that means 9 people can sit in each row.

Now we have to determine the number of rows will need to be set up if 513 people are expected to attend the show.

As, 9 people can sit in 1 row

So, 513 people can sit in [tex]\frac{513}{9}=57[/tex] row

Thus, the number of rows need will be, 57 rows.

Yes, the rows be divided into a number of equal sections as, 3 rows would be 19 sections or, 19 rows would be 3 sections.

Part B:

As we  are given that circus horses eat about 250 pounds of horse food per week. Now we have to determine the amount in pounds of food does a circus horse eat each day.

Given : 1 week = 7 days

As, in 1 week the circus horses eat about 250 pounds of horse food

or, in 7 days the circus horses eat about 250 pounds of horse food

So, in 1 day the circus horses eat about [tex]\frac{1day}{7day}{\times 250=35.71[/tex] pounds of horse food

Thus, the amount in pounds of food a circus horse eat each day is, 35.71 pounds.

Answer:

(-4,-2) U (-2,4]

Step-by-step explanation:

Domain is the set of x values for which the function is defined.

We look at the x  values on the graph

the graph starts at -4 and we have a hole at x=-4

For a hole we use parenthesis

Graph starts at -4  and ends at -2. Both -4  and -2  have hole, so we use parenthesis.

So interval is (-4,-2)

From -2  to  4 , there is no hole or break in between. the graph is continuous from -2  to 4

so interval is (-2, 4]

combine both intervals

(-4,-2) U (-2,4]

Answer:

B. (-4,-2) (-2,4)

Answer:

We have the equation y - 4 = (-2)( x - 0 );

Then, y - 4 = -2x;

Finally, y = -2x + 4;

The correct answer is B) y = -2x + 4;

Step-by-step explanation:

The equation for the line with a slope of -2 and crossing the y-axis at (0,4) is y = -2x + 4.

To find an equation for a line that crosses the y-axis at (0,4) with a slope of -2, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since we are given that the slope (m) is -2 and the y-intercept (b) is 4, the equation of the line is y = -2x + 4.

Answer:

D.)

Step-by-step explanation:

The zero's are referencing when y=0, note that when y=0 they are talking about the x-intercepts.  You can graph the function and see when the graph crosses the x-axis or solve for the x-values.  I will solve it via factoring and so:

[tex]f(x)=x^2+5x+6[/tex]

Multiply the outer coefficients, in this case 1 and 6, and 1×6=6.  Now let's think about all the factors of 6 we have: 6×1 and 2×3.  Now is there a way that if we use any of these factors and add/subtract them they will return the middle term 5?  Actually we can say 6-1=5 and 2+3=5.  Let's try both.

First let's use 6 and -1 and so:

[tex]x^2+5x+6\\\\x^2+6x-x+6\\\\x(x+6)-1(x-6)[/tex]

Notice how we have (x+6) and (x-6), these factors do not match so this is incorrect.

Now let's try 2 and 3 and so:

[tex]x^2+5x+6\\\\x^2+3x+2x+6\\\\x(x+3)+2(x+3)\\\\(x+2)(x+3)[/tex]

Notice how the factors (x+3) matched up so this is a factor and so is (x+2), now to solve for the zero's let's make f(x)=0 and solve each factor separately:

Case 1:

[tex]f(x)=x+2\\\\0=x+2\\\\x=-2[/tex]

Case 2:

[tex]f(x)=x+3\\\\0=x+3\\\\x=-3[/tex]

So your zero's are when x=-2 and x=-3.

D.) x=-3 and x=-2 because the graph crosses the x-axis at -3 and -2.

~~~Brainliest Appreciated~~~

Answer:

5 single rolls  or 3 double rolls.

Step-by-step explanation:

Ignoring doors and windows, we need to find the lateral surface ares.  We are not papering the ceiling or floor.

The lateral surface areas = P*h

                                            = 2(l+w) * h

                                             = 2(10+12) * 8  

                                             = 2(22)*8

                                              =352  ft^2

A single roll covers 72 ft^2 so we divide the number of ft^2 that we need (352^2) by the amount of a single roll

352/72 =4.88888(repeating)

Rounding up since we need to buy in full rolls.

We will need 5 rolls

Assuming a double roll will cover  twice that of a single roll

2*72 = 144 ft^2

Take 572/144 =2.4444444

Rounding up since we need to buy in full rolls.

We will need to buy 3 double rolls

Adia will need 5 single rolls or 3 double rolls of wallpaper to cover her 10' by 12' bedroom with 8' ceilings.

Adia needs to calculate the amount of wallpaper needed to cover the walls of her bedroom. To find the total wall area, we calculate the perimeter of the room and multiply it by the ceiling height. The perimeter is two times the length (12 feet) plus two times the width (10 feet), giving us 44 feet. Multiplying the perimeter by the ceiling height (8 feet) gives us the total wall area: 44 feet × 8 feet = 352 square feet.

Since each single roll covers 72 square feet, dividing the total wall area by the coverage of one roll gives us the number of rolls needed: 352 square feet / 72 square feet/roll = 4.89, which means Adia will need 5 single rolls of wallpaper.

For double rolls, we need to consider that each double roll is equivalent to two single rolls.

Therefore, we divide the number of single rolls needed by 2 to get the number of double rolls: 5 single rolls / 2 = 2.5, which means Adia will need 3 double rolls (since she can't purchase half a roll, she'll have to round up).

Answer:

The answer is C) Remote Interior Angle

Step-by-step explanation:

The name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle is the remote interior angle. Getting the values of each sides help you come up with the remote interior and exterior angles.

Answer:

Step-by-step explanation:

they are opposite angles, same value of 45°

Answer:

Actually, the equation is

power (in Watts) = I² * r

I - current in amps and r - resistance in watts

Solving this for the current (I)

I = square root (power / resistance)

I = square root (15 / 100)

I = square root (.15)

I = 0.3872983346 amps

answer is B

Step-by-step explanation:

The current in the circuit is approximately 0.39 amperes, which is option B.

The power in an electrical circuit can be calculated using the formula:

P = I^2 * R

Where:

P = Power (in watts)

I = Current (in amperes)

R = Resistance (in ohms)

In your case, you have:

P = 15 watts

R = 100 ohms

You want to find the current (I), so rearrange the formula to solve for I:

I = sqrt(P / R)

I = sqrt(15 watts / 100 ohms)

I = sqrt(0.15 A^2)

I = 0.39 A (approximately)

So, the current in the circuit is approximately 0.39 amperes, which is option B.

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