the length of the top of a rectangular desk is 24inches more than the width. What are the dimensions of the desk if the area of the top is 1,620 square inches?

Answer:

Area of the circle is following:

[tex]a = \pi \: r {}^{2} [/tex]

So there is radius=1

Putting it into formula:

[tex]a = \pi \: 1 {}^{2} \\ a = \pi \\ a = 3.14[/tex]

So the answer is

[tex]3.14 \: units {}^{2} [/tex]

Good luck!

Intelligent Muslim,

From Uzbekistan.

Answer:

Step-by-step explanation:

error in measurement  = 480 - 469 = 11 inches

Percent error = error *100/actual length

= 11 * 100 /480 = 2.9%

Answer:

Inconsistent

Step-by-step explanation:

Given system of equations.

A) [tex]y-2x=4[/tex]

B) [tex]y+2=2x[/tex]

We will solve the system of equations to check the solutions and tell whether the system is consistent or inconsistent

Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex]

Adding both sides by [tex]2x[/tex]

[tex]y-2x+2x=4+2x[/tex]

[tex]y=4+2x[/tex]

Substituting value of [tex]y[/tex] we got from A into equation B.

[tex]4+2x+2=2x[/tex]

Simplifying.

[tex]2x+6=2x[/tex]

Subtracting both sides by [tex]2x[/tex]

[tex]2x-2x+6=2x-2x[/tex]

[tex]6=0[/tex]

This is never true. So, we can say the system of equation has no solutions as the equations of the lines given are parallel.

Any system of equation with no solutions is termed as inconsistent.

Answer:

D) Consistent and Independent

Step-by-step explanation:

I did it on USA test prep.

Answer:

a = -2  and  b = 7

Step-by-step explanation:

We need to solve for the value of "a" and "b".

We need to distribute and make the left side of the equation same form as the right side of the equation and match the coefficients, simple.

We will use the distributive property shown below to expand the left side and simplify.

Distributive Property:  a(b-c) = ab - ac

Now, simplifying left hand side:

5x - 7(x - 1)

= 5x -7(x) -7(-1)

= 5x -7x +7

= -2x + 7

The right hand side is "ax + b".

If we match left-hand side and right-hand side, we see that:

a = -2

and

b = 7

THese are the only solution.

Answer:

2

2x + 3 = 5x - 3

Move x to one side:

[tex]2x-2x+3=5x-2x-3\\3=3x-3[/tex]

Remove the -3:

[tex]3x-3(+3)=(3+3)[/tex]

[tex]3x=6[/tex]

Remove the 6 to get x by itself:

[tex]\frac{3x}{3} =\frac{6}{3} \\x=2[/tex]

The number 2 from the number set would solve the equation.

2(2) + 3 = 5(2) - 3

4 + 3 = 10 - 3

7 = 7

The statement is true.

An equation is formed of two equal expressions. The number(s) from the set that will satisfy the given equation is 2.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be simplified as shown below,

2x + 3 = 5x - 3

Subtract 2x from both sides of the equation,

2x + 3 - 2x = 5x - 3 - 2x

3 = 5x - 3 - 2x

Add 3 on both sides of the equation,

3 + 3 = 5x - 3 - 2x + 3

6 = 3x

3x = 6

Divide both the sides of the equation by 3,

3x/3 = 6/3

x = 2

Hence, the number(s) from the set that will satisfy the given equation is 2.

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Answer:

7x

Step-by-step explanation:

Assuming your expression is :

[tex]e^{\ln 7x}[/tex]

Then we simplify as follows

[tex]e^{\ln 7x}=e^{\ln x+\ln 7}[/tex] since [tex]\ln A+\ln B=\ln AB[/tex]

[tex]\implies e^{\ln 7x}=e^{\ln x}\times e^{\ln 7}[/tex] since [tex]a^{m+n}=a^m\times a^n[/tex]

[tex]\implies e^{\ln 7x}=x\times7[/tex] since [tex]e^{\ln a}=a[/tex]

[tex]\implies e^{\ln 7x}=7x[/tex]

Answer:

y+4=7/4(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=7/4(x-3)

y+4=7/4(x-3)

Answer:

This board of 24.5 inches long is not enough to be cut into the four walls of the bird house.

Step-by-step explanation:

Hodi is building a birdhouse. Each of the four walls of the birdhouse needs to be 5.5 inches long.

So, to get four 5.5 inches long walls we need to have (5.5 × 4) = 22 inches ling board from which four equal 5.5 inches board can be made.

Now, Hodi has a piece of a board that is 24.5 inches long.

Therefore, this board is not enough to be cut into the four walls of the birdhouse. (Answer)

Answer:

[tex]A=6.33\ cm^2[/tex]

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=\frac{28}{3.14}\ cm[/tex]

[tex]\pi=3.14[/tex]

substitute the values

[tex]\frac{28}{3.14}=2(3.14)r[/tex]

[tex]r=\frac{28}{19.7192}\ cm[/tex]

[tex]r=1.42\ cm[/tex]

step 2

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

substitute the values

[tex]A=(3.14)(1.42)^{2}[/tex]

[tex]A=6.33\ cm^2[/tex]

A vessel of 7,560 liters

Step-by-step explanation:

This means finding the Least Common Multiple for;

108 168 180

We begin by finding the multiples of each number;

Multiples of 108:

108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, 1188, 1296, 1404, 1512, 1620, 1728, 1836, 1944, 2052, 2160, 2268, 2376, 2484, 2592, 2700, 2808, 2916, 3024, 3132, 3240, 3348, 3456, 3564, 3672, 3780, 3888, 3996, 4104, 4212, 4320, 4428, 4536, 4644, 4752, 4860, 4968, 5076, 5184, 5292, 5400, 5508, 5616, 5724, 5832, 5940, 6048, 6156, 6264, 6372, 6480, 6588, 6696, 6804, 6912, 7020, 7128, 7236, 7344, 7452, 7560, 7668, 7776

Multiples of 168:

168, 336, 504, 672, 840, 1008, 1176, 1344, 1512, 1680, 1848, 2016, 2184, 2352, 2520, 2688, 2856, 3024, 3192, 3360, 3528, 3696, 3864, 4032, 4200, 4368, 4536, 4704, 4872, 5040, 5208, 5376, 5544, 5712, 5880, 6048, 6216, 6384, 6552, 6720, 6888, 7056, 7224, 7392, 7560, 7728, 7896

Multiples of 180:

180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, 1980, 2160, 2340, 2520, 2700, 2880, 3060, 3240, 3420, 3600, 3780, 3960, 4140, 4320, 4500, 4680, 4860, 5040, 5220, 5400, 5580, 5760, 5940, 6120, 6300, 6480, 6660, 6840, 7020, 7200, 7380, 7560, 7740, 7920

The Least Common Multiple for the 3 number is;

= 7560

Therefore a vessel of 7,560 liters fills each one of them an exact number of times with no remainder.

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Answer:

[tex]5x = - 42 - x[/tex]

[tex]6x = - 42[/tex]

[tex]x = - 7[/tex]

Answer:

D. The three points could be the vertices of a triangle.

Step-by-step explanation:

Answer:

The equation representing total food consumption in [tex]x[/tex] days can be given as:

[tex]y=12x[/tex]

where [tex]y[/tex] represents total food taken which is =250 pounds and [tex]x[/tex] represnts the number of days the food will last.

The food will last for [tex]20\frac{5}{6}[/tex] days.

Step-by-step explanation:

Total pounds of food taken at the beginning =  250 pounds

Food consumed per day = 12 pounds

Let the total food at the beginning be = [tex]y[/tex] pounds

Let number of days the food will last be = [tex]x[/tex] days

Using unitary method to find the food consumed in [tex]x[/tex] days.

If in 1 day food consumed = 12 pounds

Then, in [tex]x[/tex] days food consumption = [tex]12\times x = 12x[/tex] pounds

So,the equation representing total food consumption in [tex]x[/tex] days can be given as:

[tex]y=12x[/tex]

Total food taken =250 pounds

Plugging in [tex]y=250[/tex] in the equation:

[tex]250=12x[/tex]

Solving for  [tex]x[/tex]

Dividing both sides by 12.

[tex]\frac{250}{12}=\frac{12x}{12}[/tex]

[tex]\frac{250}{12}=x[/tex]

Simplifying fractions.

[tex]\frac{125}{6}=x[/tex]

Converting fraction to mixed number by writing quotient as whole number, remainder as numerator and divisor as denominator.

∴ [tex]x=20\frac{5}{6}[/tex] days.

Thus, the food will last for [tex]20\frac{5}{6}[/tex] days.

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following points:

[tex](x_ {1}, y_ {1}) :( 4,6)\\(x_ {2}, y_ {2}): (- 2, -9)[/tex]

We can find the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-9-6} {- 2-4} = \frac {-15} {- 6} = \frac {5} {2}[/tex]

Thus, the equation is of the form:

[tex]y = \frac {5} {2} x + b[/tex]

We substitute one of the points and find "b":

[tex]6 = \frac {5} {2} (4) + b\\6 = 10 + b\\6-10 = b\\b = -4[/tex]

Finally, the equation is:

[tex]y = \frac {5} {2} x-4[/tex]

Thus, it is observed that the lines have the same y-intercept

Answer:

Option D

Answer:

1.26 kg.

Step-by-step explanation:

We have been given that Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. We are asked to find the amount of candy bought by Mr. Snow in kilograms.

First of all, we will find the amount of candy in grams by multiplying 90 grams by 14 as:

[tex]\text{Amount of candy bought in grams}=14\times 90[/tex]

[tex]\text{Amount of candy bought in grams}=1260[/tex]

We know that 1 kilogram is equal to 1000 grams. To convert 1260 grams into kg, we will divide 1260 by 1000 as:

[tex]\text{Amount of candy bought in kilograms}=\frac{1260}{1000}[/tex]

[tex]\text{Amount of candy bought in kilograms}=1.26[/tex]

Therefore, Mr. Snow bought 1.26 kilograms of candy.

Answer:

[tex]B=\frac{4}{3}A[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a proportional relationship because the line passes through the origin (0,0)

Find the value of k

[tex]k=\frac{B}{A}[/tex]

take the point (3,4)

A=3,B=4

substitute

[tex]k=\frac{4}{3}[/tex]

The equation of the line is

[tex]B=\frac{4}{3}A[/tex]

Answer:

Yes

Step-by-step explanation:

Given point to test : (5,10)

Give system of linear inequalities:

[tex]x>2[/tex]

[tex]y\geq3x-7[/tex]

To check if the point lies in the solution set for the given system of inequalities.

Solution:

In order to check if the point lies in the solution set for the given system of inequalities, we will plugin the given point in the inequalities and see if it is true or not.

For the given point [tex]x=5[/tex] [tex]y=10[/tex]

Testing the first inequality.

Plugging in [tex]x=5[/tex] in the inequality.

[tex]5>2[/tex]

The above inequality will always hold true and thus the given point will lie in the solution set of this inequality.

Testing the second inequality:

Plugging in [tex]x=5[/tex] and [tex]y=10[/tex] in the inequality.

[tex]10>3(5)-7[/tex]

Simplifying.

[tex]10>15-7[/tex]

[tex]10>8[/tex]

The above inequality will always hold true and thus the given point will lie in the solution set of this inequality also.

Thus, we can say that the point (5,10) will lie in the solution set of the given system of inequalities.

Answer:

Yes!

Step-by-step explanation:

I will show you A and B, and give you a hint how to do C, since brainly doesn't provide C option.

A.

The elimination method is how I would solve this system

[tex]

\begin{cases}

2x+5y=25 \\

3x-2y=9

\end{cases}

[/tex]

We start by multiplying the first equation by 3 and second by -2 to obtain

[tex]

\begin{cases}

6x+15y=75 \\

-6x+4y=-18

\end{cases}

[/tex]

Now add the two equations and thus eliminate the x-terms to obtain

[tex]19y=57\Longrightarrow y=\dfrac{57}{19}=3[/tex]

Then we insert the y into either of the original equations and solve for x

[tex]

2x+5\cdot3=25 \\

2x=25-15 \\

2x=10 \\

x=5

[/tex]

And we have the solution at [tex]P(5,3)[/tex].

B.

We pick one equation and express x

[tex]

2x+5y=25 \\

2x=25-5y \\

x=\dfrac{25-5y}{2}

[/tex]

Then we replace the x in other equation with expression we just calculated and solve for y

[tex]

3\cdot\dfrac{25-5y}{2}-2y=9 \\

\dfrac{75-15y}{2}-2y=9 \\

\dfrac{75-15y-4y}{2}=9 \\

75-19y=18 \\

-19y=-57 \\

y=3

[/tex]

Now we put y in either of the original equations to get x

[tex]

2x+5\cdot3=25 \\

2x=25-15 \\

2x=10 \\

x=5 \\

[/tex]

And again we get the solution [tex]P(5,3)[/tex].

C.

To find solution graphically, you need to put both lines in general form [tex]f(x)=mx+n[/tex] where [tex]f(x)=y[/tex]

[tex]

\begin{cases}

2x+5y=25\Longrightarrow y=\frac{25-2x}{5}=-\frac{2}{5}x+5 \\

3x-2y=9\Longrightarrow y=-\frac{9-3x}{2}=-\frac{3}{2}x-\frac{9}{2}

\end{cases}

[/tex]

Then plot the lines on the graph. The solution will be point [tex]P(5,3)[/tex] where lines intersect, because we can represent lines as sets of points ordered pairs. Consider our two lines represented as two functions g and f where

[tex]

f(x)=-\frac{2}{5}x+5 \\

g(x)=-\frac{3}{2}x-\frac{9}{2}

[/tex]

Graphs (sets) of these two functions are defined as (assuming [tex]f,g:D_f,D_g\to T_f,T_g=\mathbb{R}\to\mathbb{R}[/tex] since not specified):

[tex]

\displaystyle

G_f=\{(x,f(x)):x\in D_f\wedge f(x)\in T_f\} \\

G_g=\{(x,g(x)):x\in D_g\wedge g(x)\in T_g\}

[/tex]

Where D is definition zone (set of all x defined for function f or g) and T transformation zone (set of all f(x) or g(x)). Note that in our case [tex]D_f,T_f=D_g,T_g[/tex] because [tex]D_f,T_f,D_g,T_g=\mathbb{R}[/tex]

The solution is is intersection of these two sets

[tex]G_f\cap G_g=(5,3)[/tex]

Hope this helps.

Answer:

y-9=5(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-9=5(x-(-3))

y-9=5(x+3)

Answer:

you will need 4cups of flour

Answer:

D) (-2)^2-(-8)+1

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Answer:

3r-5r

Step-by-step explanation:

Answer:

The city’s total budget is [tex]\$54,860,151[/tex]

Step-by-step explanation:

we know that

31.84% of the city's total budget represent $17,467,472

so

using proportion

Find out what is the city’s total budget (100% percentage)

[tex]\frac{\$17,467,472}{31.84\%}=\frac{x}{100\%}\\\\x=\$17,467,472(100)/31.84\\\\x=\$54,860,151[/tex]

Answer: 7 and 8

Step-by-step explanation:

The square root of 7 is 49 and the square root of 8 is 64

52 is in between the 2 consecutive integers 7 and 8

Answer: b) 7 and 8

Step-by-step explanation:

The formula for calculating the square root of non perfect square is given as :

square root of non perfect square = square root of the nearest lower perfect square + (difference between the number and the perfect square)/ 2x the perfect square.

To find the square root of 52.

The nearest lower perfect square to 52 is 49 , applying the formula , we have:

[tex]\sqrt{52}[/tex] = [tex]\sqrt{49}[/tex] - [tex]\frac{52-49}{2\sqrt{49}}[/tex]

[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{2(7)}[/tex]

[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{14}[/tex]

This shows clearly that [tex]\sqrt{52}[/tex] is between the integer 7 and 8

Answer: 5 feet tall

Step-by-step explanation:

because he is beside the bird house he is 5 feet tall

The birdhouse's height is 20 feet, calculated using the proportion: [tex]\( \frac{h}{12} = \frac{5}{3} \).[/tex]

We can solve this problem using proportions.

Let [tex]\( h \)[/tex] be the height of the birdhouse.

According to the given information, the ratio of Jin's height to his shadow length is the same as the ratio of the birdhouse's height to its shadow length:

[tex]\[ \frac{h}{12} = \frac{5}{3} \][/tex]

Now, cross-multiply to solve for [tex]\( h \):[/tex]

[tex]\[ 3h = 5 \times 12 \][/tex]

[tex]\[ 3h = 60 \][/tex]

[tex]\[ h = \frac{60}{3} \][/tex]

[tex]\[ h = 20 \][/tex]

So, the height of the birdhouse is 20 feet.

Answer:

Step-by-step explanation:

Let the consecutive integers be (x - 1), x, (x + x)

x - 1 + x + x + 1 = 45

3x = 45    ---------> this is the equation

x = 45/3

x = 15

The ages are 14,15,16

Answer:

Step-by-step explanation:

consecutive integers means 1 right after the other....with x being the youngest, then x + 1 being the second friend, and x + 2 being the third friend.

so ur equation would be : x + x + 1 + x + 2 = 45......but since I cant see ur answer choices, it could also be : 3x + 3 = 45

The speed of slower car is 94 kilometers per hour.

Step-by-step explanation:

Given,

Total distance covered by both cars = 400 km

Time period = 2 hours

Let,

Speed of one car = x

Speed of slower car = x-12

Combined speed = [tex]x+(x-12)=x+x-12=2x-12[/tex]

Distance = Speed*Time

[tex]400=(2x-12)*2\\400=4x-24\\400+24=4x\\424=4x\\4x=424[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4}=\frac{424}{4}\\x=106[/tex]

Speed of slower car = x-12 = 106-12 = 94 km/h

The speed of slower car is 94 kilometers per hour.

Keywords: distance, speed, time

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Answer:

(x - 3)

Step-by-step explanation:

age in 3 years : x

age now = age in 3 years - 3 years = (x - 3)

Answer:

x-3

because...

we only have 3 so we have to find the value of x by subtracting 3 from it.

now = 3 year-3 which is equal to x-3

Answer:

Step-by-step Let's break down the problem step by step.Let "a number" be represented by 'x'.Three times a number: 3 * xIncreased by 12: 3 * x + 12One-third of the result: (1/3) * (3 * x + 12)Now, let's simplify the expression:(1/3) * (3 * x + 12)The '3's cancel out:= (1/1) * (x + 12)= x + 12So, the expression "One-third of the result of three times a number that is increased by 12" is equivalent to "x + 12."