Find the midpoint of RS

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

Answer:

y = - 10 and x = 5

Step-by-step explanation:

[tex] - 9x - 6y = 15 \\ + 9x - 10y = + 145 \\ add \: the \: two \: equations \: together \\ 0 - 16y = 160 \\ y = \frac{160}{ - 16} \\ y = - 10 \\ substitute \: for \: y\: in \: any \: equation \\ - 9x - 6( - 10) = 15 \\ - 9x + 60 = 15 \\ - 9x = 15 - 60 \\ - 9x = - 45 \\ x = \frac{ - 45}{ - 9} \\ x = 5[/tex]

Answer:

y=-10

x-5

Step-by-step explanation:

Petra can make 8 costumes with 12 yards of fabric

Given that Petra was given 12 yards of fabric to make costumes for the school play

Each costume requires [tex]1\frac{1}{2}[/tex] yards

To find: number of costume Petra can make

The number of costume Petra can make is calculated by dividing the total fabric she has by fabric needed for one costume

[tex]\text {number of costume Petra can make }=\frac{\text {total fabric she has }}{\text {fabric needed for one costume }}[/tex]

Total fabric she has = 12 yards

Fabric needed for 1 costume = [tex]1\frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}[/tex] yards

Therefore,

[tex]\text {number of costume Petra can make }=\frac{12}{3 / 2}=\frac{12}{3} \times 2=8[/tex]

Thus petra can make 8 costumes with 12 yards of fabric

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]

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:

Answer is in explanation.

Step-by-step explanation:

Part A:

The [tex]x[/tex]-coordinate of the intersection of the curves for the equations [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex] is the same as the solution to [tex]4^{-x}=2^{x+3}[/tex] because the equation [tex]4^{-x}=2^{x+3}[/tex] is the result of finding when (for what [tex]x[/tex]'s) the [tex]y[/tex]'s are the same for the the equations [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex].

Part B:

Table for [tex]y=4^{-x}[/tex]:

[tex]x[/tex]  |          [tex]y=4^{-x}[/tex]                     |  [tex](x,y=4^{-x})[/tex] |

-3                |          [tex]y=4^{-(-3)}=4^{3}=64[/tex] | [tex](-3,64)[/tex] |

-2                |          [tex]y=4^{-(-2)}=4^{2}=16[/tex]  | [tex](-2,16)[/tex] |

-1                 |          [tex]y=4^{-(-1)}=4^{1}=4[/tex]     | [tex](-1,4)[/tex]

0                 |          [tex]y=4^{-(0)}=4^{0}=1[/tex]     | [tex](0,1)[/tex]

1                  |          [tex]y=4^{-(1)}=4^{-1}=\frac{1}{4}[/tex] | [tex](1,\frac{1}{4})[/tex]

2                 |          [tex]y=4^{-(2)}=4^{-2}=\frac{1}{16}[/tex] | [tex](2,\frac{1}{16})[/tex]

3                 |          [tex]y=4^{-(3)}=4^{-3}=\frac{1}{64}[/tex] | [tex](3,\frac{1}{64})[/tex]

Table for [tex]y=2^{x+3}[/tex]:

[tex]x[/tex]  |        [tex]y=2^{x+3}[/tex]                   | [tex](x,y=2^{x+3})[/tex] |

-3                |        [tex]y=2^{-3+3}=2^{0}=1[/tex]    | [tex](-3,1)[/tex]

-2                |        [tex]y=2^{-2+3}=2^{1}=2[/tex]    | [tex](-2,2)[/tex]

-1                |        [tex]y=2^{-1+3}=2^{2}=4[/tex]    | [tex](-1,4)[/tex]

0                |        [tex]y=2^{0+3}=2^{3}=8[/tex]    | [tex](0,8)[/tex]

1                |        [tex]y=2^{1+3}=2^{4}=16[/tex]    | [tex](1,16)[/tex]

2                |        [tex]y=2^{2+3}=2^{5}=32[/tex]    | [tex](2,32)[/tex]

3               |        [tex]y=2^{3+3}=2^{6}=64[/tex]    | [tex](3,64)[/tex]

You can see in the two tables the y-coordinates are the same value of [tex]4[/tex] when [tex]x=-1[/tex]. So basically the common point in both tables is [tex](-1,4)[/tex] so [tex](-1,4)[/tex] is a solution.

Part C:

I'm going to graph both [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex] on the same coordinate plane. I will then find where they will intersect.

I'm going to graph my points from the table to [tex]y=4^{-x}[/tex] and [tex]y=2^{x+3}[/tex].

This can be seen in my drawing.

I graphed [tex]y=4^{-x}[/tex] in blue.

I graphed [tex]y=2^{x+3}[/tex] in red.

Another way:

An algebraic approach:

[tex]4^{-x}=2^{x+3}[/tex]

[tex](2^2)^{-x}=2^{x+3}[/tex] (since [tex]4=2^2[/tex] and now the bases on both side are the same)

[tex]2^{-2x}=2^{x+3}[/tex]

[tex]-2x=x+3[/tex] (since [tex]2^{a}=2^{b}[/tex] then [tex]a=b[/tex])

[tex]-3x=3[/tex] (subtracted [tex]x[/tex] on both sides)

[tex]x=-1[/tex] (divided both sides by [tex]-3[/tex])

The solution is [tex]x=-1[/tex].

Answer:

Step-by-step explanation:

error in measurement  = 480 - 469 = 11 inches

Percent error = error *100/actual length

= 11 * 100 /480 = 2.9%

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."

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:

24.4 feet

Explanation:

Let x be the length of the wooden board as shown in the diagram.

Using trigonometry ratio, we can write

[tex] \cos(35)=\frac{20}{x}[/tex]

[tex] \implies0.819= \frac{20}{x} [/tex]

cross multiplying we get:

[tex]0.819 \times x = 20[/tex]

Diving through by 0.819, we obtain

[tex]x = 24.42[/tex]

To the nearest tenth, x=24.4 feet.

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:

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

Step-by-step explanation:

Answer: 4

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.

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: 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:

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:

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

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

[tex]x = - 7[/tex]

Answer:

A

Step-by-step explanation:

Consider the values of y, that is

9, 36, 144, 576, 2304

Then the common ratio r is

r = 36 ÷ 9 = 144 ÷ 36 = 576 ÷ 144 = 2304 ÷ 576 = 4 → A

Answer:

Step-by-step explanation:

To order decimals is to subtract, line up, and comparing digits.

Comparing digits is a good way to order decimals for greatest to least.

(Most Understood.)

We could put numbers in any order to compare digits, but you should look closely:

__________________________________________

First, we pick 2 numbers to compare, maybe 8.782 and 8.981.

We look at the digits for both numbers.

We see 8's, And 7 and 9, 9 is greater, so 8.981 is the greatest and 8.782 is the 2nd greatest.

Our last 2 numbers are 7.981 and 7.982,

We look at the digits for both numbers.

We see 7's, we see 9's, and we see 8's, but 1 and 2. 2 is greater so 7.982 is the 3rd greatest and 7.981 is the least.

Best of Luck to you.

If you have any questions, feel free to comment below.

-Also if anything is confusing!!

The numbers 8.981, 8.782, 7.982, and 7.981 are ordered from greatest to least. This is determined by comparing each digit from left to right, where 8.981 is the greatest and 7.981 is the least.

The task that you are asked to do is to arrange the numbers from greatest to least. The numbers given are 7.982, 7.981, 8.782, and 8.981.

This order is determined by comparing the digits from left to right. The first digit is the most significant indicator of the size of the number. However, if the first digits are the same, then we consider the following digits and so on until we find one that differs. In our case, 8.981 has both the largest initial digit (8) and the largest subsequent digits (9 and 8 respectively) so it is the greatest. Similarly, 7.981 has the smallest digits and as a result, it's the least.

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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:

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:

(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:

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

Step-by-step explanation:

Answer:

Store A is the better buy.

Step-by-step explanation:

The first thing I did was to find a multiple that 3 and 5 share which is 15. Now, we can figure out how much each store charges for 15 oz. I put the numbers into fraction form to make it easier. 5/1.50 and 3/1.20. To get 5 to 15, I multiplied it by 3, so I also have to do that to 1.50. This leaves me with 4.50. Store A charges 4.50 for 15 oz. Next, we have to go over to the other fraction. To get 3 to 15, I multiplied it by 5. Whatever you do to the numerator, you have to do to the denominator, so you multiply 1.20 by 5. This gets you 6. Store B charges 6 dollars for 15oz, so store A has a better price. I hope this helps.

Answer:

Step-by-step explanation:

60 to 15 = x to 70

60/15 = x/70.....cross multiply

15x = 4200

x = 4200/15

x = 280 <=== answer A

Answer:

A

Step-by-step explanation:

60:15::x:70

60*70=15*x

x=4*70 =280

Answer:

1200 N

Step-by-step explanation:

Newton's second law:

F = ma

F = (300 kg) (4 m/s²)

F = 1200 N

Answer:

D)

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