A group of 21 people need to take an
elevator to the top floor. They will go in
groups of seven. They are deciding who
will go in the first group.

Step-by-step explanation:

you can convert both inequalities to slope intercept form and then graph it.

So 4x+y>-1 would convert to y>-4x-1

And x+y ≥ 2 would be y≥-x+2

Then graph it

Working with the first one

4x+y > -1

Treat as an equation and find the x and y intercept

4x+y= -1

when x=0

4(0)+y = -1

y= -1

(0,-1)

when y=0

4x+0=-1

4x= -1

divide both sides by 4

x= -1/4 or -0.25

(-0.25, 0)

working with the second one

x+y≥2

same process

when x=0

0+y=2

y=2

(0,2)

when y=0

x+0=2

x=2

(2,0)

Now on your graph you have to plot the points (0, -1) ,( -0.25,0), (0,2) ,(2,0) using an appropriate scale

Answer:

195.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

a>−64/3

Hope this helps mark me as brainiest pls

The solution of the a is greater than negative 21 and one-third. Then the correct option is A.

Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.

The inequality equation is given below.

[tex]\dfrac{3}{4} \times a > -16\\[/tex]

On solving the inequality, the value of the a will be

[tex]\rm a > -16 \times \dfrac{4}{3}\\\\a > - \dfrac{64}{3}\\\\a > - 21 \dfrac{1}{3}[/tex]

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Answer:

The length of the rectangular field is (3 a - 3) meters

Step-by-step explanation:

Given as :

The Perimeter of rectangular field = p = ( 10 a - 6 ) meters

The width of the rectangular field = w = 2 a meters

Let The length of the rectangular field = L meters

Now From The perimeter formula

Perimeter of rectangular field = 2 × Length + 2 × width

Or, p =  2 × L +  2 × w

Or,  ( 10 a - 6 ) meters =  2 × L meters + 2 × 2 a meters

Or, 10 a - 6 =  2 × L + 4 a

Or, 10 a - 4 a - 6 = 2 L

Or, 6 a - 6 = 2 L

∴  L = [tex]\dfrac{6 a - 6}{2}[/tex]

i,e L = 3 a - 3

So, The length of the rectangular field = L = (3 a - 3) meters

Hence,The length of the rectangular field is (3 a - 3) meters  Answer

Answer:

[tex]y=\frac{1}{4}(x+1)^2-9[/tex]

Step-by-step explanation:

Method 1

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^2+k[/tex]

where

a is the leading coefficient

(h,k) is the vertex

we have

(h,k)=(-1,-9)

substitute

[tex]y=a(x+1)^2-9[/tex]

Remember that

one root is (-7,0)

substitute and solve for a

[tex]0=a(-7+1)^2-9[/tex]

[tex]0=a(-6)^2-9[/tex]

[tex]0=36a-9[/tex]

[tex]a=\frac{1}{4}[/tex]

therefore

[tex]y=\frac{1}{4}(x+1)^2-9[/tex]

Method 2

I use the fact that the roots are the same distance from the vertex

the distance from the given root to the vertex is equal to

6 units

so

If one root is x=-7

then the other root is

x=-1+6=5

The general equation of the quadratic equation is equal to

[tex]y=a(x+7)(x-5)[/tex]

we have the vertex (-1,-9)

substitute the value of x and the value of y and solve for a

[tex]-9=a(-1+7)(-1-5)[/tex]

[tex]-9=a(6)(-6)[/tex]

[tex]-9=-36a[/tex]

[tex]a=\frac{1}{4}[/tex]

[tex]y=\frac{1}{4}(x+7)(x-5)[/tex]

so

Expanded the equation, complete the square and rewrite as vertex form

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st

Step-by-step explanation:

Parallel lines have:

The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{1},y_{1})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

∵ The given line passes through points (-12 , -2) and (0 , -4)

∴ [tex]x_{1}[/tex] = -12 , [tex]x_{2}[/tex] = 0

∴ [tex]y_{1}[/tex] = -2 , [tex]y_{2}[/tex] = -4

- Use the formula of the slope above to find the slope of the given line

∵ [tex]m=\frac{-4-(-2)}{0-(-12)}=\frac{-4+2}{12}=\frac{-2}{12}=\frac{-1}{6}[/tex]

∴ The slope of the given line is [tex]\frac{-1}{6}[/tex]

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = [tex]\frac{-1}{6}[/tex]

∵ The parallel line passes through point (0 , 6)

- The form of the linear equation is y = mx + b, where m is the slope

  and b is the y-intercept (y when x = 0)

∵ m = [tex]\frac{-1}{6}[/tex] and b = 6

∴ The equation of the parallel line is y = [tex]\frac{-1}{6}[/tex] x + 6

Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line

Point (-12 , 8)

∵ x = -12 and y = 8

∵ y = [tex]\frac{-1}{6}[/tex] (-12) + 6

∴ y = 2 + 6 = 8

- The value of y is equal the y-coordinate of the point

∴ Point (-12 , 8) is on the line

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line

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The point on the line that passes through (0, 6) and is parallel to the given line is (2, 8).

To find a point on a line parallel to the given line, we can use the slope of the given line, which is equal to the slope of the parallel line.

The slope of the given line can be calculated using the coordinates (-12, -2) and (0, -4):

Slope (m) = (change in y) / (change in x) = (-4 - (-2)) / (0 - (-12)) = (-2) / (12) = -1/6.

Now that we know the slope of the parallel line is -1/6, we can use the point-slope form of a linear equation to find the equation of the parallel line:

y - y1 = m(x - x1),

where (x1, y1) is the point (0, 6) and m is the slope (-1/6). Plugging in these values:

y - 6 = (-1/6)(x - 0),

y - 6 = (-1/6)x,

y = (-1/6)x + 6.

Now, we can choose any x-value to find the corresponding y-value. If we plug in x = 2 into the equation, we get:

y = (-1/6)(2) + 6 = -1/3 + 6 = 8.

So, the point (2, 8) is on the line that passes through (0, 6) and is parallel to the given line.

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Answer:

(-4,2)

Step-by-step explanation:

Answer:

(-4,2)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

85+156+34+127=402

10+18+2+14=44

44/402=10.95%

Answer is B. 10.95%

Step-by-step explanation:

[tex]\begin{array}{c|cc}12&2\\6&2\\3&3\\1\end{array}\qquad\qquad\begin{array}{c|cc}56&2\\28&2\\14&2\\7&7\\1\end{array}\\\\12=\boxed{2}\cdot\boxed{2}\cdot3\\\\56=\boxed{2}\cdot\boxed{2}\cdot2\cdot7\\\\GCF(12,\ 56)=\boxed{2}\cdot\boxed{2}=4\\\\LCM(12,\ 56)=\boxed{2}\cdot\boxed{2}\cdot3\cdot2\cdot7=168[/tex]

Of the possible numbers (1,2,3,4,5,6), 3 are greater than 3. The probability to roll a number greater than 3 is 3 over the 6 total. That can be simplified to 1/2 for the probability. If she rolls the dice 90 times 90 x 1/2 or 45 rolls will receive a number greater than 3.

answer: 45

The Value of t from given convex polygon is 41.

Step-by-step explanation:

Let us consider,

a=61°.

b=2t.

c=3t.

d=42°.

e=52°.

The sum of exterior angles of convex polygon is always 360°.

a+b+c+d+e=360°.

The exterior angles of any convex polygon is same as if any angle drawn inside a circle.

Steps to reform the angles:

Step 1: Draw the ∠a as given in the original diagram.

Step 2: The ∠b is adjacent to ∠a 's end and draw a parallel line of ∠b in the ∠a. The angle measure will also be same.

Step 3: Continue the same for next angles ∠c,∠d and ∠e.

(refer the image dotted lines are the parallel lines.)

⇒ 61°+42°+52°+2t+3t=360°.

155°+5t=360°.

5t=205°.

t=41°.

Also,

∠b=82°.

∠c=123°.

Check,

61°+82°+123°+42°+52°=360°.

Answer:

Find the complete table in attached file.

Step-by-step explanation:

Find the Incomplete table in attached file

Given:

A car travels 55 miles per hour for 2 hours.

So the speed of the car 55 miles per hour is constant for 2 hours.

Using speed  formula.

[tex]Speed=\frac{distance}{time}[/tex]

Second row.

From the second row of the table [tex]time = \frac{1}{2}=0.5\ sec[/tex] and speed is constant [tex]speed = 55\ mi/hr[/tex], so we need to find only distance.

[tex]Speed=\frac{distance}{time}[/tex]

[tex]55=\frac{distance}{0.5}[/tex]

[tex]distance = 55\times 0.5[/tex]

[tex]distance = 27.5\ mi[/tex]

Third row.

From the third row of the table [tex]time =1\frac{1}{2}=\frac{3}{2} = 1.5\ sec[/tex] and speed is constant [tex]speed = 55\ mi/hr[/tex], so we need to find only distance.

[tex]Speed=\frac{distance}{time}[/tex]

[tex]55=\frac{distance}{1.5}[/tex]

[tex]distance = 55\times 1.5[/tex]

[tex]distance = 82.5\ mi[/tex]

Fourth row.

From the fourth row of the table [tex]distance =110\ miles[/tex] and speed is constant [tex]speed = 55\ mi/hr[/tex], so we need to find time.

[tex]Speed=\frac{distance}{time}[/tex]

[tex]time=\frac{distance}{speed}[/tex]

[tex]time=\frac{110}{55}[/tex]

[tex]time = 2\ sec[/tex]

Therefore we complete the table from the above calculation.

Answer:

91.6

Step-by-step explanation:

7786/85

Answer:

OPTION B: {5, 7, 9}

Step-by-step explanation:

D [tex]$ \cap $[/tex] E is the collection of elements that are present in both D and E.

Given the set D = {5, 6, 7, 8, 9, 10}

and                 E = {1, 3, 5, 7, 9, 11}

So, the elements present in both D and E are: {5, 7, 9}.

Hence, D [tex]$ \cap $[/tex] E = {5, 7, 9}.

OPTION B is the answer.

Answer:X=5/3

Step-by-step explanation:

(2∧(3*x-4))2=(-2)²

2∧2*(3*x-4)=2²

-------------------------

2*(3*x-4)=2

3*x-4=1

3*x=5

x=5/3

Answer:

x=25  solution is not extraneous

Step-by-step explanation:

given, [tex]\sqrt{2x-1}[/tex]=7

squaring both side we get,

2x-1=7^2

2x-1=49

2x=50

x=25  solution is not extraneous  answer

Answer:

An acute triangle, because [tex]22^2 + 51^2 >54^2[/tex]

Step-by-step explanation:

Given:

The distance between city A and city B is 22 miles.

The  distance between city B and city C is 54 miles.

The distance  between city A and city C is 51 miles.

thus we have a triangle ABC with side lengths :

AB = 22 miles (shortest side)

BC= 54 miles  (longest side)

AC = 51 miles (shorter side)

For an obtuse triangle :

[tex](Shorter\ side)^2+(Shortest\ side)^2<(Longest\ side)^2[/tex]

For acute triangle :

[tex](Shorter\ side)^2+(Shortest\ side)^2>(Longest\ side)^2[/tex]

Comparing sum of squares of shorter sides with the square of longest side:

[tex]AB^2+AC^2=22^2+51^2=484+2601=3085[/tex]

[tex]BC^2=54^2=2916[/tex]

We see that:

[tex]22^2+51^2>54^2[/tex]

Thus, the condition [tex](Shorter\ side)^2+(Shortest\ side)^2>(Longest\ side)^2[/tex]  fulfills proving this triangle to be an acute triangle.

Answer:

The answer is B on Edge 2020 Thank me Later!

Step-by-step explanation:

I did the Exam

Answer:

The triangles are congruent by Angle Side Angle congruency statement and the reason is below.

Step-by-step explanation:

Given:

∠ VUW ≅ ∠ XYW

VW ≅ YW

To Prove:

Δ VUW ≅ Δ XYW

Proof:

In Δ VUW and Δ XYW

∠ VUW ≅ ∠ XYW      ……….{Given}

VW ≅ YW                 ............{Given}

∠ VWU ≅ ∠ XWY    …………..{Vertically Opposite Angles are equal}

Δ VUW ≅ Δ XYW   .….{ By Angle-Side-Angle congruence test}

......Proved

Answer:

B

Step-by-step explanation:

If we understand 2 properties of isosceles trapezoids, then we can solve for x and y easily.

First, the two sides, "2x-13" and "x-3" are equal, as shown also by red line.

So, we equate them and find x first. Shown below:

[tex]2x-13=x-3\\2x-x=-3+13\\x=10[/tex]

Now, another property is:

Any lower base angle is supplementary to any upper base angle. That means the angle y is supplementary to "3y-4". Supplementary means that if we add up the two angles, it will be 180 degrees. So:

[tex]y+3y-4=180\\4y=180+4\\4y=184\\y=46[/tex]

From the answer choices, answer choice B is right

Answer:

Its the Adding a quantity one or the bottom right

Adding equations is a legitimate method in solving systems because it utilizes the elimination process to simplify the system. It also respects the fundamental properties of equations and provides a precise analytical technique for finding solutions, which can be more accurate than graphical methods.

Adding equations, known as the method of elimination, is a valid method for solving a system of equations. This approach works because it leverages the property that if two equations both equal the same variable, they can be added together to eliminate one of the unknowns, simplifying the system. For instance, suppose we have equation a: x + 2y = 6, and equation b: 3x - y = 4. Adding them gets 4x + y = 10, which is a new equation that can help solve for one of the variables more directly. This takes advantage of the fact that equations describe relationships between variables that hold true under various mathematical operations, including addition.

Another key aspect is the understanding that solutions to equations are often not unique when they include an unknown squared, leading to two potential solutions. However, contextual knowledge can determine which solution is reasonable, such as in physics problems where time or velocity must make sense in the real world.

Moreover, while analytical methods of solving systems are precise, solving equations graphically can offer a visual understanding but may lack accuracy due to potential scaling and drawing inaccuracies. Therefore, analytical techniques, like adding equations, are generally more accurate but can be complemented with graphical methods for a better conceptual grasp.

Answer:

Part a) [tex]\$42[/tex]

Part b) [tex]\$5,642[/tex]  

Part c) [tex]\$42.32[/tex]

Part d) [tex]\$5,684.32[/tex]

Part e) [tex]\$84.32[/tex]

Step-by-step explanation:

The complete question is

Rhonda deposits $5,600 in a savings account that pays 1.5% interest, compounded semi-annually. Round to the nearest cent.

a. How much interest does the account earn in the first 6 months?

b. What is the ending balance after 6 months?

c. How much interest does the account earn in the second 6 months?  

d. What is the balance after 1 year?

e. How much interest does the account earn the first year?

we know that

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part a) How much interest does the account earn in the first 6 months?

in this part we have  

[tex]t=6/12=0.5\ years\\ P=\$5,600\\ r=1.5\%=1.5/100=0.015\\n=2[/tex]  

substitute in the formula above

[tex]A=5,600(1+\frac{0.015}{2})^{2*0.5}[/tex]  

[tex]A=5,600(1.0075)^{1}[/tex]  

[tex]A=\$5,642[/tex]  

Find out the interest

[tex]I=A-P[/tex]

[tex]I=\$5,642-\$5,600=\$42[/tex]

Part b) What is the ending balance after 6 months?

we know that

The ending balance after 6 months is the same that the final investment value of A after 6 months

so

[tex]A=\$5,642[/tex]   ----> see part a)

Part c) How much interest does the account earn in the second 6 months?

in this part we have  

[tex]t=6/12=0.5\ years\\ P=\$5,642\\ r=1.5\%=1.5/100=0.015\\n=2[/tex]  

substitute in the formula above

[tex]A=5,642(1+\frac{0.015}{2})^{2*0.5}[/tex]  

[tex]A=5,642(1.0075)^{1}[/tex]  

[tex]A=\$5,684.32[/tex]  

Find out the interest

[tex]I=A-P[/tex]

[tex]I=\$5,684.32-\$5,642=\$42.32[/tex]

Part d) What is the balance after 1 year?

we know that

The balance after 1 year is equal to the initial deposit of $5,600 plus the  interest earned in the first 6 months plus the interest earned in the second 6 months

so

[tex]\$5,600+\$42+\$42.32=\$5,684.32[/tex]

Part e) How much interest does the account earn the first year?

The total interest the first year is equal to the interest earned in the first 6 months plus the interest earned in the second 6 months

so

[tex]\$42+\$42.32=\$84.32[/tex]

Answer:

B. 60 Minutes

Step-by-step explanation:

Answer:

The equation to represent total number of pencils p that Rafael bought is 15 n .  

Step-by-step explanation:

Given as :

The total numbers of pencils packs bought by Rafael = n

The number of pencils in each pack = 15 pencils

Let The total number of pencil does Rafael bought = p

Now, According to question

The total number of pencil does Rafael bought =  total numbers of pencils packs bought by Rafael × number of pencils in each pack

i.e p = n × 15

So, The  total number of pencil does Rafael bought = p = 15 n

Hence, The equation to represent total number of pencils p that Rafael bought is 15 n .  Answer

Final answer:

The equation to represent the total number of pencils Rafael bought is p = 15 × n, where p is the total number of pencils and n is the number of packs bought.

Explanation:

To represent the total number of pencils p that Rafael bought, we create an equation that multiplies the number of packs n by the number of pencils in each pack.

Since each pack contains 15 pencils, the equation is:

p = 15 × n

Using this equation, if you know the number of packs Rafael bought, you can calculate the total number of pencils by substituting n with the number of packs.

Answer:

About 14.29 minutes

Step-by-step explanation:

Each page has 125 words

There are 4 pages

SO, total number of words:

125 * 4 = 500 words

The rate of typing is 35 wpm (words per minute)

So, to find time it will take to type 500 words is found by dividing the number of words (500) by the rate (35), so we have:

500/35 = 14.2857 minutes

So, it will take about 14.29 minutes to type up the whole documentary

Answer:

[tex]3-\frac{1}{2}n[/tex]

Step-by-step explanation:

We will use the distributive property shown below to break it down first.

Distributive Property:  [tex]a(b-c)=ab-ac[/tex]

The expression is:

[tex]\frac{1}{2}(n-8)+7-n[/tex]

Let's distribute:

[tex]\frac{1}{2}(n-8)+7-n\\=\frac{1}{2}(n)-\frac{1}{2}(8)+7-n[/tex]

Now, we multiply:

[tex]\frac{1}{2}(n)-\frac{1}{2}(8)+7-n\\=\frac{1}{2}n-4+7-n[/tex]

Now we combine like terms (variables and numbers separately):

[tex]\frac{1}{2}n-4+7-n\\=-4+7-n+\frac{1}{2}n\\=3-\frac{1}{2}n[/tex]

This is the simplified expression.

Answer: The total price of a bench is 1.008x.

Step-by-step explanation:

Since we have given that

Let the cost price be 'x'.

Mark up % = 120%

So, Mark up value would be

[tex]\dfrac{120}{100}x\\\\=1.20x[/tex]

Discount % = 20%

Amount of discount is given by

[tex]\dfrac{20}{100}\times 1.2x\\\\=0.2\times 1.2x\\\\=0.24x[/tex]

So, it becomes,

Amount after discount is given by

[tex]1.2x-0.24x\\\\=0.96x[/tex]

Sales tax = 5%

Amount of sales tax would be

[tex]\dfrac{100+5}{100}\times 0.96x\\\\=\dfrac{105}{100}\times 0.96x\\\\=1.05\times 0.96x\\\\=1.008x[/tex]

Hence, the total price of a bench is 1.008x.

Answer:

[tex]h=\frac{SA}{2\pi r}-r[/tex]

Step-by-step explanation:

The surface area of a cylinder is equal to

[tex]SA=2\pi r^{2} +2\pi rh[/tex]

Solve for h

That means ----> isolate the variable h

subtract  2πr² both sides

[tex](SA-2\pi r^{2})=2\pi rh[/tex]

Divide by 2πr both sides

[tex]\frac{SA-2\pi r^{2}}{2\pi r}=h[/tex]

Rewrite

[tex]h=\frac{SA-2\pi r^{2}}{2\pi r}[/tex]

Simplify

[tex]h=\frac{SA}{2\pi r}-r[/tex]

The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet " ⇒ D

Step-by-step explanation:

The boiling point of water (measured in degrees), at altitude (measured in feet), is modeled by the function T(a) = −0.0018 a + 212, where

The form of the linear function is f(x) = mx + b, where m is slope (the rate of change), and b is the y-intercept (the value of f(x) at x = 0)

By comparing between the form of the function and the given function

∴ m = -0.0018 ⇒ degrees per foot

∵ The sign of the slope is negative

∵ The slope = Δf(x)/Δx

- That means T(a) is decreasing function

∴ The boiling point is decreases when the altitude increasing

∵ -0.0018 = [tex]-\frac{18}{10,000}[/tex] degrees per feet

∴ The boiling point decreases by 18 degrees as the altitude

    increases by 10,000 feet or the boiling point decreases by 1.8

     degrees as the altitude increases by 1,000 feet

The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet "

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The meaning of slope is best described by the boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet. The option (D) is correct.

To understand the meaning of the slope in the given function[tex]\( T(a) = -0.0018a + 212 \)[/tex], where [tex]\( T \)[/tex] represents the boiling point of water in degrees and [tex]\( a \)[/tex] represents the altitude in feet, we need to analyze the slope of the function.

The slope of the function is given by the coefficient of [tex]\( a \)[/tex], which is [tex]\( -0.0018 \)[/tex]. This slope tells us how the boiling point of water changes with altitude. To interpret the slope in terms of degrees per foot:

A slope of [tex]\( -0.0018 \)[/tex] means that for every 1 foot increase in altitude, the boiling point decreases by 0.0018 degrees.

To find out how much the boiling point changes over an increase of 1,000 feet in altitude, we multiply the slope by 1,000:

[tex]\( \text{Change in boiling point} = \text{slope} \times \text{change in altitude} \)[/tex]

[tex]\( \text{Change in boiling point} = -0.0018 \times 1000 \)[/tex]

[tex]\( \text{Change in boiling point} = -1.8 \)[/tex]

Therefore, the correct interpretation of the slope is that the boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet, which corresponds to option D.

The complete question is:

The boiling point of water, T (measured in degrees), at altitude a (measured in feet) is modeled by the function T(a)=-0.0018a+212. In terms of altitude and temperature, which statement describes the meaning of the slope?

A. The boiling point increases by 18 degrees as the altitude increases by 1,000 feet.

B. The boiling point increases by 1.8 degrees as the altitude increases by 1,000 feet.

C. The boiling point decreases by 18 degrees as the altitude increases by 1,000 feet.

D. The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet.

Answer: number 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation: