Recall the method that the video showed to solve Gavin’s word problem. The video showed how we can use numerical expressions (with the help of a diagram) to arrive at a solution.

Compare the expression method from the video with the equation method that uses the variable b. Do both methods use the same sequence of operations?

Answer:

NOT CONGRUENT

Step-by-step explanation:

Angle Side Side doesnt work so it is not congruent

Answer:

10.

here,

h=c

b=5

p=12

,we know that,

h²=b²+p²(pythagoras theorum )

c=5²+12²

c=25+144

c=169

hence the value of c is 169.

Answer:

Step-by-step explanation:

Sorry no one answered your question sooner. First Let x = what the daughter receives

Then 180000 - x is what the son will receive. Notice that if you add these together you get the total, 180000. You write a proportion and cross multiply to solve. Since x = 80000, the son will receive 80000. The daughter will receive 100000.

93.06% of the race is longer than 236 minutes.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]

Given that μ = 310, σ = 50

For x > 236:

[tex]z=\frac{236-310}{50}=-1.48[/tex]

From the normal distribution table:

P(x > 236) = P(z > -1.48) = 1 - P(z < -1.48) = 1 - 0.0694 = 0.9306 =  93.06%

93.06% of the race is longer than 236 minutes.

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Answer:

So we will use combinations, as it does not matter what order they get chosen in.

The combinitoric that you will plug in to your calculator is: nCr(12,7)

Therefore, the answer is 792

Answer:

y = -9x + 18.

Step-by-step explanation:

The general form is y = mx + c , where m = the slope and c = y-intercept.

[tex]\huge\boxed{Hi \: there! :)}[/tex]

We are given the slope of the line: -9.

We are also given its y-intercept: 18.

Slope-Intercept Form:

[tex]\huge\sf\{y=mx+b[/tex]

Where

m is the slope and b is the y-intercept.

Plug in the values:

y=-9x+18

[tex]\huge\boxed{Therefore, \: our \: equation \: is: y=-9x+18}[/tex]~An Unknown Dreamer

Good luck!

It would cost an employee $443.52 to purchase one of these laptops at the sale.

The selling price of the laptops is $720 each. The cost price is 20 percent more than the cost price.

Cost price = Selling price - 20% of cost price

Cost price = 720 - 20% * 720 = $576

At the release, the laptops are at 23% off the store's cost. Hence:

Price of laptop at release = 576 - 23% of 576

Price of laptop at release = $443.52

It would cost an employee $443.52 to purchase one of these laptops at the sale.

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Answer:

Each number is called a factor

Step-by-step explanation:

The multiplication of two numbers is equivalent to adding as many copies of one of them

Answer:

g(x) = (5x + 3)/ x - 7

Step-by-step explanation:

Let g(x) = y

y = (7x + 3)/x - 5

Make x the subject

xy - 5y = 7x + 3

xy - 7x = 5y + 3

x(y - 7) = 5y + 3

x = (5y + 3)/ y - 7

Therefore, the inverse of the function = (5x + 3)/ x - 7

The perimeter of a triangle is the sum of its side lengths.

The perimeter of triangle ACD is 40 units

Start by calculating the values of x and y, using the following equivalent ratios

[tex]6 : 4 = x - 2 : x - 4[/tex]

[tex]6 : 10 = 6 + x - 2 : y[/tex]

So, we have:

[tex]6 : 4 = x - 2 : x - 4[/tex]

Express as fraction

[tex]\frac 64 = \frac{x-2}{x-4}[/tex]

Cross multiply

[tex]6x - 24 = 4x - 8[/tex]

Collect like terms

[tex]6x - 4x = 24 - 8[/tex]

[tex]2x = 16[/tex]

Divide both sides by 2

[tex]x = 8[/tex]

Also, we have:

[tex]6 : 10 = 6 + x - 2 : y[/tex]

Express as fraction

[tex]\frac 6{10} = \frac{6 + x -2}{y}[/tex]

Substitute 8 for x

[tex]\frac 6{10} = \frac{6 + 8 -2}{y}[/tex]

[tex]\frac 6{10} = \frac{12}{y}[/tex]

Cross multiply

[tex]6y = 120[/tex]

Divide both sides by 6

[tex]y = 20[/tex]

The perimeter of triangle ACD is then calculated as:

[tex]P =6 + x - 2 + y + x - 4 + 4[/tex]

Substitute values for x and y

[tex]P =6 + 8 - 2 + 20 + 8 - 4 + 4[/tex]

[tex]P =40[/tex]

Hence, the perimeter of triangle ACD is 40 units

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Answer:

rectangle= 22*9 = 198ft

triangle=11*10 = 110 ft

110+ 198 = 308 polygon

Answer:

No it does not

Step-by-step explanation:

Two points simplify to 1/6 whilst the other, 1/5

Answer: 31.57

Step-by-step explanation:

41% of 77 is what?

41% of 77 is Y

Equation: P% * X = Y

Solving our equation for Y

Y = P% * X

Y = 41% * 77

Converting percent to decimal:

p = 41%/100 = 0.41

Y = 0.41 * 77

Y = 31.57

Answer:

Approximately [tex]\text{$0.26$ radian}[/tex] every minute.

Step-by-step explanation:

Convert the unit of velocity (kilometers-per-hour) to meters-per-minute so as to match the unit of radius (meters) and angular velocity (per-minute.)

[tex]\begin{aligned}v &= 11\; \rm km \cdot h^{-1} \\ &= 11 \times \frac{1000\; \rm m}{1\; \rm km} \times \frac{1\; \rm h}{60\; \text{minute}} \\ &\approx 183.33\; {\rm m} \cdot\text{minute}^{-1}\end{aligned}[/tex].

Calculate the circumference of this circle:

[tex]\begin{aligned}c &= 2\,\pi\, r \\ &= 2 \, \pi \times 700\; \rm m \\ &\approx 4398.2\; \rm m\end{aligned}[/tex].

Find the time required (in minutes) for this vehicle to go around this circle:

[tex]\begin{aligned}\frac{4398.2\; \rm m}{183.33\; {\rm m} \cdot \text{minute}^{-1}} \approx 23.990\; \text{minute}\end{aligned}[/tex].

A full circle corresponds to an angle of [tex]2\, \pi \; \text{radian}[/tex] ([tex]360^{\circ}[/tex].) In other words, this vehicle would have turned [tex]2\, \pi \; \text{radian}\![/tex] in approximately [tex]23.990\; \text{minute}[/tex] if it travels at a constant speed. The rate at which this vehicle turn would be:

[tex]\begin{aligned}\frac{2\, \pi}{23.990\; \text{minute}} \approx 0.26\; \text{minute}^{-1}\end{aligned}[/tex].

In general, for angular velocity [tex]\omega[/tex], radius [tex]r[/tex], and velocity [tex]v[/tex], [tex]v = \omega\, r[/tex]. After updating the units, the angular velocity of this vehicle (the rate at which it turns) may also be found as:

[tex]\begin{aligned}\omega &= \frac{v}{r} \\ &\approx \frac{183.33\; \rm m \cdot \text{minute}^{-1}}{700\; \rm m} \\ &\approx 0.26\; \text{minute}^{-1}\end{aligned}[/tex].

[tex]-5x+3y = 10~~~~ .....(i)\\\\2x+5y =-35~~~ ....(ii)\\\\\text{Multiply equation (ii) by}~ \dfrac 35~ \text{ and do (ii) -(i)}\\\\\\\dfrac 35(2x+5y) - (-5x+3y) = \dfrac 35}(-35) - 10\\\\\implies \dfrac{6x}5 +3y + 5x -3y = -21-10 = -31\\\\\implies \dfrac{6x + 25x}5 = -31\\\\\implies 31x = -31 \times 5\\\\\implies x = -5\\\\\text{Substitute }~x=-5~ \text{in equation (ii):}\\\\2(-5) +5y =-35\\\\\implies -10 +5y = -35\\\\\implies 5y = -35 +10 = -25\\\\\implies y = - \dfrac{25}5 = -5[/tex]

[tex]\text{Hence,}~ \textbf{(x,y) = (-5, -5)}[/tex]

Answer:

At 1:40 pm you will reach the market.

Step-by-step explanation:

Distance (d) = 11 km

Average speed (v) = 3 km/h

Formula:

[tex] \rm Average \: speed = \dfrac{Distance}{Time} \\ \\ \rm 3 = \dfrac{11}{t} \\ \\ \rm t = \dfrac{11}{3} \\ \\ \rm t = 3 \frac{2}{3} \\ \\ \rm t = 3 hr \: 40min[/tex]

It will take 3 hours 40 minutes to reach the market.

So, if you set off for the market at 10 am you will reach market by 1:40 pm (10 am + 3hr 40min).

[tex]r = \sqrt{\dfrac{3V}{\pi h}}[/tex]

Step-by-step explanation:

Multiply both sides by 3 to get

[tex]\pi r^2h = 3V[/tex]

Then divide both sides by [tex]\pi h[/tex] and you'll get

[tex]r^2 = \dfrac{3V}{\pi h}[/tex]

To solve for r , you need to take the square root of both sides to get

[tex]\sqrt{r^2} = r = \sqrt{\dfrac{3V}{\pi h}}[/tex]

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, a ) and (x₂, y₂ ) = (9, - 4 )

m = [tex]\frac{-4-a}{9-6}[/tex] = [tex]\frac{-4-a}{3}[/tex]

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

2x - 3y = 6 ( subtract 2x from both sides )

- 3y = - 2x + 6 ( divide through by - 3 )

y = [tex]\frac{2}{3}[/tex] x - 2 ← in slope- intercept form

with slope m = [tex]\frac{2}{3}[/tex]

Parallel lines have equal slopes , then

[tex]\frac{-4-a}{3}[/tex] = [tex]\frac{2}{3}[/tex] , so

- 4 - a = 2 ( add 4 to both sides )

-a = 6 ( multiply both sides by - 1 )

a = - 6 → A

Answer:

Step-by-step explanation:

Answer:

a. 125

Step-by-step explanation:

the angle labeled "x" is supplementary with the angle that has a measure of 55°

Supplementary angles add up to equal 180°

This means that x + 55 must equal 180

Note that we've just created an equation that we can use to solve for x.

We now solve for x using the equation we just created.

x + 55 = 180

subtract 55 from both sides

x = 125

The answer is a

Answer:

the answer is

1. 11.33

2. 5.9

3. 8.1

Answer:

B = $140

Step-by-step explanation:

for part A, the graph is linear line with a Y intercept at (0,65) so this means that if you were to have no charms it would cost 65 dollars, since the y axis represents cost. then for every 1 increment on the x axis (number of charms) the Y value increases by 25 so the slope is [tex]\frac{25}{1}[/tex]

we also can conclude that there is no negative domain since you cannot have negative charms, and the range begins at 65 since you cannot get a bracelet for less money

for part B, y=25x+65

so for three charms, x is represented as 3 so y=25(3) +65 which is 75+65=y= $140

Answer:

2p/q

2q/p

q/p=2

p/q =2

Step-by-step explanation:

Here are some possible answers. The way your statement is formated in does not ask a question nor does it provide enough information for one to deduce what the question was.

Answer:

2,1,0,1,2

Step-by-step explanation:

Answer:

1/15

Step-by-step explanation:

2/3 x 1/10 = 2/30 or 1/15

Answer:

1/15

Step-by-step explanation:

Ratio:-

[tex]\\ \sf\longmapsto \dfrac{2}{20}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{10}[/tex]

[tex]\\ \sf\longmapsto 1:10[/tex]