in the multiplication example shown different letters represent different digits find the value of a and of b

The length of the arc KL in the given circle is 3.49 units

In a circle whose radius is R, the length of an arc defined by an angle x is given by:

Length = (x/360)*2*3.14*R

Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:

Length = (100/360)*2*3.14*2

Lenght = 3.49 units.

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Answer:

\( \frac{x + 8}{ {x}^{2} } \div \frac{2x + 16}{ {2x}^{2} } \\ \frac{x + 8}{ {x}^{2} } \times \frac{ {2x}^{2} }{2x + 16} \\ = \\ \frac{2}{x + 2} \)

The polygons are not similar because they do not have a constant similarity ratio

From the question, we have the following parameters that can be used in our computation:

The polygons

To check if the polygons are similar, we divide corresponding sides and check if the ratios are equal

So, we have

Scale factor = 150/100 = 151/100

Scale factor = 1.5 = 1.51 --- false

Hence, the polygons are not similar

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Answer:

bet

Step-by-step explanation:

The price should be higher than the AVC and ATC in order to make a profit in the short term. Therefore, in order to achieve the requisite profit, the MR curve must rise above cost = 7.

When businesses in a cutthroat sector start making money, it opens the door for more businesses to enter the market, which leads to a shift to the right in the supply curve, a drop in price, and the return of all businesses to a state of no economic profit.

If the market price is lower than the average total cost, a company will experience positive economic profit in the short term.

In the short run, a monopolistically competitive firm optimises profits or avoids losses by producing the amount where marginal revenue equals marginal cost. If the average total cost is less than the market price, the company will make a profit.

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Answer: 6

Step-by-step explanation:

x=1

=> 3.1 + y=9

=>y=9-3=6

or

y=-4.1+10

y=-4+10=6

Hello!

\(\Large \underline{\textbf{\sf We~ know:}}\\\\\sf x = 1\\\\3x + y = 9\\\\y = -4x + 10\\ \\\\\Large \underline{\textbf{\sf We~ search:}}\\\\The~ value ~of~ y\\\\\\\Large \underline{\textbf{\sf We~ solve:}}\\\\\\\)

\(\sf 3x + y = 9\\\\3*1 + y = 9\\\\3 + y = 9\\\\y = 9 - 3\\\\\boxed{\sf y = 6}\)

\(\Large \underline{\textbf{\sf We~ verify:}}\\\\\sf 3x + y = 9\\\\3*1 + 6 = 9\\\\\\\\\sf y = -4x + 10\\\\-4*1 + 10 = 6\\\\\\\Large \underline{\textbf{\sf Conclusion:}}\\\\\)

\(\sf In ~this ~system ~of~ equations,~the ~value ~of ~x~ is ~1~and~the~value~of~y~is~6.\)

200 people invested in neither stocks nor bonds for retirement.

The inclusion-exclusion principle is a counting method used to determine the size of a set created by joining two or more sets. It is predicated on the notion that if we just sum the set sizes, we can wind up counting certain components more than once (the elements that are in the intersection of the sets). We deduct the sizes of the sets' intersections from the sum of their sizes to prevent double counting.

The total number of people who invested in stocks are:

Total = Stocks + Bonds - Both

Total = 700 + 400 - 300

Total = 800

Using the inclusion- exclusion principle:

neither = Total surveyed - Total

neither = 1000 - 800 = 200

Hence, 200 people invested in neither stocks nor bonds for retirement.

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Answer:

A' (7,7)

B' (10,4)

C' (6,5)

Step-by-step explanation:

Add 9 to every x value and 3 to every y value.

Answer:

A'(7,7)

B'(10,4)

C'(6,5)

Step-by-step explanation:

⭐What is a translation?

⭐What is the translation notation?

The problem tells us to translate ΔABC 9 units to the right, and 3 units up because it is inside the <>, and the numbers are positive.

To translate the vertices of ΔABC, we have to add the respective x and y coordinates of the translation rule to each vertecie of ΔABC.

A(-2,4):

B(1,1):

C(-3,2):

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Answer:

volume of the solid = \(\frac{\pi }{3}\)

Step-by-step explanation:

As given , the region : |x| + |y| \(\leq\) 1

when y \(\geq\) 0 ,

|x| + y = 1

⇒|x| = 1 - y

when y ≤ 0 ,

|x| - y = 1

⇒|x| = 1 + y

The given region is the rectangle with sides (0, 5) , (0, -5), (5, 0), (-5, 0)

As given , the vertical cross section are semicircle

As we know that the area of semi circle  = \(\frac{1}{2}\)\(\pi x^{2}\)

Now,

Volume = \(\int\limits^0_-1 {\frac{\pi }{2} (1+y)^{2} } \, dy\) + \(\int\limits^1_0 {\frac{\pi }{2} (1-y)^{2} } \, dy\)

            = \(\frac{\pi }{2} (\frac{(1+y)^{3} }{3} )\) - \(\frac{\pi }{2} (\frac{(1-y)^{3} }{3} )\)

           = \(\frac{\pi }{6}\)[1-0] - \(\frac{\pi }{6}\)[0-1]

           = \(\frac{\pi }{6} + \frac{\pi }{6} = 2\frac{\pi }{6} = \frac{\pi }{3}\)

⇒volume of the solid = \(\frac{\pi }{3}\)

Volume of the solid is the value of the capacity of the object that can be hold by it. Thus the value of the volume of the given solid is,

\(V=\dfrac{\pi}{3} \)

The vertical cross sections of the solid is perpendicular to the y-axis.

The region of the base is,

\(|x|+ |y|\leq 1\)

Volume of the solid is the value of the capacity of the object that can be hold by it.

When the value of the variable y is greater than or equal to zero than the value of the x is,

\(|x|=1-y\)

When the value of the variable y is less than or equal to zero than the value of the x is,

\(|x|=1+y\).

Given inequality makes a square with the corners (1,0), (0,1),(-1,0),(0,-1).

Now the limit for the given solid is between 0 to 1 and area is equal to the semicircle which is,

\(A=\dfrac{\pi x^2}{2} \)

Thus the volume of the solid whose area bounded by the region 1 to -1 and vertical cross section is semicircle can be given as,

\(V=\int\limits^1_0 {\dfrac{\pi x^2}{2} } \, dx \)

\(V=\dfrac{\pi}{2} [\;\;\int\limits^1_0 {(1+y)^2} \, dy +\int\limits^1_0 {(1-y)^2} \, dy ]\)

\(V=\dfrac{\pi}{2} [\;\;\dfrac{\int\limits^1_0 {(1+y)^3}}{3} \, +\dfrac{\int\limits^1_0 {(1-y)^3} \, }{3} ]\)

\(V=\dfrac{\pi}{6} [\;\;\ {(1-0)^3} \, +{(0-1)^3} \, ]\)

\(V=\dfrac{\pi}{3} \)

Thus the value of the volume of the given solid is,

\(V=\dfrac{\pi}{3} \)

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Answer:

loan amount  = $307,000

Step-by-step explanation:

given data

monthly payment = $1,980

monthly loan constant = 6.45

to find out

loan amount

solution

we get here loan amount that is express as

loan amount = ( monthly payment ÷ monthly loan constant ) × 1000 .........1

put here value

loan amount = ( 1980 ÷ 6.45 ) × 1000

loan amount  = $307,000

Answer:

we need a picture of the problem

Step-by-step explanation:

Answer:

20/4

Step-by-step explanation:

5 = x/4

mulitply both sides by 4

x = 20

so the fraction is 20/4

Answer:

The first one

The area of the forest would decrease to 1360 km²

Divide the value of an investment at the end of the period by its value at the beginning of that period. Raise the result to an exponent of one divided by the number of years. Subtract one from the subsequent result. Multiply by 100 to convert the answer into a percentage.

Given here, an area of 2100 km² and each year it decreases by 4.25%

in the first year, the area of the forest becomes  (2100 - 4.25/100 × 2100)                                            

                                                                               = 2010.75 km²

in the second year, the area becomes 2100 × (1-4.25/100)²

                                                                       = 1925.29 km²

similarly, in the tenth year, the area becomes 2100 ×  ( 1-  4.25/100)¹⁰

                                                                         =  1360 km²

Hence, the area of the forest reduces to  1360 km²

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Answer:

Step-by-step explanation:

5.

26 red cards in a 52-card deck so 3 red cards combo = 26*25*24 = 15600

6.

4 aces in a deck so 3 aces = 4*3*2 = 24

7.

12 face cards in a deck so 3 face cards = 12*11*10 = 1320

8.

13 hearts in a deck so 3 hearts = 13*12*11 = 1716

9.

4 kinds in a deck: spade, heart, diamond and club so 3 of one kind = 4*1716

= 6864

Answer:

Step-by-step explanation:

5. half deck are red; 2nd card is 1 less n 3rd card 2 less: 26x25x24 = 15600

6. 4 aces total: 4x3x2 = 24

7. 3 face cards per suit; 12 total: 12*11*10 = 1320

8. 13 heart cards: 13x12x11 = 1716

9. 4 suits: 1716x4 = 6864

Answer:

Step-by-step explanation:

(-4 -7)/(-6+4)= -11/2

y + 4 = -11/2(x + 6)

y + 4 = -11/2x - 33

y = -11/2x - 37

The equation of the line is y = x.

To find the equation of a line given its graph, you need to follow the steps below.

Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.

Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.

Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.

Example:Let's say you are given the graph of a line below: .

Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.

Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.

Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.

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Answer:

Josiah can jog 5/6 mile in 15 min. Find his average speed in miles per hour

Answer:ANSWER FOR `1

Step-by-step explanation:

To determine the intervals of concavity for the graph of f(x) = 2 sin x - cos 2x on the interval [0, 2), we must find its second derivative and test the sign.

The first derivative of f(x) is given by:

f'(x) = 2cos x + 2sin 2x

The second derivative of f(x) is given by:

f''(x) = -2sin x + 4cos 2x

For the interval [0, 2), we can determine the sign of f''(x) and hence the concavity of f(x) as follows:

When sin x > 0 and cos 2x < 0, f''(x) < 0, so the graph is concave down.

When sin x < 0 and cos 2x > 0, f''(x) > 0, so the graph is concave up.

Next, to find the point on the curve y = 2x^2 - 7x + 6 closest to the point (0, 2), we can use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) = (0, 2) and (x2, y2) = (x, 2x^2 - 7x + 6).

Differentiating d with respect to x and setting it equal to zero, we can find the x-coordinate of the closest point.

Note: To complete this task, knowledge of multivariable calculus and optimization techniques is required.

Step-by-step explanation:

To compare the two amounts of fabric, we need to express them with a common denominator:

15/2 = 30/4

7 1/2 = 15/2

Now we can compare the two amounts:

30/4 > 15/2

This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.

Therefore, Ms. Thompson needs more red fabric than silver fabric.

Answer:

John sells candy at the lowest price.

Step-by-step explanation:

If John sells 6 candies at 10$, then that's what's called a ratio between the price and the candy. We can double the amount of candy and the price to $20 for each 12 candies, $30 for 24, $40 for 36, etc. But it would still maintain the ratio of 6 candies for each 10$. Adam however, sells candy at 13 pieces for $20. We can divide the ratio down to 6.5 candies for 10$. But since we "can't" split a candy in half, we'll round it to 7 pieces for 10$, which costs more than 6 for 10$: Therefore, John sells candy at the lower price.

Answer:

\(BC=5.1\)

\(B=23^{\circ}\)

\(C=116^{\circ}\)

Step-by-step explanation:

The diagram shows triangle ABC, with two side measures and the included angle.

To find the measure of the third side, we can use the Law of Cosines.

\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)

In this case, A is the angle, and BC is the side opposite angle A, so:

\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)

Substitute the given side lengths and angle in the formula, and solve for BC:

\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-42\cos 41^{\circ}\)

\(BC^2=58-42\cos 41^{\circ}\)

\(BC=\sqrt{58-42\cos 41^{\circ}}\)

\(BC=5.12856682...\)

\(BC=5.1\; \sf (nearest\;tenth)\)

Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:

\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)

Substitute the values of the sides and angle A into the formula and solve for the remaining angles.

\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)

Therefore:

\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)

\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)

\(B=22.5672442...^{\circ}\)

\(B=23^{\circ}\)

From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):

\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)

\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)

\(180^{\circ}-C=63.5672442...^{\circ}\)

\(C=180^{\circ}-63.5672442...^{\circ}\)

\(C=116.432755...^{\circ}\)

\(C=116^{\circ}\)

\(\hrulefill\)

Additional notes:

I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.

Answer:

x=24

Step-by-step explanation:

180-96=84

2x+x+12=84

3x+12=84

3x=72

x=24

Answer:

x=24°

Step-by-step explanation:

180-96=84

2x+x+12=84

3x+12=84

-12 -12

3x=72

3x/3=72/3

x=24

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Answer:

  D.  1

Step-by-step explanation:

The total of the listed costs is ...

  $545 +1975 +675 = $3195

The difference between this amount and the amount of Jose's check is presumed to be for the purchase of points. That difference is ...

  $4645 -3195 = $1450

As a percentage of the purchase price, that is ...

  $1450/$145,000 × 100% = 1%

A "point" is 1% of the loan amount, so the $1450 excess over the listed costs appears to be for the purchase of 1 point.

Answer:

The vertical distance between Dan and Jeff is of 26 feet.

Step-by-step explanation:

Diver Dan enjoys scuba diving. He dives to 34 feet below the surface of a lake.

His position is -34 feet.

His friend Jump in Jeff dives to 40 feet below the surface, but then descends 20 feet.

Dives to 40 feet, and descends 20 more feet. So

-(40 + 20) = -60

What is the vertical distance between Dan and Jeff?

|-34 - (-60)| = |-34 + 60| = 26

The vertical distance between Dan and Jeff is of 26 feet.

Answer:

\( = 5 \times 6 + 6 + 6 - 12 \times 2 \\ = 30 + 6 + 6 -24 \\ = 42 - 24 \\ = 18\)

Answer:

Mixed number form: 2 2/9  Decimal form: 2.2 (with a line over the second 2 it means it repeats its self for infinity) Exact form: 20/9

Step-by-step explanation:

-2 1/9- (-4 1/3)

Find a common denominator

-2 1/9 - (-4 3/9)

= 2 2/9

The length of m is 15.6 cm.

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

113/7.5

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well, the profit is clearly just 490 - 350 = 140.

Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)