60. Cities A and B are on the same east-west line.
Assume that city A is located at the origin. If the
distance from city A to city B is at least 100 miles
and x represents the distance from city B to city A,
express this using absolute value notation.

Answer:

Step-by-step explanation:

Both triangles are similar by SAS property,

that means corresponding sides are proportional,so,

5/6 = 15/N

= 6/5 = N/15

N = (6×15)/5

N = 6×3

N = 18

Answer:

Step-by-step explanation:

Is there a graph or more information?

Answer:

Check the first box, third box and fifth box

Explanation:

1st box:

Rewrite the fraction: 48

- ----

17

Check equivalency: True

Answer: True

2nd box:

Check equivalency: False

Answer: False

3rd box:

Convert the improper fraction into a mixed number:

2 × 17 + 14

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

17

Calculate the product or quotient: 34 + 14

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

17

Calculate the sum or difference: 48

- ----

17

Check equivalency: True

Answer: True

4th box:

Rewrite the fraction: 17

----

48

Check equivalency: False

Answer: False

5th box:

Rewrite the fraction: 48

- ----

17

Check equivalency: True

Answer: True

I hope this helps!

The reason that this represent in Mikal’s proof regarding the triangle is SAS.

It should be noted that a triangle is a shape that has three sides and angles.

The SAS implies the side angle side. It shows that any two sides and angles that are included between the sides of an angle are equal to the other two sides.

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Answer:

AAS

Step-by-step explanation:

2022 edge

The approximate solution of the above equation is: 55/15 (Option A). This is solved using the quartic formula, not quadratic equation.

The quartic formula has up to four various solutions including real and imaginary numbers. Read on for more explanation.

First we restate the above equation:

x²-3x+2= √(x-2) + 2

Next we remove square roots

[tex]x^{4}[/tex] - 6x³ + 9x² = x - 2

Add two to both sides

→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x - 2 +2

→  [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x

Subtract X from both sides

→  [tex]x^{4}[/tex] - 6x³ + 9x²+2 -x = x -x

→  [tex]x^{4}[/tex] - 6x³ + 9x²+2 - x= 0

Using the Quartic formula to solve the fourth order equation:
a[tex]x^{4}[/tex] + bx³ + cx² + dx + e

The resolution of x is given as:

x = 2.691085, 3.346753

Because the fraction nearest to 3.4 is 55/16

hence, the correct answer is Option A.

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The two triangles are similar by SSA similarity. Option B is correct.

A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.

If the ratio of the sides are same as well as the one angle is common between the two triangles then in that condition there will be SSA similarity.

From the triangle ABC and DEC

The ratio of the sides is;

[tex]\rm \frac{10}{12}= \frac{8}{9.6} \\\\ \frac{5}{6}= \frac{5}{6}[/tex]

One angle c is common in the two triangles.

The two triangles are similar by SSA similarity.

Hence, option B is correct.

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Answer:

sin D = 28/53

Step-by-step explanation:

sin D = opp/hyp

For angle D, the opposite leg is FE with length 28.

The hypotenuse is DE with length 53.

sin D = 28/53

Answer: sinD=28/53.

Step-by-step explanation:

[tex]sinD=\frac{FE}{DE} =\frac{28}{53} .[/tex]

Answer:

[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]

Step-by-step explanation:

So the slope-intercept form is given as: y=mx+b where m is the slope and b is the y-intercept (since if you plug in 0 as x, mx will be 0 leaving only b). You can calculate the slope with the slope formula: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] which is essentially [tex]\frac{rise}{run}[/tex]. So for this example (-8, -8) will be ([tex]x_1, y_1[/tex]) and (7, 9) will be ([tex]x_2, y_2[/tex]).

Plug values into equation:

[tex]\frac{9 - (-8)}{7 - (-8)}[/tex]

cancel out negatives

[tex]\frac{9+8}{7+8}\\[/tex]

Simplify

[tex]\frac{17}{15}[/tex]

The fraction is in the most simplified form unless you want to have a mixed fraction, otherwise you can't do anything else to the fraction.

so now we have the slope we have one part of the equation: [tex]y=\frac{17}{15}x + b[/tex], but now we need to solve for b. This can be done by using either of the points and plugging in x and y, but for this example I'll use (7, 9).

Plug in (7, 9) as (x, y)

[tex]9 = \frac{17}{15}(7) + b[/tex]

Multiply

[tex]9 = \frac{119}{15}+b[/tex]

Subtract

[tex]9-\frac{119}{15}=b[/tex]

Rewrite 9 as a fraction

[tex]\frac{135}{15} - \frac{119}{15} = b[/tex]

Subtract numerators

[tex]\frac{16}{15} = b[/tex]

now we have both pieces of information

[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]

Okay, first you need to understand that function of x, (or f(x)) is y.

We now plug in x.

f(-2) or y=-2(3)+(2•2)+4(-2)+8
f(-2)=-6+4+-8+8

f(-2)=-2

When x=-2, y=-2. Lets plug it back in to see if its true.

-2=-2(3) + (2x2) + (4(-2)) + 8

-2 = -6 + 4 + -8 + 8

-2 = -2.

Heart if it helps, comment if you need help.

The distance travelled by the train with constant speed of r miles will be 3r.

We know the formula of distance linking the speed and the time.

Distance = speed × time

Substituting the given values to get:

Distance = r × 3

Distance = 3r

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Answer:

72

Step-by-step explanation:

9×8 = 72 which means that 72 is a multiple of 9 lying between 60 and 80.

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Answer:

6 StartRoot 3 EndRoot units

Step-by-step explanation:

The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

The figure ABCD reflected over the y-axis followed by a translation to the left by 2 unit to form figure A'B'C'D'

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Answer:

14641

Step-by-step explanation:

[tex]formular \: for \: the \: digits \: in \: each \\ row \: of \: a \: pascal \: triangle \: is \: = 11 {}^{n} \\ row \: 0 = \: 11 {}^{0} = 1 \: \\ row \: 1 \: = 11 {}^{1} = 11 \\ row \: \: 2 \: = 11 {}^{2} = 121 \\ row \: 3 = \: 11 {}^{3} = 1331 \\ row \: 4 = 11 {}^{4} = 14641 \\ therefore \: the \: fourth \: row \: is \: 14641[/tex]

The explicit formula for the sequence is an = 5 + (n - 1)(-4)

The formula for calculating the nth term of an arithmetic sequence is expressed as:

an = a + (n - 1)d

where

a is the first term

d is the common difference

n is the number of terms

From the given data

a = 5

a2 = a1 - 4

a2 = 5 - 4

a2. = 1

d = a2 - a

d = 1 - 5

d = -4

Substitute

an = 5 + (n - 1)(-4)

Hence the explicit formula for the sequence is an = 5 + (n - 1)(-4)

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The radius of the circular cross-section of the can of soup is; 3.4cm.

Since, the can has a height of 10cm and the volume of the can is 363cm³, it follows that the area of the circular cross-section can be evaluated as;

A = 363/10 = 36.3cm²

Hence, it follows that the radius can be evaluated as follows;

36.3 = 3.14 × r²

r² = 36.3/3.14

r² = 11.56

r = 3.4cm

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Answer: [tex]5(3)^{n-1}[/tex]

Step-by-step explanation:

The common ratio is 15/3 = 5.

The first term is 3.

So, the explicit rule is [tex]5(3)^{n-1}[/tex]

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Using the given linear function of best-fit, the most likely approximate height of the plant after 8 weeks would be of 7.4 centimeters.

A linear function is modeled by:

y = mx + b

In which:

The line of best-fit goes through points (0,1) and (5,5). Point (0,1) means that the y-intercept is of b = 1. The slope is given as follows:

m = (5 - 1)/(5 - 0) = 4/5 = 0.8.

Hence the equation that gives the approximate height after x weeks is:

y = 0.8x + 1.

After 8 weeks, the expected height is:

y = 0.8 x 8 + 1 = 6.4 + 1 = 7.4 centimeters.

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Step-by-step explanation:

1. multiply by 8

2. divide by 2

Answer:

4096, 125

Step-by-step explanation:

In the first sequence, notice that each term increases by a factor of 8 (multiplied by 8 each time). Therefore, the fourth term would be 64*8 = 512, so the fifth term is 512*8 = 4096.

In the second sequence, each term decreases by a factor of 2 (divided by 2 each time). The fourth term would be 500/2 = 250, so the fifth term is 250/2 = 125.

Answer:

[tex]a = 18 \sqrt{3} [/tex]

[tex]c = 36[/tex]

Answer:

The answer is a since non of the other answer would go throught that point

Hope This Helps!!!

Answer:

[tex] \pink{ \rule{1pt}{3000000pt}}[/tex][tex] \red{ \rule{1pt}{3000000pt}}[/tex][tex] \purple{ \rule{1pt}{3000000pt}}[/tex]

can I get your number personally

Answer:

D. 2730

Step-by-step explanation:

I just had this question on FLVS yesterday.
you use factorials for this:

15!/12!

15*14*13*12!/12!

15*14*13

2730

Number of ways in which 3 positions can be filled are 2730.

The number of ways in which objects from a set may be selected, generally without replacements, to form subsets. This selection of subset is called permutation when order of selection is a factor.

If n things taken r at a time and n!  = n × (n-1) × (n-2) × (n-3)..........3 × 2 × 1

⇒Permutation,

                              [tex]P(n,r) =\frac{n!}{(n-r)!}[/tex]

Now it is given that number of candidates, n = 15

and number of position, r = 3

Hence number of ways positions can be filled-

                           [tex]P(n,r) =\frac{15!}{(15-3)!}[/tex]

⇒                         [tex]P(15,3) =\frac{15!}{12!}[/tex]

⇒                         P(15,3) =  (15 × 14 × 13)12!/12!

⇒                         P(15,3) =  (15 × 14 × 13)

⇒                         P(15,3) =  2730

∴ Number of ways in which 3 positions can be filled are 2730.

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Find length CD first, which is the hypotenuse of the triangle.

PD = opposite

Opposite & hypotenuse = SOH or sin

Sin(27) = 15/H

x h, then ÷ sin(27)

H = 15/sin(27)

H = 33.04....

Move to triangle CDR:

15 is length opposite the angle we're after.

So far, we've got the hypotenuse (which we just found to be 33.04....) & the opposite of our triangle

Hypotenuse & opposite = SOH

Sin(x) = 15/33.04... but, to find the angle we do inverse of sin

sin-1(15/33.04...) = x

x = 27

(33.04... means I used the full numbers displayed on my calculator)

Thus, RCD is 27 degrees

Hope this helps!

The dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.

Given that the length of the previous deck = 15 feet

The width of the previous deck = 12 feet

Since the new deck will add 5 feet to the length and 4 feet to the width,

The length of the new deck = 15 + 5 = 20 feet

The width of the new deck = 12 + 4 = 16 feet

Also given that a drawing of the new deck uses a scale of 1 inch = 2.5 feet.

So, The length of the deck in the drawing = 20/2.5 inches = 8 inches

The width of the deck in the drawing = 16/2.5 inches = 6.4 inches

Therefore, the dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.

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Answer: 11

Step-by-step explanation:

By the secant-secant theorem,

[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]