Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side BC at point M. What is the length of MC?
16 mm
24 mm
32 mm
48 mm

Answer:

56 = (0.85)w

Step-by-step explanation:

"is" translates to "=".

"of" translates to "×".

We can let "what number" translate to "w".

Then ...

56 is 85% of what number . . . . translates to ...

56 = 0.85×w

_____

Of course, you know that 85% = 85/100 = 0.85.

[tex]\displaystyle x^{\frac{2}{3}}[/tex]

The rules of exponents tell you ...

... (a^b)(a^c) = a^(b+c) . . . . . . applies inside parentheses

... (a^b)^c = a^(b·c) . . . . . . . . applies to the overall expression

The Order of Operations tells you to evaluate inside parentheses first. Doing that, you have ...

... x^(4/3)·x^(2/3) = x^((4+2)/3) = x^2

Now, you have ...

... (x^2)^(1/3)

and the rule of exponents tells you to multiply the exponents.

... = x^(2·1/3) = x^(2/3)

Answer:

x^(2/3)

Step-by-step explanation:

(x^a.x^b)^c = x^[c*(a+b)]

using the above eqn, u can simplify the given expression to

x^[1/3*(4/3+2/3)]

=x^[1/3*(6/3)]

=x^(2/3)

ans is the 2nd choice

9 students did not study in either the cafeteria or the student lounge.

How to find the number

To find the number of students who did not study in either the cafeteria or the student lounge, we solve as follows

Let

C = 92

L = 86

C ∩ L = 40

We find the number in either C, L or C ∩ L

= (92 - 40) + (86 - 40) + 40

= 52 + 46 + 40

= 138

The number  did not study in either the cafeteria or the student lounge

= 147 - 138

= 9

Answer:

$6.40 because 32 ounces is the difference 128 and 96 hence 32 is 1/3 of 96 so divide $4.80 by 3 which is $1.60 then add $1.60 + $4.80 =$6.40

Step-by-step explanation:

Answer:

So the value of x=3  and y =3

Step-by-step explanation:

5x + 3i = 15 + yi

To find out x   , set the constant terms  equal to each other and solve for x

5x= 15

Divide by 5 on both sides

x= 3

To find out y   , set the ';i' terms  equal to each other and solve for y

3= y

So the value of x=3  and y =3

Answer:  The required value of x is 3 and that of y is 3.

Step-by-step explanation:  We are given to find the values of x and y that satisfies the following equation :

[tex]5x+3i=15+yi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

[tex]a+bi=c+di~~~~~~~~~\Rightarrow a=c,~b=d.[/tex]

That is, the real and parts on both sides of the equation are equal.

From equation (i), we have

[tex]5x+3i=15+yi.[/tex]

Equating the real and imaginary parts on both sides of the above equation, we get

[tex]5x=15\\\\\Rightarrow x=\dfrac{15}{5}\\\\\Rightarrow x=3[/tex]

and

[tex]3=y\\\\\Rightarrow y=3.[/tex]

Thus, the required value of x is 3 and that of y is 3.

Answer:

1: Simplify 15/20 to 3/4

y/4=3/4

Multiply both sides by 4

y=3/4×4

Simplify 3/4×4 to 12/4

y=12/4

Simplify 12/4 to 3

y=3

2: Multiply both sides by z-3

6=8/5(z-3)

Simplify 8/5(z-3) to 8(z-3)/5

8(z-3)/5

Multiply both sides by 5

6×5=8(z-3)

Simplify 6×5 to 30

30=8(z-3)

Divide both sides by 8

30/8=z-3

Simplify 30/8 to 15/4

15/4=z-3

Add 3 to both sides

15/4+3=z

Simplify 15/4+3 to 27/4

27/4=z Switch sides z=27/4

3 ft

The statue's height is 1.5 times the length of its shadow, so we expect the same relationship for the globe.

... 1.5 × 2 ft = 3 ft

_____

Comment on the problem

As a practical matter, with the sun high enough in the sky to cast a shadow shorter than the object's height, it will be quite difficult to measure the length of the shadow of the point at the top of the globe. The shadow of other parts of the globe will interfere.

Answer:

The distance from he ball to the goal is 11.85 feet (Approx) .

Step-by-step explanation:

As given

The angle of elevation from a soccer ball on the ground to the top of the goal is 34° .

If the goal is 8 feet tall.

Now by using the trigonometric identity .

[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]

As shown in the diagram given below

[tex]\theta = 34^{\circ}[/tex]

Perpendicular = AB = 8 feet

Base = BC

Put all the values in the identity .

[tex]tan\ 34^{\circ} = \frac{AB}{BC}[/tex]

[tex]tan\ 34^{\circ} = \frac{8}{BC}[/tex]

[tex]tan\ 34^{\circ} = 0.675\ (Approx)[/tex]

[tex]BC = \frac{8}{0.675}[/tex]

BC = 11.85 feet (Approx)

Therefore the distance from he ball to the goal is 11.85 feet (Approx) .

To calculate the distance from the soccer ball to the goal with an angle of elevation of 34 degrees and a goal height of 8 feet, use the tangent trigonometric ratio. The distance is found to be approximately 11.86 feet.

Given the angle of elevation is 34 degrees and the goal's height is 8 feet, we're looking to calculate the adjacent side (distance from the ball to the goal) in a right-angled triangle where the opposite side (goal's height) and the angle are known.

To calculate the distance (let's call it d), we use the tangent function:

So, d = 8/tan(34 degrees).

Calculating this, we find:

Therefore, the distance from the soccer ball to the goal is approximately 11.86 feet.

Answer:

x=0

Step-by-step explanation:

-0.2(x-20)=4-x

The first step is to distribute the -.2

-.2 x -.2 * -20 = 4-x

-.2x +4 = 4-x

Add x to each side

x-.2x +4 = 4-x+x

.8x +4 = 4

Subtract 4 from each side

.8x +4-4 = 4-4

.8x=0

Divide by .8

.8x/.8 = 0/.8

x =0

9.9 years

A = P(1 + rt) . . . . account balance after time t at rate r starting with principal P

... 3000 = 2500(1 + 0.0202t) . . . . filling in the given numbers

... 1.2 = 1 + 0.0202t . . . . divide by 2500

... 0.2 = 0.0202t . . . . . . subtract 1

... 0.2/0.0202 = t ≈ 9.901

It will take about 9.9 years for the account balance to reach $3000.

Answer:

B. -9/4 -4i

Step-by-step explanation:

Collect terms the way you would with any algebraic expression.

= (-3 +2 -3)i + (3/4 -3)

= -4i +(3/4 -12/4)

= -9/4 -4i

The product of the complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex] is [tex]\( 5 - 4i \)[/tex].

To find the product of two complex numbers, we multiply them as we would with binomials, remembering that [tex]\( i^2 = -1 \)[/tex]. Let's perform the multiplication step by step:

Given complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex], we multiply them directly:

[tex]\[(3 - 2i) \cdot (1 + i) = 3 \cdot 1 + 3 \cdot i - 2i \cdot 1 - 2i \cdot i. \][/tex]

Now, we simplify the expression by combining like terms and using the fact that [tex]\( i^2 = -1 \)[/tex]:

[tex]\[ = 3 + 3i - 2i - 2i^2 = 3 + i - 2(-1) = 3 + i + 2. \][/tex]

Finally, we combine the real parts and the imaginary parts:

[tex]\[ = (3 + 2) + i = 5 - 4i. \][/tex]

Therefore, the product of the complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex] is[tex]\( 5 - 4i \)[/tex].

Answer:

‪0.155922‬

Step-by-step explanation:

Answer: 0.1562 kilograms

Step-by-step explanation: To convert 5.5 ounces into kilograms, we first convert 5.5 ounces into grams using the conversion factor 1 oz = 28.4 g.

Since we are going from a larger unit "ounces" to a smaller unit "grams" we multiply 5.5 by the conversion factor which is 28.4 to get 156.2.

This means that 5.5 ounces is equal to 156.2 grams.

Next, we convert 156.2 grams into kilograms using the conversion factor

1 kilogram = 1,000 grams. Since we are going from a smaller unit "grams" to a

larger unit "kilograms" we divide 156.2 by the conversion factor which is 1,000

and we get 0.1562 kilograms.

Therefore, 5.5 ounces is equal to approximately 0.1562 kilograms.

See the attachment for a labeled graph.

_____

I find it convenient to use "technology" to draw the graph. A spreadsheet, graphing calculator, or on-line graphing program can do this for you.

ANSWER:

Your answer is the 3rd one: y - 8 = -3/7(x - 5)

ABOUT POINT SLOPE FORM:

ABOUT PROBLEM:

y - Y1 = m (x - X1)

y - 8 = -3/7(x - 5) --- IN POINT SLOPE FORM

Hope this helps you!!! :)

The line with a slope -3/7 and passes through the point (5, 8) has an equation of y - 8 = (-3/7)(x - 5)

The equation of a straight line is given by:

y = mx + b;

where y,x are variables, m is the slope of the line and b is the y intercept.

Since the line has a slope -3/7 and passes through the point (5, 8), the equation of the line is:

[tex]y-y_1=m(x-x_1)\\\\y-8=-\frac{3}{7} (x-5)[/tex]

Hence a line with a slope -3/7 and passes through the point (5, 8) has an equation of y - 8 = (-3/7)(x - 5)

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Answer:

The cost of the wristband for 8 rides is $35.

Step-by-step explanation:

The expression for the cost, C, for r rides is

C = 2.5r + 15

Since she wants to go on 8 rides, r is 8.

Substitute r with 8 in the cost equation and evaluate it.

C = 2.5r + 15

C = 2.5 * 8 + 15

C = 20 + 15

C = 35

The cost of the wristband for 8 rides is $35.

2

Solve the second equation for y.

... 8x -12 = 4y . . . . add 4y -12

... 2x -3 = y . . . . . . divide by the coefficient of y

The coefficient of x is 2, so a parallel line will have an x-coefficient of 2. The line ...

... y = 2x -6 . . . . . . . . m = 2

will be parallel to the given line, so will not intersect it.

Using the smallest number she has, 9 daisies..

18/9 = 2

45/9 = 5

She can make 9 bouquets with 2 roses, 1 daisy and 5 tulips in each.

That means each bouquet would have 8 total flowers.

The correct option is the last:

[tex] a_n = -2a_{n-1}+1 [/tex]

In fact, every term in the sequence is one more than twice the opposite of the previous one:

We start with 3. Twice its opposite is -6. Plus one, we get -5.

We start with -5. Twice its opposite is 10. Plus one, we get 11.

We start with 11. Twice its opposite is -22. Plus one, we get -21.

The recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

To find a recursive formula for the given sequence, we need to determine the relation between consecutive terms.

Let's denote the sequence as an, where:

[tex]a_1 = 3\\a_2 = -5\\a_3 = 11\\a_4 = -21\\[/tex]

First, let's calculate the differences between consecutive terms:

[tex]a_2 - a_1 = -5 - 3 = -8\\a_3 - a_2 = 11 - (-5) = 16\\a_4 - a_3 = -21 - 11 = -32[/tex]

We observe that each difference is a multiple of 8 and that each difference is twice the previous difference but with alternating signs.

The recursive formula can be defined as:

[tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

Thus the recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

2/5

There are 2 units of green and 5 units of "pink," so the ratio is ...

... green/pink = 2/5

Answer :

The proof is as follows :

Step-by-step explanation:

Let NC = x

⇒ AB = 3x and AN = 2x

In Δ ABN, By using Pythagoras theorem,

AB² = BN² + AN²

⇒ BN² = AB² - AN²

⇒ BN² = (3x)² - (2x)²

⇒ BN² = 5x²

⇒ BN = x√5  .......................(1)

Now in ΔANC , Using Pythagoras theorem We have,

AC² = NC² + AN²

⇒ AC² = x² + (2x)²

⇒ AC² = 5x²

⇒ AC = x√5   ....................(2)

From equations (1) and (2) We get,

AC = BN , which is our required result

Answer:

BN=AC=√5 x.

The proof is explained in step-by-step explaination.

Step-by-step explanation:

Let NC=x. It is given that AB=3NC & AN=2NC

⇒ AB=3x & AN=2x

By applying Pythagoras theorem

In triangle ANC,

[tex]AC^{2}=AN^{2}+NC^{2}[/tex]

⇒ [tex]AC^{2} = (2x)^{2}+x^{2}[/tex]

⇒ [tex]AC^{2}=4x^{2}+x^{2} =5x^{2}[/tex]

⇒ [tex]AC=\sqrt{5}x[/tex]   →    (1)

Similarly, In triangle ABN,

[tex]AB^{2}=AN^{2}+BN^{2}[/tex]

⇒ [tex](3x)^{2}=BN^{2}+x^{2}[/tex]

⇒ [tex]9x^{2} = (BN)^{2}+4x^{2}[/tex]

⇒ [tex]BN^{2}=5x^{2}[/tex]

⇒ [tex]BN=\sqrt{5}x[/tex]   →   (2)

From eq (1) & (2),    AC=BN

Answer:

19

Step-by-step explanation:

b - 7 = 12

b = 7 + 12

b = 19

Hi there! :)

Answer:

b=19

*The answer must have a positive sign.*

Step-by-step explanation:

First, you add by 7 from both sides of an equation.

[tex]b-7+7=12+7[/tex]

Then, you add by the numbers from left to right.

[tex]12+7=19[/tex]

Final answer is b=19

I hope this helps you!

Have a nice day! :)

:D

-Charlie

Thank you so much! :)

1/3, 1/4, 1/5

40% = 40/100 = 2/5

Any fraction with a numerator of 2 and a denominator larger than 5 will be less than 40%, for example.

So, we can choose 2/6 = 1/3, 2/8 = 1/4, and 2/10 = 1/5 as some such values.

_____

We could also choose something like 39.99% = 3999/10000, or 1% = 1/100.

Answer:

the set of all points between point F and point G, including point F and point G

Step-by-step explanation:

The definition of a line segment is the set of points on a line between two given end points, including those end points. The best description is the one that matches the definition.

Answer:

the set of all points between point F and point G, including point F and point G

Step-by-step explanation:

Answer:

A = 4200 ft^2

Step-by-step explanation:

We know the formula for area is

A = l*w

We need to have the same units

convert yd to ft

1 yd = 3ft

Multiply each by 70

70 yds = 210 ft

A = 210 *20

A = 4200 ft^2

The area of the pavement section is 4200 square feet, computed by converting the length to the same unit as the width and multiplying width by length.

The subject of this question is the calculation of the area of a rectangle. The rectangle in question is a section of pavement with a width of 20 ft and a length of 70 yd. Before calculating, it's important to have the measurements in the same units. Converting 70 yards to feet (since 1 yard equals 3 feet) we get 210 feet. The formula to calculate the area of a rectangle is Area = Width x Length. Substituting the given values into the formula, we get: Area = 20 ft x 210 ft which equals 4200 square feet. Therefore, the pavement section's area is 4200 square feet.

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Final answer:

After converting their completion fractions to decimal form, Jose finished more of the race than Jenna after 30 minutes, with Jose at 2/3 (approximately 0.6667) and Jenna at 7/12 (approximately 0.5833).

Explanation:

Jose and Jenna competed in a bike race. After 30 minutes, Jose had finished 2/3 of the race, and Jenna had finished 7/12 of the race. To determine who had finished more of the race, we can compare these two fractions by finding a common denominator or converting them to decimal form.

First, let's convert them to decimal form:

2/3 is approximately 0.6667

7/12 is approximately 0.5833

Comparing the decimal values, we can see that Jose's completion (0.6667) is greater than Jenna's (0.5833). Therefore, Jose had finished more of the race after 30 minutes.

Answer:

AE

Step-by-step explanation:

Pairs of letters identify line segments:

... AE, EG, AG

... AD, DE, AE

Segment AE is common to both lists.

The number of rooms booked to produce maximum revenue is required.

The number of rooms booked to produce the maximum revenue is 250.

The revenue function is

[tex]R(x)=200x-0.4x^2[/tex]

Differentiating with respect to x we get

[tex]R'(x)=200-0.8x[/tex]

Equating with zero

[tex]0=200-0.8x\\\Rightarrow x=\dfrac{-200}{-0.8}\\\Rightarrow x=250[/tex]

Double derivative of the function is

[tex]R''(x)=-0.8x[/tex]

Substituting the value of [tex]x=250[/tex]

[tex]R''(250)=-0.8\times 250=-200[/tex]

Since, it is negative the maximum value of x will be 250.

The number of rooms booked to produce the maximum revenue is 250.

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The number of rooms that produces the maximum revenue for Fred's Estates LLC is 250 rooms, calculated using the formula -b/2a, where a and b are the coefficients of the quadratic revenue function.

To calculate the maximum revenue for Fred's Estates LLC, we need to find the value of x that maximizes the function [tex]R(x)=200*-0.4x2.[/tex]

The maximum value of a quadratic function can be found using the formula -b/2a, where a and b are the coefficients of x² and x in the function. Here, a=-0.4 and b=200.

Using the formula, [tex]x=-b/2a = -200/(2*(-0.4)) = 250[/tex] rooms. Therefore, booking 250 rooms results in the maximum revenue for Fred's Estates LLC.

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Answer:

2

Step-by-step explanation:

1/2 cup = 2/4 cups = 2 × 1/4 cup

Alonzo can make 2 batches that each require 1/4 cup.