Douglas runs 4 1/4 miles each day.About how many miles does he run in seven days?Please show your work.

Answers

Answer 1

[tex]4 \frac{1}{4} \times 7 = 28 \frac{3}{4} [/tex]

Related Questions

What is the perimeter, in feet, of the polygon?

Answers

You are given the length of every side, except for two, that can be easily derived from the others:

The long horizontal side on top is the sum of the three beneath it, so it is [tex] 22+18+14=54 [/tex]The vertical one on the right is, similarly, the sum of the opposite side to the far left, and the two small sides near it: [tex] 15+5+5=25 [/tex]

The sum of all sides, including these two, will give you the perimeter of the polygon.

The perimeter of the polygon is determined as P = 210 feet.

Given data:

The polygon of the perimeter is the total side length of all the sides of the polygon.

Let the perimeter be represented as P.

From the attached figure of the polygon:

P = ( 15 + 22 + 10 + 18 + 10 + 14 + 5 + 16 + ( 15 + 5 + 5 ) + 16 + 5 + ( 14 + 18 + 22 )

On simplifying the equation:

P = 210 feet

So, the value of P is 210 feet.

Hence, the perimeter is 210 feet.

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Parker and Company pays Selma Stokes on a variable commission scale. In a month when Selma had net sales of $155,000, what was her Gross Pay based on the following scale?

Net Sales Commission Rate
Up to $40,000 5%
Excess of $40,000 to $75,000 5.5%
Excess of $75,000 to $100,000 6%
More than $100,000 7%

Answers

Answer:

$9275

Step-by-step explanation:

Selma earns 5% on the first $40,000, which is $2000.

She earns 5.5% on the next $35,000, which is $1925.

She earns 6% on the next $25,000, which is $1500.

And she earns 7% on the last $55,000 (the amount over 100,000), which is $3850.

Altogether, Selma's commission is ...

... $2000 +1925 +1500 +3850 = $9275.

_____

Comment on the sliding scale

Each of the segments of this sliding scale could be rewritten to simplify its computation. For example, for amounts above $100,000, the formula could be either of ...

7% of the amount over $22,5007% of sales, less $1575.

What can you say about the y-values of the two functions f(x)=-5^x +2 and g(x)=-5x^2+2?

A) f(x) and g(x) have equivalent maximum values
b) The maximum y-value of f(x) approaches 2
c) g(x) has the largest possible y-value
d) f(x) has the largest possible y-value

Its multiple choice

Answers

Answer:

B) The maximum y-value of f(x) approaches 2

C) g(x) has the largest possible y-value

Step-by-step explanation:

f(x)=-5^x+2

f(x) is an exponential function.

Lim x→∞ f(x) = Lim x→∞ (-5^x+2) = -5^(∞)+2 = -∞+2→ Lim x→∞ f(x) = -∞

Lim x→ -∞ f(x) = Lim x→ -∞ (-5^x+2) = -5^(-∞)+2 = -1/5^∞+2 = -1/∞+2 = 0+2→

Lim x→ -∞ f(x) = 2

Then the maximun y-value of f(x) approaches 2


g(x)=-5x^2+2

g(x) is a quadratic function. The graph is a parabola

g(x)=ax^2+bx+c

a=-5<0, the parabola opens downward and has a maximum value at

x=-b/(2a)

b=0

c=2

x=-0/2(-5)

x=0/10

x=0

The maximum value is at x=0:

g(0)=-5(0)^2+2=-5(0)+2=0+2→g(0)=2

The maximum value of g(x) is 2

find an equation with vertical asymptotes 1 and 4 and horizontal asymptote 1 please help

Answers

Answer:

y = 1 + 1/((x -1)(x -4))

Step-by-step explanation:

To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.

To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.

Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.

... y = 1 + 1/((x -1)(x -4))

If you like, this can be "simplified" to ...

... y = (x² -5x +5)/(x² -5x +4)

_____

In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).

please help!!! I am so confused

Answers

The exercise is asking you to compute the volume of five different spheres and cylinders, choosing 5 different random values.

Remember the formulas for the volumes: given a radius [tex] r [/tex], the volume of the sphere is

[tex] \dfrac{4}{3}\pi r^3 [/tex]

Whereas the volume of the cylinder is

[tex] \pi h r^2[/tex]

In this specific case, you're told that the height of the cylinder is the same as the diameter of the sphere (i.e. twice the radius). So, the formula of the cylinder updates to

[tex] \pi (2r) r^2 = 2\pi r^3 [/tex]

So, all you need to do is to pick 5 random numbers, use them as the radius [tex] r [/tex], and for each of them compute the volume and cylinder sphere as indicated above.

For example, if you choose a radius [tex] r=5 [/tex], you will have

[tex] \text{Sphere: } V = \dfrac{4}{3}\pi 5^3 = \dfrac{500\pi}{3} [/tex]

[tex] \text{Cylinder: } V = 2\pi 5^3 = 250\pi [/tex]

Now choose your 5 random values and do the same!

If zb⊥ya , find m

A. 28

B.46

C.56

D.62

I'll give you brainliest

Answers

Answer:

A. 28

Step-by-step explanation:

We assume m is the measure of the marked unknown angles: ∠BZY ≅ ∠BZA

(5x +3)° = (2x +18)°

Divide by ° and subtract 2x+3:

... 3x = 15

... x = 5

Then ∠BZA = (2·5 +18)° = m = 28°

What are the solutions to the quadratic equation 4x2 = 64?

x = −16 and x = 16
x = −8 and x = 8
x = −4 and x = 4
x = −2 and x = 2

Answers

Greetings!

Answer:

x = −4 and x = 4

Step-by-step explanation:

4x² = 64

Lets get x² on its own. To do this we divide each sides by 4:

x² = 16

Now to get just x, we need to square root this answer:

√x² = √16

x = √16

x = 4

But this can be ±4 as it -4 and 4 squared both give 16.

So your answer is x = −4 and x = 4


Hope this helps!

Answer:

x = −4 and x = 4

Step-by-step explanation:

c on edg

A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below.

Plan A: 27 text, 21 Internet
Plan B: 13 text, 10 Internet

Answer the questions to determine a conditional probability.

How many customers are on payment plan B?

____ customers

How many of the customers on plan B text?

____ customers

What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.

_____

Answers

Answer:

23 are on plan B13 on plan B text13/23 is the probability a customer on plan B will text

Step-by-step explanation:

Assuming the categorization is mutually exclusive (customers either text or internet, but not both), the total number of Plan B customers in the sample is the sum of those in each category:

.... 13 + 10 = 23 . . . . plan B customers

The problem statement tells you

... 23 plan B customers text

Since 13 out of 23 customers surveyed use the phone for text, the empirical probability that a plan B customer will use the phone for texting is ...

... 13/23 . . . . probability that text is used most

There are 23 customers are on payment plan B.

There are 13 customers who are on plan B text.

The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.

Given

A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet.

They sort the data by payment plans, as shown below.

Plan A: 27 texts, 21 Internet

Plan B: 13 texts, 10 Internet

What is probability?

The probability is defined as the ratio of the sum of all observations and the total number of observations.

The total number of observation is;

= 13 +10 = 23

1. How many customers are on payment plan B?

There are 23 customers are on payment plan B.

2. How many of the customers are on plan B text?

There are 13 customers who are on plan B text.

3. What is the probability that a randomly selected customer who is on plan B uses the phone most often to text?

[tex]\rm Probability = \dfrac{Customer \ plan \ B}{Total \ number \ of \ customers}\\\\Probability = \dfrac{13}{23}[/tex]

The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.

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i will give brainlest answer quickly please

Answers

sine = opposite / adjacent.

since the opposite and adjacent lines are used, you need to use some to solve for x.

the answer is sine.
Answer:

The correct answer is A which is sine.

Step-by-step explanation:

The variable [tex]x[/tex] is opposite to the known angle and the known side length which is the hypotenuse.

Recall the mnemonics SOH, which means that,
the sine ratio involves the length of the opposite side and the hypotenuse.

That is,

[tex]\sin50\degree=\frac{opposite}{hypotenuse}[/tex]

[tex]\sin50\degree=\frac{x}{2}[/tex]

We can use this to solve for [tex]x[/tex].

The formula Q=MCT where Q=heat flow M=mass, C specfic heat, and T change of temperature is used to calculate heat flow Solve this formula for t

Answers

Answer:

q/mc=t

Step-by-step explanation:

q=mct

q/mc=t

Answer:

The formula for t is [tex]T=\frac{Q}{MC}[/tex]

Step-by-step explanation:

Consider the provide formula.

[tex]Q=MCT[/tex]

Where Q=heat flow M=mass, C specific heat, and T is the change of temperature is used to calculate heat flow.

We need to solve the above formula for T.

Divide both the sides by MC.

[tex]\frac{Q}{MC}=\frac{MCT}{MC}[/tex]

[tex]\frac{Q}{MC}=T[/tex]

[tex]T=\frac{Q}{MC}[/tex]

Hence, the formula for t is [tex]T=\frac{Q}{MC}[/tex]

What is the measure of angle N to the nearest whole degree?

Answers

Answer:

Step-by-step explanation:

You can make use of any of the trigonometric ratios to determine N, or you can let your calculator tell you what it is by solving the triangle.

SOH CAH TOA reminds you that

... sin(N) = 13/85 . . . . N = arcsin(13/85)

... cos(N) = 84/85 . . . N = arccos(84/85)

... tan(N) = 13/84 . . . . N = arctan(13/84)

all will tell you N ≈ 8.79741° ≈

_____

If you use inverse functions on your calculator, be sure it is in degrees mode.

Could someone help me with these please!?

Answers

Answer:

7. The sum of the measures of the interior angles of this polygon is 900°.

8. The sum of the measures of the interior angles of this polygon is 540°.

9. The polygon has 10 sides.

10. The polygon has 5 sides.

Step-by-step explanation:


7. Vertices: A, B, C, D, E, F and G

Number of vertices: n=7

Sum of the measures of the interior angles of the polygon: S=?

S=180°(n-2)

Substituting n by 7 in the formula above:

S=180°(7-2)

S=180°(5)

S=900°


8. Vertices: A, B, C, D and E

Number of vertices: n=5

Sum of the measures of the interior angles of the polygon: S=?

S=180°(n-2)

Substituting n by 5 in the formula above:

S=180°(5-2)

S=180°(3)

S=540°


9. Each interior angle of a regular polygon (i) measures 144°:

i=144°

How many sides does the polygon have?

n=?

i=180°(n-2)/n

Substituting i by 144° in the formula above:

144°=180°(n-2)/n

Solving for n: Cross multiplication:

144°n=180°(n-2)

Eliminating the parentheses on the right side of the equation applying the distributive property:

144°n=180°(n)-180°(2)

Multiplying

144°n=180°n-360°

Grouping n's on the right side of the equation: Subtracting 144°n both sides of the equation:

144°n-144°n=180°n-360°-144°n

Subtracting:

0=36°n-360°

Adding 360° both sides of the equation:

0+360°=36°n-360°+360°

Adding:

360°=36°n

Dividing both sides of the equation by 36°:

360°/36°=36°n/36°

10=n

n=10

The polygon has 10 sides.


10. Each interior angle of a regular polygon (i) measures 108°:

i=108°

How many sides does the polygon have?

n=?

i=180°(n-2)/n

Substituting i by 108° in the formula above:

108°=180°(n-2)/n

Solving for n: Cross multiplication:

108°n=180°(n-2)

Eliminating the parentheses on the right side of the equation applying the distributive property:

108°n=180°(n)-180°(2)

Multiplying

108°n=180°n-360°

Grouping n's on the right side of the equation: Subtracting 108°n both sides of the equation:

108°n-108°n=180°n-360°-108°n

Subtracting:

0=72°n-360°

Adding 360° both sides of the equation:

0+360°=72°n-360°+360°

Adding:

360°=72°n

Dividing both sides of the equation by 72°:

360°/72°=36°n/72°

5=n

n=5

The polygon has 5 sides.


Use the APR table in the Business Math Handbook to estimate the APR for the following installment purchase. You received a $2,000 rebate that brought the price of your car down to $20,000; the financing was for 48 months, and your total interest was $3,279.

Answers

Answer:

7.65%

Step-by-step explanation:

There are 200 times $100 in $20,000, so the interest amount per $100 is ...

... $3,279/200 = $16.395 per hundred

In the row of the given table corresponding to 48 months, the smallest amount of interest listed is $23.48 per $100. The APR on the loan of concern is clearly less than 10.75%.

A financial calculator says the interest rate on a loan of $20,000 with 48 monthly payments of ($20,000 +3,279)/48 = $484.98 is about 7.65%.

Joseph needs to find the quotient of 3216/8. In what place is the first digit in the quotient????

Answers

Answer:

hundreds

Step-by-step explanation:

The quotient of 3216/8 is 402. 4 is the first digit, and is in the hundreds place.

How many no real complex roots does the polynomial f (x) = x^4 - x^2- 12 have?

A. 0
B. 1
C. 2
D. 3
E. 4

Answers

Answer:2 real roots2 complex rootsStep-by-step explanation:

f(x) factors as ...

... f(x) = (x² -4)(x² +3) = (x -2)(x +2)(x² +3)

The real roots are x = ±2.

The complex roots are x = ±i√3.

___

We don't know what "no real complex roots" means. We suspect your answer may be C. 2.

can someone help wil mark brainest if u can help and show work please help if u can

Answers

Answer:

-24>

Step-by-step explanation:

1. You can use a calculator if your knowledge of arithmetic fails you.

... 98 +17 +37 -176 = 152 -176 = -24

___

2. -37/8 = -(32 +5)/8 = -4 5/8 = -4.625

This number is on the left side of zero on the number line, but is slightly closer to zero than -4.63, so is "greater than" -4.63.

In the figure below, TRS = RTU and SR = UT. Which of the following triangle congruence criteria proves that TRS = RTU

HELLP MMMEEE PLZ

Answers

Answer:

B. side-angle-side

Step-by-step explanation:

You are given that side SR matches its counterpart; angle SRT matches its counterpart; and you know side ST matches its counterpart, because they are the same segment.

Hence, you have two matching sides and the angle between them. This set of side-angle-side lets you invoke the theorem that matches that name.

The Shop and Save is starting their annual clearance and the store has sent out to all their customers a coupon book offering a variety of savings on their products. The LCD television that you have wanted was reduced by 35% prior to the annual clearance. In addition, the coupon book has a 10% off coupon for the LCD television. Determine what you would pay after applying the discounts given that the price of the LCD television was $1,325. Round your answer to the nearest cent.
a. $728.75
c. $596.25
b. $775.13
d. $46.38

Answers

Answer:

A

Step-by-step explanation:

First discount is the original price reduced by 35% prior to the annual clearance.


So, 35% of 1325 = 0.35 × 1325 = 463.75.


After the discount of $463.75, the price that remains =  1,325 -  463.75 = $861.25.


Then, additional disount of 10%.


10% of $1,325. = 0.10  × 1,325. = 132.50


The final price after discount of 10% = 861.25 - 132.50. =  728.75.


Round to the nearest cent, we get 728.75.


Therefore, you would pay $ 728.75 after applying the discounts.



Answer:

B. 775.13

Step-by-step explanation:

Edge says A was wrong.

In the 9th and 10th grades at Jefferson High School, there are 236 students. Of thoes students, 121 are in 9th grade, Of the 214 students who are right- handed, 103 of them are in 10th grade.

Answers

Total -

Right-handed: 214! Left-handed: 22!

Total of students: 236 students


I hope this helped! :D


Step-by-step explanation:

9th Grade: Right Handed: 111! Left Handed: 10!

10 Grade: Right Handed: 103! Left Handed: 22!

Add left handed for both grades. Add right handed for both grades. And add total numbers.

I hope this helped :D    


Final answer:

There are 121 students in 9th grade and 115 students in 10th grade at Jefferson High School.

Explanation:

This question involves counting and analyzing data about grade levels and handedness of students at Jefferson High School. To answer the question, we need to use the given information:

- There are 236 students in 9th and 10th grades combined.

- Out of these, 121 students are in 9th grade.

- Among the 214 right-handed students, 103 are in 10th grade.

We can use these numbers to find out how many students are in each grade level.

Let's denote the number of 9th-grade students as 'x' and 10th-grade students as 'y'.

From the given information:

x + y = 236 (total number of students)

x = 121 (number of 9th-grade students)

y = 103 (number of 10th-grade students)

To find the value of 'y', we can substitute the given value of 'x' into the first equation:

121 + y = 236

y = 236 - 121

y = 115

Therefore, there are 121 students in 9th grade and 115 students in 10th grade.

What is a quartic polynomial function in standard form with zeros -2,4,4,and 3

Answers

We can simply multiply the roots together to find the original function.

(x + 2)(x - 4)(x - 4)(x - 3)

FOIL.

x^2 - 4x + 2x - 8(x - 4)(x - 3)

Combine like terms.

x^2 - 2x - 8(x - 4)(x - 3)

FOIL.

x^3 - 2x^2 - 8x - 4x^2 + 8x + 32(x - 3)

Combine like terms.

x^3 - 6x^2 + 32(x - 3)

FOIL.

x^4 - 6x^3 + 32x - 3x^3 + 18x^2 - 96

Combine like terms.

x^4 - 9x^3 + 18x^2 + 32x - 96 is the original function with the given roots.
Final answer:

A quartic polynomial function with roots at -2,4,4,and 3 can be written in standard form as f(x) = (x + 2) * (x - 4)^2 * (x - 3)

Explanation:

A quartic polynomial function is a function of the fourth degree. Its general form is f (x) = ax^4 + bx^3 + cx^2 + dx+ e, where a, b, c, d, and e are constants, and a ≠ 0. Given the roots or zeros of the function (-2,4,4,3), we can construct the quartic polynomial function.

The quartic polynomial with roots r1, r2, r3, r4 is represented by: f(x) = a(x - r1)(x - r2)(x - r3)(x - r4). The roots of your polynomial function are -2, 4, 4, and 3. So, we substitute those roots into the equation:

f(x) = a(x - (-2)) * (x - 4) * (x - 4) * (x - 3). We may choose the leading coefficient a to be 1 (a ≠ 0) for simplicity's sake. Thus, the quartic polynomial function in standard form with zeros -2,4,4, and 3 is:

f(x) = (x + 2) * (x - 4)^2 * (x - 3)

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There are 650 visitors to an art gallery on Friday. There are 10% more visitors on Saturday than on Friday. How many visitors are there on Saturday?

Answers

Answer:

10% of 650 visitors is:

650 visitors* (10/100)= 65 visitors.

650 visitors+ 65 visitors= 715 visitors.

There are 715 visitors on Saturday

Step-by-step explanation:


Ans7wer:

715 people

Step-by-step explanation:

650÷100=6.5

6.5X10=65

650+65=715

Find the slope of the line between points A and B. Simplify your answer.


-2

2

-1

1

Answers

Answer:

-2

Step-by-step explanation:

From the given graph, the point A(1, -4) and B(-1, 0)

Slope (m) = (y2 - y1) / (x2 - x1)

x1 = 1, y1 = -4, x2 = -1 and y2 = 0

Slope (m) = (0 - (-4))/(-1 - 1)

= 4/-2

Slope = -2

Thank you.

Find the value of the variable for which the value of the expression –3(2x+1) is 20 greater than the value of the expression 8x+5

Answers

Answer:

-2

Step-by-step explanation:

20 greater than 8x +5 is ...

... 8x +5 +20 = 8x +25

We want this value to be -3(2x +1), so we want to solve the equation ...

... 8x +25 = -3(2x +1)

... 8x +25 = -6x -3 . . . . . . eliminate parentheses

... 14x = -28 . . . . . . . . . . . add 6x-25

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

The desired value of the variable is -2.

_____

Check

-3(2x+1) = -3(2(-2)+1) = -3(-3) = 9

8x+5 = 8(-2) +5 = -11

9 is 20 greater than -11, so the answer checks OK.

Answer:

X = -2

Step-by-step explanation:

find the value of both missing side ( not just y)

Answers

Answer:

y = 10(√3)/3

unnamed side = 5(√3)/3

Step-by-step explanation:

Side ratios in a 30°-60°-90° triangle are 1 : √3 : 2.

Multiplying these by 5/√3 gives ...

... unnamed side : 5 : y = 5/√3 : 5 : 10/√3

Then ...

... unnamed side = 5/√3 = 5(√3)/3

... y = 10/√3 = 10(√3)/3

If f(x) is a third degree polynomial function and g(x) = f(2x) + 2, which of the following must be true?

f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercepts.
f(x) and g(x) have the same number of zeros.
f(0) = g(0) – 2

Answers

Answer:

Choice D) which is f(0) = g(0) - 2

Step-by-step explanation:

Plug x = 0 into the g(x) function to find that....

g(x) = f(2*x) + 2

g(0) = f(2*0) + 2 .... replace every x with 0

g(0) = f(0) + 2

g(0) - 2 = f(0) + 2 - 2 .... subtract 2 from both sides

g(0) - 2 = f(0)

f(0) = g(0) - 2

Find the value of x.

10
8.3(repeating)
7
5

Answers

Answer:

5

Step-by-step explanation:

So the triangle to the right is similar to the big triangle by SAS similarity with a ratio of 1:2. So (3x-5):20 is 1:2. So 3x-5=10 or 3x=15. So x=5.

Answer:

5

Step-by-step explanation:

good luck on the test babes <3

The variables y and x have a proportional relationship, and y = 7 when x = 2.

What is the value of y when x = 5?



The variables y and x have a proportional relationship, and y = 7 when x = 2.

What is the value of x when y = 21?




Which equation represents a proportional relationship?


y=−x

y=−5(x+1)

y = 5x + 1

y=15x




Answers

Answer:

y= 35/2  when x=5

x=6 when y =21

Proportinal relatiionships:  y=−x ,  y=15x

Step-by-step explanation:

The formula for direct variation is

y= kx

If y=7 and x=2, we can solve for k

7 =k*2

Divide by 2

7/2 =k

y =7/2 x

Now if x=5

y =7/2 * 5

y =35/2


Now if y=21

21 =7/2 * x

Multiply by 2/7

21 * 2/7 = 7/2 * 2/7 x

6 =x


Which equation represents a proportional relationship?

y=−x

YES  k = -1   Some people debate about having a negative constant, but everything I have read and taught says you can have a negative constant.

y=−5(x+1)

This does not go through the origin so no

if x=0  y = -5

y = 5x + 1

if x = 0 y =1   so no

y=15x

YES  k = 15

Answer:

17.5

i just did it on my quiz and it was wrong(the other guy is wrong)

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

Answers

Answer:

16 mm  

Step-by-step explanation:

Since ABC is an equilateral triangle, all three sides are the same length.  The perimeter is found by adding together all of these equal sides; letting x represent the length of a side of the triangle, this gives us

x + x + x = 96

Combining like terms,

3x = 96

Dividing both sides by 3,

3x/3 = 96/3

x = 32

Since AM is a perpendicular bisector, it splits BC into two congruent sections. This means the length of MC, half of BC, will be 32/2 = 16.

Option (B) is correct which is 24 mm

Step 1:

Find the length of each side.

Let the side be a,

3×a = 96mm

⇒ a = 96/3

⇒ a = 32 mm

Step 2:

Length of MC = length of BC/2      (As AM is a perpendicular bisector)

⇒ MC = 32/2 = 16 mm

Step 3:

Now, in the triangle, AMC, using Pythagoras theorem,

AC² = MC² + AM²

⇒ (32)² = MC² + (16)²

After solving,

⇒ MC = 16√3 = 27.77 mm

This is closest to option (B) which is 24 mm

To learn more about triangles, you can visit:

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In △ABC, CM is the median to AB and side BC is 12 cm long. There is a point P∈CM and a line AP intersecting BC at point Q. Find the lengths of segments CQ and BQ, if P divides CM into CP:PM=1:2.

Answers

Answer:

CQ = 2.4 cmBQ = 9.6 cm

Step-by-step explanation:

This development is ugly, but it works.

Let area ΔABC = 6a. Then area ΔAMC = 3a, and area ΔAPC = a. Similarly, area ΔBMC = 3a, and area ΔBPC = a.

Let area ΔCPQ = x. Then ...

... area ΔACQ = area ΔAPC + area ΔCPQ

... area ΔACQ = a + x

Define k such that BQ : CQ = k : 1. Then ...

... area ΔBPQ + area ΔCPQ = area ΔBPC

... kx + x = a = (k +1)x

The division of BC into parts of ratio k : 1 means ...

... area ΔABQ = k × area ΔACQ

... area ΔABQ + area ΔACQ = area ΔABC

... k × area ΔACQ + area ΔACQ = area ΔABC

... (k +1)(x +a) = 6a . . . . . . . area ΔACQ = x+a

... (k +1)x +(k +1)a = 6a . . . . . distributive property

... a + (k +1)a = 6a

... k +2 = 6 . . . . . . . . . . . . . . . divide by a, simplify

... k = 4

Now, we know BQ : CQ = 4 : 1, so ...

... BQ = 4/5 × 12 cm = 9.6 cm

... CQ = 1/5 × 12 cm = 2.4 cm

Help plzzzzz I don’t know this

Answers

Answer:

$6

Step-by-step explanation:

The graph shows you that 4 pounds of apples (and no cranberries) can be purchased for $24. Thus each pound costs ...

... $24/(4 pounds) = $6/pound

4 pounds of apples cost $24
So $24/4=6
6 pounds
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