Struggling un this section

Answer:

F is the mid point of BC. (Proved)

Step-by-step explanation:

See the attached diagram.

Given AB ║ CD and EF is drawn to be parallel to AB.

So, EF ║ AB ║ CD .......... (1)

Now, in Δ ABD, E is the midpoint of AD and EG is parallel to AB.

So, G must be the midpoint of BD.

Now, in Δ BCD, G is the midpoint of DB and GF is parallel to CD. {From relation (1)}

So, we can write F is the midpoint of BC. (Proved)

[Since we know the theorem that if we joint the midpoints of two sides of a triangle then the line formed will be parallel to the third side.]

Answer:

[tex]f(1)=9[/tex]

Step-by-step explanation:

[tex]Given \ f(n+1)=f(n)\\f(3)=f(2)\\f(2)=f(1)\\f(1)=f(2)=f(3)\\f(1)=f(3)\\f(1)=9[/tex]

Answer:

The Sum Of The Integers From -6 To 58 is 1690.

Step-by-step explanation:

Given,

[tex]a=-6[/tex]

[tex]T_n=58[/tex]

We have to find out the sum of integers from -6 To 58.

Firstly we will find out the total number of terms that is 'n'.

Here [tex]a_1=-6\ and\ a_2=-5[/tex]

[tex]\therefore d=a_2-a_1=-5-(-6)=-5+6=1[/tex]

Now we use the formula of A.P.

[tex]T_n=a+(n-1)d[/tex]

On substituting the values, we get;

[tex]58=-6+(n-1)1\\\\n-1=58+6\\\\n-1=64\\\\n=64+1=65[/tex]

So there are 65 terms in between  -6 To 58.

That means we have to find the sum of 65 terms in between  -6 To 58.

Now we use the formula of Sum of n_terms.

[tex]S_n=\frac{n}{2}(2a-(n-1)d)[/tex]

On substituting the values, we get;

[tex]S_{65}=\frac{65}{2}(2\times-6+(65-1)1)\\\\S_{65}=\frac{65}{2}(-12+64)\\\\S_{65}=\frac{65}{2}\times52\\\\S_{65}=65\times26=1690[/tex]

Hence The Sum Of The Integers From -6 To 58 is 1690.

Final answer:

The sum of the integers from -6 to 58 is calculated using the formula for the sum of an arithmetic series and is found to be 1,690.

Explanation:

To find the sum of the integers from -6 to 58, we can use the formula for the sum of an arithmetic series, which is S = n/2 * (a1 + an), where S is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.

We first need to determine the number of terms in our series. Since our series starts at -6 and ends at 58, we can find the number of terms by subtracting -6 from 58 and then adding 1 (because both ends are inclusive). That gives us 58 - (-6) + 1 = 65 terms.

Now, we can plug the values into the sum formula:

S = 65/2 * (-6 + 58) = 32.5 * 52 = 1690.

Therefore, the sum of the integers from -6 to 58 is 1,690.

Answer: 1.0

Step-by-step explanation: Since a percent is a ratio that compares a number to 100, think of 100% as the ratio 100/100 or 100 divided by 100.

Now, dividing a number by 100 moves the decimal point two places to the left so 100 divided by 100 will move the decimal point two places to the left which will gives us 1.0 or simply just 1.

So 100% can be written as the decimal 1.0.

Answer:

1

Step-by-step explanation:

Byeeee, get a hundred!

Answer:

Step-by-step explanation:

7.56 × 10^3

= 7.56×1000

= 7560

Answer:

447,697.125

Step-by-step explanation:

multiply 7.65 by 10

76.5

76.5 to 3rd power is just 76.5 times 76.5 times 76.5

answer is 447,697.125

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Answer:

Step-by-step explanation:

Answer:

A. 17 , 11

f(4)=3(4) + 5

=17

f(x)= 38

38 = 3x + 5

38 - 5 = 3x

33 = 3x

x =11

Answer:

Anil would take 10 days and Sunil would take 15 days to complete the work.

Step-by-step Explanation:

To Determine:

How many days they took to complete the work?​

Information Fetching and Solution steps:

Let is consider,

The number of days taken by Anil to complete the required work = d.

The number of days taken by Sunil to complete the required work = d + 5

Work done by Anil in one day = 1÷d

Work done by Sunil in one day = 1÷ (d+5)

Work done together by Anil and Sunil for one day = 1/d + 1/(d+5)

                                                                                    = (d+5+d)/d(d+5)

                                                                                    = (2d+5)/d(d+5)  

Work done together by Anil and Sunil for 4 days = 4×(2d+5)/d(d+5) ....[A]

Work done by Sunil in 5 days = 5÷ (d+5)  ....[B]

By adding equation [A] and [B], we can determine the complete work

[A] + [B] = 1

((4×(2d+5)/d(d+5))) + (5÷ (d+5)) = 1

8d+20+5d=1d(d+5)

13d+20=d²+5d

−d²+8x+20=0

(−d−2)(d−10)=0

d=−2 or d=10

As number of days can not be negative. So, d = 10. Therefore,

The number of days taken by Anil to complete

the required work = 10 days

The number of days taken by Sunil to complete

the required work = d+5 = 15 days

Hence, Anil would take 10 days and Sunil would take 15 days to complete the work.

Keywords: days, work

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Option E

The numerator of fraction is 21

[tex]2\frac{5}{8}[/tex] is to be written as improper fraction in lowest terms

To find: numerator of fraction

An improper fraction is a fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number).

To convert a mixed fraction to an improper fraction, follow these steps:

[tex]2\frac{5}{8} = \frac{8 \times 2 + 5}{8} = \frac{16 + 5}{8} = \frac{21}{8}[/tex]

Thus the numerator of fraction is 21. Option E is correct

Answer:

SAS Reflective property

Step-by-step explanation:

By reflexive property and SAS, we prove that ΔPYJ and ΔPXK are congruent.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, JP = KP and PX = PY.

∴ JX = KY.

Hence Z is the midpoint of JY and XK.

∴ JY = XK.

Reflexive property.

And the included ∠P is common to both the  ΔPYJ and ΔPXK.

Side angle side congruency.

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Answer:

The radius of the given equation is 2 .

Step-by-step explanation:

The equation of a circle whose center (h, k) and radius is r,

(x - h)² + (y - k)² = r² ..............................(i)

Here given that-

x² + y² + 21 = 10 x

x² - 10 x + y² + 21 = 0

( To making perfect square, add and subtract 25 ) -

x² - 10 x + 25 - 25 + y² + 21 = 0

(x² - 10 x + 25) + y² -4 =0

[As we know that -

(x - 5)² = x² - 10 x + 25]

(x - 5 )² + y² = 4

(x - 5)² + (y - 0)² = 4

(x - 5 )² + (y- 0)² = 2² ................................(ii)

On comparing equation (i) and(ii)-

r = 2

Hence the radius of the given equation is 2 and center is ( 5, 0).

Answer:

$280

Step-by-step explanation:

Interest = Interest Rate x Principal x time

Interest = 0.04 x $3,500 x 2

Interest = $280

Answer:

21 mini-muffins

Step-by-step explanation:

7 multiplied by 3 equals 21

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Tony bought a total of 21 mini-muffins. This was calculated by multiplying the number of packages he bought (7) by the number of mini-muffins in each package (3).

This question is about a mathematical operation called multiplication. Tony purchases 7 packages of mini-muffins. There are 3 mini-muffins in each package. To find the total number of mini-muffins Tony buys, multiply the number of packages he bought (7) by the number of mini-muffins in each package (3). This calculation is written as 7 * 3. Therefore, Tony buys a total of 21 mini-muffins.

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There are probably some choices we're not being shown, but let's just do the whole procedure.

x² + 6x - 8 = 0

Step one: move the 8 to the other side.

x² + 6x = 8

Step two: add (6/2)²=9 to both sides.

x² + 6x + 3² = 8 + 9

Step three: Factor

(x + 3)² = 17

Step four: take the square root

x + 3 = ±√17

Step five: Solve for x,

x = -3  ± √17

Answer:

3.375 miles

Step-by-step explanation:

3/4 can be changes to 0.75. SO multiply 4.5 times 0.75 to get your answer

Answer:

41

Step-by-step explanation:

Substitute in 5 and 7 into the correct spots:

(-3)(7)+2((8)(5)-9)

Multiply and simplify:

-21+2(40-9)

-21+2(31)

-21+62

41

:)

Answer:

50

Step-by-step explanation:

-21 + 16x - 9

-21 + 80 - 9

59 - 9

50

The slope of the line is -4.

Work is provided in the image attached.

Answer:

[tex]m=-4[/tex]

Using the Slope Formula:

[tex]m= \frac{4+12}{5-9}=\frac{16}{-4} =-4[/tex]

Answer:

40x-24y

Step-by-step explanation:

Answer: 128.86cm²

Step-by-step explanation:

The circle is inscribed in the rectangle. To find the shaded portion, subtract he area of the circle from the are of the rectangle.

Area of the rectangle                                  =  11 x 12

                                                                     =  132cm²

Area of the circle with radius of 1cm          =  πr²

                                                                     = 3.142 x 1²

                                                                     = 3.142cm²

Therefore , area of the shaded  region      = 132cm²  -  3.142cm²

                                                                    = 128.86cm²

Answer:128.86

Step-by-step explanation: I got it correct on khan

Subtract the length of the tail from the whole length.

3/5 - 1/5 = 2/5

The answer is 2/5

3/5  -  1/5  = 2/5

so your answer is 2/5

Answer:

3.5 hours

Step-by-step explanation:

Given: Distance= 26.2 miles

           Speed= 12 km/h

First lets convert the unit of speed from kmh to mph.

Remember, 1 mile= 1.609 km

∴ For speed of 12 km/h= [tex]\frac{12}{1.609}= 7.45\ mph[/tex]

Speed= 7.45 mph

Next, find time taken by Allan to complete a Marathon.

[tex]Time= \frac{Distance}{speed}[/tex]

⇒ Time= [tex]\frac{26.2}{7.45}[/tex]

∴ Time= 3.516 hours ≅ 3.5 h (nearest tenth)

∴ Allan took 3.5 hours to complete marathon.

Allan takes approximately 3.5 hours to complete a marathon. This is determined by converting the marathon distance to kilometers and dividing it by his running speed.

To determine how long it takes Allan to complete a marathon, we need to convert the marathon distance from miles to kilometers and then find the time it takes based on his running speed.

1 mile is approximately 1.60934 kilometers, so:

26.2 miles × 1.60934 km/mile ≈ 42.164 km

Allan runs at an average speed of 12 kilometers per hour. The time (t) needed to complete the marathon can be calculated as:

t = distance / speed

t ≈ 42.164 km / 12 km/h ≈ 3.514 hours

Rounding to the nearest tenth of an hour, Allan takes approximately 3.5 hours to complete the marathon.

Answer:

1 quart blue + 1 1/2 quart red

Step-by-step explanation:

Given:

Ratio of blue paint : red paint = 1/3 : 1/2

simplifying this ratio into whole numbers by multiplying both sides by 2 and 3, we get:

(1/3) x (3x2) : (1/2) x (3x2)

2 : 3

From this we can determine the fractions of red and blue paint used in any total purple mix

fraction of blue paint = 2/(2+3) = 2/5 of purple mix

fraction of red paint = 3/(2+3) = 3/5 of purple mix

we are given that we want to make 2 1/2  (= 5/2) quarts of purple paint

hence

amount of blue paint

= fraction of blue paint in purple mix x total amount of purple paint

= (2/5) x (5/2) = 1 quart

amount of red paint

= fraction of redpaint in purple mix x total amount of purple paint

= (3 /5) x (5/2) = 3/2 quart = 1 1/2 quart

Answer:

The cars are travelling ar the speed 45 mph.

Step-by-step explanation:

Let the two cars are moving at the speed of x mph.

Now, Car A reaches its destination in 15 minutes i.e. [tex]\frac{15}{60} = 0.25[/tex] hours.

Therefore, Car A travels in 15 minutes by 0.25x miles.

Again, Car B reaches its destination in 35 minutes i.e. [tex]\frac{35}{60} = 0.583[/tex] hours.

Therefore, Car B travels in 35 minutes by 0.583x miles.

Given that, (0.583x - 0.25x) = 15

⇒ 0.333x = 15

⇒ x = 45 mph

Therefore, the cars are travelling ar the speed 45 mph. (Answer)

The cars travel at a speed of 3/4 miles per minute.

To find the speed of the cars, we can use the formula Speed = Distance/Time. Let's assume that Car A's speed is x miles per minute. Since Car B travels 15 miles farther than Car A and takes 35 minutes to reach its destination, Car B's speed would also be x miles per minute. Now, using the given information, we can set up two equations:

x * 15 = x * 35 - 15

Simplifying the equation, we get:

15x = 35x - 15

20x = 15

x = 0.75

Therefore, the cars travel at a speed of 0.75 miles per minute or the fraction 3/4 miles per minute.

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X is a right angle so 90 degrees.

The B will be equal to C so B is 47 degrees.

The Y is 180 degrees - X - C so Y is 43 degrees.

Hope this helps.

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]

In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.

coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.

Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].

Final answer:

The fractional coefficient in the equation 3/4y+1/2=3 1/4 is 3/4.

In the given equation, the fractional coefficient is 3/4, which is the fraction that multiplies the variable y.

Explanation:

The fractional coefficient in the equation 3/4y+1/2=3 1/4 is 3/4.

In the equation 3/4y + 1/2 = 3 1/4, the fractional coefficient refers to the fraction that is multiplied by the variable y.

In this case, the coefficient is 3/4.

When working with algebraic expressions and equations, understanding how to identify and manipulate coefficients is essential for problem-solving.

The student's query seems to be aimed at identifying the coefficient of the variable in the equation. In algebra, fractions like 3/4 can be seen as coefficients when they are directly next to a variable.

No unit cancellations are needed here as the question pertains to pure algebra and not to unit conversions or applied mathematics.

Answer:

Part a) [tex]3x+5y=30[/tex]

Part b) see the explanation

Part c) see the explanation

Step-by-step explanation:

Part a) Construct a liner equation

Let

x ----> the number of bags of  tootsie rolls

y ----> the number of bags of lolly-pops

we know that

The number of bags of tootsie rolls bought multiplied by their price ($3) plus the number of bags of lolly-pops bought multiplied by their price ($5) must equal $30

so

The linear equation that represent this problem is

[tex]3x+5y=30[/tex]

Part b) Find the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x s equal to zero

In this context, the y-intercept is the number of bags of lolly-pops that i can buy when the number of bags of tootsie rolls is equal to zero

For x=0

[tex]3(0)+5y=30[/tex]

[tex]y=6[/tex]

The y-intercept is the point (0,6)

so

I can buy 6 bags of lolly-pops and 0 bags of tootsie rolls

Find the x-intercept

The x-intercept is the value of x when the value of y s equal to zero

In this context, the x-intercept is the number of bags of tootsie rolls that i can buy when the number of bags of lolly-pops is equal to zero

For y=0

[tex]3x+5(0)=30[/tex]

[tex]x=10[/tex]

The x-intercept is the point (10,0)

so

I can buy 10 bags of  tootsie rolls and 0 bags of lolly-pops

Part c) Find the slope

we have

[tex]3x+5y=30[/tex]

isolate the variable y

[tex]5y=-3x+30[/tex]

[tex]y=-\frac{3}{5}x+6[/tex]

The slope is m=-3/5  ---> is negative because is a decreasing function        

That means ---> For every three less lollipops you get, you can have 5 more tootsie rolls

Answer:

36 trees were infected with the virus.

Step-by-step explanation:

Given:

Total number of trees =  90

Percentage of tree that had virus  40%

To find:

Number of tress that were infected by virus = ?

Solution:

Let the number trees that was affected by the virus be X.

then

X = 40% of 90

X = [tex]\frac{40}{100} \times 90[/tex]

X = [tex] 0.4 \times 90[/tex]

X= 36

Answer:

1. [tex]12x^2-13.4x-11[/tex]

- Degree: 2

- Number of terms: 3

2. [tex]7x^3+168[/tex]

 - Degree: 3

- Number of terms: 2

3. [tex]9x^4-9[/tex]

- Degree: 4

- Number of terms: 2

Step-by-step explanation:

For this exercise you need to remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]

1. Given:

[tex](4x + 2.2)(3x - 5)[/tex]

Apply the Distributive property:

[tex]=12x^2+6.6x-20x-11[/tex]

Add the like terms:

[tex]=12x^2-13.4x-11[/tex]

You can idenfity that:

- Degree: 2

- Number of terms: 3

2. Given:

[tex](-304 +503 - 12) + (7x^3 - 25 + 6)[/tex]

Add the like terms:

[tex]=187 + 7x^3 - 25 + 6=7x^3+168[/tex]

You can idenfity that:

- Degree: 3

- Number of terms: 2

3. Given:

[tex](3x^2 - 3)(3x^2 + 3)[/tex]

Apply Distributive property:

[tex]=9x^4-9x^2+9x^2-9[/tex]

Add the like terms:

[tex]=9x^4-9[/tex]

You can idenfity that:

- Degree: 4

- Number of terms: 2

Answer:

The profit = $(3x - 75) where x = number of t-shirts sold

Step-by-step explanation:

School spirit club wants to raise money by selling t-shirts. one local company charges a fixed fee of $75 for creating the design and $5 for each shirt that they print.

We have to find the club's income if they sell each t-shirt for $8.

Let the number of t-shirts that the club sell be equal to x.

So the cost of making x t-shirts = 75 + 5x

If the club sells x t-shirts , then the money they earn = 8x

Profit = selling price - cost price

          = 8x - (75 + 5x)

          = $(3x - 75)

The club also needs to sell at least 25 t-shirts to make a profit and from then on makes a profit of $3 on each t-shirt they sell.

Answer: [tex]540[/tex]

We count the number of ways that some lane can be left empty, and subtract from the total:

Each driver has three choices, so it's [tex]3^6 = 729[/tex].

Now, we count the ways where at least 1 lane is left empty:

But we have double-counted the situations where two lanes are left empty. Since each driver only has one choice, there are [tex]3(1^6)[/tex] situations we overcount. This leaves [tex]729 - (192 - 3) = 540[/tex] ways to fill all three lanes.

Also, you took this question directly from Alcumus. The source is AoPS Staff they wrote this problem, and might request this post be taken down since you technically are not allowed to post Alcumus problems on the internet or their own forums.