ABC is a triangle. D is a point, vectors 2BD = 3DC
Prove vectors 2AB + 3AC = 5AD

Answer:

198.

Step-by-step explanation:

183+15=198

Hello!

If Paul already has 183 stamps, just add 15 more because that is how much his friend gave him and you will get 198 stamps

To find the y intercept replace the x in the equation with zero and solve

-2/9(0) + 1/3

0 + 1/3

The y-intercept is:

(0, 1/3)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y intercept is 1/3

Step-by-step explanation:

[tex]f(x)=-\frac{2}{9} x+ \frac{1}{3}[/tex]

To find y intercept we plug in 0 for x

Y intercept point is a point where the graph f(x) crosses y axis.

At y intercept, the value of x is 0

to find y intercept we plug in 0 for x

[tex]f(0)=-\frac{2}{9} (0)+ \frac{1}{3}[/tex]

[tex]f(0)=\frac{1}{3}[/tex]

ANSWER

B. A(x)=0.5 (f .g)(x)

EXPLANATION

The area of a triangle is calculated using the formula:

Area=0.5 Base × Height

The base is given by

g(x)=2x

and the height of the function is

[tex]f(x)= {x}^{2} + 3[/tex]

This implies that:

A(x)=0.5f(x) × g(x)

A(x)=0.5 (f .g)(x)

Answer: 2.4 per pound you have to divide $3.36 and 1.4 pounds and you get your answer. Please mark me the brainliest answer? Hope this helped have a good day :)

OMG IS THAT A CURSED IMAGE?!?!?! :D

Based on the information given the unit rate per pound is 2.4.

Using this formula

Unit rate per pound=Costs/Pounds

Where:

Cost=$3.36

Pounds=1.4 pounds of grapes

Let plug in the formula

Unit rate per pound=$3.36/1.4

Unit rate per pound=2.4

Inconclusion the unit rate per pound is 2.4.

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Answer:

c

Step-by-step explanation:

The formula to find slope is:

[tex]\frac{y_{2}-y_{1}  }{x_{2}-x_{1} }[/tex]

[tex]y_{2} = 0\\y_{1} =3\\x_{2} = 4 \\x_{1} = 0[/tex]

so...

[tex]\frac{0-3}{4-0}[/tex]

[tex]\frac{-3}{4}[/tex] <<<the slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

-3/4

Step-by-step explanation:

The slope is given by

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

   = (0-3)/(4-0)

   = -3/4

Andrew is 1 5/8 meters tall.

Andrew's height is 5.75 meters

A variable dependent parameter equation is an equation where we solve a given problem from the statements and the data mentioned in it.

Let the height of Andrew be x meters

Given Paul is 0.25 meters taller than Andrew .

∴ Paul's height = 0.25 + x meters

  Also given that John is 1/8 meters shorter than Paul .

  John's height = 1/8(0.25 + x) meter

  Also given that John's height  is 3/4 meters.

⇒  3/4 = 1/8(0.25 + x)

⇒   6  = (0.25 + x)

∴     x = 5.75

Therefore the height of Andrew is 5.75 meters.

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Answer:

112.5 people per square mile

Step-by-step explanation:

Find the "unit rate:"

90,000 people

-----------------------  =  112.5 people per square mile

   800 miles²

Answer:

4

Step-by-step explanation:

For example, 4.

4 is rational since it can be written as a fraction of integers. 4 = 4/1

The square root of 4 is 2, and 2 is a whole number.

Answer:

No teen sent texts fewer than 1630 or more than 1854 texts in a month

Step-by-step explanation:

margin of error gives the difference that may come in the sample results from the actual population results.

Given:

Average teen sends 1742±112 texts per month

here ±112 is margin of error, calculating maximum difference:

1742+112=1854

1743-112=1630

No teen sent texts fewer than 1630 or more than 1854 texts in a month !

Answer:

5/4, 1.3, 1 8/25

Step-by-step explanation:

5/4=1.25

1 8/25=1.32

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

The numbers 1.3, 5/4, 1, and 8/25 can be rearranged from least to greatest as 0.32, 1, 1.25, 1.3 once they're all converted to decimals. Converting fractions and whole numbers to decimals is a crucial skill in Mathematics and can simplify problems like this.

To answer your question, the numbers 1.3,5/4,1 and 8/25 can be put in order from least to greatest by first converting them all to decimals or fractions. Given in their current form 5/4 equals 1.25 as a decimal and 8/25 equals 0.32 as a decimal. Hence we can put them into increasing order as 0.32, 1, 1.25, 1.3.

Understanding how to convert between fractions, decimals, and whole numbers is an essential skill in mathematics, and it can make problems like this easier to understand and solve. For instance, understanding that the fraction 5/4 is equivalent to the decimal 1.25 makes it easier to compare with other numbers.

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Answer:

The three integers are 81,82 and 83

Step-by-step explanation:

Let

x,x+1 and x+2 ----> the three consecutive integers

we know that

[tex]x+(x+1)+(x+2)=246[/tex]

Solve for x

[tex]3x+3=246[/tex]

[tex]3x=246-3[/tex]

[tex]x=243/3[/tex]

[tex]x=81[/tex]

therefore

[tex]x=81[/tex]

[tex]x+1=81+1=82[/tex]

[tex]x+2=81+2=83[/tex]

Answer:

1: Rhombus

2: Square

3: Rectangle

4: Trapezoid (isosceles trapezoid to be exact)

Answer:

1. convex

2. square

3. rectangle

4. trapezoid

Step-by-step explanation:

Answer:

[tex]y=200(1.05)^{x}[/tex]

Step-by-step explanation:

This is a compound interest problem. The principal is given as 200 and the interest rate as 5%. We can use the compound interest formula to determine the relationship between time and money;

[tex]A=P(1+r)^{n}[/tex]

where;

A is the amount of money

P is the principal invested

r is the rate of interest

n is the time duration

Substituting the information given we have;

[tex]y=200(1+\frac{5}{100})^{x}\\\\y=200(1.05)^{x}[/tex]

which is an exponential function

Find the attached for the graph of this exponential function.

Answer:

16 m < P < 19 m

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x----> the length of the third side

Applying the triangle inequality theorem

1) 3+8 > c

11 > c

c < 11 m

2) c+3 > 8

c> 5 m

so

the measure of the third side must be

5 m < c < 8 m

therefore

The perimeter of the triangle is equal to

P=3+8+c

P=11+c

The inequality is equal to

(11+5) m < P < (11+8) m

16 m < P < 19 m

Answer:

-6.

Step-by-step explanation:

y = x - 6

y = 6x - 19

To eliminate x the first equation should be multiplied by -6 giving:

-6y = -6x + 36

Adding this to the second equation will eliminate x.

Answer:

Option 1: 0.32

Step-by-step explanation:

Let

P(A) be the experimental probability of getting two

And

P(B) be the experimental probability of getting three

The dice is rolled 360 times.

So the sample space is n(S) = 360

P(A) = n(A)/n(S)

= 54/360

= 0.15

And

P(B) = n(B)/n(S)

= 62/360

= 0.172

As both the events A and B are mutually exclusive,

P(A or B)  = P(A) + P(B)

= 0.15 + 0.172

=0.322

Rounding of to one decimal gives us:

0.32

So the probability of rolling a two or three is 0.32 ..

Answer:

Amplitude is 3

Step-by-step explanation:

in y=-3sin5x

the number in front of sign is always the amplitude. Its not negative 3 because the negative simply means it reflects across the x-axis

ANSWER

The amplitude is 3

EXPLANATION

The amplitude of a periodic function is the distance from the midline of its graph to the peak.

The given function is:

[tex]y = - 3 \sin(5x) [/tex]

This function is of the form:

[tex]y = a \: \sin(bx) [/tex]

The of this function is

[tex] |a| [/tex]

By comparing the two functions, we have a=-3.

Therefore the amplitude of the given function is

[tex] | - 3| = 3[/tex]

Answer:

The solutions are (6,13) and (1,3)

Step-by-step explanation:

We want to solve

[tex]y=x^2-5x+7[/tex]

and

[tex]y=2x+1[/tex]

We equate both equations to get:

[tex]x^2-5x+7=2x+1[/tex]

[tex]x^2-5x-2x+7-1=0[/tex]

[tex]x^2-7x+6=0[/tex]

We split the middle term to get:

[tex]x^2-6x-x+6=0[/tex]

[tex]x(x-6)-1(x-6)=0[/tex]

[tex](x-6)(x-1)=0[/tex]

[tex](x-6)=0,(x-1)=0[/tex]

[tex]x=6,x=1[/tex]

When x=6, y=2(6)+1=13

When x=1, y=2(1)+1=3

The solutions are (6,13) and (1,3)

Answer:

Step-by-step explanation:

25.8/1=593.4/23

593.4 is the answer

Final answer:

To find out how many miles a minivan will travel on 23 gallons of gas with an average of 25.8 miles per gallon, multiply the gallons by the mpg to get 593.4 miles.

Explanation:

To calculate the distance a minivan will travel on 23 gallons of gas when it averages 25.8 miles per gallon, we simply multiply the number of gallons by the miles per gallon (mpg).

The formula to use is:

Distance = Number of Gallons × Average Miles per Gallon

Using the given values:

Distance = 23 gallons × 25.8 mpg

We calculate:

Distance = 593.4 miles

Therefore, the minivan can travel 593.4 miles on 23 gallons of gas, assuming it maintains the average fuel economy of 25.8 miles per gallon.

Answer:

The longest bread stick is approximately 16 in

Explanation:

The diagram representing the tray is shown in the attached image

From the diagram, we can note that the diagonal of the tray represents the hypotenuse of a right-angled triangle having legs 9.5 in and 13 in

Therefore, to get the length of the hypotenuse, we can use the Pythagorean equation which is as follows:

c² = a² + b²

where c is the length of the hypotenuse and a and b are the length of the two legs

Substitute with the givens in the above equation to get the length of the hypotenuse as follows:

c² = (9.5)² + (13)² = 259.25

c = 16.1 in which is approximately 16 in

From the above, we can conclude that:

The longest bread stick that can be fit straight along the diagonal of the tray is approximately 16 in

Hope this helps :)

Answer:

[tex]x= 11.47[/tex]

Step-by-step explanation:

By definition the cosine of an angle is the quotient between the side adjacent to the angle and the hypotenuse.

In other words:

[tex]cos (\alpha) = \frac{adjacent}{hypotenuse}[/tex]

In this triangle the length of the side adjacent to the 55 degree angle is x, and the length of the hypotenuse is 20

So:

[tex]cos(55\°) = \frac{x}{20}[/tex]

Now we solve the equation to find the value of x

[tex]x = 20cos(55\°)[/tex]

Finally

[tex]x= 11.47[/tex]

Answer:

11.47

Step-by-step explanation:

Given

Two angles of 90 and 55 degrees

and a side of length 20

Finding third angle= 180-(90+55)

                              = 35

Finding x:

Using Law of Sines to find length of side x

x/sinX=y/SinY

x/sin35=20/sin90

x=20sin35

x=11.47 !

ANSWER

[tex]f( - 3) = - \frac{9 }{7} [/tex]

EXPLANATION

The given function is

[tex]f(x) = \frac{2 {x}^{2} }{3x - 5} [/tex]

We want to find f(-3)

We substitute x=-3 into the function to get;

[tex]f( - 3) = \frac{2 {( - 3)}^{2} }{3( - 3) - 5} [/tex]

Simplify;

[tex]f( - 3) = \frac{2 \times 9 }{ - 9- 5} [/tex]

[tex]f( - 3) = - \frac{18 }{ 14} [/tex]

[tex]f( - 3) = - \frac{9 }{7} [/tex]

Answer:

[tex]2x^\frac{5}{3} - 4y^\frac{3}{4}[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt[3]{8x^5} - \sqrt[4]{256y^3}[/tex]

([tex](8x^5)^\frac{1}{3} - (256y^3)^\frac{1}{4} \\ (8^\frac{1}{3}  . x^\frac{5}{3} ) - (256^\frac{1}{4}. y^\frac{3}{4})\\ 2x^\frac{5}{3} - 4y^\frac{3}{4}[/tex] !

The initial equations of (3√8x^5) and (4√256y^3) are first changed to exponential form and then simplified to final forms of 6x^2√x and 64y respectively. The final simplified form of the entire equation therefore becomes 6x^2√x - 64y.

The given expression is (3√8x^5) - (4√256y^3). Lets breakdown and simplify each component firstly.

The first expression, 3√8x^5, can be written as 3*(8x^5)^(1/2). The number 8 can be expressed as 2^3 and x^5 as (x^2)^(5/2). So, 3√(8x^5) simplifies to 3*2x^2*√(x) = 6x^2√x.

For the second expression, 4√256y^3, can be written as 4*(256y^3)^(1/2). The number 256 can be expressed as 2^8 and y^3 as (y^2)^(3/2). So, 4√(256y^3) simplifies to 4*16y = 64y.

Now, putting these values back into the original equation, we get: 6x^2√x - 64y

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Answer:

B) y = 5x

Step-by-step explanation:

We need to find the slope

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

We have 2 points (0,0) and (6,30)

m = (30-0)/(6-0)

  = 30/6

  =5

The slope is5

y = mx+b

The y intercept is 0

y = 5x+0

y = 5x

Answer:

B:)

Step-by-step explanation:

The area of the figure is 2×3+(2×2)/2=8 square units.

Answer:

18x-8

Step-by-step explanation:

Given expression:

=4(3x-2)+6x(2-1)

The expression has to be simplified using the basic rules of mathematics,

In order to simplify the given expression,

We can see that the expression written in second bracket (2-1) which can be solved so,

=4(3x-2)+6x(1)

Multiplying 4 inside the bracket (3x-2)

=12x-(4)(2)+6x

=12x-8+6x

=18x-8  ..

Answer:

The answer is 18x - 8

Step-by-step explanation:

Answer: No, his prediction is unreasonable. After 5 minutes, the number of cells would be 400, not 32. See the explanation below for details.

-------

Remember:

-------

Identify the given information.

[tex]a_{1}[/tex] = 25

[tex]r[/tex] = 2

Use the explicit formula for geometric sequences.

[tex]a_{n} = a_{1} r^{n - 1}[/tex]

Substitute the given values.

[tex]a_{n} = (25)(2)^{n - 1}[/tex]

Substitute in 5 for [tex]n[/tex] to find out how many cells there would be after 5 minutes.

[tex]a_{5} = (25)(2)^{5 - 1} \\\\a_{5} = (25)(2)^{4} \\\\a_{5} = (25)(16)\\\\a_{5} = 400[/tex]

Final answer:

The doctor's prediction of 32 cells after 5 minutes is not reasonable, because based on exponential growth of doubling every minute, 25 initial cells should grow to 800 cells in that time period.

Explanation:

The given question involves the calculation of cell numbers in a growing population, which relates to the field of exponential growth. Using the information provided that the number of cells doubles every minute, we can apply the formula for exponential growth, which is [tex]2^{n}[/tex], where 'n' is the number of generations or minutes in this case.

Starting with 25 cells, after 5 minutes, the expected number of cells would be calculated by multiplying 25 by 25 (since the cells double every minute). This calculation gives us 25 * 32, which equals to 800 cells after 5 minutes. Therefore, the doctor's prediction that there would only be 32 cells after 5 minutes is not reasonable, as the correct calculation suggests the number should be much higher.

You just have to split the figures in different parts...

- First Picture:

- the total length is 130, so the upper and bottom rectangles have 50ft. as showed, and the middle one is 130-(50x2) = 30

- The second step is get the 2 holes área to subtract from the “total rectangle without holes area” (30x40=1200)x2 and then (20,150-1400=18,750) so, the total area from the rectangle with the holes is 18,750!

Answer:

The slope is -3

Step-by-step explanation:

This is because the slope of a line in an equation is m. In the equation given m=-3, so that makes the slope -3.

Answer:

I'm pretty sure the slope is -3.