Find the values of a and b so that the polynomial x^3 -10x^2 +ax +b is exactly divisible by x-1 as well as x-2

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

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Remember:

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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.

Answer: 100mL

Step-by-step explanation:

A 15% alcohol solution contains 15mL alcohol in 100mL solution

In 400ml there will be 400mL·15/100 = 6,000mL/100 = 60mL alcohol

Let the volume of pure alcohol to be added V.

In the new solution there will be (60 + V)mL  alcohol

And the total volume will be (400 + V)mL

Concentration required 32% = 0.32

Concentration = (60 + V)mL/(400 + V)mL = 0.32

60mL + VmL = 0.32(400 + V)mL

60mL + VmL = 128mL + V·*0.32mL

VmL - V·0.32mL = 128mL - 60mL = 68mL

V(1 - 0.32)mL = 68mL

V·0.68mL = 68mL

VmL = 68mL/0.68 = 100mL ►  alcohol volume to be added

Answer : 100mL

Verification

New solution

There will be  400mL + 100mL = 500mL total volume

There will be 60mL alcohol + 100mL alcohol = 160mL alcohol

The concentration will be   160mL/500mL = 0.32 = 32%

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

x = -1.

Step-by-step explanation:

√(x + 10) - 4 = x

√(x + 10) = x + 4

Squaring both sides:

x + 10 = x^2 + 8x + 16

x^2 + 8x - x + 6 = 0

x^2 + 7x + 6 = 0

(x + 6)(x + 1) = 0

x = -6, -1.

Check for any extraneous roots:

√(x + 10) - 4 = x

Try x = -6:

√(-6 + 10) - 4 = 2 - 4 = -2.

but we found x = -6  , so -6 is not a root.

Try x = -1:

√(-1 + 10) - 4 = 3 - 4 = -1. So x = -1 is a root.

x=-1

Step-by-step explanation:

sqrt(x+10) -4= x

sqrt(x+10) = x+4

square each side

x+10=(x+4)^2

x+10= x^2+8x+16

subtract x+10 from each side

x^2+7x+6=0

(x+6)(x+1)=0

x=-6 x=-1

Then we plug both back into the equation.

sqrt(-1+10) -4= -1

sqrt(9) -4= -1

3-4 = -1

-1=-1. this works out.

sqrt(-6+10) -4 = -6

sqrt(4) -4= -6

2-4= -6

-2= -6. this does not work so the only solution is x=-1

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:

$203.5

____________________________________________________

Step-by-step explanation:

In order to find the answer to your question, we would need to find how much money she made when selling the collars.

Lets gather the important information:

$4.75 for small collar

$7.75 for large collar

With the information above, we can solve the problem.

What we would do is multiply the amount of collars that was sold to the right price.

Therefore, we would multiply 4.75 by 20, since small collars cost 4.75 and she sold 20 of them. We would also multiply 7.75 by 14, since large collars cost 7.75 and she sold 14 of them.

Lets calculate:

[tex]4.75*20=95\\\\7.75*14= 108.50[/tex]

Now, we would add the final prices together in order to find how much revenue she made off of the collars.

[tex]95+108.50=203.5[/tex]

When you're done soplving, you should get 203.5.

This means that her revenue last month was $203.5.

$203.5 should be your FINAL answer.

____________________________________________________

Answer:

205.50

Step-by-step explanation:

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:

Angle 3 and angle 4 are linear pair

Step-by-step explanation:

* Lets revise the types of angles

- If two line intersected at a point, there are two types of

pairs of angles

- Two vertically opposite angles equal in measure

- Linear pair of angles their sum is 180°

* Now lets solve the problem

- There are two lines intersect each other at a point

- They formed between them 4 angles

- Angle 2 and angle 4 are vertical opposite angles, equal in measure

- Angle 1 and angle 3 are vertical opposite angles, equal in measure

∴ m∠2 = m∠4

∴ m∠1 = m∠3

- Angle 1 and angle 2 formed a line

∴ They are linear pair of angles

- Angle 3 and angle 4 formed a line

∴ They are linear pair, of angles

∵ m∠1 + m∠2 = 180°

∴ m∠3 + m∠4 = 180°

* Angle 3 and angle 4 are linear pair

Answer:

c

Step-by-step explanation:

Answer:

B. 14.7

Step-by-step explanation:

You would need to use the Pythagorean Theorem to find the length of the other leg. But you basically have to use it backwards. The theorem is a^2+b^2=c^2.

Substitute the values: a^2+12^2=19^2

Calculate the exponents: a^2+144=361

Subtract 144 from both sides: a^2=217

Find the square root of 217: 14.70309

Round to the nearest tenth: 14.7

Answer:

9. 1620°

10. 360°

11. 180°

Step-by-step explanation:

The answers of problems 10 and 11 give you the way to find the answer to problem 9.

__

10. The sum of exterior angles of any convex polygon is 360°.

__

11. An internal angle and an external angle are a linear pair, so always sum to 180°.

__

9. At every vertex, the sum of interior and exterior angles is 180°, so the total of those angles at all vertices is n·180°. Of that total, 360° is the sum of exterior angles, so the total of interior angles of an n-gon is ...

n·180° -360° = (n -2)·180°

For an 11-gon, the sum of interior angles is ...

(11 -2)·180° = 1620°

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:

19) sin 48° ≅ 0.7431

20) sin 38° ≅ 0.6157

21) cos 61° ≅ 0.4848

22) cos 51° ≅ 0.6293

Step-by-step explanation:

* Lets explain the meaning of trigonometry ratio

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∴ sin(A) is the ratio between the opposite side of ∠A and the hypotenuse

# cos(A) = adjacent/hypotenuse

∴ cos(A) is the ratio between the adjacent side of ∠A and the hypotenuse

# tan(A) = opposite/adjacent

∴ tan(A) is the ratio between the opposite side of ∠A and the

  adjacent side of A

# The approximation to the nearest ten-thousandth, means look to

  the fifth number before the decimal point if its 5 or greater than 5

  ignore it and add the fourth number (ten-thousandth) by 1 if it is

 smaller than 5 ignore it and keep the fourth number as it

* Now lets solve the problems

19) sin 48° is the ratio between the side opposite to the angle of

    measure 48° and the hypotenuse of the triangle

∴ sin 48° = 0.74314 ≅ 0.7431 ⇒ to the nearest ten-thousandth

20) sin 38° is the ratio between the side opposite to the angle of

    measure 38° and the hypotenuse of the triangle

∴ sin 38° = 0.61566 ≅ 0.6157 ⇒ to the nearest ten-thousandth

21) cos 61° is the ratio between the side adjacent to the angle of

    measure 61° and the hypotenuse of the triangle

∴ cos 61° = 0.48480 ≅ 0.4848 ⇒ to the nearest ten-thousandth

22) cos 51° is the ratio between the side adjacent to the angle of

    measure 51° and the hypotenuse of the triangle

∴ cos 51° = 0.62932 ≅ 0.6293 ⇒ to the nearest ten-thousandth

Answer:

Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the area of the enlarged garden

y ----> the area of the original garden

[tex]z^{2}=\frac{x}{y}[/tex]

we have that

If Tessa multiplies each dimension by 2, then the scale factor equals 2.

[tex]z=2[/tex]

substitute

[tex]2^{2}=\frac{x}{y}[/tex]

[tex]4=\frac{x}{y}[/tex]

[tex]x=4y[/tex]

The area of the enlarged garden will be equal 4 times the area of the original garden

so

If Tessa wanted to have twice as much surface, she must multiply each dimension by a square root of 2.

therefore

Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.

We have 220 students total.

140 like Chocolate.

120 like Vanilla.

140+120=260.

260 is 40 more than 220.

Therefore there are 40 students who said they like both.

I hope this helps! :)

Final answer:

By applying the principle of inclusion-exclusion, we found that 40 students like both chocolate and vanilla ice cream.

Explanation:

To determine how many students like both chocolate and vanilla ice cream, we need to use the principle of inclusion-exclusion. This principle is a fundamental counting technique in mathematics that considers the overlap of two sets.

According to the principle, if we have two overlapping sets, we can find the number of elements that are in both sets by adding the number of elements in each set (in this case, the number of students who like chocolate and the number of students who like vanilla) and then subtracting the number of elements that have been counted twice (the students who like both).

The formula we will use is: Number of students liking both = (Number of students liking chocolate) + (Number of students liking vanilla) - (Total number of students surveyed).

Applying the formula:

Number of students liking chocolate = 140

Number of students liking vanilla = 120

Total number of students surveyed = 220

Number of students liking both = 140 + 120 - 220 = 40.

Therefore, 40 students like both chocolate and vanilla ice cream.

Answer: The radius is 12 feet

Step-by-step explanation:

You know that the formula used to calculate the area the a sector of a circle is:

[tex]A=\frac{C\pi }{360}*r^2[/tex]

Where C is the central angle in degrees and r is the radius of the circle

Solve for "r" from this formula:

[tex]360*A=C\pi*r^2\\\\\frac{360*A}{C\pi}=r^2\\\\r=\sqrt{\frac{360*A}{C\pi}}[/tex]

You know the that the angle is 90 degrees and you know that the area of the sector is 36π ft², then substituting values you get that the radius of this circle is:

[tex]r=\sqrt{\frac{360(36\pi ft^2)}{90\°\pi}}=12ft[/tex]

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:

Step-by-step explanation:

[tex]a^2+a-2=a^2+2a-a-2=a(a+2)-1(a+2)=(a+2)(a-1)[/tex]

Answer:

Its diagonals are perpendicular, then it is a rhombus

Step-by-step explanation:

* Lets revise the properties of the parallelogram and the rhombus

- In the parallelogram each two opposite sides are parallel

- In the parallelogram each two opposite sides are equal in length

- In the parallelogram the diagonals bisect each other

- In the rhombus each two opposite sides are parallel

- In the rhombus all the sides are equal in length

- In The rhombus the diagonals are perpendicular to each other

- Parallelogram is a rhombus if two adjacent sides are equal in length

- Parallelogram is a rhombus if its two diagonals are perpendicular

* Now lets solve the problem

∵ The vertices of the parallelogram are

   A(-3 , 2) , B(-2 , 6) , C (2 , 7) , D (1 , 3)

- The slope of the line which passes through points (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

* lets find the slopes of the sides and the diagonals

∵ The slope of AB = (6 - 2)/(-2 - -3) = 4/1 = 4

∵ The slope of BC = (7 - 6)/(2 - -2) = 1/4 = 1/4

∵ The slope of CD = (3 - 7)/(1 - 2) = -4/-1 = 4

∵ The slope of DA = (2 - 3)/(-3 - 1) = -1/-4 = 1/4

- The product of the slopes of the perpendicular line is -1

∵ AB and BC are two adjacent sides and the product of their slopes

  = 4 × 1/4 = 1 ≠ -1

∴ AB and BC are not perpendicular

∴ The parallelogram can not be a rectangle

- Lets check the slopes of the diagonals

∵ The diagonals of the parallelogram are AC and BD

∵ The slope of AC = (7 - 2)/(2 - -3) = 5/5 = 1

∵ The slope of BD = (3 - 6)/(1 - -2) = -3/3 = -1

∵ The product of the slopes of AC and BD = 1 × -1 = -1

∴ AC and BD are perpendicular

∴ ABCD is a rhombus

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

Answer:

Yes, (0,4) is a solution

Step-by-step explanation:

We have to plug in 0 in x and 4 in y IN BOTH THE INEQUALITIES.

IF BOTH ARE TRUE, then the system of inequalities is TRUE.

Let's check:

y ≤ -3x+4

4 ≤ -3(0)+4

4 ≤ 4

Is 4 less than OR equal to 4? Yes. THis is satisfied.

Now, checking 2nd one:

y > x^2 + 3x - 2

4 > (0)^2 + 3(0) - 2

4 > -2

Is 4 greater than -2? Yes, it is. So this is satisfied as well.

Hence, (0,4) is a solution to the system of inequalities shown.

Answer:

Yes, it is the solution

Step-by-step explanation:

You are given the system of two inequalities

[tex]\left\{\begin{array}{l}y\le -3x+4\\ \\y>x^2+3x-2\end{array}\right.[/tex]

To check whether point (0,4) is the solution to this system, substitute x=0 and y=4 into each inequality:

1.

[tex]4\le -3\cdot 0+4\\ \\4\le 4 \ [\text{true}][/tex]

2.

[tex]4>0^2+3\cdot 0-2\\ \\4>0+0-2\\ \\4>-2\ [\text{true}][/tex]

Since the coordinates of the point (0,4) satisfy both inequalities, the point (0,4) is the solution to the system

Answer:

c=0

Step-by-step explanation:

x² + 11x + 0 = y

x² + 11x + 0 = 0

U already know that y=0 by looking at the equations above,

But your worksheet never state "c", so we will take that c is 0   (look at the equations above.)

So c is just 0.

In a quadratic equation of the form ax^2 + bx + c=0, 'c' is the constant term. In your equation x^2 + 11x = 0, therefore the 'c' value is 0.

The equation you provided, x^2 + 11x = 0, is a quadratic equation of the form ax^2 + bx + c = 0. In this equation, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant. Comparing your equation with this form, the values of 'a', 'b', and 'c' in your equation are 1, 11, and 0 respectively. Therefore, in your equation, the 'c' value is 0.

To find roots or solutions for the equation, we use the quadratic formula: -b ± √(b^2 - 4ac) / 2a. Substituting 'a', 'b' and 'c' values from your equation will help to find the value of 'x'.

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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:

7 to 50

Step-by-step explanation:

Answer:

a° = 80° , b° = 40° , c° = 40° , d° = 100°

Step-by-step explanation:

* Lets study the information in the question to solve it

- There is a circle and two chords of it are parallel

∵ The two chords are parallel

- The measure of b° is the same with the angle of measure 40°

   because they are alternate angles

∴ b° = 40°

- The vertex of the angle of measure 40° is on the circle

∴ This angle is inscribed angle subtended by the arc of measure a°

- There is a relation between the inscribed angle and its subtended arc,

 the measure of the arc is twice the measure of the angle

∵ The measure of the angle is 40°

∴ a = 40° × 2 = 80°

∴ a° = 80°

- In the circle any two inscribed angles subtended by the same arc

 are equal in measure

∵ The angle of measure 40° and the angle of measure c° are

  inscribed angles subtended by the same arc of measure a°

∴ c° = 40°

- The sum of the measures of the interior angles in any triangles is 180°

∴ b° + c° + d° = 180° ⇒ interior angles of a Δ

∵ b° = 40° , c° = 40°

∴ 40° + 40° + d° = 180° ⇒ add

∴ 80° + d° = 180° ⇒ subtract 80 from both sides

∴ d° = 100°

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

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:

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:

C. 17.3

Step-by-step explanation:

Using Pythagoras theorem

Divide the triangle into half

c^2=a^2+b^2

20^2=a^2+10^2

400=a^2+100

400-100=a^2

300=a^2

17.32=a^2

The height of the equilateral triangle to the nearest tenth is 17.3

Given that:

An equilateral triangle has sides of length 20.

Equilateral triangles are the type of triangles which has all the sides equal to each other.

That is, three sides will have equal length.

So all the side of the triangle is 20.

The height of the triangle is the perpendicular line drawn from any of these vertices.

Since this is an equilateral triangle, the height divides the base into equal lengths.

So each half will be 20/2 = 10.

Here, a right angle is formed.

Using Pythagoras theorem,

h = √(20² - 10²)

  = √(400 - 100)

  = √300

  = 17.3

Hence the correct option is C.

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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.

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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