Scott must choose a number between 55 and 101 that is a multiple of 2,4, and 5. Write all the numbers that he could choose.

The difference of a linear, quadratic reation.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation.

Trigonometric ratios describe these operations. The ide and trigonometric functions In the previous chapters, we discovered that the polynomial equation is the equation that results from equating a polynomial function to zero. A linear equation results from equating a function to zero if it is a linear polynomial. We get a quadratic equation if the function is a quadratic polynomial.

When we graph a linear equation, we get a straight line, however with a quadratic equation, we get a parabola.

Unlike the slope of a linear polynomial, the slope of a quadratic polynomial is constant.

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Answer:

123 423 21 34

Step-by-step explanation:

Answer:

x = -11

Step-by-step explanation:

2x - 7 = 3x - 2x - 18

2x - 7 = x - 18

collect like terms

2x - x = 7 - 18

x = -11

Answer: 6x - 4 = 68

Step-by-step explanation:

           Vertical angles are congruent to each other. The two angles given, 6x - 4 and 68, are vertical angles. This means we can set them equal to each other for our equation. Using this logic, the answer is;

                         6x - 4 = 68

Equation of a line that has a slope of 4 and passes through point (1, 6) is  y = 4x + 2 . Hence, C is the correct option.

To represent the standard form of equation of a line are:

Slope-intercept form:

y = mx + c

Here m represent the slope of the given line and c is the y intercept.

Intercept form:

x/a + y/b = 1

Generic way of representing the straight line, i.e. Ax+By+C = 0

x/(-C/A) + y/(-C/B) = 1

Hence a = -C / A and b = – C / B

Normal form:

The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:

x cos α+y sin α = p

General equation of the line is represented in the form:-

y - y1 = m (x-x1) ,

Where x1, y1 represents a point on the line whereas,

m represents the slope of the line.

    = (1 , 6) point on the line

    = Slope (m) = 4

Putting all the required values in general equation:-

y - 6 = 4 ( x-1 )

Hence, we get y = 4x + 2

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The given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given that the graph of the function has increased and decreasing orders on the coordinate plane.

The interval in which the given graph of the function is increasing is,

(-∞,-6)

(-4,-1)

(3,6)

(8,∞)

Therefore, the given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

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Answer:

Step-by-step explanation:

The measure of h from the triangle is h = 55

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

And , the measure of ∠ABC = 40°

Now , Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

So , the measure of ∠ACB = ∠BAC = y° = 70°

And , 2h + y° = 180° ( angles on a straight line )

On simplifying , we get

2h + 70° = 180°

Subtracting 70 on both sides , we get

2h = 110

Divide by 2 on both sides , we get

h = 55

Hence , the measure of h = 55

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The complete question is attached below :

(2h)

40°

(2h)

What is the value of h of the triangle?

O h=20

O h=35

O h=55

O h=70

simplification of expression will be g - 2

Our expression is  g - 16/4 + 2

16/4 = 4

so we c will write it as

g - 4 + 2

which can be further simplified to

g - 2

Therefore, our simplified expression comes out to be g - 2.

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The solutions to the inequality whose graph is as represented in the attached image are;

It follows from the task content that the graphical solutions for the inequality are represented on the graph and the points which are solutions for the inequality are to be identified.

Therefore, the points which are solutions for the inequality are points which are located in the shaded region of the graph.

Hence, such points include;

The answer choices B, D and F represents points on the border line of the inequality graph and since the line is broken, they are not solutions to the inequality.

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We get 2 complex answers

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.

Given that F(x) = 3x2 - 40x + 180

Set F(x) to 0, and you get ax2 + bx + c = 3x2 -40x + 180.

[-b +/- (b2 -4ac)(1/2)] is the quadratic formula. / 2a.

The stuff under the square root / radical (b2 - 4ac) is the KEY to your answer, and it determines whether you have two real, one real, or two imaginary answers. The discriminant is the term (b2 - 4ac).

Obviously, if (b2 - 4ac) > 0, you have two real answers, because the square root of a positive number is also a (positive) real number. And -b multiplied by a real number (and divided by 2a) yields two (real) answers.

If (b2 - 4ac) = 0, you have one correct answer because the square root of 0 is zero. And -b multiplied by a 0 real number (and divided by 2a) yields 1 (real) answer.

(b2 - 4ac) 0 yields two fictitious answers, because the square root of a negative number is a fictitious number. And -b multiplied by an imaginary number (and divided by 2a) yields two (complex) answers.

In this case, (b2 - 4ac) = ((-40)2 - 4(3)(180)) = 1600 - 2160 0 As a result of the discriminant is negative, the quadratic formula yields two complex answers.

Therefore we get two complex answers

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Answer:

[tex]x=\dfrac{20 +2\sqrt{35}\:i}{3}, \quad x=\dfrac{20 -2\sqrt{35}\:i}{3}[/tex]

2 imaginary answers.

Step-by-step explanation:

Given quadratic function:

[tex]f(x) =3x^2 - 40x + 180[/tex]

The zeros of a quadratic function can be found when f(x) = 0:

[tex]\implies 3x^2 - 40x + 180=0[/tex]

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Therefore:

Substitute the values of a, b and c into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-(-40) \pm \sqrt{(-40)^2-4(3)(180)}}{2(3)}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{1600-2160}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{-560}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{16 \cdot 35 \cdot -1}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{16}\sqrt{35}\sqrt{-1}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\sqrt{-1}}{6}[/tex]

Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex]:

[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\:i}{6}[/tex]

[tex]\implies x=\dfrac{20 \pm 2\sqrt{35}\:i}{3}[/tex]

Therefore, the solution is 2 imaginary answers.

Imaginary numbers

Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].  

An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].

The area of triangle using vertices is D)  A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

What is area of triangle using vertices ?

 The length of a triangle's three sides must first be determined if the triangle's vertices are known. The distance formula can be used to determine the length. when the vertices in the coordinate plane are known, the process to determine the triangle's area. Consider the triangle PQR, whose coordinates P, Q, and R are [tex](x_1,y_1)(x_2,y_2)[/tex], and [tex](x_3,y_3)[/tex] respectively.

If the triangle's area is zero and its vertices are P[tex](x_1,y_1)[/tex] Q[tex](x_2,y_2)[/tex], and R[tex](x_3,y_3)[/tex] then (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]] = 0 and its points are collinear.

Here the given vertices are, [tex](x_1,y_1),(x_1,y_2)[/tex] and [tex](x_3,y_3)[/tex] then the area of triangle is ,

=> A =  (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_2(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]

=> A =  (1/2) [[tex]x_1(y_2-y_3)[/tex] + [tex]x_1(y_3-y_1)[/tex]+ [tex]x_3(y_1-y_2)[/tex]]

=> A = (1/2)[ [tex]x_1y_2-x_1y_3+x_1y_3-x_1y_1+x_3y_1-x_3y_2[/tex]]

=> A = (1/2) [[tex]x_1y_2-x_1y_1+x_3y_1-x_3y_2[/tex]]

=> A = (1/2) [[tex]x_1(y_2-y_1)-x_3(y_2-y_1)[/tex]]

=> A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

Hence the correct option is D)  A = (1/2) [[tex](y_2-y_1)(x_3-x_1)[/tex]]

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The cost of plastering the rectangle walls at rate of Rs.15/[tex]m^2[/tex] is Rs.5565.

What is rectangle?

  With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The opposite sides of a quadrilateral are equal and parallel, and all the angles are equal. Around us, there are several rectangle-shaped items. Two dimensions, the length and breadth, define each rectangle shape. The width and length of a rectangle are its longer and shorter sides, respectively.

Given,

Length of room =12m

Breadth of room =10m

Height of room =6m

So, Area of four walls =2(l+b)×h

=>area of four wall=2(12+10)×6=264[tex]m^2[/tex]

Now Area of 2 doors and 3 windows =(2×1×2+3×2×1.5)

=> area of 2 doors and 3 windows = 13[tex]m^2[/tex]

Area of ceiling =l×b=12×10=120 [tex]m^2[/tex]

Thus, total area for plastering =(264−13+120)= 371[tex]m^2[/tex]

Hence, the cost of whitewashing =Rs.(371×15)=Rs.5565.

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The expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

So, the expression is:

Now, use Pascal's Triangle to expand as follows:

Therefore, the expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

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1. The number of students like Comedy in a class of 300 are 81.

2. The number of students like Action in a class of 400 are 72.

3. The number of students like Romance in a class of 350 are 49.

4. The number of students like Foreign in a class of 225 are 18.

5. The number of students like Horror in a class of 200 are 22.

6. The number of students like Science friction in a class of 175 are 14.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The pie chart is,

Comedy   27%

Action       18%

Romance  14%

Drama      14%

Horror      11%

Foreign    8%

Science    8%

Now,

1. The number of students like Comedy in a class of 300 are;

= 27% of 300

= 27/100 x 300

= 81

Thus, The number of students like Comedy in a class of 300 are 81.

2. The number of students like Action in a class of 400 are;

= 18% of 400

= 18/100 x 400

= 72

Thus, The number of students like Action in a class of 400 are 72.

3. The number of students like Romance in a class of 350 are;

= 14% of 350

= 14/100 x 350

= 49

4. The number of students like Foreign in a class of 225 are;

= 8% of 225

= 8/100 x 225

= 18

5. The number of students like Horror in a class of 200 are;

= 11% of 200

= 11/100 x 200

= 22

6. The number of students like Science friction in a class of 175 are;

= 8% of 175

= 8/100 x 175

= 14

Thus, 1. The number of students like Comedy in a class of 300 are 81.

2. The number of students like Action in a class of 400 are 72.

3. The number of students like Romance in a class of 350 are 49.

4. The number of students like Foreign in a class of 225 are 18.

5. The number of students like Horror in a class of 200 are 22.

6. The number of students like Science friction in a class of 175 are 14.

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Answer:

Step-by-step explanation:

There are four different color marbles.

Probability of blue:

Next, there are 3 marbles left in the bag since no replacement.

Probability of red after blue:

The probability of these two steps in order:

Complement of R is:

The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

The location of a circle in the Cartesian plane is represented by a circle equation. We can write the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.

The standard equation of a circle with center at

(a, b) and radius is r.

So, the standard equation circle is

(x -a)² + (y- b)² = r²

Given:

As, we know the standard form for equation of a circle is

(x-a)² + (y-b)² = b =r²

where (a, b) is the center of the circle and r is the radius of the circle.

We have

diameter = 12 units

radius = 12/2 = 6 units

So, the center will be at (0, 3)

Thus, the equation of circle

(x-0)² + (y-3)² = 6²

x²+ (y-3)² = 36

Hence, the Equation of Circle is x²+ (y-3)² = 36.

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A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

Answer:

Step-by-step explanation:

1. Put the words into math

3  3 1/4 divided by 2 3/8 equals a b/c.= 3 1/4/2 3/8

3 1/4/2 3/8=

1 7/19

2. Answer: 1 7/19

Answer:

Step-by-step explanation:

You want to know the numbers of dimes and quarters that make 475 cents using 25 coins.

Let q represent the number of quarters. Then 25-q is the number of dimes, and the total value of the coins is ...

  25q +10(25-q) = 475

Simplifying the above equation gives ...

  15q +250 = 475

  15q = 225 . . . . . . . subtract 250

  q = 15 . . . . . . . . . divide by 15; number of quarters

  25 -q = 10 . . . . number of dimes

The man has 10 dimes and 15 quarters.

If FG = 10x − 10, GH = x + 4, and FH = 16, FG is 10

information given in the question include

FG = 10x − 10

GH = x + 4

FH = 16

The problem is solved using substitution. this involves replacement of a variable with another that are same.

An instance of this a line FH having points FG and GH

FH contains FG and GH, hence adding both FG and GH gives FH

FH = FG + GH

plugging in the values

16 = 10x - 10 + x + 4

collecting like terms

16 = 11x - 6

16 + 6 = 11x

22 = 11x

rearranging the equation

11x = 22

x = 2

FG = 10x − 10

substituting the value of x

FG = 10 * 2 − 10

FG = 20 - 10

FG = 10

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The number of 3 / 16 yards pieces that can be cut from 3 / 4 yard of ribbon is 4.

The actual length of the ribbon is 3 / 4 yards.

He wants to cut 3 / 16 yards pieces from the actual length of the ribbon.

Therefore, the number of 3 / 16 yard that can be cut from 3 / 4 yard of ribbon can be calculated as follows;

number of pieces of ribbon = 3 / 4 ÷ 3 / 16

number of pieces of ribbon = 3 / 4 × 16 / 3

number of pieces of ribbon =  48 / 12

Therefore,

number of pieces of ribbon =  4 yards

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Answer:

No

Step-by-step explanation:

A right angle triangle will have a 90° angle. If you don't know what that looks like. Check the rectangle above triangle C. All of the angles in it are 90°.

Bonus:

If you wanted check the length is of the third side of triangle c. It is 17 in, this is because you look at the top of the rectangle and the top of the triangle and they are both the same length.

Answer:

I feel like it is it depends on the way you are leaning and if these sides are rounded or not

If they are rounded then yes this is a right triangle is not then no but it is close

Step-by-step explanation:

it might just be if the third side is rounded

We find out using the Pythagorean theorem

12^2+12^2=c^2

144+144

288=c^2

Square root both sides

16.97=c

Hopes this helps please mark brainliest

Answer:

[tex]d=7[/tex]

[tex]a_9=59[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]3[/tex] and the second term is [tex]10[/tex], then each successive term in the sequence is [tex]7[/tex] more than the previous term. The common difference is [tex]7[/tex] ( [tex]d=7[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=7n-4[/tex]

Therefore, the ninth term in the sequence is:

[tex]a_9=7(9)-4[/tex]

[tex]a_9=63-4[/tex]

[tex]a_9=59[/tex]

Answer:

[tex] \huge{ \boxed{r =100( \sqrt[n]{ \frac{A}{P} } - 1)}}[/tex]

Step-by-step explanation:

[tex]A = P(1 + \frac{r}{100} )^{n} \\ [/tex]

First of all in order to make r the subject we have to first divide both sides of the equation by P

That's

[tex] \frac{A}{P} = \frac{P( {1 + \frac{r}{100} })^{n} }{P} \\[/tex]

We'll finally get

[tex] \frac{A}{P} = ( {1 + \frac{r}{100}) }^{n} \\ [/tex]

Next we have to remove the power n and to do that we find the square root of 'n' of both sides as

We have

[tex] \sqrt[n]{ \frac{A}{P} } = \sqrt[n]{( {1 + \frac{r}{100} })^{n} } \\ \\ \\ \sqrt[n]{ \frac{A}{P} } = 1 + \frac{r}{100} [/tex]

Next we subtract 1 from both sides to isolate r/100

We have

[tex]\sqrt[n]{ \frac{A}{P} } - 1 = 1 - 1 + \frac{r}{100} \\ \sqrt[n]{ \frac{A}{P} } - 1 = \frac{r}{100} [/tex]

Finally to isolate r , we multiply both sides by 100

[tex] \frac{r}{100} \times 100 =100 \times (\sqrt[n]{ \frac{A}{P} } - 1)[/tex]

We have the final answer as

[tex]r =100( \sqrt[n]{ \frac{A}{P} } - 1) \\ [/tex]

Hope this helps you

Answer:

the answer to 2dp is 2536.02

Answer:

[tex]16x {}^{3} + 1[/tex]

Step-by-step explanation:

We need to differentiate the following function,

[tex]\longrightarrow f(x) = 4x^4 + x [/tex]

Let ,

[tex]\longrightarrow y = f(x) [/tex]

So that ,

[tex]\longrightarrow y = 4x^4+x [/tex]

Differentiating both sides wrt x ,

[tex]\longrightarrow \dfrac{dy}{dx}= \dfrac{d(4x^4+x)}{dx}\\[/tex]

[tex]\longrightarrow\dfrac{dy}{dx}= \dfrac{d(4x^4)}{dx}+\dfrac{dx}{dx}\\ [/tex]

[tex]\longrightarrow \dfrac{dy}{dx} = 4(4)x^{4-1} + 1 \\ [/tex]

[tex]\longrightarrow \underline{\underline{ \dfrac{dy}{dx}= 16x^3 +1}}[/tex]

The measure of the angle in line y = 3x/2 is 56.31 degrees

Comparing the given equation y = 3x/2 with equation of a line in the slope intercept form  form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

This shows the y = 3x/2 is a line with c = 0 and slope as 3/2

calculation of slope

m = (y₂ - y₁) / (x₂ - x₁)

the formula is similar to definition of tan, assuming the angle is x

tan x = 3/2 (positive x and y axis)

x = arc tan 3/2

x = 56.3099

x = 56.31 degrees (to the nearest tenth of a degree)

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