triangle ABC has vertices A(-2,-1), B (1,2) and C (2,-4), if triangle A'B'C' is a dilation of triangle ABC with a scale factor of 2,5 and center of dilation (0,0), give the coordinates of the vertices of triangle A'B'C'

Answer:

Step-by-step explanation:

Area = L times w ( length times width.)

Your lengthyot Length is 4 units and width is 4. so what is 4 times 4?

your right, its 16. Answer A is correct.

Answer:

Proved below.

Step-by-step explanation:

Parallel lines and angles:

     Given: p // q and ∠1≅ ∠2

Proof:

        p //q, l is transversal,

            ∠3 ≅ ∠1   -----(I)    {Corresponding angles are congruent}

          ∠1 ≅ ∠2   ---------(II)    {Given}

From (II) & (I),

        ∠3 ≅ ∠2

∠3 and ∠2 are alternate interior angles. Alternate interior angles are congruent only if the lines are parallel.

⇒ l // m

The zeroes of the equation f(x) is 3x² + 18x + 32 is x =  -18 -7.75/ 6 and x = -18 + 7.75/ 6

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

Given f(x) = 3x² + 18x + 32

3x^2 + 18x + 32 = 0

Here, a = 3

b = 18

c = 32

-b ±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

-18 ± [tex]\frac{\sqrt{18^2-4(3)(32)} }{2(3)}[/tex]

-18 ± [tex]\frac{\sqrt{324-84} }{6}[/tex]

-18 ± [tex]\frac{\sqrt{-60} }{6}[/tex]

-18 ± [tex]\frac{-7.75}{6}[/tex]

X = -18 (-7.75)/ 6 and x = -18 – (-7.75)/ 6

X = -18 -7.75/ 6 and x = -18 + 7.75/ 6

Therefore, the zeroes of the polynomial are X = -18 -7.75/ 6 and x = -18 + 7.75/ 6

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The measure of the top, vertex angle of an isosceles triangle is option c 100 degrees

Given,

The base angle of an isosceles triangle = 40 degrees

We have to find the top, vertex angle:

Isosceles triangle:

Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

Here,

We know that total interior angle of a triangle is 180°

In an isosceles triangle base angles will be equal.

Here, base angle is 40 degrees.

Now, the top, vertex angle = total angle - base angle × 2

= 180 - 40 × 2

= 180 - 80

= 100

That is, the top, vertex angle of an isosceles triangle is 100°

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The system of equations has one real solution (2,4).

The given system of equations is:

y = x²

y = 2x

Substitute the value of y in the second equation,

x² = 2x

x²- 2x = 0 ( Factorize it)

x(x - 2) = 0

x = 0 and x = 2

Putting the value of x in the equations to obtain the value of y,

y = x² = 0  

y = 2x = 2(0) = 0

y = x² = 2² = 4

y = 2x = 2(2) = 4

Therefore the system of equations has only one real solution (2,4).

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The length of each wooden board bought by Madelyn was 0.27 meters.

For the given question.

The number of wooden board bought by Madelyn = 7.

The length of all boards = 1.9 meters.

Thus, to find the length of each wooden board, simply divide the total length by the total board as each board is identical.

Each length = total length/number of boards

Each length = 1.9/7

Each length = 0.27 meter.

Thus, the length of each board bought by the Madelyn is 0.27 meters.

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The volume of sphere in terms of  is 288 cubic inches, if the sphere has a radius of 6 inches.

What is the volume of sphere?

In mathematics, the volume of the sphere defines the capacity of a sphere. It is measured in the cubic unit. Basically, it tells the amount of the air it can hold inside the sphere.

According to the question, the given data state that the sphere has a radius of 6 inches

Using standard formula for volume of sphere is,

Volume of the sphere = (4/3)πr³    

where, r - radius of sphere and it is 6 inches

Therefore, volume of sphere = (4/3)π(6)³ = (4/3)π(216) = 288 Cubic inches

Hence, the volume of sphere in terms of  is 288 cubic inches, if the sphere has a radius of 6 inches.

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Answer: x = -1 , F

Step-by-step explanation:

Hard to see your pic, but

[tex](-b+\sqrt{b^{2}-4ac } )/2a\\(-b-\sqrt{b^{2}-4ac } )/2a[/tex]

[tex](-5-\sqrt{5^{2}-16} ) / 8 = -1[/tex]

Your answer is: x = -1

ALL THE SHAPES HERE ARE RECTANGLES AND THE AREA OF A RECTANGLE IS =L×B

TO GET THE AREA OF THE SHADED PART WE SAY THE AREA OF THE OUTSIDE SHAPE SUBTRACT THE AREA OF THE INNER SHAPE.

LET US FIND THE AREA OF THE OUTSIDE RECTANGLE FIRST.

[tex]a1 = (x + 5)(x - 1) \\ = {x}^{2} - x + 5x - 5 \\ a = {x}^{2} +4 x - 5[/tex]

NOW LET US FIND THE AREA OF THE INNER RECTANGLE.

[tex]a2 = (x + 1)(x - 4) \\ a = {x}^{2} - 4x + x - 4 \\ \\ a = {x }^{2} - 3x - 4[/tex]

the area of the shaded part is given by

[tex]a1 - a2 = ( {x}^{2} +4 x - 5) - ( {x}^{2} - 3x - 4) \\ = {x}^{2} + 4x - 5 - {x }^{2} + 3x + 4 \\ = {x}^{2} - {x}^{2} + 4x + 3x - 5 + 4 \\ areashaded = 7x - 1[/tex]

The simplified expression for the given algebraic expression -2(3x – 2) -5(7 – x) will be ( -x - 31)

As per the question statement, we are supposed to find the simplified expression for the given algebraic expression -2(3x – 2) -5(7 – x).

For solving the above expression, we should be having good knowledge of all mathematical operators and BODMAS.

Let y =  -2(3x – 2) -5(7 – x)

y = -6x + 2*2 - 5*7 + 5x

y = -6x + 4 - 35 +5x

y = -x - 31

Therefore, the simplified expression for the given algebraic expression -2(3x – 2) -5(7 – x) will be y = ( -x - 31)

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Answer: 15/16 is written as 0.9375 in decimal form.

Step-by-step explanation:

To convert any fraction to decimal form, we just need to divide its numerator by the denominator.

Here, the fraction is 15/16 which means we need to perform 15 ÷ 16.

This gives the result 0.9375

= 15/16

= 15 ÷ 16

= 0.9375

The tree is 79 feet tall if the ground is 79 feet from the tree and the angle of elevation is 45°.

Angle of elevation:

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

Therefore, the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Given,

The angle of elevation to a nearby tree from a point on the ground is measured to be 45 degrees.

Here we need to find how tall is the tree if the point on the ground is 79 feet from the tree and we have also need to round the  answer to the nearest hundredth of a foot.

Here we know that

The angle of elevation = 45°

Distance of the point from the tree = 79 feet

Suppose h is the height of the tree.

Then the value of h is calculated as,

=> h / 79 = tan 45°

We know that, the value of tan 45° = 1,

So,

=> h/79 = 1

Then  the value of h is,

=> h = 79

Thus, the height of the tree is 79 feet.

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The interest of the CD account's of Ethan after 6 year is  $756.

For the given question;

Ethan deposit $7,000 into a certificate of deposit CD for 6 years.

The formula for finding the simple interest is;

SI = PRT/100

where,

Put the values in the formula,

SI = 7,000×1.8×6/100

Simplifying;

SI = 756.

Thus, the simple interest gained after 6 years will be $756.

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a) By definition of standard form, a light-year is equal to 5.880 × 10¹² miles.

b) By simple rule of three, a magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.

In this problem we need to convert a magnitude in miles to an equivalent magnitude in light-years and another magnitud in light-years to an equivalent magnitude in miles. Standard form is a notation used to represent both large and small number with no significant loss of precision. This form is described by the following form:

a.b × 10ⁿ

Where:

a) A light-year is equal to 5.880 × 10¹² miles.

b) The equivalent magnitude in miles is found by the following simple rule of three:

x = 4.25 ly × (5.880 × 10¹² mi / ly)

x = 2.499 × 10¹³ mi

A magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.

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Answer:

Cost per egg = 8.4/12 = 0.7

Cost per hundred egg =Rs70

Let selecting price per hundred be Rs.y

⇒ 70/y-70 ×100 = 15

⇒ 10y−700 = 105

a. The graph shows a positive correlation.

b. Using the line of best fit, his predicted score in his second paper could have been between 60 - 65.

A positive correlation is a type of correlation whereby two variables move in the same direction. That is, as one increases, the other increases also.

In a scatter plot, a positive correlation exist when both variables appear to move towards the same direction as the line of best fit slopes upwards from left to your right.

a. The scatter plot shows an upward trend on the line of best fit, therefore, the type of correlation shown by the graph is: positive correlation.

b. Using the line of best fit to make prediction, if he got 50 in his paper 1, then the score of the student in his paper 2 could have been between 60 and 65.

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Answer:

5.2 × 10 to the power of 1

Step-by-step explanation:

IF AB=3x, BC=x+5 and AC=24 then the midpoint of AC is point B.

Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.

WE have given that AB=3x, BC=x+5 and AC=24. Since B is the midpoint, then we have:

AB = BC = AC/2

Now Substitute and solve for x:

AB = BC

x + 5 = 3x

x + -3x = -5

2x = 5

x = 5/2

AB = 3(5/2) = 15/2

BC = x + 5 = 5/2 + 5 = 15/2

Hence, the midpoint of AC is point B.

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On multiplying by [3], the slope becomes 3 times the original slope and

y - intercept becomes 3 times of the original value.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

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

We have the following problem -

f(x) = ax + b, where [a] and [b] are nonzero real numbers. Now, the function f(x) is multiplied by 3.

The given straight line is -

y = f(x) = ax + b

After multiplied by [3], we get -

y' = 3f(x) = 3(ax + b) = (3a)x + (3b)

Therefore, on multiplying by [3], the slope becomes 3 times the original slope and y - intercept becomes 3 times of the original value.

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[Complete question - Given f(x) = ax + b, where a and b are nonzero real numbers, which of the following describes the differences between the graph of f and the graph of the output of f multiplied by 3 ]

Answer:

1500

Step-by-step explanation:

600 divided by 4 to see how much hotdogs are sold EACH home football game. This gives you 150 each game so you multiple it by ten in order to get the total for ten home games

Answer: x=8

Step-by-step explanation:

2x-3+x+5

2x-3+3=x+5+3 (Add 3 to both sides)

-2x=x+8

_____________

2x=x+8

2x-x=x+8-x (Subtract x from both sides)

_____________

Combine like terms

_____________

2x-x=x+8-x

1x=x+8-x

Multiply by 1

1x=x+8-x

x=x+8-x

_____________

Combine like terms

x=x+8-x

[x=8]

The x value will be 109°. The straight line formed a 180° angle. Solving the equation yields the angle.

Supplementary angles are two angels whose sum is 180°. When a straight line intersects a line, two angles form on each of the sides of the considered straight line.

Those two-two angles are supplementary angles in two pairs. That is, if two supplementary angles are adjacent to each other, their exterior sides form a straight line.

The straight line formed a 180° angle. The resulting equation is as follows:

⇒x+42°+29°=180°

⇒x=109°

Hence, the value of the x will be 109°

The complete question is:

AB is a straight line.

Work out the size of angle x.

Not drawn accurately

42°

Х

29°

А

B

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That indicates that in order to make a solution that is 60% acid, you will need to add a total of 300 milliliters of pure acid into the mixture.

This is further explained below.

In general, pure acid refers to an acid concentration of 100%. It is feasible to formulate the following equation if you assume that X represents the volume addition of the pure acid:

[tex]Va=100 \%X + 600 * 40 \%[/tex]

[tex]Va= (600+X)60 \% (M_1V_1=M_1 V_2)[/tex]

100X + 24000 = 36000 + 60x

X = 300.

In conclusion, That implies in order to generate a solution that is 60% acid, you will need to add 300 milliliters of pure acid.

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The domain of any function represents the set of values of x for which the function is true.

The function shown in the graph starts at x=3 and continues towards +∞

The domain of the function is all values of x greater than or equal to 3.

1 small pizza and 4 large pizza feeds people according to the system of equations.

Let the number of small pizza be x and the number of large pizza be y.

So, we get the two equations as:

3 x + 4 y = 19 ...(1)

5 x + 5 y = 25 ...(2)

Taking 5 common from equation 2, we get that:

x + y = 5

x = 5 - y

Put it in equation 1, we get that:

15 - 3 y + 4 y = 19

15 + y = 19

y = 4

x = 5 - 4 = 1

Therefore, we get that, 1 small pizza and 4 large pizza feeds people according to the system of equations.

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Answer: true

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

Let the number of eggs be N, and the weight be M

M is directly proportional to N.

.: M= kN

264 = 6k

.; k(the constant of proportionality is) = 264/6

k = 44.