use the law of cosines to find each missing side

Answer:

B' = (-8,-1) , C' = (4, 5)

Step-by-step explanation:

The coordinates  of A are (-5,-7)

The coordinates of C are  3 units to the right and 4 up from A.

So for a dilation  factor 3 C' will be 9 to the right and 12 up from A.

C' = (-5 + 9) , (-7 + 12)

=  (4, 5).

The point B is 1 unit to left and 2 up from A.

So B' is (-5 -3) , (-7+ 6)

= (-8, -1).

After a dilation scale factor of 3 centered at A, B'(- 18, - 15), and C'(- 6, - 9).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A triangle ABC.

The coordinate of B is (- 6, - 5), and the coordinate of C is (- 2, - 3).

After a dilation scale factor of 3 centered at A coordinates of B' would be

(- 6×3, - 5×3) = (- 18, - 15) and C'(- 2×3, - 3×3) = (- 6, - 9).

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Answer:-11

Step-by-step explanation:

use -6 to represent losing 6 yards

use -5 to represent losing 5 yards

add these together

(-6) + (-5) = -11

when adding two negative values, make sure your sum is negative

Answer:

it is 9

Step-by-step explanation:

6 plus 3 is 9

I had this for homework so I know

Answer:

The answer is 6

Step-by-step explanation:

What you do is this.  

3/9 times 18/1 because you need to make 18 a fraction and then multiply. And you will get 6

Answer:

C. 31

Step-by-step explanation:

3000 there are 3-4 errors

If we first divide 24,000 by 3,000, will get 8

then since there a error for each 3,000 books, we do 8 x 4 = 32 and 8 x 3 = 24

32 (8 x 4)  the max amount of printing errors

24 (8 x 3) the minimum amount of printing errors

So we should expect 24-32 printing errors

Only answer between the numbers is c. 31

Final answer:

The exact number of books that could have a printing error out of 24,000, given the rate of 3 to 4 errors per 3,000 books, can be calculated to be within a range, making 31 the only viable option provided.

Explanation:

The question is about determining the exact number of books that will have a printing error out of 24,000, given that there are between 3 and 4 printing errors per every 3,000 books. To find the possible number of errors, we multiply the number of books (24,000) by the rate of errors (3 to 4 per 3,000). This gives us a range of possible errors, from (24,000 / 3,000) * 3 = 24 to (24,000 / 3,000) * 4 = 32. Therefore, the only option within this range is 31.

Answer:

width = 4.16 meter

length = 6.49 meter

Step-by-step explanation:

Area of the rectangle =27 m²

Let the width of the rectangle be x meter

So, Length = 3 * width - 6

                  = 3*x - 6

                  = 3x-6 meter

Area of the rectangle = length * width

27 = (3x-6)*x

Flipping the sides of the equation, we have

(3x-6)*x =27

Distributing the left side, we get

(3x)*(x) - (6)*(x) = 27

=> 3x² - 6x = 27

Subtract 27 from both sides,

3x² - 6x -27 = 27 - 27

=> 3x² - 6x -27 = 0

Factoring out 3 from all the terms on the left side, we have

3(x² - 2x -9) = 0

Dividing both sides by 3, we have

[tex]\frac{3(x^{2}-2x-9) }{3}[/tex] = [tex]\frac{0}{3}[/tex]

Cancelling out the 3's on the left, we get

x² - 2x -9 = 0

We'll use the quadratic formula to solve for the x,

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

Comparing the quadratic equation x² - 2x -9 = 0 with ax² + bx + c = 0, we get

a = 1 (as x² has no coefficient)

b = -2

c = -9

Plugging in the values of a, b, and c into the quadratic formula, we get

x = [tex]\frac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(-9) } }{2(1)}[/tex]

=> x = [tex]\frac{2\pm\sqrt{4+36 } }{2}[/tex]

=> x = [tex]\frac{2\pm\sqrt{40}}{2}[/tex]

=> x = [tex]\frac{2\pm2\sqrt{10}}{2}[/tex]

Factoring out 2 from the top, we get

x = [tex]\frac{2(1\pm\sqrt{10})}{2}[/tex]

Canceling out the 2's from the top and bottom, we have

x = [tex]1\pm\sqrt{10}[/tex]

Either x = [tex]1+\sqrt10[/tex] or x= [tex]1-\sqrt10[/tex]

=> x = 1 + 3.162 or x = 1 - 3.162

=> x = 4.162 (possible) or x = -2.162 (not possible as width can't be negative)

So, width = 4.16 meter (rounded off to the nearest hundredth)

Now,

Area of the rectangle = length * width

27 = length * 4.16

Flipping the sides of the equation,

length * 4.16 = 27

Dividing both sides by 4.16, we get

[tex]\frac{length * 4.16}{4.16} = \frac{27}{4.16}[/tex]

Cancelling out 4.16 from the top and bottom of the left side, we get

length = 6.490

=> length = 6.49 meter (rounded off to the nearest hundredth)

Answer:

A) (1/9)^8

Step-by-step explanation:

9^-5 × 9^-3 =

Rule: a^m * a^n = a^(m + n)

= 9^-8

Rule: (a^m)^n = a^(mn)

= (9^-1)^8

Rule: a^-m = 1/a^m

= (1/9)^8

Answer: A) (1/9)^8

Answer:

Step-by-step explanation:

You just add and subtract

Answer:

The answer Is D

Step-by-step explanation: I looked it up on Google, next time just type it into Google because it will solve it on a calculator for you.

Answer: It is choice D

Step-by-step explanation: To figure out 25% of 1,200, multiply 1,200 by 0.25. 1,200 x 0.25 = 300

Answer:

(x - 3)² + (y - 2)² = 8

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre to a point on the circle

To find r use the distance formula

r = √(x₂ - x₁)² + (y₂ - y₁)²

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, 4)

r = [tex]\sqrt{(5-3)^2+(4-2)^2}[/tex] = [tex]\sqrt{4+4}[/tex] = [tex]\sqrt{8}[/tex]

(x - 3)² + (y - 2)² = ([tex]\sqrt{8}[/tex])²

(x - 3)² + (y - 2)² = 8 ← equation of circle

Answer:

AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent

In triangle RAS and triangle QAT

[tex]\angle R =\angle Q[/tex]   [Angle]

[tex]AS =AT[/tex]    [Side]                                       [Given]

By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.

⇒ [tex]\angle 5= \angle 6[/tex]      [By base ∠'s of isosceles triangle are equal]

By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.

[tex]\angle 4[/tex], [tex]\angle 5[/tex] are supplementary and [tex]\angle 6[/tex], [tex]\angle 7[/tex] are supplementary.

⇒[tex]\angle 4+ \angle 5 =180^{\circ}[/tex] and

[tex]\angle 6+ \angle 7 =180^{\circ}[/tex]  

Two [tex]\angle 's[/tex] supplementary to equal [tex]\angle 's[/tex]

[tex]\angle 4+ \angle 5 =\angle 6+ \angle 7[/tex]

Since,  [tex]\angle 5 =\angle 6[/tex]  

then, we get;

[tex]\angle 4 =\angle 7[/tex]  [Angle]

then, by AAS postulates,

[tex]\triangle RAS \cong \triangle QAT[/tex]

By CPCT[Corresponding Part of Congruent Triangles are equal]

[tex]RS = QT[/tex]              Hence Proved!

Answer:

[tex]\frac{2}{81}[/tex]

Step-by-step explanation:

Step 1

List the experimental probabilities of each color using the first letter of that color. The spinner is spun 18 times The probabilities are listed below. P(blue)=3/18, P(red=4/18), P(white) =3/18, P(yellow)=2/18, P(black)=5/18, P(purple)=1/18

Step 2

The second step is to calculate the required probability given the information in step 1. The probability that George will spin a red and then a yellow is obtained by multiplying the probability that he spins a red and the probability that he spins a yellow. This calculation is shown below,

[tex]P=P(red)\times P(yellow)=\frac{4}{18} \times \frac{2}{18} =\frac{8}{324} =\frac{2}{81}.[/tex]

The correct answer is  [tex]\frac{2}{81}[/tex]

Answer:

y = - 3

Step-by-step explanation:

Providing you mean (y - 9)/(y + 3) then it is always the variable in the denominator that is going to cause trouble. If it equals zero at any point, it's game over.

It's a little better if you get a result like 0/0. That problem has a "depends" as an answer, but by and large, you don't want to monkey around with 0 in the bottom of a fraction.

y + 3 = 0            Subtract 3 from both sides.

y + 3 - 3 = 0 - 3  Combine

y = - 3

Answer:

B

Step-by-step explanation:

well plug in x and y

so if it says y=2x-3 put it as 7=(2x2)-3  and see if it gives u 7 and if it does di the next set of x and y numbers

Answer:

B  y=2x+3

Step-by-step explanation:

We need to find the slope of the relationship in the table

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

  = (13-7)/(5-2)

   = 6/3

  =2

The slope is 2

We can use point slope form to make an equation

y-y1=m(x-x1)

y-7 = 2(x-2)

Distribute the 2

y-7 =2x-4

Add 7 to each side

y-7+7 =2x-4+7

y = 2x+3

Answer:

20%

Step-by-step explanation:

We can say that 3/15 students usually go to bed at 9 P.M. We can set up a proportion to solve this problem.

3/15=x/100

We cross multiply to find x

15x=300

Divide both sides by 15

x=20

So 20% of the classmates usually sleep at 9 P.M.

Answer:

20% of the students

Step-by-step explanation:

Answer:

x - [tex]\sqrt{7}[/tex]

Step-by-step explanation:

A polynomial has the form

first term is the term of highest degree followed by term of second etc.

note that x = [tex]x^{1}[/tex] ← degree 1

x - [tex]\sqrt{7}[/tex]

fits this description and is a polynomial of degree 1

Answer:

9/20

Step-by-step explanation:

9/10 times 1/2 equals 9/20

Answer:

9/20

Step-by-step explanation:

Answer:

4617 yd

Step-by-step explanation:

30.5 ft make 1 roll of tape

Length of tape = 454 × 30.5/1

Length of tape = 13 847 ft

1 ft = 3 yd

Length of tape = 13 847 × 1/3

Length of tape = 4617 yd

Answer:

Let y represents the ounces of first spice.

From the given statements, we draw a table as shown below:

                          ounces of spice        Percentage          ounces of salt

First spice                 y                              3%                            0.03x

Second spice           175                            6%                          175(0.06)

Final  mixture          y + 175                         5%                        (x+15)(0.05)

Now, to solve for y

we have;

Final spice = First spice + second spice

[tex]0.03y + 175(0.06) = (y+175)(0.05)[/tex]

[tex]0.03y+ 10.5= 0.05y+ 8.75[/tex]

Subtract 10.5 on both sides we have;

[tex]0.03y+ 10.5 -10.5= 0.05y+ 8.75 -10.5[/tex]

Simplify:

[tex]0.03y = 0.05y -1.75[/tex]

Subtract 0.05y on both sides

[tex]0.03y -0.05y= 0.05y -1.75-0.05y[/tex]

Simplify:

[tex]-0.02y = -1.75[/tex]

Divide both sides by -0.02, we get;

[tex]y = \frac{-1.75}{-0.02} = 87.5[/tex]

Therefore, 87.5 ounces of spices that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt

It needs 87.5 ounces of spice that is 3% salt.

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem !

[tex]\texttt{ }[/tex]

Given:

175 ounces of a spice that is 6% salt

[tex]\texttt{mass of salt from this spice} = s_1 = 6\% \times 175 = 10,5 \texttt{ ounces}[/tex]

[tex]\texttt{ }[/tex]

x ounces of a spice that is 3% salt

[tex]\texttt{mass of salt from this spice} = s_2 = 3\% \times x = 0.03x \texttt{ ounces}[/tex]

[tex]\texttt{ }[/tex]

(175 + x) ounces of a spice that is 5% salt

[tex]\texttt{total mass of salt} = s_1 + s_2[/tex]

[tex]5\% \times ( 175 + x ) = 10.5 + 0.03x[/tex]

[tex]8.75 + 0.05x = 10.5 + 0.03x[/tex]

[tex]0.05x - 0.03x = 10.5 - 8.75[/tex]

[tex]0.02x = 1.75[/tex]

[tex]x = 1.75 \div 0.02[/tex]

[tex]x = 175 \div 2[/tex]

[tex]x = 87.5 \texttt{ ounces}[/tex]

[tex]\texttt{ }[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces , Number , 51 , 33 , 1/3

Expressing the equation in the form y = mx + b where m is slope and b is y-

intercept is represented as y = -4x - 3

The slope intercept form is represented as follows:

y = mx + b

where

m = slope

b = y-intercept

Therefore,

m = -4

using the coordinate (-2, 5) lets find b

y = -4x + b

5 = -4(-2) + b

5 = 8 + b

b = 5 - 8

b = -3

Therefore,

y = -4x - 3

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The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have m = -4 and the point (-2, 5). Substitute:

[tex]y-5=-4(x-(-2))[/tex]

[tex]y-5=-4(x+2)[/tex]      use distributive property

[tex]y-5=(-4)(x)+(-4)(2)[/tex]

[tex]y-5=-4x-8[/tex]      add 5 to both sides

[tex]\boxed{y=-4x-3}[/tex]

Answer:

all is work is shown and pictured

Answer:

1+5*2 or simplified, 1+10= 11

Answer:

3

Step-by-step explanation:

Count 1 to 5 (1,2,3,4,5). You can see 3 is between 2 and 4.

A number that comes between 2 and 4 would be 3.

Used the concept of a number system that states,

A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.

Given that,

Two numbers are 2 and 4.

Let us assume that the number that comes between 2 and 4 is, x

Then,

[tex]x = \dfrac{(2 + 4)}{2}[/tex]

[tex]x = \dfrac{(6)}{2}[/tex]

[tex]x = 3[/tex]

Therefore, the number would be 3 which comes between 2 and 4.

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Answer: 145

3.7 x 60 = 222 (how far north she drove)

1.4 x 55 = 77 (how far south she drove)

222 - 77 = 145 (how far from home)

Answer:

Given: Ellentown college has approximately 3 times 10 to the 3 power students and pengrove university approximate 30,000 students.

⇒ number of students approximately in Ellentown college = [tex]3 \times 10^3[/tex]

also,

the number of students approximately in Pengrove university = 30,000 or [tex]3 \times 10^4[/tex]

We have to find how many times as much is the number of students at pengrove university as the number of students at Ellentown college.

[tex]\frac{number of students in Pengrove University}{number of students in Ellentown college}[/tex] = [tex]\frac{3 \times 10^4}{3 \times 10^3} = 1 \times 10^1 = 10[/tex]

therefore, 10 times as much is the number of students at pengrove university as the number of students at Ellentown college.

Answer:

Constant of proportionality,  [tex]r = \frac{1}{10}[/tex]

Step-by-step explanation:

Constant of proportionality states that the constant value of the ratio of two proportional quantities x and y,

it is written in the form of y = kx, where k is the constant of proportionality.

Given the equation: [tex]y =rx[/tex]                        .....[1]

where r is the constant of proportionality.

From the table we consider

x = 14 and y = 1.4

Substitute these given values in [1] to solve for r;

[tex]1.4 = r(14)[/tex]

Divide both sides by 14 we get;

[tex]r = \frac{1.4}{14} = \frac{14}{140} = \frac{1}{10}[/tex]

therefore, the Constant of proportionality,  [tex]r = \frac{1}{10}[/tex]

The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x.

The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x. For example, in the equation y = rx, 'r' represents how much y changes for every unit change in x.

For instance, if the equation is y = 2x, then the constant of proportionality is 2. This means that for every unit increase in x, y increases by 2 units.

Keywords: constant of proportionality, linear equation, rate of change

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Answer:

y ≤ -4x+25

Step-by-step explanation:

First we need to figure out the equation for the line

The y intercept is  25

Next figure out the slope

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

      = (49-25)/(-6-0)

      = 24/-6

    = -4

The equation for a line in slope intercept form is y = mx+b

y = -4x+25

This is a solid line so our inequality will have an equals in it.

It is shaded below, so y is less than.

If it was shaded above, y would be greater than

y ≤ -4x+25

Answer:

for pluto answer is 451

Step-by-step explanation:

Answer:

3030.033

Step-by-step explanation:

Multiply each piece out and add them together

3 X 1,000 + 3 X 10 + 3 X 1/100 + 3 in X 1/1000

3000 + 30+.03 + .003

3030.033

To find the quadratic equation with roots 6 and -5 and a leading coefficient of 3, we use the format 3(x - 6)(x + 5) and expand it to get the equation 3x² - 3x - 90 = 0.

The quadratic equation with roots 6 and -5 and a leading coefficient of 3 can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants. Since the roots are 6 and -5, and the leading coefficient (a) is 3, we can use the fact that a quadratic equation with roots r and s can be written as a(x - r)(x - s). Thus, our equation becomes 3(x - 6)(x + 5). 

Expanding this, we have:

The quadratic equation with the given roots and leading coefficient is 3x² - 3x - 90 = 0.