HIJ has coordinates H(-4,3), I7(-2, 0), and J (-4,1). Graph the triangle and its
translation 3 units to the right and 2 units down. What are the coordinates of J'?

Answer:

The translation from quadrilateral EFGH to quadrilateral E'F'G'H' is [tex]T_{(2, -4)}[/tex], which is two units to the right (x direction) and 4 units down (negative y direction)

Step-by-step explanation:

The coordinates of quadrilateral EFGH are;

Point E has coordinates (-1, 1)

Point F has coordinates (0, 4)

Point G has coordinates (3, 1)

Point H has coordinates (3, 0)

The coordinates of the translation are;

Point E' has coordinates (0, -3)

Point F' has coordinates (1, 0)

Point G' has coordinates (4, -3)

Point H' has coordinates (4, -4)

The change in the y-coordinate values (y values) are;

From point E to point E', we have;

(-3 - 1) = -4 which is four units down

The change in the x-coordinate values (x values) are;

From point E to point E', we have;

(0 - (-1)) = 2 which is two units to the right

The total change in translation is [tex]T_{(2, -4)}[/tex].

Answer:

{1,2,3}

Step-by-step explanation:

The others will not show all the numbers from the set to make the inequality true

Answer:

1,2,3

Step-by-step explanation:

Answer:

Answer D I believe :)

Step-by-step explanation:

x^4-33x^2-108

rewrite as a difference

x^4+3x^2-36x^2-108

factor out x^2

x^2(x^2+3)-36x^2-108

factor out -36

x^2(x^2+3)-36(x^2+3)

factor out x^2+3

(x^2+3)(x^2-36)

factor x^2-36

(x^2+3)(x-6)(x+6)

set x^2+3 equal to 0

x^2+3=0

solve for x

x=+/-[tex]\sqrt{3}[/tex]i

set at factors

(x+6)(x-6)(x+[tex]\sqrt{3}[/tex]i)(x-[tex]\sqrt{3}[/tex]i)

I hope this helps.

Answer:

bet whats the question

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

x − 3y

Let x =3 and y = -2

3 -3(-2)

3 + 6

9

Answer:

O B. 17 units

Step-by-step explanation:

The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:

[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]

The length of the chord is 17 units.

Answer:

The answer is 17 units :D

Step-by-step explanation:

Answer:

c) 100

Step-by-step explanation:

This is the best choice because the number is not too low or too high. He will get an accurate probability.

Answer:

Option (D)

Step-by-step explanation:

Given quadrilateral in the circle is a cyclic quadrilateral.

By using the property of cyclic quadrilateral,

"Sum of each pair of opposite angles is 180°".

In the given cyclic quadrilateral,

d + 57° = 180°

d = 180 - 57

d = 123°

Similarly, c + 31° = 180°

c = 180° - 31°

c = 149°

Therefore, Option (D) will be the answer.

Answer:

678 ft²

Step-by-step explanation:

The opposite sides of the cuboid are congruent, thus surface area is

2(11 × 9) ← front and back + 2(11 × 12) ← top and base + 2(12 × 9) ← sides

= 2(99) + 2(132) + 2(108)

= 198 + 264 + 216

= 678 ft²

Answer:

B. x^3 + 3x^2

Step-by-step explanation:

Volume of a rectangular prism=width * length * height

V=w*l*h

h=3 greater than the length of the base

h=x+3

Length of the base=x

Width=x

Substituting values into the formula

V=w*l*h

=(x)*(x)*(x+3)

Multiplying

=(x^2)(x+3)

=x^3 + 3x^2

Option B is the correct answer

The expression [tex]x^3 + 3x^2[/tex]  represents the volume of the prism, in cubic units.

We have given that the,

The height of a right rectangular prism is 3 units greater than the length of the base.

The edge length of the square base is x units.

[tex]Volume of a rectangular prism=width * length * height[/tex]

[tex]V=w*l*h[/tex] ......(1)

We have given that the

h=3 greater than the length of the base

and length of the base is x

Hence, [tex]h=x+3[/tex]

[tex]Length of the base=x[/tex]

[tex]Width=x[/tex]

Substituting values l h and w into the formula (1) we get,

[tex]V=w*l*h[/tex]

[tex]=(x)*(x)*(x+3)[/tex]

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

[tex]=x^3 + 3x^2[/tex]

Therefore the expression  

[tex]x^3 + 3x^2[/tex]  

represents the volume of the prism, in cubic units.

To learn more about the volume of the prism visit:

https://brainly.com/question/23963432

Answer:I think it’s 7x^3

Step-by-step explanation:

Answer:

Equation:-  [tex]x + y = 38.50[/tex]

Solution of x:-  [tex]x = 38.50 - y[/tex]

Step-by-step explanation:

Given

Total Purchase = $38.50

Required

Determine the equation for finding the cost of a bear

From the question; we understand that the cost of 1 bear is represented with x

Solving further; by representing the cost of 1 football uniform with y

So;

[tex]1\ bear + 1\ uniform = 38.50[/tex]

Substitute x for 1 bear and y for 1 uniform to give us an equation

[tex]x + y = 38.50[/tex]

Solving for x (Subtract y from both sides)

[tex]x +y - y = 38.50 - y[/tex]

[tex]x = 38.50 - y[/tex]

The equation can't be solved further

Answer:

0.8413 or 84.13%

Step-by-step explanation:

The difference from 4320 grams from the mean is:

[tex]d=4320-3958=362\ grams[/tex]

This is exactly 1 standard deviation.

According to the empirical rule, 68.26% of all data is within 1 standard deviation of the mean, which means that 34.13% of all data is within the mean and 1 standard deviation over the mean. We also know that the mean is at the 50th percent of the normal distribution.

Therefore, the probability that the weight will be less than 4320 grams is:

[tex]P(X\leq 4320) = 0.50+0.3413=0.8413 = 84.13\%[/tex]

The probability is 0.8413 or 84.13%

Step-by-step explanation:

in each equation once substitute the value of x as 0 and again y as zero by this way you will get two values of X and y .

then again find the slope for each equation by the formula

slope= -coefficient of x / coefficient of y

for example,

X+y is greater or equals to 5

or, X+y= 5

or, X=5-y

or, when y is equals to zero

X= 5

and when X is equals to zero

y= 5

then plot the above point in the graph with respect to its slope and the shaded part is the solution

Answer:

362,880 ways

Step-by-step explanation:

There are 9 letters so 9!

And none of them are repeated so 9!/0!

9! = 362,880

I hope this helps, and plz mark me brainliest!!

Answer:

0.012 millimeters

Step-by-step explanation:

First, we solve for  0.000004 m to mm = 0.004 mm x 3 = 0.012 millimeters

Answer:

Step-by-step explanation:

Using the double angle formulas,

cos(2x) = cos^2(x) - sin^2(x) ............(1)

1            = cos^2(x) + sin^2(x)............(2)

add (1) and (2)

1 + cos(2x) = 2 cos^2(x)

=> cos^2(x) = (1/2) (1+cos(2x))  ..............(3)

f(x) =  7 cos^2 (x)  

substituting (3)

f(x) = (7/2) (1+cos(2x))

Answer:

R = 21.8° to the nearest tenth

Step-by-step explanation:

To find Angle R we use tan

tan ∅ = opposite / adjacent

From the question

The opposite is 2

The adjacent is 5

So we have

tan R = 2/5

R = tan-¹ 2/5

Hope this helps you

Answer:

x=-5

Step-by-step explanation:

The answer is x = -5. The explanation and answer is in the image below.

Answer:

Y-1=4/5(x-(-2))

Step-by-step explanation:

Point slope form is written as y-y1=M(x-X1)

M is the slope

so replace the variables for the given value

Y-1=4/5(x-(-2))

Answer: y - 1 = 4/5 (x + 2)

Step-by-step explanation:

Answer:

4 Pi

Explanation:

72/360 = 1/5 so the length of the arc is (1/5) the circumference or

(1/5) ( 2 Pi * 10)  => C = 2 Pi r

(20/5) Pi =

4 Pi

Answer:

Number of blue markers  = 9

Step-by-step explanation:

Given that there are 24 red markers.

Probability of randomly choosing a red marker is 1 in 3.

Probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

That means the ratio of red markers to total markers is 1:3.

Here number of favorable cases are 24 i.e. the number of red markers

and Total number of cases are equal to total number of markers.

Let T be the total number of markers.

As per definition of probability:

[tex]\dfrac{1}{3}=\dfrac{24}{T}\\\Rightarrow \bold{T = 72}[/tex]

Also, given that the probability of choosing a blue marker is 1 in 8.

Let the number of blue markers be B.

As per definition of probability:

[tex]\dfrac{1}{8}=\dfrac{B}{72}\\\Rightarrow \bold{B = 9}[/tex]

Hence, the answer is:

Number of blue markers  = 9

Answer:

Average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Step-by-step explanation:

The formula for average rate of change of f(x) over [a,b] is

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

The given function is

[tex]r(x)=x^2+2x-5[/tex]

[tex]r(0)=(0)^2+2(0)-5=-5[/tex]

[tex]r(3)=(3)^2+2(3)-5=10[/tex]

Now,

[tex]m_1=\dfrac{r(3)-r(0)}{3-0}[/tex]

[tex]m_1=\dfrac{10-(-5)}{3}=5[/tex]

From the graph it is clear that q(0)=-4 and q(3)=5.

[tex]m_2=\dfrac{q(3)-q(0)}{3-0}[/tex]

[tex]m_2=\dfrac{5-(-4)}{3}=3[/tex]

It is given that  function p has as x-intercept at (3,0) and a y-intercept at (0,6). It menas p(0)=6 and p(3)=0.

[tex]m_3=\dfrac{p(3)-p(0)}{3-0}[/tex]

[tex]m_3=\dfrac{0-6}{3}=-2[/tex]

From the given table it is clear that s(0)=-13 and s(3)=5.

[tex]m_4=\dfrac{s(3)-s(0)}{3-0}[/tex]

[tex]m_4=\dfrac{5-(-13)}{3}=6[/tex]

Therefore, the average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Answer: 24

Expenation:  

Left handed females = x

right handed females = 348 - x

right handed males = y

left handed males = 204 - y

204 - y = 4x

348 - x = 3y

4x + y = 204  . . . . . . . (1)

x + 3y = 348  . . . . . . . (2)

From (2),  x = 348 - 3y

subsituting for x in (1), we have

4(348 - 3y) + y = 204

1392 - 12y + y = 204

12y - y = 1392 - 204

11y = 1188

y = 1188/11 = 108

x = 348 - 3y = 348 - 3(108) = 348 - 324 = 24

Answer:

24

Step-by-step explanation:

i got it right

Answer:

120

Step-by-step explanation:

! means to multiply it by every number less than itself.

Not counting 1, this means 5*4*3*2.

20*3*2

60*2

120

The answer is 120.

Answer:

120

Step-by-step explanation:

Answer:

1:3

Step-by-step explanation:

9/3 = 3

3 is the scale factor

Answer:

The number of boys, x = 12

Step-by-step explanation:

Given that the sum of the ages of the boys in a class = 84 years

The number of boys = x

A new boy aged 8 years 1 month is added and the average age increases by 1 month

We have

Average age = 84/x = y

Age of new boy = 8 years 1 month = [tex]8\frac{1}{12} \ year[/tex]

New average = y + 1/12 = [tex](8\frac{1}{12}+84) /(x + 1)[/tex] which gives;

84/x + 1/12 = [tex](8\frac{1}{12} + 84) /(x + 1)[/tex]

[tex]\dfrac{x +1008}{12 \cdot x} = \dfrac{1105}{12 \cdot x+ 12}[/tex]

(x + 1008)×(12·x + 12) = 1105× 12·x

12·x² -1152·x + 12096 = 0

x² -96·x + 1008 = 0

(x - 84)×(x - 12) = 0

Therefore, x = 12 or 84,

The number of boys are 12 or 84

For there to bee 84 boys, their average age would be one year each

Given that they are boys not babies, then there are only 12 boys.

Answer:

y = 4

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross-  multiply )

y × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

y = 4

Answer:

y=4

Step-by-step explanation:

If we have a triangle with angles A, B, and C. The law of sines says that the proportion between the sin of angle A and its opposite side is equal to the proportion between the sin of angle B and its opposite side and it is equal to the proportion between the sin of angle C and its opposite side.

So, by the law of sines we can say that:

[tex]\frac{sen(60)}{4\sqrt{3} } =\frac{sen(30)}{y}[/tex]

Solving for y, we get:

[tex]sin(60)*y=4\sqrt{3}*sin(30)\\\frac{\sqrt{3} }{2}y=4\sqrt{3}*0.5\\ \frac{1}{2} y=4*0.5\\y = 4[/tex]

Answer:

The probability that a randomly selected group of four trees can be used as timber is 4.5 × 10⁻⁵

Step-by-step explanation:

The given parameters are;

Mean = 34 cm

The standard deviation = 8 cm

The mean

The Z score is [tex]Z=\dfrac{x-\mu }{\sigma }[/tex], which gives;

For x  = 30 we have;

[tex]Z=\dfrac{30-34 }{8 } = -0.5[/tex]

P(x>30) = 1 - 0.30854 = 0.69146

For x = 40, we have

[tex]Z=\dfrac{40-34 }{8 } = 0.75[/tex]

P(x < 40) = 0.77337

Therefore, the probability that the mean of four trees is between 30 and 40 is given as follows;

P(30 < x < 40) = 0.77337 - 0.69146 = 0.08191

The probability that a randomly selected group of four trees can be used as timber is given as follows;

Binomial distribution

[tex]P(X = 4) = \dbinom{4}{4} \left (0.08191\right )^{4}\left (1-0.08191 \right )^{0} = 4.5 \times 10^{-5}[/tex]