Select all that apply.

The following graph shows an ellipse that suffered several transformations. Which of the following two sets of combinations of transformations could map ellipse 1 into ellipse 2? You may choose more than one correct answer.


Translation 3 units up and 7 units to the right
Reflection along the y-axis and translation 3 units to the left
Rotation of 90° clockwise by the origin O, and translation 2 units to the left
Reflection along y = -x, and translation 6 units to the right

Answer:

We know that the polynomial:

x²- 6y²- xy - 5x - 5y + 6

is rewritten as:

(x+ay+b)(x+cy-2)

First, lets expand the above expression:

x^2 + x*(cy) + x*(-2) + (ay)*x + (ay)*(cy) + (ay)*(-2) + b*x + b*(cy) - 2*b

Now we can simplify this to get:

x² + c*(xy) - 2*x + a*(xy) + ac*y² - 2a*y + b*x + bc*y  - 2b

now let's group together the terms with the same variables:

x² + (c + a)*(xy) + (b - 2)*x + (bc - 2a)*y + ac*y² - 2b

And that must be equal to:

x²- 6y²- xy - 5x - 5y + 6

notice that equations are equal if and only if all the correspondent factors are equal.

notice that in both cases, the factor that multiplies the x² term is 1.

for the y² term we will have:

a*c = -6

for the xy term we will have

c + a = -1

for the x term we will have

b - 2  = - 5

for the y term we will have

bc - 2a = -5

for the constant term, we will have:

-2b = 6

Then we have a lot of equations, rewriting these we have:

a*c = -6

c + a = -1

b - 2  = -5

bc - 2a = -5

-2b = 6

From the fourth equation, b - 2  = -5

we can get:

b = -5 + 2 = -3

b = -3

notice that for the last equation:

-2b = 6

b = 6/-2 = -3

we have the same solution

Then we can replace the value of b in the above equations to get:

a*c = -6

c + a = -1

-3*c - 2a = -5

Now, we need to isolate one of the variables in one of the equations.

For example, we can isolate c in the second one to get:

c = -1 - a

now we can replace that in other equation, for example the third one:

-3*(-1 - a) - 2a = -5

now we can solve that for a.

3 + 3a - 2a = -5

3 + (3 - 2)a = -5

3 + a = -5

a =  -5 - 3 = -8

a = -8

now we can use the equation "c = -1 - a" to find the value of c:

c = -1 -(-8) = -1 + 8 = 7

c = 7

then we have:

b = -3

a = -8

c = 7

then:

a + b*c = -8 + (-3)*7 = -8 - 21 = -29

Answer:

Answer is A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer is C because if swimmer A does 14 laps to start an 3 laps every day after that and on the chart swimmer B does 11 laps to start and 2 laps every day after that you would compare.

on day 3 swimmer B has 17 (shown on chart)

on day 3 swimmer A has 23 (14, 17, 20, 23)

if you would want it to complicate it 14:3 and 11:2

14 ÷ 14 is 1

3 ÷ 14 is .214

11 ÷ 11 is 1

2 ÷ 11 is .181

Answer:

Total paid: 302.40

Step-by-step explanation:

Price x percent off = amount off

700 x .60 (60%) = 420 amount off

price - amount off = sales price

700 - 420 = 280 sales price

sales price x sales tax rate = sales tax

280 x .08 (8%) = 22.40 sales tax

sales price + sales tax = total paid

280 + 22.40 = 302.40 total paid

Answer:

28

Step-by-step explanation:

7.2 is rounded down to 7, 7.3 is rounded down to 7, 6.9 is rounded up to 7, and 6.8 is rounded up to 7. Then you can add 7+7+7+7 to get an estimation of 28.

Here

[tex]\\ \sf\longmapsto \frac{7}{x} = \frac{15}{10} \\ \\ \sf\longmapsto 7 \times 10 = 15x \\ \\ \sf\longmapsto 15x = 70 \\ \\ \sf\longmapsto x = \frac{70}{15} \\ \\ \sf\longmapsto \boxed{ \sf x = 4.6cm}[/tex]

Answer:

i can help you i know this answer

Answer:

x is 21°

Step-by-step explanation:

The angles formed between the transversal t and lines m and n are; (8·x - 7)°, and (9·x - 28)°

Based on the similar location the angles are formed by the transversal, t, and lines m and n, the angles are corresponding angles

Given that lines, m and n are parallel, we have the corresponding angles formed by the transversal, t, and the lines are equal, therefore;

(8·x - 7)° = (9·x - 28)°

Simplifying the above equation to make x the subject, we get

(28 - 7)° = 9·x - 8·x = x

∴ 21° = x

x = 21°.

Answer:

1 - 4

Step-by-step explanation:

26/4 = 6.5

IQR is the 7 - 19 item

1 - 4

Answer:

Step-by-step explanation:

To answer this, we need only solve for x and then use Pythagorean's Theorem to find z. We have the length of the hypotenuse which is 15, and we also have the base angle of 60. To solve for x we can use the trig ratio

[tex]cos60=\frac{x}{15}[/tex] and

x = 15cos60 which gives us that

x = [tex]\frac{15}{2}[/tex]

Now we can use Pythagorean's Theorem to find z, the other leg of the big triangle.

[tex](\frac{15}{2})^2+z^2=15^2[/tex] and

[tex](\frac{225}{4})+z^2=225[/tex] and

[tex]z^2=225-\frac{225}{4}[/tex] and getting a common denominator:

[tex]z^2=\frac{900}{4}-\frac{225}{4}[/tex] and

[tex]z^2=\frac{675}{4}[/tex] now we take the square root by simplifying the radical to get

[tex]z=\frac{15\sqrt{3} }{2}[/tex]

and that's what goes into the blanks there, one number per blank.

Answer:

−426500

Step-by-step explanation:

Step-by-step explanation:

Concerning the peculiar interrogate, I will be providing correction(s) to the following answers inserted:

Y = 3x - 1

Slope = 3

Y-intercept = -1

X - 3 = y

Y = x - 3 <== Slope-Intercept Form.

Slope = 1

Y-intercept: -3

Y = 1 - 3x

Slope: -3

Y-intercept: 1

-x + 3 = y

Y = -x + 3 <== Slope-intercept Form.

Slope: -1

Y-intercept: 3

Thus, the following configurations have been defined or derived from the origin of the proposed interrogated.

*I hope this helps.

Answer:

2.65

Step-by-step explanation:

15.00 - 12.35 = 2.65

...I don't really know how do explain it but yeah thats the answer.

Hope it helps c:

Answer:

15 inches

Step-by-step explanation:

Since we know diagonal and a side of a right triangle, we can use the Pythagorean theorem to solve.

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

20 ^2 + b^2 = 25^2

400+b^2 =625

b^2 =625 -400

b^2 =225

Taking the square root of each side

sqrt(b^2) = sqrt(225)

b= 15

Answer:

15

Step-by-step explanation:

You can use Pythagorean theorem or if you draw it out and label the given information you may recognize that the triangle created is a 3 - 4 - 5 triangle.

[tex]25^{2}[/tex] = [tex]20^{2}[/tex] + [tex]x^{2}[/tex]             [tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]

625 = 400 + [tex]x^{2}[/tex]        

225 = [tex]x^{2}[/tex]                     Square root both sides

15 = x

A special right triangle has a leg that measures 3, another leg that measures 4. and a hypotenuse that measures 5.

The given triangle in this problem has a leg that measures 20 and a hypotenuse that measures 25. If you divide each measure by 5, you will have a leg that is 4, and a hypotenuse that is 5. That means the last leg must be 15.

Why? Because 3 x 5 = 15. or 15/5 = 3

This comes up very often when working with triangles.

Answer:

x=72

Step-by-step explanation:

Let y=kx and y=a/x^2. y(48)=8, k=(1/6). y=(1/6)*x. 12=(1/6)*x. x=72

Answer:

(−3)(+2)(3+2)

Step-by-step explanation:

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(32+8+4)

Factor by grouping

Factor by grouping

Factor by grouping

Factor by grouping

(−3)(+2)(3+2)

Answer:

bgyuhjvy;uhclgcxfghvmdxultgjvffgxfbc hgv

Step-by-step explanation:

vgfdhvczczxcgfzdsdvcxfdghcbcd

Answer:

360 cm^2

Step-by-step explanation:

Find the area of each face of the triangular prism.

Imagine the triangular prism as its net, it is composed with 2 triangular faces (these are tye bases of the prism) and 3 rectangular faces.

Areas of the 2 triangular bases (they are similar triangles):

1/2 x 8 cm x 6 cm = 24 cm^2

24 x 2 = 48 cm^2

Area of the rectangular face:

8 x 13 = 104 cm^2

Area of another rectangular face:

6 cm x 13 cm = 78 cm^2

Area of another rectangular face:

13 cm x 10 cm = 130 cm^2

Add up all the areas of all faces:

48 + 104 + 78 + 130 = 360

So the SA is 360 cm^2

Answer:

∠1=a+b/2

∠1=37+25/2

∠1=31

Answer: C) 31

-------------------------

Hope it helps...

Have a great day!!!

The angle measure of angle ∠1 is 31°.

The correct option is C.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given information:

The circle is centered at y.

As per the provided diagram,

The angle measure of an arc let a = 37°.

And b = 25°.

To find the angle measure of ∠1:

Apply formula (a + b)/2,

So as per the provided values of a = 37° and b = 25°.

Therefore,

m∠1 = (37 + 25)/2

m∠1 = 62/2

m∠1 = 31°.

Therefore, m∠1 = 31°.

To learn more about the angle measure;

brainly.com/question/14684647

#SPJ7

Answer:

Step-by-step explanation:

Answer:

y=-3/2x+4

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Both pairs of opposite angles are congruent. parallelogram, rectangle, rhombus, square. Both pairs of opposite sides are congruent. parallelogram, rectangle, rhombus, square. All consecutive angles are supplementary. parallelogram, rectangle, rhombus, square. diagonals bisect each other. parallelogram, rectangle, rhombus, square.

Answer:

true

Step-by-step explanation:

any 2 consecutive angles are supplamentary

Answer:

19 and 157

Step-by-step explanation:

Answer: 0.667

Step-by-step explanation:

6/9 ⇔ Given

2/3 ⇔ Simplify fraction

0.666... (repeating) ⇔ Convert fraction to decimal

0.667 ⇔ Round to 3 decimal (Since 6 is more than 5, thus we need to

               rounding up)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

P = 2(L + 6)

Step-by-step explanation:

The perimeter (P) of a rectangle is = 2(Length + Width)

Length = L

Width = 6

.: P = 2(L + 6)

Answer:

the answer is in the pic so like yea hope that helps

Answer:  B. Probability

For example, let's say you want to know the probability of flipping tails.

There's 1 way to get tails out of 2 sides total. So 1/2 = 0.5 is the probability of flipping tails.

We define "success" as "getting tails".

Solution :

[tex]$y=x^{3/2}, \ \ y =8, \ \ x=0$[/tex]

[tex]$v=2 \pi \int_0^4 x (8-x^{3/2}) \ dx$[/tex]

 [tex]$= 2\pi \left(\frac{8x^2}{2}-\frac{x^{7/2}}{7/2}\ \left|_0^4[/tex]

 [tex]$=2\pi \left( 4x^2-\frac{2}{7}x^{7/2}\ |_0^4$[/tex]

 [tex]$=2\pi \left( 64-\frac{2}{7} \times 32 \times 4 \right)$[/tex]

  [tex]$=2\pi \left(1-\frac{4}{7} \right) 64$[/tex]

  [tex]$=128 \pi \times \frac{3}{7}$[/tex]

 [tex]$=\frac{384 \pi}{7}$[/tex]

Answer: IT IS CONGRUENT BY ASA POSTULATE.

Step-by-step explanation:

ACCORDING TO THE GIVEN IMAGE

CONSIDER TRIANGLE 1 AS TRIANGLE ABC AND TRIANGLE 2 AS TRIANGLE PQR

IN TRIANGLE ABC AND PQR

ANGLE B = ANGLE C ( 90 DEGREES )

AC = PR ( GIVEN IN FIGURE )

A TRIANGLE HAS SUM OF INTERIOR ANGLES AS 180 DEGREES

IF ANGLE B AND ANGLE Q ARE 90 DEGREES, ANGLE A + ANGLE C = ANGLE P + ANGLE R

WE HAVE ALREADY PROVED THAT AC = PR

If two triangles have one angle equal to one angle, two sides adjoining the equal angles equal, namely, one side adjoining the equal angles, and one opposite the equal angles, and the remaining angles either both less or both not less than a right angle, then the remaining side equals the remaining side and the remaining angles equal the remaining angles.

SO ANGLE A = ANGLE P

THEREFORE BY ASA CONGRUENCY TRIANGLE ABC IS CONGRUENT TO TRIANGLE PQR

HOPE IT HELPS YOU......

(IF I HAVE MADE ANY MISTAKES PLS COMMENT BELOW)

Answer:

the constant is the number without an x attaches to it.

Ex:

y = 2x + 9

9 is a constant because it is not attached to any x

y = x^3 + 2x^2 + 10x + 19

19 is a constant because it is not attached to any x