Which sequence of rigid transformations will map the preimage ΔABC onto image ΔA′B′C′ ?
A.
a reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis
B.
a translation 4 units down and 10 units to the right
C.
a reflection across the line y = x followed by a rotation 90° counterclockwise
D.
a rotation 180° clockwise followed by a reflection across the x-axis

Answer:

Hello,

Step-by-step explanation:

3)

[tex]x^2-4x+3=0\\x^2-3x-x+3=0\\x(x-3)-(x-3)=0\\(x-3)(x-1)=0\\\\x-intercepts\ are\ x=3\ or\ x=1[/tex]

4)

[tex]-x^2-8x+12=0\\x^2+8x-12=0\\(x^2+2*4x+16)-16-12=0\\\\(x+4)^2-28=0\\\\\\(x+4-2\sqrt{7} )((x+4+2\sqrt{7} )=0\\\\x-intercepts\ are \ x=-4+2\sqrt{7}\ and\ x=-4-2\sqrt{7}\\\\[/tex]

5)

[tex]f(x)=-3(x-7)(x+4)\\=-3(x^2-3x-28)\\\\=-3(x^2-2*\dfrac{3}{2} *x+\dfrac{9}{4} )+\dfrac{27}{4} +84\\\\=-3(x-\dfrac{3}{2})^2+\dfrac{363}{4} \\\\\\Vertex\ is\ (\dfrac{3}{2},\dfrac{363}{4})[/tex]

Answer:

Yes.

Step-by-step explanation:

Minus and difference mean the same thing. To find the difference, you subtract or minus, so they are the same thing.

Answer:

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

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

5^2 + 12^2 = c^2

25+144 = c^2

169 = c^2

Taking the square root of each side

sqrt(169) = sqrt(c^2)

13 =c

Answer:

-4, 4, 7i, -7i

Step-by-step explanation:

Basically any or each bracket must be equal to 0. If x^2+16 = 0, then x can be 4 and -4, and if x^2+49 is 0, then x =7i or -7i

Answer:

hmmm I think it's true, if it's not my bad.

Answer:

6.82 cm

Step-by-step explanation:

1000=V=pi*r^2*h. 1000=pi*r^3, r=6.82 cm

9.4 × [tex]10^{2}[/tex]

1) Move the decimal point 2 times to left in the number so that number, 940 so it's between 1-10: 9.4 or 9.40

2) After we moved our decimal point to the left, the decimal count would be 12 and that we moved 2 places to the left

3) We know that the notation is a x [tex]10^{b}[/tex]

a=9.4 and 6=2

9.4 × [tex]10^{2}[/tex]=a x [tex]10^{b}[/tex]

I hope I've helped!

Answer:

9.4x10^8

Step-by-step explanation:

940 million looks like

940,000,000. in scientific notation you would move the decimal left 8 spaces

Answer:

y=3x+9......(i)

y=-4x-12...(ii)

these are the equation

Answer:

a = sqrt(7)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse

a^2 +3^2 = 4^2

a^2 +9 = 16

a^2 = 16-9

a^2 = 7

Taking the square root

a = sqrt(7)

Answer:

so thats 2/6 or 1/3

Step-by-step explanation:

A die has 6 sides your odds of getting 2 or lesser are 1/3 or 33%

Answer:

..D).... x = 8..

Step-by-step explanation:

..x = 8..

Answer:

[tex]\frac{(x+3)}{9}[/tex]

Step-by-step explanation:

Answer:

96 darling

Step-by-step explanation:

youre gonna take all the times this was teice as mich as that

like this:blueberrybagel twice as much 2

than plain bagels 1

cinnamonbags 3 times as much than

blueberry bagels 2×3= 6+

=9

EACH portion contains144:9=16 bagels

blueberry ones16×2=32

plain ones16×1=16

cinnamon ones 3×32=96

Answer:

39

Step-by-step explanation:

4x+7=9x-33

4x-9x=-33-7

-5x=-40

x=8

4×8+7=39

Answer:

x + 1

Step-by-step explanation:

Step-by-step explanation:6x^3 + 6 = 6 ^ 3+ 1 = 6(x+1) (x^2 - x + 1)

Answer:

Numerator is 7 and denominator is (m+4)

Step-by-step explanation:

(4m-17)/(m^2-16)+(3m-11)/(m^2-16)=(7m-28)/(m^2-16)=7/(m+4)

Answer:

10.34

Step-by-step explanation:

converting digits to feet,

3ft 6in = 3.5 ft

2ft 9in = 2.75 ft

now feet to yards

3.5ft = 1.16666667 yards (rounded)

2.75ft = 0.9166666667 yards (rounded)

29ft = 9.66666667 yards (rounded)

multiplying them, you'll get approximately 10.34 cubic yards (rounded), that's the volume.

or you can multiply the digits in feet,

3.5×2.75×29

= 279.125 cubic ft

now to convert to cubic yards from cubic ft,

279.125/3³

= 10.337963..

= 10.34 (rounded to the nearest hundredth)

Answer:

115 in.^2

Step-by-step explanation:

The total surface area is the sum of the areas of the square base and the 4 congruent triangular faces.

SA = b^2 + 4 * bh/2

SA = (5 in.)^2 + 4 * (5 in.)(9 in.)/2

SA = 25 in.^2 + 2 * 45 in.^2

SA = 115 in.^2

Complete question is;

The outer radius of a cylindrical metal tube is R and t is the thickness of the metal.

A) Show that the volume, V, of metal in a length, l units, of the tube is given by V = πlt(2R - t)

B) Hence calculate V when R = 7.5. t = 1 and L = 20

Answer:

A)V = πlt(2R - t)

B)V = 879.65

Step-by-step explanation:

A) Formula for volume of a hollow cylinder is; V = π(R² - r²)h

Where;

R is outer radius

r is inner radius

h is height/length of tube

Now, we are told thickness is t.

Thus; R - r = t

Also, h = l

Thus;

V = π(R² - r²)h

Let's factorize this to get;

V = π((R + r)(R - r))l

V = π((R + r))lt

Since R - r = t

Then, r = R - t

Thus;

V = π(R + R - t)lt

V = πlt(2R - t)

B) when R = 7.5, t = 1 and l= 20;

V = ​πlt(2R - t)

V = ​π × 20 × 1(2(7.5) - 1)

V = 879.65

9514 1404 393

Answer:

  y/x = -3/7

Step-by-step explanation:

Write the given relationship and solve for y/x.

  (x +y)/(x -y) = 2/5

  5(x +y) = 2(x -y) . . . . . multiply by 5(x-y)

  5x +5y = 2x -2y . . . . . eliminate parentheses

  7y = -3x . . . . . . . . . . . add 2y-5x

  y/x = -3/7 . . . . . . . . divide by 7x

Answer:

A regular polygon all the angles, as well as all the sides, are equal.

Diego's claim is the quadrilateral with four congruent sides is always a regular polygon. He is only mentioning that the sides are equals.

He has not mentioned anything about the angles, the angles may or may not be equals.

In the case, if all the angles are equal too, then the claimed quadrilateral will be a regular polygon as shown in figure(a).

So, for this case, Diego's claim is correct while  Mai's claim is also wrong.

While if all the angles are not equal, then the claimed quadrilateral will not be a regular polygon as shown in figure(b).

In this case, Diego's claim is wrong while Mai's claim is correct.

So, overall, considering both the case together, none of them have the correct claim.

So, both are wrong.

Step-by-step explanation:

Answer:

Decrease by 3.9%

Step-by-step explanation:

54,500(1-x) = 52355

x=0.03935... = 3.935% or 3.9%

Answer:

first we subtract his new salary from the old salary to get the decrease.

Then percentage decrease ,we get the decrease over the new salary and multuply by 100. to get the percentage decrease

9514 1404 393

Answer:

  quiz score if no homework is done

Step-by-step explanation:

The y-intercept is the point where the horizontal coordinate is zero. That axis is defined as "hours per week spent on homework". So, the y-intercept is the function value when zero hours per week are spent on homework.

The function value is defined as "expected quiz score".

Then the y-intercept is ...

  the expected quiz score when zero hours per week are spent on homework

Answer:

(27xy +3)/5x^2 +6x

Step-by-step explanation:

((15xy^2 )/ x^2 + 5x + 6 ) × ((2x^2 + 7x + 3) / 5x^2y)

(3y ×(2x+ 7x + 3)) / 5x^2 +6x)

Answer:

Wdym? that is fraction form, but if you ment decimal form; it is .7777 repeating and .25

Step-by-step explanation: