y=x²+2x–5
vertex form

Given:

The two points on the graph are R(-2,-4) and S(-8,-6).

To find:

The length of RS.

Solution:

Distance formula: The distance between two points is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the distance formula, the distance between R(-2,-4) and S(-8,-6) is

[tex]d=\sqrt{(-8-(-2))^2+(-6-(-4))^2}[/tex]

[tex]d=\sqrt{(-8+2)^2+(-6+4)^2}[/tex]

[tex]d=\sqrt{(-6)^2+(-2)^2}[/tex]

[tex]d=\sqrt{36+4}[/tex]

On further simplification, we get

[tex]d=\sqrt{40}[/tex]

[tex]d=6.32455532[/tex]

[tex]d\approx 6.3[/tex]

Therefore, the length of AB is about 6.3 units. So, the correct option is C.

9514 1404 393

Answer:

  15.08 m

Step-by-step explanation:

You can take the appropriate fraction of the whole circumference, or you can use the arc-length formula. You get the same answer either way.

Angle XZW is 180° -108° = 72°

The circumference is C=πd, so the arc of interest is ...

  XW = C(72°/360°) = πd/5 =π(24 m)/5 = 4.8π m

  XW ≈ 15.08 m

_____

If you use π = 3.14, then your answer will be 15.07 m.

Answer:

60: 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]$ The rate is expressed as $ \frac{mi}{hr} $ so you must divide miles by hours. $ \\ \\ \frac{240mi}{4hr}=60\frac{mi}{hr}[/tex]

Answer:

the slope is -1/7 hope this helps

Answer:

576

Step-by-step explanation:

f(2) = 4f(1) = 4*9 = 36

f(3) = 4f(2) = 4 * 36 = 144

f(3) = 4f(3) = 4 * 144 = 576

Answer:

=14bx2−7x3−4b+2x

Step-by-step explanation:

Answer: 1 1/4 hours

Step-by-step explanation: if 2/3 was her recital piece 25 is equal to 1/3. Multiply it by 3 to get 3/3 or 1. 25*3=75 minutes or 1 hour 15 mins. This can be written as 1 and a quarter hours, 1 hour 15 mins, or 5/4 an hour.

Answer:

5.41

Step-by-step explanation:

C= πd

50/360 = 5/36

5/36 x (6.2 x 2) x π = 5.410520...

Let Asia's and Rani's age be "x"

Since Asia is 10 years bigger Asia will be "x+10"

Asia's Age + Rani's Age = 200

x + x + 10 = 200

2x + 10 = 200

2x = 200 - 10

2x = 190

x = 190

     -----

       2

x = 95

Asia = x + 10

          95 + 10

          105

Rani's age is 95 and Asia's Age is 105

Answer:

8 parts

Step-by-step explanation:

1. AD≅BC                                                                Given

2. AD║BC                                                                Given

3. ∠DAC and ∠BCA                                                Def. of alt.

are alt. interior  angles                                          interior angle

4. ∠DAC ≅ ∠BCA                                           alternate interior angle theorem

5. AC ≅ AC                                                       reflexive property

6. ΔDAC ≅ ΔBCA                                                     SAS

7. AB ≅ CD                                                              CPCTC

8. ABCD is a parallelogram                                parallelogram side theorem

The proof of ABCD is a parallelogram is given in the solution.

In geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

The proof is as follows :-

AD≅BC (Given)

AD║BC (Given)

∠DAC and ∠BCA (alternate angles)

∠DAC ≅ ∠BCA (alternate angle)

AC ≅ AC (common)

ΔDAC ≅ ΔBCA (SAS rule)

AB ≅ CD (CPCT)

Hence,

ABCD is a parallelogram (by the definition of parallelogram)

Hence, proved.

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Answer:

x = 1/12

Step-by-step explanation:

2/3x + 1/4 = (8x+3) /12   (create equivalent fractions with a denominator of 12)

23/3x - 1/3 = (23x - 1) /3            *(46/6x = 23/3x)

8x + 3  =  23x - 1

    12            3

now cross-multiply:

3(8x + 3) = 12(23x - 1)

24x + 9 = 273x - 12

9 = 252x - 12

21 = 252x

x = 21/252 which reduces to 1/12

Answer:

12 foot.

Step-by-step explanation:

Given that,

A ladder leans a 15 foot ladder against a second story window.

The distance on the ground between the base of the ladder and the house is 9 feet.

We need to find the height of the ladder. Let it is h.

If we consider a right angles triangle such that 15 foot is hypotenuse, 9 feet is base, then we need to find the perpendicular height of the triangle. Using Pythagoras theorem to find it.

So, the height of the ladder that reaches the second story window is 12 foot.

There is only one property used to determine whether

[tex]4r+4t=4(r+t)[/tex].

The property is called the distributive property and in a nutshell it states, [tex]a(b+c)=ab+ac[/tex], which means [tex]a[/tex] is distributed through [tex]b+c[/tex] using multiplication. So [tex]4(r+t)[/tex] says, distribute [tex]4[/tex] to [tex]r[/tex] and [tex]t[/tex] which then translates into [tex]4r+4t[/tex].

Answer:

y < 160

Step-by-step explanation:

y + 20 < 180

    -20 < -20

y < 160

y is less than 160

so the answer is y < 160

happy to help!

Answer:

Not a function

Step-by-step explanation:

The graph does not pass the line test.

Step-by-step explanation:

A.

[tex]f(x) = \sqrt{x - 2} [/tex]

B.

[tex]g(x) = 2x [/tex]

C.

[tex]h(x) = \frac{1}{x - 2 \: } \: \: \: \: h(x) = x where x is greater than zero

4 is the value of log₃ 81.

We have,

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The equation may be changed to read:

x = log base 3 of 81.

81 being equivalent to 3 to the power of 4, we get the following:

x Equals log base 3 of 34.

We may reduce this to: Applying the rule that log base an of ab = b

4 = x

By answering the above question, we may infer that We may reduce this equation to: Applying the rule that log base an of ab = b, 4 = x.

Hence, x = 4.

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Answer:

10 flags

Step-by-step explanation:

30/3=10

3 intervals of making 10 flags to get 30 flags

Answer:

y=2x-8

Step-by-step explanation:

Subtract 4 x from both sides of the equation. − 2 y = 16 − 4 x Divide each term by − 2 and simplify. Tap for fewer steps... Divide each term in − 2 y = 16 − 4 x by − 2 . − 2 y − 2 = 16 − 2 + − 4 x − 2 Cancel the common factor of − 2 . Tap for fewer steps... Cancel the common factor. − 2 y − 2 = 16 − 2 + − 4 x − 2 Divide y by 1 . y = 16 − 2 + − 4 x − 2 Simplify 16 − 2 + − 4 x − 2 . Tap for fewer steps... Simplify each term. Tap for fewer steps... Divide 16 by − 2 . y = − 8 + − 4 x − 2 Cancel the common factor of − 4 and − 2 . Tap for fewer steps... Factor − 2 out of − 4 x . y = − 8 + − 2 ( 2 x ) − 2 Cancel the common factors. Tap for more steps... y = − 8 + 2 x Reorder − 8 and 2 x . y = 2 x − 8

Answer:

Y = 2x - 8

Step-by-step explanation:

-2y = -4x + 16

y = 2x - 8

Your welcome

Answer:

Step-by-step explanation:

Number of students:

Number of packs of paper plates:

Answer:

20 packs

Step-by-step explanation:

Because if they are sold in packs of 8, 8 times 20 is actually 160, but if she only buys 19 packs, their will only be enough plates for 152 students.

Hope this helps you. Tell me if not or if it is.

Answer:

22.4

Step-by-step explanation:

set up the equation

6x+157= -x+45

157=5x+45

112=5x

22.4=x

Answer:

DFG

Step-by-step explanation:

It is a right triangle, and so is DEF. Thus they are similar.

Answer:

c

Step-by-step explanation:

if it doubles every week, then the extra that would be bought would be equal to last weeks amount

Answer:200

Step-by-step explanation:

Answer:

1

i guess...

Step-by-step explanation:

Step-by-step explanation:

sum of all the angles in a triangle is equal to 180°

82 + 70 + (2x + 4) = 180

152 + 2x + 4 = 180

156 + 2x = 180

2x = 180 - 156

2x = 24

x = 12

Answer: D. f(x)-2

Step-by-step explanation:

Changes insides the parenthesis translate left and right. If it is [+] a number, then it is moving to the left. If it is [-] a number, then it is moving to the right.

Changes outside the parenthesis translate up and down. If it is [+] a number, then it is moving upward. If it is [-] a number, then it is moving downward.

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

Given

Translate f(x) 2 units downward

Solve

According to the rules, it should be -2 units outside of the parenthesis

Therefore, it should be f(x)-2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

D. f(x) – 2

Step-by-step explanation: