Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6?
left 1 unit, up 5 units
right 1 unit, up 5 units
left 2 units, up 2 units
right 2 units, up 2 units

Answer:

Reflected over the x-axis, vertically shrunk by a factor of 1/5, moved right 4 units and up 2 units.

Step-by-step explanation:

Parent Graph: f(x) = a(bx - h)² + k

a is vertical stretch (a > 1) or shrink (a < 1) and reflection over x-axis

b is horizontal stretch or shrink and reflection over y-axis

h is horizontal movement left (if positive) or right (if negative)

k is vertical movement up (if positive) or down (if negative)

Now that we have our rules, we simply apply it to y = -1/5(x - 4)² + 2

a = -1/5, so reflection over x-axis and vertical shrink of 1/5 (1/5 < 1)

Nothing has changed b, so no horizontal stretch/shrink

h = -4, so horizontal movement right 4 units

k = 2, so vertical movement up 2 units

Answer:

The correct option is;

[tex]\overline{AB}\cong \overline{DB}[/tex]  and  [tex]\overline{AC}\cong \overline{DC}[/tex]

Step-by-step explanation:

The steps to prove that ΔABC ≅ ΔDBC with the SSS Congruence postulate

We have;

Statement,                     Reason

BC ≅ BC,                       Reflexive property

[tex]\overline{AB}\cong \overline{DB}[/tex],                      Option selected

[tex]\overline{AC}\cong \overline{DC}[/tex],                      Option selected

ΔABC ≅ ΔDBC,              SSS Congruency Postulate

Therefore, whereby all three sides of the triangles ABC and DBC are congruent, then ΔABC is congruent to ΔDBC.                      

Answer:

AC≅DF

AB≅DE

Step-by-step explanation:

took the test :)

Answer:

230.59

Step-by-step explanation:

55 = 2.7sqrt(x) + 14

41 = 2.7sqrt(x)

15.185=sqrt(x)

x = 15.185^2

x=230.59

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

[tex]((a, b), (c, d))\in R[/tex]

Where [tex]R[/tex] is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

1. First of all, let us check reflexive property:

Reflexive property means:

[tex]\forall a \in A \Rightarrow (a,a) \in R[/tex]

Here we need to prove:

[tex]\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R[/tex]

As per the given relation:

[tex]((a,b), (a,b) ) \Rightarrow ab =ab[/tex] which is true.

[tex]\therefore[/tex] R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

[tex]\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R[/tex]

Here we need to prove:

[tex]\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R[/tex]

As per the given relation:

[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = bc[/tex]

[tex]((c,d),(a,b)) \in R[/tex] means [tex]cb = da\ or\ ad =bc[/tex]

Hence true.

[tex]\therefore[/tex] R is symmetric.

3. R to be transitive, we need to prove:

[tex]if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R[/tex]

[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = cb[/tex].... (1)

[tex]((c,d), (e,f)) \in R[/tex] means [tex]fc = ed[/tex] ...... (2)

To prove:

To be [tex]((a,b), (e,f)) \in R[/tex] we need to prove: [tex]fa = be[/tex]

Multiply (1) with (2):

[tex]adcf = bcde\\\Rightarrow fa = be[/tex]

So, R is transitive as well.

Hence proved that R is an equivalence relation.

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

https://brainly.com/question/1503196

Answer:

(x - 7)(x + 4)

Step-by-step explanation:

Note that 4 times 7 is 28, and that -7x + 4x = -3x.

Therefore, x^2 - 3x - 28 factors into (x - 7)(x + 4)

The factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Writing a number or any mathematical object as the result of several factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

The factorization will be done as below:-

x² – 3x – 28

Split the middle term as 7 and 4.

x² – 7x  +  4x – 28 = 0

x ( x - 7 ) + 4 ( x -7 ) = 0

Take x-7 common from the whole equation.

( x - 7 ) ( x + 4 ) = 0

Therefore, the factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ2

Answer:

Hey!

Well...the distance from Birmingham to Wolverhampton in about 12 miles (19km)

The length of the Golden Gate bridge is 2,737m OR 2.737 km...in miles it's 1.701

So you will have to cross it about 11.2 times (3 sf)

Step-by-step explanation:

19 km / 1.701km = 11.16990005878895

Rounded up to a degree of accuracy = 3 sf

= 11.2

Hope this helps!

Answer:

30 people

Step-by-step explanation:

If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.

Answer:

C = pi * d

Step-by-step explanation:

C = 2 * pi *r

We can replace 2 * r with d since the diameter is twice the radius

C = pi * 2*r

C = pi * d

Answer:

(2)They are perpendicular.

Step-by-step explanation:

Answer:

(x + 2)

Step-by-step explanation:

When we factor the expression x² - 8x - 20, we should get (x + 2)(x - 10).

Alternatively, we can use synthetic division or long division to get our answer.

Answer:

x + 2

Step-by-step explanation:

got it right edg '22

Answer:

126 people

Step-by-step explanation:

9/5 is the ratio tea/coffee

let x be the one who preferred coffee and x+36 preferred tea

9/5=x+36/x

9x=5x+5(36)

9x-5x=180

4x=180

x=180/4=45

x=45 coffee

x+36=45+36=81

45+81=126

check : 81/45= 9/5

Answer:

Step-by-step explanation:

Volume of a rectangular solid = l × w × h

where

l is the length

w is the width

h is the height

From the question

l = 12 feet

w = 3 feet

h = 4 feet

Volume = 12 × 3 × 4

= 144 feet

Hope this helps you.

Answer:

drop out dog

Step-by-step explanatiopensin:

Answer: 6

Step-by-step explanation: I think..... this is a division sign, nvm... so 4 divided by 8/12 is basically 4 x 12/8 which is 48/8 simplified is/equals 6!

Answer:

6

Step-by-step explanation:

4 / 8/12 = 4 * 12/8 = 4 * 3/2 = 6

Answer:

I hope it's correct

Answer:

Solve

(15x+y)and 20x+10y

2

Answer:

The car's average speed for the entire journey = 84.315 km/h

Step-by-step explanation:

Correct Question

A car travels the first 50km of its journey at an average speed of 25m/s and the next 120 km at an average speed of 80km/h. the car completes the last part of its journey at an average speed of 90km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.

Solution

Average speed is given as total distance travelled divided by total time taken.

So, we will compute the distance covered for each part of the journey and the corresponding time it takes to cover each of these distances.

- The car travels the 50 km first part of the journey at a speed of 25 m/s.

25 m/s = 90 km/h

We have the distance covered in the first part of the journey, now, we need the time taken to cover the distance.

Speed = (Distance/Time)

Time = (Distance/Speed)

Distance = 50 km, Speed = 90 km/h

Time = (50/90) = 0.5556 hr

- The next part, the car covers 120 km at a speed of 80 km/h

Time = (Distance/Speed) = (120/80) = 1.5 hr

- For the last part of the journey, the car travels with an average speed of 90 km/h for 35 minutes.

35 minutes = (35/60) hr = 0.5833 hr

Here, we need to calculate the distance covered for the last part.

Speed = (Distance/Time)

Distance = (Speed) × (Time) = 90 × 0.5833 = 52.5 km

Total distance covered = 50 + 120 + 52.5 = 222.5 km

Total time taken = 0.5556 + 1.5 + 0.5833 = 2.6389 hr

Average Speed = (222.5/2.6389) = 84.315 km/h

Hope this Helps!!!

Answer:

x = -3

Step-by-step explanation:

When asked to solve the equation for x, it mean that put x only on one side, and everything else on the other side. So....

x/3 - 1 = -2

x/3 = -1             ( add 1 on both side)

x = -3               (x3 on both side)

Answer:

Im pretty sure its C

Answer: The answer is C

Step-by-step explanation:

Answer:

she wills substitute r with 7%.

Step-by-step explanation:

Just did it.

Answer:

R = 7%

Principal (P)

Rate (R)

Time (t)

Step-by-step explanation:

The full intrest rate formula is i=prt

You are looking for r

R is the interest rate 7%

So i = 12,876*7%*3years will be the full equation.

Answer:

He will have enough paint to cover the tank with one layer of paint

Step-by-step explanation:

To calculate the area of the surface that has to be painted, we will have to calculate the lateral surface of the cylinder

Lateral surface of the cylinder is given by

A=2πrh

Where,

π=3.142

r=1.1/2m=

h=1.4m

A=2πrh

=2*3.142*1.1/2*1.4

=4.84m^2

He uses 250ml to cover 1m^2

To cover 4.84m^2, he will use

4.84m^2 × 250ml of paint

=1,210ml of paint is needed

He has 2 litres of paint

2litres =2000ml

Tublu has 2000ml of paint but needs 1210ml of paint

Therefore,

He has an excess of 2000-1210

=790ml

The answer is yes, he will have enough paint to cover the tank with one layer of paint.

Answer:

The null hypothesis: [tex]\mathbf{H_o: p=0.27}[/tex]

The alternative hypothesis: [tex]\mathbf{H_1: p \neq 0.27}[/tex]

Test statistics : z = −2.30

P-value:  = 0.02144

Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.

Conclusion: We accept the alternative hypothesis and  conclude that under the same​ circumstances the proportion of offspring peas will be yellow is not equal to 0.27

Step-by-step explanation:

From the given information:

Let's state the null and the alternative hypothesis;

Since The claim is that 27%  of the offspring peas will be yellow.

The null hypothesis state that the proportion of offspring peas will be yellow is equal to 0.27.

i.e

[tex]\mathbf{H_o: p=0.27}[/tex]

The alternative hypothesis  state that the proportion of offspring peas will be yellow is not equal to 0.27

[tex]\mathbf{H_1: p \neq 0.27}[/tex]

The test statistics:

we are given 437 green peas and 129 yellow apples;

Hence;

[tex]\hat p = \dfrac{x}{n}[/tex]

where ;

[tex]\hat p[/tex] = sample proportion

x = number of success

n = total number of the sample size

[tex]\hat p = \dfrac{129}{437+129}[/tex]

[tex]\hat p = \dfrac{129}{566}[/tex]

[tex]\mathbf{\hat p = 0.2279}[/tex]

Now; the test statistics can be computed as :

[tex]z = \dfrac { \hat p -p }{\sqrt {\dfrac{p(1-p)}{n} } }[/tex]

[tex]z = \dfrac {0.2279 -0.27 }{\sqrt {\dfrac{0.27(1-0.27)}{566} } }[/tex]

[tex]z = \dfrac {-0.043 }{\sqrt {\dfrac{0.27(0.73)}{566} } }[/tex]

[tex]z = \dfrac {-0.043 }{\sqrt {\dfrac{0.1971}{566} } }[/tex]

[tex]z = \dfrac {-0.043 }{\sqrt {3.48233216*10^{-4} } }[/tex]

[tex]z = \dfrac {-0.043 }{0.01866} }[/tex]

z = −2.30

C. P-value

P-value = P(Z < z)

P-value = P(Z< -2.30)

By using the ​ P-value method and the normal distribution as an approximation to the binomial distribution.

from the table of standard normal distribution

move left until the first column is reached. Note the value as –2.0

move upward until the top row is reached. Note the value as 0.30

find the probability value as 0.010724 by the intersection of the row and column values gives the area to the left of

z = -2.30

P- value = 2P(z ≤ -2.30)

P-value = 2 × 0.01072

P - value = 0.02144

Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.

Conclusion: We accept the alternative hypothesis and  conclude that under the same​ circumstances the proportion of offspring peas will be yellow is not equal to 0.27

Answer:

V = 3534 cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

the radius is 7.5 and the height is 20

V = pi ( 7.5)^2 * 20

V =1125 pi cm^3

Using the pi button for pi

V =3534.291735 cm^3

Rounding to the nearest whole number

V = 3534 cm^3

Answer:

b)3534 cm^3

Step-by-step explanation:

To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.

Answer:

a) 12 (Simply divide 4800/5 to get 960.  Then divide 960/80 to get 12)

b) 2100 (Simply multiply 12 by 25 by 7)

Hope it helps <3

Answer:

Option A is the correct option.

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} - 2ab \: \cos \: c \: = {c}^{2} \\ a = 4 \\ b = 5 \\ c = 2 \\ \\ 2ab \: cos \: c = {a}^{2} + {b}^{2} - {c}^{2} \\ \: \: \: \: \: \: \: \: = {(4)}^{2} + {(5)}^{2} - {(2)}^{2} \\ \: \: \: \: \: \: \: \: = 16 + 25 - 4 \\ \: \: \: \: \: \: = 41 - 4 \\ \: \: \: \: \: \: = 37[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

Please see attached picture for full solution.

Answer:  (0, 0) & (3, √3)

Step-by-step explanation:

Since we need a distance of 2, I graphed y = √x and then drew a circle at center (2, 0) and radius of 2 to see where they intersect.

The coordinates of intersection can be determined by solving a system of equations.

Equation 1: y = √x

Equation 2: (x - 2)² + y² = 2²

I will use the Substitution method with Equation 2 to solve for x:

(x - 2)² + (√x)² = 2²        substituted y with √x

x² - 4x + 4 + x = 4           expanded binomial

x² - 3x + 4 = 4                 added like terms

x² - 3x = 0                       subtracted 4 from both sides

x(x - 3) = 0                       factored

x = 0     x - 3 = 0             applied Zero Product Property

            x = 3

Next, solve for y using Equation 1:

x = 0:    y = √0 = 0

x = 3:    y = √3

Coordinates of intersection are: (0, 0) & (3, √3)

Answer:

(0, 0) & (3, √3)

Step-by-step explanation:

Answer:a

Step-by-step explanation: