The graph of function g(x) is a transformation of the graph of function f(x) = x2.

Answer:

Length of hypotenuse [tex]12\sqrt2[/tex] cm.

Step-by-step explanation:

We are given with a right angled triangle which has angles 45°-45°-90° and sides as 12 cm each.

Following labeling of dimensions is provided:

[tex]\angle XYZ = 90^\circ\\\angle YZX = 45^\circ\\\angle ZXY = 45^\circ[/tex]

Sides:

ZY = 12 cm

YX = 12 cm

Please refer to the image attached as well.

To find: The hypotenuse, XZ = ?

It is well known that if the triangle is a right angled triangle, the pythagorean theorem holds well. As per the theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Height}^{2}\\[/tex]

Here, Base is ZY = 12 cm

Height, YZ = 12 cm

And Hypotenuse XZ is to be calculated.

Putting the values:

[tex]XZ^2=12^2+12^2\\\Rightarrow XZ^2=144+144\\\Rightarrow XZ=\sqrt{144+144}\\\Rightarrow XZ=\sqrt{288}\\\Rightarrow XZ=12\sqrt{2}\ cm[/tex]

So, the answer is Hypotenuse, XZ = [tex]12\sqrt{2}\ cm[/tex].

Answer:

D

Step-by-step explanation:

Answer:

  h = 13.333 +693.333/r

Step-by-step explanation:

For h hours, Brandee's pay will be ...

  pay = 40r +(h -40)(1.5r) . . . . 40 hours at rate r + overtime (h-40) hours at 1.5r

  pay = 40r +1.5hr -60r . . . . . eliminate parentheses

  pay = 1.5hr -20r . . . . . . . . . . collect terms

Solving for h, we have ...

  pay +20r = 1.5hr . . . . . . . . . . add 20r

  h = (pay +20r)/(1.5r) . . . . . . . . divide by 1.5r

For the given pay of 800 +240 = 1040, we have ...

  h = (1040 +20r)/(1.5r)

  h = 13.333 +693.333/r . . . . . simplify to 2 terms

_____

Additional comments

You need to know r to find the number of hours Brandee worked. She got paid $800 for a presumed 40-hours of regular time, so made r = $20 per hour. The above formula will tell you she worked 48 hours in the pay period.

Answer:

D.

Step-by-step explanation:

A linear parent graph is always a solid, constantly sloped line. A linear equation looks like a line.

Exponents are a straight horizontal line that curves up after a while.

Quadratics are the big U shaped graph.

Absolute values look like a V graph.

Answer:

7

Step-by-step explanation:

We want to evaluate the fraction below for x = 3. We will put the value of x to be 3:

[tex]\dfrac{7^2}{x^2-2}\\\\= \dfrac{7^2}{3^2-2}\\\\= \dfrac{49}{9-2}\\\\= \dfrac{49}{7} = 7[/tex]

The answer is 7.

Answer:

Step-by-step explanation:

goodluck khan academy users

Answer:

[tex]3(8x ^{2} + x + 2)[/tex]

factor out 3 polynomial 8xsqurd +x+2 not factored as it doesn't have any rational roots

Answer:

This cannot be simplified any further.

Step-by-step explanation:

Answer:

AB = 10.2m

Step-by-step explanation:

Area of triangle ADC = 52m²

AD = 12m, angle D = 102°

Area of triangle ADC = ½ × a × b × sinC

52m² = ½ × 12 × CD × sin102

52 = 6 × CD × 0.9781

CD = 52/(6× 0.9781)

CD = 52/(5.8686)

CD = 8.86m = 8.9m (1 decimal place)

Using Cosine rule to find AC = d

d² = a² + c² -2×a×d ×cosD

d² = 8.9² + 12² - 2×8.9×12× Cos102

Cos102 = -0.2079

d² = 267.61744

d = √(267.61744)

AC = d = 16.4m

For ∆ABC

Using sine rule:

a/sinA = b/sinB

AB/sin46 = AC/sin120

AB/0.7193 = 16.4/0.866

AB = 14.2024 ×0.7193

AB = 10.2m (1 decimal place)

Answer: 13.6

Step-by-step explanation:

See photo

Answer:

He failed to check for extraneous solutions

Step-by-step explanation:

sqrt(x+6) -4 =x

Add 4 to each side

sqrt(x+6) -4+4 =x+4

sqrt(x+6)  =x+4

Sqaure each side

(sqrt(x+6))^2  =(x+4)^2

x+6 = x^2 +8x+16

Subtract 6 from each side

x = x^2 +8x +10

Subtract x from each side

0 = x^2 +7x +10

Factor

0 = (x+5) (x+2)

Using the zero product property

x=-5  x=-2

Check the solutions

sqrt(-5+6) -4 =-5

sqrt(1) -4 = -5

1-4 =-5

-3 does not equal -5 not a solution

sqrt(-2+6) -4 =-2

sqrt(4) -4 = -2

2-4 =-2  is a solution

Answer:

i hope this helps and its clear !

Answer:

The last answer 8.01x10^-4

Step-by-step explanation:

Answer:

5369 thanks for ur point

Answer:

  -2

Step-by-step explanation:

The floor function returns the largest integer not greater than the function's argument. The largest integer less than or equal to -1.1 is -2.

Answer:

you're answer should be b

Step-by-step explanation:

Answer:

No . Natural numbers are a subset of whole number. Negative numbers are entire numbers but not natural. And any set that contains it. For example, the set {1, 2.3, 2.236067977} or {-79000, pi, 2.236067977, sin(47)} or all real numbers, etc

Step-by-step explanation:

Answer:

10,000

Step-by-step explanation:

100/0.01 is 10k

Answer:

The answer is B.

Step-by-step explanation:

Instead of solving each equation, simply think about it alternatively.

Recall that quadratic equations can also be written as: [tex](x-a)(x-b)[/tex], where [tex]a[/tex] and [tex]b[/tex] are the solutions.

We know that 1 and -3 are solutions, so we can substitute them in for [tex]a[/tex] and [tex]b[/tex].

Thus, we have:

[tex](x-(1))(x-(-3))[/tex]

[tex](x-1)(x+3)[/tex]

Now, expand:

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

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

The answer is B.

Answer:

p= 2.5

Step-by-step explanation:

maybe you meant 15=2(3p)

so that would be the answer

Answer:

3m = 18

Step-by-step explanation:

9 + 12m = 6 + 15(m - 1)

9 + 12m = 6 + 15m - 15

3m = 18

Answer:

3m=18

Step-by-step explanation:

trust

Answer:

4 units

Step-by-step explanation:

Considering the triangle KLJ, using the trigonometric ratios defined by the notation SOH CAH TOA

Line LJ is the opposite side while LK is the hypotenuse side. Hence,

Sin 30 = LJ/8√2

LJ = 8√2 × 1/2

= 4√2

Considering triangle LJM, line LJ is now the hypotenuse while line LM which is equal to x is the opposite side.

Sin 45 = x/4√2

x = 4√2 × 1/√2

x = 4

Answer:

4

Step-by-step explanation:

Just took the test in k12

Answer:

2.66 and 4.34

Step-by-step explanation:

To evaluate, substitute the values of y and solve.

So, when y =-2

0.67y + 4 = -1.34 + 4 = 2.66

And when y = 2

0.67y + 4 = 1.34 + 4 = 4.34

Hope this helps.

Answer:

y = 2

 5.34

y = -2

- 2.66

Step-by-step explanation:

0.67y + 4

y = 2

.67(2)+2

 1.34+4 = 5.34

y = -2

-.67(2)+2

 -1.34+4 = 2.66

Answer:

7/6 or 1.166666667

Step-by-step explanation:

I solved it on calculator

To 1 d.p 1.2

Answer:

7/6

Step-by-step explanation:

7/5 × -3/12 + 7/6 + 7/5 × 1/4

Multiply first.

-21/60 + 7/6 + 7/20

Find the common LCM of the fractions.

-21/60 + 70/60 + 21/60

Add the fractions.

(-21+70+21)/60

-21 and 21 cancels.

70/60

Simplify.

7/6

Answer:

The coordinates of the image of vertex P after reflection is  (-7, 4)

Step-by-step explanation:

Given that we are to reflect the point P across the x-axis, we have;

Reflection of a point across the x-axis gives;

When a point is reflected across the x axis, the y-coordinate changes to the opposite sign while the x-coordinate remains unchanged  such that (x, y) becomes (x, -y)

Therefore, given that the point P = (-7, -4), we have;

Coordinates of point P before reflection Reflection = (-7, -4), coordinates of point P after reflection Reflection P' = (-7, 4).

Answer:

-7,4

Step-by-step explanation:

got it right on edge

Answer:

i think 9.8 but im not sure

Step-by-step explanation:

The distance between points M and N is; 9.8 meters.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

From observation, it is given that the line segment MN which joins points M and N is parallel to the line JK. which follows from the fact that M and N are midpoints of KL and JL respectively.

Hence, it states that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality:

NM/19.6 = 7.4/(2×7.4)

Solving;

NM = 19.6/2

NM=  9.8 meters.

This follows that, the ratio of corresponding sides of congruent triangles are equal.

The distance between points M and N is; 9.8 meters.

Read more on congruent triangles;

brainly.com/question/1675117

#SPJ6

Answer:

Yes

Step-by-step explanation:

A rational number is any number that can be expressed as a ratio of two integers, for example, 1/2. Rational numbers can be negative too. -15.5 can be expressed as the ratio of two integers in many ways: -31/2 or -62/4. So, yes! -15.5 is a rational number.

Answer:

a) The value of the median is 112

b) The value of the lower quartile is 95.59

Step-by-step explanation:

From the histogram, we look for the data values as follows

Score,                                       Frequency,          Cumulative , n

80 - 90,                                    2.6,                       2.6

90 - 100,                                   3.4,                       6

100 - 120,                                  5,                          11

120 - 140,                                  3,                          14

140 - 170,                                  2.4,                       16.4

170 - 200,                                 0.6,                       17

The median is therefore the (nth + 1)/2th value = (17 + 1)/2 = 9th value

The 9th value is between the 100 - 120 score values

We note that the previous n value before the 100 - 120 range = 6, therefore, the 9th value will be the weighted average in the 100 - 120 range of tha amount the 9th value is larger than the 6th value as follows;

9 - 6 = 3

The weighted average of 3 out 5 (11 - 6 = 5) of the 100 - 120 range which gives;

Therefore, the value of the median, Q₂ = 100 + (9 - 6)/(11 - 6))*(120 - 100) = 112

b) The lower quartile = Q₁ is given by the value at the (n +1)/4th position = (17 + 1)/4 = 4.5th position

From the cumulative frequency column, the 4.5th value is in the 90 - 100 score range

Similar to the previous question, we find the value of the lower quartile using the weighted average as follows;

Therefore, the value of the lower quartile, Q₁ = 90 + (4.5 - 2.6)/(6 - 2.6)×(100 - 90) = 95.59.

Answer:

b

Step-by-step explanation:

Answer:

Correct option: c) infinitely many solutions

Step-by-step explanation:

We have an equation with two variables, so as we have a system with less equations (just one) than variables (two), we have an infinite number of solutions.

To find some solutions, we can choose values for x and then just calculate the value of y:

x = 0:

-11y = 10 -> y = -10/11

x = 1:

3 - 11y = 10 -> y = -7/11

x = 2:

6 - 11y = 10 -> y = -4/11

And so on.

So the correct option is c): infinitely many solutions

A linear equation is something of the form:

y = a*x + b

Where the solutions are the pairs (x, y) such that the equality is true.

Here we will find that the correct option is c: infinitely many solutions.

In this case, we have the equation:

3x - 11y = 10

We can rewrite this as:

3x = 10 + 11*y

x = 10/3 + (11/3)*y

Ok, now we have one variable on each side, now let's see the number of solutions.

As you can see, we have one equation with two variables.

So if for example we take y = 0, we get:

x = 10/3 + (11/3)*0 = 10/3

So one solution is (10/3, 0)

If we take y = 1, we get:

x = 10/3 + (11/3)*1 = 22/3

Then another solution is (22/3, 1)

And as you can see, y can take any real value. So we have infinite values of y.

This also means that we have infinite values of x (as we have one value of x for each value of y). Then we will have infinite solutions for the linear equation.

The correct option is c.

If you want to learn more, you can read:

https://brainly.com/question/16843611

Answer:

Step-by-step explanation:

If AB is parallel to CD and there is a transversal cutting through both (as there is, although it is not named here), then by the definition of corresponding angles, angles 1 and 5 are corresponding and are therefore, congruent. If angle 1 measures 120 then so does angle 5. Learn these...they're very important and are prevalent in triangle stuff in geometry!!!