How do you figure this out?

How Do You Figure This Out?

Answers

Answer 1

Answer:

∠g and ∠h are complementary angles∠g and ∠h are acute angles

Step-by-step explanation:

Use the given information to determine what the angles can be.

  g = 2x -90 . . . . given

  g > 0 . . . . . . . . . given

  2x -90 > 0

  2x > 90 . . . . . add 90

  x > 45 . . . . . . divide by 2

__

  h = 180 -2x

  h > 0

  180 -2x > 0

  180 > 2x

  90 > x

__

The requirement that both angles be greater than zero puts limits on x:

  45 < x < 90

We can put this back into the given relations for g and h:

  g = 2x -90

  x = (g +90)/2

  45 < (g +90)/2 < 90 . . . . substitute for x

  0 < g/2 < 45 . . . . . . . . . . subtract 45

  0 < g < 90 . . . . . . . . . . . . g is an acute angle

Similarly, ...

  h = 180 -2x

  x = (180 -h)/2 = 90 -h/2

  45 < (90 -h/2) < 90 . . . . substitute for x

  -45 < -h/2 < 0 . . . . . . . . . subtract 90

  90 > h > 0 . . . . . . . . . . . multiply by -2; h is an acute angle

__

We can add the angle measures to see if they are supplementary or complementary:

  g + h = (2x -90) +(180 -2x)

  g + h = 90 . . . . . simplify; the angles are complementary

__

The relevant observations are ...

∠g and ∠h are complementary angles∠g and ∠h are acute angles

Related Questions

If g(x) = x2 + 3, find g(4).

Answers

Answer:

g(4) = 11

Step-by-step explanation:

x = 4

4(2) + 3 = 11

Answer:

19

Step-by-step explanation:

Replace the x with four

Select the two values of x that are roots of this equation x^2+3x-3=0
Apex

Answers

Answer:

C, and D are both roots of this equation

Answer:

The two values of x that are roots are:

[tex]x_{1} = \frac{-3 + \sqrt{21} }{2}[/tex]

[tex]x_{2} = \frac{-3 - \sqrt{21} }{2}[/tex]

Step-by-step explanation:

A cuadratic function has the form [tex]ax^{2} + bx +c = 0[/tex]

To calculate the roots of the cuadratic equation [tex]x^{2} + 3x -3 = 0[/tex] you have to solve the formula:

[tex]x = \frac{-b}{2a}[/tex] ±[tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]

In this case, a =1, b=3 and c= -3

Replacing the values of a,b and c in the formula:

[tex]x = \frac{-3}{(2)(1)}[/tex] ± [tex]\frac{\sqrt{(3)^{2} - (4)(1)(-3) } }{(2)(1)}[/tex]

Solving the mathematic operations:

x = [tex]\frac{-3}{2}[/tex] ± [tex]\frac{\sqrt{9 + 12 } }{2}[/tex]

The two roots are:

[tex]x_{1} = \frac{-3 + \sqrt{21} }{2}[/tex]

[tex]x_{2} = \frac{-3 - \sqrt{21} }{2}[/tex]

Use the function below to find f(3) f(x)= (1/6)^x

Answers

Hello!

The answer is:

[tex]f(3)=(\frac{1}{216})[/tex]

Why?

To find the required function f(3), we need to use the given function f(x) and evaluate "x" equal to 3 (input).

We are given the function:

[tex]f(x)=(\frac{1}{6})^{x}[/tex]

Then, evaluating "x" equal to 3, we have:

[tex]f(3)=(\frac{1}{6})^{3}[/tex]

[tex]f(3)=(\frac{1}{6})^{3}=(\frac{1}{6})*(\frac{1}{6})*(\frac{1}{6})=(\frac{1}{6*6*6})[/tex]

[tex]f(3)=(\frac{1}{6*6*6})=(\frac{1}{216})[/tex]

Hence, we have that the answer is:

[tex]f(3)=(\frac{1}{216})[/tex]

Have a nice day!

What number is equivalent to |−27| ?

Question 3 options:

a 27


-b 27


c 127

d − 127

Answers

Answer:

27

Step-by-step explanation:

Using the process of elimination and since their is no -27, 27 must be the answer

The little bars on each side of the number -27 represent absolute value. This means that you must take the positive of the number inside the absolute value. In this case the positive of -27 is...

A. 27

Hope this helped!

I love Shawn Mendes. I'll marry him one day. You'll see

A right rectangular prism is sliced parallel to its
base as shown in the figure.
What is the shape of the resulting two-
dimensional cross section?

Select from the drop-down menu to correctly complete the statement

The shape of the resulting two-dimensional

cross section is a Choose...

Pentagon

Rectangle

Trapezoid

Triangle

Answers

The answer is rectangle

Answer:

the correct answer is rectangle

Step-by-step explanation:

Find the discriminant and the number of real roots for this equation.
x^2+3x+8=0
Apex

Answers

Answer:

You got it right.

Step-by-step explanation:

Answer:

The discriminant is -23 and the equation has no real roots.

Step-by-step explanation:

Since, the discriminant of the quadratic equation [tex]ax^2+bx+c=0[/tex]

is,

[tex]D=b^2-4ac[/tex]

If D > 0, then the equation has two distinct real roots,

if D = 0, then the equation has two equal real roots,

if D < 0 then the equation has no real roots,

Here, the quadratic equation is,

[tex]x^2+3x+8=0[/tex]

Discriminant,

[tex]D=3^2-4\times 1\times 8=9-32 = -23 < 0[/tex]

Therefore, the discriminant is -23 and the equation has no real roots.

What is the exact circumference of the circle?
Show work

2π cm
4π cm
8π cm
16π cm

Answers

C=2πr

25.13 cm is the conference

Answer:

8π cm

Step-by-step explanation:

The diameter is 8 cm

We know the circumference is  pi times diameter

C = pi * d

C = pi *8

C = 8pi cm

We leave it in terms of pi since we want the exact value.

Use the data set below to answer the following question.
2, 4, 7, 2, 3, 7, 9, 3, 1,7
What is the mode of this data set?

Answers

Arranging it in ascending order:

1, 2, 2, 3, 3, 4, 7, 7, 7, 9

Mode is most frquently occuring observation..

i.e. Here ,7 Occurs the most(thrice)

So mode= ,7

Hello There!

Mode: The number that occurs most often in a set of numbers.

Although it's optional, I like to put the numbers from least to greatest because it can be easier to see what number occurs the most.

-Least To Greatest-

1 - 2 - 2 - 3 - 3 - 4 - 7 - 7 - 7 - 9

When we look at our set of data, we can notice that the number 7 appears the most so the mode for out set of data is 7.

Mode =  7

an energy bar contains 9000 milligrams of protein. how much protein does it contain in grams

Answers

Answer:

9 Grams

Step-by-step explanation:

You would move the decimal over 3 times to the left  from the end of 9000

To convert milligrams to grams, you should know that 1 gram is equal to 1000 milligrams. This is because "milli" in milligrams means one-thousandth of a gram.
If an energy bar contains 9000 milligrams of protein, to convert this amount to grams, you divide the milligrams by 1000 (because 1000 milligrams equals 1 gram).
Here's the calculation:
\( 9000 \text{ milligrams} \div 1000 = 9 \text{ grams} \)
So, an energy bar that contains 9000 milligrams of protein has 9 grams of protein.

identify the relative maximum value of g(x) for the function shown below

g(x) = 2/ x^2 +3

Answers

Answer:

The relative maximum value is [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The given function is

[tex]g(x)=\frac{2}{x^2+3}[/tex]

We differentiate to obtain;

[tex]g'(x)=-\frac{4x}{(x^2+3)^2}[/tex]

At turning points [tex]g'(x)=-\frac{4x}{(x^2+3)^2}=0[/tex]

[tex]\implies x=0[/tex]

[tex]g''(x)=\frac{16x^2}{(x^2+3)^3}- \frac{4}{(x^2+3)^2}[/tex]

We apply the second derivative test to obtain:

[tex]g''(0)=\frac{16(0)^2}{((0)^2+3)^3}- \frac{4}{((0)^2+3)^2}=-\frac{4}{9}[/tex]

Since the second derivative is negative, there is a relative maximum at x=0.

We substitute x=0 into the original function to obtain the relative maximum value.

[tex]g(0)=\frac{2}{(0)^2+3}=\frac{2}{3}[/tex]

To find the relative maximum value of g(x) = 2/(x² + 3), one should evaluate the function at x = 0, giving the relative maximum value as 2/3.

The question is asking to identify the relative maximum value of the function g(x) = 2/(x² + 3).

To find the relative maximum, we need to find the critical points by taking the derivative of g(x) and setting it to zero. However, this function does not have a simple expression where the derivative is zero.

Instead, we note that because the denominator x² + 3 is always positive and has a minimum when x = 0, the function g(x) will have a maximum value when x = 0.

Thus, the relative maximum value of g(x) is obtained by plugging x = 0 into the function: g(0) = 2/(0² + 3) = 2/3.

Rectangle
ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(2,1), B(5,1), C(5,6), and D(2,6).
Given these coordinates, what is the length of side
AB of this rectangle?

Answers

Answer:

3

Step-by-step explanation:

As we move from A(2, 1) to B(5, 1), x increases by 3 but y stays the same.

Thus, the distance from A to B is simply 3.  This is the desired length.

The length of side AB would be 3 units,

As we move from A(2, 1) to B(5, 1), x increases by 3 but y stays the same.

Thus, the distance from A to B is simply 3.  This is the desired length.

I recommend using Desmos to quickly graph things (it's much faster than doing it yourself, I use it often. You can graph points and everything).

The picture ends up looking like the attachment I have below.

This is now a simple subtraction.

A is at 2 on the x-axis and B is at 5.

5-2=3

3 units.

What are coordinate planes?

A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).

Learn more about the coordinate plane at

https://brainly.com/question/2689696

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Determine if each set of ordered pairs represents a function.

Answers

Answer: Choices 1, 3, and 5 are functions

Step-by-step explanation:

To be a function, the x value can only be used once. In choices 2 and 4, the x value is repeated; therefore they are not functions.

Answer:

Step-by-step explanation:

Describe the error in the work below.

Solve –6.1 > x + 11.3

–6.1 – 11.3 > x + 11.3 – 11.3

–17.4 > x

Answers

x should be the subject

Answer:

x should be the subject

Step-by-step explanation:

7 is what percent of 56?

Answers

Answer:

12.5

Step-by-step explanation:

7:56*100 =

(7*100):56 =

700:56 = 12.5

A rectangular prism with a volume of 6 cubic units is filled with cubes with side lengths of 1/2. How many 1/2 unit cubes does it take to fill the prism


Answers

Answer:

48 cubes

Step-by-step explanation:

[tex]V_p=6\\\\\text{Calculate the volume of a cube:}\\\\V_{c}=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}\\\\\text{Calculate how many times the volume of the prism is greater}\\\text{than the volume of the cube:}\\\\\dfrac{V_p}{V_c}=\dfrac{6}{\frac{1}{8}}=6\cdot8=48[/tex]

Find the number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1.

Answers

Answer:

8

Step-by-step explanation:

Answer:

The number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1 are:

                               36

Step-by-step explanation:

We are asked to find the number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1.

We know that a number is even if the last digit of the number is divisible by 2 i.e. even.

Hence, the only digits among the given digits which is even is: 8

Now, at the first place any of the 6 digits could come up.

( Since, the digits could be repeated)

Also, at the second palace any of the 6 digits could come up.

Hence, the total number of such numbers possible are:

                 6×6×1=36

given vector u = (6,-4) and the graph of vector v, find v - 2u and express the result of terms in i and j

Answers

Answer:

0i + 10j, or just 10j

Step-by-step explanation:

Vector u = <6, -4> and vector v = <12, 2>.

We are to find v - 2u, which is:

<12, 2> - 2<6, -4>.  We combine x components and y components to obtain:

<12-12, 2+8>, or <0, 10>.

In terms of i and j, that'd be 0i + 10j, or just 10j.

Answer:

v-2u=10j

Step-by-step explanation:

The component of vector v, are

u=<6,-4>

From the graph; vector u, has components.

v=<12,2>

We perform the subtraction;

v-2u=<12,2>-2<6,-4>

We multiply out the scalar to get:

v-2u=<12,2>-<12,-8>

This implies that;

v-2u=<12-12,2--8>

v-2u=<0,10>

v-2u=0i+10j

v-2u=10j

What is 2 1/6 ft= to inches as a mixed number?

Answers

Answer: 26

Step-by-step explanation:

because...

Feet result: 0.18055555556 ft.

Calculation: 2.1666666666666665" / 12

= 0.18055555556ft

But at the end your answer is going to 26.

So 2.1666666666666665 = 26

* Hopefully this helps:)

* Mark me the brainliest:)!!

Answer:

Step-by-step explanation:

2  1/6 ft = 24 inches plus (1/6)(12 in), or 24 inches plus 2 inches, or 26 inches.

2  1/6 is ALREADY a mixed number, in feet.

ANSWER ASAP! 25 POINTS! WILL GIVE BRAINLIEST!
Rewrite the expression in the form k * x^n (k times x to the n power)


(4x)^2

Answers

Answer:

[tex]16(x^{2})[/tex]

Step-by-step explanation:

we know that

[tex](4x)^{2} =(4^{2})(x^{2})=16(x^{2})[/tex]

therefore

The expression in the form [tex]k(x^{n})[/tex] is equal to

[tex]k(x^{n})=16(x^{2})[/tex]

where

k=16

n=2

The given line passes through the points (0, -3) and (2, 3).
on
What is the equation, in point-slope form, of the line that is
parallel to the given line and passes through the point
(-1,-1)?
y+1= (x + 1)
(23)
-
N
54-3-2-1
2
3 4
5
(0, -3)
Mark this and return
Save and Frit

Answers

Answer:

[tex]y+1=3(x+1)[/tex]

Step-by-step explanation:

step 1

Find the slope of the given line

[tex]m=(3+3)/(2-0)[/tex]

[tex]m=3[/tex]

step 2

Find the slope of the line that is  parallel to the given line

we know that

If two lines are parallel, then their slopes are the same

therefore

the slope is equal to [tex]m=3[/tex]

step 3

Find the equation in point slope form

we have

[tex]m=3[/tex]

[tex]point (-1,-1)[/tex]

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

substitute

[tex]y+1=3(x+1)[/tex] ----> equation of the line into point slope form

Help!! ASAP!!!!!! plz answer asap!!!!

Answers

Answer:

50.265

Step-by-step explanation:

Find the value of d. 2d -5=17

Answers

Answer: [tex]d=11[/tex]

Step-by-step explanation:

To find the value of "d" you need to solve for "d" from the equation given

[tex]2d -5=17[/tex]

First, you have to apply the Addition property of equality and add 5 to both sides of the equation. Then:

[tex]2d -5+(5)=17+(5)\\2d=22[/tex]

And finally, you have to apply the Division property of equality and divide both sides of the equation by 2.

Therefore, you get that the value of "d" is:

[tex]\frac{2d}{2}=\frac{22}{2}\\\\d=11[/tex]

Please give Brainliest!

Answer: The value of d is 11

Step-by-step explanation:

To find the value of "d" you need to subtract five from 2d or 2•11 which would give you 17.

2d -5=17

First you would add five to each side.

2d -5 + 5=17+5

This would show you that whatever you multipy 2 by would have to equal 22.

2d=22

The only thing times 2 that equals 22 is 11, so that would have to be your answer.

Hope this helps :)

Have a blessed evening!

Which statement is true about figure DEF?​

Answers

Side DF is congruent (the = and ~ symbol) to side DE

Answer:

The correct option is A) [tex]\overline{DF}\cong \overline{DE}[/tex]

Step-by-step explanation:

Consider the provided figure.

The coordinates of E is (-2,3)

The coordinates of D is (-5,1)

The coordinates of F is (-3,-2)

Now use the distance formula to find the length of line segment:

[tex]\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

The distance between (-2,3) and (-5,1) is:

[tex]\overline{DE}=\sqrt{\left(-5-\left(-2\right)\right)^2+\left(1-3\right)^2}=\sqrt{13}[/tex]

The distance between (-5,1) and (-3,-2) is:

[tex]\overline{DF}=\sqrt{\left(-3-\left(-5\right)\right)^2+\left(-2-1\right)^2}=\sqrt{13}[/tex]

The distance between (-3,-2) and (-2,3) is:

[tex]\overline{EF}=\sqrt{\left(-2-\left(-3\right)\right)^2+\left(3-\left(-2\right)\right)^2}=\sqrt{26}[/tex]

Hence the length of line segment DE and DF is same.

Thus the correct option is A) [tex]\overline{DF}\cong \overline{DE}[/tex]

HELP ASAP
The first triangle is dilated to form the second triangle . 4.4 arrow point to 4.4 is bigger to 1.1 small select true or false for each statement. The scale factor 0.25 the scale factor is 4

Answers

Answer:

You have to scale the bigger triangle to a small one with ratio of 1.1 to 4.4,  [tex]\frac{1.1}{4.4\\}[/tex]

the ratio is 1/4

the scale factor is 0.25 , so the statement is true

Which of the following increases at the fastest rate for larger values of x?

1) f(x)=5^x + 2
2) f(x)=5x + 2
3) f(x)=5x^3 + 2
4) f(x)=5x^2 + 2

Answers

The fastest rate for larger values of x will be observed in the function  f(x)=5^x + 2.

What is an exponential function?

An exponential function is one in which a term has been raised to a particular power as we can see in the options given.

The fastest rate for larger values of x will be observed in the function  f(x)=5^x + 2.

Learn more about exponential function:https://brainly.com/question/11487261

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The graph below shows the transformation from triangle 1 to triangle 2.
-
Which sequence of steps would transform triangle 1 to triangle 2?
reflect across the y-axis; rotate 180° counterclockwise about the origin
reflect across the x-axis; rotate 270° counterclockwise about the origin
reflect across the y-axis; rotate 90° counterclockwise about the origin
rotate 90° counterclockwise about the origin; rotate 270° counterclockwise about the origin

Answers

Answer:

reflect across the y-axis; rotate 180° counterclockwise about the origin - first choice

Answer:

Option A.

Step-by-step explanation:

The graph below shows the transformation from triangle 1 to triangle 2 as below.

1). To understand the transformation we will take a point A. Present coordinates of point A are (1, -1).

When point A is reflected across y - axis, coordinates of A' become (1, 1).

2). Now we see that triangle 2 is in 3rd quadrant having coordinates A"(-1, -1)

which reveals that A'(1, 1) has been rotated by 180° counterclockwise.

Therefore, option A. is the correct choice.

Choose the slope _intercept form of 3x+2y=5

Answers

Answer:

3x+2y=5

2y=5-3x

y=5/2-3/2x

Or you can write as:

y=2.5-1.5x

Answer: y=3/5x+5/2

Step-by-step explanation:

I also need help with this one, simplifying this radical expression. This ones weird.

Answers

Answer:

1

Step-by-step explanation:

Factorise numerators/ denominators where possible

3x² - 4x + 1 = (x - 1)(3x - 1)

x² - 1 ← is a difference of squares and factors as

x² - 1 = (x - 1)(x + 1)

Expressing the product in factored form

[tex]\frac{(x-1)(3x-1)}{(x-1)(x+1)}[/tex] × [tex]\frac{x+1}{3x-1}[/tex]

Cancel common factors on numerator/denominator, that is

Cancel (x - 1) , (x + 1) and (3x - 1), leaving the simplified form 1

Answer: 1

Step-by-step explanation:

The angles in a triangle are in the ratio 1:2:3. Show that the triangle is a right - angled triangle.

Answers

Answer:

Angles in a triangles add up to 180°

Respectively 1 : 2 : 3 is going to be 1 x , 2 x and 3 x so,

1 x + 2 x + 3 x = 180°

⇒ Simplify

6 x = 180°

⇒ Divide by 6 on both sides to isolate x

x = 30°

Since the ratio was 1 x : 2 x : 3 x and x is 30°,

30 : 60 : 90

And since there is a 90° angle, it is a right - angled triangle

What missing angle of the figure

Answers

Answer:

138

Step-by-step explanation:

152+125=277

277-135=142

around 138

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