Find the missing side

Answer:

[tex]f(x) = x^4-5x^2+3[/tex] is symmetric to the y-axis

Step-by-step explanation:

Given

[tex]f(x) = x^4-5x^2+3[/tex]

Required

Determine if it is symmetric

First, we check if the function is even by calculating f(-x)

[tex]f(x) = x^4-5x^2+3[/tex]

[tex]f(-x) = (-x)^4-5*(-x)^2+3[/tex]

[tex]f(-x) = x^4-5*x^2+3[/tex]

We have:

[tex]f(x) = f(-x) = x^4-5*x^2+3[/tex]

This implies that the function is even, and even functions are symmetric to the y-axis.

Hence:

[tex]f(x) = x^4-5x^2+3[/tex] is symmetric to the y-axis

Answer:

y = 3

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

If A and B were parallel, then 2x + 50 and 5x - 80 are same- side interior angles and sum to 180° , then

2x + 50 + 5x - 80 = 180

7x - 30 = 180 ( add 30 to both sides )

7x = 210 ( divide both sides by 7 )

x = 30

Answer:

distance=90km

time=1.5h

speed of the bus=distance /time

speed of the bus=90km/1.5h

speed of the bus=60km/h

therefore if 1.5h=60km/h

then 7.2h=(7.2x60)/1.5 =288km

Answer:

The correct answer is (-6, 10).

Step-by-step explanation:

You can find the equation of the blue line and then find out which point is on the perpendicular line to that blue line but you also can figure this out visually by looking at where the points are.

Feel free to message me if you still have questions :)

Answer:

(–6, 10)

Step-by-step explanation:

Answer:

a) 11,880

b) 7,770

Step-by-step explanation:

The number of teachers that volunteer = 6 teachers

The number of students that volunteer = 12 students

The number of people in the committee = 5 people

a) The exact number of student on the committee = 3 student

Therefore, the number of teachers in the committee of 5 = 5 - 3 = 2

The number of teachers in the committee = 2 teachers

We get;

The number of committees that can be made = ₁₂C₃ × ₆C₂ = 792×15 = 11,880

b) When there is at least one teacher and at least one student on the committee, we have;

₁₂C₄ × ₆C₁ + ₁₂C₃ × ₆C₂ + ₁₂C₂ × ₆C₃ + ₁₂C₁ × ₆C₄ = 7,770

The number of committees having at least one teacher and at least one student = 7,770

Given:

The preimage and image of a triangle in the given figure.

To find:

The dilation scale factor.

Solution:

From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).

The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).

If a figure is dilated by factor K with (0,0) as the center of dilation, then

[tex](x,y)\to (kx,ky)[/tex]

Let the scale factor be K, then the image of point A is:

[tex]A(-2,-2)\to A'(k(-2),k(-2))[/tex]

[tex]A(-2,-2)\to A'(-2k,-2k)[/tex]

From the given figure it is clear that the image of point A is A'(-4,-4).

[tex]A'(-2k,-2k)=A'(-4,-4)[/tex]

On comparing both sides, we get

[tex]-2k=-4[/tex]

[tex]k=\dfrac{-4}{-2}[/tex]

[tex]k=2[/tex]

Therefore, the dilation scale factor is 2.

Answer:

32.8 mi²

Step-by-step explanation:

Hi there!

Area of a triangle when given two sides, a and b, and the angle that conjoins them, C:

[tex]A=\frac{1}{2} ab*sinC[/tex]

Plug in the known information:

a=11, b=6, C=97°

[tex]A=\frac{1}{2} (11)(6)*sin(97)\\A=33sin(97)\\A=32.8[/tex]

Therefore, the area of the triangle is approximately 32.8 mi².

I hope this helps!

Answer:

B

Step-by-step explanation:

The trick here is to find the height. The answer is

height = sin(180 - 97) * 11

The height is found by finding the supplement of 97, taking the sin of that angle and multiplying by 11.

There is a drawing required. You need to extend ZY until a line from x meets ZY (extended) at right angles. When that happens you find the sine of the supplement.

height = sin(83)*11

height = 10.92

Now use the standard area formula.

Area = base (ZY) * height / 2

base = 6

height = 10.92

Area = 6 * 10.92 /2

Area = 32.75

Answer:

126

Step-by-step explanation:

54 + x = 180

x = 180 - 54

x = 126

Answer:

There are 400 possible dinners.

Step-by-step explanation:

There are 8 dishes to choose from column A. For each of these 8 dishes, there are 10 dishes to pair with. For each of these 10 dishes, there are 5 dishes to go with from column C.

Therefore, multiply to get [tex]8\cdot 10\cdot 5=\boxed{400}[/tex] possible dinners.

*Note: Since the order of which you choose is fixed, we do not need to account for rearrangements of the same three dishes.

Answer & Step-by-step explanation:

500 is roughly about 83% of 600 (we know this because 500/600 = 0.833)

If she is following the recipe, then if she is using 83% of the water shown in the recipe, then she will be putting in about 83% of every ingredient.

480 * 0.83 = 398g flour

12 * 0.83 = 9.96g salt

6 * 0.83 = 4.98g yeast

30 * 0.83 = 24.9ml oil

and 500ml water

Answer:

D. Negative slope

Step-by-step explanation:

The slope goes down from left to right, so it is a negative slope

Up from left to right is a positive slope

A vertical line is undefined

A horizontal line is zero slope

Answer:

3x^2 + x^4 - x^3 + 3 - 6x

Step-by-step explanation:

Find Least Common Multiplier of 3x^(2)-3x / 3x^(3)-6x^(2)+3x to 1 / x-1

3x^2 - 3 . x/3 x^3 - 6x^2 + 3x

Apply exponent rule: a^b + c = a^b a^c

x^2 = xx, x^3 x/3 = xx^2, x^2 = xx

= 3xx - 3xxx - 6xx + 3x

Rewrite -6 as 2 . 3

= 3xx - 3xxx + 2 . 3xx + 3x

Factor out common term 3x

= 3x(x - x^2(x/3) -2x + 1)

= 3x(- x^3/3 - x + 1)

Multiply each factor with the highest power:

(- x^3/3 - x + 1) . 3 . (1/x - 1\) . x

Simplify

3x^2 + x^4 - x^3 + 3 - 6x

Answer:

rhombus has all angles=90 degress

Answer:

im not sure but i think it might be 10??

Answer:

Your correct answer is 1514.27

Step-by-step explanation:

Here is my step by step for you!

Answer:

[tex]x\neq 0\\x\neq 2[/tex]

Step-by-step explanation:

simplify the equation: [tex]\frac{6}{x(x-2)}[/tex]

Since the denominator can never equal 0, x can never equal 0 or 2.

Meaning that the domain is any x-value other than 0 or 2.

Answer:

Using a calculator;

A is approximately 51.34°

G is approximately 28.36°

Step-by-step explanation:

Part 1

The given trigonometric ratio is presented as follows;

tan A = 5/4

Therefore, the angle, A = arctan(5/4)

Using a calculator,  the value of A is found as follows;

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Entering 5/4 into the calculator, using the keypad

3 . Selecting the arctan button to give, A ≈ 51.34°

Part 2

The given trigonometric ratio is cos G = 0.88

Therefore, G = arccos(0.88)

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Enter 0.88 into the calculator by typing

3. Select arccos from the function menu, to give

arcos(0.88) = G ≈ 28.36°.

Answer:

63

Step-by-step explanation:

12x6=72

72-9=63

the answer is 63

9514 1404 393

Answer:

  (b) 82.9253

Step-by-step explanation:

The first attachment shows the rectangles. The second shows the sum of their areas.

Answer:

(x-8)²+20  vertex=(8,20)

Step-by-step explanation:

(x-8)² = -20

Graphing Form: y = 1(x-8)²+20    

Draw 2 lines parallel to each other (AB and line B). Draw a point on line B and label it "C"

Given:

Melinda walked to the mall at 4 miles per hour and then rode back home in a bus at 24 miles per hour.

Total traveling time was 14 hours.

To find:

The distance between Melinda's house and mall.

Solution:

Formula used:

[tex]Time=\dfrac{Distance}{Speed}[/tex]

Let x miles be the distance between Melinda's house and mall.

Melinda walked to the mall at 4 miles per hour. So, the time taken by Melinda is [tex]\dfrac{x}{4}[/tex] hours.

Speed of bus is 24 miles per hour. So, the time taken by bus is [tex]\dfrac{x}{24}[/tex] hours.

Total traveling time was 14 hours.

[tex]\dfrac{x}{4}+\dfrac{x}{24}=14[/tex]

[tex]\dfrac{6x+x}{24}=14[/tex]

[tex]7x=14\times 24[/tex]

Divide both sides by 7.

[tex]\dfrac{7x}{7}=\dfrac{14\times 24}{7}[/tex]

[tex]x=2\times 24[/tex]

[tex]x=48[/tex]

Therefore, the mall is 48 miles far from Melinda's house.

Answer:

[tex]\text{(B) }\cos 40^{\circ}=\frac{x}{60}[/tex]

Step-by-step explanation:

In any triangle, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse (longest side) of the triangle. (a/h)

The angle marked 40 degrees has an adjacent side of [tex]x[/tex] and the hypotenuse of the triangle is 60.

Therefore, we have the equation:

[tex]\boxed{\cos 40^{\circ}=\frac{x}{60}}[/tex]

PT is 8 because since P is the incenter it's equidistant from all sides.

Answer:

[tex]\displaystyle m = 2[/tex]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

Point (2, 1)

Point (4, 5)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

32.61° is the answer

Step-by-step explanation:

Tanx=17.6/27.5

First find the gradient of L.

-6÷3=-2

gradients of perpendicular lines multiply together to give -1.

(-2)×1/2=-1

m=1/2 or 0.5

y=0.5x-1.5