Is this statement true or false? If tan 45° = 1, then tan-1 1 = 90°.

Answer

answer C

Step-by-step explanation:

Answer:

11 1/3

Step-by-step explanation:

Answer:

C.Apex(105)

Step-by-step explanation:

Final answer:

Alana's classmates ate 1 31/32 pounds of the mixed nuts.

Explanation:

To determine how much of the mixed nuts Alana's classmates ate, you need to multiply the total amount of nuts by the fraction that was eaten.

Alana bought 2 5/8 pounds of mixed nuts and her classmates ate 3/4 of them. To find out how much was eaten, you multiply 2 5/8 by 3/4.

First, convert 2 5/8 to an improper fraction:

(2 * 8) + 5 = 21/8.

Now, multiply this improper fraction by 3/4:

(21/8) * (3/4) = 63/32 pounds.

This is an improper fraction, which you can convert to a mixed number.

63 divided by 32 is 1 with a remainder of 31, so the mixed number is 1 31/32 pounds.

Therefore, Alana's classmates ate 1 31/32 pounds of the mixed nuts.

The situations that can be modeled with an equation are:

1. The sale price of a television is $125 off of the original price.

Let the original price of TV be=x

Sale price = [tex]x-125[/tex]

Let sale price be S so equation is : S= [tex]x-125[/tex]

3. Marco spent twice as much as Owen.

Let Owen spent = x

Then Macro spent = 2x

Let Macro spends $y , So, equation becomes

y = 2x

5. Ben paid a total of $75 for a shirt and a pair of shoes.

Let 'x' represent the cost of a shirt and 'y' represents the cost of a pair of shoes then equation becomes:

[tex]x+y=75[/tex]

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

[tex]5x^2+14x-3[/tex]

As we know "Split the middle term":

[tex]5x^2+15x-x-3\\\\=5x(x+3)-1(x+3)\\\\=(5x-1)(x+3)[/tex]

Since it is quadratic equation so, it has 2 roots.

So, the roots are (x+3) and (5x-1).

Hence, Option 'B' is correct.

Answer:

(5,-2).

Step-by-step explanation:

First, let's find the original center of the circle, we have

[tex]x^2 - 4x + y^2 + 2y = 4[/tex]

we are going to complete square adding and subtracting 4 for the x terms and 1 for the y terms

[tex]x^2 - 4x+4-4 + y^2 + 2y+1-1 = 4[/tex]

[tex](x-2)^2 - 4 + (y+1)^2 - 1 = 4[/tex]

[tex](x-2)^2+ (y+1)^2 - 5 = 4[/tex]

[tex](x-2)^2+ (y+1)^2 = 4+5[/tex]

[tex](x-2)^2+ (y+1)^2 = 9.[/tex]

The canonical formula of a circumference is [tex](x-h)^2+(y-k)^2=r^2[/tex]

Then, we have a circle with [tex]r^2 =9[/tex] and center (h,k)=(2,-1).

Now, if we translate the circle 3 units to right and 1 unit down, then all the points in the circle will be translated including the center. Especifically, the x values will be added 3 units and the y-vaues will be subtracted 1 unit, then the new center will be

(2+3,-1-1) = (5,-2).

Answer:

7

Step-by-step explanation:

Median is middle, the middle is 7. So the median is 7.

Answer:

5

Step-by-step explanation:

Answer:

Literally just finished the test its 83 1/3

Step-by-step explanation:

The polynomial representing the amount of paper wasted when cutting the largest possible circle out of a square of side length l is (4-π)/4 * l².

The question at hand is concerned with finding the polynomial that represents the amount of paper wasted when cutting out the largest possible circles from square pieces of paper. The side length of each square is given as l. The area of each square is l², while the area of the circle that can be cut from the square is calculated using the formula πr², where r is the radius of the circle. Because the largest circle that fits in the square touches all four sides, the diameter of the circle equals the side length l, making the radius r equal to l/2.

To find the polynomial for the wasted paper, first we calculate the area of the circle: π(l/2)², which simplifies to πl²/4. To find the wasted area, subtract the area of the circle from the area of the square: l² - πl²/4. This difference represents the wasted paper and can be further simplified to a single polynomial: (4/4)l² - (π/4)l², which simplifies to (4-π)/4 * l². This is the polynomial representing the amount of paper wasted for each square piece of paper.

to determine if it is even replace x with -x and see if the answer is identical.

 In this case, this function is even

Answer:

The function [tex]f(x)=x^6-x^4[/tex] is:

Even

Step-by-step explanation:

A function f(x) is even if:

f(-x)= f(x)

A function f(x) is odd if:

f(-x)= -f(x)

Here, we are given a function f(x) as:

[tex]f(x)=x^6-x^4[/tex]

[tex]f(-x)=(-x)^6-(-x)^4\\\\ =x^6-x^4\\\\=f(x)[/tex]

f(-x)=f(x)

Hence, the function [tex]f(x)=x^6-x^4[/tex] is:

Even

ANSWER

[tex] \boxed { \sqrt{} }30 \degree[/tex]

[tex] \boxed { \sqrt{} }210 \degree[/tex]

EXPLANATION

We want to solve

[tex] \cot( \theta) = \sqrt{3} [/tex]

where

[tex]0 \degree \: \leqslant x \leqslant 360 \degree[/tex]

We reciprocate both sides of this trigonometric equation to obtain:

[tex] \tan( \theta) = \frac{1}{ \sqrt{3} } [/tex]

We take arctangent of both sides to get;

[tex] \theta = \tan ^{ - 1} ( \frac{1}{ \sqrt{3} } ) [/tex]

[tex] \theta = 30 \degree[/tex]

This is the principal solution.

The tangent ratio is also positive in the third quadrant.

The solution in the third quadrant is

[tex]180 + \theta = 180 + 30 = 210 \degree[/tex]

Answer: SAS similarity theorem.

Step-by-step explanation:

In the given picture , we  have two triangles △PQR and △PST with common vertex P and common angle ∠P.

Also, the ratio of sides that include the common angle ∠P of ΔPQR and ΔPST is given by :-

[tex]\frac{PS}{PQ}=\frac{45}{20}=\frac{9}{4}\\\\\frac{PT}{PR}=\frac{36}{16}=\frac{9}{4}[/tex]

Therefore, SAS similarity postulate ΔPQR is similar to ΔPST.

SAS similarity postulate says that if an angle of one triangle is equal to the corresponding angle of another triangle and the sides that include this angle are proportional, then the two triangles are similar.

Final Answer:

The estimated total area of the composite figure is approximately 23.415 square units.

Explanation:

To calculate the area of the composite figure made by the vertices (−2, −2), (4, −2), (5, 1), (2, 3), and (−1, 1), we can divide the figure into simpler shapes, such as triangles and rectangles, whose area we know how to calculate. We will consider the vertices in the given order to create a polygon and find its area.

Let’s follow these steps:
1. Draw the figure by plotting the points on the coordinate plane and connecting them in the order given.
2. Divide the figure into simpler shapes (for example, a combination of triangles and rectangles).
3. Calculate the area of each part.
4. Sum the areas to find the total area of the composite figure.

Dividing the figure:
A simple way to divide this figure is into two triangles and one trapezoid.

Let’s name the vertices as follows:
A (−2, −2), B (4, −2), C (5, 1), D (2, 3), E (−1, 1).
- Triangle ABE and triangle BCD can be identified.
- Trapezoid ABED can be identified (alternatively, one could see it as a rectangle plus a triangle).

Calculating the area of each part:
Triangle ABE:
Using the coordinates (−2, −2), (−1, 1), (4, −2), we can calculate the base and height of the triangle. The base (AB) is the distance between points (−2, −2) and (4, −2), which is 6 units. The height (from point E) is the y-coordinate difference of points E and AB, which is 3 units (from y = 1 to y = -2). Thus, the area of triangle ABE is:
Area = 1/2 * base * height = 1/2 * 6 * 3 = 9 square units.

Triangle BCD:
For triangle BCD, we take CD as the base and find the perpendicular height from point B to line CD. However, since we cannot directly measure this height on the coordinate system without further calculations, we could use another method. Since the area calculations can get complicated with this arbitrary triangle, and since the coordinates given suggest that this is actually part of a grid system (not arbitrary points), we can instead calculate the area of trapezoid ABCD by treating AB as one base and CD as the other.

Trapezoid ABCD:
The bases of the trapezoid are AB and CD. Base AB is 6 units long (as before). To calculate the length of CD, we use the distance formula (distance = sqrt((x2 - x1)² + (y2 - y1)²)):
CD = sqrt((5 - 2)² + (1 - 3)²) = sqrt(3² + (-2)²) = sqrt(9 + 4) = sqrt(13) ≈ 3.61 units.

The height of the trapezoid (distance between the bases) is 3 units (from y = 1 to y = -2). Thus, the area of trapezoid ABCD is:
Area = (1/2) * (AB + CD) * height = (1/2) * (6 + sqrt(13)) * 3 ≈ (1/2) * (6 + 3.61) * 3 ≈ (1/2) * 9.61 * 3 ≈ 14.415 square units.

Summing up the areas:
Area of Triangle ABE + Area of Trapezoid ABCD = 9 + 14.415 = 23.415 square units.

Please note that in slight geometric figures, the area calculations might be complicated with non-right triangles or irregular shapes. In this case, a more advanced method such as breaking the figure into more regular pieces or using determinants (the Shoelace formula) for polygons might be required.

So the estimated total area of the composite figure is approximately 23.415 square units.

The answer is C 4xy^3