simplify:
tan² θ cos² - sin² θ

can anyone write the steps? many thanks! ​

Answer: Krysti's mistake was ordering only 12 small T-shirts when she should have ordered more. To figure out how many small T-shirts she should have ordered, we can start by finding out how many classmates wanted small T-shirts:

60% of 25 classmates = 0.60 x 25 = 15 classmates

So, 15 classmates wanted small T-shirts. If Krysti had ordered one small T-shirt for each of these classmates, she would have needed 15 small T-shirts. However, Krysti only ordered 12 small T-shirts, which means she is short by 3 shirts.

To avoid this mistake, Krysti should have double-checked her calculations and made sure that the number of small T-shirts she ordered matched the number of classmates who wanted small T-shirts.

Step-by-step explanation:

I like big black oliy men

The minimum clearance required for safety of fitting 95% of men is approximately 18.7 inches.

What is percentage ?

Percentage is a way of expressing a proportion or a ratio as a fraction of 100. It is often represented by the symbol % and is used to compare values, make comparisons, and analyze data. For example, if there are 25 red marbles and 75 green marbles in a jar, the percentage of red marbles is 25% (25/100), while the percentage of green marbles is 75% (75/100). Percentages are commonly used in many fields, including finance, business, statistics, and science.

To determine the minimum clearance required for safety of fitting 95% of men, we need to find the value of the sitting knee height at the 95th percentile for men.

Using the formula for a normal distribution, we can calculate that the sitting knee height at the 95th percentile for men is approximately 23.2 inches.

Therefore, the minimum clearance required for safety of fitting 95% of men would be the difference between the sitting knee height at the 95th percentile for men (23.2 inches) and the height of the work table.

Therefore, the minimum clearance required for safety of fitting 95% of men is approximately 18.7 inches.

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Answer:333

Step-by-step explanation:53533535

Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money accumulated, P is the principal (initial) amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this problem, we want to find the principal amount P that will accumulate to $12,000 in 3 years at an annual interest rate of 6% compounded monthly. First, we need to convert the annual interest rate to a monthly rate:

r = 0.06/12 = 0.005

Next, we can substitute the given values into the formula and solve for P:

12,000 = P(1 + 0.005/12)^(12*3)

12,000 = P(1.005)^36

P = 12,000/(1.005)^36

P ≈ $9,883.86

Therefore, the amount of money that should be deposited today is approximately $9,883.86.

Step-by-step explanation:

Answer:

Step-by-step explanation:

triangle-

b+h/2=a

5x6/2=30

rectangle-

2.5x12=30

area of drawing-

30+30=60

answer:60cm^2

A solution to the given system of linear equations is (2, 6).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x - y = 0     ......equation 1.

5x + 2y = 7  ......equation 2.

In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (1, 1).

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Answer:

x + 118 = 180

Step-by-step explanation:

Because the angle x added with 118 must be 180 degree for this to be true. So, the answer is x + 118 = 180

Answer:

2.) x + 118 = 180 degrees

Step-by-step explanation:

x + 118 = 180 can be solved as taking 118 on both sides, 118 and 180.

118=0 and 180-118= 62. The other equations in the 4 options do not work.

I hope this helps : )

In answering the question above, the solution is If a/b = 1/4 and c/d = 1/3, fraction then ad + bc = (1/4)(bd/4) + (1/3)(bd/3) = bd/16 + bd/9, which doesn't work.

A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are stated in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You may assess it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a whole number or object.

Let's start by decomposing { into two fractions:

[tex]{ = a/b + c/d\\\\{ = (ad + bc)/bd[/tex]

If [tex]a/b = 1/2 and c/d = 1/3, then ad + bc = (1/2)(bd/2) + (1/3)(bd/3) = bd/3 + bd/6 = 3bd/6 + bd/6 = 4bd/6 = 2/3,[/tex] which works.

If [tex]a/b = 1/2 and c/d = 1/4, then ad + bc = (1/2)(bd/2) + (1/4)(bd/4) = bd/4 + bd/8 = 2bd/8 + bd/8 = 3bd/8,[/tex] which doesn't work.

If [tex]a/b = 1/2 and c/d = 1/5, then ad + bc = (1/2)(bd/2) + (1/5)(bd/5) = bd/4 + bd/25 = 25bd/100 + 4bd/100 = 29bd/100[/tex], which doesn't work.

If[tex]a/b = 1/3 and c/d = 1/4, then ad + bc = (1/3)(bd/3) + (1/4)(bd/4) = bd/9 + bd/16[/tex], which doesn't work.

If[tex]a/b = 1/3 and c/d = 1/5, then ad + bc = (1/3)(bd/3) + (1/5)(bd/5) = bd/9 + bd/25,[/tex] which doesn't work.

If a/b = 1/4 and c/d = 1/3, then ad + bc = (1/4)(bd/4) + (1/3)(bd/3) = bd/16 + bd/9, which doesn't work.

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Answer:

Step-by-step explanation:

Mark decompose 5/6 into three fractions using fractions : 1/3, 5/18, 2/9

What is fraction?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given, fraction

5/6

Multiplying 3 with both numerator and denominator

15/18

= (6 + 5 + 4)/18

= 6/18 + 5/18 + 4/18

= 1/3 + 5/18 + 2/9

Hence, 1/3, 5/18, 2/9 are fractions Mark used to decompose 5/6.

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the product will be 35/3.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

product of 5 x 2 1/3

=5*7/3

=35/3

Hence the product will be 35/3.

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Answer:

The two ride-sharing companies will have the same price after 40 miles have been driven. At that point, both companies will have charged $10 in pickup fees and $10 in total for miles driven, meaning the cost of taking either service will be the same

Step-by-step explanation:

Therefore, the scale factor used in the drawing is 4000/3.

In mathematics, a factor refers to a number or algebraic expression that divides another number or expression without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these numbers can be multiplied by another whole number to produce 12 (1 × 12, 2 × 6, 3 × 4). Factors play an important role in many areas of mathematics, including algebra, number theory, and geometry, and are used to simplify expressions, solve equations, and factorize polynomials.

Given by the question.

The scale factor is the ratio of the length of an object on the drawing to the actual length of the object.

Since 6 millimeters on the drawing represents 8 meters in reality, the scale factor can be expressed as:

Scale factor = Actual length / Length on drawing

Scale factor = 8 meters / (6 millimeters)

To simplify this fraction, we need to convert meters to millimeters by multiplying by 1000:

Scale factor = (8 meters * 1000) / 6 millimeters

Scale factor = 8000 / 6

The fraction cannot be simplified further, so the scale factor is:

Scale factor = 4000/3

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Answer:

74

Step-by-step explanation:

-6 (-5 - 4) - 4(-3 - 2)

30 + 24 + 12 + 8 = 74

Answer: 10,000 or 10^4

Step-by-step explanation: I will assume in the problem that the logarithm is of base-10. We can therefore rewrite the equation in words as 10^4=x. The general form of a logarithm is log base y of x=z. This can be rewritten as y^z=x. We are doing the same thing here. We know that 10^4 is 10,000 so that is our answer.

Hope this helps!

For practice here are some problems (assume all logarithms are our base 10): log x = 3, log x = 1.

Answer:-3p

Step-by-step explanation: less = subtract -3+p=-3p

The inequality represented by the given number line is expressed as;

-3 ≤ x < 1

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Now, a square bracket at one end of an interval indicates that the interval is closed at that end (i.e., the number adjacent to the opening or closing square bracket is included in the interval).

Thus, the inequality here is expressed as;

-3 ≤ x < 1

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Answer:

look in the comments give me a minute please and thank you

Answer:

x = ± √((y + 2)/4)

Step-by-step explanation:

To find the inverse of a function, we need to solve for x in terms of y.

Steps to find the inverse of y = 4x^2 - 2:

Replace y with x and x with y:

x = 4y^2 - 2

Solve for y:

x + 2 = 4y^2

(x + 2)/4 = y^2

± √((x + 2)/4) = y

Note that we have a ± sign because the square root of a positive number can have two values, one positive and one negative.

Therefore, the inverse of y = 4x^2 - 2 is:

x = ± √((y + 2)/4)

Answer:

y=±([tex]\sqrt{x+2}/2[/tex])

Step-by-step explanation:

The total area is given as 160 sq feet. The total yard that is to be purchased is 18 yards

To get the area of the room we would first have to find the area of the sides.

We can call 1 of the areas S1.

The length l1 = 13

The width w1 = 16

area =

s1 = 13 * 16

We have

s2 with

l2 = 6

w2 = 8

then the area

s2 = 6 * 8

S1 - s2

= 208 - 48 =

160

1 square yard = 9 square foot

17.7778 = 160 square feet

Juan has to purchase approximately 18 yards

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Answer: see bellow

Step-by-step explanation: Z is 80   Y is 90 and    x is 90

This works because each measure is the same arcoss!!!

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Answer:

Step-by-step explanation:

We are interested in finding out the missing angles of the rhombus . Some properties of rhombus that needs to be kept in mind are ,

[tex]\implies z = 80^o \\[/tex]

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

Now since the opposite sides are parallel, the sum of co interior angles would be 180° .

Here x and 80° are co interior angles. So their sum would be 180° . Hence,

[tex]\implies x + 80^o = 180^o \\[/tex]

[tex]\implies x = 180^o - 80^o \\[/tex]

[tex]\implies x = 100^o\\[/tex]

Now since x and y were equal , therefore,

[tex]\implies y = 100^o \\[/tex]

Therefore the value of x is 100° , z is 80° and y is 100° .

Using the roots of the given equation, x²+x-6=0, the value of the expression, 2β²-3α², is -19

From the question, we are to evaluate the given expression.

In order, to evaluate the expression, we will solve the given quadratic equation

To solve x²+x-6=0, we can use factoring method

Solving the equation

x² + x - 6 = 0

(x + 3)(x - 2) = 0

Setting each factor equal to zero, we get:

x + 3 = 0 or x - 2 = 0

Solving for x in each case, we get:

x = -3 or x = 2

So the solutions to the equation are x=-3 and x=2.

Since α<β

Thus,

α = -3 and β = 2

Then,

2β²-3α²

= 2(2)² -3(-3)²

= 2(4) -3(9)

= 8 - 27

= -19

Hence, the value is -9

Here is the correct question:

If α and β are the roots of the equation x²+x-6=0, where α<β, evaluate 2β²-3α²

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The equation would be C = 1.25w, where c is the total cost of w pounds of oranges do not include units or a dollar sign.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.

We are given that oranges are being sold for $ 1.25 per pound.

The equation would be as;

C = 1.25w

where c is the total cost of w pounds of oranges and does not include units or a dollar sign.

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The theorem that justifies the similarity of the two triangles is given as follows:

A: AA.

The Angle-Angle (AA) Congruence Theorem states that if two pairs of corresponding angles are congruent, then the triangles are similar.

In other words, if two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle must also be equal in measure, and the two triangles are therefore congruent.

The two pairs of corresponding angles that are congruent in this problem are given as follows:

Hence the third angle will also have the same measure for both triangles.

Hence the AA theorem can be used and the correct option is given by option A.

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The angles of the triangle will be 5 °, 45 °, and 130 °.

The triangle is a two-dimensional geometric object with three straight sides and three angles. The lengths of the triangle's three sides can differ from the third side (isosceles triangle), be equal (equilateral triangle), or be any combination of the three (scalene triangle).

The sum of the angles in a triangle is always 180 degrees; the opposite angle of the longest side is the largest, and the opposite angle of the shortest side is the smallest.

Now,

Let x be the common factor that multiplies the ratio of 1:9:26. Then, the measures of the angles can be expressed as x, 9x, and 26x.

Since the sum of the angles in a triangle is always 180 degrees, we can set up an equation:

x + 9x + 26x = 180°

Simplifying the equation, we get:

36x = 180

Dividing both sides by 36, we get:

x = 5

Therefore, the measures of the angles are:

x = 5 degrees (the smallest angle)

9x = 45 degrees

26x = 130 degrees (the largest angle)

So the angles of the triangle are 5 degrees, 45 degrees, and 130 degrees.

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Answer:

C = 2 x 4.5 x π

Step-by-step explanation:

The equation to find the circumference of the circle is

C = 2π · r

r = 4.5 in

Looking at the options, the answer is C = 2 x 4.5 x π

Answer:

Below

Step-by-step explanation:

radius = 4.5       diameter = 2 x 4.5  in

the circumference of a circle is given by the formula   p * d

  substitute in the underlined equation for 'diameter')

          circumference = 2 * 4.5 * pi    inches

Answer:

Step-by-step explanation:

Let's use the following variables:

Let F be the number of sections of Finite Math

Let A be the number of sections of Applied Calculus

Let C be the number of sections of Computer Methods

We can create a system of equations based on the given information:

F + A + C = 7 (the college wishes to offer a total of seven sections)

40F + 60A + 290C = 298000 (the college wishes to bring in $298,000 in revenues)

40F + 40A + 10C = 220 (the college wishes to accommodate 220 students)

We can solve this system of equations using any method we prefer. Here's one possible way:

Multiply the third equation by 10 to get:

400F + 400A + 100C = 2200

Subtract the third equation from the second equation to eliminate C:

20A + 280C = 76000

Multiply the first equation by 40 and subtract it from the previous equation to eliminate A:

240C = 76000 - 1600

Solve for C:

C = 290

Substitute C = 290 into the third equation to solve for F:

40F + 40A + 10(290) = 220

40F + 40A = -2680

F + A = -67

Substitute C = 290 and F + A = -67 into the first equation to solve for A:

A = 10

Substitute A = 10 and C = 290 into the first equation to solve for F:

F = -3

We have a problem here: we obtained a negative number of sections for Finite Math, which is impossible. This means that the original system of equations is inconsistent, and there is no solution that satisfies all the requirements.

Therefore, the college cannot offer the desired number of sections while accommodating the desired number of students and revenue. Some adjustments need to be made, such as changing the number of students per section or the tuition fees.

Answer:

4 cookies

Step-by-step explanation:

If you can get 6 cookies for $1.50, then the cost of each cookie is:

$1.50 ÷ 6 = $0.25

This means that for $1.00, you can get:

$1.00 ÷ $0.25 per cookie = 4 cookies

Therefore, you can get 4 cookies for $1.00 at the Math munch cafe.

Correct order of steps for constructing an angle bisector of ∠DEF using only a straightedge and compass is option C.

A angle bisector is a line that bisects an angle into two equal angles. A bisector means dividing a shape or object into two equal parts. When we draw a ray that bisects an angle into two equal parts of equal magnitude, it is called a bisector.

Given,

Compass and straightedge to draw angle bisector of ∠DEF

Steps to draw angle bisector are:

1. Draw a circle with a radius less than DE and center E, and label

the points of intersection G and H.

2. Draw a line from point G to point H.

3. Draw a circle with radius GH and center G and another circle

with radius GH and center H, and then draw an equilateral triangle.

4. Use a straightedge to connect E to the rightmost vertex of the

equilateral triangle.

Hence, option C describes correct order of constructing an angle bisector of ∠DEF using only a straightedge and compass.

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