factor the expression using GCF 25+30

Answer:

E

Step-by-step explanation:

The expression given is:  sec β - cos β ( i will write "beta" instead of the symbol β)

We know that [tex]sec(x)=\frac{1}{cos(x)}[/tex]

Substituting this into the the expression and doing some algebra manipulation, we have:

[tex]sec(beta)-cos(beta)\\=\frac{1}{cos(beta)}-cos(beta)\\=\frac{1-cos^{2}(beta)}{cos(beta)}[/tex]

Using the identity  [tex]cos^{2}(x)+sin^{2}(x)=1\\[/tex] (also [tex]sin^{2}(x)=1-cos^{2}(x)[/tex]), we can now write:

[tex]\frac{1-cos^{2}(beta)}{cos(beta)}\\=\frac{sin^2(beta)}{cos(beta)}\\=\frac{sin(beta)*sin(beta)}{cos(beta)}\\=\frac{sin(beta)}{cos(beta)}*sin(beta)[/tex]

We know [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex], substituting this, we have:

[tex]\frac{sin(beta)}{cos(beta)}*sin(beta)\\=tan(beta)*sin(beta)[/tex]

Answer choice E is the right answer.

The expression sec β - cos β in terms of sine and cosine simplifies to sin2 β. This is achieved by knowing that secant is the reciprocal of cosine and using the Pythagorean identity in trigonometry.

To write the expression in terms of sine and cosine, we start by remembering that secant is the reciprocal of cosine, so sec β = 1/cos β. So, the expression sec β - cos β is equivalent to 1/cos β - cos β.

However, to remove the quotient from the expression, we multiply through by cos β to get 1 - cos2 β. So the expression sec β - cos β simplifies to 1 - cos2 β.

But remember, based on the Pythagorean identity in trigonometry, 1 - cos2 β is also equivalent to sin2 β. So that's our final simplified expression in terms of sine and cosine.

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Answer:

(A) m=0   y intercept =-4

(B)  m=1/3     y intercept = 5

(C) M=5          y intercept = -11

Step-by-step explanation:

Answerthe answer is b

Step-by-step explanation:

Answer:

1/4 (n-64)

Step-by-step explanation:

1/4  n-16

We need to factor out 1/4 from each term which means divide each term by 1/4

1/4 ( 1/4 n / (1/4) - 16 / (1/4))

Remember copy dot flip when dividing fractions)

1/4 ( n - 16 * 4/1)

1/4 (n-64)

Problem 6)

Scale factor is 1:6, so you are correct

Ratio of perimeters is also 1:6 because the perimeters are just the sum of the linear parts. The larger figure has a perimeter that is 6 times longer than the smaller figure.

The ratio of the areas is 1:36, you simply square both parts of the scale factor ratio. Imagine you had 2 squares. One is 1x1 and the other is 6x6. The first square has an area of 1 square unit. The second square has an area of 36 square units. We see that the larger square is 6 times larger in terms of linear side length, and 36 times larger in area compared to the smaller square.

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Problem 7)

You have the correct scale factor when you write 3:5

The ratio of perimeters is also the same at 3:5

The ratio of areas (small to big) is 9:25 after you square both parts of the scale factor.

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Problem 8)

The scale factor is 3:1 after you reduce the ratio 6:2

The ratio of perimeters is also 3:1

The ratio of areas is 9:1

Answer:

30

Step-by-step explanation:

its 64 mannnnnnn :p sdfghjkljhgfdsdfgh

Answer:

x=3/2,  x=-4

Step-by-step explanation:

2x^2 + 5x - 12

First lets see if we can factor this

(2x    ) ( x      )

-12 = -1*12     1*-12

    -  2*6        2 * -12

    -  3*4       3 * -4

2 * one of these pairs - the other pair = +5  

2*4 -3 = 5

Put the -3 in the first spot and the 4 in the second spot

(2x-3)  ( x+4)

Using the zero product property

2x-3 =0     x+4=0

2x=3             x=-4

x = 3/2

Answer:

6 roots

Step-by-step explanation:

f(x)=3x^6+2x^5+x4-2x^3

The number of roots is determined by the degree of the polynomial.  They may be real or complex.

Since this is a 6th degree polynomial, it will have 6 roots

f(x)=3x^6+2x^5+x4-2x^3

Answer:

6 is the total number of roots

This is what i did to get the answer.

225/ 4.5 = 50 seconds to finish the slushy.

Answer:

(a) 225 mm

(b)50 seconds

Step-by-step explanation:

Let the equation that represents this situation is y = mx+ b

Here, y represents the amount left in  milliliters and x represents the time in seconds.

It has been given that she drank the slushy at a rate of 4.5 milliliters per second.

So, m = -4.5        (negative because the amount decreases)

And after 17 seconds, 148.5 milliliters of slushy remained

So, when x = 17, y = 148.5

Substituting these values in the above model y = mx +b

148.5 = -4.5(17) + b

148.5 = -76.5 +b

b = 225

Therefore, the model is y = -4.5x + 225

(a)

When x = 0, we have to find y

y = -4.5 (0) + 225

y =225

Thus, 225 mm of slushy was originally in the cup.

(b)

Now, we have to find x for y =0

0= -4.5x + 225

4.5 x = 225

x = 50

So, Mariana took 50 seconds to drink all the slushy.

Answer:

yes, the answer is B.

I took the practice so it is correct.

Answer: The minimum is 16, probably arranged in 4 rows of 4 buttons.

Step-by-step explanation: just grab a calculator lol

Answer: tens

Step-by-step explanation:

Answer:

addition property of equality.

Step-by-step explanation:

4(3 x^2 + 2) - 9 = 8 x^2 + 7

We can add 9 to each side, by using the addition property of equality.

a=b  then a+c = b+c

Answer:

(f+g)(x) = -4^x + 5x - 2

Step-by-step explanation:

if f(x) = -4^x - 8 and g(x) = 5x + 6,

(f+g)(x) = f(x) + g(x)

= -4^x - 8 + 5x + 6

= -4^x + 5x - 2

Answer:

-4^x + 5x - 2

Step-by-step explanation:

By the additive property of function, (f+g)(x) = f(x) + g(x)

Given f(x) = -4^x - 8 and g(x) = 5x + 6

(f+g)(x) = f(x) + g(x)

= -4^x - 8 + 5x + 6

= -4^x + 5x - 2

[tex]\left\{\begin{array}{ccc}2x+7y=1\\2x-4y=12&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+7y=1\\-2x+4y=-12\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad11y=-11\qquad\text{divide both sides by 11}\\.\qquad\qquad \boxed{y=-1}\\\\\text{Put the value of y to the first equation:}\\\\2x+7(-1)=1\\2x-7=1\qquad\text{add 7 to both sides}\\2x=8\qquad\text{divide both sides by 2}\\\boxed{x=4}\\\\Answer:\ \boxed{x=4\ and\ y=-1\to(4,\ -1)}[/tex]

The answer is x > -4

To get this answer, you divide both sides by 5. This is to undo the multiplication that happens to the 'x' in '5x'. Note that 5x means 5*x or 5 times x, where x is just a placeholder for some unknown number.

Saying x > -4 means you can pick any number larger than -4.

Answer:21

Step-by-step explanation:

Divide 630 by 30. 30 goes into 630 21 times

Answer:

21 stacks

Step-by-step explanation:

Divide 630/30

21 stacks

Enjoy!

The correct graph representing the total cost for a group to visit the zoo with an admission fee of $15 per person is a linear graph starting at the origin and increasing by $15 on the y-axis for each additional visitor on the x-axis.

The question asks which graph correctly represents the total cost for a group to visit the zoo, with an admission fee of $15 per person. To depict this scenario correctly, we would look for a linear graph that starts at the origin (0, 0), indicating that no cost is incurred without visitors, and then increases positively and linearly as the number of visitors increases. This is because the total cost is directly proportional to the number of visitors, with each additional visitor adding $15 to the total cost.

For example, if 1 person visits, the cost is $15; for 2 people, it's $30, and so on. This relationship would be represented graphically by a straight line, where the slope of the line represents the cost per person ($15). Therefore, the correct graph is one that shows a linear relationship with a slope of $15, where the y-axis represents the total cost and the x-axis represents the number of visitors.

Answer:

A

Step-by-step explanation:

the days are at the bottom 1-7. each day does up by 15 (cost of the tickets)

Answer:

Part a) The number of visits mus be greater than or equal to [tex]4[/tex]

Part b)

with season pass

The total cost is [tex]\$64[/tex]

without season pass

The total cost is [tex]\$58.5[/tex]

Step-by-step explanation:

Let

x---> the number of visit to the water park

y---> the total cost to visit the water park per person

we know that

[tex]y=(14.50+5)x=19.5x[/tex]  

so

Part a) How many visits to the water park would you have to use for the season pass to be a better deal?

For [tex]y=\$64[/tex]

Substitute the value of y in the equation and solve for x

[tex]64=19.5x[/tex]

[tex]x=64/19.5=3.28\ visits[/tex]

therefore

The number of visits mus be greater than or equal to [tex]4[/tex]

Part b) What would the total cost be for 3 visits with and without a season pass?

with season pass

The total cost is [tex]\$64[/tex]

without season pass

The total cost for [tex]x=3\ visits[/tex] is

[tex]y==19.5(3)=\$58.5[/tex]  

Answer: $36.69

Step-by-step explanation:

Okay, so let's first write the equation:

2.59*10 + 3d = 135.97

Now, let's work on isolating d by first simplifying the equation:

25.9 + 3d = 135.97

25.9 + 3d - 25.9 = 135.97 - 25.9

3d = 110.07

3d/3 = 110.07/3

d = 36.69

Okay, now let's check:

2.59*10 + 3*36.69  = 135.97

25.9 + 110.07 = 135.97

135.97 = 135.97

Okay, so so it costs $36.69 per pair of shoe.

Substitute the values of x, y and z to the expression:

[tex]x=5,\ y=3,\ z=14\\\\\dfrac{5x-6y+20z}{4yz}=\dfrac{(5)(5)-(6)(3)+(20)(14)}{(4)(3)(14)}=\dfrac{25-18+280}{(12)(14)}\\\\=\dfrac{7+280}{168}=\dfrac{287}{168}=1\dfrac{119}{168}=1\dfrac{119:7}{168:7}=1\dfrac{17}{24}[/tex]

Answer:

7. n = 5r + 10

9.  [tex] 28.50j + 18s \le 100 [/tex]

Step-by-step explanation:

7.

The table gives you these values

2   20

4    30

6    40

8    50

The left side goes up by 2 each time while the right side goes up by 10 each line.

Using that pattern, fill in a few extra lines. I did it below in bold.

0    10

1     15

2   20

4    30

6    40

8    50

The line 0, 10 shows you that b in y = mx + b is 10. Also from the fist line to the second line, as x goes from 0 to 1, a difference of 1, y goes from 10 to 15, a difference of 5. The slope is difference in y over difference in x, so

slope = m = 5/1 = 5.

The equation is

y = mx + b

y = 5x + 10

The problem uses n instead of y and r instead of x, so you get

n = 5r + 10

9.

One pair of jeans costs $28.50. j is the number of jeans. j number of jeans cost 28.50j.

One shirt costs $18. s is the number of shirts. s number of shirts cost 18s.

The total cost is the cost of the jeans plus the cost of the shirts.

The total cost is 28.50j + 18s.

She can spend up to $100. The total cost of the jeans and shirts can be less than $100 or exactly $100, but it cannot be more than $100.

cost of jeans and shirts must be less than or equal to $100

[tex] 28.50j + 18s \le 100 [/tex]

Answer:

it is a polynomial

3a^2+a^2= 4a^2

4a^2+6

Step-by-step explanation:

3a^2 +a^2 = 4a^2+6

=4a^2+6

The student's question simplifies to 4a^2 + a + 6 after combining like terms.

This problem draws upon the concepts of linear equations and variables in mathematics. When you encounter 3a^2 + a^2 added to a + 6, you want first to combine like terms. In this case, 3a^2 and a^2 are like terms, meaning they can be added together. So, this results in 4a^2 + a + 6.

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PQ because it corresponds by order.

Answer:

A. -4

Step-by-step explanation:

J= Jake's Number

A= Amy's Number

2j = 3j+2

-j = 2

j = -2

check: 2(-2) = 3(-2)+2

-4 = -6+2

-4 = -4 (correct)

Jake's number is -2. Amy's is -4

Answer:

Step-by-step explanation:O would say the first answer choice

Answer:

The first one.

Step-by-step explanation: Well it is simple, the total has to be 36, none of the other ones show 36 as the total.

B. (0, 9)

Reflection across x=a is represented by the transformation ...

... (x, y) ⇒(2a-x, y)

Reflection across y=b is represented by the transformation ...

... (x, y) ⇒ (x, 2b-y)

The double reflection, across x=2, y=1 will result in the transformation ...

... (x, y) ⇒ (2·2-x, y) ⇒ (4-x, 2·1-y) ⇒ (4-x, 2-y)

For (x, y) = X(4, -7), the transformed point is ...

... X''(4-4, 2-(-7)) = X''(0, 9)

The double reflection across x=2 and y=1 transforms the point X(4, -7) to X''(0, 9), illustrating the sequential application of reflection transformations (4-x, 2-y).

The correct answer is option B.

A reflection across the vertical line x=a is represented by the transformation (x, y) ⇒ (2a-x, y). Similarly, a reflection across the horizontal line y=b is represented by the transformation (x, y) ⇒ (x, 2b-y). The double reflection, across x=2 and y=1, can be expressed by applying these transformations sequentially.

Starting with the point (x, y), the first reflection across x=2 yields (2·2-x, y), and then, the reflection across y=1 gives (4-x, 2·1-y). Combining these transformations, the double reflection is represented by the transformation (x, y) ⇒ (4-x, 2-y).

Now, applying this double reflection to the given point X(4, -7), we get X''(4-4, 2-(-7)) = X''(0, 9). Therefore, the transformed point after the double reflection is X''(0, 9) making option B the correct option.

Learn more about Transformations here:

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Answer:

Correct choice is C

Step-by-step explanation:

Let x be unknown number.

Three times a number x is [tex]3\cdot x=3x.[/tex]

Three times a number is no less than negative six means that the number [tex]3x[/tex] can be equal to -6, can be greater than -6, but cannot be less than -6.

Thus,  the inequality that could be used to solve the  problem is

[tex]3x\ge -6.[/tex]

Answer:

3x ≥ -6

Step-by-step explanation:

To graph the equation 2x + 3y + z = 6, which represents a three-dimensional plane, isolate one variable (e.g. z = 6 - 2x - 3y) and choose arbitrary values for the other two variables, then calculate z. The obtained ordered triplets (x, y, z) represent points on the plane and can be plotted to give a visual of the plane.

In order to graph the equation 2x + 3y + z = 6, we first need to understand that this is a linear equation in three variables representing a plane in three-dimensional space. Unfortunately, it's challenging to graph a three-dimensional plane manually without specific technology or software.

However, I can explain how you'd approach plotting this. The general process involves initially isolating one variable then choosing arbitrary values for the other two variables. Let's isolate z, for example:

z = 6 - 2x - 3y.

Now, you can choose values for x and y, and subsequently calculate z. You can form ordered triplets (x, y, z) and these would be points of the plane that satisfies the equation. A sufficient number of these points, plotted and confined, will depict a visual of the plane.

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To graph the equation 2x + 3y + z = 6, find the intercepts by setting two variables to zero and solving for the third. Plot these intercepts (0,2,0), (3,0,0), and (0,0,6) on a 3D coordinate system and draw a plane through these points.

To graph the equation 2x + 3y + z = 6, you need to understand that this is an equation of a plane in three-dimensional space. Unlike graphing a line, where you only need two points, graphing a plane requires you to find at least three non-collinear points (points not on the same line) to form a flat surface.

Here is a step-by-step method to graph this plane:

Set z = 0 and solve for y when x = 0 to find the y-intercept. (2(0) + 3y + 0 = 6 gives y = 2).

Set z = 0 and solve for x when y = 0 to find the x-intercept. (2x + 3(0) + 0 = 6 gives x = 3).

Set x = 0 and solve for z when y = 0 to find the z-intercept. (2(0) + 3(0) + z = 6 gives z = 6).

Plot these intercepts on a three-dimensional coordinate system.

Draw a plane that passes through these three points.

These three intercepts, (0,2,0), (3,0,0), and (0,0,6), are enough to define the plane uniquely. Connect these points to form a triangular shape which implies the plane extending infinitely in all directions within the given slope constraints.

Answer:

Option A, C and D are correct choices.

Step-by-step explanation:

Let x be the number of rides that Tomas has been on so far. Each ride costs 5 tickets. This means that cost of x rides will be 5x.

We are told that Tomas bought 80 tickets for rides at an amusement park.

To find the number of of tickets that Tomas has left we will subtract cost of x rides from total number of tickets that Thomas bought.

We can represent this information in an expression as: [tex]80-5x[/tex]

Now let us see which of our given choices in equivalent to our expression.

A. [tex]80-5x[/tex]

Upon looking at option A we can see that it is same as our expression, therefore, option A is the correct choice.

B. [tex]80+5x[/tex]

We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option B is not a correct choice.

C. [tex]5(16-x)[/tex]

Upon distributing 5 we will get,

[tex]80-5x[/tex]

Now this expression is same same as our expression, therefore, option C is the correct choice.

D. [tex]-5x+80[/tex]

This expression is also same as our expression as we can rearrange the terms in this expression as: [tex]80-5x[/tex], therefore, option D is a correct choice as well.

E. [tex]5(16+x)[/tex]

Upon distributing 5 we will get,

[tex]80+5x[/tex]

We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option E is not a correct choice.

Answer:

A D

Step-by-step explanation:

Answer:

The sum of the interior angles of a triangle is 180 degrees.

d. Scalene

e. Isosceles

f. Isosceles

g. Equilateral

h. Scalene

i. Equilateral

j. Right

l. Acute

m. Obtuse - doesn't add to 180 not a triangle

n. Acute - doesn't add to 180 not a triangle

o. Obtuse

Step-by-step explanation:

The interior angles of a triangle add to 180 degrees. There are two ways we classify triangle by side lengths and angle measures.

Side lengths: Compare the side lengths and see if any are equal to determine the type.

Angle Measures: Compare the angles measures to 90 degrees.

Answer:

Case I

$115

Case II

$125

Step-by-step explanation:

Bugles rent for $10 per month

Drums rent for $5 per month

Case I

7 bugles and 9 drums

7 *  bugle cost per month + 9 *  drum cost per month

7 * 10 + 9* 5

70 + 45

$115

Case II

9 bugles and 7 drums

9 *  bugle cost per month + 7 *  drum cost per month

9 * 10 + 7* 5

90 + 35

$125