PLZ HELP ASAP. I NEED HELP PLZ

Answer:

5(a+4)

Step-by-step explanation:

expression is equivalent to 5a+20

To get the equivalent expression we need to factor the given expression

5a+ 20

5a can be written as 5 * a

20 can be written as 5*2*2

WE can see that common factor is 5 for both 5a and 20

So GCF is 5

Now we factor out GCF 5

WE put 5 outside and write all the left of factors inside the parenthesis

5a +20

5 (a+2*2)

5(a+4)

Answer:

5(a+4)

Step-by-step explanation:

Answer:

x = 8 ; y = 8√2

Step-by-step explanation:

In the given figure, two base angles are equal.

In an isosceles triangle, the sides opposite to the equal angles are equal.

∴ x= 8

The triangle is also right angled.

Using Pythagoras theorem,

hypotenuse² = base² + perpendicular²

y² = 8² + x² = 8² + 8² = 128

y = √128 = 8√2

∴ x = 8 ; y = 8√2

Answer:

option 2

Step-by-step explanation:

tan45° = x/8

=>1 = x/8

=>x =8

for y,

cos45° = 8/y

=>1/√2 = 8/y

=>y = 8√2

Answer:

x=2, y=0

Step-by-step explanation:

x − 2y = 2

3x + y = 6

I am going to use elimination to solve this system.

Multiply the second equation by 2

2(3x+ y) =2* 6

6x +2y =12

Now add the first equation.  This will eliminate y

6x +2y =12

x − 2y = 2

-----------------------

7x = 14

Divide by 7

7x/7 =14/7

x=2

We still need to find y

3x + y = 6

3x+y=6

We know x so substitute it in

3(2) +y =6

6+y=6

Subtract 6 from each side

6+y-6 = 6-6

y=0

Answer:

23 inches

Step-by-step explanation:

If we add 5 inches to the shortest side, all sides will be the same length and the perimeter will be 69 inches. The longest sides have length that is 1/3 that, or ...

... (1/3)·(64 +5 in) = 23 in

_____

You can solve for x, but you obviously don't need to.

The perimeter is ...

... (4x -2) + 2(4x -2 +5) = 64

... 12x +4 = 64

... 12x = 60

... x = 5

... 4x -2 +5 = 4·5 +3 = 23 . . . . the length of the longest side in inches

Answer:

y = 5 or y = 0

Step-by-step explanation:

Solve for y over the real numbers:

y^2 - 5 y = 0

Factor y from the left hand side:

y (y - 5) = 0

Split into two equations:

y - 5 = 0 or y = 0

Add 5 to both sides:

Answer: y = 5 or y = 0

Answer:

y^2-5y+1

Step-by-step explanation:

If you have y^2-5y+1 and you need to subtract something from it to get 0, try it in parts. y^2-y^2=0, -5y+5y=0, 1-1=0. Remember that you are subtracting, so the y^2, the 5y, and the -1 you got are not the actual answers. Since the - in the parenthesis changes the signs, you need the remember to change the signs on the numbers you subtracted from the original numbers. So you get y^2. -5y, and 1. Put them together in a equation, and that's your answer.

Answer:

a_0 = -27

a_n = a_(n-1) * (-1/3)

Step-by-step explanation:

First evaluate given formula at n=0 and specify that as starting value

Then find how to get from n-1 to n by comparing two values. In this case the next value is formed by multiplying by -1/3.

Answer:

[tex]a_n = a_{n-1} \cdot (-\frac{1}{3})[/tex]

Step-by-step explanation:

The explicit formula for the geometric sequence is given by:

[tex]a_n = a_1 \cdot r^{n-1}[/tex]

where,

[tex]a_1[/tex] is the first term

r is the common ratio to the following terms.

As per the statement:

Given the explicit formula for geometric sequence:

[tex]a_n = 9 \cdot (\frac{-1}{3})^{n-1}[/tex]

On comparing with [1] we have;

[tex]a_1 = 9[/tex] and [tex]r = -\frac{1}{3}[/tex]

The recursive formula for geometric sequence is given by:

[tex]a_n = a_{n-1} \cdot r[/tex]

Substitute the given values we have;

[tex]a_n = a_{n-1} \cdot (-\frac{1}{3})[/tex]

Therefore, the recursive formula for the geometric sequence is, [tex]a_n = a_{n-1} \cdot (-\frac{1}{3})[/tex]

Answer: one solution

Step-by-step explanation:

The two lines have different slopes, so they can't be the same line (infinitely many solutions) or parallel (no solutions). The lines intersect at

3x+3 = -2x - 4

5x = -7

x = -7/5

3(-7/5) + 3 = -2(-7/5) - 4

-21 + 15 = 14 - 20

-6 = -6

Answer:

The answer is one solution

Step-by-step explanation:

I tried it on khan and it was correct.

Answer:

option 4

Step-by-step explanation:

tan30° = 17/x

=>1/√3 = 17/x

=>x = 17√3

for y,

sin30° = 17/y

=>1/2 = 17/y

=>y = 34

For this case we must find the value of y (Hypotenuse) and the value of x (leg adjacent to the 30 degree angle) of the triangle shown.

By definition:

[tex]Tangent (30) = \frac {17} {x}\\x = \frac {17} {Tangent (30)}\\x = \frac {17} {\frac {\sqrt {3}} {3}}\\x = \frac {17 * 3} {\sqrt {3}}\\x = \frac {51 \sqrt {3}} {3}\\x = 17 \sqrt {3}[/tex]

Now, we look for the value of y:

[tex]Sine (30) = \frac {17} {y}\\y = \frac {17} {sine (30)}\\y = \frac {17} {\frac {1} {2}}\\y = 34[/tex]

Answer:

[tex]x = 17 \sqrt {3}\\y = 34[/tex]

Option D

Answer:

Step-by-step explanation:

Given that total amount available is 90$

x represent the number of pens, and  y represent the number of pencils.

cost of each pen is 0.75 and cost of each pencil is 0.15

Then we have total cost = cost of pens + cost of pencils

= [tex]0.75x+0.15y[/tex]=90

Hence option B is right

For finding out the greatest number of each type of writing tool, we can make the other 0 and find out

Hence maximum x = [tex]\frac{90}{0.75} =120[/tex]

maximum y =[tex]\frac{90}{0.15} \\=600[/tex]

Part A

The equation that describes the number of club pens and pencils that the glee club can buy is 0.75x + 0.15y = 90

Part B

Greatest number of pens that the club can buy = 120

Greatest number of pencils that the club can buy = 600

Cost of each pen = $0.75

Number of pens = x

Cost of each pencil = $0.15

Number of pencils = y

Total cost on pens and pencils = $90

(Cost of each pen) x (Number of pens)  +  (Cost of each pencil)x(Number of pencils)  = Total cost

The equation that describes the number of club pens and pencils is:

0.75x  +  0.15y    =   90

The club buys the greatest number of pens when:

0.75x  = 90

x  =  90/0.75

x  =  120

Greatest number of pens that the club can buy = 120

The club buys the greatest number of pens when:

0.15x  = 90

x  =  90/0.15

x  =  600

Greatest number of pencils that the club can buy = 600

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Answer:

60°

Step-by-step explanation:

The triangle PTX is equilateral, so all of its angles are 60°.

___

Adding up the lengths that make PX, you find they're the same as the lengths that make PT. The sides of ΔPQU are all the same length, so all the triangles are similar and equilateral.

To find the zeros of the polynomial equation, the equation has to be transformed into a quadratic equation. Using the quadratic formula, the roots of the quadratic can be found. Finally, substituting these roots again into the original given equation will give the solutions of the polynomial.

To find the zeros of the equation x^4-6x^2-7x-6=0, we must use factoring or the quadratic formula. The quadratic formula is -b ± √b² - 4ac  2a, where a, b, and c are coefficients of the equation. However, since this equation is a quartic and not a quadratic, we first need to simplify it into a quadratic form, which can be more easily solved.

Let's write the equation as (x^2)^2 - 6*(x^2) - 7x - 6 = 0 and let y = x^2. So the equation becomes y^2 - 6y - 7x - 6 = 0. Solve this equation as a quadratic. After finding the values of y, substitute y = x^2 back into them to solve for x.

Without the original quadratic equation or an exact simplified equation, we are not able to provide concrete solutions. Applying the mentioned steps will help you find the precise solutions.

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The speed of the boat in still water is 12 mph, and the speed of the current is 9 mph.

Let's denote the speed of the boat in still water as ( b ) and the speed of the current as ( c ).

Downstream Trip:

The speed of the boat relative to the water is ( b + c ), and the distance is 210 miles.

Therefore, the time taken downstream is:

[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{210}{b + c} \][/tex]

Given that this trip took 10 hours, we have:

[tex]\[ 10 = \frac{210}{b + c} \][/tex]

Upstream Trip:

The speed of the boat relative to the water is ( b - c ), and the distance is again 210 miles.

Therefore, the time taken upstream is:

[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{210}{b - c} \][/tex]

Given that this trip took 70 hours, we have:

[tex]\[ 70 = \frac{210}{b - c} \][/tex]

Now, we have a system of two equations with two variables:

[tex]\[ 10 = \frac{210}{b + c} \][/tex]

[tex]\[ 70 = \frac{210}{b - c} \][/tex]

Solving this system of equations will give us the values of ( b ) and ( c ), which represent the speed of the boat in still water and the speed of the current, respectively. Let's solve it:

From the first equation:

[tex]\[ b + c = \frac{210}{10} = 21 \][/tex]

From the second equation:

[tex]\[ b - c = \frac{210}{70} = 3 \][/tex]

Adding the two equations:

(b + c) + (b - c) = 21 + 3

2b = 24

b = 12

Substituting ( b = 12 ) into ( b + c = 21 ):

12 + c = 21

c = 21 - 12

c = 9

So, the speed of the boat in still water is 12 mph, and the speed of the current is 9 mph.

Answer:

The correct answer is 1 / 18.

Step-by-step explanation:

We are given the following equation for which we need to solve for the variable n:

[tex]-\frac{7}{3n} =-42[/tex]

So for solving this, we will rearrange the equation in a manner that isolates the variable n, making it the subject of the equation.

[tex]-\frac{7}{3n} =-42[/tex]

[tex]-\frac{7}{42} =3n[/tex]

[tex]\frac{1}{6} =3n[/tex]

[tex]n=\frac{1}{6*3} \\\\n=\frac{1}{18}[/tex]

Therefore, the value of n is equal to 1 / 18.

The real solutions are -5, -4, 4, 5. There are no complex solutions.

The equation ...

... x^4 -41x^2 +400 = 0

can be factored as ...

... (x^2 -16)(x^2 -25) = 0

... (x -4)(x +4)(x -5)(x +5) = 0

So, all roots are real and are ...

... x ∈ {-5, -4, 4, 5}

_____

These are the values of x that make the factors zero.

Final answer:

The real solutions of the polynomial equation x^4 - 41x^2 = -400 are x = 4, -4, 5, and -5. There are no complex solutions since the equation can be factored into real numbers without the need for complex terms.

Explanation:

To find the real and complex solutions of the polynomial equation x^4 - 41x^2 = -400, we can begin by rewriting the equation in a more familiar quadratic form. Adding 400 to both sides gives us:

x^4 - 41x^2 + 400 = 0

We can set y = x^2, which turns our equation into:

y^2 - 41y + 400 = 0

Factoring this quadratic equation, we get:

(y - 16)(y - 25) = 0

So, y = 16 or y = 25. Since y = x^2, we solve for x:

x^2 = 16 → x = ±4

x^2 = 25 → x = ±5

Therefore, the real solutions are x = 4, -4, 5, -5. There are no complex solutions in this case because all values of x are real numbers.

See attached.

When graphing equations presented in standard form, it is often convenient to convert them to intercept for. You do this by dividing by the constant on the right, and expressing the x- and y-coefficients as denominators:

... x/(x-intercept) + y/(y-intercept) = 1

Dividing your equation by 48, you get ...

... x/12 + y/(-8) = 1

That is, the intercepts of the line are (12, 0) and (0, -8). A line through these points will be the graph of the equation.

The given linear equation describes how the amount of hay decreases by 3.5 bales for each day cows are being fed. The initial amount of hay is given as 105 bales.

The equation provided, y=-3.5x + 105, is a linear equation wherein y represents the amount of hay remaining (in bales) and x represents the days of feeding cows. This equation tells us that for every day that passes (an increase in x by 1), the amount of hay decreases by 3.5 bales. When x = 0, which represents the beginning before any hay has been eaten, there are 105 bales of hay available.

To further illustrate, after one day (x = 1), the amount of hay left would be calculated as y=-3.5(1) + 105 = 101.5 bales. After two days (x = 2), y=-3.5(2) + 105 = 98 bales, and so on.

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a) Out of each 7 tickets sold, 6 were regular tickets and 1 was a discount ticket. Thus the number of regular tickets sold was ...

... (6/7)×1456 = 1248 . . . regular tickets

b) At 98 seats per showing, it takes ...

... 1248 seats/(98 seats/showing) = 12.7347 showings

to accommodate all the ticket sold.

That is, the least number of showings there could have been is 13.

Answer:

4.32%

Step-by-step explanation:

Step 1:

To solve this, we must know how to find sales tax first. Let's use this equation:

t = p × r

Let t stand for the total amount of sales tax

Let c stand for the purchase

Let r stand for the sales tax rate.

Step 2:

Now, let us plug in what is given. We know that the purchase made cost $2,500:

t = $2,500 x r

Annddd, we also know that the sales tax is $108:

$108 = $2,500 x r

Therefore, our equation is:

$108 = $2,500 x r

Step 3:

We can simplify this to:

$108 = $2,500r

Step 4:

All we need to do is divide each side by 2500 because the goal is get r all by itself

[tex]\frac{108}{2500} =\frac{2500r}{2500}[/tex]

Step 5:

This gives us:

r = 0.0432

Step 6:

We're not done! Since we are dealing with a percentage, we would multiply .0432 by 100% and that gives us our final answer of

4.32% is our sales tax

Answer:

a = 0, b = 1/2

Step-by-step explanation:

Multiplication and division of complex numbers in polar form is pretty simple.

... a·Cis(α) × b·Cis(β) = ab·Cis(α+β) . . . . . multiply magnitudes; add angles

... a·Cis(α) / (b·Cis(β)) = (a/b)·Cis(α-β) . . . divide magnitudes, subtract angles

In your case, you have ...

... 2·Cis(120°) / (4·Cis(30°)) = (2/4)·Cis(120° -30°) = (1/2)·Cis(90°)

Of course, Cis(90°) = cos(90°) +i·sin(90°) = 0 +i.

... (1/2)·Cis(90°) = 1/2·(0 +i) = 0 + 0.5i

_____

Comment on the use of a calculator

It helps to be aware of how your calculator handles complex numbers. This one can express complex numbers in exponential format, equivalent to a polar form, but requiring specific notation. In this case, the variable D has been assigned the value π/180 so multiplying by it converts degrees to radians. The result of the division is (1/2)i, not 1/(2i).

To determine how many pages have illustrations, 25% of the total 140 pages are calculated, resulting in 35 pages with illustrations.

The student's question pertains to calculating the number of pages with illustrations based on a given percentage of the total pages in a book.

To find the answer, we need to calculate 25% of 140 pages. To do this, we multiply the total number of pages by the percentage of pages that have illustrations, remembering that 25% is the same as 0.25 in decimal form.

Therefore:

Number of pages with illustrations = 140 pages × 0.25 = 35 pages

So, there are 35 pages with illustrations in the book.

"Easiest" depends on several factors, including your understanding of what you're trying to do and of how the mean is calculated.

The most straight-forward way is to

One of my favorite ways is this.

If the distribution is reasonably symmetrical, this second method gives you fewer (and smaller) products to compute, and you can probably do them in your head.

Answer:

2 cis (7/6 pi)

Step-by-step explanation:

r = sqrt( a^2 + b^2)

r = sqrt (-sqrt(3) )^2 + (-1)^2)

   = sqrt(3 +1)

    = sqrt(4)

    = 2

theta  = arctan (b/a)

theta = arctan (-1/-sqrt(3))

theta = 30

but this is in the third quardrant  -a and -b

so add 180

theta = 210 degrees

convert this to radians

210 * pi/180 = 210/180 * pi = 21/18 * pi = 7/6 * pi

r cis (theta)

2 cis (7/6 pi)

6. f(1)+g(2) = 4

8. g(4)-f(0) = 18

10. 2g(-4) = 22

Put the number where the variable is and do the arithmetic.

f(1) = 2·1 -5 = -3

g(2) = |-3·2-1| = |-7| = 7

f(1) + g(2) = -3 + 7 = 4

___

g(4) = |-3·4 -1| = |-13| = 13

f(0) = 2·0 -5 = -5

g(4) - f(0) = 13 -(-5) = 18

___

g(-4) = |-3·(-4)-1| = |11| = 11

2g(-4) = 2·11 = 22

Answer:

option C

Step-by-step explanation:

to find the solution for the equation 4x + 2 = x + 3, graph the equations

y= 4x+2  and y=x+3

Lets make a table for each equation

x          y= 4x+2

-1          4(-1) + 2= -4+2 = -2

0           4(0) + 2= 2

1             4(1) + 2= 6

plot all the points on graph

Lets make table for second equation

x          y= x+3

-1          -1+3 = 2

0           0+3 = 3

1             1+3 = 4

Plot the point on the graph and make a line

option C is correct

Answer:

The required graph of the equation is shown below:

Step-by-step explanation:

Consider the provided equation.

[tex]4x + 2 = x + 3[/tex]

Solve the equation for x.

[tex]4x-x=3-2[/tex]

[tex]3x=1[/tex]

[tex]x=\frac{1}{3}[/tex]

Now substitute x=1/3 in [tex]y=4x + 2[/tex]

[tex]y=\frac{4}{3} + 2=\frac{10}{3}[/tex]

So, the graph will be the lines which intersect at (1/3,10/3)

The correct graph is 3rd one.

Alternate method:

The equation [tex]4x + 2 = x + 3[/tex] can be written as:

[tex]y= 4x + 2 \\y= x + 3[/tex]

Draw the graph for both equation.

For [tex]y= 4x + 2[/tex]

Substitute x=0 in above equation,

[tex]y= 4(0) + 2[/tex]

[tex]y=2[/tex]

Substitute y=0 in above equation,

[tex]0= 4x + 2[/tex]

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

[tex]x=\frac{-1}{2}[/tex]

Now use the coordinate (0,2) and (-1/2,0) to draw the graph of straight line.

For [tex]y=x + 3[/tex]

Substitute x=0 in above equation,

[tex]y=3[/tex]

Substitute y=0 in above equation,

[tex]0=x + 3[/tex]

[tex]x=-3[/tex]

Now use the coordinate (0,3) and (-3,0) to draw the graph of straight line.

Hence, the required graph of the equation is shown below:

Answer:

20.4

Step-by-step explanation:

The rule for secants is pretty simple. The product of the distance to one intersection with the circle and the distance to the other intersection with the circle is a constant. (This same rule applies when the secants intersect outside the circle.)

Here, that means ...

8 × 23 = 9 × x

x = 8·23/9 ≈ 20.4 . . . . . divide by 9

The first graph, X is multiplied by 2 (2x) which compresses the graph horizontally by the factor of 2.

Then 3 is added , which shifts the graph up 3 units.

The answer would be: B. It is compressed horizontally by a factor of 2 and translated up 3.

Answer:

rational: √81, √121

irrational: √89, √131

Step-by-step explanation:

You know your squares, so you know that 81 = 9² is a perfect square. Its square root is 9, a rational number.

And you know that 121 = 11², another perfect square. Its square root is 11, a rational number.

The remaining numbers are not the roots of squares of integers, so will be irrational.

The side length of the original square is calculated by associating the area of the triangle with the square's side length. It is determined to be 1.2 units.

To find the side length of the original square, we need to first understand how the area of a triangle is related to the square. When a square is cut on the diagonal, it forms two triangles. The area of a triangle is given by the formula 1/2 * base * height. In the case of these triangles, the base and height are the same, and equal to the side length of the square, which we'll call 'a'.

The area of one triangle is given as 0.72 square units. So, 0.72 = 1/2 * a * a. Simplifying this, we get a² = 2*0.72 = 1.44. Taking the square root of both sides, we find that a = √1.44 or a = 1.2 units.

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Answer:

C - 1

Step-by-step explanation:

The mean is the sum total of all the given value within the data set divided by the number of values in the data set. By counting, you can find that we have 6 values in our data set.

First thing you need to do is add all the numbers given together in order to get the sum of the values in the given data set. Follow these steps presented below:

-2 + 9 - 10 + 3 + 5 + 1

7 - 10 + 3 + 5 + 1

- 3 + 3 + 5 + 1

0 + 5 + 1

5 + 1

6

Now, in order to find the mean, take the sum (6) and divide by the amount of numbers there are; 6.

6/6 = 1

Therefore, the mean is 1.

Hope this helps!