The library has allotted $480 for spring landscaping and has decided
to spend the money on flowering bushes. There is room to plant a total
of 36 bushes. Rose bushes cost $25 each and lavender bushes cost $5
each.
a. (2 PTS) Define your variables.
b. (3 PTS) Write an equation to represent the total number of bushes you
can purchase.
c. (3 PTS) Write an equation to represent the total cost of the bushes.
d. (3 PTS) How many of each type of bush should you purchase?

Answer:

Option B.

Step-by-step explanation:

We have the equation:

x^2 + 6*x - 2 = 0

Remember that:

(a*x + b)^2 = (a*x)^2 + 2*a*b*x + b^2

Because the term with x^2 has a coefficient equal to 1, then a = 1.

(x + b)^2 = x^2 + 2*b*x + b^2

The ter with x is: 6*x

then:

2*b*x = 6*X

2*b = 6

b = 6/2 = 3

we have:

(x + 3)^2 = x^2 + 6*x + 9

Now, our equation is:

x^2 + 6*x - 2 = 0

Now we can add the term (11 - 11) = 0

x^2 + 6*x - 2 + (11 - 11) = 0

x^2 + 6*x - 2 + 11 - 11 = 0

x^2 + 6*x + (11 - 2) - 11 = 0

x^2 + 6*x + 9 - 11 = 0

And we know that:

x^2 + 6*x + 9  = (x + 3)^2

Then we can rewrite our equation as:

(x + 3)^2 - 11 = 0

Then the correct option is B.

The equation that matches our result is option B. (x+3)² - 11. Therefore, rewriting x² + 6x - 2 = 0 by completing the square gives us (x+3)² - 11 = 0.

To rewrite the equation x² + 6x - 2 = 0 by completing the square, we need to follow these steps:

Move the constant term (-2) to the other side of the equation:

x² + 6x = 2

Take half of the coefficient of x (which is 6) and square it. Add the result to both sides of the equation:

x² + 6x + (6/2)² = 2 + (6/2)²

x² + 6x + 9 = 2 + 9

x² + 6x + 9 = 11

Now, let's look at the answer choices:

A. (x+3)² = 18

B. (x+3)² - 11

C. (x+3)² - 2

D. (x+3)² - 9

Among the answer choices, the equation that matches our result is option B. (x+3)² - 11. Therefore, rewriting x² + 6x - 2 = 0 by completing the square gives us (x+3)² - 11 = 0.

To know more about equation:

https://brainly.com/question/29657983

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Step-by-step explanation:

We have cartisean points. We are trying to find polar points.

We can find r by applying the pythagorean theorem to the x value and y values.

[tex]r {}^{2} = {x}^{2} + {y}^{2} [/tex]

And to find theta, notice how a right triangle is created if we draw the base(the x value) and the height(y value). We also just found our r( hypotenuse) so ignore that. We know the opposite side and the adjacent side originally. so we can use the tangent function.

[tex] \tan(x) = \frac{y}{x} [/tex]

Remeber since we are trying to find the angle measure, use inverse tan function

[tex] \tan {}^{ - 1} ( \frac{y}{x} ) = [/tex]

Answers For 2,5

[tex] {2}^{2} + {5}^{2} = \sqrt{29} = 5.4[/tex]

So r=sqr root of 29

[tex] \tan {}^{ - 1} ( \frac{5}{2} ) = 68[/tex]

So the answer is (sqr root of 29,68).

For -3,3

[tex] { -3 }^{2} + {3}^{2} = \sqrt{18} = 3 \sqrt{2} [/tex]

[tex] \tan {}^{ - 1} ( \frac{3}{ - 3} ) = - 45[/tex]

Use the identity

[tex] \tan(x) = \tan(x + \pi) [/tex]

So that means

[tex] \tan(x) = 135[/tex]

So our points are

(3 times sqr root of 2, 135)

For 5,-3.5

[tex] {5}^{2} + {3.5}^{2} = \sqrt{37.25} [/tex]

[tex] \tan {}^{ - 1} ( \frac{ - 3.5}{ - 5} ) = 35[/tex]

So our points are (sqr root of 37.25, 35)

For (0,-5.4)

[tex] {0}^{2} + { - 5.4}^{2} = \sqrt{} 29.16 = 5.4[/tex]

So r=5.4

[tex] \tan {}^{ - 1} (0) = undefined[/tex]

So our points are (5.4, undefined)

Answer:

-9989799993

Step-by-step explanation:

Put it in a calculator

Ty for points

Answer:

Step-by-step explanation:

-989,799,993

Answer

[tex]f(t) = 91000 *1.0376^t[/tex]

Explanation

Given

[tex]a = 91000[/tex] -- initial

[tex]r = 3.76\%[/tex]

Required

The exponential equation

The exponential equation is:

[tex]y =ab^t[/tex]

Where

[tex]b=1 +r[/tex]

We used minus, because the rate increases..

So, we have:

[tex]b=1 +3.76\%[/tex]

[tex]b=1 +0.0376[/tex]

[tex]b=1.0376[/tex]

So:

[tex]y =ab^t[/tex]

[tex]y = 91000 *1.0376^t[/tex]

Hence:

[tex]f(t) = 91000 *1.0376^t[/tex]

Answer:

t = 5.79

Step-by-step explanation:

Given the regression line equation :

Cˆ=182+2.2A

Null ; H0:β=0

Alternative ; Ha:β≠0

Comparing with the general for of a linear regression equation :

y = bx + c

b =slope Coefficient ; c = intercept

b = 2.2 (from equation given)

The test statistic :

t = (Slope, b - null, β) / standard error of slope, E

(b - β) / E

(2.2 - 0) / 0.38

t = 2.2 / 0.38

t = 5.7894736

t = 5.79

Answer:

3x²+4

Step-by-step explanation:

To find the derivative of something with respect to x, for each term multiply the power on the x in that term by the coefficient in the same term, and then lower the x's power by one.

For example, if we had to find the derivative of 2x³, we would first multiply the power on the x (3) by the coefficient (2): 6x³. Then lower the x's power by one: 6x². So the derivative of 2x³ is 6x².

To find the derivative an expression with several terms added together, you just do the same for each terms.

d(x³+4x)/dx

= [tex]\frac{d}{dx}[/tex] x³+4x

= 3x²+4

Answer:

x = 26.4°

Step-by-step explanation:

Defence angle = x

Side length Opposite to reference angle = 4

Hypotenuse length = 9

Apply trigonometric ratio, SOH. Thus:

Sin x = Opp/Hyp

Sin x = 4/9

[tex] x = sin^{-1}(\frac{4}{9} [/tex]

x = 26.3878° = 26.4° (nearest tenth)

Answer:

(3 x 4) - 1    and  3 x 4 - 1

Step-by-step explanation:

Hope this helps!

Answer:

409 i would say

Step-by-step explanation:

very sorry is its wrong!!! :(

Answer:

prob d im guessing :^)

Step-by-step explanation:

tell me if i got it right or wrong i will fix if needed

Answer: sum: 51 + -31 = 20

Step-by-step explanation: The sum of two numbers is 20 and their difference is 92. What are the two numbers? Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 20. In other words, x plus y equals 20 and can be written as equation A:

x + y = 20

The difference between x and y is 92. In other words, x minus y equals 92 and can be written as equation B:

x - y = 92

Now solve equation B for x to get the revised equation B:

x - y = 92

x = 92 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 20

92 + y + y = 20

92 + 2y = 20

2y = -72

y = -36

Now we know y is -36. Which means that we can substitute y for -36 in equation A and solve for x:

x + y = 20

x + -36 = 20

X = 56

Summary: The sum of two numbers is 20 and their difference is 92. What are the two numbers? Answer: 56 and -36 as proven here:

Answer:

The percentage in mark up is 503.56%.

Step-by-step explanation:

The percentage in markup is the change(retail - cost) divided by the initial cost, and multiplied by 100%.

In this question:

Cost: 1.49

Change: 8.99 - 1.49 = 7.5

Percentage change:

(7.5*100%)/1.49 = 503.56%.

The percentage in mark up is 503.56%.

Answer:

The value of log 8 is 0.9030

Step-by-step explanation:

To find:

Value of log 8

Solution:

Let we take,

x=log8

x=log (2)^3

x=3log2

x=3*0.3010

x=0.9030

Hence, the value of log 8 is 0.90.

Answer:

d.) 1/12

Step-by-step explanation:

As it is equal to 0.083 and it is nearest to zero

Answer:

d. 1/12

Step-by-step explanation:

Since all of the fractions are positive and you want the one closest to 0, you need to find the smallest fraction. With fractions, especially when all of the numerators are 1, the larger the denominator becomes, the smaller the fraction. 12 is the largest denominator; therefore, 1/12 must be the smallest fraction. Which makes 1/12 the closest to 0.

Answer:

Step-by-step explanation:

6x4=24+1=25 75/25=3 .

oh and btw go back to high school

12 pieces ! ( > < )

for future reference, this will be a lot easier to do than using points !! so simple :))

use your calculator to divide the large number by the small number !! that should give your answer

and remember if a fraction is out of four think of it like quarters or 25 cents :3

so 75 divided by 6.25 is 12 !!

good job !!! ♡♡

Answer:

5

Step-by-step explanation:

when finding a y intercept thevalue of x must be0,,,,,,when xis changed to 0the answer left is 5

Answer:

14.4

Step-by-step explanation:

6 x (t1/3 + t1/2) = 12(6)

2t + 3t = 72

5t = 72 /5

t= 14.4

Answer:

-10m-9

Step-by-step explanation:

-3(4m+3)+2m

combine like terms

-12m-9+2m

-10m-9

Answer:

No solution

Step-by-step explanation:

4x+15 doesn't equal anything so it's impossible to solve.

Unless you forgot to add what it equals I can't solve it for you :(

Given:

[tex]f(x)[/tex] is continuous, [tex]f(3)=1,f(1)=6,f(6)=-2,f(-2)=3[/tex].

To find:

The value of [tex]\lim_{x\to 6^+}f(x)[/tex] and [tex]\lim_{x\to -2^-}f(x)[/tex].

Solution:

If a function f(x) is continuous at [tex]x=c[/tex], then

[tex]\lim_{x\to c^-}f(x)=f(c)=\lim_{x\to c^+}f(x)[/tex]

It is given that the function [tex]f(x)[/tex] is continuous. It means it is continuous for each value and the left-hand and right-hand limits are equal to the value of the function.

The function is continuous for 6. So,

[tex]\lim_{x\to 6^-}f(x)=f(6)=\lim_{x\to 6^+}f(x)[/tex]

[tex]\lim_{x\to 6^+}f(x)=f(6)[/tex]

[tex]\lim_{x\to 6^+}f(x)=-2[/tex]

The function is continuous for -2. So,

[tex]\lim_{x\to -2^-}f(x)=f(-2)=\lim_{x\to -2^+}f(x)[/tex]

[tex]\lim_{x\to -2^-}f(x)=f(-2)[/tex]

[tex]\lim_{x\to -2^-}f(x)=3[/tex]

Therefore, [tex]\lim_{x\to 6^+}f(x)=-2[/tex] and [tex]\lim_{x\to -2^-}f(x)=3[/tex].

Step-by-step explanation:

Cardboard needed to make tube =

Circumference of Circle base (remember the base is hollow therefore there is no area needed.) x Length of Tube

given r = 2.25cm

L = 24cm

Cardboard needed =

[tex]2\pi \: rl = \\ 2\pi(2.25)(24) \\ = 2\pi(54) \\ = 108\pi {cm}^{2} \\ = 339 {cm}^{2} [/tex]

The cardboard is needed to make the inner tube for a roll of paper if the tube has a radius of 2.25 cm and is 24 cm long will be 339 cm². Option B is correct.

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

The cardboard is needed to make the inner tube for a roll of paper is found as;

Surface area of cardboard;

A=2πRL

A=2×3.14×(2.25)(24)

A=339 cm².

Hence,the cardboard is needed to make the inner tube for a roll of paper will be, 339 cm².

To learn more about the surface area, refer to the link;

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Answer:

the length of side X is 37

Answer:

75.5 cm

Step-by-step explanation:

S = (a+b)*h/2

h = 2 * S / (a+b) = 2 * 7701 / 204 = 75.5 cm

9514 1404 393

Answer:

  use the rules of exponents

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

  (a^b)^c = a^(bc)

  (ab)^c = (a^c)(b^c)

__

Applying these to the left-side expression, we can simplify it so it looks like the right side expression.

  [tex]\dfrac{(12x^5)(2x^7)}{(2x^2)^3}=\dfrac{12\cdot2x^{5+7}}{2^3x^{2\cdot3}}=\dfrac{24x^{12}}{8x^6}\\\\=3x^{12-6}=\boxed{3x^6}[/tex]

Answer:

[tex]x^2 + (y-60)^2 = 30,625[/tex]

Step-by-step explanation:

There are 42 carts, so there is 42 spaces in between them; if one of those spaces are 25pi/3 feet long, then 42 of them would be 25*42*pi/3 = 350pi (Perfect! no fractions)

350pi is the circumference. Now if we plug that into the circumference equation we get:

C = 2pi*r

350pi = 2pi*r

Divide both sides by pi to get rid of it

350 = 2r

Divide both sides by 2

r = 175 feet

So the new equation to graph it is:

x^2+y^2 = 175^2 = 30,625

We also know that the center of the Ferris wheel has to be at least 60 feet from the ground. Since the radius is more than that, a good bit of the Ferris wheel has to be underground OR we can make it higher (keyword: at least) if we want it to be above ground. I'll do the equation for underground since it more closely represents the question.

subtracting a number from y, shifts the graph up that much so:

[tex]x^2 + (y-60)^2 = 30,625[/tex]

I can't really draw it electronically but I can graph it:

9514 1404 393

Answer:

  20%

Step-by-step explanation:

The discount was $35 -28 = $7. As a percentage of the original price, that is ...

  $7/$35 × 100% = 20%

Mai's coupon was for a 20% discount.

Answer:

252

Step-by-step explanation:

60+61+11