Ms. Forestal is purchasing greeting cards in preparation for the upcoming winter holidays. At Store A she can get 3 greeting cards for $15.00. At Store B, she can get 6 greeting cards for $24. Which is the better buy?

5 + 2x ≤ 30

2x ≤ 25

x ≤ 12.5

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Answer:

Step-by-step explanation:

56:84:196 would be the answer

Answer:

x=9.84375

Step-by-step explanation:

...

Answer:

16.1=x

Step-by-step explanation:

2.1(0.2x-1.4)=1.3(0.4x-3.5)  Distribute          

0.42x-2.94=0.52x-4.55  Combine like terms

+4.55                     +4.55  

0.42x+1.61=0.52x

-0.42x         -0.42x  

1.61=0.1x

0.1     0.1              

16.1=x

Answer:

"Your grade, g, must be at least  75 to pass this class'' is translated as:

Step-by-step explanation:

Given the grade is denoted by 'g'.

In algebra '≥︎' denotes that something must be 'greater than or equal to'. In other words, it means 'at least'.

As the gade must be at least 75, it means it can be greater than 75, but it can not be less than 75.

Therefore, "Your grade, g, must be at least  75 to pass this class'' is translated as:

Answer:

Step-by-step explanation

The shortest length of the right-angled triangle is 4 cm.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or anyone angles is a right angle.

Given is, the diagram shows a right-angle triangle.

We have area of the right-angle triangle = 18 cm²

We know that area of a right-angle triangle = 1/2(base)(height)

18 =  1/2(x - 1)(x + 4)

36 = (x - 1)(x + 4)

x² + 4x - x - 4 = 36

x² + 3x - 4 = 36

x² + 3x - 4 - 36 = 0

x² + 3x - 40 = 0

x² - 5x + 8x - 40 = 0

x(x - 5) + 8(x - 5) = 0

x + 8)(x - 5) = 0

x = -8 or 5

we can only use positive numbers because length can't be negative,

Thus, x = 5

The shortest side is definitely one of the 2 legs. The hypotenuse of a triangle is the longest side.

Therefore,

height = x - 1 = 5 - 1 = 4 cm

base = x + 4 = 5 + 4 = 9 cm

Hence, the shortest length of the right-angled triangle is 4 cm.

learn more on right-angled triangle here:

brainly.com/question/2292567

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Answer:

Step-by-step explanation:

[tex]\dfrac{x^2-8x+12}{x^2-7x+10}\\\\x^2-7x+10\ne0\ \iff\ x=\frac{7\pm\sqrt{49-40}}{2}\ne0\ \iff\ x\ne5\ \wedge\ x\ne2\\\\\\\dfrac{x^2-8x+12}{x^2-7x+10}=\dfrac{x^2-2x-6x+12}{x^2-2x-5x+10}=\dfrac{x(x-2)-6(x-2)}{x(x-2)-5(x-2)}=\\\\\\ =\dfrac{(x-2)(x-6)}{(x-2)(x-5)}=\dfrac{x-6}{x-5}\\\\\\f(x)=x-6\\\\g(x)=x-5[/tex]

Answer:

sad

Step-by-step explanation:

Answer:

(p + 6)(p + 2)

Step-by-step explanation:

I believe you meant  p^2 + 8p + 12 = 0, in which " ^ " indicates exponentiation.

Note that 12 = 2*6, and that these two factors, 2 and 6, add up to 8.  Thus,

p^2 + 8p + 12 = 0 = (p + 6)(p + 2)

Answer: yes

Step-by-step explanation:

Answer:

The answer is b because h = hours and 45 is the mph

Step-by-step explanation:

Answer:

option 1

Step-by-step explanation:

y = -2  ;   x = -4

Therefore, y = (1/2)x

When x = 8,

[tex]y = \frac{1}{2}*8\\\\\y = 4[/tex]

Answer:

b  is the correct answer

Answer:

Step-by-step explanation:

Number of successful free throws:

3=1/2(x+4)

x+4= 3×2

x+4= 6

x=6-4

x=2

Answer:

You input the equation they give you into the table to get an outcome. The Equation they gave you is x=y. simply, what ever X is, thats what y is. x=y. On the table it says that X is 3. If x is 3 then y is three because they are equal. if X is 7 then Y is 7. its the same throughout the whole table. To write it as an ordered pair you write (X,Y) if x is three y is three so the ordered pair would look like (3,3)

Answer:

$59.40

Step-by-step explanation:

8% is equal to 0.08

since you are adding the tax to the original cost you will multiply 55 by 1.08 to get the cost of the shoes plus the tax.

Answer:

55 times .8 =44$

Step-by-step explanation:

Answer:

68

Step-by-step explanation:

Given is an isosceles triangle, therefore measures angles opposite to equal sides would be equal.

Hence,

56° + 56° + x° = 180°

112° + x° = 180°

x° = 180° - 112°

x° = 68°

x = 68

Answer:

Step-by-step explanation:

The triangle is isosceles as two sides have same length

Angles opposite to same sides have same value, therefore two of them  equal to 56°

Answer:

0.0049

Step-by-step explanation:

Answer: 0.0049

There u go luv, have a nice day :)

Answer:

C

Step-by-step explanation:

You have to add the whole equation not only a part of it.

Answer:

the answer is A

Answer:

it depends how many hours both of them make but here is what you can do:

Valeria needs to do 2 hours more than Daniel. This is because Daniel makes $18 and hour and Valeria makes only 10. If you do 10*2 or 10+10 you get 20 which is greater than 18. I hope this helps and good luck!

Answer

x is 1.62 or -0.62

Step-by-step explanation:

Quadratic Formula:

[tex] \boxed{ \bf{x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}}[/tex]

Given Quadratic Equation:

x² + x - 1 = 0

a = 1 (Quadratic coefficient)

b = 1 (Linear coefficient)

c = -1 (Constant coefficient)

By substituting values in the formula, we get:

[tex] \rm \longrightarrow x = \dfrac{-1 \pm \sqrt{1^2 - 4(1)( - 1)}}{2 \times 1} \\ \\ \rm \longrightarrow x = \dfrac{ - 1 \pm \sqrt{1 + 4} }{2} \\ \\ \rm \longrightarrow x = \dfrac{ - 1 \pm \sqrt{5} }{2} [/tex]

Answer:

x= 1, y= -2, z= 5

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

C

Step-by-step explanation:

Its not A because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its not B because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its C because The left side 5 is less than the right side 6, which means that the given statement is always true.

Its not D because The left side is 5 is not less than the right side 6, which means that the given statement is false.

Answer:

As

[tex]\:\left(\frac{\left(x^2y^3\right)^{-1}}{\left(x^{-2}y^2z\right)^2}\right)^2=x^4y^{-14}z^{-4}[/tex]

Step-by-step explanation:

Given the expression

[tex]\left[\frac{\left(x^2y^3\right)^{-1}}{\left(x^{-2}y^2z\right)^2}\right]^2[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]

[tex]\left(\frac{\left(x^2y^3\right)^{-1}}{\left(x^{-2}y^2z\right)^2}\right)^2=\frac{\left(\left(x^2y^3\right)^{-1}\right)^2}{\left(\left(x^{-2}y^2z\right)^2\right)^2}[/tex]

                      [tex]=\frac{\left(\left(x^2y^3\right)^{-1}\right)^2}{\left(\left(x^{-2}y^2z\right)^2\right)^2}[/tex]

as

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}[/tex]

so the expression becomes

                       [tex]=\frac{\frac{1}{x^4y^6}}{\left(\left(x^{-2}y^2z\right)^2\right)^2}[/tex]       ∵ [tex]\left(x^2y^3\right)^{-1}=\frac{1}{x^2y^3}[/tex]

as

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]

so the expression becomes

                      [tex]=\frac{\frac{1}{x^4y^6}}{\frac{y^8z^4}{x^8}}[/tex]                    ∵ [tex]\left(x^{-2}y^2z\right)^2=\frac{y^4z^2}{x^4}[/tex]

as

[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]

so the expression becomes

                          [tex]=\frac{1\cdot \:x^8}{x^4y^6y^8z^4}[/tex]

                         [tex]=\frac{x^8}{x^4y^6y^8z^4}[/tex]

as

[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]

so the expression becomes

                        [tex]=\frac{x^{8-4}}{y^8y^6z^4}[/tex]

                        [tex]=\frac{x^4}{y^8y^6z^4}[/tex]

                        [tex]=\frac{x^4}{y^{14}z^4}[/tex]

as

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}[/tex]

so the expression becomes

                           [tex]=x^4y^{-14}z^{-4}[/tex]

Therefore,

Answer:

C

Step-by-step explanation:

Distance: 8.6 miles; Bearing: 44.7 degrees East of North.

The distance of the ship which leaves port on a bearing of 20.2 degrees East of North is 8.6 miles and its bearing is 44.7 degrees East of North.

When the three sides of a triangle is known, then to find any angle, the law of cosine is used.

It can be given as,

[tex]c^2=a^2+b^2-2ab\cos C\\a^2=c^2+b^2-2ab\cos A\\b^2=a^2+c^2-2ab\cos B[/tex]

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

A ship leaves port on a bearing of 20.2 degrees East of North and travels 6.5 miles. The ship then turns due East and travels 3.8 miles.

This problem is shown in the image. The distance of ship from initial point is,

[tex]c=\sqrt{6.5^2+3.8^2-{2\times6.5\times3.8\times\cos (110.2)}}\\c\approx8.6\rm\; miles[/tex]

The measure of the angle x is,

[tex]\angle x=\cos^{-1}\dfrac{8.6^2+3.8^2-6.5^2}{2\times8.6\times3.8}\\\angle x=44.7^o[/tex]

Hence, the distance of the ship which leaves port on a bearing of 20.2 degrees East of North is 8.6 miles and its bearing is 44.7 degrees East of North.

Learn more about the law of cosine here;

https://brainly.com/question/4372174

Answer:

The required distance away from the foot of the tree is 238.0 feet.

Step-by-step explanation:

The height of the redwood tree = 340 feet, and the angle of elevation to its top = [tex]55^{o}[/tex].

let the required distance be represented by x, applying the appropriate trigonometry function, we have;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan [tex]55^{o}[/tex] = [tex]\frac{340}{x}[/tex]

⇒ x = [tex]\frac{340}{Tan 55^{o} }[/tex]

      = [tex]\frac{340}{1.4282}[/tex]

      = 238.062

x = 238.0 feet

The required distance away from the foot of the tree is 238.0 feet.

Answer:

Option D StartFraction w Over 6 EndFraction is correct option.

Step-by-step explanation:

We need to find algebraic expression that represents “the class was divided into six equal groups”

Let complete class strength is w

Dividing into six equal groups we get w/6

The algebraic expression that represents “the class was divided into six equal groups” is w/6

So, Option D StartFraction w Over 6 EndFraction is correct option.

Answer:

d

Step-by-step explanation:

i got it right