A recipe to make 5 cupcakes calls for 10 tablespoons
of sugar. Alicia wants to make 10 cupcakes using this
recipe. What equation will she need to use to find out
how many tablespoons of sugar to use?

Counterexamples are simply used to disprove conjectures.

(a) Elephants and Giraffes

This conjecture may or may not be true.

However, it can be disproved by the following counterexample

There are sometimes more elephants in a zoo than giraffes

The word "sometimes" disproves the original conjecture

(b) The oldest leatherback sea turtle

This conjecture is not true.

This is so because the oldest leatherback sea turtle in captivity is actually 400 years old.

So, the conjecture can be disproved by the following counterexample

The oldest leatherback sea turtle in captivity is 400 years old.

(c) American bison

This conjecture may or may not be true.

However, it can be disproved by the following counterexample

American bison are sometimes over 6 feet tall

The word "sometimes" disproves the original conjecture

Read more about conjectures and counterexamples at:

https://brainly.com/question/1619980

Answers:

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Explanation:

For equation A, I'll transform the right hand side into a similar form as the left side. Throughout the steps below, the left hand side stays the same.

[tex]\sqrt{448x^c} = 8x^3\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{(8x^3)^2}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{3*2}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}*7x}\\\\\sqrt{448x^c} = \sqrt{64*7x^{6+1}}\\\\\sqrt{448x^c} = \sqrt{448x^{7}}\\\\[/tex]

Therefore, c = 7

Notice that 7/2 = 3 remainder 1. The quotient 3 is the exponent for the term outside the root for [tex]8x^3\sqrt{7x}[/tex] while the remainder 1 is the exponent for the x term inside the root.

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We do the same idea for equation B.

[tex]\sqrt[3]{576x^{d}} = 4x\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{(4x)^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3*9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64*9x^{3+2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{576x^{5}}\\\\[/tex]

This must mean d = 5

Note: 5/3 = 1 remainder 2, which means [tex]\sqrt[3]{x^5} = x^1\sqrt[3]{x^2} = x\sqrt[3]{x^2}[/tex]

Answer:

64 ft

Step-by-step explanation:

A square has to be equal on all 4 sides for it to be considered a square. Considering that it is 8 feet on one side it would be 8 feet on all the others as well. From there you multiply 8*8 and receive the solution of 84 feet for the area of the garden.

Add the sales tax to the bill:

Bill with tax = 14.60 x 1.09 = $15.95

Multiply the total bill by the tip percentage:

Tip = 15.95 x 0.19 = 3.02

Tip = $3.02

Histograms are used to represent data, where the length of each bar represents the frequency of the data element

The histogram is not given; So, I will give a general explanation.

Assume that the number of commuters that travel more than 45 minutes is 450, while the total number of commuters surveyed is 500.

The percentage of commuters that travel more than 45 minutes is the quotient of the commuters that travel more than 45 minutes and the total number of surveyed commuters.

So, we have:

[tex]\%Percentage = \frac{450}{500}[/tex]

Divide 450 by 500

[tex]\%Percentage = 0.9[/tex]

Express as percentage

[tex]\%Percentage = 90\%[/tex]

Hence, the percentage of commuters that travel more than 45 minutes is 90%

Read more about histograms at:

https://brainly.com/question/2776232

[tex]\begin{cases} f(x) = x^4+14x\\ g(x) = 6-x \end{cases}\qquad \qquad h(x) = f(x) + g(x) \\\\\\ h(x) = (x^4+14x)+(6-x)\implies h(x) = x^4+14x-x+6 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill h(x) = x^4+13x+6~\hfill[/tex]

now, if we graph h(x), Check the picture below, we can see that horizontally the line keeps on moving towards the left, going going and going towards -infinity, and it also keeps on moving towards the right, going going and going towards +infinity, and since the horizontal area used by the function is the domain of it, the domain for h(x) will be (-∞ , +∞).

Answer:

each cup would cost $0.52

Step-by-step explanation:

there are 16 cups in 1 gallon so you multiply that by two. Then you have 32 so you divide 16.64 by 32 and you end up with 0.52.   hope this helped :))

Tell me I got this wrong

Answer:

y = -8

Step-by-step explanation:

-7y + 11 = 75 + y

Bring the "y" variable on one side, and rest on the other.

Rearranging, we get,

-7y - y = 75 - 11

-8y = 64

-y = 8

y = -8

Hope it helps :)

Answer:

The height of cuboid is 50 cm.

Step-by-step explanation:

Given :

To Find :

Using Formulas :

[tex]\star\small{\underline{\boxed{\sf \pink{SA_{(Cuboid)} = 2(lb + bh + lh)}}}}[/tex]

Solution :

Substituting all the given values in the formula to find height of cuboid :

[tex]{\longrightarrow{\sf{SA_{(Cuboid)} = 2(lb + bh + lh)}}}[/tex]

[tex]{\longrightarrow{\sf{14800= 2(60 \times 40 + 40 \times h + 60 \times h)}}}[/tex]

[tex]{\longrightarrow{\sf{14800= 2(2400 + 40h + 60h)}}}[/tex]

[tex]{\longrightarrow{\sf{14800= 2(2400 + 100h)}}}[/tex]

[tex]{\longrightarrow{\sf{14800= 4800 + 200h}}}[/tex]

[tex]{\longrightarrow{\sf{200h = 14800 - 4800}}}[/tex]

[tex]{\longrightarrow{\sf{200h = 10000}}}[/tex]

[tex]{\longrightarrow{\sf{h = \dfrac{10000}{200}}}}[/tex]

[tex]{\longrightarrow{\sf{h = \cancel{\dfrac{10000}{200}}}}}[/tex]

[tex]{\longrightarrow{\sf{\underline{\underline{\red{h = 50 \: cm}}}}}}[/tex]

Hence, the height of cuboid is 50 cm.

[tex]\underline{\rule{220pt}{3.5pt}}[/tex]

Answer:

32. A.

Step-by-step explanation: because i did 4/5 of 40 and got 32.

Answer:

  see attached

Step-by-step explanation:

The "slope-intercept" form of an equation for a line is ...

  y = mx + b . . . . . . slope m, y-intercept b; m = rise/run

__

There are several ways to graph equations for a line. One is to make use of the intercepts. That is easiest when their coordinates are integer values. The second inequality is in slope-intercept form, so it is easy to see that its y-intercept is -2.

The first inequality can be put into slope-intercept form by solving for y. That is easily done here by subtracting 6x:

  y ≤ -6x +10

This shows you the boundary line has a slope of -6 and a y-intercept of 10. To graph it, you can plot the points (0, 10) and (1, 4) and draw a line through them. The point (1, 4) is found by using a "rise" of -6 and a "run" of 1 from the y-intercept:

  m = -6 = rise/run = -6/1

  (y-intercept) + (run, rise) = (0, 10) +(1, -6) = (1, 4) . . . . another point on the line

__

Similarly, the boundary line of the second inequality goes through its y-intercept (0, -2) and the point (y-intercept) +(1, 5) = (1, 3). Points (0,-2) and (1, 3) are two points on that boundary line.

__

In both cases, the inequality includes the "or equal to ..." case, so the boundary line is part of the solution set. Accordingly, each is drawn as a solid line (not dashed).

__

To determine where the shading is, you can choose any term with a positive coefficient and look at where it is in relation to the inequality symbol. For your two inequalities, we can look at the left side of the inequality.

  first: 6x ≤

  second: y ≥

These tell you the first solution set is shaded to the left of the boundary line (where x-values are less than those on the line). The second solution set is shaded above the boundary line (where y-values are greater than those on the line). The solution set for the system of inequalities is the doubly-shaded area to the left of both boundary lines.

_____

Additional comment

The x-term in the second inequality has a positive coefficient also. If we were to look at that one, we would see ≥ 5x. That is, the boundary line has greater x-values than those in the solution set, so it, too, will be shaded to the left. (Left and above are the same half-plane for a line with positive slope.)

If both coefficients are negative, you can multiply by -1, which will also reverse the inequality symbol.

Example: -x-y>6 ⇒ x+y<-6; shaded left or below dashed line.

Step-by-step explanation:

-4y= -17x+20

4y=17x-20

y= 4.25x-5

Slope intercept form

[tex]\\ \tt\Rrightarrow 17x-4y=20[/tex]

[tex]\\ \tt\Rrightarrow 17x-20=4y[/tex]

[tex]\\ \tt\Rrightarrow y=17/4x-5[/tex]

A = 180-90-31

A = 59

Answer: 59

Answer:

$87.50

Step-by-step explanation:

how many 2/3 are in 9/8?

or another way to put it will be

how many times does 2/3 go into 9/8?

well, is simply a division.

[tex]\cfrac{9}{8}\div \cfrac{2}{3}\implies \cfrac{9}{8}\cdot \cfrac{3}{2}[/tex]

Answer:

32

Step-by-step explanation:

Answer:

a. 6

b. 21

c. 78

d. 13.5

e. 14

f. 24

Hope that helps!

Answer:

$50.00 is the discount price

Answer:

  5y +6 +7y = 2 (6y + 3 )

Step-by-step explanation:

We can name the blanks 'a' and 'b'. Then we have ...

  5y +6 +7y = a(6y +b)

This will have infinitely many solutions when both sides simplify to the same expression.

  12y +6 = 6ay +ab

To have these expressions be the same, we must have ...

  12 = 6a . . . . same coefficient of y

  6 = ab . . . .  same constant

The first of these equations tells us ...

  a = 12/6 = 2

Then the second equation tells us ...

  b = 6/a = 6/2 = 3

The equation with the blanks filled in is ...

  5y +6 +7y = 2 (6y + 3 )

Answer:

The exterior and interior angles must add up to 180 degrees. Thus, 180 divided by five gives the exterior angle as 36 degrees (and hence the interior angles as 144 degrees).

Answer:

10 Sides

Step-by-step explanation:

Int Angle + Ext Angle = 180

4Ext + Ext = 180

Ext = 36 degrees

-----

360/36 = 10 sides

Answer:

multiply by 2

Step-by-step explanation:

Step-by-step explanation:

3/5 are done, that means 2/5 are still to do.

that means these 30 km are these 2/5.

2/5 x = 30

2x = 150

x = 75

the total distance is 75 km.

Answer:

75 km

Step-by-step explanation:

2/5 = 30 km

→ Find 1/5

1/5 = 15 km

→ Now find 5/5 or 1

1 = 75 km

Answer: store b because you can get more ground beat.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A. 2 toys/5 minutes

y/x

Step-by-step explanation:

Why use brainly for this

Answer:

Step-by-step explanation:

If you're supposed to plot that, it would be a line from (0, 10) to (5, 0)

slope would be -2 mi/hr

Answer:

3/2

Step-by-step explanation:

Since the shape is an equilateral triangle, all the angles are equal measure, 60° and all the sides are also of equal measure that was given, root3. So half of the triangle has length (root3)/2. The perpendicular drawn in the interior is also an angle bisector. The triangles created are 30°-60°-90° triangles. The sides of this special right triangle are in the ratio

s : 2s : sroot3

The longest side of the 30-60-90 triangle is given. The shortest side is half the length of the longest side. The length of the long leg is the short leg × root3

In this diagram the short leg is (root3)/2 .

(root3)/2 × root3 = 3/2

See image.

Answer:

true

Step-by-step explanation:

Answer:3 to 5

Step-by-step explanation:i took the quiz