Piko filled a box with 4 layers of cubes that measured one foot on each side. If the bottom of the box fit 6 cubes, what is the volume of the box?

The length of the segment AB will be equal to 9.848 units.

It states that in the right-angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.

The length of segment AB will be calculated as:-

Points are A(1,7) and B(10,3)

AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

AB = [tex]\sqrt{(10-1)^2+(3-7)^2}[/tex]

AB = √(81+16)

AB = √97

AB = 9.848

Therefore the length of the segment AB will be equal to 9.848 units.

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Answer:

600

Step-by-step explanation:

So I'm assuming an outfit is considered one shirt, and one pair of pants... But anyways, this can be expressed in a graph. So for each shirt, there are going to be 15 possible pants you can chose. And this goes for each shirt. So in other words you're simply adding up 15, 40 amount of times. Or 15 * 40, which is 600. I attached an image that illustrates this graph. You can also think of it in terms of choosing one of 15 pants and then for each pant, there are 40 possible shirts to choose from. This is essentially adding up 40, 15 times, or in other words 40 * 15, which is going to get you the same result. But in my diagram I used it in terms of choosing a shirt first.

Answer:

600

Step-by-step explanation:

Pair 1 of pants goes with 40 shirts

Pair 2 of pants goes with 40 shirts

Pair 3 of pants goes with 40 shirts

Pair 4 of pants goes with 40 shirts

Pair 5 of pants goes with 40 shirts

Pair 6 of pants goes with 40 shirts

Pair 7 of pants goes with 40 shirts

Pair 8 of pants goes with 40 shirts

Pair 9 of pants goes with 40 shirts

Pair 10 of pants goes with 40 shirts

Pair 11 of pants goes with 40 shirts

Pair 12 of pants goes with 40 shirts

Pair 13 of pants goes with 40 shirts

Pair 14 of pants goes with 40 shirts

Pair 15 of pants goes with 40 shirts

Add up everything (not including the 1,2,3,4,5,...14,15 pairs of pants because each pair of pants goes with 40 different shirts so u just add up all the 40's)  and you would get 600 outfits.

Another simple way of doing this would just be multiplying 40x15

Answer: 14.79

Step-by-step explanation:

[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]

Evidence is used in proofs to support a claim.

It should be noted that evidence simply means a claim that's is used to support a proposition that's it's true.

In this case, evidence is used in proofs to support a claim. On the other hand, counterexample is used to disprove a theory.

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Answer:

7

Step-by-step explanation:

a^3 = 2^3 = 8

b^3 = -3^3 = -27

(8 - (-27))/5= (8+27)/5 =35/5=7

Based on the relevant congruent theorems, all of the statements are correct except: D. △RST ≅ △UST by SAS.

Two triangles that have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles are proven to be congruent by the AAS congruence theorem.

Thus, △RWS ≅ △UWT by AAS because they have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles.

△RST cannot be proven to be congruent to △UST by SAS because there is no sufficient information.

Based on the reflexive property, ST ≅ ST. Also, using the CPCTC, all parts of the two congruent triangles are equal, therefore, ∠WTU ≅ ∠WSR.

The only statement that is incorrect is: D. △RST ≅ △UST by SAS.

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Answer:

A, B, C and E

Step-by-step explanation:

Step-by-step explanation:

let's call the top of the pole T, and the ground point of the pole G.

so, the situation gives us 2 right-angled triangles:

PTG and QTB.

from both triangles we know one leg (TG, the pole = 9 m), the inner angles at G (90° in both cases), and actually the inner angles at T, because we know the angles of depression there.

the inner triangle angles at T are just the complementary angles of the angles of depression (that means they add up together to 90°).

the inner angle at PTG = 90 - 4 = 86°

the inner angle at QTG = 90 - 7 = 83°

and because the sum of all angles in a triangle is always 180°, we even know the third angles at P and Q :

angle P = 180 - 90 - 86 = 4°

angle Q = 180 - 90 - 83 = 7°

yes, they are the same as the angles of depression (must be the same).

so, we know from both triangles 1 side and all 3 angles.

with the law of sine we can get every missing side.

particularly we need the second legs (sides in the ground) to get the distance between both points.

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c being the sides always opposite of their related angles.

TG/sin(4) = PG/sin(86)

PG = 9×sin(86)/sin(4) = 128.7059963... m

TG/sin(7) = QG/sin(83)

QG = 9×sin(83)/sin(7) = 73.29911785... m

the distance between P and Q can have now 2 solutions :

if P and Q are on different sides of the pole, then

PQ = 128.7059963... + 73.29911785... = 202.0051142... m

but if they are on the same side of the pole, then their distance is

PQ = 128.7059963... - 73.29911785... = 55.40687846... m

due to the phrasing of the first sentence I suspect the first solution to be right.

but just in case, I gave you also the second possible solution.

Answer:

A. 2640

Step-by-step explanation:

44 feet per second 30 miles per hour is 2640 feet per minute

Answer: C

Step-by-step explanation:

[tex]\sqrt10 10=10\sqrt{10}[/tex]

The rule of 72 is a rule of thumb that is used to determine the doubling time for an investment given the annual interest rate.

The equation Miguel needs to set up is r = 72/16.

The interest rate is 4.5%.

The rule of 72 is used to determine the time it would take an investment to double in value. The doubling time is determined by dividing 72 by the interest rate.

Number of years it would take an investment to double = 72 / interest rate

n = 72 / r

r = 72 / n

72 / 16 = 4.5%

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Using Sarai's measurements, Line 3 must be parallel to Line 5 by option (A) Converse of Alternate Exterior Angles Theorem.

The alternate Exterior Angles theorem states, "If two lines are parallel and they are intersected by the same straight line then the alternative exterior angles formed by the figure are equal to each other."

The converse of this theorem states that "If two lines intersected by one transverse and formed alternate exterior angles, and if they are equal to each other then that two lines are parallel to each other."

Here in Sarai's measurement, we can conclude that Line 3 and Line 5 are intersected by one straight line, and the formed alternate exterior angles both are 65, which shows they are equal to each other.

Hence by Converse of the Alternate Exterior Theorem, we can say that both lines are parallel to each other.

So, Line 3 must be parallel to Line 5 according to the Converse of Alternate Exterior Angles Theorem.

Hence Option (A) is correct.

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Answer:

A. Square

Step-by-step explanation:

Hope this helps!

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The value of ST is 3

The given parameters are:

RT = 8

RS = 5

To calculate ST, we make use of the following straight line theorem

RT = RS + ST

This gives

8 = 5 + ST

Subtract 5 from both sides

ST = 3

Hence, the value of ST is 3

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Answer:

50 [tex]cm^{2}[/tex]

Step-by-step explanation:

Area of a trapezoid: [tex]\frac{a+b}{2} h[/tex]

[tex]\frac{a+b}{2} h[/tex]

= [tex]\frac{14+6}{2} (5)[/tex]

= [tex]\frac{20}{2} (5)[/tex]

= [tex]10(5)[/tex]

= 50 sq. cm

Answer: B. G(x) = (x-5)^2

Step-by-step explanation:

This will shift the graph 5 units right

Answer:

[tex]\huge\boxed{\sf 9x^2+12x+4 \ units^2}[/tex]

Step-by-step explanation:

Given that,

Length of cube = l = 3x + 2 units

[tex]= l \times l\\\\= (3x+2)(3x+2)\\\\= 3x(3x+2)+2(3x+2)\\\\= 9x^2+6x+6x+4\\\\= 9x^2+12x+4 \ units^2\\\\\rule[225]{225}{2}[/tex]

Answer:

14

Step-by-step explanation:

24/12=2

(2)7=14 hours

Answer:

[tex]a)\ y=-(x-5)^2;\\b)\ y=4x^2-5;\\c)\ (y-2)^2=4*(x+3).[/tex]

Good luck!

Answer:

Slope = 1/3

Step-by-step explanation:

  [tex]\sf \ x_1=-1 ; \ y_1=-2\\\\ x_2 = 2 ; \ y_2=-1[/tex]

      [tex]\sf \boxed{\bf \ Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                  [tex]\sf = \dfrac{-1-[-2]}{2-[-1]}\\\\ =\dfrac{-1+2}{2+1}\\\\= \dfrac{1}{3}[/tex]

Answer:

[tex]\displaystyle{y=2\sqrt{x+4}}[/tex]

Step-by-step explanation:

We are given parametric equations of:

[tex]\displaystyle{x=t^2-4}[/tex] and [tex]\displaystyle{y=2t}[/tex]

Isolate t-variable in [tex]\displaystyle{x=t^2-4}[/tex] first by adding both sides by 4:

[tex]\displaystyle{x+4=t^2-4+4}\\\\\displaystyle{x+4=t^2}[/tex]

Square root both sides then write plus-minus:

[tex]\displaystyle{\sqrt{x+4}=\sqrt{t^2}}\\\\\displaystyle{t=\pm \sqrt{x+4}}[/tex]

Since the choice determines y-term as a function and only positive t-value exists, substitute only [tex]\displaystyle{t=\sqrt{x+4}}[/tex] in [tex]\displaystyle{y=2t}[/tex].

Therefore, the answer is [tex]\displaystyle{y=2\sqrt{x+4}}[/tex]

Answer:

c

Step-by-step explanation:

By taking the product between the number of boys and the number of rocks that each gets, we conclude that they collected 75 rocks.

We know that there are 3 boys, and each boy collected 25 rocks.

If we take the product between the number of boys and the number of rocks that each boy collected, we get:

R = 3*25 rocks = 75 rocks.

We conclude that the boys collected 75 rocks in total.

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Answer: [tex]\displaystyle d=\sqrt{1 7}\;\text{or about 4.123 units}[/tex]

Step-by-step explanation:

     We can use the distance formula to solve. Let (4, 6) be point one and (5, 2) be point two.

     [tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]

     [tex]\displaystyle d=\sqrt{(5-4)^2 +(2-6)^2}[/tex]

     [tex]\displaystyle d=\sqrt{(1)^2 +(-4)^2}[/tex]

     [tex]\displaystyle d=\sqrt{1 +16}[/tex]

     [tex]\displaystyle d=\sqrt{1 7}[/tex]

The point (0, 0) lies in the shaded region and satisfies the solution for the inequality y ≥ 3x - 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the inequality y ≥ 3x - 2, since the point (0, 0) lies on the shaded region, hence:

0 ≥ 3(0) - 2

0 ≥ -2

The point (0, 0) satisfies the solution for the inequality y ≥ 3x - 2

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The equation that relates x and y is y = 2.5x.

The values of x and y vary directly. Therefore,

y α x

where

Hence,

y = kx

where

Therefore,

x = 2

y = 5

5 = 2k

k = 5 / 2

k = 2.5

Hence, the equation that relates x and y are as follows;

y = 2.5x

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Answer:

28.31

Step-by-step explanation:

So in this case you're going to need to use the law of sines which essentially states that: [tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex] which should apply to any of the sides. the lowercase a and b are the opposite sides of the angles A and B. In this example the angle A is given and C is given, but not in the text. Since you have the right angle thing in the diagram, angle C is a right angle (90 degrees).

Given information:

[tex]\angle A = 32\\a=15\\\angle C = 90 \text{(the right angle symbol in the diagram of the triangle)}[/tex]

Law of sines equation:

[tex]\frac{a}{sinA}=\frac{b}{sinB} \text{ can be applied to any two sides }[/tex]

Plug in known information:

[tex]\frac{15}{sin(32)}=\frac{c}{sin (90)}[/tex]

since sin(90) = 1, simplify the fraction

[tex]\frac{15}{sin(32)} = c[/tex]

Calculate sin(32)

[tex]\frac{15}{0.530}\approx c[/tex]

Divide

[tex]28.306\approx c[/tex]

If you haven't learned law of sines yet and don't quite understand why it works you can also use the definition of tan to find what b equals and then use the Pythagorean Theorem to solve for c

tan is defined as: [tex]\frac{opposite}{adjacent}[/tex]

[tex]tan(32)=\frac{15}{b}[/tex]

now multiply both sides by b

[tex]b * tan(32)=15[/tex]

Divide both sides by tan 32

[tex]b = \frac{15}{tan(32)}[/tex]

[tex]b\approx 24.005[/tex]

Now use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

[tex](24.005)^2+15^2=c^2\\[/tex]

Square known values

[tex]576.241+225=c^2[/tex]

Add the values

[tex]801.241 = c^2[/tex]

take the square root of both sides

[tex]28.306\approx c[/tex]

Rounding to the nearest hundredth gives you 28.31

Answer:

Step-by-step explanation:

Answer: f(n + 1) = (–0.5)f(n)

Step-by-step explanation:

This is a geometric series with common ratio -0.5.

There are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

It is given that at least two of them should have the same remainder when divided by 15.

Division algorithm.

Let aa be an integer and d a positive integer. Then there are unique integers q and r with [tex]0\leq r < d[/tex] such that [tex]a=dq+r[/tex]

q is called the quotient and r is called the remainder

q=a div d

r=a mod d

Pigeonhole principle If k is a positive integer and k+1or more objects are placed into k boxes, then there is at least one box containing two or more objects.

Hence, there are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

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Answer:

(-4,-2)

Step-by-step explanation:

Isolate x:

2x - 5y = 2

2x = 5y + 2

x = 5/2y + 1

Substitute and solve for y:

3(5/2y + 1) + 2y = -16

15/2y + 3 + 2y = -16

7.5y + 2y = -16 - 3

9.5y = -19

y = -2

Substitute and solve for x:

2x - 5y = 2

2x - 5(-2) = 2

2x + 10 = 2

2x = -8

x = -4