Enrique is saving money to buy a graphing calculator. So far he has saved $30.
His math teacher told him he has saved 40% of what he will need. How much
does the calculator cost?

⇒ Choose three values for [tex]x[/tex] and substitute in to find the corresponding [tex]y[/tex] values.

[tex](0,6),(1,11),(2,16)[/tex]

The expansion of the series is 2 + 6 + 8 + 10

The summation expression is given as:

[tex]\sum\limits^4_{n=1} 2(n + 1)[/tex]

When n = 1, we have:

2(n + 1) = 2(1 + 1)  = 4

When n = 2, we have:

2(n + 1) = 2(2 + 1)  = 6

When n = 3, we have:

2(n + 1) = 2(3 + 1)  = 8

When n = 4, we have:

2(n + 1) = 2(4 + 1)  = 10

So, we have:

[tex]\sum\limits^4_{n=1} 2(n + 1) = 2 + 6 + 8 + 10[/tex]

Hence, the expansion of the series is 2 + 6 + 8 + 10

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Answer:

The correct option is actually d. 4 + 8 + 16 + 32

Step-by-step explanation:

A cylinder is a three-dimensional structure formed by two parallel circular bases connected. The height of the can that has a volume of 1250 cm³ if the radius is 8 cm is 6.217 cm.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.

Given the volume of the cylinder is 1250 cm³, and the radius of the cylinder is 8 cm. Therefore, the volume of the cylinder can be written as,

[tex]\text{Volume of the cylinder} = \pi r^2h[/tex]

[tex]1250 = \pi \times (8)^2 \times h\\\\h = 6.217\rm\ cm[/tex]

Hence, the height of the can that has a volume of 1250 cm³ if the radius is 8 cm is 6.217 cm.

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Answer:

7x - 30

Step-by-step explanation:

5x -2(15-x)

Distribute -2 to the parenthesis

= 5x -30 +2x

Combine like terms

7x-30

Answer:

i think its D.

Step-by-step explanation:

i just counted

Answer:

22 degrees F

Step-by-step explanation:

[tex]20--2=20+2[/tex]

Subtracting a negative number makes the sign positive, so 20 + 2 = 22 degrees F.

Pythagoras' theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The measure of the other leg of the triangle is 5.1961 units.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

Let the length of the other leg can be represented by x.

Given the hypotenuse of a right triangle measures 6 cm and one of its legs measures 3 cm. Therefore, the measure of the other legs can be written as,

Hypotenuse² = 3² + x²

6² = 3² + x²

36 = 9 + x²

x² = 27

x = √27

x = 5.1961

Hence, the measure of the other leg of the triangle is 5.1961 units.

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Answer:

d) 190,172,154

Step-by-step explanation:

208-18=190

190-18=172

172-18=154

Answer: Max. Max has a 49% chance of getting a 1 or 2 when Josie only has a 33% chance of getting a green block

............................................................................

Answer:

5x^2 - 4x - 3 = 0

Step-by-step explanation:

For the equation

ax^2 + bx + c = 0

the  roots are   [-b +/- √(b^2 - 4ac)] / 2a

So comparing the terms to the values in the question:

a = 5

b = -4

c = -3

Answer:

d = 306 m

Step-by-step explanation:

calculate the distance d using the distance formula

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

with (x₁, y₁ ) = (10, 20) and (x₂, y₂ ) = (280, 164) ← house and beach coordinates

d = [tex]\sqrt{(280-10)^2+(164-20)^2}[/tex]

   = [tex]\sqrt{270^2+144^2}[/tex]

   = [tex]\sqrt{72900+20736}[/tex]

   = [tex]\sqrt{93636}[/tex]

   = 306 m

Answer:

The distance from Francesca's house to the beach is 306 meters.

Step-by-step explanation:

Use the Pythagorean Theorem to find the straight-line distance from Francesca's house to the beach.

Step 1 Find the length of the horizontal leg.

The length of the horizontal leg is the absolute value of the difference between the x- coordinates of the points (280,20) and (10,20).

|280 - 10| = 270

The length of the horizontal leg is 270 meters

Step 2 Find the length of the vertical leg.

The length of the vertical leg is the absolute value of the difference between the y- coordinates of the points (280,164) and (280,20)

|164 - 20| = 144

The length of the vertical leg is 144 meters.

Step 3 Let a = 270 and b = 144. Let c represent the length of the hypotenuse. Use the Pythagorean Theorem to find c.

a² + b² = c²

270² + 144² = c² Substitute into the formula.

72900 + 20736 = c² Simplify.

93636 = c² Add.

√93636 = c Take the square root of both sides.

306 = c Simplify.

The distance from Francesca's house to the beach is 306 meters.

Answer:

9.5 feet

Step-by-step explanation:

Area of square garden = side length²

⇒ 90 = l²

⇒ l = √90

⇒ l = 3√10

⇒ l = 9.5 feet (nearest tenth)

The length of one side lies between the whole numbers 9 and 10.

Answer:

9 and 10

side length = 9.5 ft (nearest tenth)

Step-by-step explanation:

Area of a square = s²  (where s is the side length)

Therefore, if the square garden measures 90 ft², the length of one side will be √90.

To find the two whole numbers that √90 lies between, find the perfect square either side of 90.

Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...

Therefore, 90 lies between 81 and 100:  

⇒ 81 < 90 < 100

Square root the numbers:

⇒ √81 < √90 < √100

⇒ 9 < √90 < 10

Therefore, the length of one side of Grandma's garden is between 9 and 10.

To estimate √90 to the nearest tenth, find the difference between the three numbers:

[tex]81 \overset{+9}{\longrightarrow} 90 \overset{+10}{\longrightarrow} 100[/tex]

As 90 is almost in the middle of 81 and 100,

⇒ √90 = 9.5 (nearest tenth)

According to the calculator, √90 = 9.486832981... = 9.5 (nearest tenth)
which verifies the estimation.

Answer:

100

100 is not an odd number, its higher than 90 but not 100

and 100-100=0

Step-by-step explanation:

Hope it helps

Answer:

x = 8

z = 65

Step-by-step explanation:

Through various rules, we are able to assert: (6x + 67)° = 115°.

Now, we want to solve for x:

6x + 67 = 115

6x = 48

x = 8

We know that z° is equal to the complement of (6x + 67)°, and together these must sum to 180°. Therefore, we can simply take 180° - 115° to find that z° = 65°.

The correct student is Marcus because the power of the polynomial decreases till  0

The polynomial expressions are given as:

Marcus: 3x³ - 4x²y + y³ + 2

Ariel: y³ - 4x²y + 3x³ + 2

The standard form of a polynomial with the variable x is:

P(x) = ax³ + bx² + cx + d

This means that the power of the polynomial decreases till it gets to 0

Using the above form as a guide, the correct student is Marcus.

Marcus is correct because the power of the polynomial decreases till it gets to 0

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Answer:

h=3

Step-by-step explanation:

Here's the explanation

Move 10 to the other side

5h=25-10

5h=15

h=15/5

h=3

10+5h=25

10+5h-10=25-10

5h=15

[tex]\frac{5h}{5}=\frac{15}{5}[/tex]

h=3

the answer is 3

Answer: Choice D

y-4 = -3(x+1)

========================================================

Explanation:

Let's first find the slope of the line through (-1,4) and (1,-2)

[tex](x_1,y_1) = (-1,4) \text{ and } (x_2,y_2) = (1,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 4}{1 - (-1)}\\\\m = \frac{-2 - 4}{1 + 1}\\\\m = \frac{-6}{2}\\\\m = -3\\\\[/tex]

The slope is -3, which tells us that the answer must be choice D.

Choices A,B, & C can be eliminated because choices A and B have a slope of -13, while choice C has a slope of 3.

Refer to the point-slope format [tex]y-y_1 = m(x - x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point the line goes through.

Answer:

0.2165 to the nearest ten thousandth.

Step-by-step explanation:

Sin(15) × cos(15) × cos(30)​

= 0.258819 * 0.965926 * 0.866025

= 0.216506

Answer:

C) 15, 20, 25

Step-by-step explanation:

If you plug this in pythagorean theorem, it works. The others don't.

Answer:

Output: 3

Step-by-step explanation:

(x, y)

(Input, Output)

(2, 3)

Answer:

In quadrant I, the answer is A. sin(x) ≈ 0.97

The sequence is recursively defined by

[tex]\begin{cases}a_1 = 1 \\ a_2 = 2 \\ a_n = a_{n-1} a_{n-2} & \text{for } n \ge 3\end{cases}[/tex]

By this definition,

[tex]a_{n-1} = a_{n-2} a_{n-3} \implies a_n = a_{n-2}^2 a_{n-3}[/tex]

[tex]a_{n-2} = a_{n-3} a_{n-4} \implies a_n = (a_{n-3} a_{n-4})^2 a_{n-3} = a_{n-3}^3 a_{n-4}^2[/tex]

[tex]a_{n-3} = a_{n-4} a_{n-5} \implies a_n = (a_{n-4} a_{n-5})^3 a_{n-4}^2 = a_{n-4}^5 a_{n-5}^3[/tex]

[tex]a_{n-4} = a_{n-5} a_{n-6} \implies a_n = (a_{n-5} a_{n-6})^5 a_{n-5}^3 = a_{n-5}^8 a_{n-6}^5[/tex]

and so on.

Recall the Fibonacci sequence, {1, 1, 2, 3, 5, 8, 13, 21, …}, where the next term in the sequence is the sum of the previous two terms. If [tex]F_n[/tex] is the n-th Fibonacci number, then continuing the pattern above we would arrive at

[tex]a_n = {a_2}^{F_{n-1}} {a_1}^{F_{n-2}} = 2^{F_{n-1}}[/tex]

Notice that the sequence of positive powers of 2 leaves a periodic sequence of residues mod 10 :

[tex]2 \equiv 2 \pmod{10}[/tex]

[tex]2^2 \equiv 4 \equiv 4 \pmod{10}[/tex]

[tex]2^3 \equiv 8 \equiv 8 \pmod{10}[/tex]

[tex]2^4 \equiv 16 \equiv 6 \pmod{10}[/tex]

[tex]2^5 \equiv 2 \times 2^4 \equiv 2 \times 6 \equiv 2 \pmod{10}[/tex]

[tex]2^6 \equiv 2^2 \times 2^4 \equiv 4 \times 6 \equiv 4 \pmod{10}[/tex]

and so on; the period of this sequence of residues is 4.

The period of [tex]F_n[/tex] taken mod 4 is 6 :

[tex]\{1, 1, 2, 3, 5, 8, \ldots\} \equiv \{1, 1, 2, 3, 1, 0, \ldots\} \pmod 4[/tex]

(This follows from the "properties" section in the link in comment. In this case, π(4) = 3/2 × 4 = 6.)

It follows that

[tex]34 \equiv 4 \pmod 6 \implies F_{34} \equiv 3 \pmod 4 \implies 2^{F_{34}} \equiv 2^3 \equiv 8 \pmod{10}[/tex]

which means the last digit of [tex]a_{35}[/tex] is 8.

-7/6 = - 1.167 in simplest form

Answer:

Step-by-step explanation:

You cant simply this into fraction but you can simplify it to decimal form

which is - 1.17 round off

The length of arc JL is 24.46 units see attachment for diagram.

An arc is a part of the circumference of a circle that meets two radii of a circle to form a sector.

Analysis:

From bigger triangle, if we bisect 144, the line meets JL at 90°.

To find AL,

sin 72 = AL/6

AL = 6 sin 72 = 5.71

To find the angle at O

∠O = 2∠K ( twice angle at circumference is equal to angle at center)

∠O = 2 (144) = 288°

For smaller right-angled triangle,

sin 144 = AL/OL

sin 144 = 5.71/OL

OL = radius of circle =  5.71/0.587 = 9.73 unit

length of arc JL = ∅/360 x 2πr

= 144/360 x 2 x 3.142 x 9.73 = 24.46 units

In conclusion, the length of arc JL is 24.46 units

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======================================================

Explanation:

Draw out a right triangle as you see below.

Let's use the pythagorean theorem to find 'a'

[tex]a^2 + b^2 = c^2\\\\a = \sqrt{c^2 - b^2}\\\\a = \sqrt{(9.9)^2 - (7.3)^2}\\\\a = \sqrt{44.72}\\\\a \approx 6.6873\\\\a \approx 6.7\\\\[/tex]

Table 3 will fit snugly in the corner of the room.

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

From the given data we will check the value of the diagonal by applying the Pythagorean theorem.

So by using the Pythagorean theorem:-

D ²  =    L²   +   W²

D²   =    ( 2.4 )²  +  ( 3.2 )²

D²   =    ( 5.76   +    10.24 )  =   16

D     =   √16   =  4  feet

Therefore table 3 will fit snugly in the corner of the room.

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Answer:

Table 3.

Step-by-step explanation:

Person above is correct, I'm takin the test!!

Answer:

  3000

Step-by-step explanation:

The multiplier associated with each percentage change (p) is (1 +p). We can use this fact to relate the original number to the modified number.

__

Let x represent the original number. Then the discounted number is ...

  x(1 -20%)(1 -25%)(1 -20%) = x(0.8)(0.75)(0.8) = 0.48x

After those discounts, the increased number is ...

  (0.48x)(1 +20%)(1 +25%)(1 +20%) = (0.48x)(1.2)(1.25)(1.2) = 0.864x

The difference from the original is ...

  x - 0.864x = 408

  0.136x = 408 . . . . simplify

  x = 3000 . . . . . . . divide by the coefficient of x

The original number was 3000.

Answer:

2340

Step-by-step explanation:

4590*.51=2340.9

Because you can not have .9 people, you round down to 2340

2341 students are in the freshman class.

Percentage is defined as ratio expressed as a fraction of 100.

Total no. of students in the freshman Economics majors = 4590

51% students of a university's freshman class,

Let x no. of students in the freshman class,

x = 51/100×(4590)

x = 0.51×(4590)

x = 2340.9

x = 2340.9 ≈ 2341

Hence, 2341 students are in the freshman class.

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Area of base

Area of one triangle side

Area of 4 sides

TSA

20+25=45ft²

Answer:

C)  45 ft²

Step-by-step explanation:

Formulae

Area of a square = x²  (where x is the side length)

Area of a triangle = 1/2 × base × height

The surface area of a square pyramid comprises:

⇒ area of square base = 5² = 25 ft²

⇒ area of triangular face = 1/2 × 5 × 2 = 5 ft²

⇒ Total surface area = area of square base + 4 triangular areas

                                   = 25 + 4(5)

                                   = 25 + 20

                                   = 45 ft²

Answer:

(2) Graph 2

Step-by-step explanation:

Question 40