In the basketball game a player scored 4 three-pointers. How many points did he achieve with the 8 three-pointers? ​

Answer:

80 units

Step-by-step explanation:

So first i plotted all of the points. Then i connected all the dots until i made a rectangle. Then I counted what the length and height of the rectangle is. Since the length x height = the area, then i multiplied the measurements together. Then i got 80 units. Here is a picture below (sorry for the bad quality its night where i live)

Answer:

80 units²

Step-by-step explanation:

Given vertices of a rectangle:

As points A and D share the same x-coordinate, and points B and C share the same x-coordinate, the difference between the different x-coordinates is the length of the rectangle:

\(\begin{aligned}\implies \textsf{Length} & = x_B-x_A\\& = 2-(-8)\\& = 2+8\\& = 10\; \sf units\end{aligned}\)

As points A and B share the same y-coordinate, and points C and D share the same y-coordinate, the difference between the different y-coordinates is the width of the rectangle:

\(\begin{aligned}\implies \textsf{Width} & = y_A-y_D\\& = 5-(-3)\\& = 5+3\\& = 8\; \sf units\end{aligned}\)

Therefore:

\(\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\&=8 \times 10\\&=80 \sf \; units^2\end{aligned}\)

Answer:

$6.80

Step-by-step explanation:

$8.16 ÷ 12 = $0.68

$0.68 x 10 = $6.80

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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The limit of the expression is determined as 0.

The limit of the expression is calculated as follows;

The given expression = lim (x ---> 9) [ ( x - 9 ) / √x - 3)

For the given limit in the expression, we have x maps to 9 or x tends to 9.

When x tends to 9, we will have;

x ---->9 = (9 - 9 ) / (√9 - 3)

= (0)/(-3 - 3)

note: since √x can be negative or positive, we will choose negative so that our solution will not be undefined.

= 0/-6

= 0

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\(\sf \longrightarrow \: \: \lim_{x\to \: 9} \: \: \: \frac{x \: - \: 9}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ({ \sqrt{x} \: )}^{2} \: - \: {(3)}^{2} }{ \sqrt{x} - 3 } \\ \)

Now , by using Identity:-

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)( \sqrt{x} - 3)}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3) \cancel{( \sqrt{x} - 3)}}{ \cancel{ \sqrt{x} - 3} } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)(1)}{1 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)(1) \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{9} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \sqrt{9} + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 3 + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 6\\ \)

The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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Answer:

C

Step-by-step explanation:

7/8 is a fraction. It's value is less than 1. It's decimal equivalent must also be less than 1. Finally, it's percent must be less than 100%.

7/ 8 is equivalent to 0.875

As a % 0.875 * 100 = 87.5%

C

Answer:

24 is the number. The sum of its digits is 6.

Step-by-step explanation:

There are four two-digit numbers the product of whose digits is 8: 18, 24, 42, and 81. Of these numbers, 24 is four times the sum of its digits:

24 = 4 × 6 = 4 × (2 + 4)

Using simple interest formula, the number of years the money has been in the account is 11 years.

He £1120 into a bank account which pays simple interest at a rate of 4% per year.  After a certain number of years, the account has paid a total of £492.80 in interest.

The number of years the money has been in the account can be calculated as follows;

I = prt / 100

where

Therefore,

I = 492.80

p = 1120

r = 4%

t = ?

Therefore,

t = 100I / pr

t = 100 × 492.80 / 1120 × 4

t = 49280 / 4480

t = 11 years

Therefore, the money has been in the account for 11 years.

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The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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Using the Divergence Theorem, we get the flux of F across the closed surface S is π/2 (27√2 - 27).

To apply the Divergence Theorem, we will first compute the divergence of F as follows -

div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 1 + 1 + 1

= 3

Now we will calculate the flux of F across the closed surface S that completely surrounds T. By the Divergence Theorem, this is equal to the triple integral of the divergence of F over the region T and is given by -

∫∫S F•n dS = ∭T div(F) dV

We can describe the region T using cylindrical coordinates:

0 ≤ r ≤ 2

-π/2 ≤ θ ≤ π/2

0 ≤ z ≤ √(9 - r sin θ)

The bounds on r and θ come from the fact that the half cylinder is contained within the plane x = 2, and the plane y = ±3. The bounds on z come from the equation of the half cylinder.

Now we can write the triple integral as follows -

∭T div(F) dV = ∫0^2 ∫-π/2^π/2 ∫0^√(9 - r sin θ) 3 r dz dθ dr

Evaluating this integral, we get,

∭T div(F) dV = π/2 (27√2 - 27)

Therefore, the flux of F across the closed surface S is π/2 (27√2 - 27).

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Answer:

B: rectangle JKLM ~ rectangle QRSP

Step-by-step explanation:

5/6=0.83

12.5=0.83

JK corresponds to QR

JM corresponds to PQ

rectangle JKLM ~ rectangle QRSP

Answer:

35 i think

Step-by-step explanation:

The key features of the dashed graph are

A graph is a pictorial representation of a function

To describe the key features of the dashed graph, we proceed as follows.

So, the key features of the dashed graph are

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16.

Given the figure, we can deduce the following information:

Coordinate for Art Museum = (6,1)

Coordinate for Animal Shelter = (6,-2)

To determine the coordinates of the new location for the art museum and the animal shelter as a reflection across the y-axis, we first note that the reflection of point (x,y) across the y-axis is (-x,y). So,

Art Museum = (6,1)=(-6,1)

Animal Shelter = (6,-2)=(-6,-2)

Hence, the new locations are:

Art Museum =(-6,1)

Animal Shelter =(-6,-2)

Next, we determine the distance between Art Museum and the Animal Shelter:

Distance = 1-(-2)=3

Hence, there are 3 blocks from each other. We can also conclude that it is the same distance as in question 12 as when we reflect a point across the y axis, the y-coordinate remains the same.

Answer:

x = -25 / 3

Step-by-step explanation:

10 / 3 = x / (-5/2)

10 / 3 * (-5 / 2) = x

x = -50 / 6

x = -25 / 3

Answer:

\(x=\frac{-25}{3}\)

Step-by-step explanation:

\(\frac{10}{3}=\frac{x}{\frac{-5}{2} } \\\\\frac{-5}{2}*\frac{10}{3}=\frac{x}{\frac{-5}{2} }*\frac{-5}{2} \\\\\frac{-25}{3} =x\\\\x=\frac{-25}{3}\)

option d. 37/2 ÷ 17/4 is correct.

Step-by-step explanation:

\(18\ \frac{1}{2} \div 4\ \frac{1}{4} \)

\( = > \frac{37}{2} \div \frac{17}{2} \)

The area represented by g(x) is the definite integral of g(x) with respect to t from t=0 to t=x:

g(x) = ∫(t^4) dt from 0 to x

To find g'(x) using Part 1 of the Fundamental Theorem of Calculus, we know that:

g'(x) = d/dx (∫(t^4) dt from 0 to x) = (t^4) evaluated at x = x^4

To find g'(x) using Part 2 of the Fundamental Theorem of Calculus, we can evaluate the integral:

g(x) = ∫(t^4) dt = (1/5)t^5 evaluated from 0 to x = (1/5)x^5

then take the derivative of g(x) with respect to x:

g'(x) = d/dx ((1/5) x^5) = (1/5) * 5x^4 = x^4

Both ways give the same result of g'(x) = x^4

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Given:

A sphere with radius of 12 in.

Then:

Lateral Area = A sphere has no sides.

Surface Area =

Volume =

Explanation

to figure out if a pair is a solution, just replace x and y values and check if the equation is true,then

Step 1

Step 2

Step 3

Answer:

Remember to add up the 2 angles they give you and subtract it from 180. Then you will get the answer for each question.

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

Answer:

3^x-1×27^x+1

___________

81^x

81^x+x-1+1

_________

81^x

81^2x

_____

81^x

81^2x-1x

81^1x

Answer:

See Picture. I made a 100.

Step-by-step explanation:

Weekly- $17253.46

Daily- $17254.01

Continuously- $17254.11

Monthly- $17251.29

Semi-annually- $17237.36

Quarterly- $17245.69

Compound interest is the addition of interest on the interest of the principal amount.

Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,

\(A = P(1+ \dfrac{r}{n})^{nt}\)

As it is given that the principal amount is $15,000; while the rate of interest is 2.8%, and the amount is invested for a period of 5 years.

A.) When the interest is charged weekly,

As we know that there are 52 weeks in a year, therefore, n = 52, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{52})^{52 \times 5}\\\\A = \$17,253.46\)

B.) When the interest is charged daily,

As we know that there are 365 days in a year, therefore, n = 365, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{365})^{365 \times 5}\\\\A = \$19,554.55\)

C.) When the interest is charged Continuously,

As we know that the formula for continuous compounding is given as,

\(A = Pe^{rt}\)

Substitute the values, we will get,

\(A = 15000 \times (e^{0.024 \times 5})\\\\A= \$16,912.45\)

D.) When the interest is charged Monthly,

As we know that there are 12 months in a year, therefore, n = 12, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{12})^{12\times 5}\\\\A = \$15211.23\)

E.) When the interest is charged Semi-annually,

As we know that the interest is charged Semi-annually, therefore, n = 2, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{2})^{2\times 5}\\\\A = \$17,237.36\)

F.) When the interest is charged Quarterly,

As we know that the interest is charged Quarterly, therefore, n = 4, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{4})^{4\times 5}\\\\A = \$17,245.7\)

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Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Answer:

The equation that represents the situation is: 30w = 150.

Step-by-step explanation:

We can set up an equation to find the value of w:

30w = 150

To solve for w, we can divide both sides of the equation by 30:

w = 150 / 30

w = 5

So April walks dogs for 5 weeks to earn $150.

Answer:

\(\frac{1}{x^21y^12}\)

Step-by-step explanation:

We want to five the lowest common multiple of these 5 numbers. We will see that the lowest common multiple is:

\(98^{91}\)

A multiple of a number N is any product between N and a positive integer. Here we want to get the smallest common multiple of the 5 numbers in the given set.

Here, the set is:

\({98^{53}, 98^{64}, 98^{73}, 98^{88}, 98^{91}\)

Remember the rule:

\(a^n*a^m = a^{n + m}\)

Then we can see that:

\(98^{91} = 98^{91}*1 = 98^{88}*98^{3} = 98^{73}*98^{18} = 98^{64}*98^{27} = 98^{53}*98^{38}\)

So:

\(98^{91}\)

Is a common multiple of all the numbers in the set, and is the smallest common multiple because is equal to the largest number in the set.

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Answer:

B

Step-by-step explanation:

y+4x=0

-y-2x=-2

2x=-2

x=-1

y+4(-1)=0

y-4=0

y=4

Distance traveled after toll payment is 1.2 miles on highway 40.

The distance may be calculated using a curved route. Displacement measurements can only be made along straight lines. Distance is path-dependent, meaning it varies depending on the direction followed. Displacement simply depends on the body's beginning and ending positions; it is independent of the route.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The entire length of the journey taken between two points is known as the distance traveled. Travel distance is not a vector.

Distance traveled before toll payment =3/5 miles on highway 40

Distance traveled after toll payment =2*3/5  = 6/5 =

1.2 miles on highway 40.

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