evaluate the dot product of (8,4) and (-3,5)

Answer:

408 in²

Step-by-step explanation:

Given in the question that,

length of a show box = 15 in

width of a show box = 7 in

height of a show box = 4.5 in

Formula to calculate the surface area of shoe box is as following

Plug values in the formula

2*(15*7 + 15*4.5 + 7*4.5)

2(105 + 67.5 + 31.5)

408 in²

The surface area of the box = 408 in²

Answer:

The length L is 10 cm

Step-by-step explanation:

We need to find the length of the arc subtended by a central angle of 2 radians and the circle has radius of 5cm.

So, the formula used will be:

l = r  Θ

Where L= length of arc

r= radius of circle

and  Θ is angle

In The given question

L=?

r = 5 cm

Θ = 2 radians

Putting values in formula:

L = r  Θ

L = 5 * 2

L = 10 cm

So, the length L is 10 cm

Final answer:

The length of the arc subtended by a central angle of 2 radians in a circle of radius 5 cm is 5 cm.

Explanation:

The length of an arc subtended by a central angle can be found using the formula:

Length of arc = (central angle / 2π) × circumference of the circle

In this case, the central angle is 2 radians and the radius of the circle is 5 cm. The circumference of the circle is given by 2πr, where r is the radius. So, the length of the arc can be calculated as:

Length of arc = (2 / 2π) × (2π × 5) = 5 cm

let's firstly convert the mixed fractions to improper fractions, and then add them up.

[tex]\bf \stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}}~\hfill \stackrel{mixed}{7\frac{2}{3}}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}+\cfrac{23}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~+~~(2)23}{6}}\implies \cfrac{51+46}{6}\implies \cfrac{97}{6}\implies 16\frac{1}{6}[/tex]

Answer:

Option C.

The measure of the complement angle is [tex]18\°[/tex]

Step-by-step explanation:

Let

x-----> the angle

we know that

The complement of an angle is equal to [tex](90-x)\°[/tex]

The supplement of an angle is equal to [tex](180-x)\°[/tex]

we have

The complement of an angle is one-sixth the measure of the supplement of the angle

[tex](90-x)\°=(1/6)(180-x)\°[/tex]

solve for x

[tex](540-6x)\°=(180-x)\°\\ (6x-x)=(540-180)\°\\ (5x)=(360)\°\\ x=72\°[/tex]

Find the measure of the complement angle

[tex](90-x)\° ----> (90-72)=18\°[/tex]

Answer:

Option C. 18

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]-x^2-9\geq0\qquad\text{change the signs}\\\\x^2+9\leq0\\\\\text{the parabola}\ x^2\ \text{is op}\text{en up and shifted 9 units up. Therefore is whole}\\\text{over the x-axis (only positive values)}.\\\\\bold{CONCLUSION}:\\\\\bold{no\ solution}[/tex]

Answer:

[tex]226.08\ in^{2}[/tex]  or  [tex]72\pi\ in^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of a cylinder ( curved area of the vase) is equal to

[tex]LA=2\pi rh[/tex]

we have

[tex]r=6/2=3\ in[/tex] ------> the radius is half the diameter

[tex]h=12\ in[/tex]

substitute the values

[tex]LA=2\pi (3)(12)=72\pi\ in^{2}[/tex] -----> exact value

assume

[tex]\pi=3.14[/tex]

[tex]72(3.14)=226.08\ in^{2}[/tex] ----> approximate value

Answer:

Your answer will be C. y= 4x-1

Step-by-step explanation:

On the x value side, the numbers represent what to fill in x with, and y should be the output of it.

For example :

4(1) = 4 - 1 = 3

4(2) = 8 - 1 = 7

4(3) = 12 -1 = 11

Hope this helps and was correct

This  y = 4x-1, equation is  represented by the table

On the x value side, the numbers represent what to fill in x with, and y should be the output of it.

For example :

4(1) = 4 - 1 = 3

4(2) = 8 - 1 = 7

4(3) = 12 -1 = 11

The correct answer is option C.

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The answer is (-4,3) so C

Answer:

[tex]\boxed{\text{c) (-4, 3)}}[/tex]

Step-by-step explanation:

When you reflect a point (x, y) across the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign: it becomes (-x, y).

Thus, if a point A, say, (4, 3) is reflected across the y-axis, its reflection A' is at

[tex]\boxed{\textbf{(-4, 3)}}[/tex]

Answer:

B

Step-by-step explanation:

it is 64 units so 8 units long each

Answer:

B) (21, -14) and (21, -22)

Step-by-step explanation:

Given,

The area of the square = 64 square unit,

Let x be the side of the square,

[tex]\implies x^2 = 64[/tex]

[tex]\implies x = 8[/tex]

Hence, the side of the square = 8 unit,

⇒ The distance between the adjacent vertices in the square = 8 units,

By the distance formula,

The distance between (3, -35) and (3, -28) is,

[tex]\sqrt{(3-3)^2+(-28-(-35))^2[/tex]

[tex]=\sqrt{0+(-28+35)^2}[/tex]

[tex]=\sqrt{7^2}[/tex]

[tex]=7\neq 8[/tex]

Thus, (3, -35) and (3, -28) can not be the vertices of the square.

The distance between (21, -14) and (21, -22) is,

[tex]\sqrt{(21-21)^2+(-22-(-14))^2[/tex]

[tex]=\sqrt{0+(-22+14)^2}[/tex]

[tex]=\sqrt{8^2}[/tex]

[tex]=8[/tex]

Thus, (21, -14) and (21, -22) are the vertices of the square.

The distance between (32, -42) and (32, -7)  is,

[tex]\sqrt{(32-32)^2+(-7-(-42))^2[/tex]

[tex]=\sqrt{0+(-7+42)^2}[/tex]

[tex]=\sqrt{35^2}[/tex]

[tex]=35\neq 8[/tex]

Thus, (32, -42) and (32, -7)  can not be the vertices of the square.

The distance between  (74, 19) and (82, 27) is,

[tex]\sqrt{(82-74)^2+(27-19)^2[/tex]

[tex]=\sqrt{8^2+8^2}[/tex]

[tex]=\sqrt{64+64}[/tex]

[tex]=\sqrt{128}[/tex]

[tex]=8\sqrt{2}\neq 8[/tex]

Thus, (74, 19) and (82, 27) can not be the vertices of the square.

Answer:

6,24

Step-by-step explanation:

6,24^2-16= 22,9376 -> 23

Answer:

3. Additive

4. [tex]x<2[/tex]

5. Graph the linear line. Then, make the line dotted and shade below the line.

Step-by-step explanation:

3. Adding -15 to both sides to isolate the variable.

4.

[tex]-3x+8>2x-2\\5x<10\\x<2[/tex]

Answer: 80 feet

Step-by-step explanation:

10 yard= 30 feet

2[l + b]

2{30+10}

Answer:

60+6= 66, 66/3= 22 in 6 years time his father will be 44 years. now his father age will 38 and George age will be 22

The present age of the father is 42 years and George is 18 years.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the sum of the present ages of George and his father is 60 years. In 6 years his father will be twice as old as George will be.

Make the two linear equations and solve them to get the present ages.

G + F = 60

2 ( G + 6 ) = F + 6

2G + 12 = F + 6

2G + 12 = 60 - G + 6

3G = 54

G = 18 years

Father's age will be,

F = 60 - 18

F = 42 years

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Answer:

B

Step-by-step explanation:

To rationalise the denominator.

Multiply the numerator/denominator by the radical on the denominator.

The radical on the denominator is [tex]\sqrt{11}[/tex], thus

Multiply the fraction by

[tex]\frac{\sqrt{11} }{\sqrt{11} }[/tex] → B

The expression (√11 /√11 ) needs to be multiplied to rationalize the denominator.

Those numbers which can be written in the form p/q such that q > 0 ae called Rational Numbers.

The expression given is

( 2 √10) /( 3 √11 )

To rationalize the denominator , the radical √11 needs to be rationalize

( 2 √10) /( 3 √11 ) * (√11 /√11 )

(2√110) / 33

Therefore (√11 /√11 ) needs to be multiplied to rationalize the denominator.

Option B is the answer.

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Answer:

5/51

Step-by-step explanation:

The probability of Kevin choosing a white sock on the first pick, there are 6 white socks and 18 socks total so the chances are 6/18. But 6/18 simplified is 1/3. On the second choice he has to pick another sock and there are 5 left out of 17 socks total remaining. So the chances of him picking another sock are 5/17. If you multiply 1/3 by 5/17 you will end up with your answer, 5/51.

Probabilities are used to determine the chances of an event.

The given parameters are:

[tex]\mathbf{White = 6}[/tex]

[tex]\mathbf{Black = 4}[/tex]

[tex]\mathbf{Grey = 3}[/tex]

[tex]\mathbf{Red = 5}[/tex]

So, the total is:

[tex]\mathbf{Total = 6 + 4 + 3 + 5}[/tex]

[tex]\mathbf{Total = 18}[/tex]

The probability that both selections are white socks is:

[tex]\mathbf{Pr = \frac{White}{Total} \times \frac{White - 1}{Total - 1} }[/tex]

1 is subtracted from the fractions of the second factor, because it is a selection without replacement.

So, we have:

[tex]\mathbf{Pr = \frac{6}{18} \times \frac{6 - 1}{18 - 1} }[/tex]

[tex]\mathbf{Pr = \frac{1}{3} \times \frac{5}{17} }[/tex]

So, we have:

[tex]\mathbf{Pr = \frac{5}{51} }[/tex]

Hence, the probability that both selections are white socks is 5/51

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Answer:

$66.50

Step-by-step explanation:

lets break this down a bit:

the tickets are $16 each

there is an additional $2.50 added when tickets are bought online, its a one time fee and does not apply to every ticket

n represents the amount of tickets bought

you're on the right track so far, the expression is as follows:

16n +2.50   <---n is placed next to the 16 because we are calculating the amount of tickets bought and their price plus the one time service fee of $2.50

we are then told that 4 tickets were bought

in this expression, n = 4, so we substitute 4 into the equation for n

16(4) + 2.50

16 x 4 = 64

instead of multiplying like you did on the worksheet, you would add since the original expression we wrote plus 2.50, not times 2.50

64 + 2.50 = 66.50

so, the total price for 4 tickets bought online is $66.50

you were on the right track! let me know if you need anything else cleared up about expressions

Answer:

Option D. minor arc

Step-by-step explanation:

we know that

In a circle the measure of minor arc plus the measure of major arc is equal to 360 degrees

The measure of minor arc is less than 180 degrees

The measure of major arc is greater than 180 degrees

In this problem

Arc BDC is a major arc

Arc BC is a minor arc

Answer:

D

Step-by-step explanation:

Given that the ratio of side lengths = 8 : 3, then

ratio of volumes = 8³ : 3³ = 512 : 27 → D

ANSWER

The correct answer is option D.

EXPLANATION

The given pyramids are similar and the side lengths are in the ratio 8:3

Volume is in cubic units, therefore the volume of the two similar pyramids are in the ratio;

[tex] {8}^{3} : {3}^{3} [/tex]

This simplifies to

[tex]512 : 27[/tex]

The correct answer is option D.

A unit circle has radius 1, and thus circumference [tex]2\pi[/tex].

Since an angle of [tex]\frac{\pi}{4}[/tex] is one eighth of a whole turn, the length of an arc that subtends an angle of  [tex]\frac{\pi}{4}[/tex] radians will be one eighth of the whole circumference:

[tex]l = \dfrac{2\pi}{8} = \frac{\pi}{4}[/tex]

In fact, the radians have the property that, in the unit circle, the length of the arc is exactly the measure of the angle. In general, you have

[tex]l = r\cdot\alpha[/tex]

where l is the length of the arc, r is the radius and [tex]\alpha[/tex] is the angle in radians. So, if [tex]r=1[/tex], you have [tex]l=\alpha[/tex]

The length of an arc in a unit circle that subtends an angle of π/4 radians is simply π/4, because in a unit circle, the length of an arc is the angle (in radians) multiplied by the radius (which is 1).

In Mathematics, particularly in the study of a unit circle, an interesting concept to learn is the length of an arc that subtends an angle. Here, the given angle is π/4 radians. In a unit circle, the length of an arc can be calculated by simply multiplying the angle (in radians) by the radius of the circle. In this case, since the radius is 1 (as it's a unit circle), the length of the arc is simply the measurement of the angle in radians, which is π/4.

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(N-2)180

(130-2)180

128 x 180

23040

Final answer:

The sum of the interior angles of a convex 130-gon is 23040 degrees, calculated using the formula S = (n - 2) × 180° with n equal to the number of sides.

Explanation:

The sum of the interior angles of any polygon can be calculated by using the formula S = (n - 2) × 180°, where S is the sum of the interior angles and n is the number of sides in the polygon. In the case of a convex 130-gon, with n = 130, the calculation would be S = (130 - 2) × 180°. This simplifies to S = 128 × 180°, which is S = 23040°. Therefore, the sum of the interior angles of a convex 130-gon is 23040 degrees.

Answer:

6x(x - 2)

Step-by-step explanation:

Find the common factors of 6x² - 12x, which is 6x.

Answer:

1. Not simplified correctly. It  is (3/7)x + 1

2. Not simplified correctly. It is (3/x)

3. Not Simplified correctly. I believe it is as simplified as it can get

Step-by-step explanation: When a polynomial is over a denominator, ALL elements of the polynomial is affected

Point C is the answer

Answer:

Point C

Step-by-step explanation:

Answer: x² + y² + 16y - 242 = 0

Step-by-step explanation: The equation of circle is given in the form (x -a)² + (y - b)² = r², where (a,b) is the center of the circle and r is the radius. But r is the distance from (0,-8) to (9,7)

the equation is (x-0)² + (y + 8)² = r²

                           x² + (y + 8)² = r²

hence r² = (x₁ - x₂)² + (y₁ - y₂)²

          r² = (0 - 9)² + (-8 - 7)² = 81 + 225 = 306

hence the equation is

                x² + y²+16y+64 = 306

                x² + y² + 16y - 242 = 0                        

Answer: You take $18.80 divide by 2 =$9.40 then $18.80+$9.40=$28.20

$28.20 x's 5.5=$$155.10

$18.80 x's 40=$752.00

then add 752.00+155.10=$907.10

Step-by-step explanation:

Answer:

95086

Step-by-step explanation:

We let the population one year ago be x, the relationship between x and the present population is;

(105/100)*x = 104832

This is because the present population exceeds the population one year ago by 5%.

therefore,

1.05*x =  104832

x = 99840

We now let the population two years ago be y, the relationship between y and the population one year ago is;

(105/100)*y = 99840

This is because the population one year ago exceeds the population two years ago by 5%.

Therefore,

1.05*y = 99840

y = 95085.7

Rounding to the nearest whole number;

95086

Answer:

7

Step-by-step explanation:

Answer:

an = -773 + 48n

Step-by-step explanation:

an = a + (n -1)d

a15 = a + (15 - 1)d = -53

         a + 14d = -53 .........1

a16 = a + (16 - 1)d = -5

         a + 15d = -5 ............2

subtract equation 2 from 1

a - a + 14d - 15d = -53 + 5

-d = -48

d =48

substitute d =48 in equation 1

a + 14(48) = -53

a +672 = -53

a = -53 -672

a = -725

an = -725 + (n -1)48

an = -725 + 48n - 48

an = -773 +48n

Final answer:

Eudora's balance at the end of the year will be $7,750.03.

Explanation:

To calculate Eudora's balance at the end of the year, we need to calculate the interest for each period separately and then add them together. The credit card offers an introductory APR of 7.8% for the first 3 months, so we will calculate the interest for this period first.

Step 1: Calculate the interest for the introductory period:

Interest = Balance * Introductory APR * (Introductory Period / 12) = $6400 * 0.078 * (3/12) = $156.00

Since the card compounds interest monthly, we need to calculate the interest for each month of the remaining 9 months at the standard APR of 26.5%:

Step 2: Calculate the interest for each month of the remaining 9 months:

Interest for each month = Balance * Standard APR / 12 = $6400 * 0.265 / 12 = $139.67

Step 3: Add up the interest for the introductory period and the remaining 9 months:

Total interest = Interest for the introductory period + (Interest for each month * Number of months) = $156.00 + ($139.67 * 9) = $1,350.03

Step 4: Calculate the final balance at the end of the year:

Final balance = Balance + Total interest = $6400 + $1,350.03 = $7,750.03

Therefore, Eudora's balance at the end of the year will be $7,750.03.