Are -345° and 2185° co-terminal?​

Answer:

1032x

Step-by-step explanation:

[tex]3x+4x+\cdots+43x=x(3+4+\cdots+45) \\ \\ =43x\left(\frac{45+3}{2} \right) \\ \\ =43(24x) \\ \\ =1032x[/tex]

Answer:

634342

FACTOR:

2 x 317171

The unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].

To find the unit vector:

Differentiate y = x² with respect to x.

We get, dy/dx = 2x.

The slope of a tangent:

[tex]\mathrm{P}(2,4)=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{atP}(2,4)}=2 \times 2=4[/tex]

Tangent P equation is:

y = 4x is the equation of a line passing through the origin O and parallel to the tangent at P.

This line's direction ratios are 1, 4, and 0, and its direction cosines are:

[tex]\pm \frac{1}{\sqrt{1^2+4^2+0^2}}, \pm \frac{4}{\sqrt{1^2+4^2+0^2}}, 0\\\pm \frac{1}{\sqrt{17}}, \pm \frac{4}{\sqrt{17}}, 0[/tex]

The number of unit vectors parallel to the tangent line at P(2,4) is:

[tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\bar{j}\right)[/tex]

Therefore, the unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].

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The correct question is given below:
Find the unit vectors that are parallel to the tangent line to the parabola y=x^2 at the point (2, 4).

Answer:

8−5=3

Step-by-step explanation:

Answer: B (18.5b-21.2)

The required expression −18.5b − 21.2 is equivalent to the given expression which is the correct answer that would be option (A).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have been given the expression below as

5(−2.3b − 4.1) − (7b + 0.7)

Open the parentheses and apply the distributive property of multiplication,

⇒ −2.3b × 5 − 4.1 × 5 − 7b - 0.7

⇒ -11.5 - 20.5 − 7b - 0.7

Rearrange the likewise terms and apply the arithmetic operation,

⇒ −18.5b − 21.2

Hence, the required expression −18.5b − 21.2 is equivalent to the given expression.

Thus, the correct answer would be an option (A).

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The cost for her to purchase the fence is $108.

Since she wants to put a wire fence around her garden which is 12 feet long and 6 feet wide, the total perimeter will be:

= 2(length + width)

= 2(12 + 6)

= 36 feet

Therefore, the cost will be:

= Total feet × Amount

= 36 × $3

= $108

Therefore, the cost for her to purchase the fence is $108.

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The value of y for the given input x=7 is 15.

The given function is  y=2x+1.

We need to graph the given function.

Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, need some skill and some mathematical concepts to understand.

Now,

Graph the line using the slope and y-intercept, or two points.

Slope: 2

y-intercept: (0, 1)

Plot the points (0, 1) and (1, 3)

The value of y for x=7 is y=2(7)+1=15

Therefore, the value of y for the given input x=7 is 15.

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Answer:

16 each

Step-by-step explanation:

Since you didn't say how much of the yield Jacob gave to the restaurant or the neighbor, I'm going to assume he kept an even share and gave them each the same share.

Assuming that, we would have to divide his harvest by 3

48/3 = 16

this means that 16 went to his neighbor, 16 to the restaurant and 16 were saved for himself.

Hope this helps! ^^

Answer:

It has 1 line off symmetry.

Step-by-step explanation:

it has one straight from the top point all the way down.

The number of miles in a day at which the rental costs for Company A and Company B are the same will be 10 miles.

Let the number of miles be represented by x.

Therefore the equation for the first company will be 90 + 0.4m

The equation for the second company will be 60 + 0.7m

Therefore, we will equate them. This will be:

90 + 0.4m = 60 + 0.7m

Collect like terms

90 - 60 = 0.7m - 0.4m

0.3m = 30

m = 30/0.3

m = 10

The number of miles will be 10 miles.

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-14 is the 81th term.

The first step is to determine the relationship between the numbers in the sequence. When examined, it can be seen that the number decline by 1/5.

To confirm : 2 1/5 - 2 = 1/5

The linear equation that can be used to determine the position of a number is:

2 1/5 - 1/5(x)

Where x is the position of the number

For example, the third number is

2 1/5 - 1/5(3)  = 1 4/5

Given the number, the position of the number can be determined using the above linear equation:

-14 = 2 1/5 - 1/5(x)

In order to determine the value of x, take the following steps:

Multiply through by 5

(-14 x 5) = (11/5 x 5) - (x / 5 x 5)

-70 = 11 -x

Combine similar terms: 70 + 11 = x

Add similar terms: x = 81

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Answer:

a = 6

Step-by-step explanation:

Hello!

First, let's isolate the Absolute Value bracket.

Based on the definition of Absolute value, the outcome should always be a positive number. Therefore, if the product, 4 - a, is a negative number, it will have no solutions.

That means a has to be greater than 4 for it to be negative. a should be 6.

a = 6

Answer:

5^(1/2)

Step-by-step explanation:

Square root means to the power of (1/2)

cube root means to the power of (1/3)

and so on

You will $0.29, if you will purchase 2 small bags of flour instead of 1 big bag.

For the given question;

The total cost of one big bag that is 10-lb bag of flour = $3.69.

Now, the cost of one small bag that is 5-lb = $1.55.

Thus, the cost for two small bag that is 5-lb = $3.10.

The difference in the cost = big bag cost - 2 small bag costs.

The difference in the cost = $3.69 - $3.10

The difference in the cost = $0.29.

Thus, you will save $0.29 for the purchase of 2 small bags of floor instead of one big bag.

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Answer:

12*10^4 lbs.

Step-by-step explanation:

This is the correct answer because you have to count using scientific notation by seeing the amount of times the decimal point has moved to the left which makes it positive.

The total weight of the two animals is 12x10⁴ lbs if the approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

The approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.

The total weight = 5.36 x 10⁴ + 6.2 x 10⁴

The total weight = (5.36+ 6.2)10⁴

The total weight = 11.56x10⁴

Or

The total weight = 12x10⁴ lbs

Thus, the total weight of the two animals is 12x10⁴ lbs if the approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.

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Camille need 5 balls of wool to crochet a blanket for her new baby cousin.

Unitary Method:

Unitary method is the method in which the value of a unit quantity is first calculated to get the value of any quantity is called the unitary method.

Given,

Camille wants to crochet a blanket for her new baby cousin. her pattern calls for 900 yards of thick, soft wool. she already has 200 feet of wool left from another project. at the craft store, she notices that each ball has 500 feet of wool.

Here we need to find the number of wool balls she need.

Let us consider x be the amount of wool balls she need.

Then,

wool needed - 900 yards

We know that,

1 yard = 3 feet

Then 900 yards will be equal to

=>  900 x 3 = 2700 feet

Now, She has - 200 feet

And we know that,

each ball at store contains - 500 feet

So it can be written as,

=> 200 + 500x = 2700

=> 500x = 2500

=> x = 2500/500

=> x = 5

Hence she need to buy 5 balls of wool from the store to get the required length of wool.

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The location of the point A' after dilation is; A'(-10, 15)

We are given that the Quadrilateral BASE is located at the following coordinates;

B(3, 4), A(-2, 3), S(4, 0), and E(-2, 5).

Now, if it is dilated by a scale factor of, it means that each of the coordinates values would be multiplied by 5 to get the new coordinates as;

B'(15, 20), A'(-10, 15), S'(20, 0), and E'(-10, 25).

Thus, we can conclude that the location of the point A' after dilation is; A'(-10, 15)

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The value of x in the figure is 5

From the figure, we have the following parameters are:

NM = 9

ML = 2x - 7

NL = x + 7

This means that

NL = NM + ML

So, we have:

x + 7 = 9 + 2x - 7

Collect the like terns

x - 2x = 9 - 7 - 7

Evaluate

-x = -5

This gives

x = 5

Hence, the value of x in the figure is 5

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The required coordinates are (6, 5).

Let A denotes the point (4, 3), and B denotes the point (9, 8).

Let C denote the point which divides the line segment AB in the ratio of 2:3.

The distance between A(4, 3) and B(9, 8) is given by

AB = √{(x₂ - x₁)² + (y₂ -y₁)²}

= √{(9 - 4)² + (8 - 3)²

= √{5² + 5²}

= √(2×5²)

= 5√2

We have AC + BC = AB

AC and BC are in the ratio 2:3.

Therefore 2x + 3x = AB

⇒5x = 5√2

⇒x = √2.

Therefore, AC = 2√2 and BC = 3√2.

Using the distance formula,

AC = √{(x - 4)² + (y - 3)²}

⇒ 2√2 = √{(x - 4)² + (y - 3)²}

⇒ √(2² + 2²) = √{(x - 4)² + (y - 3)²} (taking the 2 inside the square root.)

⇒ x - 4 = 2 ⇒ x = 6

⇒ y - 3 = 2 ⇒  y = 5.

Therefore the required coordinates are (6, 5).

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Answer:

D. Fail to reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.

Step-by-step explanation:

Let μ = mean time to complete a role-playing game.

The company claims that their role-playing games take over 65 hours to complete, so the hypotheses are:

H₀: μ = 65       H₁: μ > 65

Therefore, this is a one-tailed test.

The significance level is 1%, so α = 0.01.

Find the value of the test statistic (z):

[tex]\textsf{sample mean }\overline{x}=63,\quad \sigma=10, \quad n=300[/tex]

[tex]\implies z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}=\dfrac{63-65}{10 / \sqrt{300}}=-2\sqrt{3}=-3.4641...[/tex]

Using the “Percentage Points of The Normal Distribution” table, the critical value is z = 2.3263 meaning the critical region is Z > 2.3263.

Since z = -3.4641... < 2.3263, the observed value of the test statistic lies outside the critical region.  Therefore, the result is not significant.

Conclusion

There is sufficient evidence at the 1% level of significance to fail to reject H₀ and to oppose the alternative hypothesis that the mean time to complete the role-playing game is more than 65 hours.

Answer:

A) Reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.

Step-by-step explanation:

The test statistic needs to fall within the rejection regions that are above and below the critical z-score associated with a 1% level of significance in order to reject the null hypothesis. Otherwise, we will fail to reject the null hypothesis.

Answer:

35

Step-by-step explanation:

The value of given equation i.e. [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]

Given a equation i.e.[tex]\frac{m-1}{m}[/tex]=3 and asked  to calculate the value of the equation  [tex]m^{3} -\frac{1}{m^{3} }[/tex]

To calculate the value of   [tex]m^{3} -\frac{1}{m^{3} }[/tex] , Need to use various operations like subtraction and division)

Given .[tex]\frac{m-1}{m}[/tex]=3

⇒m-1=3m ( cross multiplies 3 and m)

⇒2m=-1( subtraction is used)

⇒m=-[tex]\frac{1}{2}[/tex]( division is used)

Thefore the value of m in the given equation i.e.[tex]\frac{m-1}{m}[/tex]=3 is -[tex]\frac{1}{2}[/tex]

⇒ [tex]m^{3} -\frac{1}{m^{3} }[/tex]

Here the value of m =-[tex]\frac{1}{2}[/tex]

Substituting the value of m in the given equation

⇒[tex](\frac{-1}{2} )^{3}[/tex]-[tex](-2)^{3}[/tex]

⇒[tex]\frac{-1}{8}[/tex]+8(addition is used)

⇒[tex]\frac{64-1}{8}[/tex]

⇒[tex]\frac{63}{8}[/tex]

Therefore, the value of the given equation i.e.  [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]

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Answer:

It is the last answer [tex]\frac{16\pi }{3}[/tex]

Step-by-step explanation:

the volume of the cylinder is the area of the base times the height.  The area of a circle is

a = [tex]\pi r^{2}[/tex]  We are give the diameter is 8.  The radius is 1/2 of the diameter so the radius is 4. [tex]4^{2}[/tex] = 16

a = 16[tex]\pi[/tex]  If the cone is 1/3 of that, we divide this answer by 3 to get

a = [tex]\frac{16\pi }{3}[/tex]

Using translation concepts, we have that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is:

g(x) = |x|.

The translated function is:

f(x) = 3|x + 1| - 6.

The multiplication by 3 means that the function was stretched vertically by a factor of 3, hence:

The 3 will make the parent function vertically stretch by a factor of 3.

At x -> x + 1, we have that the function was shifted one unit left, hence:

The x + 1 will make the parent function shift horizontally left 1 unit.

For the subtraction by 6, the function was shifted down 6 units, hence:

The -6 will make the parent function shift vertically down 1 unit.

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The ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

For given question,

We have been given the unit conversion.

A traditional unit of length in Japan is the ken

and 1 ken = 1.97 m

We need to find the the ratios of (a) square kens to square meters.

First we find the square of 1 ken.

⇒ 1 square kens = (1.97 m)²

⇒ 1 square kens = 1.97 × 1.97 m²

⇒ 1 square kens = 3.88 m²                  ..................(1)

And 1 square meters = 1 m²                 ................. (2)

Now we take the ratio of square kens to square meters.

From (1) and (2),

⇒ 1 ken² / 1 m² = 3.88 / 1

⇒ 1 ken² / 1 m² = 3.88

Therefore, the ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

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The G.C.F of the given algebraic expression is; ⁴⁹/₆a xy

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

We are given the algebraic expression;

(3 x y * 4x²y * ¹/₁ * 5x³y ^ z * 4)7a * 1/1 * 7*6

Expanding this further gives;

⁴⁹/₆a((3xy * 4x²y * 20x³y ^ z )

Now, the GCF of the terms inside the bracket would be x y. Thus, expanding the GCF  we have;

⁴⁹/₆a xy((3 * 4x * 20x²y^(z - 1))

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Answer:

give a situation where you are adapted a holistic view in looking at a problem or situation: my own