Who is the Father of Algebra ?

The given expression is equivalent to -1 + cos θ. Option B

Trigonometry can be seen as the branch of mathematics that deals with the relations of the sides and angles of triangles and with the functions of any angles.

The problem deduced from the information is;

[tex]-tan\frac{\alpha }{2} ( -5 sin\alpha)[/tex]

It is simplified thus

[tex]\frac{\frac{sin\alpha }{2} }{\frac{cos \alpha }{2} }[/tex] × [tex](- 2 sin\frac{\alpha }{2} * cos \frac{\alpha }{2} )[/tex]

We then have

[tex]-1 + cos \alpha[/tex]

Therefore, the given expression is equivalent to -1 + cos θ. Option B

The complete question is;

Which expression is equivalent to (tangent (StartFraction theta Over 2 EndFraction) ) (negative sine theta)?

– 1 – cos(ϴ)

– 1 + cos(ϴ)

1 + cos(ϴ)

1 – cos(ϴ)

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Answer:

5

Step-by-step explanation:

Original equation:

[tex]7(2)^x=224[/tex]

Divide both sides by 7

[tex]2^x=32[/tex]

Rewrite in log

[tex]log_232=x[/tex]

You can do mental math to realize this equals 5, or plug this into your calculate (if it allows you to set the base), but if you can't do either, you can use the change of base formula:

[tex]log_ba=\frac{log (a)}{log(b)}[/tex]

You get:

[tex]log_232=\frac{log(32)}{log(2)}[/tex]

When you calculate using a calculator you should get 5

Answer: x = 5

Step-by-step explanation:

[tex]7(2)^x=224[/tex]

start by dividing 7 from both sides

[tex]\frac{7(2)^x}{7} =\frac{224}{7}[/tex]

[tex]2^x=32[/tex]

take the log of both sides

[tex]log(2^x) = log(32)[/tex]

move the x to the left of the log

[tex]xlog(2) = log(32)[/tex]

divide both sides by log(2)

[tex]x=\frac{log(32)}{log(2)}[/tex]

use change-of-base formula

[tex]\frac{log(a)}{log(b)} =logx_{b} (a)[/tex]

[tex]x = log_{2} (32)[/tex]

since [tex]2^5 = 32[/tex], x = 5

The probability of being dealt a five card hand that is two pair from a well shuffled standard deck of cards is 40.

According to the statement

I have 10 starting cards, from Ace to 10, and 4 suits,

and by this way we get the 40 subsets and because of these subsets there is a probability becomes 40.

So, The probability of being dealt a five card hand that is two pair from a well shuffled standard deck of cards is 40.

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The values of x, EF, and FG from the line segment are 10, 8 and 15 respectively.

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

EG = EF + FG (segment addition postulate)

Hence:

23 = (2x - 12) + (3x - 15)

x = 10

EF = 2(10) - 12 = 8

FG = 3(10) - 15 = 15

The values of x, EF, and FG from the line segment are 10, 8 and 15 respectively.

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The ratio of the number of children to the number of adults in this group is 2 : 3

The admission is given as:

Children=4

Adult = 6

Express as ratio

Ratio = Children : Adult

This gives

Children : Adult = 4 : 6

Simplify

Children : Adult = 2 : 3

Hence, the ratio of the number of children to the number of adults in this group is 2 : 3

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Answer:

(1, 0 )

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then

y = [tex]log_{3}[/tex] (x + 2) - 1

to find the zero let y = 0 , that is

[tex]log_{3}[/tex] (x + 2) - 1 = 0 ( add 1 to both sides )

[tex]log_{3}[/tex] (x + 2) = 1 , then

x + 2 = [tex]3^{1}[/tex] = 3 ( subtract 2 from both sides )

x = 1

the zero is (1, 0 )

Answer:

Step-by-step explanation:

to be honest, I have no idea what topic this is anymore but to solve it plug in 5 for f(x) and then use -3 for x and then simplify for B.

A)1/4

Step-by-step explanation:

1/2=2/4

2/4+1/4=3/4

4/4-3/4=1/4

Applying the centroid theorem, the length of BO is: A. 2.2.

Based on the centroid theorem, the length of BO equals two third of the length of BY.

That is:

BO = 2/3(BY)

Plug in the values

BO = 2/3(3.3)

BO = 2.2.

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The function in the given graph obtained from the y and x-intercept is the option;

[tex]y = cot \left( \frac{3}{4} \cdot \left(x - \frac{\pi}{6} \right)\right)[/tex]

From the given graph, we have;

Similarly;

The above relationship corresponds with the following function;

[tex]y = cot \left( \frac{3}{4} \cdot \left(x - \frac{\pi}{6} \right)\right)[/tex]

The function graphed is therefore;

[tex]y = cot \left( \frac{3}{4} \cdot \left(x - \frac{\pi}{6} \right)\right)[/tex]

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Answer:

Step-by-step explanation:

Answer: 400 520<15x+400x 15x+400>520

Step-by-step explanation:

The cyclist that will come to stop first when the brake is applied, is the cyclist with lesser mass which is Cyclist B because of its lesser inertia.

The law of inertia states that an object at rest or uniform motion in a straight line will continue in that path unless acted upon by an external force.

Inertia depends on mass of the object, the more massive an object is, the more reluctant it will be to stop and vice versa.

Thus, the cyclist that will come to stop first when the brake is applied, is the cyclist with lesser mass which is Cyclist B because of its lesser inertia.

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Answer:

Step-by-step explanation:

add all sides, the top is the same as the bottom, (the side of 6 must be counted only once).

[2 * ( 18 + 3 + 7)] + 6 =  

(2 * 28) + 6  =

56 + 6 =

62

62 m is the parameter of the given figure.

The perimeter of a two-dimensional form is the space surrounding it. It represents the total length of the shape's sides. The units used to measure the sides of the form, such as meters, centimeters, inches, or feet, determine the units used to measure the perimeter.

In a statistical context, parameters often refer to the unknown values of a probability distribution. In this case, parameters can be estimated using statistical methods such as maximum likelihood estimation or Bayesian inference.

Add all sides, the top is the same as the bottom, (the side of 6 must be counted only once).

[2 * ( 18 + 3 + 7)] + 6 =  

(2 * 28) + 6  =

56 + 6 =

62

The perimeter of the given arrow is 62 m.

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The graph is shown in the attached image.

Answer:

(3,-2)

Step-by-step explanation:

See attached image.

The first five months Paul paid  and in the next seven months he paid 24.

Discounts are defined as lowered prices or the sale of an item for less than it would typically cost. The fundamental formula for calculating a discount is to multiply the original price by the given percentage rate in decimal form. We must deduct the discount from the original price to determine the item's sale price. A discount is an amount that is subtracted from the regular price of an item.

Paul represent his plan in the form of equation:

[tex]5 x+7(x+8.50)=245.50[/tex]

Where x  is an amount for the first [tex]5[/tex] months that is paid by Paul after the discount and [tex](x+8.50)[/tex]  is an amount for the next [tex]7[/tex] month after discount.

[tex]&\Rightarrow \quad 5 x+7 x+59.50=245.50 \\&\Rightarrow \quad 12 x=186 \\&\Rightarrow \quad x=\frac{186}{12} \\&\Rightarrow \quad x=15.50\end{aligned}[/tex]

For the next 7 month:

[tex](x+8.50)=(15.50+8.50)=\$ 24[/tex]

Therefore, The first [tex]5[/tex] months Paul paid $ 15.50, and in the next [tex]7[/tex] months he paid $ 24.

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Answer:

Points shouldn't be connected by straight lines but rather a curve

Step-by-step explanation:

None of the points seem to be incorrect, and the x and y-axis are labeled correctly as well as the points, the only issue I would say there is, is that this is a quadratic equation, so Brogan shouldn't be drawing straight lines between points, but rather a curve.

Fractions are written as the ratio of two integers. The sum of 5 3/10 and 2 1/5 is 7 1/2

Fractions are written as the ratio of two integers. Given the following expression

5 3/10 + 2 1/5

convert the mixed into improper fraction

53/10 + 11/5

Find the LCM

53+22/10

75/10

7.5

Hence the sum of 5 3/10 and 2 1/5 is 7 1/2

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Answer:

See image below

Step-by-step explanation:

Every point starting at the y axis and extending left to ∞ represents the inequality x ≤ 0

Using the latest observation in a sequence of data to forecast the next period is a naïve forecast. Option C

What is a  naïve forecast?

A naïve forecast is a forecasting technique in which the last sequence of data are used for the next period's forecast without predictions or adjusting the factors that could affect it.

Forecasts that are  produced using a naïve approach are equivalent to the final observed value gotten.

Thus, using the latest observation in a sequence of data to forecast the next period is a naïve forecast

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The height of the cone is 4√2  inches.

The circumference of the base of each cone will be the arc length of one of the sectors  

= 2 [tex]\pi[/tex] (6)  / 3  

=  4 [tex]\pi[/tex]  inches

So, the radius, r, of each cone (in inches) is given  by :

4pi  =  2 [tex]\pi[/tex] * r

4  = 2r

2  = r  

Using the Pythagorean Theorem, the cone height, h, is given by :

h  = √[ slant height^2  - radius^2 ]  

=  √ [ 6^2  - 2^2 ]

= √32  

=  4√2  inches

In arithmetic, the Pythagorean theorem, or Pythagoras' theorem, is a essential relation in Euclidean geometry a few of the three facets of a right triangle. It states that the vicinity of the square whose facet is the hypotenuse is identical to the sum of the regions of the squares on the other two facets.

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Answer:

1

Step-by-step explanation:

f(x) = x² - 8x - 4 ← is in standard form

with leading term x² and so

leading coefficient is the coefficient of the x² term, that is 1

Answer:

1) 3 more people

2) 9 teams

Step-by-step explanation:

The divisibility rule for 5 is that it must end in 5 and 0

so the next one is 45, so 3 more people

----------------------- ----------------------- ----------------------- -----------------------

45/5=9 teams

Answer: (2;-9).

Step-by-step explanation:

[tex]\left \{ {{2x-y=13\ |*(-3)} \atop {6x+5y=-33}} \right. \ \ \ \ \left \{ {{-6x+3y=-39} \atop {6x+5y=-33}} \right. .\\Summing\ up\ these\ equations:\\8y=-72\ |:8\\y=-9.\\2x-(-9)=13\\2x+9=13\\2x=4\ |:2\\x=2.[/tex]

The required ratio is give by $40/m, 4 miles/min, 30 mile/liter. .

Let, just assume a vehicle is given an economy of $280 of 7m.

The ratio can be defined as the comparison of the fraction of one quantity towards others. E.g.- water in milk.

Now,
The ratio can be given as for economy = 280/7
=  $40/m

here for new values,
suppose the vehicle travel for 40miles in 10 mins
ratio = 40/10= 4 miles/min
and vehicle consumes 2 liter fuel on 60 miles of distance ratio can be given as
ratio = 60/2 = 30 mile/liter.

Thus the required ratios can be given as $40/m, 4 miles/min, 30 mile/liter.

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Answer:

3,4 and 5 is the ratio between the sides of a right triangle, therefore also the multiples (6-8-10 .... 9-12-15 etc.)

Step-by-step explanation:

3,4 and 5 is the ratio between the sides of a right triangle, therefore also the multiples (6-8-10 .... 9-12-15 etc.)