PLEASE HELP DUE TODAY WILL GIVE BRAINLIEST TO CORRECT ANSWER

After a few mathletes join the team, the team is able to solve 40% more problems per session. Of the team can solve 42 problems per session now, how many problem were they able to solve before the new mathletes joined?

Answers

Answer 1

Step-by-step explanation:

the answer is 16.8 :)hope this helps

Answer 2

Answer: 30 :) have a nice day!!!


Related Questions

Robin can make 8 puppets with the material she already has. For each additional sheet of felt she buys, she can make 5 more puppets. What is an equation that shows how the total number of puppets she can make, y, depends on the number of sheets of felt she buys?

Answers

Let the number of sheet she buy be x.
Therefore the equation is
y = 5x + 8

Hope it helps

divide 7.39 divide 0.72 rounded quotient of the nearest hundredth

Answers

Answer:

10.26 I believe you wanted me to divide 7.39/0.72. If so, you get 10.2638 that rounds to 10.26

Step-by-step explanation:

Can u give me brainliest please

The value of the expression 7.39 ÷ 0.72 is 10.26 to the nearest hundredths.

We have,

Expression:

7.39 ÷ 0.72

Now,

The expression can be written as,

= 7.39 / 0.72 ______(1)

Simplify the numerator and denominator.

Numerator = 7.39 = 739/100 _____(2)

Denominator = 0.72 = 72/100 ______(3)

Now,

From (1), (2), and (3).

7.39 / 0.72

= (739/100) / (72/100)

= 739/100 x 100/72

100 is the common factor so it gets canceled.

= 739/72

= 10.2638888.....

Rounding to the nearest hundredths.

= 10.26

Thus.

The value of the expression 7.39 ÷ 0.72 is 10.26 to the nearest hundredths.

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Compute the exact value of the height h of the square-based straight pyramid, given that the base is a square with sides 34 feet long, and all other edges are 50 feet long.

Answers

Answer:

  31√2 feet

Step-by-step explanation:

The height can be found using the Pythagorean theorem. The height of the pyramid will be the height of the right triangle whose sides are half the diagonal of the square base, the distance from the base to the peak, and the edge from the peak back to the corner of the base.

Setup

Let h represent the height of the pyramid. The diagonal of the square base will be √2 times the side of the base. So, half the diagonal will be 17√2 ft. The Pythagorean theorem tells us ...

  h² +(17√2)² = 50²

Solution

Subtracting the constant on the left gives ...

  h² = 2500 -578 = 1992

  h = √1992 = 31√2

The height of the square pyramid is exactly 31√2 feet.

__

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Which graph represents the function f(x) =3(2)*?

Answers

I assume you meant [tex]f(x)=3(2)^x[/tex].


You have a job earning $12.50 per hour, and you receive a raise so that you earn $13.25 per hour. What is the percent change in your salary

Answers

[tex]increase = 13.25 - 12.50 \\ increase = 0.75 \: dollars[/tex]

[tex]12.50 = 100\% \\ 0.75 = x\%[/tex]

[tex]12.50x = 100(0.75) \\ x = \frac{100(0.75)}{12.50} = \frac{75}{12.5} = 6\%[/tex]

Deondra has 57 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 340 square meters. List each set of possible dimensions
(length and width) of the field.

Answers

(L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters. This can be obtained by forming quadratic equation for the data.

 

Calculate the set of possible dimensions (length and width) of the field:

Let length be L and width be W.

Given that,

three sided fence has a length of 57m,

⇒ 2W + L = 57 m ⇒ L = 57 - 2W

the area of the land is 340 square meters

length × width = 340 ⇒ L × W = 340

(57 - 2W)W = 340

57W - 2W² = 340

2W² - 57W + 340 = 0

Solve for W using quadratic formula,

a = 2, b = -57, c = 340

W = (-b±√b²-4ac)/2a  

   = (57±√3249-2720)/4

   = (57±√529)/4

   = (57±23)/4

W = 20 m and W = 8.5 m  

For W=20, L=57-2(20) = 17

For W=8.5, L=57-2(8.5) = 40

Hence (L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters.

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articipation Activity #6
This is similar to Try It #11 in the OpenStax text.
A satellite is rotating around Earth at 0.2 radians per hour at an altitude of 252 km above Earth. If the radius of Earth is 6,378 kilometers, find the linear speed of the satellite in kilometers per hour.



Enter the exact answer.



The linear speed of the satellite is
Number
kilometers per hour.

Answers

The linear speed based on the information is 1326 km/h.

How to calculate the speed?

The radius will be:

= 6378 + 252

= 6630 km

The angular speed is 0.2. The linear speed will be:

= 6630 × 0.2

= 1326 km/h.

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If (x, 68, 85) form a Pythagorean Triple, what is the value of x?

Answers

Answer:

x = 51

Step-by-step explanation:

If (x, 68, 85) form a Pythagorean Triple, what is the value of x?

to solve we again use Pythagoras, x is the smallest number, so 68 is a cathetus and 85 the hypotenuse

x = √(85²- 68²)

x = (7225 - 4624)

x = √2601

x = 51

Answer:

  x = 51

Step-by-step explanation:

The missing value of the Pythagorean triple can be found using the Pythagorean theorem, or it can be found by comparing the values in the triple to known triples.

What are Pythagorean triples?

A Pythagorean triple is a set of integers {a, b, c} that satisfy the equation of the Pythagorean theorem:

  a² +b² = c²

The smallest such triple is {3, 4, 5}. It is also the only triple that is an arithmetic sequence. Other triples of small integers are ...

  {5, 12, 13}, {7, 24, 25}, {8, 15, 17}

There are an infinite number of "primitive" Pythagorean triples, ones that are not multiples of another triple.

What is this triple?

The given values of the triple have the ratio ...

  68/85 = (4·17)/(5·17) = 4/5

Only the values in the {3, 4, 5} triple and its multiples will have this ratio.

The value of x is 3·17 = 51, so the triple is {51, 68, 85}.

  x = 51

__

Additional comments

Any primitive triple will have two odd numbers.

The ratios of numbers in a primitive triple are unique to that triple. That is, the numbers are mutually prime.

For any pair of positive integers m > n, there is a Pythagorean triple {2mn, m²-n², m²+n²}. Such triples will not be primitive if m and n have the same parity.

__

The above triple can be verified using the Pythagorean theorem:

  51² +68² = 2601 +4624 = 7225 = 85²

a weather balloon is released and reaches a maximum altitude of 5000 meters.A week later, the balloon is recovered at 3750 metwrs. What was the change in altitude between the maximum height and the height at which the balloon was recovered

Answers

The change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

How to determine the change

It is important to note that the maximum height is the peak altitude the balloon reached

To find the difference, we use the formula

Change = Maximum height - recovery height

Maximum height = 5000 meters

Recovery height = 3700 meters

Substitute the values

Change = 5000 - 3700

Change = 1300 meters

Thus, the change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

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Which of the following is The function f(x)=2x2−1 is/has

A. order 2 rotational 2 symmetry about the origin
B. symmetry about the y-axis
C. neither symmetric about the y-axis nor has order 2 rotational symmetry about the origin
D. odds a good way to get someone to participate in a group?

Answers

The given function has symmetry about the y - axis.

Symmetry of the Function

If we reflect a function's graph about the y-axis, we will get the same graph since if the function is symmetrical about the y-axis. We can reflect a function about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as the even function and odd function.

The given function is,

f(x) = 2x² - 1

It is an even function since the function remains same for both x and -x.

Putting f(x) = 0, we get,

2x² - 1 = 0

2x² = 1

x² = 1/2

x = ±1/2

⇒ Axis of symmetry is, x=0

Hence, the function f(x) is symmetric about y-axis.

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I need answers please and thank you!

Answers

If h have 2 to be left it will be 2 to the power of 5

Which equation has no solution?
O 1-x-31=5
O 12x-11=0
O15-3x = -8
O|-x+91=0

Answers

Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)

What linear equation has no solution?

Herein we must check each choice to find if a solution exists or not by algebra properties. Now we proceed to check each case:

Choice A

1/(x - 31) = 5

1 = 5 · (x - 31)

1 = 5 · x - 155

5 · x = 156

x = 31.2

Choice B

12 · x - 11 = 0

12 · x = 11

x = 11/12

Choice C

15 - 3 · x = - 8

3 · x = 23

x = 23/3

Choice D

- x + 91 = 0

x = 91

Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)

Remark

The statement presents typing mistakes and is incomplete. Correct form is shown below:

Which equation has no solution?

A. 1/(x- 31) = 5

B. 12 · x - 11 = 0

C. 15 - 3 · x = - 8

D. - x + 91 = 0

E. Neither of all

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In AABC, m/A = 15°, a = 9, and b = 12. Find c to the nearest tenth.
A. 20.0 B. 17.4 C. 8.4 D. 11.5​

Answers

Answer:

Step-by-step explanation:

This is a Law of Sines problem. The expanded formula is

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex] where the capital letters are the angles and the lowercase letters are the side lengths. We only use 2 of these ratios at a time. And in order to do that, we can only have one unknown per set of ratios. I have angle A and side a, so I'll use that ratio, but I don't have angle C to help me find side c. I also don't have angle B. But I do have side b, so I'll use the A and B sin stuff and then solve for C indirectly.

[tex]\frac{sin15}{9} =\frac{sinB}{12}[/tex] to solve for angle B. Cross multiply:

[tex]sinB=\frac{12sin15}{9}[/tex]

[tex]sinB=.3450926061[/tex]  Use the inverse and sin keys on your calculator (in degree mode) to get that

B = 20.2°.  Now that we have that, we can find the measure of angle C:

180 - 15 - 20.2 = 144.8°

Now we can use the sin ratio involving the angle C, side c (our unknown), and angle A and side a:

[tex]\frac{sin144.8}{c}=\frac{sin15}{9}[/tex] and cross multiply to solve for c:

[tex]c=\frac{9sin144.8}{sin15}[/tex] gives us that

c = 20.0

What is the missing exponent in the equation 3 TO THE SEVENTH POWER EQUALS 27

Answers

Answer: 3 to the 3rd power equals 27

Step-by-step explanation: Because a exponent is the number times itself 3x3 equals 9 that's already 2 then 9x3 equals 27 so anything above is to much

Name a pair of complementary angles in this figure.
a protractor, with segment DEF along the bottom, EH point to the 55 degree on the left, EJ to 90 degrees, EK to the 30 degrees on the right
angles DEH and HEJ
angles DEH and DEJ
angles DEH and DEK
angles DEF and DEH

Answers

The answer choice which represents a pair of complementary angles in the task content is; angles DEH and DEJ.

Which pair of angles represent complementary angles?

It follows from the concept of angle geometry that two or more angles are said to be complementary when the sum of their measures is 90°.

It follows from the task content therefore that since, DEJ = 90° and the sum of the measures of angles DEH and DEJ amounts to 90°.

Hence, the pair of angles are complementary.

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Will give brainliest

Answers

Answer:

Step-by-step explanation:

will give brainiest wrrwrwvrwvr

slove each problem include a diagram. a. A 6m long wheelchair ramp makes an angle of 15 with the ground. How high abouve the ground does the top end of the ramp reach. b.two treees are 120m apart. From the point halfway between them, then angle of the elevation to the top of the trees is 36 and 52. how much taller is one tree than the other.

Answers

The wheelchair ramp must have a height of approximately 1.553 meters. One tree is approximately 310.309 meters taller than the other one.

How to determine measures with trigonometric functions

In this problem we have two cases in which geometric diagrams and trigonometric functions are utilized to determine side lengths. Based on all informations presented in the images attached below, we proceed to find the side lengths:

Case A

h = (6 m) · sin 15°

h ≈ 1.553 m

Case B

Δh = 60 m /cos 36° - 60 m /cos 52°

Δh ≈ 310.309 m

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In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 35 and 48 minutes on the treadmill.

Answers

Using the normal distribution, there is a 0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation for this problem are given, respectively, by:

[tex]\mu = 42.5, \sigma = 4.8[/tex]

The probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill is the p-value of Z when X = 48 subtracted by the p-value of Z when X = 35, hence:

X = 48:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{48 - 42.5}{4.8}[/tex]

Z = 1.15

Z = 1.15 has a p-value of 0.8749.

X = 35:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{35 - 42.5}{4.8}[/tex]

Z = -1.56

Z = -1.56 has a p-value of 0.0594.

0.8749 - 0.0594 = 0.8155.

0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.

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A ternary string of length n is a sequence of n digits in which only 0, 1, or 2 appear.
For example, (0,1,0,2) and (1,1,2,2) are ternary strings of length 4 and can be seen as: 0102 and 1122.
How many ternary strings of length 2n are there in which the zeros appear only in odd positions?

Answers

dunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunno

dunno

Q19. When a resistor is placed across 230M supply (de) the
current is 12A. What is the value of resistor that must
De connected in parallel to increase the load current
to 16a

Answers

The value of the resistor that must be connected in parallel is 57.47 ohms

How to determine the resistor connected across the 230 V supplyVoltage (V) = 230 VCurrent (I) = 12 AResistor 1 (R₁) =?

V = IR

230 = 12 × R₁

Divide both sides by 12

R₁ = 230 / 12

R₁ = 19.17 ohms

How to determine the total resistanceVoltage (V) = 230 VCurrent (I) = 16 ATotal resistance (Rₜ) =?

V = IR

230 = 16 × Rₜ

Divide both sides by 12

Rₜ = 230 / 16

Rₜ = 14.375 ohms

How to determine the resistor connected in paralleResistor 1 (R₁) = 19.17 ohms Total resistance (Rₜ) = 14.375 ohmsResistor 2 (R₂) = ?

1/Rₜ = 1/R₁ + 1/R₂

Collect like terms

1/R₂ = 1/Rₜ - 1/R₁

R₂ = (Rₜ × R₁) / (R₁ - Rₜ)

R₂ = (14.375 × 19.17) / (19.17 - 14.375)

R₂ = 57.47 ohms

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Country A has an exponential growth rate of 3.8​% per year. The population is currently ​,000, and the land area of Country A is ​35,000,000,000 square yards. Assuming this growth rate continues and is​ exponential, after how long will there be one person for every square yard of​ land?

Answers

The number of years it would it take for there to be one person for every square yard is 93.6 years.

How many years would it take for there to be one person for every square yard?

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

FV = future population PV = present population r = rate of growth

(In 35 billion / 1 billion) / 0.038 = 93.6 years

Here is the complete question:
Country A has an exponential growth rate of 3.8​% per year. The population is currently 1,000,000 ,000 and the land area of Country A is ​35,000,000,000 square yards. Assuming this growth rate continues and is​ exponential, after how long will there be one person for every square yard of​ land?

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Se dispone de 800 000 para invertir. Una cuenta paga el 18% de interés anual, y otra paga el 21%. ¿Cuánto debe invertirse en cada cuenta para ganar 150 000 en intereses en un año?

Answers

Se debe depositar $ 600 000 en la cuenta con 18 % de interés anual y $ 200 000 en la cuenta con 21 % de interés anual para recibir $ 150 000 en intereses.

¿Cuánto se debe invertir en cada cuenta para alcanzar las ganancias deseadas en un período dado?

En este problema tenemos un depósito repartido en dos cuentas, que adquiere ganancias de manera continua en el tiempo. En consecuencia, tenemos por interés compuesto la siguiente ecuación a resolver:

x · (18/100) + (800 000 - x) · (21/100) = 150 000

168 000 - (3/100) · x = 150 000

(3/100) · x = 18 000

x = 600 000

Se debe depositar $ 600 000 en la cuenta con 18 % de interés anual y $ 200 000 en la cuenta con 21 % de interés anual para recibir $ 150 000 en intereses.

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I need help with b and c please and thank you!!

Answers

Answer:

rjdjdj shiejd shsuisis shusisos

Which of the following is NOT a criterion for making a decision in a hypothesis test?
Choose the correct answer below.
OA. If P-values a, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
OB. If the test statistic falls within the critical region, the decision is to reject the null hypothesis.
OC. If a confidence interval does not include a claimed value of a population parameter, the decision is to reject
the Inull hypothesis.
OD. If the P-value is less than 0.05, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null
hypothesis.

Answers

If the p-value less than 0.05, the decision is to reject the Null hypothesis.

What is hypothesis testing?Hypothesis testing is statistical reasoning using information from a sample to draw conclusions about a population parameter or population probability distribution. The parameter or distribution is initially bestguessed. Because it is the underlying assumption, the null hypothesis is often referred to as H0.For instance, you might explore and find that a specific drug effectively manages headaches. But nobody will believe what you find if you can't do that experiment again.A hypothesis seeks to provide an answer to a question. We will be forced to think about the results an experiment should try to achieve by a formulated hypothesis.The independent variable is the first variable. Results with seriousness.

The following should NOT be used as a decision-making standard in a hypothesis test.

If the p-value less than 0.05, the decision is to reject the Null hypothesis.

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ienes una cuerda que mide 90 cm. Hay que partir la cuerda en 2 segmentos (A y B). La cuerda B debe ser 5 veces más grande que la cuerda A. ¿Cuánto mide la cuerda B?

Answers

Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.

¿Cuánto mide cada segmento de cuerda?

En este problema debemos hallar dos segmentos de cuerda que cumple la siguiente relación, basada en el enunciado citado:

5 = (90 cm - x)/x     (1)

5 · x = 90 cm - x

6 · x = 90 cm

x = 15 cm

Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.

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Ayayai inc. Has a customer loyalty program that rewards a customer with 1 customer loyalty point for every $10 of purchase. Each point is redeemable for $3 discount on any future purchases . On july 2, 2020 customers purchase pro for $370000 (with a cost of $210900 )and earn 37000 points redeemable for future purchases. Ayayai is expected 31500 points to be redeemed. Ayayai estimates a standalone selling price for $2.50 per point (or $92500 total ) on the basis of the likelihood of redemption . The points provide a material right to customers that they would not receive without entering into a contract. As a result. Ayayai concludes that the points are separate performance obligation. Determine the transaction price for the product and the customer loyalty points. Product purchases, loyalty points, total transaction price

Answers

The transaction price for Ayayai's product and the customer loyalty points are $92500 and 37000 points respectively.

How to determine the transaction price?

Based on the information provided about Ayayai inc., the transaction price for their product and the customer loyalty points would be allocated as follows:

                                            SSP            PA              TTP                    AA____

Product purchases       $370,000       80%         $370,000         $296,000

Loyalty points               $92,500*       20%         $370,000         $74,000__

                                      $462,500                                                 $370,000

*37,000 × 2.50 = $92,500

Note:

SSP means Standalone selling prices.PA means Percent allocated.TTP means Total transaction price.AA means Allocated amounts.

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Complete the left-hand column of the table below following the steps indicated in the right-hand column to show that "sin a sin b = 1/2[cos(a-b)-cos(a+b)]" is an identity. Use the definitions of sum and difference formulas for cosine.

Answers

The equations which completes the left-hand column of the table are;

[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]

cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))

sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))

Which equations and identities complete the left-hand column of the table?

The given expression on the right is written as follows;

First row;

[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]

The definition of the sum and difference of cosine are;

cos(a - b) = cos(a)•cos(b) + sin(a)•sin(b)

cos(a + b) = cos(a)•cos(b) - sin(a)•sin(b)

Therefore;

Second row;

cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))

cos(a - b) - cos(a + b) = 2•sin(a)•sin(b)

Which gives;

[tex] sin(a) \cdot sin(b) = \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]

Third row;

sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))

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Solve for x in sin xtan x + tan x – 2sin x + cos x = 0 for 0 ≤ x ≤2π rads.

Answers

The value of x = 4.71, 0.41, or 5.89 radian value

Specification:

sinxtanx + tanx -2sinx + cosx = 0

tanx = sinx / cosx

sinx (sinx / cosx) + sinx / cosx -2sinx + cosx = Multiply 0

cosx to remove the fraction

sin ^ 2 (x) + sinx -2sinxcosx + cos ^ 2 (x) = 0

sin ^ 2 (x) + cos ^ Replace with 1. 2 (x) = 1

sinx -2sinxcosx + 1 = 0

sinx (1-2cosx) = -1

1-2cosx = -1 / sinx

-2cosx = -1 / sinx -1

2cosx = 1 / sinx + 1

cosx = 1 / 2sinx + 1/2

sqr (1-sin ^ 2 (x)) = 1 / 2sinx + 1/2

Squared on both sides

1-sin ^ 2 (x) = 1 / 4sin ^ 2 (x) + 1 / 2sinx + 1/4

4sin ^ 2 (x) Multiply

4sin ^ 2 (x) -4sin ^ 4 (x) = 1 + 2sinx + sin ^ 2 (X)

4sin ^ 4 (x) -3sin ^ 2 (x) + 2sinx +1 = 0

y = sinx

4y ^ 4 -3y ^ 2 + 2y + 1 = 0

sinx = y = -1 or -0.3478

x = 270, 180-22.61 or -22.61 degrees

x = 270, 157.39 or 337 .39 degrees

or

x = 3pi / 2, 0.13pi or 1.87pi radians

or

x = 4.71, 0.41 Or 5.89 radians

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What is the slope of the line that contains the points (9,-4) and (1,-5)?
OA. 1
OB.1/5
O C.-1/8
O D. -1

Answers

Answer:

Step-by-step explanation:

hello .....

note : the slope of the line (AB) is :

m = (YB -YA)/(XB - XA)

given  :  A(9,-4) and B (1,-5)

m= ((-5)-(-4))/(1-9)

m= 1/8

A ball is thrown from an initial height of 5 feet with an initial upward velocity of 31 ft/s. The ball's height (in feet) after t seconds is given by the following.
h=5+31t-16t^2

Find all values of t for which the ball's height is 19 feet.
t= _ seconds
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Answers

Solving a quadratic function, it is found that the ball has a height of 19 feet at t = 0.72 seconds and t = 1.22 seconds.

What is a quadratic function?

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

In this problem, the function is:

h(t) = -16t² + 31t + 5

The height is of 19 feet when h(t) = 19, hence:

19 = -16t² + 31t + 5

16t² - 31t + 14 = 0.

Then:

[tex]\Delta = (-31)^2 - 4(16)(14) = 65[/tex][tex]x_1 = \frac{31 + \sqrt{65}}{32} = 1.22[/tex][tex]x_2 = \frac{31 - \sqrt{65}}{32} = 0.72[/tex]

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