Question 2 2.1. If sin35=t, express the following in terms of t 2.1.1. sin325 2.1.2. cos35 2.1.3. tan215 (Hint: use a diagram) (2) (3) (2)​

Answer:

[tex]3x^3(x-1)(2x^3+2x^2+2x+3)[/tex]

Step-by-step explanation:

We can start by factoring out x³ because it's the greatest factor of every term:

[tex]6x^7+3x^4-9x^3=x^3(6x^4+3x-9)[/tex]

Next, notice that each coefficient is divisible by 3, so this can be factored out as well:

[tex]x^3(6x^4+3x-9)=3x^3(2x^4+x-3)[/tex]

While it may not look like we can factor out 2x⁴+x-3, we actually can! Notice the following:

[tex]2x^4+x-3=(2x^4+2x^3+2x^2+3x)+(-2x^3-2x^2-2x-3)=x(2x^3+2x^2+2x+3)-1(2x^3-2x^2+2x+3)=(x-1)(2x^3+2x^2+2x+3)[/tex]

By grouping, we were able to condense this factor. Thus:

[tex]6x^7+3x^4-9x^3=\bf{3x^3(x-1)(2x^3+2x^2+2x+3)}[/tex]

The measure of angle 75 degrees with steps are;

To construct a degree of 75 degree, we have to;

Note that 75 is an acute angle

Learn more about construction at: https://brainly.com/question/27665779

#SPJ1

Check the picture below.

Answer:

sin (M) = 1/11 * √34 or (√34) / 11

Step-by-step explanation:

The sine ratio is sin (reference angle) = opposite / hypotenuse.

Plugging in M for the reference angle gives us:

sin (M) = (√34) / 11.  Dividing by 11 is the same as multiplying by 1/11 so alternatively, you could write sin (M) = 1/11 * (√34)

The expression is already in simplest radical form as there are no perfect squares which divide evenly into 34.

Answer:

a. q^2 = sqr(225) can be solved.

q^2 = sqr(225) means q^2 = 15^2. So, q can be found by taking the square root of both sides:

q = ±15

Step-by-step explanation:

The number of more hotdog buns than kaya buns there are in the bakery, obtained from the fractions and ratios of the number of buns are 192 hotdog buns

A ratio is a quantitative representation of the number of times one quantity is contained in another quantity.

The fraction of the buns that are coffee buns = 3/11

The amount of the hotdog buns and kaya buns = The rest of the buns

The ratio of the hotdog buns to the kaya buns = 7 : 5

The total number of hotdog buns and kaya buns = 720 more than the number of coffee buns

The difference between the number of hotdog buns and kaya buns are therefore;

Let x represent the number of buns in the bakery

The number of coffee buns = 3·x/11

The number of hotdog buns and kaya buns = x - 3·x/11 = 8·x/11

8·x/11 = 3·x/11 + 720

Therefore;

8·x/11 - 3·x/11 = 720

5·x/11 = 720

5·x = 11 × 720 = 7920

x = 1584

The number of hotdog buns and kaya buns = 8×1584/11 = 1152

The number of hotdog buns = (7/(7 + 5)) × 1152 = 672

The number of kaya buns = (5/(7 + 5)) × 1152 = 480

The difference = 672 - 480 = 192

Part of the question, obtained from a similar question posted on the internet is; How many more hotdog buns than kaya buns are there in the bakery.

Learn more on ratios here: https://brainly.com/question/30828672

#SPJ1

11 x (7 + 5) = 132

(3/11) x 132 = 36 (coffee)

(8/11) x 132 = 96 (hotdog and kaya)

96 – 36 = 60

720/60 = 12

(2/12) x 96 = 16

16 x 12 = 192

Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.

Answer:

Step-by-step explanation: To determine the number of cubes of sugar equivalent to one mango fruit, we need to know the weight of a mango. Since you haven't provided that information, I cannot give you an accurate answer. However, on average, a medium-sized mango weighs around 150-200 grams. If we assume the weight of the mango is 150 grams, we can calculate the number of sugar cubes:

150 grams ÷ 5 grams/cube = 30 cubes

Therefore, if a mango weighs around 150 grams, it would be roughly equivalent to 30 cubes of sugar, assuming each cube weighs 5 grams.

The expression implies that the number of fish that are not angelfish can be represented as 3/4

In this expression, "z" represents the total number of fish in the aquarium. The statement mentions that one-fourth of the fish are angelfish, which means that 1/4 of "z" fish are angelfish.

To determine how many fish are not angelfish, we need to subtract the number of angelfish from the total number of fish. Since 1/4 of the fish are angelfish, 3/4 of the fish must be non-angelfish.

Therefore, the expression implies that the number of fish that are not angelfish can be represented as 3/4 of "z," which can be mathematically written as (3/4)z.

In summary, the expression represents the number of fish that are not angelfish based on the total number of fish "z" in the aquarium.

To learn more about the expression;

brainly.com/question/24242989  

#SPJ1

The statement means that for the set X there exist another set Y where each member x in X has a unique element y satisfying (x, y), and Y contains exactly those y values.

A key axiom in set theory is the Axiom Schema of Replacement. It claims that for any set theory formula (x, y), if a set A exists, then there exists a set B where each member x in A has a unique element y satisfying (x, y), and B contains exactly those y values.

To put it another way, it enables us to "replace" components of a set A with their equivalent images in accordance with a specified formula to create a new set B.

The existence of sets acquired through specific replacement processes is guaranteed by this postulate.

Learn more about set theory at: https://brainly.com/question/13458417

#SPJ1

Answer:

See below for an explanation

Step-by-step explanation:

The function [tex]f(x)=\sin(x)[/tex] oscillates between -1 and 1 as it should with equal periods of 2π, but [tex]f(x)=\sin(\sqrt{x})[/tex] has increasingly longer periods of oscillations because of the exponent for x being small (recall that [tex]\sqrt{x}=x^{\frac{1}{2}}[/tex]). If the exponent were to increase, the frequency of these oscillations increase substantially.

I hope this explanation helps!

Check the picture below.

I usually like to see sine and cosine as a distance of a "dark light" over the circle as you see there in the picture, so if the flashlight moves up, the vertical shadow(sine) becomes larger and the horizontal shadow(cosine) becomes smaller, and the same happens on all four Quadrants as the flashlight moves over the arc.

If we look at the value tables there, let's notice, whilst "x" is less than 10 is all honky dory all positive for sine, we hit x = 10 and kaboom it turns negative, thus the drop you see in the sinusoid curve above at x =  10 or close, not exactly but very close.

well, by the time x = 9.5, its root becomes about 3.08 radians and sine of that is still positive, recall, π is about 3.1416 radians, and below π radians, the vertical shadow drops to the III and IV Quadrants, thus negative, so if we square say 3.1416², which is about 9.87, so when "x" is about 9.87, its root will turn to close to 3.1416 radians and sine of that will run to the negative, having the drop you see above, then it goes back up and then back down like any sinusoidal curve as the values of the angle iterate over the Quadrants.

Answer:

The expression involves repeatedly taking the square root of 9999999999999999, and since there are an even number of roots, the result will be positive.

To calculate the value of x, we can simplify the expression by taking the square root of 9999999999999999 first and then applying the square root function repeatedly.

The square root of 9999999999999999 is approximately 9999999.9999999995357676.

Taking the square root of this number yields approximately 316227.76601683793.

Continuing this process of taking the square root yields:

√(√(9999999999999999)) ≈ 316227.76601683793

√(√(√(9999999999999999))) ≈ 56.23413251903491

√(√(√(√(9999999999999999)))) ≈ 2.9831226258719656

√(√(√(√(√(9999999999999999))))) ≈ 1.4565131116848164

√(√(√(√(√(√(9999999999999999)))))) ≈ 1.1084260329045203

√(√(√(√(√(√(√(9999999999999999))))))) ≈ 1.0323583730781274

√(√(√(√(√(√(√(√(9999999999999999)))))))) ≈ 1.0109720093876667

√(√(√(√(√(√(√(√(√(9999999999999999))))))))) ≈ 1.0028950382728386

√(√(√(√(√(√(√(√(√(√(9999999999999999)))))))))) ≈ 1.0007212764795355

√(√(√(√(√(√(√(√(√(√(√(9999999999999999))))))))))) ≈ 1.0001798850712478

√(√(√(√(√(√(√(√(√(√(√(√(9999999999999999)))))))))))) ≈ 1.0000449706330375

√(√(√(√(√(√(√(√(√(√(√(√(√(9999999999999999))))))))))))) ≈ 1.000011242264439

√(√(√(√(√(√(√(√(√(√(√(√(√(√(9999999999999999)))))))))))))) ≈ 1.0000028105696245

√(√(√(√(√(√(√(√(√(√(√(√(√(√(√(9999999999999999))))))))))))))) ≈ 1.0000007026370322

Step-by-step explanation:

This was too easy.

Answer:

1.33

Step-by-step explanation:

[tex] \sqrt[129]{9999999999999999 = 1.33} [/tex]

To find the total in the retirement account after 38 years of investing with monthly contributions and an interest rate of 4.99%, we can use the compound interest formula.

The formula for the future value of an investment with regular monthly contributions is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value or the total in the retirement account.

P is the monthly contribution amount.

r is the monthly interest rate (annual interest rate divided by 12).

n is the number of monthly contributions (years invested multiplied by 12).

Let's calculate the total:

P = $225

r = 4.99% / 100 / 12 = 0.0041583 (monthly interest rate)

n = 38 * 12 = 456 (number of monthly contributions)

FV = $225 * [(1 + 0.0041583)^456 - 1] / 0.0041583

Using a financial calculator or spreadsheet, we can evaluate this expression to find the future value or total in the retirement account.

The calculated total may vary depending on the compounding frequency and rounding used.

Answer: a=101 b=79 c=83 d=97

(x + 12)° + (5x)° = 90°

m∠1 = 25° and m∠2 = 65°

We know that the little box represents 90 degrees. We will write an equation using this information.

      (x + 12)° + (5x)° = 90°

Next, we will solve by isolating the x variable with inverse operations and combing like terms.

      (x + 12)° + (5x)° = 90°

      x° + 5x° = 78°

      6x° = 78°

      x = 13°

Lastly, we will find the value of each angle by substituting.

       m∠1 = (x + 12)° = ((13) + 12)° = 25°

       m∠2 = (5x)° = (5(13))° = 65°

Answer:

a is g(x) b is f(x)

Step-by-step explanation:

because a increases faster

Answer:

X = 10

Z = 67

Step-by-step explanation:

We see that the angles are formed by the intersection of two lines.

Angles z and  67° are vertically opposite angles and therefore they are equal to each other

z°= 67°

Angles z and (7x + 43) are supplementary angles. The sum of these angles add up to 180°

z + 7x + 43 = 180

67 + 7x + 43 = 180

7x + 110 = 180

7x = 180 -110 = 70

x = 70/7 = 10

Step-by-step explanation:

Vertical angles are equal   r = 70 degrees

Answer:

8/15

Step-by-step explanation:

Assuming that a is in the 1st quadrant, based on sin a = 8/17 you can build a right triangle as in the picture. Third side you compute with Pythagoras [tex]x^2 + 8^2 = 17^2 \implies x = 15[/tex].

At this point the tangent is the ratio of the two segments, or 8/15.

Else, you can calculate cos a  based on the fact that [tex]cos\ a = \sqrt{1-sin^2\ a}[/tex] (under the same assumption as the beginning. Then it's just a matter of plugging numbers.

For the given parabola the zeroes are -2 and 6, the axis of symmetry is x = 2, the parabola has a maximum and the vertex is (2, 14)

The given figure is a  parabola, a plane curve which is mirror-symmetrical and is approximately U-shaped is called parabola

The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis).

The zeroes are -2 and 6

The parabola has a maximum as the vertex has posititve

The axis of symmetry for a parabola is the line which will separate a parabola into two equal halves

The axis of symmetry is x = 2

The vertex of a parabola is the point of intersection of the parabola and the axis of symmetry.

The vertex is (2, 14)

To learn more on Parabola click:

https://brainly.com/question/29267743

#SPJ1

The statements that are true of the dot plot of the recent math assignment include:

The dot lot shows that the math scores from the assignment are:

5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9

This means that the number of math scores are 20 in total. There are no gaps in the data as from the score of 5, there is a consecutive score till 9.

The data is also clustered around 8 and 9 scores as most people scored either 8 or 9.

Find out more on dot plots at https://brainly.com/question/16038513

#SPJ1

Answer:

[tex]-8x^3\sqrt{7}[/tex]

Step-by-step explanation:

Step 1:  Let's start by simplifying -4x^2 * (√63x^2) using the following steps:

1.1: Separate √63x^2 into two terms:  

-4x^2 * (√63 * √x^2)

1.2:  Find the largest perfect square that we can factor out of 63.  It's 9 as 3^2 = 9 and 9 * 7 = 63.  Furthermore, √x^2 simplifies to x:

-4x^2 * (√9 * 7 * (x))

-4x^2 * (3√7 * x)

1.3:  We can multiply x and 3:

-4x^2 * (3x√7)

1.4:  We can distribute -4x^2 to 3x√7.  

-12x^3 * √7

Step 2:  Now we can work on simplifying x^3√112 using the following steps:

2.1:  Find the largest perfect square you can factor out of 112.  It's 16 since 4^2 = 16 and 16 * 7 = 112:

x^3 * √16 * 7

x^3 * 4√7

2.2:  Multiply x^3 and 4√7:
4x^3 * √7

Step 3:  Thus, -4x^2 * √63x^2 simplified individually is -12x^3 * √7 and x^3 * √112 simplified individually is 4x^3 * √7

3.1:  Add -12x^3 * √7 + 4x^3 * √7:

-8x^3√7

Optional Step 4:  We can check that we've correctly simplifed the equation by plugging in a number for x in both the radical expression not yet simplified and the simplified radical expression.  If we get the same answer, then we've simplified the expression correctly.  We can plug in 2 for x.

Plugging in 2 for x in -4x^2 * (√63x^2) + x^3 * (√112):

(1.) -4(2)^2 * √63(2)^2 + 2^3 * √112:

(2.) -4(4) * √63(4) + 8 * √112

(3.) -16 * √252 + 8 * √112

(4.) -16 * √36 * 7 + 8 *√16 * 7

(5.) -16 (6 * √7) + 8(4 *√7)

(6.) -96 * √7 + 32 * √7

(7.) -64√7

(8.) -169.3280839

Plugging in 2 for x in -8x^3√7:

(1.) -8(2)^3 * √7

(2.) -8(8) * √7

(3.) -64 * √7

(4.) -169.3280839

Therefore, we've correctly expressed the expression in simplest radical form

Answer:

30°

Step-by-step explanation:

angles on a straight line add up to 180°.

angles in a triangle add up to 180°.

XYZ = 180 - 105 = 75°.

angle YZX = 180 - 2x.

so we have YZX + 2x = 180, YZX = 180 - 2x.

angles in triangle add up to 180:

x + YZX + 75 = 180,

x + (180 - 2x) + 75 = 180,

-x + 180 + 75 = 180,

-x = 180 - 180 - 75 = -75,

x = 75°.

YZX = 180 - 2x = 180 2(75) = 180 - 150 = 30

Answer:

  C. S

Step-by-step explanation:

You want the center of rotation when figure QRSP is rotated 90° CW to become UVST.

The center of rotation is the point of coincidence of the perpendicular bisectors of the segments between a preimage point and the corresponding image point. It is also the only point on the plane that is invariant with the rotation.

The rectangle names tell us the rotation maps the points as follows:

The fact that point S does not move tells us that it is the center of rotation. As a check, we can see if the perpendicular bisectors of QU, RV and PT intersect at point S. (They do.)

Point S is the center of rotation.

__

Additional comment

Unfortunately, the image attached to the problem statement distorts the lines and angles. Hence, it cannot be used to find the precise location of the center of rotation. (In fact, the "rectangles" shown are only conceptual rectangles, not actual congruent rectangles.)

The perpendicular bisector of QU seems to pass through S, as it must if S is the center of rotation.

<95141404393>

Answer: The cost of each sandwich (S) is $4 and the cost of each bottle of water (B) is $2.

Step-by-step explanation:

10S + 6B = 52 (Equation 1) -- Ramon's purchase

1S + 3B = 10 (Equation 2) -- Wallace's purchase

To solve these equations, we can use a method called substitution. We'll solve Equation 2 for S and substitute it into Equation 1:

From Equation 2, we can isolate S:

1S = 10 - 3B

S = 10 - 3B

Substituting S into Equation 1:

10(10 - 3B) + 6B = 52

100 - 30B + 6B = 52

100 - 24B = 52

-24B = 52 - 100

-24B = -48

B = -48 / -24

B = 2

Now, substitute the value of B back into Equation 2 to find S:

S + 3(2) = 10

S + 6 = 10

S = 10 - 6

S = 4

Answer:

The answer for the width of the building 5m

Step-by-step Explanation:

3cm=1m

15cm=x

cross multiply

x×3=15×1

3x=15

divide both sides by 3

3x/3=15/3x=5m

Hello !

45min = 3/4h = 0,75h

[tex]\frac{45km}{0,75h} \\\\= \frac{45km*\frac{1}{0,75} }{0,75h*\frac{1}{0,75} } \\\\= \frac{60km}{1h}[/tex]

s = 60km/h

[tex]s=\dfrac{d}{t}\\\\d=45\text{ km}\\t=45\text{ min}=0.75\text{ h}\\\\s=\dfrac{45\text{ km}}{0.75\text{ h}}=60\dfrac{\text{km}}{\text{h}}[/tex]

If p(x) ⊆ p(y), then it means that every element of the power set of x is also an element of the power set of y. This implies that set x is a subset of set y, written as x ⊆ y.

Here,

Let A be the set x and B be the set y. Then the power sets of A and B are p(A) and p(B) respectively.

Suppose p(A) ⊆ p(B). This means that for every element a in p(A), a is also an element of p(B).

Now consider any element a in A. Since a is an element of A, it is also an element of its power set p(A). Thus, if p(A) ⊆ p(B), a must also be an element of p(B). This means that a is an element of B.

Therefore, we have established that every element of A is an element of B. That is, A ⊆ B.

Thus, if p(x) ⊆ p(y), then x ⊆ y.

learn more about relationship between x and y: brainly.com/question/29634017

#SPJ1

They are 68.27% of emergency calls have a firefighter response time between 7 and 11 minutes.

To determine the percentage of emergency calls with a firefighter response time between 7 and 11 minutes, we need to calculate the area under the normal distribution curve between these two values.

First, let's standardize the values of 7 and 11 using the z-score formula:

z1 = (7 - mean) / standard deviation

= (7 - 9) / 2

= -2 / 2

= -1

z2 = (11 - mean) / standard deviation

= (11 - 9) / 2

= 2 / 2

= 1

Next, we can use a standard normal distribution table or a statistical calculator to find the area under the curve between these z-scores.

The area between z = -1 and z = 1 represents the percentage of emergency calls with a firefighter response time between 7 and 11 minutes.

Using a standard normal distribution table, we get between z = -1 and z = 1 is approximately 0.6827.

know more about normal distribution here:

https://brainly.com/question/4079902

#SPJ11

Answer:

2x squared - 5

= 2(x)^2 - 5

= 2(4)^2 - 5

= 2(16) - 5

= 32 - 5

= 27