please help me: I have inserted the question below:

[tex]\boxed{sin^{2}x + cos^{2}x = 1}[/tex]

a) [tex]cos^{2}x = 1 - sin^{2}x[/tex]

b) [tex]3sin^{2}x - 4cos^{2}x = 3sin^{2}x - 4(1 - sin^{2}x) = \\[/tex]

[tex]= 3sin^{2}x - 4 + 4sin^{2}x = 7sin^{2}x - 4[/tex]

12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex].

The weight of 12 blue whales will be the product of the weight of a single blue whale and the number of blue whales. To find the product, we simply multiply the weight of a single blue whale by the number of blue whales.

So, the weight of 12 blue whales will be:

[tex]\( 1.8 \times 10^{6} \mathrm{~kg} \) × 12 = \( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Therefore, 12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Multiplication refers to binary operations in which different numerical sets are established. In mathematics the process of multiplication is elementary in several operations, it is also accompanied by addition, subtraction and division. Multiplication is the opposite of division.

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Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

4x + 21 + x - 10 + 2x + 8 = 180

7x + 19 = 180 ( subtract 19 from both sides )

7x = 161 ( divide both sides by 7 )

x = 23

Then angles in triangle are

4x + 21 = 4(23) + 21 = 92 + 21 = 113°

x - 10 = 23 - 10 = 13°

7x + 8 = 7(23) + 8 = 161 + 8 = 169°

the only 2 possible angle measures are A and E

The number is 63. The difference between the digits of a two-digit number is 1.

Number is a mathematical object used to count, measure, and label. Numbers can be represented in a variety of forms, such as numerals, symbols, or words. Numbers are fundamental to mathematics, and all other areas of science and technology. They are used to represent amounts of money, measurements, dates, and amounts of time. Numbers are also used to identify objects and people, and to create equations and formulas. Number is essential for understanding the world around us.

To solve this, the first thing to do is find the sum of the digits. Since the number is one more than five times the sum of its digits, the sum of the digits is (63/5)-1=12.5-1=11.5. This means that the tens digit is 11 and the unit digit is 11 + 1 = 12. Therefore, the two-digit number is 63.

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Answer:

Step-by-step explanation:

f(x)=x^4−x^2+9

Answer:

10

Step-by-step explanation:

27-[tex]3x^{3}[/tex]+(4 x [tex]2x^{2}[/tex]) - 6

= 27 - 27 + (4 x 4) - 6

= 0 + 16 - 6

= 10

Answer: 10

Step-by-step explanation:

27 - 3^3 + 4 × 2^2 - 6

= 27 - 27 + 4 × 4 - 6 (since 3^3 = 27 and 2^2 = 4)

= 0 + 16 - 6= 10

Therefore, the simplified value of the expression is 10.

Answer:

image is blur dear!!!

Step-by-step explanation:

The polygons are classified as :-

1.CONVEX

2.CONCAVE

3.CONCAVE

4.REGULAR

5.CONCAVE

6.IRREGULAR

A polygon is a geometrical figure, with finite sides and angles, they can be regular and irregular.

Regular Polygon

A regular polygon is that which has all its sides and angles equal, for example an equilateral triangle and a square.

Irregular Polygon

A irregular polygon is that which has all its sides and angles unequal,

For example, a scalene triangle, a rectangle, a kite, etc.

Convex Polygon

A Convex polygon is that which has all its angles less than 180 degrees,

Concave Polygon

A Concave polygon is that which has its angles greater than 180 degrees,

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The complete question attached

The equation of the parallel line is y = -4x - 23.

To find the equation of the perpendicular line that passes through (-7, 5), we need to first find the slope of the given line y = -4x + 6. The slope of this line is -4. The slope of a perpendicular line is the negative reciprocal of the original slope, so the slope of the perpendicular line is 1/4.

Next, we can use the point-slope form of an equation to find the equation of the perpendicular line:

y - y1 = m(x - x1)

y - 5 = (1/4)(x - (-7))

y - 5 = (1/4)(x + 7)

y = (1/4)x + 9/4 + 5

y = (1/4)x + 29/4

The equation of the perpendicular line is y = (1/4)x + 29/4.

To find the equation of the parallel line that passes through (-7, 5), we can use the same slope as the original line, -4, and the point-slope form of an equation:

y - y1 = m(x - x1)

y - 5 = -4(x - (-7))

y - 5 = -4(x + 7)

y = -4x - 28 + 5

y = -4x - 23

The equation of the parallel line is y = -4x - 23.

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The linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.

The linear speed of the circle can be found by calculating the length of the arc traveled in 25 seconds. The length of an arc is given by the formula L = rθ, where r is the radius of the circle and θ is the central angle in radians. Converting the given angle from degrees to radians, we have:

θ = 145 degrees * π/180 = 2.53 radians

Substituting the values into the formula, we get:

L = 21 cm * 2.53 = 53.13 cm

Therefore, the linear speed of the circle is:

v = L/t = 53.13 cm/25 s = 2.125 cm/s

The angular speed of the circle can be found by dividing the central angle by the time taken to travel that angle. Therefore, the angular speed of the circle is:

ω = θ/t = 2.53 radians/25 s = 0.1012 rad/s

Hence, the linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.

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Answer:

= -4

Step-by-step explanation:

To solve this expression, we need to perform the division in the correct order, following the rules of mathematical operations. We can simplify the expression as follows:

(-168) ÷ (-14) ÷ (-3) = (-168) ÷ [(-14) x (-3)] [dividing by a negative number is the same as multiplying by its reciprocal]

= (-168) ÷ 42

= -4

Therefore, the quotient of (-168) ÷ (-14) ÷ (-3) is -4.

The probability that the selected marble is red is 0

From the question, we have the following parameters that can be used in our computation:

Number of marbles = 10

Blue = 3

Yellow = 7

Using the above as a guide, we have the following:

P(Red) = Number of red/Number of marbles

Substitute the known values in the above equation, so, we have the following representation

P(Red) = 0/10

Evaluate

P(Red) = 0

Hence, the probability is 0

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Tower B is 2.34 miles far from the point on the road closest to the fire.

The point on the road closest to the fire can be found by drawing a line perpendicular to the road that passes through the fire location. Let x be the distance from tower B to this point. Then, using trigonometry, we can find that the distance from tower A to the fire location is x/tan(22) and the distance from tower B to the fire location is (5 - x)/tan(37). Since the fire location is the same from both towers, these distances must be equal, so we can set up the equation x/tan(22) = (5 - x)/tan(37) and solve for x, which is approximately 2.34 miles.

To sketch the fire location, draw a straight road with two fire towers located 5 miles apart. From tower A, draw a line at an angle of 22 degrees towards the north side of the road to represent the direction of the fire location. From tower B, draw a line at an angle of 37 degrees towards the same side of the road. The point where these two lines intersect represents the location of the fire. Draw a line perpendicular to the road passing through this point to find the closest point on the road to the fire.

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V(t)=S ert-W/r

a. The rate at which the account changes (dt/dV) is equal to the interest rate (r) times the value of the account (V) minus the amount withdrawn (W). This can be written mathematically as dt/dV=rV-W. This is a separable differential equation, which can be solved by integrating both sides of the equation with respect to time. The solution is V(t)=S ert-W/r.

b. The value of the Jones' account at the end of 10 years can be found using the solution V(t) from part a: V(10)=500,000 e5%x10-50,000/5% = $387,468.51.

c. To keep their account unchanged at $500,000, the Jones' must withdraw an annual amount W such that V(t)=500,000. From the solution V(t)=S ert-W/r, we can solve for W: W = 500,000e5%x10 - 500,000/5% = $47,613.30.

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The restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.

The restrictions on the variablex in the expression √6x-2 are determined by the fact that the square root of a negative number is not a real number. Therefore, the expression under the square root must be greater than or equal to zero. This gives us the following inequality:

6x-2 ≥ 0

Solving for x, we get:

6x ≥ 2

x ≥ 2/6

x ≥ 1/3

So the restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.

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The polynomial  3x³ - 4x² + 9x - 12 as a product of binomials is (3x - 4)(x² + 3).

To rewrite the polynomial 3x³ - 4x² + 9x - 12 as a product of binomials, we need to factor the polynomial. One method to do this is by grouping. Here are the steps:

1. Group the first two terms and the last two terms: (3x³ - 4x²) + (9x - 12)
2. Factor out the common factor from each group: x²(3x - 4) + 3(3x - 4)
3. Notice that (3x - 4) is a common factor in both groups, so we can factor it out: (3x - 4)(x² + 3)
4. Now we have the polynomial rewritten as a product of binomials: (3x - 4)(x² + 3)

Therefore, the polynomial 3x³ - 4x² + 9x - 12 can be rewritten as (3x - 4)(x² + 3).

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The graph of the quadratic function is on the image at the end.

Here we have the quadratic function:

f(x) = (x + 1)*(x - 5)

To graph this, we need to find some points of the parabola and then connect them.

So let's evaluate the function.

if x = -1

f(-1) = (-1 + 1)*(-1 - 5) = 0

if x = 0

f(0) =  (0 + 1)*(0 - 5) = -5

if x = 1

f(1) =  (1 + 1)*(1 - 5) = 2*-4 = -8

if x = 5 then:

f(5) =   (5 + 1)*(5 - 5) = 0

So we have the points (-1, 0), (0, -5), (1, -8) and (5, 0).

With these we can graph the parabola (you can try to find more points to get a better graph).

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Jill played for 10 mins. 25+15=40 50-40=10

vector u can be written as a linear combination of the vectors in set S with the scalars a = 1 and b = 0.

To write vector u as a linear combination of the vectors in set S, we need to find scalars a and b such that:

u = a[1] + b[0]

Substituting the values of vector u and the vectors in set S into this equation, we get:

[1] = a[1] + b[0]

This equation can be simplified to:

[1] = [a] + [0]

Since the scalar b is being multiplied by the zero vector, it will always equal the zero vector, and can therefore be eliminated from the equation. This leaves us with:

[1] = [a]

We can see that the scalar a must equal 1 in order for this equation to be true. Therefore, vector u can be written as a linear combination of the vectors in set S as follows:

u = 1[1] + 0[0]

In conclusion, vector u can be written as a linear combination of the vectors in set S with the scalars a = 1 and b = 0.

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Option (b) "3/4 to the power of 2 - 6/16" is the expression that is  equivalent to 3/16.

A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:

The expression is (number/variable, arithmetic operator, number/variable).

Solution according to the given information:

Given, x = 3/4

Option(a): 2x+1/16 = (2×3/4) +1/16

                              = 3/2 + 1/16

                              =25/16

Which is not equal to 3/16

Option(b): (3/4)² - 6/16 = 9/16 - 6/16 = 3/16

Which is equivalent to 3/16

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There are no values of x that satisfy the equation -6-(4x)/(x+2)=(8)/(x+2).

To find the values of x for the equation -6-(4x)/(x+2)=(8)/(x+2), we need to follow the following steps:

Multiply both sides of the equation by (x+2) to eliminate the fractions:
(x+2)(-6-(4x)/(x+2))=(x+2)(8)/(x+2)

Simplify the equation:
-6(x+2)-4x=8

Distribute the -6:
-6x-12-4x=8

Combine like terms:
-10x-12=8

Add 12 to both sides:
-10x=20

Divide both sides by -10:
x=-2

However, we need to check our answer to make sure it does not result in a zero denominator in the original equation. If we plug in x=-2 into the original equation, we get a zero denominator, which is not allowed. Therefore, there are no values of x that satisfy the equation.

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Answer:

-2

Step-by-step explanation:

[tex]m=\frac{4-(-8)}{-4-2} \\m=\frac{4+(+8)}{-4-2} \\m=\frac{12}{-6} \\m=\frac{2}{-1} \\m=-2[/tex]

The standard equation of this ellipse is x²/144 + y²/80 = 1.

The standard equation of an ellipse is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center of the ellipse, a is the semi-major axis, and b is the semi-minor axis.

In this case, the center of the ellipse is (0,0) since the vertices and foci are both on the y-axis. The distance between the vertices is 24 (12 - (-12)), so the semi-major axis is 12. The distance between the foci is 16 (8 - (-8)), so the distance between the center and each focus is 8. Using the formula c² = a² - b², where c is the distance between the center and each focus, we can solve for b:

c² = a² - b²
8² = 12² - b²
64 = 144 - b²
b² = 80

So the equation of the ellipse is (x-0)²/12² + (y-0)²/80 = 1, or x²/144 + y²/80 = 1.

You keep getting (x²)/80 + (y²)/144 because you are switching the values of a and b. The semi-major axis should be in the denominator of the x term, and the semi-minor axis should be in the denominator of the y term.

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Answer: We can write the piecewise defined function for the monthly cost C(x) as follows:

C(x) =

45.75 - 9.55, if x ≤ 500

45.75 - 9.55 + 0.35(x - 500), if x > 500

Explanation:

For the first 500 minutes, the monthly cost is a flat rate of $45.75 for the plan fee and $9.55 for taxes, so the total cost is simply the sum of these two amounts: C(x) = 45.75 + 9.55 = 55.30, for x ≤ 500.

For any additional minutes beyond the 500-min limit, there is an additional charge of $0.35 per minute, so the cost increases linearly with the number of extra minutes used. The expression (x - 500) represents the number of minutes beyond the limit, so we multiply this by the rate of $0.35 per minute and add this amount to the base cost of $55.30, giving the piecewise expression:

C(x) =

55.30, if x ≤ 500

55.30 + 0.35(x - 500), if x > 500

Therefore, the piecewise defined function for the monthly cost C(x) is:

C(x) =

45.75 - 9.55, if x ≤ 500

45.75 - 9.55 + 0.35(x - 500), if x > 500

Note: The two expressions are equivalent, but the second expression is simplified by combining the constants.

Step-by-step explanation:

The mass of the chemicals being propelled is 0.41 kilograms.

The correct answer is: 0.41 kilograms.

To find the mass of the chemicals being propelled, we can use the formula for momentum:

momentum = mass x velocity

Since the momentum of the cracker before it is launched is zero, and the momentum after it is launched is the sum of the momentum of the cracker and the momentum of the chemicals, we can set up an equation:

0 = (1.5 kg)(15 m/s) + (mass of chemicals)(55 m/s)

Next, we can rearrange the equation to solve for the mass of the chemicals:

(mass of chemicals)(55 m/s) = -(1.5 kg)(15 m/s)

mass of chemicals = -(1.5 kg)(15 m/s) / (55 m/s)

mass of chemicals = -22.5 kg / 55 m/s

mass of chemicals = -0.41 kg

So the mass of the chemicals being propelled is 0.41 kilograms.

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It is not possible to use Cramer's Rule to solve the system of equations you provided. This is because Cramer's Rule can only be applied to systems of linear equations that have the same number of equations as there are unknowns.

In the system you provided, there are four equations but only two unknowns. This means that Cramer's Rule cannot be applied.

Instead, you can use other methods such as substitution or elimination to solve the system. However, it is important to note that with more equations than unknowns, it is possible that there may be no solution or an infinite number of solutions.

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The sum of these probabilities is 1, the mean number of runs per inning is 0.46, and the standard deviation of this probability distribution is 0.839.

The sum of these probabilities is simply the sum of the values in the table:

EP(x) = 0.74 + 0.12 + 0.07 + 0.04 + 0.03 = 1

The mean number of runs per inning can be calculated using the formula for the expected value of a discrete random variable:

E(x) = ∑xP(x) = (0)(0.74) + (1)(0.12) + (2)(0.07) + (3)(0.04) + (4)(0.03) = 0.46

The standard deviation of this probability distribution can be calculated using the formula for the standard deviation of a discrete random variable:

σ = √[∑(x - E(x))^2P(x)]

=> √[(0 - 0.46)^2(0.74) + (1 - 0.46)^2(0.12) + (2 - 0.46)^2(0.07) + (3 - 0.46)^2(0.04) + (4 - 0.46)^2(0.03)]

=> 0.839
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Answer:

Step-by-step explanation:

Given: [tex]f(x)=x^{2} -3x - 8[/tex]

To find:

a) f(8)

To find f(8), replace x with 8 in f(x)

[tex]f(8) = 8^{2} -3(8) -8 = 32[/tex]

b)  f(x+9)

To find f(x+9), replace x with x +9 in f(x)

[tex]f(x+9) = (x +9)^{2} -3(x +9) -8 = x^{2} +18x+81-3x-27-8=x^{2} +15x+46[/tex]

c) f(-x)

To find f(-x), replace x with -x in f(x)

[tex]f(x)=(-x)^{2} -3(-x) - 8 =x^{2} +3x-8[/tex]

This is how we simplify these expressions.

∆ABC = ∆BCD because they are congruent

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

AB is parallel to CD and AB is equal to CD,

Therefore AC = BD( opposite sides of a parallelogram are equal

therefore CB is common to both triangle

We can therefore say that all the corresponding three sides of the two triangles are equal

i.e AC = BD

AB = CD

CB = CB

therefore triangle ABC and BCD are congruent

This means ;

∆ABC = ∆BCD

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