Construct triangle ABC, in which AB = 6cm, angle BAC = 96° and angle ABC = 35°.
Measure the length of BC.
Give your answer to 1 d.p.

Answer: D.

Step-by-step explanation:

Equilateral, scalene, and isosceles are all valid types of triangles.

Answer: $173.96

Step-by-step explanation: If I'm not mistaken first you have to take 106 and multiply it by 2 to count for the round trips so that makes 212 miles for one trip, then you have to multiple by 8 to figure out how many miles in total which equals  1696, then you divide by the 35 to figure out how many gallons she use, which is 48.457(rounded) then you multiple that by the rate of gas which is 3.59 which means she spent 173.96(rounded to the nearest tenth)

The equations after the transformations are given as follows:

a) Shifted 7 units up: [tex]y = 3^x + 7[/tex].

b) Shifted 6 units left: [tex]y = 3^{x + 6}[/tex]

c) Reflected over the x-axis and over the y-axis: [tex]y = -3^{-x}[/tex].

There are four cases for the translation of an image, and their rules are listed as follows:

In this problem, the function is:

y = 3^x.

For a shift of 7 units up, we have that:

y = f(x) + 7 = 3^x + 7.

For a shift of 6 units left, we have that:

y = f(x + 6) = 3^(x + 6).

The rules for reflections over the axes are given as follows:

Hence, for a reflection over both axes, the rule is:

y = -f(-x).

Considering the function in this problem, the rule is:

[tex]y = -3^{-x}[/tex]

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After 31 seconds, the bottle of Jason and Pedro will have the same amount of water.

According to the question,

We have the following information:

Jason's water bottle has 20 ounces of water, and he is drinking at the rate of 1 ouncer per second. Pedro's water bottle contains 65 ounces of water, and he is drinking at a rate of 2.5 ounces per second.

So, the water is decreasing at the constant rate. So, there will arithmetic progression where d is the rate.

Formula used to find nth term of an A.P:

an = a+(n-1)d where a is the first term

For Jason:

an = 20+(n-1)-1

an = 20-n+1

an = 21-n

For Pedro:

an = 65+(n-1)-2.5

an = 65-2.5n+2.5

an = 67.5-2.5n

Now, we have the following expression for equal amount of water:

21-n = 67.5-2.5n

21-67.5 = -2.5n+n

-46.5 = -1.5n

n = 46.5/1.5

n = 31

Hence, after 31 seconds, the bottle of Jason and Pedro will have the same amount of water.

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Answer:

Step-by-step explanation:

You can the greatest common factor and least common multiple of two numbers by prime factorization by finding common prime numbers and the prime numbers that account for both numbers respectively

A prime number has two factors, 1 and itself e.g. 2, 3, 5, 7, 11, etc.

When a number is written as a product of its prime factors, we have the prime factorization of the number e.g 8 = 2×2×2

By writing the prime factorization of two numbers we can find the greatest common factor(GCF) and least common multiple (LCM) of the numbers. For example 8 and 24:

The prime factorization of  8 and 24 is:

8 = 2×2×2

24 = 2×2×2×3

The greatest common factor of the two numbers is 2×2×2 = 8 because 2×2×2 appears in the prime factorization of both numbers

The least common multiple of the two numbers is 2×2×2×3 = 24 because all the elements of the prime factorization of both numbers must be accounted for

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The arc length of the curve [tex]y = ln(cos x)[/tex] from [tex]x = 0[/tex] to [tex]x = \pi /4[/tex] is [tex]\ln\left|\sqrt{2} + 1\right|[/tex]

To find the arc length of the curve[tex]y = ln(cos x)[/tex] from[tex]x = 0[/tex]to [tex]x = \pi /4[/tex], we will use the arc length formula for a curve given by y = f(x):

[tex]\text{Arc length} (L) = \int_a^b \sqrt{1 + \left[ f'(x) \right]^2} \, dx[/tex]

Where:

- a and b are the limits of integration (starting and ending points of the curve).

- f'(x) is the derivative of the function y = f(x).

First, we find the derivative of y = ln(cos x):

[tex]y = \ln(\cos x)\\y' = \dfrac{d}{dx}[\ln(\cos x)][/tex]

To find the derivative of ln(cos x), we use the chain rule:

[tex]y' &= \frac{1}{\cos{x}} \cdot (-\sin{x}) \\&= \frac{-\sin{x}}{\cos{x}}[/tex]

Now, we can find the arc length from x = 0 to x = π/4:

[tex]\text{Arc length } (L) = \int_0^{\frac{\pi}{4}} \sqrt{1 + \left( \frac{-\sin x}{\cos x} \right)^2} \, dx\text{Arc length } (L) = \int_0^{\frac{\pi}{4}} \sqrt{1 + \frac{\sin^2 x}{\cos^2 x}} \, dx\text{Arc length } (L) = \int_0^{\frac{\pi}{4}} \sqrt{\frac{\cos^2 x}{\cos^2 x} + \frac{\sin^2 x}{\cos^2 x}} \, dx\text{Arc length } (L) = \int_0^{\frac{\pi}{4}} \sqrt{\frac{\cos^2 x + \sin^2 x}{\cos^2 x}} \, dx[/tex]

Remember that [tex]cos^2 x + sin^2 x = 1[/tex], so the expression becomes:

[tex]\text{Arc length (L)} = \int_0^{\frac{\pi}{4}} \sqrt{\frac{1}{\cos^2 x}} \, dx[/tex]

Now, simplify the expression inside the square root:

[tex]\text{Arc length (L)} = \int_0^{\frac{\pi}{4}} \sqrt{\frac{1}{\cos x}} \, dx[/tex]

Integrate with respect to x:

[tex]\text{Arc length (L)} = \int_0^{\frac{\pi}{4}} \sqrt{Sec x} \, dx[/tex]

Now, evaluate the integral:

[tex]\text{Arc length} (L) = \ln\left| \sec x + \tan x \right| ~\text{from}~ 0 ~\text{to}~ \frac{\pi}{4}\text{Arc length} (L) = \ln\left| \sec \left( \frac{\pi}{4} \right) + \tan \left( \frac{\pi}{4} \right) \right| - \ln\left| \sec (0) + \tan (0) \right|[/tex]

[tex]\sec\left(\frac{\pi}{4}\right) = \sqrt{2}, \quad \tan\left(\frac{\pi}{4}\right) = 1\\\sec(0) = 1, \quad \tan(0) = 0\\\text{Arc length} (L) = \ln|\sqrt{2} + 1| - \ln|1 + 0|\\\text{Arc length} (L) = \ln|\sqrt{2} + 1|[/tex]

Using the property of natural logarithms, ln(a) - ln(b) = ln(a/b), we get:

[tex]\text{Arc length (L)} = \ln\left|\sqrt{2} + 1\right| - \ln\left|1\right|\\\text{Arc length (L)} = \ln\left|\sqrt{2} + 1\right|[/tex]

The arc length of the curve [tex]y = ln(cos x)[/tex] from [tex]x = 0[/tex] to [tex]x = \pi /4[/tex] is [tex]\ln\left|\sqrt{2} + 1\right|[/tex]

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Answer:

4,096

Step-by-step explanation:

=4^8 / 4^2

=4^6

=4,096

The answer is earthquakes: open up large cracks in Earth’s crust tsunamis: erosion of beaches.

What is tsunamis?

Giant waves that are brought on by ocean floor movement are known as tsunamis. Landslides, underwater volcanic eruptions, earthquakes, and even meteorite collisions can cause the ocean floor to tremble. These are often referred to as seismic sea waves, albeit they are sometimes misidentified as tidal waves. A tsunami is a set of waves that are caused by a disturbance in the ocean or another body of water, such as an earthquake, landslide, volcanic eruption, or meteorite strike.

The water above shifts up or down as a result of undersea earthquakes, which often take place along tectonic plate borders. Earth’s crust tsunamis: erosion of beaches.

Hence, earthquakes: open up large cracks in the Earth’s crust tsunamis: and erosion of beaches.

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These triangles can be proven congruent by using ASA RULE.

What is congruent triangles and its rules ?

When two triangles are congruent, their three sides and their three angles match precisely.

If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.

ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.

Main Body:

In ΔTUV and ΔTWV

VT =VT                 ----(1)

∠VTU=∠TVW      -----(2)

As TUVW is a parallelogram

so, ∠T = ∠U

hence, ∠TVU =∠VTW    ----(3)

taking equation 1, 2,3

therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.

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Answer:

(a.):  m∠ ACB = 40°; (b.):  m ∠CBA = 25°; (c.):  m ∠CAB = 115°

Step-by-step explanation:

Because Lines AB and DE are parallel, we can use the angle relationships to find the angles.

(For context of the problem, we can label the 40° angle as ∠C and the 155° as ∠B)

(a.) Angles C and ACB are vertical angles, which means they're congruent.  Thus m ∠ACB = 40°.

(b.) AB is a straight line and angles B and CBA are supplementary angles.  This means their total sum is 180°.  We need to subtract angle B from 180 to find m ∠CBA:

[tex]180-155=CBA\\25=CBA[/tex]

(c.) We know that the sum of all the angles is 180°.  Thus, we can subtract the sum of angles CBA and CBA from 180 to find the m ∠CAB:

[tex]180-(40+25)=CAB\\180-65=CAB\\115=CAB[/tex]

Answer:

Step-by-step explanation:

u=31/3

y=-11/9

Using the subtraction operation, the difference between 7x² + 3x - 5 and 2x² - 2x - 6 is 5x² + x + 1.

Mathematically, the difference is the result of a subtraction operation.

The difference is the product that results when the subtrahend is deducted from the minuend.

A subtraction operation is one of the basic mathematical operations, including addition, division, and multiplication.

  7x² + 3x - 5

-  2x² - 2x - 6

= 5x² + x + 1

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The equation which is quadratic in form is, [tex]6(2x+4)^2 = (2x+4)+2[/tex].

What is quadratic equation?

The polynomial equations of degree two in one variable of type

f(x) = ax^2 + bx + c = 0 and with a, b, c ∈  R and a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

Consider the given equations,

[tex]x^4-6x^2-27=0\\3x^4=2x^2\\2(x+5)^4+2x^2+5=0\\6(2x+4)^2=(2x+4)+2\\6x^4=-x^2+5\\8x^4+2x^2-4x=0[/tex]

The first, second, third, fifth and sixth equation are all having 4th degree.

So, by the definition of quadratic equation, these equations are not a quadratic.

Consider, the fourth equation,

[tex]6(2x+4)^2=(2x+4)+2\\[/tex]

Simplifying this, we get

[tex]6(4x^2 + 16x + 16 = 2x + 6\\24x^2 + 96x + 96 = 2x + 6\\24x^2 + 96x - 2x + 96 - 6 = 0\\24x^2 + 94x + 90 = 0[/tex]

This equation having degree 2.

Therefore the equation [tex]6(2x+4)^2 = (2x+4)+2[/tex] is a quadratic equation.

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Answer:5/25 0.18

and then .66 for 2/3 them multiply both of those numbers

Step-by-step explanation:.467

The area of the rectangle that has a width of 2√3 cm and a length of 5√27 cm is calculated as: 90 cm².

The area of a rectangle is calculated by multiplying the length and the width of the rectangle. It is given by the formula: Area = length × width.

Therefore, we are given the following dimensions:

length of rectangle = 5√27 cm

width of rectangle = 2√3 cm

Substitute the values into the area formula:

Area of rectangle = 5√27 * 2√3

= 5*3√3 * 2√3

= 15√3 * 2√3

Area of rectangle = 90 cm²

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Answer:

5

Step-by-step explanation:

Length is a positive number.  Count the spaces from -2 to -7

The side x is 6 cm when the triangle inside the parallelogram.

Given that,

In the picture we have triangle inside the parallelogram.

We have to find x side.

The parallelogram is ABCD.

Taking E as a midpoint of the AD.

The triangle is CDE.

The side CD is 6cm and ∠E is 90°.

The side ED is x cm.

Taking the trigonometric ratios that is

SinE= Opposite side/ hypothesis

Sin90° = 6cm /x cm

1= 6cm /x cm

x=6cm

Therefore, The side x is 6 cm when the triangle inside the parallelogram.

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The function f(x) = 12×[tex]5^{x-1}[/tex], x = week number

Given data,

week 1 = 12 visitors

week 2 = 60 visitors

week 3 = 300 visitors

week 4 = 1500 visitors

week 5 = 7500 visitors

The function can be given by :

f(x) = 12×[tex]5^{x-1}[/tex], x = week number

f(1) = 12×[tex]5^{0}[/tex] = 12

f(2) = 12×[tex]5^{1}[/tex] = 60

f(3) = 12×[tex]5^{2}[/tex] = 300

f(4) = 12×[tex]5^{3}[/tex] = 1500

f(5) = 12×[tex]5^{4}[/tex] = 7500

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The factors of (12+21) and (16x-36) using GCF are 3(4+7) and 4(4x-9) respectively.

According to the question,

We have the following two expressions:

(12+21) and (16x-36)

Now, in order to find the factors of given expressions using GCF, first we should know what is GCF.

GCF stands for Greatest Common Factor which means that the highest number which can divide all the terms of an expression.

So, we have:

12+21

3 can divide both 12 and 21:

3(4+7)

For second expression:

16x-36

4 can divide both the terms:

4(4x-9)

Hence, the factors of (12+21) and (16x-36) using GCF are 3(4+7) and 4(4x-9) respectively.

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Answer:

7 cm

Step-by-step explanation:

assuming you require the length of the 3 equal sides.

let one of the equal sides be x then perimeter is

P = 3x + 5

given P = 26 , then

3x + 5 = 26 ( subtract 5 from both sides )

3x = 21 ( divide both sides by 3 )

x = 7

the 3 equal sides are 7 cm each in length

a. For selling 1000 shoes, profit earned will be $140,000

Given,

Danielle is engineering a new brand of shoes. For x shoes sold,

in thousands, a profit of p(x) = -3x4 + 4x³ - 2x² + 5x + 10 dollars, in ten thousands, will be earned.

we are asked to determine the profit for selling 1000 shoes = ?

when sold 1000 shoes

X = 1 (in thousands)

substitute X=1 into p(x) = -3x⁴+4x³-2x²+5x+10

thus p(1) = -3×1⁴ + 4×1³ - 2×1² + 5×1 + 10

= -3+4-2+5+10

= 14 (in ten thousand)

so the profit is 14×10000 = 140,000

b. X intercepts means that when he sold X shoes, the profit p(x) equals zero, but the value doesn't make sense, because as long as he sold shoes, the profit would not be zero.

y intercepts means that when he sold zero shoes, the profit he earns,

calculate p(0)=10, the profit is greater than zero , it doesn't make sense, because if he sold zero shoes, there would not be income and profit.

Hence we get the required answers.

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Answer:

90

Step-by-step explanation:

14/20 = 0.7

28/40 = 0.7

63/90 = 0.7

Hope this helps.

Answer:

Step-by-step explanation:

The answer is D. 90 because the other numbers

14/20=.7

28/40=.7

63/90=.7

therefore, it would be 90.

The trigonometric equation cos² 2x is equivalent by reduction formulas to the expression 1 - 4 · cos² x + 4 · cos⁴ x.

Herein we find the case of a trigonometric equation involving a double angle that must be reduced into a single one by means of reduction formulas. First, write the trigonometric equation:

cos² 2x

Second, use the trigonometric fundamental formula:

1 - sin² 2x

Third, reduce the double angle by the sine formula for the double angle:

1 - 4 · sin² x · cos² x

Fourth, use again the trigonometric fundamental formula and expand the resulting expression:

1 - 4 · (1 - cos² x) · cos² x

1 - 4 · (cos² x - cos⁴ x)

1 - 4 · cos² x + 4 · cos⁴ x

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Answer:

550 coins

Step-by-step explanation:

2% = 2/100 = 0.02

11/0.02 = 550

The collection consists of 550 coins

Hope this helps

Answer:

39 bad checks because due to the math, 7 bad checks are received in a day

The probability of having at least one white marble, using the hypergeometric distribution, is of:

0.7778 = 77.78%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

In this problem, the values of these parameters are listed as follows:

The probability of having at least one white one is:

P(X > 0) = 1 - P(X = 0).

In which:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,10,5,2) = \frac{C_{2,0}C_{8,5}}{C_{10,5}} = 0.2222[/tex]

Then:

P(X > 0) = 1 - 0.2222 = 0.7778 = 77.78%.

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The solution to the questions are:

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

Length = 350 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

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

A = (350 - 2x) * x

Evaluate

A = 350x - 2x²

Differentiate and set to 0

350 - 4x = 0

So, we have

4x = 350

Divide by 4

x = 87.5

Recall that

Length = 350 - 2x

So, we have

Length = 350 - 2 x 87.5

Evaluate

Length = 175

The area is then calculated as

Area = Length x Width

So, we have

Area = 175 x 87.5

Evaluate

Area = 15312.5 square meters

Hence, the area is 15312.5 square meters

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The factorized form of the given polynomial is F(x) = 2x^4 + 3x³ + 4x² + 5x + 6.

We are given a polynomial. The highest degree of the polynomial is four. The polynomial is a biquadratic equation. We will try to find a solution by hit and trial method. We will use the positive and negative of the factors of the constant term. The factors of 6 are 1, 2, 3, and 6. One by one, we will substitute -1, 1, -2, 2, -3, 3, -6, and 6 in the polynomial equation and check if the equation becomes zero. We see that none of these numbers make the equation zero. So, the equation cannot be factorized.

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Answer:

which statement is true about these eight angles that are formed from parallel lines being cut by a transversal the answer is C