please help me on this

Answer:

Height of the cliff = 13.66 m

Step-by-step explanation:

Let the height of the cliff is 'x' m and distance between the base of the cliff and the boat is 'y' m.

From right triangle AOC,

tan 30° = [tex]\frac{\text{Opposite triangle}}{\text{Adjacent side}}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{x}{y}[/tex]

y = [tex]x\sqrt{3}[/tex] ------(1)

From right angle triangle BOC,

tan 45° = [tex]\frac{x}{y-10}[/tex]

[tex]1=\frac{x}{y-10}[/tex]

x = y - 10

y = x + 10 -------(2)

From equations (1) and (2),

[tex]x\sqrt{3}=x+10[/tex]

[tex]x(\sqrt{3}-1)=10[/tex]

[tex]x=\frac{10}{\sqrt{3}-1 }[/tex]

x = 13.66 m

Therefore, height of the cliff is 13.66 m.

Answer:

√ is 10

Step-by-step explanation:

Answer:

------->

Step-by-step explanation:

corresponding parts - angles or sides in the same position on similar figures

congruent - having the same exact size and shape

similar figures - figures that have the same shape but not necessarily the same size

congruent figures - figures that have the same size and shape

scale factor - the ratio between the lengths of corresponding sides in similar figures

Answer:

[tex]\huge\boxed{ x = 75 k}[/tex]

Step-by-step explanation:

The given ratio is:

=> 5 : 1

Given that the smallest one is 15k

So, Let's built a proportion:

=> 5 : 1 = x : 15   [Where x is the unknown one]

Product of Means = Product of Extremes

x = 5 * 15

=> x = 75 k

Answer:

The number of pennies are 91 pennies

Step-by-step explanation:

The given parameters are

When we split the pennies in twos the number left = 1

When the pennies are split in 3s the number left = 1

When the pennies are split in 5s the number left = 1

When the pennies are split in 7 the number left = 0

Therefore, 7 is a factor of the number

Given that when the pennies are split in 5s the number left = 1, the number ends with a 1

We have the products of 7 ending with 1 from Excel as 21 and 91, 161...

We check 91 given 21 is directly divisible by 3 as follows;

91/2 = 45 remainder 1

91/3 = 30 remainder 1

91/5 = 18 remainder 1

91/7 = 13 remainder 0

Therefore, the number of pennies are 91 pennies.

Answer:

10 weeks

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Remove parentheses.

|9+1|

Simplify  9+1  to 10.

|10|

simplify

10

Answer:

9xx2401x=21609x

Step-by-step explanation: 3x3=9. 40x40=1600, 40x9=360x2 because there are 2 of the same problem because the number is the same. 9x9=81.

Now we add them up. 1600+720+81=2401. 2401x9=21609

But don't forget to add the x at the end or the answer is wrong!!!

Answer:

The 7th roots are : [tex]$ 1, \frac{2 \pi}{7}, \frac{4 \pi}{7}, \frac{6 \pi}{7}, \frac{8 \pi}{7}, \frac{10 \pi}{7}, \frac{12 \pi}{7}$[/tex]

Step-by-step explanation:

The roots of unity are evenly spread around the unit circle.      

The roots of unity can be find by using the relation

[tex]$ 1= 1 ( \cos 0 ^\circ +i \sin ^\circ )$[/tex]

[tex]$\sqrt[n]{1} = 1 [\cos (\frac{2k \pi}{n}})+ i \sin (\frac{2k \pi}{n}) ] $[/tex]

Now z be a polynomial.

[tex]$z^7=1 \Rightarrow z = 1^{\frac{1}{7}}$[/tex]

therefore, cos 0 = 1.

[tex]$ z = \cos (2k \pi)^{\frac{1}{7}}$[/tex]                [tex]$ (\cos \theta)^n = \cos n \theta $[/tex]

[tex]$ z = \cos \frac{2k \pi}{7} $[/tex]

Now, for k=0, z = 1

[tex]$ k=1 \Rightarrow z = \cos \frac{2 \pi}{7} = \cos 3 \frac{2 \pi}{7}+ i \sin \frac{2 \pi}{7}$[/tex]

[tex]$ k=2 \Rightarrow z = \cos \frac{4 \pi}{7} = \cos \frac{4 \pi}{7}+ i \sin \frac{4 \pi}{7}$[/tex]

[tex]$ k=3 \Rightarrow z = \cos \frac{6 \pi}{7} = \cos \frac{6 \pi}{7}+ i \sin \frac{6 \pi}{7}$[/tex]

[tex]$ k=4 \Rightarrow z = \cos \frac{8 \pi}{7} = \cos \frac{8 \pi}{7}+ i \sin \frac{8 \pi}{7}$[/tex]

[tex]$ k=5 \Rightarrow z = \cos \frac{10 \pi}{7} = \cos \frac{10 \pi}{7}+ i \sin \frac{10 \pi}{7}$[/tex]

[tex]$ k=6 \Rightarrow z = \cos \frac{12 \pi}{7} = \cos \frac{12 \pi}{7}+ i \sin \frac{12 \pi}{7}$[/tex]

[tex]$ k=7 \Rightarrow z = \cos \frac{14 \pi}{7} = \cos \frac{14 \pi}{7}+ i \sin \frac{14 \pi}{7}$[/tex]

Then the 7th roots are : [tex]$ 1, \frac{2 \pi}{7}, \frac{4 \pi}{7}, \frac{6 \pi}{7}, \frac{8 \pi}{7}, \frac{10 \pi}{7}, \frac{12 \pi}{7}$[/tex]

Answer:

they are equivalent

Step-by-step explanation:

[tex]\frac{3}{6} = \frac{1}{2} (both \: can \: be \: divide \: by \: 3)[/tex]

[tex] \frac{4}{8} = \frac{1}{2} (both \: can \: be \: divide \: by \: 4)[/tex]

The two (2) fractions are equivalent.

In this exercise, you're required to determine whether or not given fractions are equivalent (equal). In order to do this, we would reduce the fractions to the lowest term.

Given the following fractions;

For Fraction A, we would divide both the numerator and the denominator by 3 because it's common to both them.

Fraction A = [tex]\frac{3}{6} = \frac{1}{2}[/tex]

Simplifying Fraction B, we have;

Fraction B = [tex]\frac{4}{8} = \frac{1}{2}[/tex]

Also, for two (2) fractions to be equivalent, their sums must be equal to one (1).

[tex]Fraction \;A + Fraction \;B = 1[/tex]

[tex]\frac{1}{2} + \frac{1}{2} = 1[/tex]

Therefore, we can deduce from the calculations that the two (2) fractions are equivalent.

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Work Shown:

Straight lines DF and EC intersect at point A. Because of this, angle DAF is a 180 degree angle.

Angles DAB, BAC, and CAF all combine to form a straight 180 degree angle.

Add up the angles mentioned, set the sum equal to 180, and solve for x

-----------

(angle DAB) + (angle BAC) + (angle CAF) = 180

x + 80 + 60 = 180

x + 140 = 180

x + 140-140 = 180-140 ... subtract 140 from both sides

x = 40

Answer:

[tex]\Huge \boxed{x=40\°}[/tex]

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

We can create an equation and solve for x.

x + 80 + 60 = 180

Add the numbers on the left side.

x + 140 = 180

Subtract 140 from both sides.

x + 140 - 140 = 180 - 140

x = 40

Answer:

63.057

Step-by-step explanation:

circumference= πd

Answer:

[tex] \boxed{ \boxed{ \bold{ \sf{63.05 cm}}}}[/tex]

Step-by-step explanation:

Given,

Circumference ( C ) = 198 cm

Diameter ( d ) = ?

Now, let's find the diameter of the circle :

We have,

[tex] \sf{c \: = \: \pi \: d}[/tex]

plug the values

⇒[tex] \sf{198 = 3.14 \: d}[/tex]

Swap the sides of the equation

⇒[tex] \sf{3.14 \: d \: = 198}[/tex]

Divide both sides of the equation by 3.14

⇒[tex] \sf{ \frac{3.14 \: d}{3.14} = \frac{198}{3.14} }[/tex]

Calculate

⇒[tex] \sf{d = 63.05}[/tex] cm

[tex] \underline{ \underline{ \sf{ \bold{ \blue{further \: more \: information}}}}}[/tex]

▪️[tex] \sf{ \bold{ Circumference}}[/tex]

⇒The perimeter of a circle is called it's circumference. It is the total length of the curved line of the circle.

▪️[tex] \sf{ \bold{ Radius}}[/tex]

⇒It is the line segment that joins the center of a circle and any point on its circumference.

▪️[tex] \sf{ \bold{Diameter}}[/tex]

⇒A line segment that passes through the centre of a circle and joins ant two points on its circumference is called the diameter of the circle. The length of a diameter is two times radius.

Hope I helped!

Best regards!!

Answer:

2x/3 - 5 = 21

2x/3 = 26

2x = 78

x = 39

Step-by-step explanation:

Answer:

x = 39

Step-by-step explanation:

Answer:

  maybe

Step-by-step explanation:

To use ASA, you need to show the side between the angles is congruent to the corresponding side. In ΔACB, you have shown that angles B and C are congruent to their counterparts. The side between angles B and C is BC.

To use ASA, you must show BC ≅ FE.

__

Not enough information is given here for us to tell how one might prove congruence of the triangles. Hence your approach may work, or it may not--depending on the given information.

Answer:

"statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] of the number of girls." is true.

Step-by-step explanation:

Given:

Ratio of Number of boys to the number of girls = 4 : 5

Total number of students = 270

To find:

Number of boys in terms of number of girls = ?

Solution:

As per given statement,

Let, Number of boys = [tex]4x[/tex]

Let, Number of girls = [tex]5x[/tex]

Total number of students = Number of boys + Number of girls = 270

[tex]\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}[/tex]

Therefore, number of boys = 4 [tex]\times[/tex] 30 = 120

And, number of girls = 5 [tex]\times[/tex] 30 = 150

As per Statement 1:

Finding [tex]\frac{4}5[/tex] of the number of girls:

[tex]\dfrac{4}{5}\times 150 = 4 \times 30 = 120[/tex] = Number of boys.

Finding [tex]\frac{4}9[/tex] of the total number of students:

[tex]\frac{4}{9}\times 270= 4 \times 30 = 120[/tex] = Number of boys.

Number of boys is equal to [tex]\frac{4}9[/tex] of total number of students.

So, "statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] of the number of girls." is true.

Answer:

-2 + 9i

Step-by-step explanation:

( 3 + 2i ) + ( -5 + 7i )

→ Remove brackets

3 + 2i +- 5 + 7i

→ Remember that the negative cancels out the plus

3 + 2i - 5 + 7i

→ Add the whole numbers together

-2 + 2i + 7i

→ Add the i values together

-2 + 9i

Answer:

[tex]\huge\boxed{-2 + 9i}[/tex]

Step-by-step explanation:

[tex]\sf (3+2i)+(-5+7i)\\Expanding \ Parenthsis\\3+2i -5 +7i\\Combining \ like \ terms\\3-5 + 2i+7i\\-2 + 9i[/tex]

This is the required answer in the form a + b i

Answer:

2.3 x 10^11.

Step-by-step explanation:

There are 11 digits after the first digit (2).

The answer is 2.3 x 10^11.

This is called scientific notation.

Answer:

(-8)/27

Step-by-step explanation:

Simplify the following:

(-2)/(3 (2 + 1/4))

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:

(-2)/(3 (4×2)/4 + 1/4)

4×2 = 8:

(-2)/(3 (8/4 + 1/4))

8/4 + 1/4 = (8 + 1)/4:

(-2)/(3 (8 + 1)/4)

8 + 1 = 9:

((-2)/3)/(9/4)

Multiply the numerator by the reciprocal of the denominator, ((-2)/3)/(9/4) = (-2)/3×4/9:

(-2×4)/(3×9)

3×9 = 27:

(-2×4)/27

-2×4 = -8:

Answer: (-8)/27

Answer:

-8/27

Step-by-step explanation:

-2/3 ÷ 2  1/4

Change to an improper fraction

-2/3 ÷ ( 4*2+1)/4

-2/3 ÷9/4

Copy dot flip

-2/3 * 4/9

-8/27

Answer:

c is the answer

Step-by-step explanation:

Answer:

D. 400 cu ft/

Step-by-step explanation:

1620 - 1180

= 440.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{10 {x}^{2} - 8x + 8}}}}}[/tex]

Option A is the correct option

Step-by-step explanation:

[tex] \sf{8 {x}^{2} + x - 5 + (2 {x}^{2} - 9x + 13)}[/tex]

When there is a ( + ) in front of an expression in parentheses , there is no need to change the sign of each term.

That means, the expression remains the same.

Also, Remove the unnecessary bracket

⇒[tex] \sf{8 {x}^{2} + x - 5 + 2 {x}^{2} - 9x + 13}[/tex]

Collect like terms

⇒[tex] \sf{8 {x}^{2} + 2 {x}^{2} + x - 9x - 5 + 13}[/tex]

⇒[tex] \sf{10 {x}^{2} - 8x - 5 + 13}[/tex]

Calculate

⇒[tex] \sf{10 {x}^{2} - 8x + 8}[/tex]

Hope I helped!

Best regards!!

Answer:

y = -3x + 13

Step-by-step explanation:

For slope-intercept form, you need the slope and the y-intercept.  To find the slope, you need to rearrange the given equation to slope-intercept form.

x - 3y = 9

-3y = -x + 9

y = 1/3x - 3

The slope for the given equation is 1/3.  The slope of a perpendicular line will be the negative reciprocal.  This means that the slope of the perpendicular line will be -3.

You can now solve for the y-intercept (b) using the slope (m) and the given point in slope-intercept form.

y = mx + b

1 = (-3)(4) + b

1 = -12 + b

13 = b

b = 13

Now that you have both the slope and y-intercept, you can find the equation.

y = -3x + 13

The equation of the line is y = -3x + 13

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The slope intercept form is given by:

y = mx + b

m = slope and b = y-intercept

We have,

A line perpendicular to line x - 3y = 9 and the line passes through the point (4, 1).

Make the line x - 3y = 9 in slope-intercept form.

-3y = 9 - x

y = (9 - x) / -3

y = (1/3)x - 3

The slope of the line x - 3y = 9 is:

m1=  1/3

Since the line required to find is perpendicular to the line x - 3y = 9

Let the required line slope be m2

m1 x m2 = -1

m2 = -1 / (1/3) = -3

The required line passes through the point (4, 1).

Let the required line be y = mx + b

we have,

1 = (-3)4 + b

1 = -12 + b

b = 13

We can write as:

y = -3x + 13

Thus the equation of the line is y = -3x + 13

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Answer:

A

Step-by-step explanation:

Answer:

The probability that a jar contains more than 466 g is 0.119.

Step-by-step explanation:

We are given that a jar of peanut butter contains a mean of 454 g with a standard deviation of 10.2 g.

Let X = Amount of peanut butter in a jar

The z-score probability distribution for the normal distribution is given by;

                                Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 454 g

           [tex]\sigma[/tex] = standard deviation = 10.2 g

So, X ~ Normal([tex]\mu=454 , \sigma^{2} = 10.2^{2}[/tex])

Now, the probability that a jar contains more than 466 g is given by = P(X > 466 g)

            P(X > 466 g) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{466-454}{10.2}[/tex] ) = P(Z > 1.18) = 1 - P(Z [tex]\leq[/tex] 1.18)

                                                                  = 1 - 0.881 = 0.119

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

Answer:

The answer is

Step-by-step explanation:

To make m the subject send n to the left side of the equation

That's

Divide both sides by 5

We have

Find the square root of both sides to make m stand alone

That's

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

r = 5m² - n

Add n to both sides

r + n = 5m² - n +n

r + n = 5m²

Divide both sides by 5

(r+n)/5 = 5m²/5

(r + n)/5 = m²

Take square root ,

[tex]\sqrt{\frac{r + n}{5}} =\sqrt{m^{2}} \\\\\sqrt{\frac{r + n}{5}}=m\\\\\\m=\sqrt{\frac{r + n}{5}}[/tex]

Answer: 1/4

Step-by-step explanation: In algebra, we use the word slope to describe how steep a line is and slope can be found using the ratio rise/run between any two points that are on that line.

So for the line you see here, let's use these two points to find its slope.

Let's go from left to right.

To get from the point that has the coordinates (0,1) to (4,2),

we rise 1 unit and run 4 units to the right and we end up the other point.

So the slope of this line is 1/4.

===============================================

Explanation:

To go from term to term, we are multiplying by 2

-7 * 2 = -14

-14 * 2 = -28

-28 * 2 = -56

This means the common ratio is 2 and this sequence is geometric.

---------

Alternatively, you can divide each term by its prior term

-56/(-28) = 2

-28/(-14) = 2

-14/(-7) = 2

Each time we get the same result showing the common ratio is 2.

Answer:

Geometric

Step-by-step explanation:

It multiplies by two each time

Answer:

B. Sen α = BC/b

Step-by-step explanation:

Para un ángulo recto, el lado opuesto es el lado opuesto al ángulo, el lado adyacente es el lado entre el ángulo y el ángulo recto y la hipotenusa es el lado más largo (el lado opuesto al ángulo recto).

De identidades trigonométricas:

[tex]sen\ \alpha=\frac{opuesto}{hipotenusa}[/tex]

De la figura, el lado opuesto = altura = BC y la hipotenusa = b. Por lo tanto:

[tex]sen\ \alpha=\frac{opuesto}{hipotenusa}\\\\sen\ \alpha=\frac{BC}{b}[/tex]

Answer:

50 miles per hour =73.33 feet per second (the conversion rate)

now if Morris is travelling 3 feet per second less than Aneesha so, the speed of Morris is 70.33 feet per second;

if we convert this to Miles per hour;

70.33 feet per second= 48 miles per hour (approximately)  

so here the last last option is the right

48 miles per hour

Answer:

48 miles per hour

Step-by-step explanation:

Answer:

In the problem, the sum of the two functions is 2x + 2

Step-by-step explanation:

For this problem, we have to add together f(x) and g(x).

f(x) = 9 - 3x

g(x) = 5x - 7

(f + g)(x) = (9 - 3x) + (5x - 7)

Combine like terms.

(f + g)(x) = 2x + 2

So, when you combine the two functions together, you will get 2x + 2.

The value of f(x)+g(x) according to the question given is; 2x + 2.

To evaluate the sum of functions f(x) and g(x); we have;

Therefore;

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