(Geometry)
I don’t know how to prove this

Answer:

Step-by-step explanation:

The value of measurement of the closest to the height of the mountain cliff in feet is,

⇒ Mountain Height = 360 feet

Given that;

When Donetle stands at point R, he is 1000 feet from point S at the base of a cliff.

And, When he looks up at an angle of 20 degrees, he sees a friend at the top of the mountain cliff at point T

Hence, By graph we get;

⇒ tan 20° = Mountain Height / 1000

⇒ 0.36 = Mountain Height / 1000

⇒ 0.36 × 1000 = Mountain Height

⇒ Mountain Height = 360 feet

Thus, The value of measurement of the closest to the height of the mountain cliff in feet is,

⇒ Mountain Height = 360 feet

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Let's see

[tex]\\ \rm\rightarrowtail x^2+12x+36=0[/tex]

[tex]\\ \rm\rightarrowtail x^2+6x+6x+36=0[/tex]

[tex]\\ \rm\rightarrowtail x(x+6)+6(x+6)=0[/tex]

[tex]\\ \rm\rightarrowtail (x+6)(x+6)=0[/tex]

[tex]\\ \rm\rightarrowtail x=-6[/tex]

Answer:

D

Step-by-step explanation:

The quotient is the result of dividing one number by another.

[tex]\frac{10}{\frac{1}{7} } = ?[/tex]

is how you would represent the quotient of 10 and 1/7.

The opposite of division is multiplication, and those we can rearrange that and get:

[tex]? * \frac{1}{7} = 10, or, ?/7 = 10[/tex]

or in other words, "what number divided by 7 is 10"

The answer becomes clearer, 70 is that number.

D represents this idea.

Answer:

144

Step-by-step explanation:

The equation to find c is:

[tex](\frac{b}{2} )^{2}[/tex]

So put -24 into b:

[tex](\frac{-24}{2} )^{2}[/tex]

Which simplifies to:

144

So if you want to test this:

x^2 - 24x + 144

is

(x-12)^2

Answer:

x = 3, y = 1

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}x+4y=7\\ 4x-3y=9\end{bmatrix}[/tex]

Solve:

[tex]\mathrm{Substitute\:}x=7-4y[/tex]

[tex]\begin{bmatrix}4\left(7-4y\right)-3y=9\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}28-19y=9\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=7-4y[/tex]

[tex]\mathrm{Substitute\:}y=1[/tex]

[tex]x=7-4\cdot \:1[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x=3[/tex]

[tex]\mathrm{The\:Answer\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=3,y=1[/tex]

Check Answer:

3 + 4(1)

7 (1) = 7

True

4(3) - 3(1)

12 - 3 = 9

True

Hence, x = 3 , y =1

~lenvy~

Question 1: Area of the base

          ⇒ Area of a Triangle --> [tex]\frac{1}{2}*(base)*(height)[/tex]

                ⇒ Area = [tex]\frac{1}{2} * 6 * 8 = 3 * 8 =[/tex] 24 square kilometers

Question 2: Height of Pyramid

          ⇒ Height = 12 km

          ⇒ [tex]\frac{1}{3} *24 * 12 = 8 * 12[/tex] = 96 cubic kilometers

Hope that helps!

The value which shows the true solution to the given logarithmic equation is 1.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

The given logarithmic equation is,

[tex]\rm log_{2} (x) + log_{2} (x +7) = 3.[/tex]

Use the addition property of log in the above expression.

[tex]\rm log_{2} (x \times (x +7) )= 3.\\ (x \times (x +7) ) = 2^{3} \\x \times (x +7) = 8\\x^{2} +7x-8=0[/tex]

Solve the quadratic equation we get,

[tex](x+8)(x-1)=0[/tex]

x = -8, 1

Here, the logarithmic function is defined only for positive real numbers as its input.

Thus, the value which shows the true solution to the logarithmic equation solved above is 1.

Learn more about the domain and range of the function:

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Answer:X=1

Step-by-step explanation:b on edge

Answer:

Melanie: y = 0.25x

Patrick: y = 0.03x + 5

Patrick's service is cheaper when 50 texts are sent or received in one month.

Step-by-step explanation:

Let's find out Melanie's monthly texting cost function using the table. We are given multiple points that the line describing her monthly text costs passes through, so we can use the slope formula to calculate the slope of this line first.

Substitute (5, 1.25) and (10, 2.50) into this formula.

Now we can use the point-slope equation to determine the line that describes Melanie's monthly texting cost.

I'm going to use the point (5, 1.25) and the slope m = 0.25.

We have Melanie's function:

We have Patrick's function:

We want to determine which service is cheaper when 50 texts are sent/received in one month.

The number of texts sent and received is represented with the variable "x", and the cost of this service is represented with the variable "y".

All we need to do is substitute 50 for x in both equations to see if Melanie or Patrick's service is cheaper.

Starting with Melanie:

Now with Patrick:

Patrick's service is substantially cheaper than Melanie's service when 50 texts are sent or received in one month.

Answer:

84

Step-by-step explanation:

Area of paralellogram: base x height

Now we multiply!!

6 x 14 = 84 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

A. (-4,-13)

Step-by-step explanation:

y = 2x - 5

y = 4x + 3

-2(y = 2x - 5) ==> -2y = -4x + 10

y = 4x + 3     ==>     y = 4x + 3

-2y = -4x + 10

y = 4x + 3

___________

-y = 13

/-1    /-1

y = -13

Now we find x, by substituting -13 for y

y = 2x - 5

-13 = 2x - 5

+ 5        +5

-8 = 2x

/2    /2

-4 = x

(x, y) ==> (-4, -13)

Check your answer:

y = 2x - 5

-13 = 2(-4) - 5

-13 = -8 -5

-13 = -13

This statement is correct

Hope this helps!

Answer:

x² + y² - 12x - 6y + 29 = 0

Step-by-step explanation:

Simplifying the equation using (a + b)² = a² + 2ab + b²:

(x - 6)² + (y - 3)² = 16

⇒ [x² - 2(x)(6) + 6²] + [y² - 2(y)(3) + 3²] = 16

⇒ [x² - 12x + 36] + [y² - 6y + 9] = 16

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

General form of a circle = x² + y² + Cx + Dy + E = 0

Before we reorganize the equation in general form, we need to have the R.H.S as 0. For that, we need to subtract 16 both sides.

Subtract 16 both sides:

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

⇒ x² - 12x + 36 + y² - 6y + 9 - 16 = 16 - 16

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

Reorganizing the equation in general form:

x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x - 6y + 20 + 9 = 0

⇒ x² + y² - 12x - 6y + 29 = 0

Thus, the equation in general form is x² + y² - 12x - 6y + 29 = 0.

The Hypotheses are; Null Hypothesis; H₀: μ = 76.4 and Alternative Hypothesis; Hₐ: μ > 76.4 where μ is the true mean height of all trucks.

We are given;

Population Mean; μ = 76.4 inches

Sample Mean; x' = 77.1 inches

Sample standard deviation; s = 5.2 inches

Sample size; n = 100 trucks

Now we can thus define the hypotheses as;

Null Hypothesis; H₀: μ = 76.4

Alternative Hypothesis; Hₐ: μ > 76.4

where μ is the true mean height of all trucks

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The conclusion based on the mean of the ball and the distance traveled is D. Inferences cannot be made about all the golf balls produced on that day.

From the information given, a golf pro randomly selects a ball, not knowing the type of ball, hits it and end of the session, the mean distance traveled for the new type of golf ball was found to be greater than the mean distance for the original-style golf ball.

In this case, inferences cannot be made about all the golf balls produced on that day; however, the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.

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Answer:

should be A. Inferences can be made about all the golf balls produced on that day, and the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.

Step-by-step explanation:

correct for edge, nov. 2022

Answer:

Step-by-step explanation:

Basic propotionality theorem: If a line is drawn paralle to one side of a triangle and intersect other two sides in distinct points, then the line segment divide the two linesin same ratio.

[tex]\sf \dfrac{LP}{PN}=\dfrac{LO}{OM}\\\\\dfrac{x+12}{5}=\dfrac{22}{8}\\\\\text{cross multiply,}\\\\[/tex]

8*(x + 12) = 22*5

8x + 8*12 = 110

 8x + 96 = 110

        8x = 110 - 96

        8x = 14

          x = 14/8

          x = 1.75

Answer:

21

Step-by-step explanation:

-9=9

9+12=21

Answer:

Step-by-step explanation:

???? Could you verify the question please?

The probability of winning when there is only one prize, is:

P = 1/2,790,720

Each ticket has 6 different numbers, in order, from 1 to 20.

The total number of possible combinations is given by the product between the numbers of options, so there are:

C = 20*19*18*17*16*15 = 27,907,200 possible tickets.

So, if Trina purchases 10 tickets, she has a probability of 10 out of 27,907,200 winning (when we assume that there is only one prize)

Then the probability is:

P = 10/27,907,200 = 1/2,790,720

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The object attached to a string illustrates a sinusoidal trigonometric function

The trigonometric function is H(t) = 5sin(π/2(t-0.2))-20, and the object's height after 0.6 seconds is  -17.06 cm

The trigonometry model of the object is a sine function represented by:

H(t) = Asin(B(t - c)) + D

The maximum height is 5 cm.

So, we have:

Amplitude, A = 5

The average height is - 20 cm.

So, we have

Vertical shift, D = -20

Its first average height is at t = 0.2.

So, we have:

Horizontal shift, C = 0.2

The period B is then calculated as:

B = π/t

The object reaches the maximum height every 2 seconds.

So, we have:

B = π/2

Substitute these values in H(t) = Asin(B(t - c)) + D

H(t) = 5sin(π/2(t-0.2))-20

Hence, the trigonometric function is H(t) = 5sin(π/2(t-0.2))-20

Substitute 0.6 for t in H(t)

H(0.6) = 5sin(π/2(0.6-0.2))-20

Evaluate

H(0.6) = -17.06

Hence, the object's height after 0.6 seconds is  -17.06 cm

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Answer:

What is the importance of biology laboratory?

Biological Science Laboratory Apparatus is essential for meeting our basic needs of food, clothing, shelter, health, energy, clean air, water and soil. Biological Science Laboratory Apparatus enrich the quality of life in numerous ways by providing new solutions to problems in health and materials and energy usage.

Answer:

899 ft

Step-by-step explanation:

if point a is 400 feet from the base and 499 feet away from the top you would need to add 400+499 together to get 899

The answer is: Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.

Answer:

1 pound of potatoes costs $0.87

Answer:

-2

Step-by-step explanation:

The average rate of change is the slope using the points (0, 10) and (3, 4).  The slope is found using the formula [tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{4-10}{3-0}= \frac{-6}{3}=-2[/tex]

Answer:

5a + ab = 40

Step-by-step explanation:

Sub in 10 for a, making the equation 5 x 10 + 10 x b

Then sub in - 1 for b making it 5 x 10 + 10 x - 1

Then multiply making it 50 + - 10

Then subtract since adding negative is actually subtracting and you get 40

Hey there!

In order to evaluate this expression, all we should do is plug in the values of the variables and simplify.

We are given that

a=10

b=-1

Plug in the values:

5(10)+(10)(-1)

multiply 5 times 10 and 10 times (-1) and add the products:

50+(-10)

or... actually subtract.

50-10

40

Hence, the answer is

[tex]\boxed{\boxed{\bold{40}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#LearningDoesn'tEnd

:-)

The number [tex]4.5*10^{-3}[/tex] is written in scientific notation whereas the rest of the numbers are not written in scientific notation.

Given numbers are:

1)[tex]4.5*10^{-3}[/tex]

2)[tex]14.5*10^{2}[/tex]

3)[tex]0.78*10^{-6}[/tex]

4)[tex]5.7*4^8[/tex]

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

In the first number [tex]1 < 4.5 < 10[/tex] multiplied by [tex]10^{-3}[/tex]

As per the definition [tex]4.5*10^{-3}[/tex] is written in scientific notation.

The Rest of the numbers do not follow the definition of scientific notation so they are not in scientific notation.

Hence, the number [tex]4.5*10^{-3}[/tex] is written in scientific notation whereas the rest of the numbers are not written in scientific notation.

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Answer:

4 1/14

Step-by-step explanation:

1 5/14 x 3 = 4 1/14

Answer:

4 1/14 pages

Step-by-step explanation:

multiply 1 5/14 by 3

start by multiplying 1 by 3 which is 3

then multiply 5/14 by 3, you just have to multiply the 5 and you get 15/14 which is 1 1/14

add 3 and 1 1/14 and you get 4 1/14

Answer:

30 fish

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

5 tanks with 30 fish each so 5x30

5x30=150

Answer:

 (x3 - 2x2 - 4) • (x + 2)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 (((x4) -  22x2) -  4x) -  8

STEP

2

:

Checking for a perfect cube

2.1    x4-4x2-4x-8  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x4-4x2-4x-8

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x4-8

Group 2:  -4x2-4x

Pull out from each group separately :

Group 1:   (x4-8) • (1)

Group 2:   (x+1) • (-4x)

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(x) = x4-4x2-4x-8

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -8.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4 ,8

Answer:

5, 6, 7

Step-by-step explanation:

5 + 6 + 7 = 18

Answer:

15,16,17

Step-by-step explanation:

The question states, The sum of three consecutive, positive, even integers is 18 more than twice the smallest.

Let a,b,c be positive integers

Let a be the smallest integer.

Because the answer says the sum of the integers has to be 18 more than   2 x  the smallest integer. It means the situation can be represented as:

a + b + c = 2a + 18

Because these numbers are consecutive, meaning they are right besides each other. Every variable can be written in terms of a.

a = a

b = a + 1

c = a + 2

Now we can solve for a:

a + (a+1) + (a+2) = 2a + 18

a + a + 1 + a + 2 = 2a + 18

3a + 3 = 2a + 18

a + 3 = 18

a = 15

then we can fill in the rest.

b = (15) + 1 = 16

c = (15) + 2 = 17

Now we verify.

15 + 16 + 17 = 2(15) + 18 ?

15 + 16 + 17 = 48

2(15) + 18 = 48

We now have the solution. The consecutive numbers, are, and can only be

15,16,17

Hello!

The first step is to subtract 1 from both sides.

[tex]\bf{3x+1=38}[/tex]

[tex]\bf{3x=37}[/tex]

Now, divide both sides by 3:

[tex]\bf{\displaystyle\frac{37}{3} }[/tex]

Can this fraction be simplified? Nope.

Why? Because 37 and 3 do not have any common factors, except 1 (and what's the point of dividing by 1?)

Hence, the answer is

[tex]\huge\boxed{\text{Answer:{\boxed{\circ\star{\frac{37}{3} }}}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#KeepOnLearning

[tex]\boxed{An~Emotional~Helper!}[/tex]

Scalene triangle: if none of the three sides of a triangle are equal to each other, it is called a scalene triangle.

Equilateral triangle: An equilateral triangle is a triangle in which all three sides have the same length.

Isosceles triangle: An isosceles triangle is a triangle that has two sides of equal length.

Acute Triangle: An acute triangle is a triangle with three acute angles.

Right Triangle: A triangle in which one of the interior angles is 90° is called a right triangle.

Obtuse Triangle: An obtuse triangle is a triangle with one obtuse angle and two acute angles.