A pebble falls off a cliff at a height of
1,296ft . If the equation for height as a
function of time is
h(t) = -16t2 + initial height where t is time
in seconds and h(t) is height in feet, how
many seconds will it take for the pebble
to hit the ground?
[?] seconds
Enter

Answer:

4

Step-by-step explanation:

Since the base angles are the same, the side have to be the same

ML = MN

4x = x+3

Subtract x from each side

4x-x = x+3-x

3x= 3

Divide by 3

3x/3 = 3/3

x = 1

We want the length of MN

MN = x+3 = 1+3 = 4

The measurement of MN side is 4

The properties of the triangle are:

1. The sum of all the angles of a triangle (of all types) is equal to 180°.

2. The sum of the length of the two sides of a triangle is greater than the length of the third side.

3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

Since the base angles are the same, the side have to be the same

ML = MN

4x = x+3

Subtract x from each side

4x-x = x+3-x

3x= 3

Divide by 3

3x/3 = 3/3

x = 1

We want the length of MN

MN = x+3 = 1+3 = 4

Learn more about triangles here:

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Answer:

Measure of angle M = 41°

Step-by-step explanation:

From the figure attached,

NM ≅ NO [Given]

Therefore, ∠O ≅ ∠M [Opposite angle of the equal sides]

By triangle sum theorem,

m∠O + m∠N + m∠M = 180°

m∠O + m∠N + m∠O = 180° [Since, ∠M ≅ ∠O]

By substituting the values of the given angles,

(4y - 15)° + (7y)° + (4y - 15)° = 180°

(15y - 30) = 180

15y = 210

y = 14

Therefore, m∠M = (4y - 15)°

                           = 4(14) - 15

                           = 56 - 15

                           = 41°

Answer:

0.5(5 × 10) - 1

Step-by-step explanation:

((5 × 10) × 0.5) - 1

((50) × 0.5) - 1

25 - 1

24

Answer:

The angle of elevation of the plane measured from Ahmed is approximately 36.67°

Step-by-step explanation:

The given parameters of the float plane are;

The height of the float plane above the water, y = 350 m

The horizontal distance of the float plane from Ahmed, x = 470 m

Given that Ahmed is sitting on the dock, by the water, by trigonometric ratios, we have;

The height of the float plane, the distance of the plane from Ahmed and the line of sight forming the angle of elevation of the plane measured from Ahmed, form a right triangle

[tex]tan\angle X = \dfrac{Opposite \ leg \ length}{Adjacent \ Leg\ length}[/tex]

Therefore

[tex]tan(\theta) = \dfrac{y}{x}[/tex]

Where;

θ = The angle of elevation of the plane measured from Ahmed

y = The leg of the right triangle opposite the reference angle

x = The leg  of the right adjacent to reference angle

Therefore;

θ = arctan(y/x) which gives;

θ = arctan(350/470) ≈ 36.67°

The angle of elevation of the plane measured from Ahmed, θ ≈ 36.67°.

Answer:

n

Step-by-step explanation:

hb

Answer:

[tex] \displaystyle B) {x} = \log_{6} 118[/tex]

Step-by-step explanation:

we would like to solve the following exponential equation:

[tex] \displaystyle 2 \cdot {6}^{x} = 236[/tex]

to do so divide both sides by 2 which yields:

[tex] \displaystyle {6}^{x} = 118[/tex]

take log of base 6 in both sides so that we can solve the equation for x by using [tex]\log_ab^c=c\log_ab[/tex] and that yields:

[tex] \displaystyle \log_{6} {6}^{x} = \log_{6} 118[/tex]

use the formula:

[tex] \displaystyle {x} = \log_{6} 118[/tex]

hence,

our answer is B)

Answer:

[tex]\boxed{\sf Option \ B }[/tex]

Step-by-step explanation:

A equation is given to us and we need to find out the value of x . The given equation is ,

[tex]\sf\dashrightarrow 2 \times 6^x = 236 [/tex]

Transpose 2 to RHS , we have ,

[tex]\sf\dashrightarrow 6^x = \dfrac{236}{2} [/tex]

Simplify ,

[tex]\sf\dashrightarrow 6^x =118 [/tex]

Use log both sides with base "6"

[tex]\sf\dashrightarrow log_6 ( 6^x) = log_6 118 [/tex]

Using the property of log ,

[tex]\sf\longmapsto \bigg\lgroup \red{\bf log_p q^r = r log_p q}\bigg\rgroup[/tex]

[tex]\sf\dashrightarrow x \ log_6 6 = log_6 118 [/tex]

Again we know that ,

[tex]\sf\longmapsto \bigg\lgroup \red{\bf log_p p= 1}\bigg\rgroup[/tex]

We have ,

[tex]\sf\dashrightarrow x \times 1 = log_6 118 [/tex]

Therefore ,

[tex]\sf\dashrightarrow\boxed{\blue{\sf x = log_6 118 }} [/tex]

Hence option B is correct .

Answer:

100 mm

Step-by-step explanation:

Square root the area to find the length of each side

[tex]\sqrt[]{625} =25[/tex]

Multiply 25 by 4 to get the sum of all four sides for the perimeter

25 x 4 = 100

Answer:

2/5

Step-by-step explanation:

First, we can draw the rectangle out, as shown. The length is twice the width, and the diagonal, y, cuts across the rectangle. This forms a right triangle, and using the Pythagorean Theorem, we can say that

y² = x² + (2x)²

y² = x² + 4x²

y² = 5x²

square root both sides

y=√(5x²)

The diagonal, or y, is equal to √(5x²). This is equal to one side of the square

The area for the rectangle, which we need to find for the ratio, is length * width = x * 2x = 2x²

The area for the square, which we also need to find for the ratio, is (side length)² = √(5x²) = 5x²

The ratio for the area of the rectangle to the area of the square is therefore 2x²/5x² = 2/5 (crossing out the x² in both the numerator and the denominator). We know to put the rectangle on top because of the specific wording of "the ratio of the area of the rectangle to..."

The area of the trapezoid is 10 square units

The formula for finding the area of the trapezoid is expressed as:

A = 0.5(a+b)h

where:

a and b are the sides

h is the height

Given the following

a = 3

b = 2

h = 4

Substitute

A = 0.5(3 + 2)*4

A = 0.5(20)

A = 10 square units

Hence the area of the trapezoid is 10 square units

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Answer:

B) 5 Square Units

Step-by-step explanation:

Answered from another colleague :)

B1 = 2

B2 = 3

H = 2

A = 1/2 (B1 + B2) H

1/2 (2+3) 2

1/2 (5) 2

(2.5)2

5

Answer:

x> 1

Step-by-step explanation:

X-7>-6

Add 7 to each side

X-7+7>-6+7

x> 1

Answer:

proportion

Step-by-step explanation:

6.6/1.1 = 0.3/0.05

Using cross products

6.6 * .05 = 1.1 * .3

.33 = .33

Since this is a true statement, the statement is a proportion

Answer:

Q.D.E=(5+2i).(5-2i).i = (25-4i²)i = 25i-4i³

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

that is the procedure above

Step-by-step explanation:

4x = 6x-10

10 = 6x-4x

2x = 10

x = 5

Answer:

there is no diagram ......

Answer:

The answer is 26.4

Answer:

y = -2x + 1

Step-by-step explanation:

y2 - y1 / x2 - x1

-3 - 11 / 2 - (-5)

-14/ 7

= -2

y = -2x + b

-3 = -2(2) + b

-3 = -4 + b

1 = b

Answer:

the answer is point G

It is found that Point G is the midpoint of AB.

Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.

We are Given two points A and B which are located at -6 and 8 on the number line. We need to find the midpoint of AB.

First we have to calculate the distance between AB which can be calculated as;

8-(-6)=14 units

Now, to find the midpoint we have to divide the total distance by 2.

Hence, the mid point of AB is 7 units apart from both points A and B then G.

Learn more about midpoint here;

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Answer:

6

Step-by-step explanation:

We can find the common difference by subtracting one number in the sequence from the one ahead of it.

27-21=6

21-15=6

15-9=6

9-3=6

The differences between each number is 6.

Because the difference is the same between each number in the sequence, that makes 6 the common difference.

[tex]\fbox{Hii\:student!}[/tex]

__________________________________________________________

[tex]\multimap\parallel\boldsymbol{Answer.}\parallel\gets[/tex]

[tex]\textsl{the common difference is 6!}[/tex]

__________________________________________________________

[tex]\multimap\parallel\boldsymbol{Explanation.}\parallel\gets[/tex]

[tex]\textsl{here's how we find the common difference in the sequence:}[/tex]

[tex]\sf 27-21=6 \\ 21-15=6 \\ 15-9=6 \\ 9-3=6 \\the\;result\;is\;the\;common\;difference}[/tex]

[tex]\maltese\boldsymbol{\therefore,\:6\:is\;the\;common\;dif\!ference}[/tex]

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]

[tex]\boldsymbol{-Greetings!-}[/tex]

________________________________________________________

Answer:

LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . ... Example: In this example, the powers were multiplied together to give the answer which is 3 to the power of 6.

Answer:

B. 18 cm

Step-by-step explanation:

24 / 12 = 2.

9 x 2 = 18 cm.

Hope this helps!

Answer:

-11

Step-by-step explanation:

x = -7

To find = 3x + 10

= 3(-7) + 10

= -21 + 10

= -11

Answered by GauthMath if you like please click thanks and comment thanks.

Answer:

The perimeter is 10+10+5+5, or 30.

Step-by-step explanation:

The formula to find area is A=LW. Since the area is 50, we can assume that the width is 5, because 10x5=50. The perimeter is made up of the sides of a rectangle, or L+L+W+W. This is 10+10+5+5.

Answer:

[tex]\boxed{\sf sin\ C =\frac{40}{41}}[/tex]

Step-by-step explanation:

We need to find out the value of sinC using the given triangle . Here we can see that the sides of the triangle are 40 , 41 and 9 .

We know that the ratio of sine is perpendicular to hypontenuse .

[tex]\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}[/tex]

Here we can see that the side opposite to angle C is 40 , therefore the perpendicular of the triangle is 40. And the side opposite to 90° angle is 41 . So it's the hypontenuse . On using the ratio of sine ,

[tex]\sf\longrightarrow sinC =\dfrac{ p}{h}\\\\\sf\longrightarrow sin\ C =\dfrac{AB}{AC}[/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow \boxed{\blue{\sf sin\ C =\dfrac{40}{41}}}[/tex]

Hence the required answer is 40/41.

Answer:

Below in bold.

Step-by-step explanation:

x^2 - y^2 = 11

2x^2  + y^2 = 97

From the first equation:

y^2 = x^2 - 11

Substituting in the second equation:

2x^2 + x^2 - 11 = 97

3x^2 = 108

x^2 = 36

x = 6, -6.

Substituting  for x in the first equation:

(6)^2 - y^2 = 11

y^2 = 36 - 11 = 25

y = 5, -5.

Answer:

Its B

Step-by-step explanation:

You're correct

Answer:

Step-by-step explanation:

Given rule for the multiple translations is,

[tex]T_{5,-0.5}.R_{0.180^{\circ}}(x,y)[/tex]

Apply the rule [tex]R_{0,180^{\circ}}[/tex] first.

(x, y) → (-x, -y)

This rule illustrates a rotation of the triangle FGH by 180° about the origin,

Vertices of ΔFGH are,

F → (1, 1)

G → (4, 5)

H → (5, 1)

After rotation vertices of the image triangle are,

F' → (-1, -1)

G' → (-4, -5)

H' → (-5, -1)

Further apply the rule,

[tex]T_{5,-0.5}[/tex]

(x, y) → (x + 5, y - 0.5)

By this rule of translation,

F'(-1, -1) → F"{(-1 + 5), (-1 - 0.5)}

            → F"(4, -1.5)

G'(-4, -5) → G"[(-4 + 5), (-5 - 0.5)]

              → G"(1, -5.5)

H'(-5, -1) → H"[(-5 + 5), (-1 -0.5)]

             → H"(0, -1.5)

9514 1404 393

Answer:

  (-1, 1)

Step-by-step explanation:

Find the differences between an f(x) value and the previous one

  3 -18 = -15

  0 -3 = -3

  3 -0 = 3

  6 -3 = 3

  3 -6 = -3

Where the differences are positive, the function is increasing on the interval. Here, it is increasing on the intervals (-1, 0) and (0, 1). Then the longest increasing x-interval is (-1, 1).

Answer:

We can also graph inequalities on the number line. The following graph represents the inequality x≤2 . The dark line represents all the numbers that satisfy x≤2 . If we pick any number on the dark line and plug it in for x, the inequality will be true.

Answer:

Step-by-step explanation:

If it's for x:

-4 ≤ x ≤ 3