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:

x> 1

Step-by-step explanation:

X-7>-6

Add 7 to each side

X-7+7>-6+7

x> 1

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

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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..."

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:

-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.

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:

0.5(5 × 10) - 1

Step-by-step explanation:

((5 × 10) × 0.5) - 1

((50) × 0.5) - 1

25 - 1

24

Answer:

n

Step-by-step explanation:

hb

Answer:

Its B

Step-by-step explanation:

You're correct

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:

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

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.

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Answer:

B. 18 cm

Step-by-step explanation:

24 / 12 = 2.

9 x 2 = 18 cm.

Hope this helps!

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:

there is no diagram ......

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:

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:

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:

[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:

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:

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.

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:

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:

[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:

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

Step-by-step explanation:

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)

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 26.4