From the top of a vertical cliff 75.0m high, forming one bank of a river, the angles of depression of the top and bottom of a vertical cliff which forms the opposite bank are 22° and 58° respectively. Determine the height of the second cliff and width of the river

Answer:

According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.

Step-by-step explanation:

Let consider a second-order polynomial of the form [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex], [tex]\forall \,x \in\mathbb{R}[/tex]. The procedure is presented below:

1) [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex] (Given)

2) [tex]a\cdot x^{2} + b \cdot x = -c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)

3) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x = -4\cdot a \cdot c[/tex] (Compatibility with multiplication)

4) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x + b^{2} = b^{2}-4\cdot a \cdot c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)

5) [tex](2\cdot a \cdot x + b)^{2} = b^{2}-4\cdot a \cdot c[/tex] (Perfect square trinomial)

According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.

Answer: D

Step-by-step explanation:

EDGE 2023

Answer:

c = 6√2

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 30°

Opposite = 3√2

Hypothenus = c

The value of 'c' can be obtained by using the sine ratio as shown below:

Sine θ = Opposite /Hypothenus

Sine 30° = 3√2/c

Cross multiply

c × sine 30° = 3√2

Divide both side by sine 30°

c = 3√2 / sine 30°

But: sine 30° = 1/2

c = 3√2 / sine 30°

c = 3√2 ÷ 1/2

c = 3√2 × 2

c = 6√2 yard

Therefore, the value of 'c' is 6√2 yard.

Answer:

subtract 3 from both sides

Step-by-step explanation:

Given

- 4.5x + 3 = 2 - 8.5x ( add 8.5x to both sides )

4x + 3 = 2 ( subtract 3 from both sides )

4x = - 1 ( divide both sides by 4 )

x = - [tex]\frac{1}{4}[/tex]

Answer:

subtract 3 from both sides

Step-by-step explanation:

D, the last one

Answer:

1/19

Step-by-step explanation:

Let's say there are x yellow cubes.

That means there are 3x blue cubes.

Therefore, there must be 15x green cubes.

In total: we have 19x cubes.

Therefore the probability of a cube being yellow is x / 19x

which simplifies to 1/19

Answer:

1/19

Step-by-step explanation:

Solution:-

- First we will define the distribution of colors in the bag.

- We will use variable:

                     x: the number of yellow cubes in bag

- The following color distribution can be made by using the data given in the question:

                   Color                     Number of cubes

                   Yellow                               x

                   Blue                                  3*x = 3x

                   Green                               3x*5 = 15x

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

                  Total                                 19x

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

- Sarah is to draw a cube from the bag. We are to determine the probability that the randomly picked cube would be yellow. We will denote our event as randomly picking a yellow cube from the bag with a defined finite distribution.

         p ( Picks Yellow cube ) = [ Number of yellow cubes ] / [ Total cubes ]

         p ( Picks Yellow cube ) = [ x ] / [ 19x ]

         p ( Picks Yellow cube ) = 1 / 19   .... Answer

Answer:

10

Step-by-step explanation:

nCr = 5!/(3! × (5 - 3)!)

= 10

123/ 124/ 125/ 134/ 135/ 145/ 234/ 235/ 245/ 345

The formula for combinations is generally n! / (r! (n -- r)!), where n is the total number of possibilities to start and r is the number of selections made. In our example, we have 52 cards; therefore, n = 52.

Answer: get 2 more frames

Step-by-step explanation:

angle HDG = angle HFE

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

Explanation:

We have the statement [tex]\triangle DHG \cong \triangle FHE[/tex] given to us. Note that "H" is in the middle for both sequences of three letters. For DHG, start at H and move back one space to get to D. Move back another unit to wrap around to G. So the new sequence is HDG which forms the first angle.

Follow the same pattern but for FHE now. Start at H, move backward one spot to F, then move back again to wrap around to E. We have HFE

This shows angle HDG pairs up with angle HFE. The corresponding angles are congruent due to CPCTC

CPCTC = corresponding parts of congruent triangles are congruent

Notice how angles HDG and HFE are alternate interior angles, which lead to showing DG is parallel to EF.

Answer:

Length is 12 feet, and Width is 10 feet

Step-by-step explanation:

You can use an equation to come up with the answer but you are looking for width × (width + 2) = 120.

Answer:

You just need to demonstrate that the expression is not equivalent. To do that, we just need to evaluate the expression with a specific number.

[tex]\frac{3}{8}x+2 \neq \frac{3}{2}x+5[/tex]

For [tex]x=0[/tex], we have

[tex]\frac{3}{8}(0)+2 \neq \frac{3}{2}(0)+5\\2 \neq 5[/tex]

Notice that the answer is true because 2 is not equivalent to 5.

Therefore, the expression is actually non-equivalent.

Answer:

B) Reflection along y-axis; Translation: (x, y) → (x, y – 3)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a new position. If an object is transformed, all its points are also transformed. Types of transformation are dilatation, rotation, reflection and translation.

The point of triangle ABC are A(-4, 4), B(-7, 1) and C(-3, -2) while for triangle A'B'Ç' is at A'(4, 1), B'(7, -2) and C'(3, -5)

If a point C(x, y) is reflected along y axis, the y coordinates is the same and the x coordinate is opposite (negated), i.e C'(-x, y). If a point C(x, y) is translated 3 units down, the new point is (x, y - 3).

ΔABC transformation to ΔA'B'C', the x coordinate is opposite and the y coordinate is 3 units downward, therefore this is a Reflection along y-axis; Translation: (x, y) → (x, y – 3)

Answer: c

Step-by-step explanation:

The answer is c bc you reflect across the y axis and then translate

Answer:

105 m

Step-by-step explanation:

Given that Jules has a mirror that has a shape of a triangle, the length of the border Jules would add = the perimeter of the triangular mirror.

The perimeter of the triangular mirror is simply the sum of all the 3 sides of the triangle.

Since, each side is of equal length (35 cm), therefore, perimeter of the mirror = 35 + 35 + 35 = 105 m

Perimeter of mirror = length of border to add = 105 m

The border is 105 m long.

Answer:

7.5 jars

Step-by-step explanation:

There are 25 students in the art class.

Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.

The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.

That is:

25 * 0.3 = 7.5 jars of paint

Mr Jones needs 7.5 jars of paint for the art project.

Answer:

0.4.84

Step-by-step explanation:

you divide the 40 by 100

Answer:

They are on their simplified form.

Step-by-step explanation:

Since these numbers are prime numbers we can't simplify them. But we can change them to decimal.

1/2=0.5

1/3=0.3 (in which 3 repeats itself)

Hope this helps ;) ❤❤❤

Answer:

a) x° = 108°

b) vertically opposite angles (C) justifies my answer.

Answer:

The answer is option c.

Its an vertically opposite angle because when two lines intersect eachother then theangles formed opposite to it is called v.o.a (vertically opposite angle)

Hope it helps...

Answer: 1/10

Step-by-step explanation:

given:

numbers contained in the i.d

1,4,3,7,6

1. permutations of 5 possible outcome

T = 5

= 5 * 4 * 3 * 2 *1

= 120 times.

2. permutations  of  3 odd numbers

( 1,3 and 7 )

T = 3

= 3 * 2 * 1 * 2 * 1

= 12

probability of of first three digits being odd numbers

P = 12 / 120

= 1 / 10

Answer: The probability is 0.10

Step-by-step explanation:

The ID number has five digits, and the digits can be 1, 4, 3, 7 and 6, and I will assume that each digit appears only once.

Then if we want to calculate the probability that the first 3 digits will be odd is:

Suppose that we have 5 slots, we want that in the first two slots to have odd numbers.

In our set, we have only 3 odd numbers {1, 3 and 7}

Then if we want an odd number in the first digit, we have 3 options

If we want an odd number in the second digit, we have two options (because we already selected one in the first selection)

If we want an odd number in the first digit, we have only one option.

For the fourth digit we have one of the two remaining even options, so we have 2 options.

For the fifth digit, we have only one digit.

The number of combinations is equal to the product of the number of options in each selection:

c = 3*2*1*2*1 = 12

Now, the total number of combinations is:

For the first digit we have 5 options

for the second digit we have 4 options.

for the third digit we have 3 options.

for the fourth digit we have 2 options.

for the fifth digit we have 1 options.

The number of combinations is:

C = 5*4*3*2*1 = 120.

Then the probability that the first 3 digits are odd numbers, is equal to the quotient between number of combination that start with 3 odd digits and the total number of combinations:

P = c/C = 12/120 = 0.10

Answer:  D) 9, 15, 21, 27, ...

Step-by-step explanation:

Notice that the difference (d) for each option is 6.

Divide 2019 by 6 to see what the REMAINDER is (this is the first term).

2019 ÷ 6 = 336 r.3

None of the options start with 3 so the next option would be 3 + 6 = 9.

The only option that starts with 9 is option D.

Answer:

15 mL of the solution with 20% water will be needed.

Step-by-step explanation:

Use the inverse relationship

10 mL * (18-15)% = x mL * (20-18)%

x = 10 mL * (3/2) = 15 mL

Answer: 15mL

Step-by-step explanation:

Create a table. Multiply across and add down. The bottom row (Mixture) creates the equation.

                   Qty     ×     %             =      Total          

Solution A     10         15% → 0.15          10(0.15) = 1.5

Solution B      x          20% → 0.20        x(0.20) = 0.20x

Mixture      10 + x   ×    18% → 0.18   =    1.5 + 0.20x

                                  (10 + x)(0.18) = 1.5 + 0.20x

                                    1.8 + 0.18x  = 1.5 + 0.20x

                                    1.8               = 1.5 + 0.02x

                                    0.3              =          0.02x

                                                15  =  x

Answer:

The 1st selection is appropriate.

_____

2nd: the rotation would need to be 90° CCW

3rd, 4th: rotation or double reflection will give the original orientation. This figure is reflected an odd number of times, so has its orientation reversed.

Hope it helps.. Mark brainliest

The sequence of transformations are reflection over the y-axis and then a rotation 90 clockwise about the origin.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, figure G is rotated 90° clockwise about the origin and then reflected over the x-axis, forming figure H.

Vertices of triangle G are (-3, 1), (-1, 2) and (-2, 5).

The reflection of point (x, y) across the y-axis is (-x, y).

On reflection over x-axis, we get coordinates as (3, 1), (1, 2) and (2, 5)

90° clockwise rotation: (x, y) becomes (y, -x)

On 90° clockwise rotation, we get coordinates as (1, -3), (2, -1) and (5, -2)

Triangle H has points (2, -1), (1, -3), (5, -2).

Hence, the sequence of transformations are reflection over the y-axis and then a rotation 90° clockwise about the origin.

Learn more about the rotation of 90° counterclockwise here:

brainly.com/question/1571997.

#SPJ6

Answer:

Hey there!

3x+y=7

2x+y=6

3x+y=7

-2x-y=-6

Add these two equations vertically so the y terms cancel out (this is known as the elimination method)

x=1

3x+y=7

3(1)+y=7

3+y=7

y=4

(x=1, y=4)

Hope this helps :)

Answer:

 3.0 mi/h < σ < 8.54 mi/h

Step-by-step explanation:

Given:

Sample data:  x: 65 62 62 55 62 55 60 59 60 70 61 68

Confidence = c = 98% = 0.98

To find:

Construct a 98​% confidence interval estimate of the population standard deviation.

Solution:

Compute Mean:

number of terms in data set = n = 12

Mean = Sum of all terms / number of terms

          = 65 + 62 + 62 + 55 + 62 + 55 + 60 + 59 + 60 + 70 + 61 + 68 / 12

          = 739/12

Mean  = 61.58

Compute standard deviation:

s = √∑(each term of data set - mean)/ sample size - 1

s = √∑([tex]_{x-} {\frac{}{x} }[/tex])²/n-1

  = √( 65 - 61.58)² + (62 - 61.58)² + (62 - 61.58)² + (55 - 61.58)² + (62 - 61.58)² + (55 - 61.58)² + (60 - 61.58)² + (59 - 61.58)² + (60 - 61.58)² + (70 - 61.58)² + (61 -61.58)² + (68 - 61.58)² / 12-1

  = √(11.6964 + 0.1764 + 0.1764 + 43.2964 + 0.1764 + 43.2964 + 2.4964 + 6.6564 + 2.4964 + 70.8964 + 0.3364 + 41.2164) / 11

  = √222.9168/11

  = √20.2652

  = 4.50168

  = 4.5017

s =  4.5017

Compute critical value using chi-square table:

For row:

degree of freedom = n-1 = 12 - 1 = 11

For Column:

(1 - c) / 2 = (1 - 0.98) / 2 = 0.02/2 = 0.01

1 - (1 - c) / 2 = 1 - (1-0.98) / 2 = 1 - 0.02 / 2 = 1 - 0.01 = 0.99

[tex]X^{2} _{1-\alpha/2}[/tex] = 3.053

[tex]X^{2} _{\alpha/2}[/tex] = 24.725

Compute 98​% confidence interval of standard deviation:

[tex]\sqrt{\frac{n-1}{X^{2} _{\alpha/2}} } s[/tex]  = [tex]\sqrt{\frac{12-1}{24.725} } ( 4.5017)[/tex] = [tex]\sqrt{\frac{11}{24.725} } ( 4.5017)[/tex] =  [tex]\sqrt{0.44489}(4.5017)[/tex]

             = 0.6670 (4.5017) = 3.0026

[tex]\sqrt{\frac{n-1}{X^{2} _{\alpha/2}} } s[/tex]  =  3.0026

[tex]\sqrt{\frac{n-1}{X^{2} _{1-\alpha/2}} } s[/tex] =  [tex]\sqrt{\frac{12-1}{3.053} } ( 4.5017)[/tex] =  [tex]\sqrt{\frac{11}{3.053} } ( 4.5017)[/tex] =  [tex]\sqrt{3.6030} (4.5017)[/tex]

               =  1.8982 ( 4.5017) = 8.5449

[tex]\sqrt{\frac{n-1}{X^{2} _{1-\alpha/2}} } s[/tex]  = 8.5449

3.0026 mi/h < σ < 8.5449 mi/h

Answer:

Alternate interior angles theorem

Step-by-step explanation:

DG // EF   and GE is the transversal. So, alternate interior angles are congruent

Therefore, ∠HGD ≅ ∠HEF

DG // EF   and DF is the transversal. So, alternate interior angles are congruent

Therefore, ∠HDG ≅ ∠HFE

Answer:

Step-by-step explanation:

it is ASA

by definition if two pairs of corresponding angles and the side between them are known to be congruent, the triangles are congruent. This shortcut is known as angle-side-angle (ASA)

Answer:

B.

Step-by-step explanation:

We know that

Line FG is 7.0 meters

Angle G is 90 degrees

Angle G is 25 degrees

All of the angles of a triangle add up to 180 degrees

We need to find the angle of F

90+25+f=180

115+f=180

f=65 degrees

Now we have narrowed our answers down to A, B, and D

Next we need to find the measure of line GH

For this we will need to use one of the three, Sin, Cos, Tan.

We will be using Tan because we have our variable adjacent to our angle and our number 7 opposite of our angle.

We are looking for the measure of GH

Tan60=7/x

x=3.3

Answer:

1.) Zero ( 0 )

2.) 55.47 feet , 8.6 feet

3.) 17.2 feet

Step-by-step explanation:

The height, in feet, of the ball is given by the equation h(x)=−.25x2+4.3x, where x is the number of feet away from the golf club (along the ground) the ball is.

1.) Since the equation has no intercept,

The ball will start zero feet above the ground.

2.) The distance of the ball at the maximum height will be achieved by using the formula

X = -b/2a

Where b = 4.3, a = -0.25

Substitutes both into the formula

X = -4.3 / 2( - 0.25 )

X = - 4.3 / - 0.5

X = 8.6 feet

Substitute X into the function to get the maximum height

h(x) = −.25(8.6)^2 + 4.3(8.6)

h(x) = 18.49 + 36.98

h(x) = 55.47 feet

3) As the ball returns to the ground, the height will be equal to zero, therefore,

0 = -0.25x^2 + 4.3x

0.25x^2 = 4.3x

X = 4.3/0.25

X = 17.2 feet

The ball returns to the ground at about 17.2 feet away

Answer:

20 miles

Step-by-step explanation:

Given that :

When the car traveling north 'N' had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading east

Let the distance moved by the east bound car be e,

therefore, distance between the cars when the northbound car had traveled a distance of 15 miles = e + 5

Using Pythagoras rule:

(Hypotenus)^2 = (adjacent)^2 + (Opposite)^2

(e+5)^2 = 15^2 + e^2

(e+5)(e+5) = 225 + e^2

e^2 + 5e + 5e + 25 = 225 + e^2

e^2 + 10e + 25 = 225 + e^2

e^2 - e^2 + 10e = 225 - 25

10e = 200

e = 200 / 10

e = 20 miles

Check attached picture for solution diagram

Answer:

-6

Step-by-step explanation:

the position is labeled -6 since it goes down

Answer:

  -6

Step-by-step explanation:

Ground level is taken to be zero on this scale, so 6 feet below ground level will be designated as -6.

Answer: $60

Step-by-step explanation:

Given the following :

Total cost of renting a personal water craft = $64.20

Sales tax charged = 7%

Let the pretax cost = y

Therefore,

total cost = pretax cost + tax

$64.20 = y + 7% of y

$64.20 = y + 0.07y

$64.20 = 1.07y

y = $64.20 / 1.07

y = $60

Therefore, the rental cost of a personal watercraft for half an hour before tax is $60

Answer:

(x-1.3)^2 + (y+3.5)^2 = 37

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-1.3)^2 + (y--3.5)^2 = (sqrt(37))^2

(x-1.3)^2 + (y+3.5)^2 = 37