10. What is the equation of the directrix for the parabola-8(y - 3)=(x +4)2?A) y=5B) y=1C) y=-2D) y=-6

Given the numbers:

Let's find their greatest common factor:

Step 1: Let's determine the factors of the numbers.

a.) 570

The factors of 570 are: 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570

b.) 615

The factors of 615 are: 1, 3, 5, 15, 41, 123, 205, 615

Their common factors are: 1, 3, 5, 15

But the greatest among all factors is 15.

Therefore, their greatest common factor (GCF) is 15.

DEF is an acute angke because the measure we can notice is less than a right angle

then the value is less than 90°

then right option should be D and E

C isnt because we can notice the angle is

Answer:

46

Explanation:

In each number to the right of the equality sign, the tenths place is always the rightmost number in addition and the one place is the result of the addition.

For example, in 1 +3 = 34

Therefore, for 2 + 4 we have

Hence,

which is our answer!

Solution

Using BODMAS to solve the fraction

Therefore the answer = -3/4

Answer:

B and C

Step-by-step explanation:

y in equation 1

-28=3 is false, therefore the system of equations has no solution

The frequency of the longitudinal wave is 5/2 cm.

Given:

A longitudinal wave has 20 compressions and 20 rarefactions in 0.1s.

we are asked to determine the frequency of the wave = ?

1 wave ⇒ 1 compression + 1  rarefactions

therefore,

20 waves:

0.2 s ⇒ 20 waves.

1 & ⇒ 20/0.02 × 10/1

1 & ⇒ 200/2

1 & ⇒ 100 hz

20 > = 50 cm

⇒ 50/20

= 5/2 cm

Hence we get the frequency as 5/2 cm

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Angle of depression is 7.7 °  made by the line of sight from the canyon edge to the fire .

The angle of depression is the angle created by the object and the horizontal line as seen from the horizontal line. The distance between two objects is often calculated when the angles and spacing of an object from the ground are known.

let f be the the fire

b is the base of the sheer canyon wall

o be the cliffs of insanity point that is canyon edge

so OB = 7117 Feet

bf = 10 miles = 10 * 5280 = 52800 feet

angle of depression is < xof which is equal to < ofb

let the angle of depression is [tex]\theta[/tex]

now from triangle obf ; it is a right angle triangle , where of = hypotenuse

bf = base , ob = height < ofb = [tex]\theta[/tex]

so , tan [tex]\theta[/tex] = ob/bf = 7117/52800

[tex]\theta[/tex] = [tex]tan^{-1}[/tex] ( 7117/52800) = 7.68 ° = 7.7 °

so angle of depression is 7.7 °

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Answer:x=12

y=−186

Step-by-step explanation:x=63x+4y=12

Consider the first equation. Subtract 63x from both sides.

x−63x=4y

Combine x and −63x to get −62x.

−62x=4y

Divide both sides by −62.

x=−

62

1

​

×4y

Multiply −

62

1

​

 times 4y.

x=−

31

2

​

y

Substitute −

31

2y

​

 for x in the other equation, 63x+4y=12.

63(−

31

2

​

)y+4y=12

Multiply 63 times −

31

2y

​

.

−

31

126

​

y+4y=12

Add −

31

126y

​

 to 4y.

−

31

2

​

y=12

Divide both sides of the equation by −

31

2

​

, which is the same as multiplying both sides by the reciprocal of the fraction.

y=−186

Substitute −186 for y in x=−

31

2

​

y. Because the resulting equation contains only one variable, you can solve for x directly.

x=−

31

2

​

(−186)

Multiply −

31

2

​

 times −186.

x=12

The system is now solved.

x=12,y=−186

The Sine rule formula is,

Given:

Let us solve for solve for the measure of angle B

Therefore,

Hence, there are no possible solutions for this triangle (OPTION C).

Answer:

18

Step-by-step explanation:

Equation 9 x 4 / 2 = 18

First do 9 x 4 which is 36

Next do 36 / 2 which is 18

Also the "/" is another way to say to divide

The required system of equations to express Stevens monthly fee is

22.5 + 0.12 m = c

Given : A flat monthly fee which is charged for Stevens =  $22.5

The cost of each phone call = $ 0.12

Let the cost of each monthly call be represented by the letter m

And the total monthly fee be represented by the letter c

thus according to the question the equation can be expressed as :

22.5 + 0.12 m = c

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Mean is 5.25, Median is 5 and mode is 3.

Given,

In the question:

There are numbers:

3, 4, 5, 7, 6, 8, 8, 5, 3, 6, 4, 5, 3, 3, 7, 7.

To find the mean, median and mode.

Let's Know :

How do you find the mean median and mode?

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Now, According to the above statement :

To find Mean:

[tex]\frac{3+4+ 5+ 7+ 6+ 8+ 8+ 5+ 3+ 6+ 4+ 5+ 3+ 3+ 7+ 7}{16}[/tex]

= 84/16 = 5.25

For Median

Arrange in ascending order

3, 3, 3, 3, 4,4, 5,5,5, 6,6, 7, 7, 7, 8,8.

There is an even no. of observations. i.e., 16 numbers.

then, there is no single middle value; the median is then usually defined to be the mean of the two middle values: so the median of

Middle two values is : (5 + 5)/2 = 10/2 = 5

Middle value is 5

For Mode:

The mode is the number that occurs most often in a data set.

Mode is 3 .

Hence, Mean is 5.25, Median is 5 and mode is 3.

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Answer: The highest common factor of 91, 112 and 49 is 7

hope this helps :)

B ] seventy two over twenty five is the quotient of two and two fifths ÷ five sixths.

Quotient refers to the number produced by division of two numbers.

According to question,

Division of two numbers,

⇒ 12/5 / 5/6

⇒ 12/5 * 6/5

⇒ 72/25

Hence, 72/25 i.e., seventy two over twenty five is the quotient of two and two fifths ÷ five sixths.

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Answer:

Explanation:

The dimensions of the golf hole found using the indicated variable expressions are as follows;

a. The area of the golf hole is 4·x² + 12·x

b. The perimeter of the golf hole is 8·x + 8

c. The perimeter of the golf hole if the area of the hole is 216 square feet is 56 feet

The perimeter of a geometric figure is found by the length of the boundary of the figure.

a. The area of the gulf hole is found as follows;

The area is a composite figure, which consists of a rectangle of length 3·x and width (x + 4) and a square of length x

Which indicates that the area is A = 3·x × (x + 4) + x×x = 3·x² + 12·x + x²

The area of the hole, A = 3·x² + 12·x + x² = 4·x² + 12·x

The area of the hole is A = 4·x² + 12·x

b. The perimeter of the hole is found as follows;

P = (x + 4) + 3·x + (x + 4) + x + x + x = 8·x + 8

The perimeter of the hole = 8·x + 8

c. The area of the golf hole = 216 square feet, which indicates;

4·x² + 12·x = 216

4·x² + 12·x - 216 = 0

x² + 3·x - 54 = 0

(x + 9)·(x - 6) = 0

x = 6 or x = -9

The perimeter of the golf hole is therefore;

P = 8 × 6 + 8 = 56

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Given:

Triangle ABC is mapped onto triangle ADE.

Required:

The transformation that maps triangle ADE similar to triangle ABC.

Explanation:

A dilation process from A by a factor 3 maps triangle ABC onto triangle ADE.

In the dilation process, the transformed angle value remains constant.

Also,

Therefore above transformation makes triangle ABC similar to triangle ADE.

Answer:

Thus from the explanation given above, the above transformation makes triangle ABC similar to triangle ADE.

Answer: 10.8 seconds

Step-by-step explanation:

[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]

The length of the second shelf is 114 centimetres.

Consider the four shelves as A, B, C and D. According to the question, the length of the four shelves is 2.5 cm.

A + B + C + D = 250 cm ( 1 m = 100 cm ⇒ 2.5 * 100 = 250 ) → 1  

The length of the second shelf is 18 cm longer than twice the length of the first shelf.

B = 2A + 18   →  i

The length of the third shelf is 12 cm shorter than the first shelf.

C = A - 12      →  ii

The length of the fourth shelf is 4 cm longer than the first shelf.

D =  A + 4      →  iii

Substitute i,ii and iii in 1  ⇒  A + B + C + D = 250  

A + 2A + 18 + A - 12 + A + 4 = 250

5A + 22 - 12 = 250

5A + 10 = 250

5A = 250 - 10

5A = 240

A = 240/5

A = 48

Substitute A = 48 in i, ii, iii and then we get,

B = 11, C = 36 and D = 52

Therefore, the length of the second shelf B is 114 cm.

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The complete question is

Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 centimetres longer than twice the length of the first shelf. The third shelf is 12 centimetres shorter than the first shelf. The remaining shelf is 4 centimetres longer than the first shelf. If Robert must use the entire 2.5 meter board for the shelves, what is the length of the second shelf, in centimetres?

Answer:

-5+0=-5

(-6)+1=-5

-7+2=-5

Step-by-step explanation:

the temperature in the morning was 1 degree celsius

then rise of 3 degree

so now the total temperature is 1 + 3 = 4 degree

so the temperature of the afternoon is 4 degrees.

For this problem, we are given the graph of an ellipse, and we need to determine its expression in the standard form.

The standard equation of an ellipse is given below:

Where (h,k) is the center of the ellipse, a is the horizontal radius and b is the vertical radius.

The center of the ellipse on our problem is (-2,2), the vertical radius is 2 and the horizontal radius is 3. We have:

In order to calculate the Foci, we need to first find the eccentricity of the ellipse, which is given by the following formula:

The coordinates of the foci are given by:

The coordinates for the foci are: (-2-sqrt(5), 2) and (-2+sqrt(5), 2).

Answer: The answer would be

B. 1/2

C. 1/3

Step-by-step explanation:

The solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.

SOLUTION

In mathematics, a ratio indicates how many times one number contains another.

And when we write quantities in ratio form, we represent ratio with the symbol :

For example: The ratio of A to B is written mathematically as A:B

Another important thing we must note when writing ratios is to always express both quantities in their simplest form.

With the above explanation, we can proceed in answering the question.

The ratio of adults to children which is 400 to 150, can be written mathematically in ratio form as:

Final answer: The ratio of adults to children is:

y-6 = -5/3 (x+2) is the point - slope equation of the line through (-2 , 6 ) ( 1 , 1 ) using exact numbers.

For linear equations, the typical form is y-y1=m(x-x1). It highlights the line's slope and a line point (that is not the y-intercept).

The two approaches for determining the equation of a line given a point and its slope are as follows:

(a). Input the slope and the (x, y) point values into the equation y = mx + b, then solve for b using the substitution technique

b) Point-slope form: (x 1, y 1), where (y 1, x 1) is the point and (m, the slope) is the specified slope.

First you need to find the slope, (y2-y1)/(x2-x1).  This is (1-6)/(1-(-2)) or -5/3

Now that you know the slope you can use that for the point-slope equation

The point-slope equation is y-y1 = m(x-x1).  If we start with y-6, the x value is -2 (from our point (-2,6)

     y-6 = -5/3 (x-(-2))

or, y-6 = -5/3 (x+2)

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Answer:

f(x)=(6x+6)(x+10)

Explanation:

Given the quadratic expression:

First, we can rewrite it in the form below:

Next, factor the terms:

Thus, the quadratics as a product of two binomials is:

Answer:

slope is -3

y intercept is 2

Step-by-step explanation:

3x+y=2 [subtract 3x from both sides]

y=-3x+2

slope is -3

y intercept is 2

Answer: with what???