How long does it take a runner to run 12km if he is running at a speed of 7km/h

Answer:

$12

Step-by-step explanation:

30% is 0.3

So 0.3 × 40 = 12

The value of c from the given equation is 34.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given equation is x²+19x+c=0

Vieta's Theorem is If f(x) = ax² + bx + c is a quadratic equation with roots α and β then,

Sum of roots = α + β = -b/a

(x + a) (x + b) = x² + (a + b) x + ab

a + b = 19

a - b = 15

a = 17

b = 2

c = ab = 34

Therefore, the value of c from the given equation is 34.

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Using Vieta's Theorem, the difference of the roots was used to set up two equations. Solving them simultaneously gave us the individual roots, which were then multiplied to find the required product, c, which is 34.

To solve for c in the quadratic equation x^2 + 19x + c = 0 using Vieta's Theorem, we need to find the two roots of the equation and their relationship to the coefficients.

According to Vieta's formulas, for a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots -b/a and the product of the roots c/a. Since the coefficient a is 1 in our equation (x^2 + 19x + c = 0), the sum of the roots is -19, and the product is c.

We are told the difference of the two roots is 15. Let's denote the larger root as r1 and the smaller one as r2. Thus, r1 - r2 = 15. But we also know that r1 + r2 = -19 (the negative coefficient of x).

We can now set up two equations:

By solving these two equations simultaneously, we add them together to eliminate r2:

2r1 = -4

r1 = -2

Substitute r1 back into one of the original equations to find r2:

r1 + r2 = -19

-2 + r2 = -19

r2 = -17

Now, we use the product of the roots to find c:

c = r1 * r2

c = -2 * -17

c = 34

Therefore, the value of c in the quadratic equation is 34.

Answer:

86 cm

Step-by-step explanation:

Answer:

The simplified expression is -4x and the value is -516

Step-by-step explanation:

−12x+14x−6x

Combine like terms

2x-6x

-4x

Let x =129

-4*129

-516

Answer:

d) 10

Step-by-step explanation:

Answer:

The answer is 10

Step-by-step explanation:

1. y = 2/3x - 5

2. 4x - 6y = 30

Divide 2. by 2

3. 2x - 3y = 15

Substitute 1. into 3.

4. 2x - 3(2/3x - 5) = 15

5. 2x - 2x + 15 = 15

6. 15 = 15

False. There are an infinite number of solutions.

Answer:

B.350

Step-by-step explanation:

let's hope it helps

To find the missing constant term, we want to think about what two numbers would add up to 2. Of the numbers we've thought of, we want to find the numbers that are the same. In this case, that would be 1 and 1. If we multiply, or square, 1 and 1 together, we get 1. So, the missing constant term in the perfect square given here would be 1.

Hope this helps!! :)

Answer:

B.

Step-by-step explanation:

Answer:

B is the correct answer

Step-by-step explanation:

Answer:

Yes, there s a vertical shift to the right by 1

Step-by-step explanation:

If you distribute the 2 among the (x+2) you get:

              2x+4-5

Combine like terms:

              2x+1

There fore the line shifts right by one.

Answer:

Yes, the equation shifts down by five.

Step-by-step explanation:

In equations, vertical shifts happen when the ENTIRE equation, or y, is added or subtracted a number.

Horizontal shifts happen when JUST the x value is added or subtracted a number, but this is a little different.

The formula for the equation you gave us is

m(x - h) + k

Since "h" is already negative, we have to flip the sign of the +2, so the horizontal shift would be LEFT two units.

As far as the vertical shift goes, we just have to look at the "+k."

Since k = -5, the equation shifts down five units.

Answer:

d

Step-by-step explanation:

Answer:

42ft

Step-by-step explanation:

Area of a triangle = 1/2 * base * height

So that little triangle section:

 1/2 * 2 * 3 = 1/2 * 6 = 3

Now we do the rectangle Section:

Area of a rectangle = length * width

So that rectangle is 3 * 7 = 21

If you eliminate those two shapes, you are left with a trapezoid.

Area of a trapezoid is 1/2 * (base 1 + base 2) * height

Base 1 is 3 which is the width of the rectangle.

Base 2 is the 6.

The height is the given 11 feet subtracted by the 7 feet from the length of the rectangle which is 4.

Plug all this in to the formula you get 1/2 * (6 + 3) * 4 = 1/2 * 9 * 4 = 1/2 * 36 = 18.

Now add all of your areas together;

21 + 3 + 18 = 24 + 18 = 42

Answer:

Area=42 ft.²

Step-by-step explanation:

This is an area problem. But since there are multiple shapes (2 triangles and a rectangle) we have to split the shapes and work each one separately. First we will start on the far right, with the small triangle. This one is the easiest one since the line is already drawn to separate it from the rest of the shape.

    Area of a triangle=1/2 bh

                               A=1/2(2x3)

                               A=1/2(6)

                               A=3

The next shape is the the rectangle in the middle.  Looking at the first image, I've drawn a line across the bottom, we need to find the area of that new image, the width is 3 ft and the length is 11 ft.

    Area of a rectangle=lw

                                  A=(11x3)

                                  A=33

Finally, we need to find the area of the last triangle. Looking at the second image, I've add the correct base and height, 4 and 3. So now we need to use the triangle formula and solve

    Area of a triangle=1/2bh

                               A=1/2(4x3)

                               A=1/2(12)

                               A=6

Now we can add the three areas together and get the total area:

  3+33+6=42 ft

I hope this helps:)

Answer:

No.

Step-by-step explanation:

17+18 is not greater than 35.

17 + 18 = 35

so three sides of those lengths form a degenerate triangle, three collinear points.  A degenerate triangle is not a triangle.  The triangle inequality is not satisfied.

Answer: NO

Answer:

a. 4/21

b. 4/7

Step-by-step explanation:

Please kindly check the attached files for explanation.

Answer:

A) 3/12

B)7/12

Step-by-step explanation:

I used a tree diagram to go through this with my daughter, bear in mind the second question asks for the probability of exactly one red counter to be taken from the bag.

Answer:

14:20 :)

Step-by-step explanation:

Answer:

84.82 or 27pi

Step-by-step explanation:

Area of a circle is A=pir^2

so the area of the whole circle would be 6^2pi

so area is 36pi but only 3/4 is shaded so

36pi*3/4=27pi

27*pi≈84.82

Answer:

84.78cm²

Step-by-step explanation:

Angle at the centre:

360 - 90 = 270

Area:

(270/360) × pi × r²

(3/4) × pi × 6²

27pi cm²

27(3.14) = 84.78 cm²

Answer: 0.34

Step-by-step explanation:

Answer:

Step-by-step explanation:

The domain of a function simply encompasses the set of input values which satisfies a given function. Hence, the values within the domain of the function are ; - 6, - 4, - 2, 4

Hence, the x-values in the option which satisfies the function are - 6, - 4, - 2, 4

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Answer:

the surface area

Step-by-step explanation:

the surface area refers to the area on the surface of each side added all together

Answer:

Surface-area.

Step-by-step explanation:

Surface-area. If a solid is composed of flat surfaces, such as the cube on the right, the surface area is simply the sum of the areas of the flat surfaces (called faces).

Answer:

yes.... i need da coordinatees

Step-by-step explanation:

Answer:

f(x) = y

y = 7.50x

To find the inverse, swap x and y

x = 7.50y

Now solve for y

y = x/7.50

f-1(x) = x/7.50

Answer:

the circumference= 175.92918860102841m

Step-by-step explanation:

Answer:

175.929

Step-by-step explanation:

Because to solve this you need to use this formula

Write down the formula for calculating the circumference of a circle; C = πd, where C = circumference, π = 3.14 and d = diameter.

Density = Mass / Volume

The volume is length * width * height, which equals 25 * 10 * 15, making it 3750 cm^3.

Mass / Volume = 3000 g / 3750 cm^3 = 0.8 g/cm^3

Answer:

Density = Mass / Volume

The volume is length * width * height, which equals 25 * 10 * 15, making it 3750 cm^3.

Mass / Volume = 3000 g / 3750 cm^3 = 0.8 g/cm^3

Step-by-step explanation:

To draw an integer chips model for the subtraction problem, first draw nine positive chips to represent the grapes Mary took, then draw four negative chips for the grapes she gave back. Subtract the negative from the positive chips to get the final answer.

In this integer subtraction problem, you would first draw 9 positive chips, symbolizing the 9 grapes Mary initially received from Rohin. Positive chips can be represented by circles or squares. You could use different colors, such as blue for positive (or grapes Mary has).

Next, to represent the 4 grapes that Mary returned to Rohin, you would draw 4 negative chips. Negative chips (or the grapes Mary gave back) could be represented by a different color, such as red.

Subtracting 4 from 9, we then remove 4 positive chips from the model, leaving five positive chips, representing the 5 grapes Mary has left after she returned 4 to Rohin.

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Answer:

Yes!

Step-by-step explanation:

Answer:

615.75216....

Step-by-step explanation:

The formula is A = π * (ø/ 2)^2

A = Circle area

π = Pi = 3.14

ø = Circle diameter

A= 3.14  (28/2)^2

Answer:

Area = 615.44 inches

Step-by-step explanation:

Diameter = 2 * radius

28 = 2 * radius

Divide both sides of the equation by 2

14 = radius

Find area

A = π r²

A = 3.14 (14)²

A = 3.14 (196)

A = 615.44

Hope this helps :)

Answer:

D. 6:40 AM

Step-by-step explanation:

The LCM of 12 and 9 is 36. Add this to the original time and you have your answer.

[tex]p - \sqrt{q} = 1 \\ q + p = 7[/tex]

[tex]p = 7 - q[/tex]

[tex]7 - q - \sqrt{q} = 1 \\ - q - \sqrt{q } = - 6 \\ q + \sqrt{q } = 6 \\ q = 4[/tex]

[tex]p = 7 - 4 = 3[/tex]