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2 years ago

Write the quadratic equation whose roots are

1 answer:

maks197457 [2]2 years ago

5 0

The quadratic equation $y = ax^2 +bx+c$ can be written in the form:
$y = a(x-p)(x-q)$
Where p and q are the roots of the equation.
Given p = 4, q = -2, a = 3, the quadratic will look like this:
$y = 3(x-4)(x+2)$
Finally, distribute and combine like terms to put it in standard form.
$y = 3(x^2 - 4x+2x -8) \\ \\ y = 3(x^2 -2x-8) \\ \\ y = 3x^2 -6x -24$

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Graph a line with a slope of -2/5 that contains the point (-3,5)

kotykmax [81]

$y=-\frac{2}{5}x+\frac{19}{5}$

Further explanation:

We have to find the equation of the line first to graph the line.

The general form of slope-intercept form of equation of line is:

$y=mx+b$

Given

$m=-\frac{2}{5}$

Putting the value of slope in the equation

$y=-\frac{2}{5}x+b$

To find the value of b, putting the point (-3,5) in equation

$5=-\frac{2}{5}(-3)+b\\5=\frac{6}{5}+b\\5-\frac{6}{5}+b\\b=\frac{25-6}{5}\\b=\frac{19}{5}$

Putting the values of b and m

$y=-\frac{2}{5}x+\frac{19}{5}$

The graph is made by using online graphing tool Desmos.

Keywords: Equation of line, graph of line

Learn more about graphs at:

#LearnwithBrainly

4 0

2 years ago

5 equally sized boxes of cake mix fell off the back of Jake's truck. Together they weigh 925.98 pounds. How much does each ball

uysha [10]

we are given

5 equally sized boxes of cake mix fell off the back of Jake's truck

it means that

total number of balls =5

Together they weigh 925.98 pounds

total weighs =925.98 pounds

each ball weighs = (total weights)/(total number of balls)

now, we can plug values

each ball weighs = $\frac{925.98}{5}$

each ball weighs is 185.196 pounds..................Answer

4 0

1 year ago

WY bisects UV at Y. If UV=x-7 and YV = 3x-29, find UV

gayaneshka [121]

Answer:

3.2 units

Step-by-step explanation:

Given that:

WY bisects UV at Y.

$UV=x-7$ and

$YV = 3x-29$ ,

To find: UV = ?

Solution:

First of all, let us draw the diagram of the given dimensions and bisector line WY of UV.

As UV is bisected i.e. divided in two equal parts at Y by the line WY

Therefore, UY = YV

UV = UY+YV

Now, let us put the given values to solve for $x$ :

$x-7=2 \times (3x-29)\\\Rightarrow x-7=2 \times 3x-2 \times 29\\\Rightarrow x-7=6x-58\\\Rightarrow 6x-x=58-7\\\Rightarrow 5x=51\\\Rightarrow \bold{x =10.2 }$

Now, we are given that:

$UV=x-7$

Putting value of $x$ as solved in above step to get the value of UV:

$UV=10.2-7\\\Rightarrow \bold{UV=3.2}$

So, answer is <em>UV = 3.2 units</em>

3 0

2 years ago

Kate recorded what she ate for breakfast every day for six months. Her findings are shown in the graph below. A bar graph titled

Amiraneli [1.4K]

Answer: The correct answer is option B: 19%

Step-by-step explanation: The bar graph according to the question has the following set of data;

Cereal ----------34

Eggs and Bacon ----------21

Pastries ----------39

Bagels ----------48

Waffles ----------38

The total from this set of data is 180 (that is the summation of all the observed data). The portion taken up by cereals can be derived as follows;

Cereal = (34/180) x 360

Cereal = 68 degrees

Note that we have used degrees as the unit since the data would be transferred to a pie chart. Hence on the pie chart it occupies 68 degrees of the entire 360 degrees.

In order to find out what percentage this represents we can now express 68 degrees as a percentage as follows;

Cereal = (68/360) x 100

Cereal = 18.8888888

Cereal ≈ 19

Therefore cereal occupies 19 percent of the pie chart.

8 0

1 year ago

Read 2 more answers

An indoor sport exhibition is coming to the arena. Your supervisor has asked you to help set up a handball pitch and seating are

Sphinxa [80]

Answer:

Perimeter: 174.8 m

Area: 1,394 sq m

Step-by-step explanation:

First, the perimeter.

Before we start, let's calculate the circumference of the half-circles at the ends of the field.

The measurement says 2,000 cm, so let's convert it to 20 m for ease.

Circumference of a circle: πd, where d = diameter.. in our case d = 20 m

Circumference of a 20m diameter circle: 20π = 62.8 m

We have 2 half circles... so the perimeter of each half-circle will be: 31.4 m

We also have 800 cm measurement for the "height" of the seating areas... let's convert that in 8 m

We also need to find out the space between the seating area... We know the whole rectangular pitch is 40 m, then we have to subtract the width of both seating areas (20 and 15 m)... so the space between them is 5m

So, starting with the upper left corner of the rectangular pitch, and working our way clockwise, we encounter the following lengths:

P = 40 + 31.4 + 8 + 10 + 8 + 5 + 8 + 25 + 8 + 31.4 = 174.8 m

The total perimeter is then of 174.8 m

For the area, we need to calculate the area of all forms:

Large rectangular pitch:

LR = 40 x 20 = 800 sq m

The two half circles, form a circle, so A = πr², where r is the radius, which is half the diameter.

AC = π (10)² = 100 π = 314 sq m

Then the seating areas:

SA1 = 25 x 8 = 200 sq m

SA2 = 10 x 8 - 80 sq m

Then, we add up everything:

TA = LR + AC + SA1 + SA2

TA = 800 + 314 + 200 + 80 = 1,394 sq m

3 0

2 years ago