graph the following system of equations and find the x coordinate of the soloution x3=3y=3 y=1/2x+2

The quadratic expression for the curves is written as

The curve opening up y = a(x + 4)² - 7

The curve opening down y = -1/8(x - 4)² + 3

The equation of the quadratic equation is written using the formula

y = a(x - h)² + k

where h and k are points of the vertex v(h, k)

The curve opening up

h = -4 and k = ?

using points C and B

-5 = a(0 + 4)² + k, -5 = 16a + k

1 = a(4 + 4)² + k, 1 = 64a + k

solving simultaneously

-5 = 16a + k

1 = 64a + k

subtraction

-6 = -48a

a = 1/8

solving for k

-5 = 16a + k

-5 = 16 * 1/8 + k

k = -7

substituting the values

y = a(x + 4)² - 7

The curve opening down

A is the vertex (4, 3)

y = a(x - 4)² + 3

using D (0, 1) to solve a

1 = a(0 - 4)² + 3

1 - 3 = 16a

a = -1/8

hence the equation is y = -1/8(x - 4)² + 3

Learn more about Quadratic equation here:

https://brainly.com/question/29339843

#SPJ1

Answer:  Lily babysits for less than 4 hours.

Step-by-step explanation:

We can start by multiplying 4 hours by 7/8 to find out how many hours Lily spends babysitting.

4 * (7/8) = 7/2 = 3.5 hours

Since 3.5 is less than 4, Lily babysits for less than 4 hours.

Answer: Less than 4. (3 1/2 hours)

Step-by-step explanation:

When you multiply a number by a number smaller than 1, the answer gets smaller.

Lily babysits for 3 1/2 hours because 4 x 7/8 = 3 1/2

Answer:

a₄ = 25

Step-by-step explanation:

using the recursive formula [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] and a₁ = 4 , then

a₂ = 2a₁ - 1 = 2(4) - 1 = 8 - 1 = 7

a₃ = 2a₂ - 1 = 2(7) - 1 = 14 - 1 = 13

a₄ = 2a₃ - 1 = 2(13) - 1 = 26 - 1 = 25

The diameter of the circle is 16.66 units.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given a circle,

and two segments intersect at a point and form a right angle,

the length of the segment to the point of intersection is 6 units and 8 units as given in the figure,

and a segment pass from the center of the circle,

let the distance from point of intersection to center be x

so radius of circle be 6 + x from figure,

it forms a right triangle as shown in the figure, with hypotenuse 6 + x, base x, and perpendicular 8 units,

using Pythagoras theorem

h² = b² + p²

(6 + x)² = x² + 8²

36 + x² + 12x = x² + 64

12x = 64 - 36

12x = 28

x = 28/12

x = 2.333

radius of circle = 6 + x = 6 + 2.33 = 8.33

diameter of circle = 2r = 2 x 8.33 = 16.66 units

Hence the diameter is 16.66 units.

Learn more about circles;

https://brainly.com/question/29142813

#SPJ1

The approximate surface area of the tower is 156.33 feet².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

The given tower is a composite of a cylinder and a cone.

But cylinder does not have the bases and cone also does not have it's base.

Surface area of the curved surface of cylinder = 2π r h

where r is the radius of the base and h is the height of the cylinder.

Given h = 8 feet and r = 2.5 feet

Curved surface area of cylinder = 2π × 2.5 × 8 = 40π feet²

Surface area of the curved surface of the cone = π r √(h² + r²)

where r is the radius of the base of the cone and h is the perpendicular height of the cone.

Given r = 2.5 feet and h = 3 feet

Curved surface area of cone = π × 2.5 [√(2.5² + 3²)]

                                                = 9.76π feet²

Total surface area = 40π + 9.76π

                              = 156.33 feet²

Hence the total surface area of the tower is approximately 156.33 feet².

Learn more about Surface Area here :

https://brainly.com/question/29298005

#SPJ1

Answer:

1the answer for this is easy it is 4.4

Answer:

[tex] \frac{2257}{2400} [/tex]

Step-by-step explanation:

2400 - (120+23)

=2400 - 143

=2257

Therefore,

2257

2400

The value of expression is ,

10) 6

11) 18

12) 2

13) 4

14) [tex]\frac{1}{4}[/tex]

15) [tex]\frac{1}{3}[/tex]

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression

10) 7+x+(-3)

Put x=2 then

=> 7+2-3

=> 7-1 = 6

11) 4[tex]x^2[/tex]+2

put x=2 then

=> [tex]4*2^2+2[/tex]

=> 4*4+2

=> 16+2=18

12) Ix+10I

put x=-12 then

=> I-12+10I

=> I-2I = 2

13) |2x + 1|

put x= 3/2 then

=> I2*[tex]\frac{3}{2}[/tex]+1I

=> I3+1I

=> I4I = 4

14)(x - 3)/4

put x=4 then

=> [tex]\frac{4-3}{4}[/tex]

=> [tex]\frac{1}{4}[/tex]

15) (5 - x)/6

put x=3 then

=> [tex]\frac{5-3}{6}[/tex]

=> [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

To learn more about expression refer the below link

https://brainly.com/question/112703

#SPJ1

Answer:

A, B and E

Step-by-step explanation:

The probability of randomly picking a peach from from the fruit bowl is 29 %

To find the probability of picking a peach from the fruit bowl at random, you first need to sum up the number of fruit :

= 10 Limes + 5 peaches + 2 mangoes

= 17 fruit

The probability of picking a peach from the fruit bowl can then be found to be :

= Number of peaches in fruit basket / Number of fruit in the fruit basket

= 5 / 17

= 29 %

Find out more on probability at https://brainly.com/question/9738029

#SPJ1

The rest of the question is:

The probability of randomly picking a peach from from the fruit bowl is _________.

Answer:

So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.

Step-by-step explanation:

Ingrid's time of 13.9 seconds was originally measured to 2 decimal places, which means that her actual time could be rounded to 13.9 seconds. To find the slowest time she could have run, we need to find the greatest value that could have been rounded down to 13.9 seconds.

Since the time was measured to 2 decimal places, this means that the hundredths place is known and the thousandths place can be anything between 0 and 9. So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.

Answer:

A. 2¾

Step-by-step explanation:

The person needs the difference. This is a subtraction problem.

3 1/2 - 3/4 =

3/4 is just a fraction, but you can think of 3/4 as a mixed numeral by writing 3/4 as 0 3/4. The whole part is 0 and the fractional part is 3/4.

= 3 1/2 - 0 3/4

Now we are subtracting two mixed numerals. You need to subtract the whole part, 0, from the whole part, 3, and the fractional part, 3/4, from the fractional part, 1/2.

For the fractional parts, we need a common denominator of 4.

= 3 2/4 - 0 3/4

Now we have both fractions with a common denominator of 4, but since we cannot subtract 3/4 from 2/4, we borrow 1 from 3 as 4/4.

3 goes down 1 to 2, and the 1 which is borrowed as 4/4 is added to the 2/4 to give you 2 6/4. 2 6/4 has the same value as 3 2/4. Now we have:

= 2 6/4 - 0 3/4

We subtract 0 from 2, and we subtract 3/4 from 6/4.

= 2 3/4

Answer: 2 3/4

Answer:

one's place

Step-by-step explanation:

After calculating The perimeter of rectangle is 46.52 in the given rectangle.

What is area of rectangle?

area of rectangle can be defined as the product of length and breadth.

Given ,

A rectangle has a length 20 5 /6 and

breadth = 2 3/7

The perimeter of rectangle  = 2 (l+b)

length = (120 + 5 ) / 6 = 125/ 6

breadth = (14+3) / 7  = 17/7

perimeter  = 2 (125/6 + 17/7 )

= 2 ( (125*7 + 17 * 6) / 42 )

= 2 (875+102) / 42

= 2 * 23.26

= 46.52

Hence, after calculating The perimeter of rectangle is 46.52 in the given rectangle.

To learn more about area of rectangle from the given link.

https://brainly.com/question/20693059

#SPJ1

the solution of number line is all the options are correct.

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

Here,

Kendra and Jamal are standing in line. The number line shows their positions in meters with positive numbers representing positions to the right.

The position of Kendra is -6 and Jamal is 0.

Kendra is 6 meters left of Jamal.

Kendra and Jamal are 1-6 meters apart.

Jamal is 6 meters right of Kendra.

Hence, all the options are correct.

Learn more about number line, by the following link

https://brainly.com/question/28726930

#SPJ1

Answer: The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width of the rectangle.

We know that the rectangular school banner has a length of 44 inches and a perimeter of 156 inches. And we can use the formula above to find the width of the rectangular school banner:

P = 2L + 2W = 156 inches

P = 2(44) + 2W = 88 + 2W = 156 inches

So the width of the rectangular school banner is W = 156 inches - 88 inches = 68 inches

Now, we know that the cheerleaders make signs similar to the banner. the length of a sign is 11 inches, we can use the same formula to find the perimeter of the sign.

P = 2L + 2W = 2(11) + 2W

So the perimeter of the sign is P = 22 + 2W inches

Since we don't know the width of the sign (W) we can't find the perimeter of the sign.

Step-by-step explanation:

Answer:

Average speed = Total distance travelled / Total time taken

 = 170 miles / 2.34 hours

 = 72.65 miles per hour or 72.65 mph

Pls mark as brainliest. I rlly need it for some reason. Thanks

Answer:

Since slope of line passing through two points (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) is m=

x

2

​

−x

1

​

y

2

​

−y

1

​

​

We now find the slope of the line passing through the points (2,3) and (4,6) as shown below:

m=

4−2

6−3

​

=

2

3

​

Therefore, the slope of the line is  

2

3

​

.

Now use the slope and point (2,3) to find the y-intercept.

y=mx+b

⇒3=(

2

3

​

×2)+b

⇒3=3+b

⇒b=3−3=0

Write the equation in slope intercept form as:

y=mx+b

⇒y=

2

3

​

x+0

⇒y=

2

3

​

x

Step-by-step explanation:

The rate of change is $6 per hour while the initial value is $20

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Let y represent the total amount of money that Larry would have after working x hours.

From the graph, the y intercept is at (0, 20). Using point (0, 20) and (5, 50):

Slope = (50 - 20)/(5 - 0) = 6

The slope is $6 per hour

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

-15,-14,-13

Step-by-step explanation:

Let x = the first integer

Let x + 1 = the second integer

Let x + 2 = the third integer

The addition of all three equal -42

x + x + 1 + x + 2 = -42  Combine like terms

3x + 3 = -42  subtract 3 from both sides

3x + 3 - 3 = -42 - 3

3x = -45  Divide both sides by 3

x  = -15

Check

-15 + -14 + -13 = -42

-42 = -42

The mean is of 0.15. The standard deviation is of 0.0326.0.1774 of incoming kindergarteners are nearsighted.

The central limit theorem and the normal distribution are used to determine that:

a) A 0.15 is the mean.

b) A standard deviation of 0.0326 is present.

c) There is a 0.063 = 6.3% chance that fewer than 10% of the kindergarten applicants have nearsightedness.

d) 0.1774 percent of kindergarten students have nearsightedness.

The mean is of 0.15.

Item b:

s = p (1-p)/n = 0.15(0.85)/120

=  0.0326.

The standard deviation is of 0.0326.

Item c:

The probability is the p-value of Z when X = 0.1.

By the Central Limit Theorem

Z=  0.1 -0.15/ 0.0326.

=  -1.53

Z = -1.53 has a p-value of 0.063.

There is a 0.063 = 6.3% probability that less than 10% of the incoming kindergarteners are nearsighted.

Item d:

X = 0. 1774

The proportion is X when Z has a p-value of 0.8, so X when Z = 0.84.

0.1774 of incoming kindergarteners are nearsighted.

To learn more about normal distribution  refer

https://brainly.com/question/27130932

#SPJ1

Answer:

  rhombus

  (b) The diagonals are perpendicular but not congruent.

Step-by-step explanation:

You want to know what sort of figure the parallelogram JKLM is, given the vertices J(-2,7), K(7, 2), L(-2,-3), M(-11,2).

The x-values of points J and L on diagonal JL are the same, so that diagonal is a vertical line. Its length is 7 -(-3) = 10.

The y-values of points K and M on diagonal KM are the same, so that diagonal is a horizontal line. Its length is 7 -(-11) = 18.

The diagonals are perpendicular and not congruent, so the parallelogram is a rhombus.

Step-by-step explanation:

hope this helps!:).....

Answer:

[tex]y=-(x-6)^2+6[/tex]

Step-by-step explanation:

Vertex form of a parabola is expressed as: [tex]y=a(x-h)^2+k[/tex]

It's also important to note that the axis of symmetry is a vertical line which passes through vertex, so in this form, that axis of symmetry can be defined as such: [tex]x=h[/tex]

So if we're given the axis of symmetry we know the x-coordinate of the vertex.

Since we're given the axis of symmetry to be: [tex]x=6[/tex] then that means the x-coordinate of the axis of symmetry is six. Another important thing to note about the vertex is it's y-value is either a minimum or maximum depending on whether it's opening up or down. So when we're given the maximum height to be 6, that's the y-coordinate of the vertex.

So now we know the coordinates to the vertex: [tex](6, 6)[/tex]. Using this we can plug in some values into the vertex form: [tex]y=a(x-6)^2+6[/tex], but we still don't know the "a" value in front (besides that it's negative). Luckily we're given a point on the equation! We can plug in the coordinates given: [tex](7, 5)[/tex] into the vertex form as (x, y) to solve for the "a" value, so let's do that.

Original Equation:

[tex]y=a(x-6)^2+6[/tex]

Passes through the point (7, 5), so substitute it for (x, y)

[tex]5=a(7-6)^2+6[/tex]

Simplify inside parenthesis:

[tex]5=a(1)^2+6[/tex]

Square the one:

[tex]5=a+6[/tex]

Subtract 6 from both sides:

[tex]-1=a[/tex]

So now let's plug this back into our equation: [tex]y=-1(x-6)^2+6[/tex], although we don't have to explicitly put the one, and just put the negative sign which does the same thing: [tex]y=-(x-6)^2+6[/tex]

Answer:

25

Step-by-step explanation:

5/9 x 45  Cross cancel the 9 and 45. 9 goes into 9 once and 9 goes into 45 5 times

5/1 x 5/1 = 25/1 = 25

Answer:

6375 mcg

Step-by-step explanation:

hopes this helps :)

Step-by-step explanation:

fufj5655 and I hope that you will be able to help me with the following to help me with the application for the role of the temple and many other people in the forest and a small village known as change in indirect speech to be the oldest

The cost of a candy bar is equal to $1.61.

In order to write an equation that model this situation, we would assign variables to the cost of candy bars and the cost of soda respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that three (3) candy bars and one (1) soda costs $5.63 as follows;

3x + y = 5.63   ...equation 1.

Additionally, one candy bar and four sodas cost $4.81 at the same price;

x + 4y = 4.81 ...equation 2.

x + 4(5.63 - 3x) = 4.81

x + 22.52 - 12x = 4.81

11x = 22.52 - 4.81

x = 17.71/11

x = $1.61

Read more on equations here: brainly.com/question/3382177

#SPJ1

The slope intercept form is  y= 2x+1

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let's take 2 points :

(x1,y1) = ( 1,  -1)

(x2,y2) = ( 2,  -3)

slope  , m = (y2-y1) /(x2-x1)

                = (-3-(-1))/(2-1)

                = (-3+1)/1

                = -2

Slope intercept form:

y-y1=m(x-x1)

y-(-1) = -2 (x-1)

y+1=-2x+2

=> y=2x+2-1

=> y= 2x+1

Thus, the slope intercept form is  y= 2x+1

To learn more about the slope from the given link

https://brainly.com/question/16949303

#SPJ1