What are the vertex focus and directrix of the parabola with equation y=x^2-6x+15.

3 x 5 x 7 = 105, which is the smallest result that can be obtained by the process. To reach this result, the three chosen numbers must be 3, 5, and 7. The first step is to add two of the three numbers, which in this case is 3 + 5 = 8. Then, the sum of the two numbers is multiplied by the third number, which in this case is 7.

The product of 8 x 7 is 56, which is the smallest result that can be obtained by this process.  In general, the chosen numbers must be the smallest possible numbers in order to obtain the smallest result. The process involves adding two of the three chosen numbers and then multiplying the sum by the third number.

Thus, the three chosen numbers must be the numbers with the lowest sum when added together, and the third number must be the smallest number of the three. By following this process, the smallest result that can be obtained is the product of the three chosen numbers multiplied together.

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The length of the segment SY is equivalent to 22.

Given is a triangle ΔTSU.

The medians are divided into a 2 : 1 ratio by the centroid. So, we can write that -

SY/YP = 2/1

SY/YP + 1 = 2/1 + 1

(SY + YP)/YP = 3/1

SP/YP = 3/1

(2x + 3)/11 = 3/1

2x + 3 = 3 x 11

2x + 3 = 33

2x = 30

x = 15

Now, SY = SP - YP = (2 x 15 + 3) - 11 = 33 - 11 = 22

SY = 22

Therefore, the length of the segment SY is equivalent to 22.

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The graph represents the relationship between the temperature and hours after sunrise. The slope shows the temperature changes per hour and the y-intercepts shows the temperature at the time of sunrise. The linear equation of this condition is y = 4x + 4.

From the graph, we can get some informations:

The temperature at the time of sunrise is 4 degrees celcius. This information is represented by the y-intercepts on 4 or point (0, 4). This is the initial temperature of the day.

Next, we will try to find the slope of the graph. We take 2 points:

(0, 4)

(1, 8)

Slope (m) = y₂ - y₁

                    x₂ - x₁

m = (8 - 4)

       (1 - 0)

m = 4

However, as the hour goes by, the temperature increases by 4 degrees celcius. This information is known based on the slope of the graph. The slope represents the degree celcius of temperature change per hour.

Based on the found y-intercepts and slope, we can formulated the linear equation of the graph as:

y = 4x + 4

where:

y = temperature

x = hours after sunrise

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The value of a in the equation 3/4(12a+8) =27.6 is

2.4

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

The equation 3/4(12a+8) =27.6 can be solved as follow:

3/4(12a+8) =27.6

multiply both sides by 4/3

12a + 8 = 27.6 × 4/3

12a + 8 = 36.8

collect like terms

12a = 36.8 - 8

12a = 28.8

divide both sides by 12

a = 28.8/12

a = 2.4

therefore the value of a is 2.4

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When one multiplies a negative numer and a positive number, the product integer will be negative.

The rule to assist the multiplication of signed integers is -

Case I - Product of postive and negative integer will be negative.

Case II - Product of two positive integers will be positive.

Case III - Product of two negative integers will be positive.

Case IV - Product of negative and positive integer will be negative.

Let us understand this will example. Taking two integer numbers 2 and 5. Changing the signs as per the requirement.

Case I - 5 and (-2) = -10

Case II - 5 × 2 = 10

Case III - (-5) × (-2) = 10

Case IV - (-5) × 2 = -10

Thus, the result according to question will be negative number.

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The range of this function #( x 3x2 6x 8 is (-infinity(∞), infinity(∞)) .

What is function ?

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Have given function ,

f(x) = #( x 3x2 6x 8

The range of a function is the set of all possible output values (y-values) for a given input (x-values). Since this is a polynomial function, it can take any value for y as long as we input real numbers for x.

Therefore, the range of this function #( x 3x2 6x 8 is (-infinity(∞), infinity(∞)).

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The speed of River's mom drove for 10 miles distance is 0.234 mph

The speed of  River's mom drove for 25 miles is 10.234 mph  

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

Given as :

The first distance cover by River's mom = 10 miles

The rate of speed = x mph

The second distance cover by river's mom = 25 miles

The rate of speed = x + 10 mph

The total driving time = 45 min

Now, According to question

Time = speed/distance

So, 45 =10/x  +  25/(x+10)

Or, 9 =2/x  + 5/(x+10)

Or, 9 × x × ( x + 10 ) = 2 × ( x + 10 ) + 5 x

Or, 9 x² + 90 x = 2 x + 20 + 5 x

Or, 9 x² + 90 x = 7 x + 20

Or, 9 x² + 90 x - 7 x - 20 = 0

Or, 9 x² + 83 x - 20 = 0

Solving this quadratic equation

x = 0.234 , - 9.4567

so, the value is,

I.e x = 0.234 , - 9.4567

now,

We consider x = 0.234

So, The speed for 10 miles distance = x = 0.234 mph

and The speed of 25 miles = x + 10 = 0.234 + 10 = 10.234 mph

Hence The speed of River's mom drove for 10 miles distance is 0.234 mph

and The speed of  River's mom drove for 25 miles is 10.234 mph

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The two numbers used by mumtaz are 70 and 33

Let p and q be the two-digit numbers chosen by Mumtaz.

When these two two-digits number is divided one by the other, the answer was 2.1212...

Let us assume that r = p/q

and p/q = 2.1212...

we need to find the number r .

We know that a decimal number that consists of digits repeating after a fixed interval after the decimal point is a repeating decimal.

We can write a decimal number 2.1212... as [tex]2.\bar{12}[/tex]

[tex]r = 2.\bar{12}\\\\r=2+0.\bar{12}\\\\r=2+\frac{12}{99}\\\\r=\frac{70}{33}[/tex]

We can observe that 70/33 = 2.1212...

p/q = 70/33

So 70 and 33 are the required numbers.

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Under the sign for the square root, in the quadratic formula b2-4ac, is the discriminant.

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Answer:

X = 8

Step-by-step explanation:

1) -3x+7x-8=34+9x-2

2) -3+7x-9x=8+34-2

3) -5x=40

4) x= 40/-5= -8

Answer: I think A.  x=8 ?

Step-by-step explanation: I hope this helps<3

3(n + 1) = 5.4

3n + 3 = 5.4

3n = 5.4 - 3

3n = 2.4

n = 2.4/3

n = 0.8

If she has a total of $1.45, The equation that could be used to determine the number of dimes is[tex]$$0.05(a+8)+0.10(a)+=1.45$$[/tex]

Let [tex]$\boldsymbol{a}$[/tex] be the number of dimes.

There are eight more nickels than dimes. Thus, there are [tex]$\mathbf{a}+\mathbf{8}$[/tex]number of nickels.

The total of all the coins is [tex]$\mathbf{\$ 1 . 4 5}$[/tex].

[tex]$$0.05(a+8)+0.10(a)+=1.45$$[/tex]

The above equation may be used to find the value of a which is the number of dimes.

The complete question is,

Cathy has eight more nickels than dimes.

If she has a total of $1.45, write an equation that could be used to determine the number of dimes.

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Answer:

-8.7 degrees

Step-by-step explanation:

22.2-30.9=-8.7

Answer:

5

Step-by-step explanation:

No, X² is not an exponential function.

An exponential function is a function of the form f(x) = aˣ where a is a positive constant and x is a real number. The value of the function increases exponentially as x increases.

On the other hand, x² is a polynomial function, a function that can be written as the sum of a finite number of non-negative integer powers of x. The highest power of x is 2, it's called a quadratic function. And it can be represented as f(x) = ax² + bx + c where a, b, and c are real numbers and a is not 0.

Therefore, X² is not an exponential function but a polynomial function.

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Answer:

13.8 watts

Step-by-step explanation:

23% of 60 is 13.8

The measure of elevation refers to angle of elevation. And the angle of elevation is: 68°

The angle of elevation is generated by the intersection of the horizontal line and the line of sight. The angle created is an angle of elevation if such sight line is upward from the horizontal line. An angle having one arm above horizontal and one arm below it is referred to as an angle of elevation. An elevation angle typically ranges from 0° to 90°.

The altitude angle—also referred to as the "solar elevation angle"—describes how high the sun looks in the sky. The observer's position on a horizontal plane and an imaginary line from the sun to the observer are used to calculate the angle.

The problem forms a right triangle, and we know its hypotenuse and the horizontal leg. Using trigonometric reason we find the angle,

cosθ = 9/24

θ = cos⁻¹ (9/24)

θ = 67.97 ≈ 68°

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Answer:

9 + 18q

Step-by-step explanation:

You have to multiplied this polynomial expression in order to simplified it:

3(3 + 6q)

9 + 18q

Answer:

9+18q

Step-by-step explanation:

3[3+6q]

[3times 3]+[3times 6q]

that is how we arrive at the answer

9+18q

The descending order sum of a quadratic term, a linear term, and a constant are several ways to express a quadratic equation.

1. Regular format

2.Vertex shape

3. Detect type

4. Point-slope form

Let's examine the format of these forms.

1. Typical form:

When utilizing factoring or the quadratic formula to locate the equation's roots, this form works well.

[tex]y=ax^2+bx+5c[/tex]

2.Vertex shape

When attempting to determine the vertex (highest or lowest point) of a quadratic equation, this form works best.

y=a[tex](x+h)^2[/tex]+k

3.Intercept type:

y=a(x-p)(x-q)

4.Point-slope form

The usual form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points.

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No, a triangle cannot have two sides.

A triangle is a three-sided polygon with three edges and three vertices in geometry. The total of a triangle's internal angles equals 180 degrees, which is its most important feature. This is known as the angle sum property of a triangle.

Triangle is a closed two-dimensional shape. It is a three-sided polygon. All sides are made of straight lines.

If ABC is a triangle, it is denoted as ABC, where A, B, and C are the triangle's vertices. In Euclidean geometry, a triangle is a two-dimensional shape represented by three non-collinear points in a single plane.

Thus, No, a triangle cannot have two sides.

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To see the graph in the bottom.

Now, According to the question:

The given equation y = 1/2x

y=1/2x [The slope is (1/2) the y-intercept is zero (but isn't shown)

y=(1/2)x + 0

Plot the y-intercept (0,0). Using the slope of 1/2, move up one space from (0,0) and move to the left two spaces. Plot point (2, 1). From (2,1) move up one space and over two spaces to point (4, 2).

Stating over, go to the y-intercept again. Using the the slope (-1/-2)(same slope, different form). Move down one space and to the left two spaces to point (-2, -1). From (-2,-1) move down one space and to the left two spaces to point (-4, -2).

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Rainfall decreases as latitude increases between thirty and sixty degrees latitude is the best description of the rainfall trend.

At thirty degrees latitude, the Intertropical Convergence Zone (ITCZ) is located, which is a band of low pressure that circles the Earth near the equator.

This zone experiences high precipitation due to the rising and falling of air masses caused by the warm equatorial waters. As we move away from the equator towards sixty degrees latitude, the ITCZ shifts northward and the land and sea temperatures decrease, resulting in less precipitation and less humidity.

This trend is known as the latitudinal rainfall gradient, which states that precipitation decreases as latitude increases. This can be observed in the subtropical regions such as the Mediterranean, the western United States, and the southern parts of Africa, among others.

Also, the trade winds blowing from east to west towards the equator, which are prevailing winds in the tropics, push the clouds and precipitation towards the equator, this is why the equatorial regions receive more rainfall than the regions located away from the equator.

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Answer:

The equation of the line can be written in slope-intercept form as y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line that passes through the point (-2, 1) and has a slope of 1/2, we can use the point-slope form of the equation of a line. The point-slope form is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

So, using the point (-2, 1) and the slope of 1/2, we can write the equation of the line as:

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

Which can be re-arranged to the slope-intercept form

y = (1/2)x + (3/2)

Therefore, the equation of the line that passes through the point (-2, 1) and has a slope of 1/2 is y = (1/2)x + (3/2)

This equation can be used to find the y-coordinate of any point on the line, given its x-coordinate.

The solution to equation 7x - 9 = 16 is x = 3.57

Consider given equation 7x - 9 = 16

We solve above equation for x.

⇒ 7x - 9 = 16

Add 9 on both the sides of equation.

⇒ 7x - 9 + 9 = 16 + 9

⇒ 7x + 0 = 25                                   ...........(simplify)

⇒ 7x = 25                                        

Now we divide each side of equation by 7.

⇒ 7x / 7 = 25/7

⇒ x = 25/7                                         ..................(simplify)

If we simplify above fraction, we get.

⇒ x = 3.57

Thus, x = 3.57 is a solution to given equation.

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The complete question is:

'How do you solve 7x - 9 = 16?

Answer:

f(-1) = -2

f(-2) = -3

Step-by-step explanation:

See the attached worksheet.

f(-1) = is asking for the value of the function, f, when x = -1.

f(x) = -3 is asking what value of x will cause the function to produce a - 3.

The range in which at least 88.9% of the data will reside is (6.8,8).

mean=7.2

standard deviation=0.2

we find the range in which at least 88.9% of the data will reside

1-1/k²=0.889

⇒1/k²=1-0.889

⇒1/k²=0.111

⇒k²=1/0.111=9.009

⇒k=3.002

so, k=3

The range of values can be computed as mean±k(standard deviation).

Thus, the range in which at least 88.9% of the data will reside in

(mean-k(standard deviation), mean+ k(standard deviation))

(7.2-3(0.2),7.2+3(0.2))

=(7.2-0.6,7.2+0.6)

= (6.6, 7.8)

Thus, the range in which at least 88.9% of the data will reside is (6.8,8).

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The complete factorization of the quadratic equation 6x² + 15x - 36 is given by:

How to factor a quadratic equation?

A quadratic equation is modeled by:

Considering the roots and , it can be factored as:

In this problem, the function is:

Hence the coefficients are , and:

Hence:

Answer:

Step-by-step explanation:

Answer:

To factor the expression 6x² + 15x - 36 = 0, we can use the technique of factoring by grouping.

First we will write the expression as two binomials:

6x² + 15x - 36 = (6x² + 18x) - (3x + 36) = 0

Next we will factor out the greatest common factor (GCF) of the first binomial:

6x² + 18x = 3x(2x + 6)

Next we will factor out the GCF of the second binomial:

3x + 36 = 3x(1 + 12)

Bring the factors out of the parentheses:

3x(2x + 6) - 3x(1 + 12) = 3x(2x-1+6-12) = 3x(2x-6) = 0

So the expression is factored completely as 3x(2x-6) = 0.

We can see that the factors of the expression 6x² + 15x - 36 = 0 are 3x and (2x-6)

The ribbon is 11 inches long while the car travels at 184800 feet per hour

An equation shows the relationship between numbers and variables in an expression.

1) A ribbon is 28 cm long

1 inch = 2.54 cm

Converting the ribbon length to inches:

28 cm = 28 cm * 1 in per 2.54 cm = 11 inches

The ribbon is 11 inches long

2) A car travels 35 miles per hour

5280 feet = 1 mile

Converting to feet per hour:

35 miles per hour = 35 miles per hour * 5280 feet per mile = 184800 feet per hour

The car travels at 184800 feet per hour

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Expressions that perform similarly but differ in appearance are said to be equivalent expressions.

Examples:

The Complete Question.

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An equation to determine the length would be L = 63 inches.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements

Given, The width is one-third the length of the picture and the width is 21 inches.

Assuming the length of the rectangle to be 'L'.

Therefore, An equation to determine the length would be,

(1/3)×L = 21.

L = 63.

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