Find the vertex of this function and decide if it is a maximum point or a
minimum point

Answer:

I think the answer is 'congruent'. :)

Step-by-step explanation:

Answer:

The equation in point slope form is [tex]y-6=\frac{1}{3}(x-4)[/tex]

The equation in slope intercept form is [tex]y=\frac{1}{3}x-\frac{14}{3}[/tex]

Step-by-step explanation:

step 1

Find the slope m

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex](-5,3),(4,6)[/tex]

Substitute the values

[tex]m=\frac{6-3}{4+5}[/tex]

[tex]m=\frac{3}{9}[/tex]

simplify

[tex]m=\frac{1}{3}[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{1}{3}[/tex]

[tex](4,6)[/tex]

substitute

[tex]y-6=\frac{1}{3}(x-4)[/tex] ---> equation in point slope form

step 3

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

[tex]y-6=\frac{1}{3}(x-4)[/tex] ----> convert to slope intercept form

[tex]y-6=\frac{1}{3}x-\frac{4}{3}[/tex]

[tex]y=\frac{1}{3}x-\frac{4}{3}+6[/tex]

[tex]y=\frac{1}{3}x-\frac{14}{3}[/tex]

Answer:

It is about 3.18 inches

Step-by-step explanation:

54 divide by 17 equals to 3.17647058824

estimate 3.17647058824 to hundredth place equals to 1.18

Answer:

Since, an airplane descended 4,000 feet before landing.

Now, we have to determine the integer which represents the number of feet, the airplane was above the ground before its descent.

Before the descent, airplane was at the height of 4,000 feet.

And the distance above the ground is represented by the positive integers and distance below the ground is represented by the negative integers.

Since, 4,000 feet is the distance of airplane above the ground.

So, the airplane was +4,000 feet above the ground before its descent.

Answer:

The correct answer is B.

Step-by-step explanation:

In this graph we can see a "Parabola", this is the curve for a second degree polynomial function, and based on "Fundamental theorem of algebra" we can know that this polynomial has 2 roots (they can be real or imaginary).

In this graph, the curve doesn't touch the X axis, so we know that this function has not real root. So both roots are complex

Answer: 3/10

Step-by-step explanation:

18/60 divide each number by 3

6/20 divide by 2

3/10

Answer: 3/10

Step-by-step explanation: To write the fraction 18/60 in lowest terms, we divide the numerator and the denominator by the greatest common factor of 18 and 60 which is 6.

Final answer:

The dimensions of the rectangle with a perimeter of 44 m, where the length is 4 m more than twice the width, are 6 m for the width and 16 m for the length.

Explanation:

The perimeter of a rectangle is given as 44 m, and the length (L) is said to be 4 m more than twice the width (W). To find the dimensions, we can set up the following equations based on the properties of a rectangle:

Perimeter P = 2(L + W)

L = 2W + 4

Since the perimeter is 44 m, we can substitute the length expression into the perimeter equation:

44 = 2((2W + 4) + W)

By solving this equation for width (W), we get:

44 = 2(3W + 4)

44 = 6W + 8

36 = 6W

W = 6 m

Now that we have the width, we can determine the length using the expression for L:

L = 2(6) + 4 = 16 m

Therefore, the final answer for the width is 6 m and the length is 16 m.

Answer:

base is 28 feet squared

height is 25 feet squared

From the conditions given, we set up an equation (1/2) * (h + 3) * h = 350. By solving for h, we find the height of the triangle is 20 feet and the base, which is 3 feet more, is 23 feet.

In this problem, we are given that the base of a triangle exceeds the height by 3 feet and the area of the triangle is 350 square feet. We need to use the formula for the area of a triangle, which is (1/2)bh, where b is the base and h is the height. We can set up an equation from the given conditions: (1/2) * (h + 3) * h = 350. Solving for h, we get h = 20 feet. Therefore, the base b = h + 3 = 20 + 3 = 23 feet. So, the height of the triangle is 20 feet and the base is 23 feet.

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Answer:

3/2

Step-by-step explanation:

1) Reduce the numbers with greatest common divisor (2 goes into 4 2 times, so your new problem would be 3/2 x1)

2) Multiply (3/2 times 1 equals 3/2)

Answer:

5

Step-by-step explanation:

Multiply (3x2)=6

the 4 on top add that with 6 (6+4)= 10

keep the denominator so 10/2

10/2 = 5/1 = 5

25^(3/2) = sqrt{25^3}

Now 25^3 = 15,625.

sqrt{15, 625} = 125

Done.

Answer:

x = -12

Step-by-step explanation:

9x + 12 = 10 + 8x - 10

9x + 12 = 8x + 10 -10

9x + 12 = 8x

12 = 8x -9x

12 = -x

12/-1

x = -12

Answer:

y=-3

Step-by-step explanation:

-7y+11y+9=-3

1) Combine alike terms:

4y+9=-3

2) subtract a 9 on both sides:

4y=-12

3) divide both sides by 4:

y=-3

Answer:   33

Step-by-step explanation:

The ratio of Adhy's to Ben's is 3:4 so let

Adhy = 3x

Ben = 4x

Since Ben = Adhy + 9

then   4x   =    3x    + 9

-->        x    =  9

So, Adhy = 3x  = 3(9)   = 27

     Ben   = 4x   = 4(9)   = 36

*************************************************************

The ratio of Ben's to Clayson's is 3:5

How do we get Ben's ratio of 3 equal to 36? by multiplying by 12

Ben  :  Clayson

3 x 12    5 x 12

 36          60

So, Clayson = 60

***********************************************************

The difference between Adhy and Clayson is:

Clayson - Adhy

   60     -    27    = 33

Answer:

33.25

Step-by-step explanation:

Answer: 36.5

Step-by-step explanation:

The statement for which the inverse is false is A, because if one angle of a triangle equals 60°, the triangle is not necessarily equilateral.

The question asks for which statement the inverse is false. To answer this, we analyze each statement and its inverse:

A. If a triangle is an equilateral triangle, then one angle equals 60°. Inverse: If one angle of a triangle equals 60°, then the triangle is equilateral. This could be false if the triangle is not equilateral but one angle happens to be 60°.

B. If a triangle is a right triangle, then the other two angles add up to 90°. Inverse: If two angles of a triangle add up to 90°, then it is a right triangle. This is true, given the geometric principle that the sum of angles in a triangle is 180°.

C. If a triangle is an equilateral triangle, then each of the angles equals 60°. Inverse: If each angle of a triangle equals 60°, then it is an equilateral triangle. This is true, as by definition, an equilateral triangle has all angles equal.

D. If a triangle is a right triangle, then one angle equals 90°. Inverse: If one angle of a triangle equals 90°, then it is a right triangle. This is true, as by definition, a right triangle has one 90° angle.

Therefore, the statement for which the inverse could be false is A.

4x - 10y = 12

4x - 12 = 10y

y = (4x - 12)/10

y = 2x/5 - 6/5

Answer:   [tex]\bold{x=\bigg\{4,-\dfrac{2}{7}}\bigg\}[/tex]

Step-by-step explanation:

7x² - 26x - 8 = 0            

Find two numbers whose product equals (7)(-8) and sum equals -26.

                        -28 × 2 = 56, -28 + 2 = -26

Replace -26x with -28x + 2x:      7x² - 28x + 2x - 8 = 0

Factor the left two terms & right two terms:    7x(x - 4) + 2(x - 4) = 0

Notice that both sides have a common factor of (x - 4)  -->  This is one of the factors.  The other factor is what is on the outside of (x - 4) --> 7x + 2

Rewrite the expression as two factors:   (x - 4)(7x + 2) = 0

set each factor equal to zero and solve for x.

              x - 4 = 0                7x + 2 = 0

                   x = 4                 7x       = -2

                                              x       [tex]=-\dfrac{2}{7}[/tex]

Answer:

the answer = 0.000089x

Step-by-step explanation:

Answer:

f(x)=-1 and 15

Step-by-step explanation:

What you do is you put -2 and 2 into the x.

f(x) = -4(-2) + 7 = -1

f(x) = -4(2) + 7 = 15

f(x)=-1 and 15 are your answers.

After substituting the values of x into the function f(x)=-4x + 7, when x = 2 the result is -1, and when x= -2 the result is 15, indicating specific points on the graph of the function.

To evaluate the function f(x) = -4x + 7 for specific values of x, we need to substitute the x values provided into the function.

When x = 2, f(2) = -4(2) + 7 = -8 + 7 = -1.

When x = -2, f(-2) = -4(-2) + 7 = 8 + 7 = 15.

So, f(2) = -1 and f(-2) = 15. These values represent specific points on the graph of the function f(x) = -4x + 7.

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Answer:

H = -3

Step-by-step explanation:

H - 26 = -29

    +26   +26

H = -3

H-26=-29

move -26 to the other side

sign changes from -26 to +26

H-26+26=-29+26

H=-29+26

Answer: H=-3

60,000 rounded to the nearest thousand is 6000

Answer:

Linear decreasing

Step-by-step explanation:

We are given that a graph

We have to find the type of graph.

Increasing  function: If [tex]x_1 \leq x_2[/tex]

Then ,[tex]f(x_1)\leq f(x_2)[/tex]

Decreasing function:If [tex]x_1\leq x_2[/tex]

Then, [tex]f(x_1)\geq f(x_2)[/tex]

The given graph is not exponential graph because exponential graph is type of curve.

But given graph is  line graph.

The equation of line

[tex]y=mx+c[/tex]

The equation of line is linear equation.

When x increasing then value of function decreasing with increasing value of x.

Hence, the graph is linear decreasing.

Final answer:

The graph depicts a logistic growth model, signified by an S-shaped curve, which represents population growth that begins exponentially, slows as resources deplete, and stabilizes at the carrying capacity.

Explanation:

The graph you are referring to seems to describe a logistic growth model, which is characterized by an S-shaped curve. This type of growth is common in populations where initially there is exponential growth due to plenty of resources and few individuals. However, as the population increases, resources become limited, slowing the growth rate; eventually, the population size stabilizes at the carrying capacity of the environment. When categorizing the graph:

Initially, the growth is exponential.

Over time, as resources become scarce, the growth rate decreases.

Finally, growth becomes nearly zero as the population reaches the environment's carrying capacity.

At different time intervals, we can annotate changes in the growth rate:

During the first phase, growth rate increases linearly with the number of individuals (exponential growth).

During the second phase, the growth rate decreases in proportion to the square of the number of individuals.

In the third phase, when carrying capacity is reached, the rate of growth is zero (no net increase in population).

This can be contrasted with the exponential growth model which is represented by a J-shaped curve and shows unbounded growth over time.

Answer:

m=88

Step-by-step explanation:

First we have to isolate the variable. In this case, it would be by multiplying the reciprocal of the fraction the both sides. M will be alone and the other side should come out to be 88. Assuming you know how to multiply with fractions, of course.

Answer: 10.676 cm

Step-by-step explanation:

We know that ,

The circumference of a circle is given by :_

[tex]\text{Circumference}=\pi d[/tex] , where d= diameter.

Given : Diameter of circle = 3.4 cm

Then Circumference of circle = [tex](3.14)(3.4=10..676\text{ cm}[/tex]

Hence, the circumference of a circle with a diameter of 3.4 cm is 10.676 cm.

The telephone company offers a $15 monthly discount for customers who also sign up for their internet service. The annual discount is calculated by multiplying the monthly discount by the number of months in a year, resulting in an annual discount of $180.

The telephone company offers a discount of $15 every month for customers that also enroll in their internet service. To find out the annual discount, we need to multiply this monthly discount by the number of months in a year.

So, the calculation is as follows: $15 (monthly discount) x 12 (months in a year) = $180. Therefore, the annual discount offered by the company is $180.

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Answer:

-30

Step-by-step explanation:

1) Remove unnecessary parenthesis:

-20-10

2) Calculate the difference:

-30

Hey!

-----------------------

Solution:

= (-20) - (10)

= -20 - 10

= -30

-----------------------

Answer:

A. -30

-----------------------

Hope This Helped! Good Luck!

Answer:

5^12

Step-by-step explanation:

When you have a question where a number is raised to the power of twice you just multiply both exponents. In this case 4x3=12

So 5 to the power of 4 to the power of 3 is 5 to the power of 12

The fraction [tex]\( \frac{2}{3} \)[/tex] results in a repeating decimal [tex]\( 0.\overline{6} \)[/tex], which falls between 0.5 and 1.

Sure, here's a step-by-step explanation:

1. Start with the fraction: We begin with the fraction [tex]\( \frac{2}{3} \)[/tex].

2. Convert to decimal: To convert this fraction to a decimal, divide the numerator (2) by the denominator (3).

[tex]\[ \frac{2}{3} = 0.66666... \][/tex]

The decimal representation of [tex]\( \frac{2}{3} \) is \( 0.\overline{6} \)[/tex], which means the digit 6 repeats infinitely.

3. Determine where it falls between 0.5 and 1: Since the decimal [tex]\( 0.\overline{6} \)[/tex] is greater than 0.5 and less than 1, the fraction [tex]\( \frac{2}{3} \)[/tex] indeed fits the criteria of being a fraction with a repeating decimal between 0.5 and 1.

Answer:

6

Step-by-step explanation:

3 1/2 = 3.5

21/3.5 = 6

The cost of one yard of fabric is required.

The cost of one yard of fabric is [tex]\$6[/tex]

Cost of [tex]3\dfrac{1}{2}\ \text{yards}[/tex] of fabric is [tex]\$21[/tex]

[tex]3\dfrac{1}{2}=\dfrac{7}{2}\ \text{yards}=\$21[/tex]

We need to divide both sides by [tex]\dfrac{7}{2}[/tex]

[tex]1\ \text{yard}=\dfrac{21}{\dfrac{7}{2}}[/tex]

[tex]=21\times \dfrac{2}{7}=\$6[/tex]

The cost of one yard of fabric is [tex]\$6[/tex]

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