A quadratic equation is shown below:

4x^2 − 12x + 10 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 2x^2 − 13x + 21 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answer:

a)the length of each side is [tex]5\sqrt3[/tex] feet

b)In the nearest tenth the length of the side is 8.7 feet.

Step-by-step explanation:

The area of the square garden is 75 square feet.

a) Let x  be the length of each side.

We know that,

[tex]\text{Area of square}=\text{(Side)}^2[/tex]

Hence, we have

[tex]75=x^2\\\\x=\sqrt{75}\\\\x=5\sqrt{3}[/tex]

Thus, the length of each side is [tex]5\sqrt3[/tex] feet

b)

In the nearest tenth the length of the side is 8.7 feet.

Answer:

Step-by-step explanation610:

Answer:

(D)[tex]96^{\circ}=(arc)BC[/tex]

Step-by-step explanation:

It is given from the figure that m∠BAC=48° and arcAC=110°.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Now, using the above property, we have

[tex]m{\angle}BAC={\frac{1}{2}}(arc)BC[/tex]

Substituting the given values, we get

[tex]48^{\circ}=\frac{1}{2}(arc)BC[/tex]

[tex]96^{\circ}=(arc)BC[/tex]

Thus, the measure of the arc BC is 96 degrees.

Hence, option D is correct.

Next time you should write the correct form of equation because it affects greatly the answer. I believe the correct form would be:

f (x) = 2 * x^2 + 1

where the second 2 is a power of x

The average rate of change is also defined as the slope of the equation. Therefore:

average rate of change = slope

Where slope is:

m = (y2 – y1) / (x2 – x1) = [f (0) – f (-1)] / (x2 – x1)

Calculating for f (0): x2 = 0

f (0) = 2 * 0^2 + 1 = 1

Calculating for f (-1): x1 = -1

f (-1) = 2 * (-1)^2 + 1 = 3

Substituting the known values to the slope equation:

average rate of change = (1 – 3) / (0 – 1)

average rate of change = -2 / -1

average rate of change = 2

Answer: 2

Answer:

I believe the proper form of this question is actually... as I have also come across this question.

"For the graphed function f(x) = (2)^(x + 2) + 1, calculate the average rate of change from x = −1 to x = 0."

Step-by-step explanation:

the y2 - y1/ x2 - x1, will actually be (-1,3) and (0,5).

This means you will get a 5 + 1 (because subtracting a -1 is the same as adding 1) over 0 - 3.

Next you have 6/-3 which will give you a answer of -2

Now I do believe the proper answer is actually 2 because the graph shows a chart that is growth, not decay, but the math gives a -2 which is confusing.

Answer:  

[tex]\bf \textbf{Probability that the person is female or a doctor = }\frac{13}{16}[/tex]

Step-by-step explanation:

Number of nurses in the hospital = 12

Number of doctors in the hospital = 4

Number of male nurses = 3

Number of male doctors = 2

Number of male persons = 5

So, Number of female persons = 16 - 5 = 11

Number of female doctors = 4 - 2 = 2

So, Probability that the person is female or a doctor = Probability that a person is female + Probability that a person is doctor - Probability that a person is female doctor

[tex]\implies\text{Probability that the person is female or a doctor = }\frac{11}{16}+\frac{4}{16}-\frac{2}{16}\\\\\implies\bf \textbf{Probability that the person is female or a doctor = }\frac{13}{16}[/tex]

Answer:

6^2 + x^2 = 9^2

36 + x^2 = 81

81-36= 45

square root of 45 is approximately 6.71 miles

Step-by-step explanation:

Using the theram theroy is very important to know the fulma and steps

To use the linear combination method and addition to eliminate the y-terms, the second equation should be multiplied by 4.

An equation is like a relationship between two or more variables. It is expressed in equal to form. Equation of two variables looks like: ax+ by=c.

It is solved to find the value of variables.

The given equations are 7x+16y= -2 and 9x-4y=22 and we have to solve using linear combination method.

First we have to change  -4y to -16y because after we have to do addition so we will multiply the second equation by 4 which makes the equation as under:

36x-16y=88

Adding equation 1 and 2

7x+16y+36x-16y=-2+22

42x=20

x=20/42

x=10/21

Put the value of x in 7x+16y=-2

7(10/21)+16y=-2

10/3+16y=-2

16y=-2-10/3

16y=-16/3

y=-1/3

Hence to solve the equations we need to first multiply second equation by 4 which is option D.

Learn more about equation at https://brainly.com/question/2972832

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Answer:

2400

Step-by-step explanation:

Given : The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each.

To Find: If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?

Solution:

No. of faces of first die = 6

No. of faces of second die = 4

No. of faces of third die = 10

No. of faces of fourth die = 10

Now we are supposed to find the the number of possible outcomes exist.

So, Number of possible outcomes if all the dice are thrown together :

= [tex]6 \times 4 \times 10 \times 10[/tex]

=[tex]2400[/tex]

Hence there are 2400 possible outcomes if all the dice are thrown together and their combination dictates a certain outcome of the game.

Final answer:

To determine when the number of new cars reaches 15,000, the quadratic equation 26t^2 + 168t + 4208 = 15,000 is solved for t and then added to 1958.

Explanation:

To find the year when the number of new cars reaches 15,000, we need to set the equation C = 26t^2 + 168t + 4208 equal to 15,000 and solve for t, where t is the number of years since 1958.

First, set up the equation: 15,000 = 26t^2 + 168t + 4208.

To solve for t, we subtract 15,000 from both sides to get the quadratic equation: 0 = 26t^2 + 168t - 10,792.

Next, we use the quadratic formula [tex]t = (-b \pm \sqrt{b^2 - 4ac}) / (2a)[/tex], where a = 26, b = 168, and c = -10,792.

Plugging the values into the quadratic formula, we get the two possible solutions for t. After calculating the roots, we discard any negative value as it would not make sense in the context of time since 1958. The positive year will give us the answer we need.

Adding the positive value of t to 1958, we obtain the year in which the number of new cars purchased will reach 15,000.

Final answer:

Using the formula for combinations with repetition, with 15 different toppings and no limit on the number of toppings per pizza, we find that there can be 32,768 different possible pizzas.

Explanation:

The question you're asking relates to combinations with repetition, a topic in combinatorics, a branch of mathematics. Given 15 different pizza toppings and the possibility of choosing any number of these toppings for a single pizza (including the possibility of a pizza with no toppings at all), we're essentially looking at how many different pizzas can be created.

To calculate the total number of different pizzas that can be ordered, we use the formula for combinations with repetition, which is (n+r-1)C(r), where 'n' is the number of toppings to choose from (15 in this case), 'r' is the number of toppings chosen, and 'C' represents the combination function. Since there's no limit to the number of toppings, 'r' can vary from 0 (a pizza with no toppings) to 15 (a pizza with all the toppings). However, because the question allows any number of toppings and we consider repetitions, the calculation simplifies to 2ⁿ, where n is the number of toppings.

Therefore, calculating this gives us 2¹⁵, which equals 32,768 different possible pizzas. This includes every combination from no toppings at all to a pizza with all 15 toppings.

The possible rational roots are given by the ratio of the constant term to the leading coefficient. That is [tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2,  [tex]\pm[/tex]1/5,  [tex]\pm[/tex]1/10,  [tex]\pm[/tex]1/20, and so on and this can be determined by using the arithmetic operations.

Given :

Polynomial Equation -- [tex]2x^3+5x^2-8x-20=0[/tex]

The following steps can be used in order to determine the rational roots of the given polynomial equation:

Step 1 - Write the given polynomial equation.

[tex]2x^3+5x^2-8x-20=0[/tex]

Step 2 - The coefficient of [tex]x^3[/tex] is 2. So the factors of 2 are [tex]\pm[/tex]1, [tex]\pm[/tex]2.

Step 3 - The constant term of the given polynomial is -20 and the factors of the constant term are  [tex]\pm[/tex]1,  [tex]\pm[/tex]2,  [tex]\pm[/tex]5,  [tex]\pm[/tex]10,  [tex]\pm[/tex]20.

Step 4 - The rational roots are given by the ratio of the constant term to the leading coefficient. That is,

[tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2,  [tex]\pm[/tex]1/5,  [tex]\pm[/tex]1/10,  [tex]\pm[/tex]1/20, and so on.

For more information, refer to the link given below:

https://brainly.com/question/12254880

Sample Response:

Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.

Final answer:

The provided sequence is a geometric sequence that converges to 0 because its common ratio's absolute value is less than 1.

Explanation:

The sequence provided is 48, 12, 3, 3/4, suggesting a pattern where each term is divided by 4 to get the next term (this is a common ratio r = 1/4). This type of sequence is known as a geometric sequence, and to determine if it converges, we can apply the ratio test.

In a geometric sequence, successive terms approach zero if |r| < 1. Since the absolute value of the common ratio here is less than 1, the terms of the sequence will get progressively smaller and approach zero. Therefore, we can conclude that this geometric sequence converges, and the limit is 0.

The given statement is a false statement.            

Collinear Points--

Two or more points are said to be collinear if they lie on a straight line.

Coplanar--

Set of points are said to be coplanar if they lie on the same plane.

If the set of points are collinear then we may get a line such that it will contain all these points and as we know that line always lie in a plane also there may be infinite number of planes which may contain the same line.

So, all the points on the line will also lie in the same plane.

Yes, collinear points are necessarily coplanar.

Answer:

Option B is correct.

(1 , -5) lies on the graph.

Step-by-step explanation:

Given the points (4,1) and (-2 , -11)

First find the linear equation for the given points.

Equation of line for two points [tex](x_1, y_1)[/tex] and  [tex](x_2, y_2)[/tex]

is given by:   [tex]y-y_1 = (\frac{y_2-y_1}{x_2 - x_1}) (x-x_1)[/tex]

Substitute the given points (4,1) and (-2 , -11)  in above equation to find the equation of line:

[tex]y-1=(\frac{-11-1}{-2-4})(x-4)[/tex]

or

[tex]y-1=(\frac{-12}{-6})(x-4)[/tex]

or

[tex]y-1=2(x-4)[/tex]

Using distributive property on RHS ( i.e,  [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex] )

we have;

y -1 = 2x-8

Add 1 to both sides of an equation;

y-1+1 = 2x-8+1

Simplify:

y = 2x -7

Therefore, the equation of line for the given point is: y =2x - 7     ....[1]

To find which points lies on the graph ( i.e, Line)

Substituting the given options in equation [1] we have;

A . (1,1)

Put x =1 and y =1

[tex]1 = 2\cdot 1 -7 = 2-7[/tex]

1 = -5 which is not true.

Similarly

B. for (1, -5)

[tex]-5= 2\cdot 1 -7 = 2-7[/tex]

-5 = -5 which is true.

C. for (1, 2)

[tex]2= 2\cdot 1 -7 = 2-7[/tex]

2 = -5 which is not true.

And

D.  For (1 , -7)

[tex]-7= 2\cdot 1 -7 = 2-7[/tex]

-7 = -5 which is also not true.

Therefore, the only point which lies on the  line graph [1] is; (1 ,-5)