L3.8.3 Test (CST): Quadratic Equations and Functions
Which of the following are solutions to the quadratic equation below?
Check all that apply.
x²+2x-8=0
A-4
B, 6
C. 2
D. 8
E. -1

Answer:

84%

Step-by-step explanation:

The total is 25 students. (21+4)

The students that voted are 21

21/25 = 0.84

The slope of the line that cuts through the points (1, -5) and (3, 5) is equal to 2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (5 - (-5))/(3 - 1)

Slope (m) = (5 + 5)/(2)

Slope (m) = 10/2

Slope (m) = 2.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 2.

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Answer:

2(x + 5) = 3(x - 4)

2x + 10 = 3x - 12

x = 22

Answer:

(a) Area of the big circle

= π(9^2) = 81π square cm

(b) Area of both little circles

= 2π(4.5^2) = 40.5π square cm

= 81π/2 square cm

(c) Area of the blue section

= 81π - 40.5π = 40.5π square cm

= 81π/2 square cm

The volume of the rectangular prism which is as described in the task content is; 67½ cm³.

It follows from the task content that the value of the rectangular prism which is as described is required to be determined.

Since the rectangular prism has width as six centimeters, the length as two and a half centimeters and the height as four and a half centimeters;

Volume = l × w × h

Volume = 2½ × 6 × 4½

Volume = 5/2 × 6 × 9 / 2

Volume = 67½ cm³.

Ultimately, the volume of the prism is; 67.5 cm³.

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Answer:

the sum of Z1 and Z2 is 4.553 + j 5.326.

Step-by-step explanation:

To add two phasors, we add their real and imaginary parts separately.

Given:

Z1 = 2 / 63°

Z2 = 5 / 42°

Converting them to rectangular form:

Z1 = 2 cos(63°) + j 2 sin(63°) = 0.921 + j 1.862

Z2 = 5 cos(42°) + j 5 sin(42°) = 3.632 + j 3.464

Adding them:

Z1 + Z2 = (0.921 + 3.632) + j (1.862 + 3.464)

= 4.553 + j 5.326

Therefore, the sum of Z1 and Z2 is 4.553 + j 5.326.

hope this helped you!;))

The volume of the cone is  37.70 cm³.

The volume of the cone is calculated as follows;

V = ¹/₃πr²h

where;

The radius of the cone is calculated by applying the following formula;

r = √ (5² - 4²)

r = 3 cm

The volume of the cone is calculated as;

V = ¹/₃πr²h

V = ¹/₃π(3)²(4)

V = 37.7 cm³

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The summary of Angle Relationships in a Circle is given.

The following is an overview of angle relationships in a circle:

The vertex of a central angle is the center of the circle. A central angle's length equals the length of the arc it crosses.

Inscribed angle: An angle with a circle as its vertex and sides that intersect two separate arcs. An inscribed angle has half the length of the arc it intersects.

Tangent-chord angle: A tangent-chord angle is generated when a tangent and a chord cross at the point of tangency. The length of this angle is half the length of the intercepted arc.

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When graphing an equation on graph paper I have to have all of these but: B. work shown.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics and Geometry, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

In conclusion, you do not need to have your algebraic work shown when graphing an equation on graph paper.

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Answer:

Step-by-step explanation:

Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph

The y- intercept for both function is 0 and 5.8.

We have First function

y= [tex]9^x[/tex]

Now , the y intercept of the equation is when x = 0

So , when x = 0

y= [tex]9^0[/tex]

y= 0

and, the second function is

y= [tex]9^{0.8[/tex]

y= 5.799

Hence, second function have intercept 5.8.

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The equivalent expression for 8y + 12 + 2y + 8 will be 10y + 20.

The number of problems that she get wrong is 4.

The days that Jared work to make 20 bird houses is 15 days.

The equivalent expression for 8y + 12 + 2y + 8 will be:

= 8y + 12 + 2y + 8

= 10y + 20

The number of problems that she get wrong is:

= (1 - 84%) × 25

= 0.16 × 25

= 4.

The days that Jared work to make 20 bird houses is:

= 3/4 × 20

= 15 days.

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Write an equivalent expression for 8y + 12 + 2y + 8

Maria’s math test had 25 questions. She got 84% correct. How many problems did she get wrong?

Jared made 4 bird houses in 3 days. How many days will Jared work to make 20 bird houses?

The difference between the median math test score, as shown by the ox plots, is: 12.5.

The median of a data set is displayed in a box plot as the value that is at the vertical line that divides the rectangular box. This is also 50% mark of the data set.

Thus, the data set for afternoon, as shown in the box plot has a median that is 75, while the median of the data set for morning is 87.5.

Find the difference of their medians:

Difference of their medians = 87.5 - 75 = 12.5.

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The probability that he plays a rock song than a hip hop song is greater than 0.1. The Option B is correct.

Probability helps to find out the likelihood of the occurrence of an event by measuring the chance of an event happening and is equal to the number of favorable events divided by the total number of events.

Given that:

Total of songs = 40

Prob (playing rock) = 15/40

Prob (playing hip-pop) = 11/40

How much greater probability he plays a rock song than a hip hop song will be:

= 15 / 40 - 11/40

= 15 - 11 / 40

= 4/40

= 1/10

= 0.1

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Answer:

I think it’s

False

True

True

True

True

False

True

False

The inequality represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks is 50 ≥ 3.5x + 5

We are given that Sydney started with no money in her piggy bank and adds $3.50 each day. Destiny started with $50 in her piggy bank and spends $5 of her money each day.

We need to find the equation or inequality that represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks.

Sydney started with zero money in her piggy bank and adds $3.50 each day means 0 + 3.50 and Destiny started with $50 in her piggy bank and spends $5 of her money each day then

the inequality  becomes as ;

50 ≥ 3.5x + 5

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Answer:  [tex](x+7)^2 + (y+1)^2 = 9[/tex]

center = (-7, -1)

radius = 3

======================================================

Explanation:

The highest point on the circle is at (-7,2)

The lowest point is at (-7, -4)

Connecting these endpoints gets us one diameter of this circle.

Apply the midpoint formula to these endpoints.

[tex]\text{Endpoints: }(x_1,y_1) = (-7,2) \text{ and } (x_2,y_2) = (-7,-4)\\\\\text{Midpoint} = (x_m, y_m)\\\\\begin{array}{|l|l|}\cline{1-2}x_m = \frac{x_1 + x_2}{2} & y_m = \frac{y_1 + y_2}{2}\\ & \\x_m = \frac{-7 +(-7)}{2} & y_m = \frac{2 +(-4)}{2}\\ & \\x_m = \frac{-14}{2} & y_m = \frac{-2}{2}\\ & \\x_m = -7 & y_m = -1\\\cline{1-2}\end{array}\\\\\text{The midpoint is located at }(-7, -1)\\\\[/tex]

This midpoint of a diameter is also the location of the center of the circle. Recall that all diameters are a special type of chord that pass through the center of a circle.

The circle is centered at (-7, -1)

---------

Now compute the distance from the center (-7,-1) to a point on the circle's edge. Let's say we picked (-7,2)

The distance between these points is 3 units, which we can find by subtracting the y coordinates and using absolute value

distance = |2 -(-1)| = |2+1| = |3| = 3

You could use the distance formula, but it's probably easier to subtract and then use absolute value.

The distance of 3 units represents the radius of the circle. It's how far you need to go from the center to get to the circle's edge.

Circle radius = 3

---------

Summary

We plug those items into the circle template equation.

[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-(-7))^2 + (y-(-1))^2 = 3^2\\\\(x+7)^2 + (y+1)^2 = 9[/tex]

That last equation is the final answer.

There will be about 105.28 pounds of radioactive material in the concrete vault after 140 years.

The function [tex]A = A_0e^{(-0.0077x)}[/tex] gives the amount A of the radioactive material, where A0 is the initial amount of the material, x is the number of years since it was put in the vault, and e is the mathematical constant approximately equal to 2.71828.

We are given that the initial amount of material put into the vault is 300 pounds.

Therefore, [tex]A_0 = 300[/tex].

We want to find the amount of material that will be left after 140 years. Therefore, x = 140.

Substituting these values into the function, we get:

[tex]A = A0e^{(-0.0077x)}\\A = 300e^{(-0.0077 * 140)}\\A = 105.28[/tex]

Therefore, after 140 years, approximately 105.28 pounds of radioactive material will be left in the concrete vault.

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From 1970 to 2013, the price of postal stamps increased at an average yearly rate of 4.851%.

The formula for compound interest is:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where A represents the total sum, P represents the beginning sum, r represents the yearly interest rate, n is the number of times the interest is compounded annually, and t represents the number of years.

In this instance, we may consider the initial cost of postal stamps in 1970 as the principal and the rise in price as the interest. The yearly rate of rise, r, may be calculated using the formula.

Let P represent the price in 1970 ($0.06) and A represent the price in 2013 ($0.46). Let t be the duration, or 43 years, from 1970 to 2013.

Then, we can write:

[tex]A = P(1 + r)^t[/tex]

Substituting the values, we get:

[tex]0.46 = 0.06(1 + r)^{43[/tex]

Dividing both sides by 0.06, we get:

[tex]7.67 = (1 + r)^{43[/tex]

Taking the 43rd root of both sides, we get:

[tex](1 + r) = 7.67^{1/43}\\(1 + r) = 1.04851[/tex]

Subtracting 1 from both sides, we get:

r = 0.04851 = 4.851%

Therefore, the average annual rate of increase in the price of postage stamps from 1970 to 2013 is 4.851%.

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answer 95 I think that is the answer do you know it it is hard

Answer:

Total cost = $132

Step-by-step explanation:

We can find the total cost using the formula

total cost = (item 1 quantity * cost) + (item 2 quantity * cost)

We essentially find the sum of the product of item quantity and cost for each item:

Thus, for 2 chairs costing $37/chair and 1 table costing $58/table, the total cost is:

Total cost = (2 * $37) + (1 * $58)

Total cost = $74 + $58

Total cost = $132

The expected profit for the first mall is $425,000.

To calculate the expected profit for the first mall, we need to multiply the profit for each outcome by its probability, and then add up the results.

Let S denote success and F denote failure for the first mall.

Then the expected profit is:

Expected profit for the first mall = (probability of success) × (profit for success) + (probability of failure) × (profit for failure)

Expected profit for the first mall = (1/2) × $1,275,000 + (1/2) × (-$425,000)

Expected profit for the first mall = $637,500 - $212,500

Expected profit for the first mall = $425,000

Therefore, the expected profit for the first mall is $425,000.

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The volume of this sphere is 1607. 68 in³

It is important to note that the formula that is used to calculate the volume of a sphere is expressed as;

V = 4/3 πr3

Given that the parameters are;

From the information given,

Substitute the values, we have;

Volume = 4/3 × 3.14 ×8³

Find the cube values, we get;

Volume = 4/3 × 3.14 × 512

Multiply the values

Volume = 2143. 57 in³

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Answer:

Number three is D.

Step-by-step explanation:

Answer: im pretty sure the answer is in the pdf, when you scroll down. its 126 cm^2

Step-by-step explanation:

The algebraic expression is represented as 12 - 4x

It is important that we note that algebraic expressions are those expressions that are made up of some variables, certain terms, coefficients, factors and constants.

These algebraic expressions are also identified with the presence of arithmetic operations, such as;

From the information given,

Let the number by x

We then have;

The coefficient is 4

The constant is 12

The variable is x

Substitute the terms

12 - 4x

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We can see here that the probability that it is yellow is: 2.4.

Probability is a way to gauge how likely something is to happen. It is stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the event.

Probability that the marble is yellow:

Total marbles = 12

Yellow marbles = 5

Probability that the marble is yellow: 12/5 = 2.4

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Answer:

Step-by-step explanation:

Les opinions des 450 élèves d'un lycée quant à savoir s'ils soutiennent le candidat A à la présidence du corps étudiant sont présentées ci-dessous. Masquez et mélangez toutes les valeurs. Prenez un échantillon aléatoire de 25 valeurs de la population. Sur la base de cet échantillon, trouvez la proportion de l'échantillon et utilisez cette valeur pour créer un intervalle de confiance à 95 % pour la véritable proportion de la population qui soutient le candidat A, en arrondissant au millième le plus proche.

Échantillon Oui : 19 Échantillon N° : 6 Échantillons : 25

The proportion of the babies born

Given that

Uniform Distribution from 1 – 53

This means that

a = 1 and b = 53

So, we have

Mean = (a + b)/2 = (1 + 53)/2 = 27

Standard deviation = √[(b – a)² / 12] = √[(53 – 1)² / 12] = 15

After the 40th week of the year

The z-score is calculated as

z = (x - mean)/Standard deviation

So, we have

z = (40 - 27)/15 = 0.8667

So, we have

Proportion = P(z > 0.8667)

Proportion = 80.7%

Before the 10th week of the year

z = (10 - 27)/15 = -1.133

So, we have

Proportion = P(z < -1.133)

Proportion = 12.9%

Between the 10th and 40th week of the year

This is calculated as

Proportion = (-1.133 < z < 0.8667)

So, we have

Proportion = 67.8%

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Answer:

124

Step-by-step explanation:

To find the number that should be added to the data so that the range of the data is 63, we first need to find the current range of the data.

The range of a set of data is the difference between the largest and smallest values in the set.

So, to find the current range of the data, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value

Range = 97 - 61

Range = 36

This means that the current range of the data is 36.

To increase the range to 63, we need to add a number that is 63 - 36 = 27 larger than the current range.

To do this, we can add 27 to the largest value in the data set, which is 97:

97 + 27 = 124

So, we should add 27 to the data set to increase the range to 63.

Therefore, the complete set of data would be:

78, 61, 95, 77, 85, 97, 124

Check:

To find the range of the data set 78, 61, 95, 77, 85, 97, 124, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value

Range = 124 - 61

Range = 63

Therefore, the range of the data set 78, 61, 95, 77, 85, 97, 124 is 63.