What are the roots of the function?
f(x) =x^2 + 2x – 80

The number of cars Angela sold is 48 cars.

Angela sold eight more new cars this year than Carmen.

They sold a total of 88 cars.

The number of cars Angela sold is as follows:

Therefore,

let

x = number of cars Carmen sold

Hence,

Number of cars Angela sold = x + 8

They sold a total of 88 cars.

Hence,

x + x + 8 = 88

2x + 8 = 88

2x = 88 - 8

2x = 80

divide both sides by 2

x = 80 / 2

x = 40

Therefore, Angela sold 48 cars.

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The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

91

Step-by-step explanation: 7*13 = 91

91/7 = 13

Step-by-step explanation:

M = y

b

That is the answer

Explanation:

There may be a more direct way to do this, but here's one way. We make no claim that the statements used here are on your menu of statements.

Statement . . . . Reason

2. ∆ADB, ∆ACB are isosceles . . . . definition of isosceles triangle

3. AD ≅ BD

and ∠CAE ≅ ∠CBE . . . . definition of isosceles triangle

4. ∠CAE = ∠CAD +∠DAE

and ∠CBE = ∠CBD +∠DBE . . . . angle addition postulate

5. ∠CAD +∠DAE ≅ ∠CBD +∠DBE . . . . substitution property of equality

6. ∠CAD +∠DAE ≅ ∠CBD +∠DAE . . . . substitution property of equality

7. ∠CAD ≅ ∠CBD . . . . subtraction property of equality

8. ∆CAD ≅ ∆CBD . . . . SAS congruence postulate

9. ∠ACD ≅ ∠BCD . . . . CPCTC

10. DC bisects ∠ACB . . . . definition of angle bisector

The answer is:

-32

Work/explanation:

Remember the integer rule:

\(\blacktriangleright\phantom{333}\sf{a\times(-b)=-ab}\)

In other words, we multiply a positive times a negative which results in a negative product.

Therefore,

8*(-4) = -32

\(1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}\)

we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.

V = 594mm^3

In order to calculate the volume of a prisma you must multiply the area of the base times the height. The base is a triangle.

However, we don't have the value of the height in it, but we find it by solving the Pythagorean theorem on the triangle.

Answer:The correct anserw is B.

Step-by-step explanation:

The zeros of the polynomial function are x = -1 and x = 5

From the question, we have the following parameters that can be used in our computation:

y = x⁴ - 4x³ - 4x² - 4x - 5

To calculate the zeros of the polynomial function, we create a graph of the polynomial

The point where the graph intersect with the x-axis are the zeros of the polynomial function

using the above as a guide, we have the following:

Zeros: x = -1 and x = 5

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6 hours

30 divided by 4 miles = a base rate of 7.5

7.5 times 48  = 360 minutes and 360 minutes = 6 hours

Answer:

curtiss can buy 7 pounds of pistachios

Step-by-step explanation:

5 cappuccinos x $5 = 25, 32 - 25=7

The number of pounds of pistachios will be 7 pounds.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The cost of cappuccinos is $5.00 each. The cost of pistachios is $1.00 per pound. Assuming Curtiss has paid $32.00 and buys 5.00 cappuccinos.

Let 'x' be the number of pounds of pistachios. Then the correct option is given as,

1x + 5 × 5 = 32

x + 25 = 32

x = 32 - 25

x = 7 pounds

The number of pounds of pistachios will be 7 pounds.

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The probability that each bill is a $1 bill is given as follows:

1/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The bills are replaced, hence we consider that for each trial, there is a 1/4 probability of selecting a $1 bill, as one out of the four bills are of $1.

Hence the probability that each bill is a $1 bill is obtained as follows:

p = 1/4 x 1/4

p = 1/16.

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The area of the composite figure is 122.24 units².

The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.

Hence,

area of the composite figure = area of the rectangle + 2(area of semi circle)

Therefore,

area of the composite figure = 9 × 8 + 2(1 / 2 πr²)

area of the composite figure = 72 + πr²

where

r = 8 / 2 = 4 units

Therefore,

area of the composite figure = 72 + 3.14 × 4²

area of the composite figure = 72 + 3.14 × 16

area of the composite figure = 72 + 50.24

area of the composite figure = 122.24 units²

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There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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Answer:

x = 5/4

y = 15/16

Step-by-step explanation:

System of 2 equations

Applying substitution method

3/4x = y

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

5/2 x + 6/4 x = 5

16/4 x = 5

4x = 5

x= 5/4

3/4 * 5/4 = 15/16

Answer: $5,250

Step-by-step explanation:

1) Half of 5000 is 2500. But that's 50%.
2) Divide the remaining value by 10. You now have 250, which is 5%.

It's a given rule in math that if you're working with the Powers of 10, by either multiplying or dividing them, all you need to do is add or remove some zeros.

In choosing Fran's company over Shirley's company, the customer saves $160

What is Algebra?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)

As per the given details:

Fran charges f(h) = 25 +135h

Shirley charges s(h) = 65 + 150h

h = number of hedges

Cost in Fran's company for 8 hedges = 25 + 135(8)

= $1105

Cost in Shirley's company for 8 hedges = 65 + 150(8)

= $1265

Cost saved by the customer in choosing Fran's company:

Cost in Shirley's company - Cost in Fran's company

=  $1265 - $1105

=  $160

A customer saves $160 in choosing Fran's company over Shirley's company.

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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The posterior probability of a sensor fault increases as the number of consecutive measurements below 1m increases.

Let P(F) be the prior probability of a sensor fault and P(M|F) be the probability of measurements below 1m given a faulty sensor. Then, the posterior probability of a sensor fault given N consecutive measurements below 1m is given by

P(F|M1 ,M2 ,...,MN )=P(F)P(M1|F)P(M2|F)....P(MN |F)/P(M1 ,M2 ,...,MN )

P(M1 ,M2 ,...,MN ) = P(M1)P(M2)....P(MN) = (1/3)^N

Therefore,

P(F|M1 ,M2 ,...,MN )=P(F)(1/3)^N

For N = 1,2,...,10

P(F|M1 ,M2 ,...,MN ) = 0.01 (1/3)^N

For N = 1, P(F|M1)= 0.01/3

For N = 2, P(F|M1,M2)= 0.01/9

For N = 3, P(F|M1,M2,M3) = 0.01/27

Similarly, for N= 4,5,6,7,8,9,10

P(F|M1,M2,M3,M4,M5,M6,M7,M8,M9,M10) = 0.01/81, 0.01/243, 0.01/729, 0.01/2187, 0.01/6561, 0.01/19683, 0.01/59049 respectively.

The posterior probability of a sensor fault increases as the number of consecutive measurements below 1m increases.

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On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x).

\(lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5\)

from the graphs n f (x) and g( x) are 1 and 5 .

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Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer: x = 1

Step-by-step explanation:

Apply the exponent rule for multiplication, add the exponents

\(3^{2x+3+x-2}=81\)

\(3^{3x+1}=81\)

Convert 81 into exponential form with a base of 3

3*3*3*3=81

3^4=81

\(3^{3x+1}=3^4\)

Since the bases are the same, set the exponents equal

3x+1=4

3x=3

x=1

Answer:

Step-by-step explanation:

Given the function f(x) = x⁴-18x²+9 at the interval [-5, 5], the  absolute maximum and minimum values at this end points are as calculated;

at end point x = -5

f(-5) = (-5)⁴-18(-5)²+9

f(-5) = 625-450+9

f(-5) = 184

at end point x = 5

f(5) = (5)⁴-18(5)²+9

f(5) = 625-450+9

f(5) = 184

To get the critical point, this points occurs at the turning point i.e at

dy/dx = 0

if y = x⁴-18x²+9

dy/dx = 4x³-36x = 0

4x³-36x = 0

4x (x²-9) = 0

4x = 0

x = 0

x²-9 = 0

x² = 9

x = ±3

Using the critical points [0, ±3]

when x = 0, f(0) =  0⁴-18(0)+9

f(0) = 9

Similarly when x = 3, f(±3)=  (±3)⁴-18(±3)²+9

f(±3) = 81-162+9

f(±3) = -72

It can be seen that the absolute minimum occurs at x= ±5 and and absolute minimum occurs at x =±3

absolute maximum = 184

absolute minimum = -72

option A is correct answer.

because angle JKL is half of of arc JL .

so, angle JK is equal to 64°.

hope it helps...

There's probably a more efficient way to do it, but the following method works.

First, note that

x² - x - 2 = (x + 1) (x - 2)

Now use synthetic division to divide

a x⁴ + b x³ - x² + 2x + 3

by the two factors above.

Division by x + 1 :

-1   |   a           b               -1                   2                3

…   |               -a          a - b      -a + b + 1      a - b - 3

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

…   |   a      b - a     a - b - 1      -a + b + 3           a - b

which is to say,

(a x⁴ + b x³ - x² + 2x + 3) / (x + 1)

= a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3) + (a - b) / (x + 1)

Division by x - 2 :

2   |    a        b - a           a - b - 1          -a + b + 3

…   |                 2a          2a + 2b       6a + 2b - 2

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

…   |    a       a + b        3a + b - 1       5a + 3b + 1

meaning,

(a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3)) / (x - 2)

= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2)

Putting everything together, we have

(a x⁴ + b x³ - x² + 2x + 3) / (x² - x - 2)

= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)

Combine the remainder terms:

(5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)

= ((5a + 3b + 1) x + (6a + 2b + 1)) / (x² - x - 2)

We're given that the remainder is 3x + 5, so

5a + 3b + 1 = 3

6a + 2b + 1 = 5

Solve this system for a and b :

5a + 3b = 2

6a + 2b = 4

5a + 3b = 2

3a + b = 2

5a + 3b = 2

-9a - 3b = -6

(5a + 3b) + (-9a - 3b) = 2 + (-6)

-4a = -4

a = 1

5 • 1 + 3b = 2

3b = -3

b = -1

Answer:

x ≥ 40

Step-by-step explanation:

3x - 55 ≥ 65

combine like terms

3x  ≥ 65 + 55

3x  ≥120

divide both sides of the equation by 3

x  ≥ 40

Check the picture below.

Maria will earn $38,750 this year

Amount she earned = $38,750

She is paid semi-monthly. 14% of her gross pay will be withheld for federal income tax,

i.e 14% of 38750 spend on the federal income tax

So, Amount paide