The graph shows a system of inequalities.

Graph of two inequalities. One is a solid line increasing from left to right passing through negative 3 comma 0 and 0 comma 3, and it has shading below the line. The second is a solid upward opening parabola with a vertex at 1 comma negative 4 and x-intercepts at negative 1 comma 0 and 3 comma 0. This parabola is shaded inside the curve.

Which system is represented in the graph?

A. y > x2 –2x – 3
y > x + 3
B. y < x2 – 2x – 3
y < x + 3
C. y ≥ x2 – 2x – 3
y ≤ x + 3
D. y > x2 – 2x – 3
y < x + 3

Step-by-step explanation:

b + 35° = 180° ( supplementary angle )

b = 180° - 35°

b = 145°

Answer: [tex]\Large\boxed{b=145^\circ}[/tex]

Step-by-step explanation:

Given information

∡1 = 35°

∡b = ?

Total Angle = 180° (Supplementary Angle)

Derived formula from the given information

∡1 + ∡b = Total Angle

Substitute values into the given formula

(35) + b = 180

Subtract 35 on both sides

35 + b - 35 = 180 - 35

[tex]\Large\boxed{b=145^\circ}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

It is the second answer

Step-by-step explanation:

The standard form of an ellipse is

x^2/a^2 + y^2/b^2  or x^2/b^2 + y^2/a^2 = 1

If the x is the main axis we use the first form.  If the y is the main axis we use the second form.  We will use the second form.

our a is 3 and our b is 4

x^2/3^2 + y^2/4^2

Answer:

five-hundredths

Step-by-step explanation:

Since the values on both sides are equal, hence the system of equation given has no solution

Simultaneous equations are equations that consists of two or more equation and unknowns.

Given the equation below

2х+4у=4

x + 2y = 3

​

From equation 2;

x = 3 - 2y

Substitute into equation 1

2(3-2y) + 4y = 4

Expand

6 - 4y + 4y = 4

6 = 4

Since the values on both sides are equal, hence the system of equation given has no solution

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Answer:

277 miles

Step-by-step explanation:

Answer:

810 is the number that represents the same amount.

Hope this helps :)

Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which may also be given in the form of a statement. Therefore the required statement in the question is option C. Add 3 to the product of one-fourth and 8, then divide by 5.

Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which can be given in the form of a statement. When a given expression consists of both numbers and alphabets, then it forms an algebraic expression. It can also be given in the form of a statement.

Given in the question:

([tex]\frac{1}{4}[/tex] x 8 + 3) ÷ 5

This can be given in a statement form as; Add 3 to the product of one-fourth and 8, then divide by 5.

The appropriate statement that describes the given expression is: Add 3 to the product of one-fourth and 8, then divide by 5 i.e Option C.

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The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.

Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.

The discriminant is described below:

Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d²      (1)

Where:

If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:

Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²

Δ = - 1024

The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

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Answer:

The original number is 72.

Step-by-step explanation:

Let the number by

[A][B]

The reverse number is

[B][A]

Original number:

A = B + 5

[A][B] - 2[B][A] = [A][B]/4

10A + B - 20B - 2A = (10A + B)/4

8A - 19B = (10A + B)/4

32A - 76B = 10A + B

22A - 77B = 0

22(B + 5) - 77B = 0

22B + 110 - 77B = 0

-55B = -110

B = 2

A = B + 5 = 2 + 5 = 7

The original number is 72.

The reverse is 27.

Let's check.

"the tens digit of a 2 digit number is 5 greater than the units digit"

7 is 5 greater than 2,so 72 looks good so far.

"if you subtract twice the reverse number the result is one fourth the original"

The reverse number is 27. Twice 27 is 2 × 27 = 54.

Subtract 54 from 72: 72 - 54 = 18

18 is 1/4 of 72. It works.

Answer: the original number is 72

Answer:

The answer is 2970

Step-by-step explanation:

Collectively, all the students can make about 54 books rds per minute (27 * 2)

Therefore in 55 minutes there should be 2970

(54*55) :)

Answer:

x₁ = -4

x₂ = 3

Step-by-step explanation:

x²+ x + 12 = 0

x = {-1±√((1²)-(4*1*-12))} / (2*1)

x = {-1±√(1+48)} / 2

x = {-1±√49} / 2

x = {-1±7} / 2

x₁ = {-1-7} / 2 = -8/2 = -4

x₂ = {-1+7} / 2 = 6/2 = 3

Check:

x₁

-4² + (-4) - 12 = 0

16 - 4 - 12 = 0

x₂

3² + 3 - 12 = 0

9 + 3 - 12 = 0

Answer:

6x⁴ - 2x² +3

Step-by-step explanation:

[tex]\frac{12x^6-4x^4+6x^2}{2x^2}=6x^4 - 2x^2 + 3[/tex]

Answer:

A, C

Step-by-step explanation:

See attached image.

The domain and range of the given graphs are as follows,

(b) Domain: x ∈ (-∞, ∞), Range: y ∈ (-∞, ∞)

(c) Domain: x ∈ [-2, ∞), Range: y ∈ [1, ∞)

Determining the Domain and Range from a Graph

The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The various output values are represented on the y-axis as the range.

Thus, in graph (b),

Since the values of the given curve extends infinitely (denoted by arrowhead of the curve) on positive as well as negative sides for both the axes, x and y, its domain and range both are (-∞, ∞).

Similarly, in graph (c),

The minimum value on x-axis or abscissa is -2 and maximum is infinity. Hence, its domain is [-2, ∞). The minimum ordinate value or y-coordinate is 1 and maximum is infinity. Thus, its range is [1, ∞).

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The decimal notation for the given value in scientific notation is 215400.

Very large or very small numbers are denoted in scientific notation to simplify complex calculations.

The scientific notation is represented by: a × 10ⁿ

Wher a - any number or decimal number

n - the power of 10; it is an integer number

To convert this into decimal notation,

The given number is in the scientific notation,

2.154 × 10⁵

Since the power of 10 is positive, the decimal point in the number 2.154 moves towards the right. I.e,

2.154 × 10⁵ = 215400

Here power is 5. So, the decimal point moved five places to the right.

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a) The slope of the secant lines are: q = 5, f(q) = 2,076: m = - 131.1, q = 10, f(q) = 1,299: m = - 106.8, q = 20, f(q) = 357: m = - 81.6, q = 25, f(q) = 84: m = - 68.1, q = 30, f(q) = 0: m = - 51.

b) The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.

In this problem we must determine the slope of several lines based on the information given by the table and using the secant line formula:

m = [f(q) - f(p)] / (q - p)     (1)

If we know that a = 15 and p = 765, then the slope of the secant lines are:

q = 5, f(q) = 2,076

m = [2,076 - 765] / (5 - 15)

m = - 131.1

q = 10, f(q) = 1,299

m = [1,299 - 765] / (10 - 15)

m = - 106.8

q = 20, f(q) = 357

m = [357 - 765] / (20 - 15)

m = - 81.6

q = 25, f(q) = 84

m = [84 - 765] / (25 - 15)

m = - 68.1

q = 30, f(q) = 0

m = [0 - 765] / (30 - 15)

m = - 51

The slope of the line tangent to the curve at the point (x, y) = (15, 765) can be estimated by averaging the slopes of the closest secant lines:

m' = [(- 106.8) + (- 81.6)] / 2

m' = - 94.2

The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.

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Answer:

y= -1

Step-by-step explanation:

(2) (0) − y = 1

0 + − y = 1

(−y) + (0) = 1

−y = 1

Step 2: Divide both sides by -1

Y = −1

Answer:

C...........................

Answer:

10

Step-by-step explanation:

the sequence follows the rule of adding the number and then the number -1 depending on the number before it. for example, you can see in order to get from 2 to 2, it adds 0 or subtracts by 0. After that to get from 2 to 4, you add 2. After that, you subtract 1 from 2 and you subtract that number which is 1 from 4 to get 3 and so on. Following that rule, you get 10 as the next number in the sequence

Answer:

C

Step-by-step explanation:

Area of a 1/4 sector of a circle = 1/4 * pi r^2

Givens

100 of these quarter sectors

pi = 3.14

r = 12

Solution

You are using area because you are going to paint each one of the sectors. You must cover every cm^2 with paint.

Area = 1/4 * 3.14 * r * r

Area = 1/4 * 3.14 * 12 * 12

Area = 113.25

But there are 100 of them. so the area is

100 * Area = 11325 cm^2

Rounded to the nearest 100 hundreds = 11300 cm^2

Answer:

The answer is 11,300 cm²

Step-by-step explanation:

I got it right on edmentum jope this helps your question.

The psi that the TPMS would trigger a warning for this car is = 23.36 psi

The target tire pressure of the car is = 32 psi (pounds per square inch.)

The Tire pressure monitoring systems (TPMS) warns the car below 27% of 32psi

That is , 27/100 × 32

= 864/100

= 8.64psi

Therefore, 32 - 8.64 = 23.36. When the car is below 23.36psi, TPMS would trigger a warning for this car.

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Complete question:

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.)

At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is above or below?

Answer:

C

Step-by-step explanation:

Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.

The correct option is:

b. Most of students' test scores are around the mean.

A large range indicates that there is a significant difference between the highest and lowest scores in the set.

On the other hand, a small standard deviation indicates that the data points (test scores) are clustered closely around the mean.

When the range is large but the standard deviation is small, it means that most of the students' test scores are relatively close to the mean, and there are no extreme values that are significantly far from the mean. In other words, the majority of students performed similarly on the test, with only a few outliers having scores much higher or much lower than the mean.

Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.

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Answer:

36 years old

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

sum the parts of the ratio , 3 + 5 = 8

divide the sum of their ages by 8 to find the value of one part of the ratio

96 ÷ 8 = 12 ← value of 1 part of the ratio , then

3 parts = 3 × 12 = 36 ← Sadias age

Answer: x = 9

Step-by-Step Solution:

Hypotenuse = 15 units

Base = 12 units

Altitude = x units

Using Pythagoras Theorem,

=> Hypotenuse^2 = Base^2 + Altitude^2

(15)^2 = (12)^2 + x^2

225 = 144 + x^2

225 - 144 = x^2

81 = x^2

x^2 = 81

x = √81

=> x = 9

Therefore, Altitude = 9 units

Answer:

2/3rds of liad's run

Step-by-step explanation:

3 min 45s = 3 3/4 min = 15/4 min; 10/(15/4) = 8/3 laps

2min 30s = 2 1/2 min = 5/2 min; 10/(5/2) = 4 laps

(8/3)/4 = 2/3

Using simple interest, it is found that:

Simple interest is used when there is a single compounding per time period.

The amount of money after t units of time in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

For this problem, the parameters are given as follows:

A(0) = 875, r = 0.0004273, t = 32.

Hence the amount paid is given by:

A(32) = 875 x (1 + 0.0004273 x 32) = $887.

The amount of interest is given by:

I = 887 - 875 = $12.

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Steve's expected win from the lottery ticket purchase is $3 because his chance of winning the $300 prize is only 1%.

The expected winnings for Steve are a function of the probability of some predictable outcomes.

In this situation, the predictable outcome is the size of the lottery prize.

The probability that Steve will win the prize is 1% (1/100), depicting his chance of winning.

Sale price per ticket = $5

Lottery prize = $300

Value of lottery prize to Steve if he wins = $295 ($300 - $5)

Probability of winning = 1% (1/100 x 100)

Expected win = $3 ($300 x 1%)

Thus, Steve's expected win is $3, which outweighs the cost of a ticket.

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