17.1
What is the solution to the equation --+?
X=-5
X=-4
X-5
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On solving the provided question, we can say that the function is

[tex]f(z) = 3 - 4z^2[/tex]  and f(-2) = -13 and f(0) = 3.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the function is

[tex]f(z) = 3 - 4z^2[/tex]

[tex]f(-2) = 3 - 4(-2)^2[/tex]

= 3 -  4(4)

= 3 - 16

=-13

[tex]f(0) = 3 - 4(0)^2[/tex]

= 3 - 4(0)

= 3 - 0

= 3

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Answer: A) Dashed line with shading below

Step-by-step explanation:

because, as you can see the < sign is only less than not 'less than and equal to' so it will be dashed...

Answer:

A

Step-by-step explanation:

A dashed line is used if < or > is used to indicate that the boundary is not part of the solution. Then shade the appropriate region.

As in the question, y is less than 4/3x + 2 therefore, the region below the line is shaded.

The relations that represent functions are given as follows:

A relation represents a function when each input value is mapped to a single output value.

Hence the two items that are not functions in this problem are given as follows:

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The limits lim x→ −4 f(x) is 5

The method is substitution method

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

−5x − 15 ≤ f(x) ≤ x² + 3x + 1

The limits is given as

lim x→ −4 f(x)

By direct substitution, we have

−5(-4) − 15 ≤ f(x) ≤ (-4)² + 3(-4) + 1

Evaluate the exponents and the products

20 − 15 ≤ f(x) ≤ 16 - 12 + 1

Evaluate the difference

5 ≤ f(x) ≤ 5

This means that

f(x) = 5

So, we have

lim x→ −4 f(x) = 5

The method used is the direct substitution method

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Answer:

the answer is 25c²

Step-by-step explanation:

(5c-3d)²-9d²

5²c²+3²d²-9d²

25c²+9d²-9d²

25c²

Answer:

= 25c² - 30cd

Step-by-step explanation:

(5c-3d)²-9d²

[tex](5c - 3d)(5c - 3d) - 9 {d}^{2} \\ 5c(5c - 3d) - 3d(5c - 3d) - 9{d}^{2} \ \\ 25 {c}^{2} - 15cd - 15cd + 9 {d}^{2} - 9 {d}^{2} \\25 {c}^{2} - 30cd[/tex]

Answer:12

Step-by-step explanation:30-6=24

24 divided by 2 =12

The value of x in the proportion equals 50.

Proportion is referred to as a part, share, or number considered in comparative relation to a whole. Proportion can be defined as when two ratios are equivalent, they are in proportion. It is an equation or statement used to show that two ratios or fractions are equal.

In proportion, if two sets of numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol  ":" or "=".

16/50 = x/156.25

x = 156.25 x 16 / 50

x = 2500 / 50

x = 50

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Refer to the attached images.

**Should be arctan(tanx)=x on the last page**

answer c)

cross x  at x = -2, x = 3, and x = 1

the square root tells us that it bounces off that location rather than intercepting

Answer:

Step-by-step explanation:

The sum of interior angles in a quadrilateral is 360°, from the picture we have a 90°, 160° and 70°.

so

take off from 360° the know angles and we will find the angle "?"

360 - 90 - 160 - 70 =

40° (your answer)

By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).

To solve the system of equations, graph the given two lines' first equation. Now determine whether the lines are parallel, intersect, or are the same line.

In the next step, we need to Identify the solution to the system.

If the lines are intersected, the point of intersection is the solution.

If the lines are parallel, the system will have no solution.

If the lines are the same or coincident, then the system will have an infinite number of solutions.  

Here we have

y = x  ----- (1)

y = 2x+2 ---- (2)

From (1) and (2)

=> y = 2y + 2

=> 2y - y = -2

=> y = - 2

Hence, the solution of the given system of the equation is (-2, -2)

We can check it by graphing the lines as shown figure.  

Therefore,

By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).

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Using an exponential function, it is found that the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year is given by:

P= 100%[([tex]1.03^{t}[/tex]) - 1]

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

An increasing exponential function is modeled by:

A(t)= A(0)[tex](1+r)^{t}[/tex]

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

As a percentage, the increase is modeled by:

P= 100%[[tex](1+r)^{t}[/tex] - 1]

In this problem, the growth rate is of r = 0.03, hence:

P= 100%[      [tex](1+0.03)^{t}[/tex]- 1]

P= 100%[[tex](1.03)^{t}[/tex]- 1]

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The number of rotational symmetries that the figure has would be C. 1 at 360 degrees.

The number of times the geometric figure is similar to the original figure after undergoing a full revolution is known as the order of rotational symmetry. The order of rotational symmetry is determined by how many times the rotated figure perfectly fits within the original figure.

When the Figure F is rotated, the only times that it can be rotated to be able to give the same figure of F, is once, and that once has to be a full revolution of 360 degrees.

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Answer:

41°

Step-by-step explanation:

We know that,

y°+49°= 90°

y° = 90°-49°

y=41°

So, the value of y is 41°

The height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.

What is called height?

Height, altitude, and elevation mean the vertical distance either between the top and bottom of something or between a base and something above it. height refers to something measured vertically whether high or low.

Each time the ball bounces, it reaches a height of 75% of its previous height.

Since the ball was dropped from a height of 2 meters, its height after the first bounce will be:

2 meters x 0.75 = 1.5 meters

After the second bounce, the height of the ball will be:

1.5 meters x 0.75 = 1.125 meters

After the third bounce, the height of the ball will be:

1.125 meters x 0.75 = 0.84375 meters

After the fourth bounce, the height of the ball will be:

0.84375 meters x 0.75 = 0.6328125 meters

After the fifth bounce, the height of the ball will be:

0.6328125 meters x 0.75 = 0.474609375 meters

Therefore, the height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.

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Answer:

Step-by-step explanation:

Given a family net income of $13150, Lisa's current annual gross of $76200, deductions of 20% of Lisa's gross salary, you want to know Lisa's monthly net income and the new family net income if Lisa makes 35% less by working part-time.

Lisa's current annual income is $76200, and her annual net income is 80% of that, or $60960. On a monthly basis, her net income is ...

  $60960/12 = $5080 . . . . . . Lisa's current net monthly income

If her income is reduced by 35%, the reduction is ...

  0.35 × $5080 = $1778

Then Lisa's part-time monthly net income will be ...

  $5080 -1778 = $3302 . . . . . Lisa's part-time monthly net income

The family net income will be reduced by the same amount:

  $13150 -1778 = $11372 . . . . . new family monthly net income

__

Additional comment

It appears the total of budgeted items is $10343, so those items can be paid even if Lisa works part-time. The family's current surplus income of $2807 would be reduced to $1029, about a 63% reduction. That gives a lot less cushion to pay for off-budget expenses that may come up.

answer

C(9, 5) - C(6, 5) + C(3, 1) = 126 - 6 + 3 = 123

explanation

The first term, C(9, 5), represents the number of ways to select 5 restaurants out of 9, regardless of type. The second term, C(6, 5), represents the number of ways to select 5 non-seafood restaurants out of 6. To find the number of ways that at least one of the selected restaurants will serve seafood, we subtract the number of ways to select 5 non-seafood restaurants and add the number of ways to select exactly 1 seafood restaurant, represented by C(3, 1).

The result, 123, represents the number of ways that at least one of the selected restaurants will serve seafood.

15) Evaluating the mathematical expression -10 -144/(-12) shows that 144 is being divided by 12 before subtracting 10, following the application of PEMDAS.

16) The value of the algebraic expression is 2.

The evaluation of an expression is finding its value by substituting variables and applying the PEMDAS rule.

PEMDAS means the order of algebraic operations that applies parentheses, exponents, multiplication, division, addition, and subtraction.

-10 -144/(-12)

-10 + (144/12)

-10 + 12

= 2

Thus, we have evaluated the expression to have a value of 2.

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The perimeter of each shape is obtained adding all of their outer side lengths.

The perimeter of a polygon is composed by the sum of the lengths of the outer edges of the figure.

Hence, for each polygon, you must identify the outer side lengths, and then add them.

The problem is incomplete, hence the standard procedure to find the polygon of a shape was presented.

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The time take to fill the pool will be 494 hours.

Inlet pipe fills in  38 hours = 1 pool

Inlet pipe fills in 1 hours = 1/38

Drain pipe empty in 39 hours = 1 pool

Drain pipe empty in 1 hour = 1/39

If both pipes are opened together then in pool fills in 1 hour =  1/38 - 1/39

= 1/1482

Therefore, 1/1482 fills in 1 hour.

. Therefore, 1/3 will be:

= 1/3 × 1482

= 494 hours.

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The needed amount of each solution is given as follows:

The amounts are obtained using a system of equations, for which the variables are given as follows:

Faith needs 300 milliliters of the solution, hence:

x + y = 300.

x = 300 - y.

The percentage is of 57%, hence:

0.5x + 0.6y = 0.57 x 300

0.5x + 0.6y = 171.

Replacing the first equation into the second, the value of y is obtained as follows:

0.5(300 - y) + 0.6y = 171

0.1y = 21

y = 21/0.1

y = 210.

The value of x is then given as follows:

x = 300 - 210

x = 90.

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On solving the provided question, we can say that by linear equation If The Grant is thinking of two numbers, they are 13 and 26.

A linear equatiοn is one that has the form y = mx+b in algebra. B is the slοpe, and m is the y-intercept. It's usual to refer tο the previous clause as a "linear equation with twο variables" because y and x are variables. The twο-variable linear equations knοwn as bivariate linear equations.

There are several instances οf linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred tο as being linear when an equation has the fοrm y = mx+b, where m stands for the slοpe and b for the y-intercept. When an equatiοn has the formula y = mx+b, with m denοting the slope and b the y-intercept, it is referred tο as being linear.

x be the first number and y be the secοnd number:

x = 2y

x + y = 39

Plug x = 2y in the other equation:

2y + y = 39

3y = 39

y = 13

x = 26

If The Grant is thinking of two numbers, they are 13 and 26. He claims that the total of the two numbers is 39 and that one of the numbers is double the other.

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Answer:

There is no value of x that makes the equation be true since an absolute value can never be negative.

No solution

Step-by-step explanation:

The first order derivative of the given function is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

The given function is [tex]f(x)=\sqrt{x+\sqrt{x+\sqrt{x} } }[/tex].

The derivative using the chain and power rules is

f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex]

Therefore, the first order derivative is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].

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The true statement is (d) The area of triangle XYZ is equal to the area of triangle X'Y′Z

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

Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y'Z'.

The rotation is a rigid transformation

This means that it does not change the side length and angles of a shape when applies

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

The image and the preiamage have the same area

Hence, the true statement is (d)

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Complete question

Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y′Z'.

y. z. y. x. x.

Which statement is true?

The sum of the angle measures of triangle XYZ is 90° less than the sum of the angle measures of triangle X'Y′Z'.

The angle measures of triangle XYZ are less than the corresponding angle measures of triangle X'Y′Z'.

Triangle XYZ is not congruent to triangle X'Y′Z'.

The area of triangle XYZ is equal to the area of triangle X'Y′Z

The others operate in a similar manner. The following must be done, however, in order to determine the probability of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:  1 - P(kit-kat)

You only need to multiply the quantity of the selected candy by the total number of candies if you choose to put each piece of candy back after choosing it.

In this case, the desired confectionery is P(snickers). 12 in number.

In total, the bag contains 20 sweets.

P(snickers) = 12/20 = 3/5

The others function in the same way. The following must be done, however, in order to determine the likelihood of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:

1 - P(kit-kat)

The complete question is:

Suppose a bag of candy contains 12 Snickers, 5 Kit-Kats, and 3 Three Musketeers. Find each probability if you choose one piece of candy at random.

a) P(Snickers) b) P(Kit-Kat) c)P(Three Musketeers) d) P(not Kit-Kat)

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Answer:

0.209.

Step-by-step explanation:

The probability that someone files their taxes on time is 1 - 0.351 = 0.649.

To find the probability that 6 out of 10 people file their taxes on time, we can use the binomial distribution. The binomial formula for the probability of k success in n trials is given by:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

Where (n choose k) is the number of combinations of n items taken k at a time, and p is the probability of success in a single trial.

So, for the problem at hand:

P(6) = (10 choose 6) * 0.649^6 * (1 - 0.649)^(10 - 6) = 0.209

Therefore, the probability that 6 out of 10 people file their taxes on time is approximately 0.209.

The value of x is 5, while the value of y is 24

In order to get the value of x we would first have to find the value of y

The sum of angles on a straight line = 180

hence we would have:

5y + 2y + 12 = 180

7y = 180 - 12

7y = 168

y = 24 degrees

The angle that is made at R is 90 degrees

we would have

2y + 12 + 5x = 90

y = 24

2 * 24 + 12 + 5x = 90

60 + 5x = 90

5x = 90 - 60

5x = 30

x = 30 / 6

x = 5

Hence the value of x is 5

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Answer:if their corresponding sides are proportional.

Step-by-step explanation:

The required measure of angle p in triangle DBC is given as ∠p = 59.14°.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,

Consider triangle ABD

Apply the Pythagorean theorem to determine the measure of DB,
DB² = AD² + AB²
DB² = 6² + 5²
DB² = 61
DB = 7.81

Now,
Apply the trig ratio in triangle DCB,
cosp = 4/7.81
p = 59.14°

Thus, the required measure of angle p in triangle DBC is given as ∠p = 59.14°.

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