Evaluate.

(a - 2b)^2 when a = -4 and b = -1/2


25



9



-9



-25

Answer:

a ≈ 3.009075116

Step-by-step explanation:

cos(α) = adj/hyp

cos(53°) = a/5

a = 5 * cos(53°)

a ≈ 3.009075116

The polynomial p(x) must have at least two zeros, since it has three relative extrema.

What is polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x²- 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Here i would think that since there are only 3 critical points given and no other information other than that those are the only critical points that p(x) would not have any real zeros.

At each of the relative extrema, the value of the function changes from increasing to decreasing or vice versa, meaning that the function crosses the x-axis at that point, which is a zero. Therefore, p(x) must have at least two zeros.

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Answer:

  D.  66 cm

Step-by-step explanation:

You have parallelogram MNPR with diagonals that cross at E, and ME = 7x-30, and PE = 5x-12. You want to know the length of MP.

The diagonals of a parallelogram bisect each other this means point E is the midpoint of diagonal MP, and ...

  ME = PE

  7x -30 = 5x -12

  2x = 18 . . . . . . . . . add 30-5x

  x = 9

Then the length of the half-diagonal is ...

  ME = 7x -30 = 7(9) -30 = 33

So, the full diagonal is ...

  MP = 2·33 = 66 . . . . . cm

Answer:

Its been a minute since I've done this math

Step-by-step explanation:

This statement demonstrates the substitution property.

The substitution property states that if two expressions are equal, then we can substitute one expression for the other in any equation or inequality. In this case, "A" is an acute angle, and "m2A" is the measure of twice that angle. The statement says that if we double the measure of an acute angle, the result will be 30 degrees. Therefore, we can substitute "m2A" for 30 degrees in any equation or inequality.

The reflexive property states that any number or object is equal to itself. The symmetric property states that if a = b, then b = a. The transitive property states that if a = b and b = c, then a = c. None of these properties are demonstrated in the given statement.

Answer:$22.50 regular price

Step-by-step explanation: RP=Regular Price

RP-20%of RP=18

RP-0.20RP=18........RP =1RP

1RP-0.20RP=18

0.80RP=18

RP=18/0.80

RP=$22.50

Answer:

22.50

Step-by-step explanation:

other answer is cryptic so here is a full explaination

To find the regular price of the hat, we need to determine the amount of the discount and then add that amount to the discount price.

The discount on the hat is 20% of the regular price, or 20/100 * regular price. The discount price is $18, so we can set up the equation:

discount price = regular price - (20/100 * regular price)

Substituting the known values into the equation, we get:

$18 = regular price - (20/100 * regular price)

Solving for the regular price, we find that the regular price is $22.50. This is the price of the hat before the discount.

confidence level to be about 1.5%. Then the survey would you recommend is 1537

The first thing is to apply the corresponding formula of this case, it is the calculation of a sample size without knowing the population. The equation is as follows, let n be the sample size:

n = (z * s / E) ^ 2

We know that z the corresponding z score of 95% of the confidence level, that this case is 1.96.

s, is the standard deviation and has a heat of 10.

Finally E, would be the error that is 0.5.

Now it's just replace in the formula:

n = (1.96 * 10 / 0.5) ^ 2 = 1536.64, that is approximately the sample must be 1537.

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Answer:

The interest earned is $10.00

Step-by-step explanation:

Interest = principal x rate x time

I= 100(.01)(10)

I = 10

Answer:

Step-by-step explanation:

a because if you divide  everything under the fraction number you get answer a

The solution for the given expression is x = 4³/₅. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is x - 17⁴/₅ = -13¹/₅. The given expression will be solved as,

x - 17⁴/₅ = -13¹/₅

x = 17⁴/₅ -13¹/₅

x = 89 / 5 - 66 / 5

x = 23 / 5

x = 4³/₅

The expression will be equivalent to x = 4³/₅.

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Answer: first choice!

sin2Theta= -4rt21/25

cos2Theta = 17/25

Step-by-step explanation:

Use Double Angle Formulas.

You can find cos2Theta immediately because one of the formulas needs only sin(theta) and that was given.

Cos2Theta =

1 - 2(sinTheta)^2

= 1 - 2(-2/5)^2

= 1 - 2(4/25)

= 1 - 8/25

= 25/25 - 8/25

= 17/25

The only answer with cos2theta=17/25 is the first choice.

Use a simple graph and Pythagorean Theorem to find cos(theta). Then you can use the Double Angle Formula for sin2theta. This would kinda be a double check if you have time. Since the first part of the solution eliminated all choices except the first choice, if you're pressed for time just do cos2theta calculation and pick the first choice.

See image for sin2theta calculation.

a) The category that shows a decrease in the average monthly expenditure between 2010 and 2020 is Leisure.

b) The average monthly expenditure on food was 175 euros more in 2020 than in 2010.

c) The total expenditure in 2020 is of: 1,625 euros.

The bar chart shows the average monthly expenditure in five categories, considering that:

Then a decrease happens for the category which the blue bar is greater than the gray bar, which is Leisure.

The averages on Food are given as follows:

Hence the difference is of:

325 - 150 = 175 euros.

From the gray bars, the 2020 total is given as follows:

250 + 425 + 325 + 550 + 75 = 1,625 euros.

The bar graph is given by the image shown at the end of the answer.

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The height increases by 0.48  meters each year.

The available regression equation is: Predict height= 0.29 + 0.48 (age).

Here, the predict height is dependent variable and the  age is in-dependent variable.

Intercept = 0.29

Slope      = 0.48

The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.

The height increases, an average, by 0.48 m per year.

Because co-efficient of slope variable indicate the positive sign and we increase 1 year in age then automatically height increased is 0.48 m.

The height increases, on average, by 0.48 meter each year.

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The available regression equation is: Predict height= 0.29 + 0.48 (age).

Here, the predict height is dependent variable and the  age is in-dependent variable.

Intercept = 0.29

Slope      = 0.48

The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.

The evaluation is 10.67 of given geometric progression.

A geometric progression is a set of elements where each succeeding element is created by multiplying the one before it by a number called the common ratio. The standard representation for a geometric progression series is a, ar, ar²,..., where an is the first term and r is the common ratio of the sequence.

The ratio between two consecutive numbers, or a number divided by the number before it in the sequence, is known as the common ratio since it is the same for all numbers or common.

The sum of a finite geometric series can be found using the formula:

[tex]a (1-r^{n}) / (1-r)}[/tex].

Where a is the first term and r is the common ratio between successive terms.

To find the ratio of successive terms by plugging into the formula

r = aₙ +1 / (aₙ)

Simplifying,

r =1/4

And the first term is;

when n=1, a = 8

Substituting all the values to the formula,

The summation of GP

= 8 x { 1 - (1/4)¹⁰ } / {1- (1/4)}

= 8 { 1 - (1/1048576) / (3/4)

= 8 x {(1048576 - 1) / 1048576} x (4/3)

= 8 x (1048575 / 1048576) x (4/3)

= 8 x 349525 / 262144

= 2796200 / 262144

= 10.6666

The decimal form is 10.67.

Therefore, the evaluation is 10.67.

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If Sue's home is the origin and the positive direction is assumed to the right, then her position is 2 mi.

Therefore, the answer is 2mi.

Origin depends on the frame of reference, it depends on from where the observer is viewing.

From the figure, distance between home and Sue = 2 - 0 = 2mi

and the distance between Cinema and Sue = 5 - 2 = 3mi

Sue's position is 2mi right to her home and 3mi left to the Cinema. So if her home is the origin and positive direction is to the right x is +2 mi.

--The question is incomplete without the figure, answering to the figure attached--

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Answer:

1. B

2. A

3. B

4. D

5. C

If the function f(x) = |x-5| + 2, then the value of f(3) is 4

The function

f(x) = |x-5| + 2

The function is defined as the mathematical statement that shows the relationship between the independent variable and the dependent variable. The function consist of different variables, numbers and mathematical operators

Here the function consist of the absolute value symbol.

|-a| = a

The absolute value of the positive and the negative number will be always positive.

The function is f(x) = |x-5| + 2

Then,

f(3) = |3-5| + 2

= |-2| + 2

= 2 + 2

= 4

Therefore, the value of f(3) is 4

I have answered the question in general, as the given question is incomplete

The complete question is:

If f(x)=|x−5| + 2, find the value of f(3).

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Answer:

Step-by-step explanation:

To find the slope of a line that passes through two points, we can use the slope formula, which is written as follows:

slope = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of the two points.

Given the points (-7, -2) and (-15, -14), we can substitute their coordinates into the slope formula to find the slope of the line:

slope = (-14 - (-2)) / (-15 - (-7))

= -12 / -8

= 3/2

Therefore, the slope of the line that passes through the points (-7, -2) and (-15, -14) is 3/2. In simplest form, this is equal to 1.5.

We can see two transformations.

1) ΔABC  → ΔA'B'C', it is a translation 10 units left and 2 units up.

2)  ΔA'B'C'  → ΔA''B''C'', it is a reflection across the x-axis.

Answer:

the HL Postulate

Step-by-step explanation:

The diagram gives us the information that 2 sides and 1 angle are congruent. Since the sides we know are a leg and the hypotenuse, and it is a right angle- we know to use the HL (Hypotenuse-Leg) Postulate.

If the angle given was the angle between the hypotenuse and the leg, we could use the SAS (Side-Angle-Side) Postulate. But, since it is the right angle instead- we know to use the HL Postulate!

Answer: no solution

Step-by-step explanation:

1. distribute through both sides to get 3x-6+1 ≥ x+2x+4

2. then combine like terms to get 3x-5 ≥ 3x+4

3. then make sure like terms are together on either side -> 3x -3x ≥ 4+5 ->

4. since the 3x-3x = 0, there are no solutions

The equivalent expressions of 9/7x-3/4 are 9/7x+(-3/4) and -3/4+9/7x.

An expression is combination of variables, numbers and operators.

The given expression is 9/7x-3/4.

Nine by seven times of x minus three by four.

x is the variable of expression.

The equivalent expression is an expression whose value is same but looks different.

9/7x-3/4.

By commutative property

-3/4+9/7x is an equivalent expression of 9/7x-3/4.

9/7x+(-3/4).

When we simplify we get 9/7x-3/4.

-9/7x+3/4 is also a equivalent expression we get it by multiplying with negative.

Hence, 9/7x+(-3/4) and -3/4+9/7x are equivalent expressions of 9/7x-3/4.

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To determine the input number, we can use the following steps:

Calculate the change in the input number as a percentage of the input number. In this case, the input number decreased by 15%, so the change is -0.15 * input number.

Add the change to the output number to find the input number. In this case, the output number is 50, so the input number is 50 + (-0.15 * input number).

Solve for the input number. In this case, we can solve for the input number by rearranging the equation and solving for x:

input number = 50 / (1 - 0.15)

input number = 50 / 0.85

input number = 58.82

Therefore, the input number is 58.82.

Note that this process can also be used to determine the output number given the input number and the percentage change. For example, if the input number is 100 and it increases by 85%, the output number would be:

output number = 100 * (1 + 0.85)

output number = 100 * 1.85

output number = 185

Answer:

[tex]x \times \frac{85}{100} \times \frac{185}{100} = 50[/tex]

[tex]x = 50 \times \frac{ {100}^{2} }{85 \times 185} [/tex]

[tex]31.8[/tex]

it seems to be a long number so I rounded

There might be a mistake because I wasn't able to check.

Using a ruler and compass, draw a line through point A parallel to line PQ by first drawing a line segment from A to any point on PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. Finally, use the ruler to draw a line through the arc, parallel to PQ.

Drawing a line parallel to an existing line can be done using a ruler and compass. First, draw a line segment from point A to any point on line PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. This arc should intersect with the first line segment. Finally, use the ruler to draw a line through the arc, parallel to PQ. This line will be parallel to PQ since it is the same distance from each point on the original line. The use of the compass ensures that the resulting line is the same distance away from the original line throughout, thus resulting in a line parallel to PQ.

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Given all angle information, the assumption that sides [tex]\overline {BC}[/tex] must not be congruent to [tex]\overline{DA}[/tex] to give an appropriate answer. (Right choice: None)

Any quadrilateral can be divided into two triangles by adding a diagonal. By Euclidean geometry, the sum of the measures of internal angles equals 180°. Likewise, we can determine how short or long a side is in terms of side BD by law of sine:

AD / sin 60° = AB / sin 63° = BD / sin 57°

1.155 · AD = 1.122 · AB = 1.192 · BD

AD = 0.971 · AB = 1.032 · BD

BC / sin 57° = CD / sin 55° = BD / sin 68°

1.192 · BC = 1.221 · CD = 1.079 · BD

BC = 1.024 · CD = 0.905 · BD

By direct inspection and use of equality properties, we find the existence of an absurdity, because 1.032 · BD = 0.905 · BD, then [tex]\overline {BC}[/tex] must not be congruent to [tex]\overline{DA}[/tex] to satisfy all angle conditions.

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We determined the conditional probability of drug assigned people who survived at least 5 years = 101/344

The possibility of occurring an event connected to the previous other event. That means occurring of two events is related to each other.

We determine the probability by the following way.

At first, we will make a chart with the given data.

                        survived 5yrs        get other result      total

Drug assign         101                         243                      344

placebo               299                        179                       478

total                     400                       422                       822

 We need to determine the probability of 5 years survived persons from drug assigned

Let, it is denoted by P(Sr/Dr)

As per conditional probability P(Sr/Dr) = P(Sr and Dr)/P(Dr)

                                                               = 101/344

As from the above chart, we find P (Sr and Dr) =101 and

P(Dr) = total drug assigned = 344

hence, P(Sr/Dr) = 101/344

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Answer:

83% to (rare photos) becaheyhw euehem e the same time of 6year and I was in a group with my wife and a daughter and my daughter in the night and I was so happy 4and was a 4ship 4in who 5is and my daughter and my husband were so young that I was in the same 5 year olds and I was in the

Answer:

Step-by-step explanation:

She could order 7 boxes. if each box has 32 flowers, then you would multiply 6 by 32 which is 192. If you subtract 218 from 192 you get 26. meaning that if she orders 6 boxes of 32 flowers then she would only have 192 flowers and there would be 26 flowers remaining, so then it's better for her to order 7 boxes it's better to have more than what she wants instead of having less than what she wants... that way she is able to plant 218 flowers even if there are some left.

The solution to the inequality statement is x < 3/16

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

negative one eighth is less than the product of negative two thirds and a number.

Express as numbers and operators

So, we have

-1/8 < -2/3x

Divide both sides by -2/3

So, we have the following representation

1/8* 3/2 > x

Evaluate the produdts

3/16 > x

Rewrite as

x < 3/16

Hence, the solution is x < 3/16

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Answer:   The written description of x - 14 is given as the difference of variable x and integer 14 gives x -14.

Step-by-step explanation:

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

Let x be a variable,

And 14 is an integer.

By using mathematical operations,

The difference of x and 14 can be given as,

x - 14.

Answer:

[tex] \sf \: x = 25[/tex]

Step-by-step explanation:

Given equation,

→ (x - 7)2 = 36

Now the value of x will be,

→ 2(x - 7) = 36

→ (2 × x) - (2 × 7) = 36

→ 2x - 14 = 36

→ 2x = 36 + 14

→ 2x = 50

→ x = 50/2

→ [ x = 25 ]

Hence, the value of x is 25.

Answer:

x = 25

Step-by-step explanation:

(x-7)2 = 36

divide both sides by 2

x-7 = 18

add 7 to both sides

x = 25

An expression that models the series of events is 2(6,218 - 92 + 417).

The possible events are:

120 followers stop following Zuberi's blog.

The number of followers triples.

312 followers start following Zuberi's blog.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

At a certain point, she has 6,218 followers.

Events happened in order:

92 people stop following Rida's blog.

417 people start following Rida's blog.

The number of followers doubles.

An expression that models this series of events.

= 2(6,218 - 92 + 417)

The current number of followers.

= 3 (945 - 120) + 312

The possible events.

120 followers stop following Zuberi's blog.

The number of followers triples.

312 followers start following Zuberi's blog.

Thus,

An expression that models the series of events is 2(6,218 - 92 + 417).

The possible events are given above.

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