A playground is in the shape of a square with each side equal to 109 yards. It has skating rinks in the shape of the quadrants of a circle at each corner. If the area of the remaining field is 9055, find the radius of each skating rink. Also, find the cost of cementing the skating rinks at $2.50 per square yards. Use

Answer:

(1/2)x+3/2

or

0.5x+1.5

Step-by-step explanation:

Hopefully you mean to have that dot between f and g closed because if it open it means something totally different.

So closed dot means multiplication

Open dot means you are composing a function with another one

So here you are just doing (x+3)  *  (1/2)

Just use distributive property   (1/2)x+(1/2)(3)

(1/2)x +3/2

or

0.5x+1.5

Answer: 30

Step-by-step explanation: Start off by multiplying the two numbers.

3 x 10 = 30.

30 is a common multiple. Find any multiples below 30. Let’s start off using the biggest number of the two, which is 10, to see what other numbers can be multiples. 10, 20, and 30 can be. 3 can’t be divided into 10 or 20, so your least common multiple is 30.

Answer:

The sequences are arithmetic

1).-8.6, -5.0, -1.4, 2.2, 5.8

2).  5, 1, -3, -7, -11

3). -3, 3, 9, 15, 21

Step-by-step explanation:

If a sequence is a an AP then there is a common difference d.

1) Check sequence 1

-8.6, -5.0, -1.4, 2.2, 5.8

-5.0 - - 8.6 = 3.6

-1.4 - -5.4 = 3.6  It is an AP

2) Check sequence 2

2, -2.2,2.42, -2.662, 2.9282

-2.2 - 2 = -4.2

-2.662 - 2.42 = -5.082 Not AP

Similarly AP sequences are

5, 1, -3, -7, -11

-3, 3, 9, 15, 21

The sequence that are arithmetic are as follows:

5, 1, -3, -7, -11.

-3, 3, 9, 15, 21

-8.6, - 5.0, -1.4, 2.2, 5.8

Arithmetic sequence is a list of numbers with a definite pattern. Therefore, let's find the sequence with a definite pattern.

5, 1, -3, -7, -11.

This is a sequence as it as a definite pattern. The value are reduced by 4. Therefore, the common difference is 4.

-3, 3, 9, 15, 21

This is a sequence because it has a common difference of 6.

-8.6, - 5.0, -1.4, 2.2, 5.8

This is a sequence because it has a common difference of 3.6.

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Answer:

9

Step-by-step explanation:

Whatever you do to the denominator, you've got to do to the numerator, and vice versa. So for 8 to become 24, you multiply by 3. do that to the numerator 3 as well. 3 × 3 is 9.

For the sake of showing work I will replace the empty space with an x like so...

[tex]\frac{3}{8} =\frac{x}{24}[/tex]

To find out what x is you must cross multiply (aka butterfly)

***Image of this step is attached below

3*24 = 8*x

72 = 8x

Next divide 8 to both sides to finish isolating x. Since 8 is being multiplied by x, division (the opposite of multiplication) will cancel 8 out (in this case it will make 8 one) from the right side and bring it over to the left side.

72 ÷ 8 = 8x ÷ 8

9 = 1x

9 = x

To make these fractions equivalent the empty spot must be 9

[tex]\frac{3}{8} = \frac{9}{24}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

(x,y)  (2,-1)

Step-by-step explanation:

Answer:

the first one is 2 the second one is 3

Step-by-step explanation:

The percent of the cash discount being offered is 5%.

The terms 5/10 EOM mean that the customer is eligible for a cash discount of 5% if the invoice is paid within 10 days from the end of the month. In this case, the invoice date is August 1st, so the end of the month is August 31st. To calculate the number of days allowed for the cash discount, we subtract 10 days from August 31st, which gives us August 21st. Therefore, the cash discount is valid until August 21st and the percent of the cash discount being offered is 5%.

x+19= 26

x+19-19= 26-19

x= 7

Check answer by using substitution method

x+19= 26

7+19= 26

26= 26

Answer is x= 7 (D.)

To find the solution we need to solve for x

We need to get x alone to solve for x.

To remove any number, always do the opposite operation

Opposite of +19 is -19

To remove +19 , subtract 19 from both sides

x+19=26

x+19 -19 =26-19 =7

x=7

So the value of x=7

The solution to this equation Option D.  x=7

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

An equation is a mathematical statement that two things are equal. It consists of two expressions, one on each side of an 'equals' sign. For example x=y is an equation where two expressions x and y are equal. Whereas f(x)=x is a function with variable x and hence f(x)=x is not an equation.

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Answer:

tan(90 - A) = 1/tan(A) ⇒ last answer

Step-by-step explanation:

* Lets revise some important information for the right triangle

- In any right triangle

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

∵ The sum of the interior angles of any triangle is 180°

∵ m∠B = 90°

∴ m∠A + m∠C = 180° - 90° = 90°

- If the measure of angle A is x°

∴ The measure of angle C = 90° - x°

- tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB  ⇒(1)

- tan(C) = opposite/adjacent

∵ The opposite to ∠C is AB

∵ The adjacent to ∠C is BC

∴ tan(C) = AB/BC ⇒  (2)

- From (1) and (2)

∴ tan(A) = 1/tan(C)

∵ m∠A = A , m∠C = (90 - A)

∴ tan(A) = 1/tan(90 - A)

OR

∴ tan(90 - A) = 1/tan(A)

Answer:

LAST OPTION.

Step-by-step explanation:

Remember that:

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

[tex]\frac{cos(x)}{sin(x)}=cot(x)=\frac{1}{tan(x)}[/tex]

[tex]sin(x\±y) = sin(x)cos(y)\±cos(x)sin(y)\\\\cos(x\±y) =cos(x)cos(y)\± sin(x)sin (y) [/tex]

[tex]sin(90\°)=1\\cos(90\°)=0[/tex]

Then, you need to rewrite [tex]tan(90-A)[/tex]:

[tex]tan(90-A)=\frac{sin(90-A)}{cos(90-A)}[/tex]

Applying the identities, you get:

[tex]tan(90\°-A)=\frac{sin(90\°)cos(A)-cos(90\°)sin(A)}{cos(90\°)cos(A)-sin(90\°)sin(A))}[/tex]

Finally, you must simplify. Then:

[tex]tan(90\°-A)=\frac{(1)cos(A)-(0)sin(A)}{(0)cos(A)-(1)sin(A))}\\\\tan(90\°-A)=\frac{cos(A)}{sin(A)}\\\\tan(90\°-A)=\frac{1}{tan(A)}[/tex]

The correct answer is 1980 or A:)

Answer:

D

Step-by-step explanation:

To evaluate f(5) substitute x = 5 into f(x)

f(5) = (3 × 5) + 2 = 15 + 2 = 17 → D

[tex]f(5)=3\cdot5+2=17\Rightarrow\text{D}[/tex]

The equation of f(x) is  B. F(x) = -√x. Therefore , B. F(x) = -√x is correct.

Here's why:

The parent function of the graph is the square root function, which means the original equation is f(x) = √x.

The graph is reflected across the x-axis.

This means that the y-values are multiplied by -1. In other words, if the original point was (x, √x), the reflected point would be (x, -√x).

Therefore, the equation of the reflected function is f(x) = -√x.

The other options are incorrect because:

A. F(x) = √x is the original equation, not the reflected equation.

C. F(x) = √x - 1 shifts the graph down one unit, but it does not reflect it across the x-axis.

D. F(x) = √x + 1 shifts the graph up one unit, but it does not reflect it across the x-axis.

A fifth-degree polynomial has three real roots and two imaginary roots.

The given polynomial function f(x) is a fifth-degree polynomial, meaning it has five roots. We are given three of the roots: -2, 2, and 4 + i. Since the coefficients of a polynomial with real coefficients are either real or come in conjugate pairs for complex roots, the remaining two roots must be the complex conjugates of 4 + i, which are 4 - i. Therefore, f(x) has three real roots -2, 2, and 4, and two complex roots 4 + i and 4 - i.

Answer: D. f(x) has three real roots and two imaginary roots.

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The function f(x), a fifth degree polynomial, has three real roots and two complex (imaginary) roots due to the Conjugate Root Theorem. The roots are –2, 2, 4, 4 + i and 4 - i. Therefore, option D is correct.

The function f(x) is a fifth degree polynomial. Given the roots available, –2, 2, and 4 + i, we already have three roots, two real and one complex (or imaginary). From the Conjugate Root Theorem, which states that if a polynomial has real coefficients, then any imaginary root must have its conjugate as a root. Thus, the conjugate of 4 + i, which is 4 - i, is also a root of this function. Therefore, the fifth degree polynomial has three real roots –2, 2, and 4, and two imaginary roots 4 + i and 4 - i, indicating that option D: 'f(x) has three real roots and two imaginary roots' is correct.

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Answer:

1155

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

:))

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+(y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) = (- 4,2)\\(x_ {2}, y_ {2}) = (1, -3)[/tex]

Substituting we have:

[tex]d = \sqrt {(1 - (- 4)) ^ 2+(-3-2) ^ 2}\\d = \sqrt {(1 + 4) ^ 2+(-5) ^ 2}\\d = \sqrt {(5) ^ 2+(-5) ^ 2}\\d = \sqrt {25 + 25}\\d = \sqrt {50}\\d = 7.07units[/tex]

Answer:

Option B

Answer: Option B

[tex]d=7.07[/tex]

Step-by-step explanation:

The distance between two points is calculated using the following formula

[tex]d=\sqrt{(x_1-x_0)^2+(y_1-y_0)^2}[/tex]

In this problem we have the following points

(-4,2) and (1,-3)

Therefore

[tex]x_0=-4\\y_0 = 2\\x_1=1\\y_1=-3[/tex]

Then the distance d is:

[tex]d=\sqrt{(1-(-4))^2+((-3)-2)^2}[/tex]

[tex]d=\sqrt{(1+4)^2+(-3-2)^2}[/tex]

[tex]d=\sqrt{(5)^2+(-5)^2}[/tex]

[tex]d=\sqrt{50}[/tex]

[tex]d=5\sqrt{2}[/tex]

[tex]d=7.07[/tex]

Answer:

82 notes

Step-by-step explanation:

3×8=24

16×3=48

4×3=12

24+48+12=84

Final answer:

To find the total number of notes played throughout the song, add the notes from each measure (8 + 16 + 4 = 28) and multiply by the times they are played (28 x 3), resulting in 84 notes played in total.

Explanation:

The question pertains to calculating the total number of notes played in a song where specific measures of music are repeated a certain number of times. First, we need to calculate the number of notes in a single iteration of the three measures:

Measure 1: 8 notes

Measure 2: 16 notes

Measure 3: 4 notes

Adding these together, we get a total of 28 notes for one iteration of the 3 measures. Since these measures are played 3 times throughout the song, we multiply 28 by 3, which equals 84 notes. Therefore, 84 notes are played throughout the song.

Answer:

6 more than 5 times the measure of mn is (5mn + 6)

Step-by-step explanation:

Answer:

parallel

Step-by-step explanation:

we have

2x=-3-y

isolate the variable y

y=-2x-3 ----> equation A

4+y=-2x-2

isolate the variable y

y=-2x-2-4

y=-2x-6 -----> equation B

Remember that

If two lines are parallel, then their slopes are the same

Line A and Line B have the same slope m=-2 and different y-intercept

therefore

The lines are parallel

Answer:

Second option: Parallel.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" in each equation:

Equation 1

[tex]2x=-3-y \\\\2x+y=-3\\\\y=-2x-3[/tex]

Equation 2

[tex]4+y=-2x-2\\\\y=-2x-2-4\\\\y=-2x-6[/tex]

You can notice that the slope of the Equation 1 is:

[tex]m_1=-2[/tex]

And the slope of the Equation 2 is:

[tex]m_2=-2[/tex]

Observe that [tex]m_1=m_2[/tex], then you can conclude that the lines are: Parallel.

Answer:

Step-by-step explanation:

[tex]\text{We have:}\\\\A_{PQRS}=45\ cm^2\\\\A_{PQRS}=a(7+b)\\\\A_{PXYS}=10\ cm^2\\\\A_{PXYS}=ab\\\\\text{Therefore we have the system of equations:}\\\\\left\{\begin{array}{ccc}a(7+b)=45&\text{use the distributive property}\\ab=10\end{array}\right\\\left\{\begin{array}{ccc}7a+ab=45&(1)\\ab=10&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\7a+10=45\qquad\text{subtract 10 from both sides}\\7a=35\qquad\text{divide both sides by 7}\\a=5\\\text{Put it to (2):}\\5b=10\qquad\text{divide both sides by 5}\\b=2[/tex]

Answer:

∠C = 143°

Step-by-step explanation:

For the quadrilateral to be a parallelogram

Then ∠C = ∠A

Given ∠B = ∠D then consecutive angles are supplementary, that is

∠C + ∠D = 180

∠C + 37 = 180 ( subtract 37 from both sides )

∠C = 143°

Answer:

(x - 15)(x + 3)

Step-by-step explanation:

Consider the factors of the constant term (- 45) which sum to give the coefficient of the x- term (- 12)

The factors are - 15 and + 3, since

- 15 × 3 = - 45 and - 15 + 3 = - 12, hence

x² - 12x - 45 = (x - 15)(x + 3)

[tex]\bf \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\\\ \textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 3^{x+1}=15\implies \log_{10}(3^{x+1})=\log_{10}(15)\implies (x+1)\log_{10}(3)=\log_{10}(15) \\\\\\ x+1=\cfrac{\log_{10}(15)}{\log_{10}(3)}\implies \stackrel{\textit{change of base rule}}{x=\cfrac{\log_{e}(15)}{\log_{e}(3)}-1}\implies x\approx 1.47[/tex]

Answer:

[tex]x=\frac{log(15)}{log(3)}-1[/tex]

Step-by-step explanation:

[tex]3^{x+1} = 15[/tex]

LEts convert exponential form to log form

[tex]b^x=a[/tex] can be written as [tex]log_b(a)=x[/tex]

WE apply the same rule to convert the given exponential form to log form

[tex]3^{x+1} = 15[/tex]

[tex]log_3{15} = x+1[/tex]

HEre the base of log is 3. Lets apply change of base formula

[tex]log_b(a)=\frac{log(a)}{log(b)}[/tex]

[tex]log_3{15} = x+1[/tex]

[tex]\frac{log(15)}{log(3)} = x+1[/tex]

Now subtract 1 from both sides

[tex]x=\frac{log(15)}{log(3)}-1[/tex]

Answer:

C) a= -1, b=5, c= -7

Step-by-step explanation:

To get the values of a, b and c we must first write the equation in the form

ax²+bx+c=0 where a b and c are the coefficients.

Therefore, -x² +5x=7 can also be written as:

-x²+5x-7=0

a= -1 ( coefficient of x²)

b=5 (coefficient of x)

c= -7 ( the constant in the equation)

Answer:

a=-1, b=5 and c=-7

Step-by-step explanation:

We have the following equation:

[tex]-x^{2} + 5x = 7[/tex] → [tex]-x^{2} + 5x - 7 = 0[/tex]

Given the equation of a parabola: [tex]ax^{2} +bx + c = 0[/tex]. By comparison, we know that:

a=-1, b=5 and c=-7

So the correct option is Option C.

Answer:

True.

Step-by-step explanation:

It's true.

The sin of 30 in degrees equals 1/2 and the cos of 30 degrees equals sqrt(3)/2.

I am attaching a table that can be useful for remembering the values of the cosine and sine of some angles.

Answer:

True

Step-by-step explanation:

Answer:

Distribute the -9 into the values in the parentheses.

STEP BY STEP

-9(-2x-3)

-9*-2x=18x

-9*-3=27

Therefore, the equation then becomes: 18x+27.

The answer is the first choice, or A.

Answer:

Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction

Step-by-step explanation:

Samantha will be offered the choice of using the coupon or the sale discount. If she chooses tht 50% coupon, her savings will be $30. If she chooses the marked sale discount, her savings will be $15.  

The scenario above assumes she gets 50% off the sale price of $45, so saves $15+22.50 = $37.50 off the original price.

Answer: Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction so the answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

-5 -3 ×2 /8

-11/8

Hence the answer is,

-11/8

Answer:

A

Step-by-step explanation:

Just try to label the data in a table for every choice. It is clearly A. If you tried to solve it you will find that =

(-2)² = 4

(-1)² = 1

1² = 1

2² = 4

Answer:

sin(B)=cos(90°-B)

Step-by-step explanation:

we know that

In the right triangle of the figure

sin(B)=b/c -----> The sine of angle B is equal to divide the opposite side to angle B by the hypotenuse

cos(A)=b/c -----> The cosine of angle A is equal to divide the adjacent side to angle A by the hypotenuse

we have that

sin(B)=cos(A)

Remember that

A+B=90° -----> by complementary angles

so

A=90°-B

therefore

sin(B)=cos(A)

sin(B)=cos(90°-B)

Answer:

sin(B) = cos(90 -B)

Step-by-step explanation:

In triangle ABC by using angle sum property, ∠A + ∠B + ∠C= 180°

∠A + ∠B + 90°= 180°

∠A + ∠B= 180°-90°

∠A + ∠B = 90°

∠A = 90°- ∠B

sin B = b/a.

cos A = b/a.

Hence, sin B = cos A

put the value of ∠A = 90°- ∠B in cos A

sin (B) = cos (90°-B)

Thus, the correct answer is option (2).

Answer:

$[tex]1g[/tex]

Explanation:

If the number of granola bars is represented by the variable [tex]g[/tex], and each granola bar costs $1, then we need to multiply the amount per granola bar by the number of granola bars.

This is $[tex]1 * g[/tex], or $[tex]1g[/tex].

In this scenario, the total cost of the granola bars can be represented by the mathematical expression 'g', as each granola bar costs $1.

If each granola bar costs $1 and 'g' is representing the number of granola bars, then the total cost of the granola bars can be represented by the expression 1 * g or simply g. This is because for every granola bar you buy, you are adding $1 to your total. So if you bought 'g' granola bars, your total cost would be $1 times the number of granola bars 'g'. This is an example of direct proportionality, where the total cost increases with the increase in number of granola bars.

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Answer:

C. AB/XY = AC/XZ

Step-by-step explanation:

Dilation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The original figure either stretches or shrinks by a certain factor.

In the problem, the dilation is by a factor of 5 and we can see that ABC shrinks to form XYZ.

So, ABC and XYZ are similar triangles which means that the ratio of their corresponding sides will be equal:

AB/XY = AC/XZ = BC/YZ = 5

Answer with explanation:

When ΔABC is dilated by a Scale factor of 5 we will get ΔX Y Z.

Pre-Image = ΔABC

Image = ΔX Y Z

When a triangle is dilated , then the two Triangles that is Original ΔABC and Triangle after dilation ΔX Y Z will be Similar.

⇒Similar triangles has Corresponding sides proportional as well as Corresponding  Angles are congruent.

≡Corresponding congruent Angles are

→∠A=∠X

→∠B=∠Y

→∠C=∠Z

≡Corresponding congruent Sides are

     [tex]\frac{AB}{XY}=\frac{AC}{XZ}=\frac{BC}{YZ}[/tex]

The Proportionality statement which proves two triangles are Similar

Option B

 [tex]\frac{AB}{XY}=\frac{AC}{XZ}[/tex]