Given the functions f(x) = 4x2 − 1, g(x) = x2 − 8x + 5, and h(x) = –3x2 − 12x + 1, rank them from least to greatest based on their axis of symmetry. A) g(x), h(x), f(x)
B) f(x), h(x), g(x)
C) g(x), f(x), h(x)
D) h(x), f(x), g(x)

Answer:

  the last choice shown here: F'(0, -4), G'(-3, -1), H'(-2, 2), I'(0, -2)

Step-by-step explanation:

The translation vector tells you that the new coordinates are found by adding -4 to each of the old coordinates. When you realize that the answer choices differ in their values for H' and I', you can conclude that you only need to find one of those to determine the correct answer.

  H' = H + (-4, -4) = (2-4, 6-4) = (-2, 2) . . . corresponds to the last choice shown

_____

When you subtract 4 from each of the coordinates of the other points, you find they also match the last answer selection.

Final answer:

The translation of the figure along the vector ⟨−4,−4⟩ results in the vertices F'(0,-4), G'(-3,-1), H'(-2,2), and I'(0,-2).

Explanation:

The student is asking about a translation of a geometric figure in the coordinate plane. To translate a figure, we add the translation vector to each vertex of the figure. In this case, the translation vector is ⟨−4,−4⟩, which means we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate of each vertex of the figure.

Therefore, the translated figure will have vertices F'(0,-4), G'(-3,-1), H'(-2,2), and I'(0,-2).

Answer:

[tex]\sqrt[6]{200}[/tex]

Step-by-step explanation:

First of all, you need to know that you cannot multiply those radicals without having a common index (the little number outside the radical that sits in the curve of the radical).  One is a 3 and the other, without being stated outright, is understood to be a 2.  BUT we can make them like.  The index of a radical is the denominator of the exponential equivalent.  

[tex]\sqrt[3]{5}=5^{\frac{1}{3}}[/tex] and

[tex]\sqrt{2}=2^{\frac{1}{2}}[/tex]

See how the indexes are now the denominators of the rational exponents.  We can make them like by finding the LCM of 3 and 2...which is 6:

[tex]5^{\frac{1}{3}}=5^{\frac{2}{6}}[/tex] and

[tex]2^{\frac{1}{2}}= 2^{\frac{3}{6}}[/tex]

Now that the indexes are like, we rewrite them as radicals again:

[tex]\sqrt[6]{5^2}*\sqrt[6]{2^3}[/tex] which, simplified, is

[tex]\sqrt[6]{25}*\sqrt[6]{8}[/tex]

Now we can find the product which is

[tex]\sqrt[6]{200}[/tex]

The product of ∛5 ×√2 is approximately 2.41. The correct option is b) [tex]\sqrt[6]{200}[/tex], which matches the calculated value.

To find the product ∛5 × √2, we first take the cube root of 5 (∛5) and then multiply it by the square root of 2 (√2).

∛5 ≈ 1.71 (approximately, rounded to two decimal places)

√2 ≈ 1.41 (approximately, rounded to two decimal places)

Now, let's calculate the product:

∛5 × √2 ≈ 1.71 × 1.41 ≈ 2.41 (approximately, rounded to two decimal places)

Now, let's check the options:

a. [tex]\sqrt[6]{10}[/tex] ≈ 1.72 (approximately, rounded to two decimal places)

b. [tex]\sqrt[6]{200}[/tex] ≈ 2.41 (approximately, rounded to two decimal places) <-- Matches our calculated value.

c. [tex]\sqrt[6]{500}[/tex] ≈ 2.80 (approximately, rounded to two decimal places)

d.[tex]\sqrt[6]{100000}[/tex] ≈ 5.62 (approximately, rounded to two decimal places)

The correct answer is option b)[tex]\sqrt[6]{200}[/tex].

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Answer:

5 but its probaly not right bc im just looking for pointsStep-by-step explanation:

Answer:

parameter

Step-by-step explanation:

Answer:

1 : 1000

In the real life, it measures as:

62 mm = 62000 mm = 6.2 m

54 mm = 54000 mm = 5.4 m

It ask how large is it, I don't know if you want area or primeter, so I will give you both of them.

Area:

6.2 x 5.4 = 33.48 m^2

Primeter:

(6.2 + 5.4)2 = 23.2 m.

The z-score for a student who scored 75 on the test with an average of 80 and a standard deviation of 6 is approximately -0.833, indicating the score is 0.833 standard deviations below the mean.

To calculate the z-score for a student who scored 75 on a history test, we can use the z-score formula:

[tex]Z = \( \frac{X - \mu}{\sigma} \)[/tex]

Where:

X is the raw score (75 in this case)

[tex]\( \mu \)[/tex] is the mean score (80)

[tex]\( \sigma \)[/tex] is the standard deviation (6)

Inserting the values, we get:

[tex]Z = \( \frac{75 - 80}{6} \) = \( \frac{-5}{6} \) = -0.833\[/tex]

The z-score for a student who earned 75 on the test is approximately -0.833, rounded to the nearest thousandth. This z-score indicates that the student's score is about 0.833 standard deviations below the mean

Answer:

A glide reflection is a composition of transformations.In a glide reflection, a translation is first performed on the figure, then it is reflected over a line. Therefore, the only required information is the translation rule and a line to reflect over. ... The first one is a translation rule.

Final answer:

In a glide reflection, the translation occurs first, moving the figure along a straight line, followed by a reflection over a line parallel to the translation vector, resulting in a figure that has been moved and potentially reoriented.

Explanation:

In a glide reflection, a transformation that combines a translation with a reflection, the proper sequence is important. The translation part comes first, where the figure is slid along a straight line called the translation vector. After the figure has been moved, the second step is the reflection over a line parallel to the vector of the translation. This two-step process results in a final image that has the same size and shape as the original figure but is in a different position and may have a different orientation.

Imagine a point undergoing a glide reflection. Initially, it is translated along a vector, and then it is reflected across a line that is parallel to the direction of translation. The end result is that the point has 'glided' to a new location, as if it had slid across a mirror placed at an angle to its original path.

Answer:

B.

Step-by-step explanation:

the denominator you want is 16 so 4(4) is 16, which makes 3(4) 12 so 12/16. 7/16 is already perfect. 8(2) is 16 therefore 5(2) is 10 which makes 10/16.

Answer:

The value of slope m = -1

Step-by-step explanation:

x = -2 + 4t

and y = 1 + 4t

Solving the both equations

x +2 = 4t

=> t = (x+2)/4     eq(1)

y-1 = 4t

=> t = (y-1)/4      eq(2)

Putting eq(1) = eq(2) as left hand side of both equations are same

(x+2)/4 = (y-1)/4

Cross multiplying

4(x+2) = 4(y-1)

4x + 8 = 4y -4

4x +4y = -4 -8

4x + 4y = -12

4(x+y) = -12

x+y = -12/4

x+y = -3

y = -x -3

The slope intercept form of line is:

y = mx + b

where m is the slope. Comparing with y = -x-3

The value of slope m = -1

The slope of the line defined by the parametric equations x=-2+4t and y=1+4t is mathematically given as

m = -1

Question Parameter(s):

the parametric equations x=-2+4t and y=1+4t

Generally, the equation for the Equations   is mathematically given as

x=-2+4t

y=1+4t

Therefore

t = (x+2)/4..1

t = (y-1)/4 ...2

 Hence

(x+2)/4 = (y-1)/4

4(x+2) = 4(y-1)

y = -x -3

In conclusion, slope intercept

y = mx + b

Hence

y = -x-3

The slope is m = -1

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For this case we must indicate the graph corresponding to the following equation:

[tex]y = 2e ^ x[/tex]

Then, we evaluate the equation for[tex] x = 0[/tex]

[tex]y = 2e ^ 0[/tex]

We have by definition, any number raised to zero results in 1.

So:

[tex]y = 2[/tex]

Now we evaluate the equation for x = -1

[tex]y = 2e ^ {-1}\\y = \frac {2} {e}\\y = 0.736[/tex]

We already have two points to graph:

[tex](0,2)\\(-1,0.736)[/tex]

Observing the options, we realize that the correct option is option C.

It should be noted that graphs A and D, by definition, do not correspond to the exponential function.

Answer:

Option C

Answer: Option C

Step-by-step explanation:

By definition, a relation is considered a function if and only if for each input value x there is only one associated output y value.

To verify if the graph of a relation is a function, trace on the graph vertical lines parallel to the y axis. If one of these vertical lines cuts the graph in 2 or more points, then the relationship is not a function

By definition, a function is considered a one-to-one function if and only if there is no equal output value and, for two different input values.

For example, the following ordered pairs do not correspond to a one-to-one function, because the output value y = 6 is associated with two input values ​​x = 1 and x = 3

(1, 6) (3, 6)

To verify if the graph of a relation is a function, draw on the graph horizontal lines parallel to the x axis. If one of these horizontal lines cuts the graph in 2 or more points, then the relationship is not a one-to-one function.

When you draw vertical lines on the plot shown, you will see that they always intersect at a single point. Therefore the relationship is a function

When drawing horizontal lines on the displayed graph you will notice that they always intersect at a single point. Therefore the function is a one-to-one function

the answer is C

The total number of seats in all 7 rows is 24

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that  there are 16 rows and each row has either 20 or 24 seats.

Therefore,

7 x 24 = 168

9 x 20 = 180

If the total number of seats in all 16 rows is 348,

168 + 180 = 348

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Answer:

a = -4

b = 6

Step-by-step explanation:

See attached

Answer:

a=-4 and b=6

Step-by-step explanation:

[tex]\frac{a}{x-8} +\frac{b}{x+4} =\frac{2x-64}{(x-8)(x+4)}[/tex]

First, add the fractions by finding the common denominator.

In this case, (x-8)(x+4).

[tex]\frac{a(x+4) + b(x-8)}{(x-8)(x+4)} =\frac{2x-64}{(x-8)(x+4)}[/tex]

Therefore, the numerators are equal:

[tex]a(x+4) + b(x-8) =2x-64[/tex]

Simplify:

[tex]ax+4a + bx-8b =2x-64\\(a+b)x+4a-8b=2x-64[/tex]

Now match the coefficients.

[tex]a+b=2, 4a-8b=-64[/tex]

Solve the system of equations.  I'll use substitution, but you can also use elimination if you prefer.

[tex]4a-8b=-64\\a-2b=-16\\(2-b)-2b=-16\\2-3b=-16\\-3b=-18\\b=6\\a=-4[/tex]

Therefore, a=-4 and b=6.

Answer:

  see below

Step-by-step explanation:

A proportional relationship has a graph that always goes through the origin. This fact by itself eliminates all the wrong answers.

A slope of 2/3 means the rise is 2 for each horizontal run to the right of 3. The two given points are 2 vertical units and 3 horizontal units apart, demonstrating a slope of 2/3.

There are a total of 2,000 students in the school.

1.) There are 540 students in the 6th grade. 540 is only 27% of students compared to the total. To find the total students in the whole school, we divide 540 by 27%.

2.) We first change 27% into a decimal by moving the point two times to the left. (Rule to change the percent into a decimal)

27% = .27

3.) Before we divide, we remove the decimal by moving the decimal two times to the right and so do we to 540.

.27 = 27

540. = 54000.

4.) Now we have 54000 divided by 27 which give us the answer of 2,000.

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Answer:

2,000 students are in school i do not know if it’s decimals because decimals are like % percentage but ok 2,000 is my answer I hope this helped

Answer:

81

Step-by-step explanation:

3 digits ^4 number options

3^4=81

Answer:

15.5 in

Step-by-step explanation:

Use property of secant and tangent segments in the circle:

If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.

In your case,

Tanget - x in

External secant - 10 in

Total secant - 10+14 in

So,

[tex]x^2=10\cdot (10+14)\\ \\x^2 =10\cdot 24\\ \\x^2 =240\\ \\x\approx 15.5\ in[/tex]

Answer:

Part A)

scientific notation ------> [tex]2.56*10^{11}\ bits[/tex]

standard notation ----->  [tex]256,000,000,000\ bits[/tex]

Part B)

scientific notation ------> [tex]5.12*10^{11}\ bits[/tex]

standard notation ----->  [tex]512,000,000,000\ bits[/tex]

Part C)

scientific notation ------> [tex]1.28*10^{11}\ bits[/tex]

standard notation ----->  [tex]128,000,000,000\ bits[/tex]

Part D)

scientific notation ------> [tex]6.4*10^{10}\ bits[/tex]

standard notation ----->  [tex]64,000,000,000\ bits[/tex]

Part E)

scientific notation ------> [tex]3.2*10^{11}\ bits[/tex]

standard notation ----->  [tex]320,000,000,000\ bits[/tex]

Step-by-step explanation:

we know that

[tex]1\ Gigabyte=1*10^{9}\ bytes\\ 1\ byte=8\ bits[/tex]

therefore

[tex]1\ Gigabyte=8*10^{9}\ bits[/tex]

Part A

Theresa and her brother, Ruben, are getting phones that each have 32 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation

we know that

Each phone have 32 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{32}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=32*8*10^{9}\\ \\x=256*10^{9}\ bits\\ \\x=2.56*10^{11}\ bits[/tex]

scientific notation ------> [tex]2.56*10^{11}\ bits[/tex]

standard notation ----->  [tex]256,000,000,000\ bits[/tex]

Part B

Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation.

we know that

Each phone have 64 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{64}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=64*8*10^{9}\\ \\x=512*10^{9}\ bits\\ \\x=5.12*10^{11}\ bits[/tex]

scientific notation ------> [tex]5.12*10^{11}\ bits[/tex]

standard notation ----->  [tex]512,000,000,000\ bits[/tex]

Part C

Because they are getting four new phones, the family also gets two free tablets. Each tablet has 16 gigabytes of storage. How many bits of storage come with each tablet?

we know that

Each tablet have 16 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{16}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=16*8*10^{9}\\ \\x=128*10^{9}\ bits\\ \\x=1.28*10^{11}\ bits[/tex]

scientific notation ------> [tex]1.28*10^{11}\ bits[/tex]

standard notation ----->  [tex]128,000,000,000\ bits[/tex]

Part D

Theresa talked her parents into getting SD cards for her phone and her brother’s phone. Inserting an SD card into a phone gives it more storage. They both get 8-gigabyte SD cards. How many bits of storage come with each SD card? Type your answer in both scientific and standard notation

we know that

Each SD card have 8 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{8}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=8*8*10^{9}\\ \\x=64*10^{9}\ bits\\ \\x=6.4*10^{10}\ bits[/tex]

scientific notation ------> [tex]6.4*10^{10}\ bits[/tex]

standard notation ----->  [tex]64,000,000,000\ bits[/tex]

Part E

With their plan, the family also gets access to storage on the cloud. They can store a total of 40 gigabytes on the cloud. How many bits of storage do they get on the cloud? Type your answer in both scientific and standard notation

we know that

The cloud have 40 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{40}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=40*8*10^{9}\\ \\x=320*10^{9}\ bits\\ \\x=3.2*10^{11}\ bits[/tex]

scientific notation ------> [tex]3.2*10^{11}\ bits[/tex]

standard notation ----->  [tex]320,000,000,000\ bits[/tex]

The solutions obtained are Part (A) 2.75 × 10¹¹ bits of storage, Part (B) 5.50 × 10¹¹ bits of storage ,Part (C) 1.37 × 10¹¹ bits of storage, Part (D) 6.87 × 10¹⁰ bits of storage, Part (E)  3.44 × 10¹¹ bits of storage.

Phone and Tablet Storage Measurement

Let's break down each part of the question to help Theresa and her family understand the storage capacity in bits.

Part A

Theresa and Ruben's phones each have 32 gigabytes (GB) of storage. To find the number of bits:

→ Convert gigabytes to bytes: 32 GB = 32 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits (since 1 byte = 8 bits): 32 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 32 × 1024 × 1024 × 1024 × 8 = 274,877,906,944 bits.

→ In scientific notation, this is approximately 2.75 × 10¹¹ bits.

Part B

Cal and Julia's phones each have 64 gigabytes (GB) of storage:

→ Convert gigabytes to bytes: 64 GB = 64 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits: 64 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 64 × 1024 × 1024 × 1024 × 8 = 549,755,813,888 bits.

→ In scientific notation, this is approximately 5.50 × 10¹¹ bits.

Part C

The family gets two free tablets with 16 gigabytes (GB) of storage each:

→ Convert gigabytes to bytes: 16 GB = 16 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits: 16 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 16 × 1024 × 1024 × 1024 × 8 = 137,438,953,472 bits.

→ In scientific notation, this is approximately 1.37 × 10¹¹ bits.

Part D

Theresa and Ruben each get 8-gigabyte (GB) SD cards:

→ Convert gigabytes to bytes: 8 GB = 8 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits: 8 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 8 × 1024 × 1024 × 1024 × 8 = 68,719,476,736 bits.

→ In scientific notation, this is approximately 6.87 × 10¹⁰ bits.

Part E

The family gets 40 gigabytes (GB) of cloud storage:

→ Convert gigabytes to bytes: 40 GB = 40 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits: 40 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 40 × 1024 × 1024 × 1024 × 8 = 343,597,383,680 bits.

→ In scientific notation, this is approximately 3.44 × 10¹¹ bits.

Answer:

  4 cm

Step-by-step explanation:

You have done all of the parts except the final division.

  13 = 3.25x

  13/3.25 = x = 4 . . . . . divide both sides by 3.25

The missing base measure of the enlarged trapezoid is 4 cm.

Answer:

4 CM

Step-by-step explanation:

Answer:

2(2r + 1)(2r - 5)

Step-by-step explanation:

Given

8r² - 16r - 10 ← factor out 2 from each term

= 2(4r² - 8r - 5)

To factorise the quadratic

Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.

product = 4 × - 5 = - 20 and sum = - 8

The factors are + 2 and - 10

Use these factors to split the r- term

4r² + 2r - 10r - 5 ( factor the first/second and third/fourth terms )

= 2r(2r + 1) - 5(2r + 1) ← factor out (2r + 1) from each term

= (2r + 1)(2r - 5), so

4r² - 8r - 5 = (2r + 1)(2r - 5) and

8r² - 16r - 10 = 2(2r + 1)(2r - 5) ← in factored form

The factored form of the given quadratic equation 8r² - 16r - 10 will be 2(2r + 1)(2r - 5) .

A quadratic equation is the second-order degree algebraic expression in a variable.

The standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

It is Given that

8r² - 16r - 10

= 2(4r² - 8r - 5)

To factorize the quadratic

Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.

The factors are + 2 and - 10

Use these factors to split the r- term

4r² + 2r - 10r - 5

= 2r(2r + 1) - 5(2r + 1)

= (2r + 1)(2r - 5),

4r² - 8r - 5 = (2r + 1)(2r - 5)

and

8r² - 16r - 10 = 2(2r + 1)(2r - 5)

The factored form of the given quadratic equation 8r² - 16r - 10 will be 2(2r + 1)(2r - 5) .

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Answer:

ZX

Step-by-step explanation:

A diameter is a chord of a circle that passes through the center of the circle.

A chord of a circle is a segment inside the circle whose endpoints are on the circle.

Chords of the circle:

ZY, ZX, YW, UV

Of all those chords, only two pass through the center of the circle:

ZX, YW

Of the two diameters, only one is a choice:

ZX

Answer: B. ZX

Answer:

zx

Step-by-step explanation:

A pex

Perimeter of the square backyard=56m

Perimeter of a square=4*side

Side=

56=4*side

56/4=side

side=14 cm

Area of a square=side*side

=14*14

=196cm^2

So,the area of the square backyard is 196m^2.

Answer:

A=196

Step-by-step explanation:

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Check the picture below.

[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=3\\ b=2 \end{cases}\implies \cfrac{(x-0)^2}{3^2}+\cfrac{(y-0)^2}{2^2}=1\implies \cfrac{x^2}{9}+\cfrac{y^2}{4}=1[/tex]

Answer:

The missing coefficient of the x-term of the product (-x-5)2 is 10.

Step-by-step explanation:

Through whole square formula.

(-x-5)2 = (-x)^2 -2(-x)(5)+(5)^2

=x^2+10x+25

Therefore, the missing coefficient of the x-term of the product is 10

Answer:

10

Step-by-step explanation:

The given expression is

[tex](-x-5)^2[/tex]

We need to find the coefficient of x.

According to the property of algebra.

[tex](a-b)^2=a^2-2ab+b^2[/tex]

In the given expression a=-x and b=5.

Substitute a=-x and b=5 in the above formula.

[tex](-x-5)^2=(-x)^2-2(-x)(5)+(5)^2[/tex]

On further simplification we get

[tex](-x-5)^2=x^2+10x+25[/tex]

Coefficient of x is a multiplicative factor of x.

Therefore, the coefficient of x is 10.

Answer:

  $1,000 at 2%; $1,800 at 4%

Step-by-step explanation:

Let x represent the amount invested at 2%. Then x+800 was invested at 4% and the total interest earned was ...

  x·2% + (x+800)·4% = 92

  x·6% + 32 = 92 . . . . . . . . . simplify

  x·0.06 = 60 . . . . . . . . . . . . subtract 32; write 6% as a decimal

  x = 60/0.06 = 1000 . . . . . divide by the coefficient of x

$1000 was invested at 2%; $1800 was invested at 4%.

Answer:

2000 m/h

Step-by-step explanation:

speed = distance/time

Mila's distance was (2/3)·(750 m) = 500 m, so her speed was ...

(500 m)/(1/4 h) = 2000 m/h

Mila swam 500 meters in 0.25 hours. Hence, her average speed was 2000 meters/hour.

To calculate Mila's average speed, first we need to calculate the distance she swam. Mila swam 2/3 of Logan's distance, which is 2/3 * 750 meters = 500 meters.

Now, we need to find out how long she swam in hours as her time was given in quarters of an hour. As Mila swam for 1/4 of an hour, this translates to 1/4 * 60 minutes = 15 minutes, or 0.25 in hours.

Speed is calculated as distance/time, therefore Mila's average speed is 500 meters/0.25 hours = 2000 meters/hour.

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Answer:

4th option

Step-by-step explanation:

The given expression is:

[tex]\frac{1}{1+\sqrt{3}}[/tex]

In order to simplify this expression we have to multiply and divide it with the conjugate of the denominator i.e multiply and divide the entire expression with [tex]1-\sqrt{3}[/tex], as shown below:

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

Thus, 4th option gives the correct answer.

Answer:

The right option is D -1+√3/2

Step-by-step explanation:

To find the quotient of the sure function 1/1+√3, we will rationalize the surd function by multiplying the numerator and the denominator of the surd by the conjugate of its denominator.

Given he denominator to be 1+√3, the conjugate of 1+√3 is 1-√3

Multiplying by 1-√3 will result in the following;

1/1+√3×1-√3/1-√3

= 1-√3/(1+√3)(1-√3)

= 1-√3/1-√3+√3-√9

= 1-√3/1-√9

= 1-√3/1-3

= 1-√3/-2

= -(1-√3)/2

= -1+√3/2

The right option is D -1+√3/2

Answer:

[tex]\large\boxed{a.\ -44}[/tex]

Step-by-step explanation:

[tex]\dfrac{y}{4}+8=-3\qquad\text{subtract 8 from both sides}\\\\\dfrac{y}{4}+8-8=-3-8\\\\\dfrac{y}{4}=-11\qquad\text{multiply both sides by 4}\\\\4\!\!\!\!\diagup^1\cdot\dfrac{y}{4\!\!\!\!\diagup_1}=(4)(-11)\\\\y=-44[/tex]

Answer:

a.  -44.

Step-by-step explanation:

y/4 + 8 = -3

Subtract 8 from both sides:

y/4 = -3 - 8

y/4 = -11

Now multiply both sides by 4:

y = 4 * -11 = -44 (answer).

Answer:

{2, 2, -6}

Step-by-step explanation:

synthetic division is one of the easier ways of determining whether or not a given number is a root of a polynomial.  Here we're told that -6 is a root.  Let's go through the steps of synthetic division:  keep in mind that if there is no remainder (that is, the remainder is zero), then the divisor (such as -6) is a zero of the polynomial.

The coefficients of f(x)=x^3+2x^2-20x+24 are {1, 2, -20, 24}.

Setting up synthetic div.:

       -6   )   1    2    -20    24

                      -6     24    -24

             ----------------------------

                 1    -4       4     0

Here the remainder is zero (0), so it is safe to assume that -6 is a zero of the original polynomial.

We can continue with synth. div. to determine the remaining zeros of the original function  f(x)=x^3+2x^2-20x+24.   The coefficients {1,  -4,  4} represent the quadratic x^2 - 4x + 4.  Let's check whether the factor 2 of 4 is indeed a zero:

2   )   1    -4    4

               2   -4

    -----------------

       1      -2    0

Here the remainder is zero.  Thus, 2 is a zero of f(x)=x^3+2x^2-20x+24.  Notice that the remaining coefficients are {1, -2}; they represent x - 2 = 0, so the third root is 2.

Thus, the zeros of f(x)=x^3+2x^2-20x+24 are {2, 2, -6}

The  fraction of the animals at the shelter are dogs 74/100 or 37/50

A relative value indicating hundredth parts of any quantity.

Given:

74% of the animals at an animal shelter are dogs.

We know the percent is considered as 100.

If we need to estimate anything in percent we compare it with 100%.

So,  fraction of the animals at the shelter are dogs be,

=74% of 100%

=74/100*100/100

= 74/100

=37/50

Hence,  fraction of the animals at the shelter are dogs be is 74/100 or37/50.

Learn more about percentage here:

https://brainly.com/question/16797504

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Answer:

276.75

Step-by-step explanation:

Deposit 1230. paying 2.25 % 10 yrs.

the interest is 276.75 and the amount is 1506.75

Answer:

The answer to the first question is $276.75     and the answer to the second question is $4882.50

Step-by-step explanation:

Johnny deposited $1230 in a savings account at 2.25 percent interest. How much interest will the account earn in 10 years?

To solve this, we simply use the simple interest formula;

Simple Interest = PRT / 100

where p is the principal, R is the rate and T is the time (in years)

In this question principal = $1230  rate = 2.25   and time = 10

We can now plug the variables into the formula;

Simple Interest = PRT / 100

                           =$1230  × 2.25× 10    /     100

                             = $27675  / 100

                              = $276.75

Therefore, the amount of interest earn in 10 years is  $276.75

Will got an insurance check of $4500 after a car accident. He deposited it into a savings  account at 1.7 percent interest for five years. What was the total amount of money in the  account after five years?

We can also solve this second part of the question using the simple interest formula, here;

principal = $4500

Rate =1.7

Time =5

We will now insert our values into the simple interest formula, thus;

Simple Interest = PRT / 100

                          =$4500 × 1.7 × 5   / 100

                          =$38250 / 100

                          =$382.50

Simple interest =$382.50

Total amount = $4500 + $382.50

                      =$4882.50

Therefore, the total amount in the account after five years is $4882.50