Over the summer, Manny read 45 books and 15 magazines. The value of the book to magazine ratio is

Answer:

Length of garden will be 30 metres.

Step-by-step explanation:

Let the Width of garden be x metres.

then,

Length of garden will be (x+6) metres.

Area = Length × Breadth

720 = x X (c+6)

720 = x²+6x

0 = x²+6x-720

As we can see above equation is a quadratic equation in the form of ax²+bx+C.

so,

[tex] = \frac{ - b ± \sqrt{{b}^{2} - 4ac} }{2a} \\ = \frac{ - 6 ± \sqrt{{6}^{2} - 4 \times 1 \times - 720} }{2} \\ = \frac{ - 6 ± \sqrt{36 + 2880} }{2} \\ = \frac{ - 6 ± \sqrt{2916} }{2} \\ = \frac{ - 6 ± 54}{2}\\= \frac{-6+54}{2} ... \frac{ - 6 - 54}{2} \\ = \frac{48}{2} ... \frac{ - 60}{2} \\ = 24... - 30[/tex]

One of the Roots of the Quadratic equation is 24 and other is -30.

And as we know width of any garden cannot be negative so the width of garden will be 24 metres.

As we got the width,

adding 6 to it will give us the Length,

So,

24 metres + 6 = 30 metres.

Length of the garden is 30 metres.

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Answer:

14

Step-by-step explanation:

d=c/pi

45/pi=14

Answer:

14

Step-by-step explanation:

c = pi d

45 = 22/7 d

45 * 7/22 = d

2* 7      = d (approx.)

d = 14 approxiamtely

So the closest estimate dor d is 14

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Answer:

No, it is not.

Step-by-step explanation:

This is not proportional, however, it is linear

The answer is C. because the train will arrive any minute. This is because an adverb clause is a clause that functions as an adverb, and it modifies or describes a verb, adverb or adjective.

The blue triangle is the dilated shape from the red triangle.

The dimensions of the blue triangle are half the red one.

The answer is B)1/2.

Answer:1/2

Step-by-step explanation:

Took the test on edge

Answer:

The value of k is [tex]K=100[/tex]

Step-by-step explanation:

we know that

[tex]h(x)=\frac{20x-k}{x}+50[/tex]

we have

[tex]x=20\\ h(20)=65[/tex]

substitute in the function and solve for k

[tex]65=\frac{20(20)-k}{20}+50[/tex]

[tex]65-50=\frac{400-k}{20}[/tex]

[tex]15=\frac{400-k}{20}[/tex]

[tex]15*20=400-k[/tex]

[tex]300=400-k[/tex]

[tex]k=400-300=100[/tex]

Answer:

K=100

Step-by-step explanation:

Answer:

1556.25

Step-by-step explanation:

5 3/16.25×300=1556.25

Quadrilateral. If you add the angles up on any quadrilateral, it equals 360 (it should always add to 360 for a quadrilateral)

The polygon you're describing is a kite.

To verify this, let's calculate the sum of the interior angles of the polygon:

Sum of interior angles = [tex](n - 2) * 180 degrees[/tex]

For a polygon with 4 sides: [tex](4 - 2) * 180 = 360 degrees[/tex]

Now, let's add up the given angle measures: 80 + 100 + 80 + 100 = 360 degrees

Since the sum of the interior angles matches the calculated sum for a four-sided polygon, and the sides are congruent, the polygon is indeed a kite.

1. Calculate the sum of interior angles: The sum of interior angles of any polygon can be found using the formula (n - 2) * 180 degrees, where 'n' represents the number of sides. For a four-sided polygon, the sum is (4 - 2) * 180 = 360 degrees.

2. Add up the given angle measures: The given angle measures are 80, 100, 80, and 100 degrees. Adding them together gives a total of 360 degrees, which matches the sum calculated for a four-sided polygon.

3. Confirming the polygon type: Since the sum of the interior angles matches the calculated sum for a four-sided polygon, and the sides are congruent (meaning all sides have the same length), the polygon fits the definition of a kite.

Therefore, the polygon with four congruent sides and angle measures of 80, 100, 80, and 100 degrees is indeed a kite.

Complete question:

What is the name of a polygon that has four congruent sides and these angle measures 80,100,80,100

Answer:

2.5 & 1.1

Step-by-step explanation:

that answer is correct ^

Answer:

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

Step-by-step explanation:

Given that three roots of a fifth degree polynomial function f(x) are -2,2 and (4+i).

Now we need to find about which of the given statements describes the number and nature of all roots for this function.

We know that imaginary roots always occur in conjugate pairs.

So if (4+i) is root then (4-i) must also be the root.

So now we have total 4 roots

-2, 2, (4+i) and (4-i).

Degree of the polynomial is 5 so that means 1 root is still remaining. It can't be imaginary as that must be in pairs

So that means 5th root is real.

Hence correct choice is :

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

Answer:

-1/3

Step-by-step explanation:

Answer:

19.50 divided by 3

Step-by-step explanation:

Answer:

3h = 19.50

Step-by-step explanation:

First lets define the price of each hat as the variable h.

Next we know that there are 3 hats so we can write that variable as 3h

We also know that the cost of all 3 hats was $19.50. This means that we can set each side of this equation equal to each other.

This gives us the equation 3h = 19.50

If you were to solve for h, you would get

[tex]h = \frac{19.50}{3}[/tex]

Which would simplify to

h = 6.50

This means that each hat costs $6.50

Answer:

2x^2+7x-61

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given y = 5(x + 1) = 5x + 5 ← in slope- intercept form

with slope m = 5

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{5}[/tex], thus

y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (10, 2) into the partial equation

2 = - 2 + c ⇒ c = - 2 + 2 = 4

y = - [tex]\frac{1}{5}[/tex] x + 4 ← in slope intercept form

Multiply all terms by 5

5y = - x + 20 ( add x to both sides )

x + 5y = 20 ← in standard form → D

Answer:

Step-by-step explanation:

The answer is a I am not sure

The relationship described by y = 4x + 4 is not proportional because Option D. the graph does not pass through the origin. The y-intercept is 4, indicating it does not meet the criteria for direct proportionality.

The equation y = 4x + 4 describes a linear relationship between x and y. However, for two quantities to be directly proportional, their relationship must be of the form y = kx, meaning that the graph of their relationship must pass through the origin (0, 0).

In the equation y = 4x + 4, the y-intercept is 4, not 0. Therefore, the graph of this equation does not pass through the origin.

Option D) No, because the graph of the equation does not pass through the origin.

[tex]d[/tex] stands for distance.

[tex]

d(J, K)=\sqrt{(7-2)^2+(8-4)^2}=\sqrt{25+16}\approx6.4

[/tex]

[tex]

d(J, L)=\sqrt{(1-2)^2+(-1-4)^2}=\sqrt{1+16}\approx4.12

[/tex]

[tex]d(J, K)>d(J, L)[/tex] therefore the answer is D.

Answer:

1.1818...

Step-by-step explanation:

Divide 13 by 11

13 ÷ 11 = 1.1818...

Answer: 1.1818...

The decimal 1.182 is equivalent to 13/11.

A fraction can be converted to a decimal by dividing the numerator by the denominator.

The fraction is given as 13/11.

The numerator is 13 and the denominator is 11.

We are asked to find the decimal form of the given fraction.

This can be done by simplifying the fraction and dividing the numerator by the denominator.

This can be done as shown below:

The fraction = 13/11

= 1.1818

≈ 1.182

The decimal form of the fraction is found. The decimal form of the fraction is 1.182.

Therefore, we have found that the decimal 1.182 is equivalent to 13/11.

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22.27

You need to divide the amount of servings by the amount of ounces in total

Step-by-step explanation:

So if segment QS and segment PR are equal then all parts are equal which means segment QT= segment PT, segment TR= segment TS. segment QS id equal to 12 which means segment PR is equal to 12. You get segment TR by subtracting 4.9 from 12. Now you know that segment TR is 7.1 which means that segment TS is 7.1.

You also know that segment PS is equal to segment QR so you know that segment QR is 9cm because segment PS is 9cm.

m∠QPR is 33° because you know that ΔQPR's sum is 180 and you know that ∠PQR is 114° b/c 44+70 is 144, 180-144=66 now you take 66 and divide it by 2 (for the two angles left) that equals 33.

m∠STR is 92°. You know this by taking the base angle in ΔPTQ and multiplying it by two (which now equals 88, the base angle is 44°) and you take this number and subtract it from 180. 180-88=92. 92 is you measure of angle STR.

ANSWER

[tex]x \: < \: 9[/tex]

EXPLANATION

The given inequality is

[tex]5x \: < \: 45[/tex]

We divide through by 5 to get:

[tex]x \: < \: \frac{45}{5} [/tex]

This will simplify to

[tex]x \: < \: 9[/tex]

Therefore the solution to the inequality is

[tex]x \: < \: 9[/tex]

x < 9

Start with 5x < 45.

Divide both sides of the inequality by 5 to get x < 45 / 5, or x < 9.

Answer:

10^5 = 100.000

Step-by-step explanation:

We know that 10^5 = 10 * 10* 10 * 10 * 10 = 100.000.

So, we have that 10^5 = 100.000

For this case we have the following expression:

[tex]10 ^ 5[/tex]

Then, as the exponent is positive, we must move the decimal as many times as indicated by the exponent. In this case, we must move it 5 spaces to the right, that is:

[tex]10 ^ 5 = 100000[/tex]

Answer:

[tex]10 ^ 5 = 100000[/tex]

The answer is 2^(9/10). I did it assuming with the ^5 you mean the 5th root of 4

ANSWER

[tex] {2}^{ \frac{9}{10} } [/tex]

EXPLANATION

The given expression is

[tex] \sqrt[5]{4} \times \sqrt{2} [/tex]

Recall that:

[tex] \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } [/tex]

[tex]\sqrt[5]{ {2}^{2} } \times \sqrt{ {2}^{1} } [/tex]

[tex]\sqrt[5]{ {2}^{2} } \times \sqrt{ {2}^{1} } = {2}^{ \frac{2}{5} } \times {2}^{ \frac{1}{2} } [/tex]

Recall that:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We now apply this property of a exponents to obtain:

[tex]\sqrt[5]{ {2}^{2} } \times \sqrt{2} = {2}^{ \frac{2}{5} + \frac{1}{2} } = {2}^{ \frac{9}{10} } [/tex]

Answer:

it's the 2nd one

Step-by-step explanation:

d = 3 + at^2

-3 | -3

d - 3 = at^2

d - 3/a = t^2

√d - 3/a = √t^2

t = √d - 3/a

the answer is negative 5

It’s negative 5, because you have to substitute the x in 3x for negative one, so the equation looks like f(x)= 3(-1) - 2. Then, you solve

the possible solutions of this equation. Is that they are not real.

Answer:

Step-by-step explanation:

6x-2y<10 :  3x -y <5

then :  3x -y -5< 0

given the line : 3x-y-5 = 0

the points is a solution to the system of equalities? 6x-2y<10 Located on the line : 3x-y-5 = 0 and under the x - axis.

Based on the phrase they gave, the inequality would look like this:

[tex]\frac{4-g}{8} >-15[/tex]

[tex]\frac{4-g}{8}\leq-15[/tex]

the quotient(÷) of [the difference(- subtraction) of 4 and a number(g) and 8] is at MOST -15.

since the sign is ≤, this means that the inequality is less than or equal to -15, so -15 is the maximum number for the inequality.

Your answer is the last option

Answer:

(D)

Step-by-step explanation:

I got it right on edge/quiz.

Answer:

Z = 5 + 3i and Z = -8 - 2i

Step-by-step explanation:

* Lets study the drawing of the complex numbers

- The x-axis is the real axis

- The y-axis is the imaginary axis

* Look to the attached figure

- Any point in the first quadrant is above the real axis and right

 to the imaginary axis (Z4)

# Z = x + yi

- Any point in the second quadrant is above the real axis and left

 to the imaginary axis (Z2)

# Z = -x + yi

- Any point in the third quadrant is below the real axis and left

 to the imaginary axis (Z3)

# Z = -x - yi

- Any point in the fourth quadrant is below the real axis and right

 to the imaginary axis (Z1)

# Z = x - yi

* Now lets solve the problem

- The point above the real axis and right to the imaginary axis lies

 in the first quadrant

∴ The real part is positive and the imaginary part is positive

∴ Z = 5 + 3i

- The point below the real axis and left to the imaginary axis lies

 in the third quadrant

∴ The real part is negative and the imaginary part is negative

∴ Z = -8 - 2i

A complex number that lies above the real axis and to the right of the imaginary axis could be '2 + 3i', while a complex number that lies below the real axis and to the left of the imaginary axis could be '-2 - 3i'. The direction in the coordinate system (upward or rightward is positive, downward or leftward is negative) determines the signs of real and imaginary components.

In the complex plane, a complex number is considered to lie above the real axis if its imaginary part is positive, and to the right of the imaginary axis if its real part is positive. Hence, an example of a complex number that lies above the real axis and to the right of the imaginary axis is 2 + 3i, where 2 is the real part and 3i is the imaginary part.

Conversely, a complex number lies below the real axis if its imaginary part is negative, and to the left of the imaginary axis if its real part is negative. So, an example of such a number could be -2 - 3i, where -2 is the real part and -3i is the imaginary part.

Remember, in the coordinate system used to plot complex numbers, motion upward or to the right is usually considered positive, while motion downward or to the left is considered negative.

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Answer:

I think the answer is  w = 16

Step-by-step explanation:

start by dividing -5 from both sides.

-5w=-80

/

-5

w=-16

y = 3(-x - 2)

Any horizontal transformations or reflections you make to y = x must be within the parentheses.

The transformed function is g(x) = -7 [tex]log_6[/tex] (-x) +2

The given base function is

f(x) = [tex]log_6[/tex] (x)

Then we have to find the transformed function.

First of all, the graph of the base function f(x) = [tex]log_6[/tex] (x) is vertically stretched by a factor of 7, then the newly transformed function becomes y = 7[tex]log_6[/tex](x)

Then the graph of y = 7[tex]log_6[/tex](x) is reflected over the x-axis, then the newly transformed function becomes y = -7log6(x)

Then the graph of y = -7[tex]log_6[/tex](x) is reflected over the y-axis, then the newly transformed function becomes y = -7[tex]log_6[/tex](-x)

And finally, the graph of y=7log6(-x) is vertically shifted up by 2 units, then the newly transformed function becomes

y = -7 [tex]log_6[/tex] (-x) +2

which is the required equation for the transformed function.

Step-by-step explanation:

[tex]\text{Put}\ x=-2,\ x=0\ \text{and}\ x=3\ \text{to the equation}\ y=4^x:\\\\y=4^{-2}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\y=\dfrac{1}{4^2}=\dfrac{1}{16}\\-----------------\\\\y=4^0=1\\-----------------\\\\y=4^3=64[/tex]