How do the expressions 72 / 9 and -72/ (-9) compare when they are evaluated?


A. They have different values and are different signs.

B. They have different values but are the same sign.

C. They have the same value but are different signs.

D. They have the same value and the same sign.

Answer:

Part 1) The length of the new rectangle is [tex]87.5\ ft[/tex]

Part 2) The area of the new rectangle is [tex]4,375\ ft^{2}[/tex]

Step-by-step explanation:

we know that

If two rectangles are similar, then the ratio of its corresponding sides is proportional

step 1

Find the length of the new rectangle

Let

L-----> the length of the new rectangle

[tex]\frac{50}{20}=\frac{L}{35}\\ \\ L=50*35/20\\ \\L=87.5\ ft[/tex]

step 2

Find the area of the new rectangle

we know that

The area of the rectangle is

[tex]A=LW[/tex]

we have

[tex]L=87.5\ ft[/tex]

[tex]W=50\ ft[/tex]

substitute

[tex]A=(87.5)(50)=4,375\ ft^{2}[/tex]

Since PQRS is isosceles, the horizontal distance between PQ and RS is the same, i.e. it's [tex]a[tex].

Moreover, point C is horizontally aligned with point Q, which implies that they share the y coordinate.

So, point R has coordinates [tex](c-a,b)[/tex]

Answer:

⅖  pizza

Step-by-step explanation:

Divide each pizza into five slices.

Then there will be 10 slices, and each person will get two slices.

Two slices = ⅖ pizza

Each person will receive ⅖ pizza.

Each of the five people will receive 2/5 of a pizza when two pizzas are shared equally amongst them.

The student asked how much pizza each person will receive if five people are sharing two pizzas equally. To answer this, we divide the total number of pizzas by the number of people. Since there are 2 pizzas and each pizza is usually considered to be 1 whole, when split among 5 people, each person will get 2/5 of a pizza.

To determine the number of apples John picks on the 10th day, we use the formula for the nth term of an arithmetic sequence. Given the first day's pick at 150 apples and an increase of 100 apples each day, we find that John picks 1050 apples on the 10th day.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the preceding term.

In this case, the first term (the number of apples picked on the first day) is 150, and the common difference (the increase each day) is 100 apples.

To find the number of apples picked on the 10th day, we use the formula for the nth term of an arithmetic sequence, which is:

an = a1 + (n - 1) × d

Where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. For the 10th day:

a10 = 150 + (10 - 1) × 100

a10 = 150 + 9 × 100

a10 = 150 + 900

a10 = 1050

Therefore, John picks 1050 apples on the 10th day.

Answer is ( 2, -2 ) so x=2 and y=-2

Answer:

(2,-2)

Step-by-step explanation:

This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations. It may be solved by substitution in that one of the variable is made the subject of the equation and the result is substituted into the second equation.

Given that Y = 7x – 16, y = 2(2x – 5)

Equating both equations

7x - 16 = 4x - 10

7x -4x = 16 - 10

3x = 6

x = 2

Substituting the value of x into Y = 7x – 16

y = 7(2) - 16

y = 14 - 16

y = -2

hence

(x,y) = (2,-2)

Answer:

option(b)

9/13

Step-by-step explanation:

Given the expression

[tex]\frac{2n+7n}{13n}[/tex]

=[tex]\frac{9n}{13n}[/tex]

n will cancel out on both sides

so,

9/13 will remain

As 9/13 is a constant so any value of n when approaches to a constant will not affect it. Hence limit = 9/13

The limit of a constant function is equal to the constant.

Answer:

B

Step-by-step explanation:

It’s a 50/50 chance since there is only 2 sides. (1?2)

Answer:

C. 4

Step-by-step explanation:

(3x/5) - 0.5 = 1.9

+ 0.5 +0.5

3x/5 = 2.4

*5 *5

3x = 12

— —

3 3

X = 4

Answer is C

I hope I helped!

Let me know if you need anything else!

~Zoe

parallel slopes always has the same exact slope.

The equation of required line is [tex]y=-\frac{3}{4} x-\frac{9}{4}[/tex]

Equation of line which is given,

                   [tex]-3x-4y=9\\\\y=\frac{-3x+9}{4} =-\frac{3}{4}x+\frac{9}{4}[/tex]

Compare above equation with [tex]y=mx+c[/tex]

Where m is slope of line, [tex]m=-\frac{3}{4}[/tex]

The slope of parallel lines are always equal.

So that, slope of required line is also [tex]-\frac{3}{4}[/tex].

                      [tex]y=-\frac{3}{4} x+c[/tex]

the line that passes through the point [tex]P(1,-3)[/tex]

Substitute given point in required equation of line.

               [tex]-3=-\frac{3}{4} *1+c\\\\c=-3+\frac{3}{4} \\\\c=-\frac{9}{4}[/tex]

The equation of required line is [tex]y=-\frac{3}{4} x-\frac{9}{4}[/tex]

Learn more about the slope-intercept form of line here:

https://brainly.com/question/1884491                      

Answer:

20

Step-by-step explanation:

You multiply the 80 and the 18 and then you add 82

Answer:

150 minutes

Step-by-step explanation:

Since your solving for minutes you need to change the 2.5 hours into minutes. There is 60 minutes in 1 hour. you take 60 and multiply it by 2.5 because you need to find the total minutes. When you multiply those teo you get 150 minutes. Please give me the brainliest answer.

:D Hoped this helped!!! Have a good day!! <3

Answer:

150 minutes

Step-by-step explanation:

1 hours = 60 minutes

We need to use the conversion factor with minutes on top

2.5 hours * 60 minutes

                   -------------

                    1 hour

Canceling hours

2.5 *60 minutes

150 minutes

A)

The lawyer in 20 years earns 3,620,000

The mathematician in 40 years earns 3,160,000

Subtract to find the difference:

3,620,000 - 3,160,000 = 460,000

The answer is the first one.

B)

Interest would be a credit of 27.23, balance = 700 + 27.23 = 723.23

Transfer would be a debit of 176.02 balance = 723.23 - 176.02 = 547.21

Deposit would be a credit of 157.00 balance = 547.21 + 157.00 = 704.21

A check would be a debit of 47.13 balance = 704.21 - 47.13 = 657.08

Answer:

4

Step-by-step explanation:

1/4 is a quarter at up 1/4 4 time and it gives you a whole, 1/4+1/4+1/4+1/4=1

Answer:

All statements are true

Step-by-step explanation:

1. The statement [tex]S_{500}>S_{499}[/tex] is true, because [tex]S_{499}[/tex] is the sum of first 499 terms,  [tex]S_{500}[/tex] is the sum of first 500 terms,  and all these terms are positive, then the sum of smaller number of terms is less than the sum of larger number of terms.

2. The statement [tex]S_{500}>a_{500}[/tex] is true, because [tex]S_{500}[/tex] is the sum of first 500 terms,  [tex]a_{500}[/tex] is 500th term and the sum of 500 terms is greater than the 500th term.

3. The statement [tex]S_1=a_1[/tex] is true, because [tex]S_1[/tex] is the sum of first 1 term that is exactly  [tex]a_1.[/tex]

All statements are true.

Answer:

The graph is attached below

Step-by-step explanation:

The function has three asymptotes. Before we can graph the function, we can find them.

Vertical asymptotes in the values that make the denominator zero.

The denominator becomes zero in:

[tex]x = -2\\x = 1\\[/tex]

Then the vertical asymptotes are the lines

[tex]x = -2\\x = 1\\[/tex]

The horizontal asymptote is found using limits

[tex]\lim_{x\to \infty}\frac{(2x+3)(x-6)}{(x+2)(x-1)}[/tex]

Then:

[tex]\lim_{x\to \infty}\frac{(2x^2-12x +3x -18)}{x^2-x+2x-2}[/tex]

We divide the numerator and the denominator between the term of greatest exponent, which in this case is [tex]x ^ 2[/tex]

The terms of least exponent tend to 0

[tex]\lim_{x\to \infty}\frac{(2\frac{x^2}{x^2}-0 +0 -0)}{\frac{x^2}{x^2}-0+0-0}\\\\\lim_{x\to \infty}\frac{2}{1} = 2\\\\[/tex]

The function has a horizontal asymptote on y = 2 and has no oblique asymptote

The graph is attached below

Answer:

Step-by-step explanation:

For f(x) = 4x + 3 and g(x) = 9x

(a) (f o g) (x)

= f (g (x))

= f (9x)

= 4(9x) +3

= 36x + 3

Its domain is any real number.

(b) (g o f) (x)

= g (f (x))

= g (4x + 3)

= 9 (4x + 3)

= 36x + 27

Again its domain is any real number.

(c) (f o f) (x)

= f (f (x))

= f (4x + 3)

= 4(4x + 3) + 3

= 16x + 12 + 3

= 16x + 15

Again its domain is any real number.

(d) (g o g) (x)

= g ( g (x))

= g (9x)

= 9(9x)

= 81x

Again its domain is any real number.

Answer:

solution given:

f(x) = 4x + 3

g(x) = 9x

answer:

a.fog(x)=f(9x)=4×9x+3=36x+3

domain=real number

b.gof (x)=g(4x+3)=9(4x+3)=36x+26

domain=real number

c.fof(x)=f(4x+3)=4(4x+3)+3=16x+12+3

=16x+15

domain: real number

d.

gog(x)=g(9x)=9×9x=81x

domain: real number.

[tex] \frac{5 \: = \: number \: of \: favorable \: outcomes}{6 \: = \: number \: of \: possible \: outcomes} [/tex]

Since there are 6 possible outcomes, that will become the denominator. In addition, since we are trying to find the probability of rolling 5 numbers out of that 6, 5 would be the numerator.

So the answer is,

[tex] \frac{5}{6} [/tex]

The probability that the number is 2,6,3,4, or 1 is 5/6.

Probability is the ratio that shows the likelihood that an event will occur from a given set of events.

A cube has six sides. Each side has a unique number.

We have to find the probability of getting 2,6,3,4, or 1.

The total number of favorable events = 5

The sample space has 6 events.

Therefore, the probability is given by 5/6.

Therefore, we have found the probability that the number is 2,6,3,4, or 1 to be 5/6.

Learn more about probability here: https://brainly.com/question/24756209

#SPJ2

Answer:

N is a population parameter; the computation using an estimate of N is a statistic.

Step-by-step explanation:

A parameter is a measure of a population.  The number of warplanes fielded total is N; this makes it the population.  Thus N is a parameter.

A statistics is a measure of a sample.  The number computed using an estimate of N would be based on a sample, since it is an estimate of N; this makes it a statistic.

The expression (8.320)(1)/(3) simplifies to approximately 2.7733.

The expression (8.320)(1)/(3) can be simplified as:

Therefore, the answer is 2.7733, which is not among the provided options.

To determine if the number is a solution to the equation, we have to substitute n with the number given.

56= 8 + 4(6)

56= 8 + 24

56= 32

So no, the number is not a solution to the equation.

The number is a solution of a linear equation if both sides of the equation namely RHS and LHS are equivalent.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here, the equation as  56 = 8 + 4n  and to verify for n=6

Here, LHS =56 and RHS when n=6 is 8+4×6=32

Thus LHS≠RHS

Hence n=6 is not a solution to the equation.

Learn more about the solution of a linear equation here:

https://brainly.com/question/545403

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Answer: 60 degrees

Step-by-step explanation:

the line is 180 degrees so minus 50 equals 130 minus 10 120 divide my 2 60

Answer:

D. -36x+9

Step-by-step explanation:

−12(3x−

3/4)

=(−12)(3x+  −3/

4)

=(−12)(3x)+(−12)(

−3/4)

=−36x+9

Answer:

D. -36x + 9

Step-by-step explanation:

[tex]-12[3x - \frac{3}{4}] \\ -36x + 9[/tex]

I am joyous to assist you anytime.

Answer:

option (c)

4√34

Step-by-step explanation:

Given in the question is a right angle triangle

height of triangle = 20 cm

base of triangle = 12 cm

To find the length of missing side of the triangle we will use pythagorus theorem

hypotenuse² = 20² + 12²

hypotenuse² = 400 + 144

hypotenuse²  = 544

take square root on both sides

√hypotenuse² = √544

hypotenuse = 4√34 cm

Hence,  the length of missing side of the triangle is4√34 cm

Answer:

Diameter 16, radius 7, circumference 37.68, diameter 8

Step-by-step explanation:

Largest area will be in a circle with the largest radius. So let's find all radii.

d = 8, so r = 4;

r = 7;

circumference = 2pi*r = 37. 68, so r = 6

diameter 18, so r = 8

AO is a line segment containing the radii of both circles, which are AK and OE, so AO = AK + OE = 9.

Extend AO to a point P on the line KE. Then we get two similar triangles APK and OPE. Let [tex]x[/tex] be the length of KE, [tex]y[/tex] the length of EP, and [tex]z[/tex] the length of OP.

By similarity, we have

[tex]\dfrac{OE}{AK}=\dfrac{EP}{KP}=\dfrac{OP}{AP}\iff\dfrac45=\dfrac y{y+x}=\dfrac z{z+9}[/tex]

OPE is a right triangle, so

[tex]OP^2=OE^2+EP^2\implies z=\sqrt{16+y^2}[/tex]

Now,

[tex]\dfrac45=\dfrac y{y+x}\implies 4(y+x)=5y\implies 4x=y[/tex]

and we also have

[tex]z=\sqrt{16+(4x)^2}=\sqrt{16+16x^2}=4\sqrt{1+x^2}[/tex]

Substituting this into the expression containing [tex]z[/tex] gives us an equation that we can solve for [tex]x[/tex]:

[tex]\dfrac45=\dfrac z{z+9}=\dfrac{4\sqrt{1+x^2}}{4\sqrt{1+x^2}+9}[/tex]

[tex]16\sqrt{1+x^2}+36=20\sqrt{1+x^2}[/tex]

[tex]9=\sqrt{1+x^2}[/tex]

[tex]\implies KE=x=\sqrt{80}=3\sqrt{10}[/tex]

Answer:

1. The area of the triangle PQR is 40 cm^2.

2. 321.4 cubic cm

Step-by-step explanation:

1. We are given two triangles, ABC and PQR, which are similar to each other.

Given that area of the triangle ABC is [tex]40cm^2[/tex], we are to find the area of the triangle PQR.

For that, we can use the ratio method:

[tex] \frac { P Q R } { 4 0 } = \frac { 6 } { 4 } [/tex]

Area of triangle PQR = [tex] \frac { 6 \times 40 } { 4 } = 60cm^2 [/tex]

2. We are given the diameter of a spherical model to be 8.5 cm so its radius will be 4.25 cm.

Finding the volume of the spherical model as we know that the volume of a sphere is given by:

[tex]\frac{4}{3} \pi r^3[/tex]

Substituting the given value of radius in the formula to get:

Volume of spherical model = [tex]\frac{4}{3} \times 3.14 \times (4.25)^3[/tex] = 321.4 cubic cm

Answer:

x=-5

Step-by-step explanation:

Set up the rational expression with the same denominator over the entire equation.

2x-2/6=3x+3/6

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

2x−2=3x+3

Move all terms containing x to the left side of the equation.

−x−2=3

Move all terms not containing x to the right side of the equation.

-x=5

Multiply each term in x=−5 by −1

x=−5

The correct answer is D.

$55 per hour x 4 hours = $220

$220 + $50 service charge = $270 total

Hope this help.

Answer:

D. $270

Step-by-step explanation:

$55 per hour for 4 hours = $55 * 4 = $220

$50 service fee

total = hourly amount + service fee

total = $220 + $50

total = $270

Answer:

x = 70

Step-by-step explanation:

70 % of x = 52.50

75 out of 100  X = £ 52.50

Answer:

The Original Price of the Winter Jacket is $70

Step-by-step explanation:

The Original Price is calculated by using the given information on a Simple Rule of Three formula, which looks like the following.

X --------> 100%

$52.50 --------> 75%

The Rule of Three simply asks if $52.50 is 75% then What is 100%? We solve the Rule of Three by multiplying $52.50 by 100 and then dividing the result by 75.

[tex]X = \frac{52.50*100}{75}[/tex]

[tex]X = 70[/tex]

According to the formula the Original Price of the Winter Jacket was $70

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

[tex]A=53.13\°[/tex]

Step-by-step explanation:

The figure shows a right triangle.

To calculate the measure of the angle A, you can use the inverse trigonometric function arctangent:

[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]

Identify the angle [tex]\alpha[/tex], the opposite side and the adjacent side:

[tex]\alpha=A\\opposite=4cm\\adjacent=3cm[/tex]

Substitute into [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex].

The measure of the angle A is:

[tex]A=arctan(\frac{4}{3})\\\\A=53.130\°[/tex]

Rounded to the nerarest hundreth:

[tex]A=53.13\°[/tex]

The answer is m∠A = 53.13 °