Plot each set of points. Choose all that correctly define the quadrilateral in the coordinate plane. A(0, 0), B(0, 5), C(2, 5), D(2, 0) is a rectangle A(?2, 4), B(2, 4), C(4, 2), D(?2. 2) is an isosceles trapezoid A(0, 4), B(4, 1), C(0, ?5), D(?4, 1) is a square A(4, ?3), B(?2, ?3), C(?1, 1), D(5, 1) is a parallelogram

Answer:

The solutions to your three problem question are:

1.

       a.    10x^2 −2x -12

       b.    14x^2 + 7x -41

2.   30x^3 + 9x^2 + 32x  - 7

3.

     n1 = 8

     n2 = -2

Step-by-step explanation:

1. First problem

We need to Add or subtract the expressions to find the equivalent terms

a) (−2x^2 −4x + 13)+ (12x^2 + 2x −25)

We add together the terms with the same exponent

= (−2x^2 + 12x^2 ) +  (−4x + 2x) + (13 - 25)

= (10x^2 ) +  (−2x) + (-12)

=  10x^2 −2x -12

b) (7x^2 + 4x − 26)− (−7x^2 − 3x + 15)

= (7x^2 + 4x − 26) +  (7x^2 + 3x - 15)

We add together the terms with the same exponent

= (7x^2 + 7x^2 ) +  (4x + 3x) + (- 26 -15)

= (14x^2 ) +  (7x) + (-41)

=  14x^2 + 7x -41

2. Second problem

(5x − 1)(6x^2 + 3x + 7)

We need to multiply to find the equivalent expression\

(5x − 1)(6x^2 + 3x + 7) = (5x)*(6x^2 + 3x + 7) + (-1)*(6x^2 + 3x + 7)

= [(5x)*(6x^2 + 3x + 7)]  + [-6x^2 - 3x - 7]

=  [(5x*6x^2) + (5x*3x) + (5x*7)]  +  [-6x^2 - 3x - 7]

= [(30x^3) + (15x^2) + (35x)]  +  [-6x^2 - 3x - 7]

We add together the remaining terms

= [(30x^3) + (15x^2 - 6x^2) + (35x - 3x)  - 7]

= (30x^3) + (9x^2) + (32x)  - 7

= 30x^3 + 9x^2 + 32x  - 7

3. Third problem

f(n) = n^2 − 6n − 16

We need to find the roots for the polynomial f(n)

That is, the values of n for which f(n) = 0

We can find an analysis of the function in the images below.

Lets use the quadratic formula

Let   y = ax2 + bx + c

a = 1

b = -6

c = -16

x = -b/(2*a) ± sqrt(b^2 -4ac)/(2*a)

x = 3 ± 10/2  = 3 ± 5

roots

n1 = 8

n2 = -2

Answer:

The answer is the first answer

P = 8 + 8√17 cm

A = 96 cm²

Step-by-step explanation:

* Lets study the figure

- Its a kite with two diagonals

- The shortest one is 12 cm

- The longest one is 26 ⇒ axis of symmetry of the kite

* To find the area reserved for the logo divide

 the hexagonal piece into two congruent trapezium

- The length of the two parallel bases are 4 cm and 8 cm and

  its height is 8 cm

- The length of non-parallel bases can calculated by Pythagoras rule

∵ The lengths of the two perpendicular sides are 2 cm and 8 cm

- 8 cm is the height of the trapezium

- 2 cm its the difference between the 2 parallel bases ÷ 2

  (8 - 4)/2 = 4/2 = 2 cm

∴The length of the non-parallel base = √(2² + 8²) = 2√17

* Now we can find the area of the space reserved for the logo

- The area of the trapezium = (1/2)(b1 + b2) × h

∴ The area = (1/2)(4 + 8) × 8 = (1/2)(12)(8) = 48 cm²

∵ The space reserved for the logo are 2 trapezium

∴ The area reserved for the logo = 2 × 48 = 96 cm²

* The area of the reserved space for the logo = 96 cm²

* The perimeter of the reserved space for the logo is the

  perimeter of the hexagon

∵ The lengths of the sides of the hexagon are:

   4 cm , 4 cm , 2√17 cm , 2√17 cm , 2√17 cm , 2√17 cm

∴ The perimeter = 2(4) + 4(2√17) = 8 + 8√17 cm

* The perimeter of the reserved space for the logo = 8 + 8√17 cm

Answer:

b. [tex]y=3.9^x[/tex]

Step-by-step explanation:

Remember that the standard exponential function is [tex]y=ab^x[/tex]

where

[tex]a[/tex] is the coefficient

[tex]b[/tex] is the base

If [tex]b>0[/tex], the function is growing

If [tex]0<b<1[/tex] the graph is decaying

We can infer from the graph that the function is growing, so we can discard [tex]y=0.45^x[/tex] and [tex]y=0.73^x[/tex].

Now, to evaluate our tow remaining equations, we are using the test values [tex]x=0[/tex] and [tex]x=1[/tex]:

For [tex]y=1.8^x[/tex]

For [tex]x=0[/tex]

[tex]y=1.8^0[/tex]

[tex]y=0[/tex]

For [tex]x=1[/tex]

[tex]y=1.8^1[/tex]

[tex]y=1.8[/tex]

The graph passes through the points (0,1) and (1, 1.8)

For [tex]y=3.9^x[/tex]

[tex]x=0[/tex]

[tex]y=3.9^0[/tex]

[tex]y=0[/tex]

[tex]x=1[/tex]

[tex]y=3.9^1[/tex]

[tex]y=3.9[/tex]

The graph passes through the points (0,1) and (1, 3.9)

We can see in the graph when [tex]x=1[/tex], [tex]y[/tex] is almost 4, so we can conclude that the correct equation is [tex]y=3.9^x[/tex]

Answer:

[tex]\log_2(ab^3)^{\frac{1}{2}}=\frac{1}{2}[\log_2(a)+3\log_2(b)][/tex].

Step-by-step explanation:

The given logarithmic expression is [tex]\log_2\sqrt{ab^3}[/tex].

We rewrite the radical as an exponent to obtain;

[tex]\log_2(ab^3)^{\frac{1}{2}}[/tex].

Recall that; [tex]\log_a(M^n)=n\log_a(M)[/tex]

We apply this rule to obtain;

[tex]=\frac{1}{2}\log_2(ab^3)[/tex].

We now use the rule: [tex]\log_a(MN)=\log_a(M)+\log_a(N)[/tex]

This implies that;

[tex]=\frac{1}{2}[\log_2(a)+\log_2(b^3)][/tex].

We again apply: [tex]\log_a(M^n)=n\log_a(M)[/tex]

[tex]=\frac{1}{2}[\log_2(a)+3\log_2(b)][/tex].

Answer:

D

Step-by-step explanation:

This function graphed as the picture attached below show is a function. It passes the vertical test. However, it does not pass the horizontal line. This means the function is not one-to-one but many-to -one.

55º

vertical angles are congruent

El costo total por concepto de la reparación del automóvil es de 170,56 soles.

¿Cómo calcular el costo total de la reparación de un automóvil?

En este problema se debe determinar el costo total por concepto de la reparación de un automóvil. Dimensionalmente hablando, se tiene que el costo total se determina mediante la siguiente fórmula:

C = c · Δt

Donde:

A continuación, el costo total se calcula según la información suministrada por el enunciado de la pregunta:

C = (32,8 soles / hora) · (1,5 horas + 0,2 horas + 0,75 horas + 1,45 horas + 1,3 horas)

C = 170,56 soles

Answer: option c.

Step-by-step explanation:

 To solve this problem you must keep on mind the properties of logarithms:

[tex]ln(b)-ln(a)=ln(\frac{b}{a})\\\\ln(b)+ln(a)=ln(ba)\\\\a*ln(b)=ln(b)^a[/tex]

Therefore, knowing the properties, you can write the expression gven in the problem as shown below:

[tex]ln2x+2lnx-ln3y=ln2x+lnx^2-ln3y\\\\=ln(2x)(x^2)-ln3y\\\\=ln(\frac{2x^3}{3y})[/tex]

Therefore, the answer is the option c.

Answer:

C

Step-by-step explanation:

We can use 3 properties here to write this as single logarithm:

1. Log (a^b) = b Log a

2. Log x + Log y = Log (x*y)

3. Log x - Log y = Log (x/y)

We can use property #1 first to write:

[tex]ln2x+2lnx-ln3y\\=ln2x+lnx^2-ln3y[/tex]

Now we can use property #2 and property #3 to write this as single logarithm:

[tex]ln2x+lnx^2-ln3y\\=ln(\frac{(2x)(x^2)}{3y})\\=ln(\frac{2x^3}{3y})[/tex]

Answer choice C is right.

Answer:

THERE IS NO PICTURE OR VISUAL REPRESENTATION

Step-by-step explanation:

Answer:

f(x) = (x + 6)(x – 2)

Step-by-step explanation:

The roots of a polynomial are the solutions to its factors. This means you can set the factors equal to 0 and the roots are the solution. Working backwards, if the roots are x = -6 and x = 2 then they must have resulted from factors x + 6 and x - 2. This is true since x + 6 = 0 has solution x = -6. And x-2 = 0 has solution x = 2.

So the polynomial has factors (x+6)(x-2). The solution is f(x) = (x + 6)(x – 2).

Answer:

the answer is 4

Step-by-step explanation:

just did it on edge.

your welcome

Answer:

5 minutes

Step-by-step explanation:

300 seconds / x minutes = 60 seconds / 1 minute

300 = 60x; divide both sides by 60 to get x; 5 = x

Answer:

43 miles per hour

Step-by-step explanation:

We know that in Cherokee County, the speed tickets amounts are calculated on the basis of $17 for each mile above the speed limit.

Since Kirk was fined $221, we can easily calculate the excess speed he was caught at by dividing $221 by $17/mile, which gives us 13 miles.

Since he was caught in a zone where the posted speed limit was 30, and that he exceeded it by 13 miles per hour... we know he was going at 43 miles per hour.

Answer:

Popcorn costs: $5.75, and drink costs: $2.25.

Step-by-step explanation:

Answer:

44.50 = 3 x + 4 y

84= 4x +8 y

each popcorn bag costs $2.5

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations:

The total cost for Kevin (44.50) is equal to the product of the number of popcorn bags bought (x ) and the price of each bag, plus the product of the number of drinks purchased (y) and the price of each drink (y).

Mathematically speaking

Kevin : 44.50 = 3 x + 4 y

Using the same process for Levi:

Levi : 84= 4x +8 y

The system is  

44.50 = 3 x + 4 y (k)

84= 4x +8 y (L)

If we multiply Kevin's equation by 2 and subtract it to Levi's equation:

89 = 6x +8y

          -

( 84= 4x +8 y)

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

5 = 2x

solving for x

5/2= x

2.5 =x

each popcorn  costs $2.5

Answer:

22, no: 24, yes

Step-by-step explanation:

22 wouldn't be a triangle because when you square both sides

8^2+6^2= 81 (but 9^2 is 81) the 2 values surpasses 81

24 would be a triangle because

8^2+6^2=10^2

64+36=100

Answer:

[tex]\large\boxed{c\approx3.31}[/tex]

Step-by-step explanation:

Use cosine:

[tex]cosine=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]\cos\theta=\dfrac{b}{c}[/tex]

We have:

[tex]\theta=25^o\to\cos25^o\approx0.9063\\\\b=3[/tex]

Substitute:

[tex]\dfrac{3}{c}=0.9063[/tex]

[tex]\dfrac{3}{c}=\dfrac{9063}{10000}[/tex]          cross multiply

[tex]9063c=30000[/tex]          divide both sides by 9063

[tex]c\approx3.31[/tex]

30 ounces of the coffee John likes consists of

To this mixture we're adding [tex]x[/tex] ounces of water, so that the new mix has a total volume of [tex]30+x[/tex] ounces and matches the composition of the coffee Lily likes. This means it would consist of

Solve for [tex]x[/tex]:

[tex]0.973(30+x)=28.8+x\implies29.12+0.973x=28.8+x[/tex]

[tex]\implies0.39=0.027x[/tex]

[tex]\implies x\approx14.4[/tex]

###

Just to confirm: the new mixture consists of

giving a total volume of [tex]43.2+1.2=44.4[/tex] ounces of coffee, and [tex]\dfrac{43.2}{44.4}\approx0.973[/tex], as required.

Answer :-      Just try area/2 or half the area of the triangle

Answer:

Step-by-step explanation:

The area of triangle abc would be half the area of the parallelogram.  The two triangles are of equal area.

Answer:

18 cm

Step-by-step explanation:

The area (A) of a kite is

A = [tex]\frac{1}{2}[/tex][tex]d_{1}[/tex][tex]d_{2}[/tex], that is

[tex]\frac{1}{2}[/tex] × 8 × [tex]d_{2}[/tex] = 72

4 × [tex]d_{2}[/tex] = 72 ( divide both sides by 4 )

[tex]d_{2}[/tex] = 18 cm

 the proper term is tax LIABILITY ( i e what you would owe if you had not paid in anything ).  

then because the liability is greater than the w/h ; 1374 - 678 = owed

Hope this helps!

The tax due is $1,324 and the tax withheld is $678. By subtracting the tax withheld from the tax due, we find that an additional $646 is owed and no refund is expected.

Tax is due or the expected refund, you need to compare the total tax owed to the amount of tax withheld. In this scenario, the tax due is $1,324, and the tax withheld is $678.

First, subtract the tax withheld from the tax due: $1,324 (tax due) - $678 (tax withheld) = $646.

If the result is positive, as it is in this case, it means that you owe $646 more in taxes. If the result were negative, it would indicate an expected refund of that amount.

Therefore, no refund is expected because the tax withheld does not cover the total amount of tax due. The individual will owe an additional $646.

Answer:

[tex]\large\boxed{A\subset B}[/tex]

Step-by-step explanation:

[tex]A=\{1,\ 2\},\ B=\{1,\ 2,\ 3,\ 4\}\\\\A\subset B,\ \text{because all elements of the set A are the elements of the set B.}[/tex]

Henley can draw 7.2 sketches in 3 hours based on the proportion of 12 sketches in 5 hours; however, when rounding to the nearest whole number, she can complete 7 sketches.

The problem at hand is a simple proportion problem where we want to find out how many sketches Henley can make in 3 hours given that she can make 12 sketches in 5 hours. To solve this, we set up a ratio that relates her drawing rate to the time spent drawing:

12 sketches    x sketches

----------- = ------------

 5 hours        3 hours

We can solve for x by cross-multiplying and then dividing by the coefficient of x:

12 sketches [tex]\times[/tex] 3 hours = 5 hours [tex]\times[/tex] sketches

x = ([tex]12 sketches \times 3 hours[/tex]) / 5 hours

x = 7.2 sketches

Therefore, Henley can draw 7.2 sketches in 3 hours. However, since one cannot draw a fraction of a sketch, we round down to the nearest whole number. Henley can thus draw 7 sketches in 3 hours assuming a consistent drawing speed.

Answer:

farther

Step-by-step explanation:

The negative sign means that it is 10 feet down while -8 is only 8 feet down

An elevation of -10 feet is farther from the surface of the ocean than - 8 feet.

Time can not be negative as we can not go to past.Time is unidirectional.

According to the given question we have to determine Is an elevation of -10 feet closer or farther from the surface of the ocean than an elevation of -8 feet.

We know that -10 is less than -8 as it is present in the left of -8 in the number line that is one case.

But here we are measuring elevation which is length and we know length can not be negative so going by the idea of length an elevation of -10 feet is farther from the surface of the ocean we are diving 10 feet below here so more distance.

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Answer:

It's D.

Step-by-step explanation:

The shorter period loan has the same total interest for the same loan amount, so it has the higher effective interest rate: 80/12 is higher than 89/14.

A payday credit for $1900 that is expected in 12 days with an expense of $80, since it has the less limited time frame. Then the correct option is D.

When buying or recovering proposals in a common asset, a financial backer may be paid a business fee or commission. Deals with fees can be set up in a variety of ways.

Banks and insurance providers may offer their clients a grace period, which allows them to postpone payment for a predetermined amount of time after the time limit (after the payment deadline).

A payday credit for $1900 that is expected in 14 days with a charge of $80 or a payday credit for $1900 that is expected in 12 days with a charge of $800.

A payday credit for $1900 that is expected in 12 days with an expense of $80, since it has the less limited time frame. Then the correct option is D.

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Answer: 90 Degrees

Step-by-step explanation:

I believe the answer is 90° because the diagonals of a rhombus, just like a square form right triangles. in reality, a rhombus is just a square that was pulled to the side a bit.

A good source to play with rhombuses is on mathisfun. It can help you build a study guide and further your understanding of the subject.

Answer:

A. 6m and 2m

E. 11.25m and 3.75m

Step-by-step explanation:

we know that

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

so

Verify each case

case A) 6m and 2m

[tex]\frac{6}{4.5}=\frac{2}{1.5} \\ \\6(1.5)=2(4.5)\\ \\9=9[/tex]

therefore

The legs are proportional

case B) 8m and 5m

[tex]\frac{8}{4.5}=\frac{5}{1.5} \\ \\8(1.5)=5(4.5)\\ \\12\neq22.5[/tex]

therefore

The legs are not proportional

case C) 7m and 3.5m

[tex]\frac{7}{4.5}=\frac{3.5}{1.5} \\ \\7(1.5)=3.5(4.5)\\ \\10.5\neq15.75[/tex]

therefore

The legs are not proportional

case D) 10m and 2.5m

[tex]\frac{10}{4.5}=\frac{2.5}{1.5} \\ \\10(1.5)=2.5(4.5)\\ \\15\neq11.25[/tex]

therefore

The legs are not proportional

case E) 11.25m and 3.75m

[tex]\frac{11.25}{4.5}=\frac{3.75}{1.5} \\ \\11.25(1.5)=3.75(4.5)\\ \\16.875=16.875[/tex]

therefore

The legs are proportional

Answer:

  (a) √2

  (b) 1/2

Step-by-step explanation:

(a) The ratio of distances will be the magnitude of the ratio f(z)/(f(z) -z), so will be ...

  |(1+i)z/((1+i)z -z)| = |(1+i)/i| = |1-i| = √(1+1) = √2

___

(b) You want |g(z) -0| = |g(z) -z|, so you have ...

  |(a +2i)z -0| = |(a +2i)z -z|

  |(a +2i)|·|z| = |a-1 +2i|·|z|

Dividing by the magnitude of z and squaring both sides, we have ...

  a^2 +4 = (a-1)^2 +4

  0 = -2a +1 . . . . . . subtract a^2+4 and simplify

  1/2 = a . . . . . . . . . divide by -2, add 1/2

Answer:

Probability of winning first situation:  0.0793

Probability of winning second situation:  0.0146

You should go with the first option

Step-by-step explanation:

See attached photo for answers.   For this situation you need to identify p-hat, p, q and n.

P-hat, p, and q all stay the same for both situations, only n changes.

p-hat is the proportion of green balls we want, which is 0.7

p = 98/159 = 0.62

q = 0.38 because q = 1 - p, which in this case is q = 1 - 0.62 = 0.38

n = 73 for the first situation, and n = 175 for the second situation

Using the normal probability distribution and the central limit theorem, it is found that:

a)

With 73 draws, there is a 0.0808 = 8.08% probability of getting more than 70% green balls.

With 175 draws, 0.015 = 1.5% probability of getting more than 70% green balls.

b)

Due to the higher probability of getting more than 70% green balls, 73 draws should be chosen.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

Central Limit Theorem

Item a:

Out of 73 draws:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6203(0.3797)}{73}} = 0.0568[/tex]

The probability of more than 70% green balls is 1 subtracted by the p-value of Z when X = 0.7, thus:

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.7 - 0.6203}{0.0568}[/tex]

[tex]Z = 1.4[/tex]

[tex]Z = 1.4[/tex] has a p-value of 0.9192.

1 - 0.9192 = 0.0808

With 73 draws, there is a 0.0808 = 8.08% probability of getting more than 70% green balls.

Out of 175 draws:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6203(0.3797)}{175}} = 0.0367[/tex]

Then:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.7 - 0.6203}{0.0367}[/tex]

[tex]Z = 2.17[/tex]

[tex]Z = 2.17[/tex] has a p-value of 0.985.

1 - 0.985 = 0.015.

With 175 draws, 0.015 = 1.5% probability of getting more than 70% green balls.

Item b:

Due to the higher probability of getting more than 70% green balls, 73 draws should be chosen.

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The base of the middle triangle is 3 and the base of the larger one is 6, so the larger triangle is twice the size of the middle one.

Multiply the height of the middle one by 2 to get the height of the larger one, which is labeled n.

n = 5 x 2 = 10

Answer:

10

Step-by-step explanation:

We are taking 5m and dividing by 1/2 m

5 ÷ 1/2

Copy dot flip

5 * 2/1

10

We can get 10 pieces from the rope

10 pieces of rope of length 0.5 meter can be cut from the rope of total length 5 meters.

Given :

Total length of Rope = 5 m.

Division is about breaking something into many pieces. The number you are dividing is called the dividend. The number you are "dividing by" is the divisor. The answers to your division problems are called quotients.

Number of pieces of rope of length 0.5 meter will be calculated as follows:

[tex]=\dfrac{5}{0.5}[/tex]

[tex]=10[/tex]

10 pieces of rope of length 0.5 meter can he cut from it.

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Answer:

Sum of cubes. I just did this test.

Step-by-step explanation:

Honestly I have no real explanation other than a sum would be adding, whereas difference would be subtracting.

Hence, the polynomial identity shows the sum of cubes.

What is the polynomial?

Polynomials are sums of terms of the form [tex]kx^n[/tex], where [tex]k[/tex] is any number and [tex]n[/tex] is a positive integer.

Here given that,

[tex]64+27=91[/tex]

Addition of two values gives us the third number.It is representing the sum of cubes.

Hence, the polynomial identity shows the sum of cubes.

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