Write the quadratic equation whose roots are 3 and 4, and whose leading coefficient is 2.
(Use the letter x to represent the variable.)

Answer:

$97

Step-by-step explanation:

First, what do we know? Client A payed 488, Client B payed 294. They were supposed to pay equal amounts, but clearly that hasn't happened. If they had been fair, they would have divided the total of each bill equally between them. There is a way for us to do this, simply add the two amounts, and then divide by two.

[tex]488+294=782[/tex]

[tex]\frac{782}{2} =391[/tex]

So, both clients A and B were each supposed to pay 391. How much did client A overpay? We can find this number by looking at the difference between (or subtracting) the amount due (391) and the amount paid (488)

[tex]488-391=97[/tex]

We can verify this is correct by adding 97 to 294, to see if client B will now have paid as much as client A.

[tex]294+97=391[/tex],

which is what client B should have payed, and will have payed once he pays client A the 97 dollars owed.

Thus, client A is owed $97.

Answer:

Parallel lines

Step-by-step explanation:

Parallel lines have equal slopes

The product of the slopes of perpendicular lines equals - 1

The equation of a line in slope- intercept form is

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

Rearrange the 2 equations into this form and compare slopes

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

5y = x + 5 ( divide all terms by 5 )

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

with slope m = [tex]\frac{1}{5}[/tex]

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

5y = x - 5 ( divide all terms by 5 )

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

with slope m = [tex]\frac{1}{5}[/tex]

Since slopes are equal then the lines are parallel

Answer:

Parenthesis

Step-by-step explanation:

The parenthesis are always the first step in the order of operations.

:)

Answer:

The correct answer is D. 114

Step-by-step explanation:

There are 252 students of twelfth grade at Vista View High School.

99 walked to school

11 went by bicycle

28 used the school bus

To find the amount of twelfth graders that rode in a car, we do this calculation:

Amount of twelfth graders that rode in a car = Total of twelfth graders - those who walked - those who went by bicycle - those who used the bus

Replacing with the real values, we have:

Amount of twelfth graders that rode in a car = 252 - 99 - 11 - 28 = 252 - 138 = 114

The correct answer is D. 114

Answer:

114

Step-by-step explanation:

Answer:

Step-by-step explanation:

8h – 3 = 11h + 12

Collecting like terms

8h - 11h = 12 + 3

- 3h = 15

h = 15/-3

h = -5

The polynomial equation with zeroes 2i, -2i, 2 is [tex]x^3 -2x^2 + 4x - 8 = 0[/tex]

Given that zeros of polynomial are 2i, -2i, 2

To find: polynomial equation in standard form

zeros of polynomial are 2i, -2i, 2. So we can say,

x = 2i

x = -2i

x = 2

Or x - 2i = 0 and x + 2i = 0 and x - 2 = 0

Multiplying the above factors, we get the polynomial equation

[tex](x - 2i)(x + 2i)(x - 2) = 0\\[/tex] ------- eqn 1

Using a algebraic identity,

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

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

We know that [tex]i^2 = -1[/tex]

[tex]Thus (x - 2i)(x + 2i) = x^2 - (2i)^2 = x^2 -4(-1) = x^2 + 4[/tex]

Substitute the above value in eqn 1

[tex](x^2 + 4)(x - 2) = 0[/tex]

Multiply each term in first bracket with each term in second bracket

[tex]x^3 -2x^2 + 4x - 8 = 0[/tex]

Thus the required equation of polynomial is found

This is the new equation obtained after performing the subtraction.

[tex]\[ 9x - 2y = 0 \][/tex]

When subtracting one equation from another, we subtract the corresponding elements of the equations. Here's the step-by-step process:

Given the two equations:

1. [tex]\( x - 3y = 6 \)[/tex] (First equation)

2. [tex]\( -8x - y = 6 \)[/tex] (Second equation)

We want to subtract the second equation from the first. We do this by subtracting each term of the second equation from the corresponding term in the first equation:

Step 1: Subtract the x-terms:

[tex]\[ x - (-8x) = x + 8x = 9x \][/tex]

Step 2: Subtract the y-terms:

[tex]\[ -3y - (-y) = -3y + y = -2y \][/tex]

Step 3: Subtract the constants:

[tex]\[ 6 - 6 = 0 \][/tex]

So after subtracting the second equation from the first, the result is:

[tex]\[ 9x - 2y = 0 \][/tex]

This is the new equation obtained after performing the subtraction.

s = 3x - 15 is the required expression for perimeter of table top

Perimeter of square tabletop is 240 cm

Solution:

A square tabletop has an area given as:

[tex](9x^2 - 90x+225) cm^2[/tex]

The dimensions  of the tabletop have the form cx - di  ,where cand d are whole numbers

To find perimeter of tabletop when x = 25 centimeters

Let us first find the length of each side of square

Given area is:

[tex]area = (9x^2 - 90x+225)[/tex]

We know that,

[tex]area = (side)^2 = s^2[/tex]

Therefore,

[tex]s^2 = (9x^2 - 90x+225)\\\\s^2 = (3x - 15)(3x - 15)\\\\s^2 = (3x - 15)^2[/tex]

Taking square root on both sides,

s = 3x - 15

The above expression is the required expression for perimeter of table top

To find perimeter when x = 25 centimeter

The perimeter of square is given as:

[tex]perimeter = 4s[/tex]

perimeter = 4(3x - 15)

Substitute x = 25

perimeter = 4(3(25) - 15)

perimeter = 4(60) = 240

Therefore perimeter of square tabletop is 240 cm

To find the area of this rectangle, we first solve for the width using the given perimeter, yielding 4 inches. The length, three times this, is 12 inches. Multiplying these values together gives an area of 48 square inches.

We are dealing with a rectangle whose length is three times its width. If we call the width of the rectangle 'w', then its length is '3w'. The perimeter of a rectangle is 2 times the sum of its length and width.

So 2*(w+3w) = 32. This simplifies to 8w = 32. Solving for 'w', we find that the width of the rectangle is 4 inches. Then, the length would be three times the width, which is 12 inches.

Having determined these dimensions, we can find the area of the rectangle. The area of a rectangle is its length multiplied by its width. So in this case, it would be 4 inches (width) times 12 inches (length) to give us an area of 48 square inches.

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Answer: -30.75=-75

Step-by-step explanation: Multiply -6.15 by 5.

Hope this helps you out.

Answer:

17

Step-by-step explanation:

Given

[tex]b(1)=16\\ \\b(n)=b(n-1)+1[/tex]

Finding the second term of the sequence means to find [tex]b(2).[/tex] To find [tex]b(2)[/tex] substitute [tex]n=2[/tex] into the second expression:

[tex]b(2)=b(2-1)+1\\ \\b(2)=b(1)+1\\ \\b(2)=16+1\\ \\b(2)=17[/tex]

Answer:

Therefore the distance across the patch of swamp water is 50 ft

Step-by-step explanation:

Given:

VW = 100 ft

WX = 60 ft

XZ = 30 ft

To Find:

ZY = l = ?

Solution:

In  Δ VWX and Δ YZX

∠W ≅ ∠ Z    …………..{measure of each angle is 90° given}

∠VXW ≅ ∠YXZ      ..............{vertically opposite angles  are equal}

Δ ABC ~ Δ DEC ….{Angle-Angle Similarity test}

If two triangles are similar then their sides are in proportion.

[tex]\frac{VW}{YZ} =\frac{WX}{ZX} =\frac{VX}{YX}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

On substituting the given values we get

[tex]\frac{100}{l} =\frac{60}{30}\\\\l=\frac{3000}{60}=50\ ft[/tex]

Therefore the distance across the patch of swamp water is 50 ft

Answer:

  y = -3x -16

Step-by-step explanation:

For problems like this, I like to start with a variation of the point-slope form of the equation of a line:

  y = m(x -h) +k . . . . . for a line with slope m through point (h, k)

For your given values, this is ...

  y = -3(x +3) -7

  y = -3x -9 -7 . . . . eliminate parentheses; next, combine terms

  y = -3x -16

Answer:

-3x-16

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

2x+3y=27

3x-2y=8

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

3(2x+3y)=3(27)

-2(3x-2y)=-2(8)

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

6x+9y=81

-6x+4y=-16

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

13y=65

y=65/13

y=5

2x+3(5)=27

2x+15=27

2x=27-15

2x=12

x=12/2

x=6

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

x+y=6+5=11

Answer:

-5

Step-by-step explanation:

-7u+9=2

-7u=2-9

-7u=-7

7u=7

u=7/7

u=1

3(1)-8=3-8=-5

Answer:

10

Step-by-step explanation:

Given

[tex]x+y=8\\ \\4x-y=22[/tex]

Add these two equations:

[tex]x+y+4x-y=8+22\\ \\5x=30\\ \\x=6[/tex]

Substitute it into the first equation:

[tex]6+y=8\\ \\y=8-6\\ \\y=2[/tex]

Then

[tex]2x-y=2\cdot 6-2=12-2=10[/tex]

Answer:

Lack of information.

Step-by-step explanation:

We can't get the answer because this question haven't provide the information enough.

Have a nice day and hope it helps ;)

Answer:

Nine less than two-thirds of number is less than the number plus one.

Step-by-step explanation:

I jus got it right on edge.

Nine less than two-thirds of the number is less than the number plus one.

Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.

The expression is given below.

2/3y − 9 < y + 1

Then complete the sentence.

Then we have

Nine less than two-thirds of the number is less than the number plus one.

More about the Algebra link is given below.

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Line XD equals line XE and is also equal to line XF that proved by using AAS postulate of congruence ⇒ B

Step-by-step explanation:

Let us revise the cases of congruence

In Δ ABC

∵ Ray AL bisects ∠A ⇒ (divides it into two equal angles)

∴ m∠DAX = m∠EAX

∵ Ray BM bisects ∠B ⇒ (divides it into two equal angles)

∴ m∠EBX = m∠FBX

∵ XD ⊥ AC

∴ m∠XDA = 90°

∵ XE ⊥ AB

∴ m∠XEA = 90°

∵ XE ⊥ BC

∴ m∠XFB = 90°

Now lets prove that Δ ADX and ΔAEX are congruent

In Δs ADX and AEX

∵ m∠ADX = m∠AEX ⇒ (their measures are 90°)

∵ m∠DAX = m∠EAX ⇒ proved

∵ AX is a common side in both triangles

- By using the AAS postulate of congruence

∴ Δ ADX ≅ Δ AEX

∴ XD = XE

Let us do the same with Δ BEX and Δ BFX

In Δs BEX and BFX

∵ m∠BEX = m∠BFX ⇒ (their measures are 90°)

∵ m∠EBX = m∠FBX ⇒ proved

∵ BX is a common side in both triangles

- By using the AAS postulate of congruence

∴ Δ BEX ≅ Δ BFX

∴ XE = XF

∵ XE = XD

∵ XE = XF

- If one side is equal two other sides then the two other sides are

  equal, that means the three sides are equal

∴ XD = XF

∴ XD = XE = XF

Line XD equals line XE and is also equal to line XF that proved by using AAS postulate of congruence

Learn more:

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The given relation is a function

Step-by-step explanation:

When a relation is given in the form of ordered pairs, for each ordered pair, the first element of ordered pair represents elements of domain and the second element represents elements of set of range.

In order for a relation to be a function, there should be no repetition in domain i.e. every element should be unique.

Given relation is:

{(2, 2), (3, 2), (4, 3), (5,4)}

As we can see that the domain of given relation is:

{2,3,4,5} i.e. every element is unique

So,

The given relation is a function

Keywords: Relations, functions

Learn more about functions at:

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The provided set of ordered pairs {(2, 2), (3, 2), (4, 3), (5,4)} represents both a relation and a function. This holds because each input maps to exactly one output, with no repeating input values.

In mathematics, a set of ordered pairs is a relation if input values (also known as the domain or x-values) may have any number of corresponding output values (the range or y-values). A set of ordered pairs is a function if each input value maps to exactly one output value.

Considering the set of ordered pairs: {(2, 2), (3, 2), (4, 3), (5,4)}, we can see that each input (x-value) matches with one corresponding output (y-value) and none of the input values is repeating. Hence, according to the definition, this set of ordered pairs represents both a relation and a function.

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Answer:

The product is [tex]x^3+5x^2[/tex]

Step-by-step explanation:

This is because we apply the distributive property of multiplication.

Thus from [tex]x(5x+x^2)[/tex]

we get this:

[tex]x*5x+x*x^2[/tex]

[tex]x*5x[/tex] is [tex]5x^2[/tex] and [tex]x*x^2[/tex] is [tex]x^3[/tex]

Answer:

[tex]y=(x-3)^2-2[/tex]

Step-by-step explanation:

Given vertex of parabola [tex](3,-2)[/tex]

Where [tex](h,k)[/tex] is the vertex.

[tex](h,k)=(3,-2)\\h=3\ and\ k=-2[/tex]

Also parabola opens up.

The equation of parabola with vertex [tex](h,k)[/tex]

[tex]y= a(x - h)^2 + k[/tex]

If [tex]a>0[/tex] parabola opens up.

[tex]a<0[/tex] parabola opens down.

As the parabola opens up the value of [tex]a[/tex] will greater than zero.

Plugging vertex of parabola in equation [tex]y= a(x - h)^2 + k[/tex]

[tex]y= a(x - 3)^2 -2[/tex]

Let us plug [tex]a=1[/tex]

The equation will be [tex]y= a(x - 3)^2 -2[/tex]

Answer:

y-y/x-x

1--1/3-4

1+1/3-4

2/-1

= -2

then you plug in with any one of the points

y=mx+b

1= -2(3) + b

1 = -6 + b

b = 1+6

b = 7

so the equation is: y = -2x+7

Answer:

[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]  

[tex]p_v =2*P(Z>1.869)=0.0616[/tex]  

If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .  

Step-by-step explanation:

1) Data given and notation

n=232 represent the random sample taken

X represent the adults were no longer smoking after one month

[tex]\hat p=0.849[/tex] estimated proportion of adults were no longer smoking after one month

[tex]p_o=0.80[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.8.:  

Null hypothesis:[tex]p=0.8[/tex]  

Alternative hypothesis:[tex]p \neq 0.8[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(Z>1.869)=0.0616[/tex]  

If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .  

Answer:

The whole number temperatures, in kelvin, at which Andrew can conduct his experiment are 287, 288, 289,290,291.

Step-by-step explanation:

The temperature in degrees Celsius is 273.13 less than the temperature in kelvin; mathematically this means:

[tex]k=c+273.15[/tex]

Where [tex]k[/tex] is the temperature in kelvin and [tex]c[/tex] is the temperature in Celsius.

From this relationship we convert Andrew's temperature range—

13.5°c to 18.5°c—to kelvin:

[tex]k_1=13.5^oc+273.15=286.65[/tex]

[tex]k_2=18.5^oc+273.15=291.65[/tex]

Thus Andrew can conduct his experiment between 286.65 and 291.65 kelvin, and the whole number temperatures between these extremes are 287, 288, 289,290,291.

Thus the whole number temperatures, in kelvin, at which Andrew can conduct his experiment are 287, 288, 289,290,291.

Final answer:

To convert the temperature range from Celsius to Kelvin, add 273.15 to each end of the Celsius range given. The range for Andrew's experiment in Kelvin is from 287 K to 291 K, inclusive.

Explanation:

When converting temperatures from Celsius to Kelvin, one applies the simple formula: K = °C + 273.15. For Andrew's experiment, the temperature must be kept between 13.5°C and 18.5°C. Converting these to the Kelvin scale, we get:

Andrew can conduct his experiment at whole number Kelvin temperatures that fall within this range. Therefore, the range in Kelvin is from 287 K to 291 K, inclusive.

Answer:

Step-by-step explanation:

The word "sum" means adding. So, we have 11 + .....

The thing that 11 is being added to is a "product" a product means two things multiplied together. The things being multiplied are the number 2 and the number "r".

Answer:

1,3,5

Step-by-step explanation:

The domain is the set of all first elements of ordered pairs (x-coordinates).

The range is the set of all second elements of ordered pairs (y-coordinates).

Answer:

Step-by-step explanation:

y = 7 - 2x

x =1; y = 7 - 2*1 = 7- 2 = 5

x = 2; y = 7 - 2*2 = 7 - 4 = 3

x = 3; y = 7 - 2*3 = 7- 6 = 1

Range = { 1,3,5}

Answer:

8.987 (Approximate)

Step-by-step explanation:

We have to find the sum of a G.P. series up to sixth terms.

The first term of the series is 6 and common ratio is [tex]\frac{1}{3}[/tex].

So, the sum is  

[tex]6 + 2 + \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81}[/tex]

= [tex]6 \times \frac{1 - (\frac{1}{3})^{6}}{1 - \frac{1}{3} }[/tex]

= 8.987 (Approximate) (Answer)

We know the sum of a G.P.

a + ar + ar² + ar³ + ......... up to n terms = [tex]a\frac{1 - r^{n}}{1 - r}[/tex]  

where -1 < r < 1.

Answer:

a) [tex]8^8\sqrt{8}[/tex]

Step-by-step explanation:

Given,

[tex]\sqrt{8^1^7[/tex]

We have to simplify the expression by using "The Law of Indices".

[tex]x^m\times x^n=x^m^+^n[/tex]

So we can rewrite the expression as,

[tex]\sqrt{8^1^7[/tex]=[tex]\sqrt{8^1^+^1^6} =\sqrt{8}\times \sqrt{8^1^6}[/tex]

Now according to law of indices, which is;

[tex](x^m)^n=x^m^n[/tex]

So we can rewrite the expression as

[tex]\sqrt{8}\times \sqrt{8^1^6}=\sqrt{8}\times (8^1^6)^\frac{1}{2} \ \ \ \ Or\ \ \ \sqrt{8}\times 8^{16\times\frac{1}{2}} = 8^8\sqrt{8[/tex]

Hence the final Answer is [tex]8^8\sqrt{8[/tex].

Final answer:

The length of wire required to fence the circular field is found by calculating the circumference of the field. The number of times the field can be fenced with a given length of wire is found by dividing the total wire length by the circumference.

Explanation:

To find the length of wire required to fence the circular field, we need to find the circumference of the field. The formula to calculate the circumference of a circle is C = πd, where C is the circumference and d is the diameter. So, in this case, the circumference is C = π * 56 cm. Next, to find how many times the field can be fenced with 704m of wire, we divide the total length of wire by the circumference of the field. Therefore, the number of times the field can be fenced is 704 m / (π * 56 cm).