Solve the quadratic equation x2 + 14x = 51 by completing the square.
Question 3 options:

A)

x = –17, x = –3

B)

x = –17, x = 3

C)

x = 3, x = 17

D)

x = –3, x = 17

Answer:

Following are the description of the given course code:

Step-by-step explanation:

The given course code is Pre-Algebra, which is just an introduction arithmetic course programs to train high school in the Algebra 1. This course aims to strengthen required problem solving skills, datatypes, equations, as well as graphing.

Answer:

A

Step-by-step explanation:

Answer:

(2x-4i) (x+2i)

Step-by-step explanation:

2x^2+8

Factor out 2

2 ( x^2+4)

Writing as the difference of squares  a^2 -b^2 = (a-b) (a+b)

2 ( x^2 -(2i)^2)

2 ( x-2i) (x+2i)

Multiplying the 2 into the first term

(2x-4i) (x+2i)

Answer:

The frequency table is shown below.

Step-by-step explanation:

The data set arranged ascending order is:

S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58,  60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}

It is asked to use the minimum value from the data set as the lower class limit for the first row.

So, the lower class limit for the first class interval is 33.

To determine the class width compute the range as follows:

[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]

          [tex]=84-33\\=51[/tex]

The number of classes requires is 5.

The class width is:

[tex]\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10[/tex]

So, the class width is 10.

The classes are:

33 - 42

43 - 52

53 - 62

63 - 72

73 - 82

83 - 92

Compute the frequencies of each class as follows:

Class Interval                  Values                        Frequency

   33 - 42                      33 , 34 , 39                             3

   43 - 52                      48 , 49 , 50                            3

   53 - 62          53 , 54 , 55 , 56 , 58 , 58,  60              7

   63 - 72                 63 , 64 , 65 , 70 , 71                      5

   73 - 82                              74                                  1

   83 - 92                             84                                   1

   TOTAL                                                                   20

Compute the relative frequencies as follows:

Class Interval          Frequency        Relative Frequency

   33 - 42                        3                   [tex]\frac{3}{20}\times 100\%=15\%[/tex]

   43 - 52                        3                   [tex]\frac{3}{20}\times 100\%=15\%[/tex]

   53 - 62                        7                   [tex]\frac{7}{20}\times 100\%=35\%[/tex]

   63 - 72                        5                   [tex]\frac{5}{20}\times 100\%=25\%[/tex]

   73 - 82                         1                   [tex]\frac{1}{20}\times 100\%=5\%[/tex]

   83 - 92                         1                   [tex]\frac{1}{20}\times 100\%=5\%[/tex]

   TOTAL                        20                          100%

Answer:

a ≈ 2.2

Step-by-step explanation:

Using the Cosine rule in Δ ABC

a² = b² + c² - 2bc cos A

Here b = 3, c = 4 and A = 32° , thus

a² = 3² + 4² - (2 × 3 × 4 × cos32° )

    = 9 + 16 - 24cos32°

    = 25 - 24cos32° ( take the square root of both sides )

a = [tex]\sqrt{25-24cos32}[/tex] ≈ 2.2

Answer:

80202

Step-by-step explanation:

Simply add according to number value:

200 - 2 goes into hundreds place

2 - 2 goes into ones place

80000 - 8 goes into ten-thousands place

Answer:

B

Step-by-step explanation:

The contractor gets $75 for every single customer she sets up. Okay, so if she sets up 1 customer, she gets $75, if she sets up 2, she gets $150 and so on.

This is a multiplication expression since multiplication is just repeated addition, which is what is happening in this case, where the contractor gets $75 added to her account every time she sets another person up.

At this point you can just eliminate the other answer options except for B, so it is B.

But to double check... if you multiply 75 by 8, you would get $600, which is B.

Answer:

d

Step-by-step explanation:

75/c; $9.78

Answer:

0

Step-by-step explanation:

multiply the negative thru the right part of the equation so, 5j+5-5j-5. The 5j and the 5 than cancel out with each other. Hope this helps!

Answer:

0

Explanation:

step 1 - remove the parenthesis from the expression

(5j + 5) - (5j + 5)

5j + 5 - 5j - 5

step 2 - combine like terms

5j + 5 - 5j - 5

5j - 5j + 5 - 5

0 + 0

0

therefore, the simplified form of the given expression is 0.

Answer:

There are 65 dimes. There are 55 nickels.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of dimes

y is the number of nickels.

There are a total of 120 coins in the bag

This means that x + y = 120.

The total value of the coins is $9.25.

The dime is worth $0.10 and the nickel is worth $0.05. So

0.1x + 0.05y = 9.25

System:

[tex]x + y = 120[/tex]

[tex]0.1x + 0.05y = 9.25[/tex]

From the first equation:

[tex]y = 120 - x[/tex]

Replacing in the second:

[tex]0.1x + 0.05y = 9.25[/tex]

[tex]0.1x + 0.05(120 - x) = 9.25[/tex]

[tex]0.1x + 6 - 0.05x = 9.25[/tex]

[tex]0.05x = 3.25[/tex]

[tex]x = \frac{3.25}{0.05}[/tex]

[tex]x = 65[/tex]

[tex]y = 120 - x = 120 - 65 = 55[/tex]

There are 65 dimes. There are 55 nickels.

Answer:

[tex]f(x)=4(x+6)^2-134[/tex]

Step-by-step explanation:

We are required to write the function[tex]f(x) = 4x^2 + 48x + 10[/tex] in vertex form.

First, bring the constant to the left-hand side.

[tex]f(x) -10= 4x^2 + 48x[/tex]

Factorize the right hand side.

[tex]f(x) -10= 4(x^2 + 12x)[/tex]

Take note of the factored term(4) and write it in the form below.

[tex]f(x) -10+4\Box= 4(x^2 + 12x+\Box)[/tex]

[tex]\Box = (\frac{\text{Coefficient of x}}{2} )^2\\\\\text{Coefficient of x}=12\\\\\Box = (\frac{12}{2} )^2 =6^2=36[/tex]

Substitute 36 for the boxes.

[tex]f(x) -10+4\boxed{36}= 4(x^2 + 12x+\boxed{36})[/tex]

[tex]f(x) -10+144= 4(x^2 + 12x+6^2)[/tex]

[tex]f(x) +134= 4(x+6)^2\\f(x)=4(x+6)^2-134[/tex]

The function written in vertex form is [tex]f(x)=4(x+6)^2-134[/tex]

Answer:

C

Step-by-step explanation:

I just finished the unit test on Edge. and got a 100% and I selected "c" as my answer.

Answer:

20 teachers

Step-by-step explanation:

Because if you take 100 and minus it by 29, 23, 4 and 24 you get 20.

Answer: D

Step-by-step explanation:

According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year

The initial population Po = 114000

Rate = 1.5% = 0.015

The declining population formula will be:

P = Po( 1 - R%)x^2

The decay formula

Since the population is decreasing, take away 0.015 from 1

1 - 0.015 = 0.985

Substitutes all the parameters into the formula

P(s) = 114000(0.985)x^2

P(s) = 114000× 0985x^2

The correct answer is written above.

Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.

Answer:

B

Step-by-step explanation:

A is not a function because the same x value is repeated twice with different y values. The same goes for C and D so the answer is C.

Answer:

B.

Step-by-step explanation:

Well a relation is a set of points and a function is a relation where every x value corresponds to only 1 y value.

So lets see which x values in these relations have only 1 y value.

A. Well a isn’t a function because the number 3 which is a x value had two y values which are -1 and 4.

B. This relation is a function because there are no similar x values.

C. This is not a function because the x value 4 has two y values which are 4 and -3.

D. This is not a function because the number 1 has 2 and 3 as y values.

Answer:

Hey there!

There are a few ways you could solve this problem, but the easiest would to be writing an equation.

You could say-

2.3x=69

Divide by 2.3

x=30

Hope this helps :)

Answer:

30

Step-by-step explanation:

the answer is 30 bc increasing something by 130% is multiplying it by 2.3 so technically you have to divide 69 by 2.3 which equals to 30

Answer:

16 ounces = 1 pound

Step-by-step explanation:

You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this

Answer:  [tex]H_0:\mu=421[/tex]

[tex]H_a : \mu\neq421[/tex]

Step-by-step explanation:

Given: A 37 bag sample had a mean of 421 grams.

Let [tex]\mu[/tex] be the population mean.

Then, the null hypothesis would be:

[tex]H_0:\mu=421[/tex]

whereas the alternative hypothesis would be:

[tex]H_a : \mu\neq421[/tex]

Circumference = πd

~substitute → (π)(6 cm)

~simplify → 6π cm.

So the circumference of the circle shown here is 6π cm.

Answer:

18.85 cm

Step-by-step explanation:

The circumference of a circle has a formula.

Circumference = π × diameter

The diameter is 6 centimeters.

Circumference = π × 6

Circumference ≈ 18.85

The circumference of the circle is 18.85 centimeters.

Answer:

D

Step-by-step explanation:

Answer:

x = y = 26 cm; z = 13 cm

Step-by-step explanation:

We can calculate the dimensions of the square base as

∛(2·8788) = 26 cm

the height of the box will be half of 26/2 which is 13 cm.

x = y = 26 cm; z = 13 cm

then the minimum area for the given volume can be calculated using what we call Lagrange multipliers, this makes it easier

area = xy +2(xz +yz)

But we were given the volume as 8788

Now we will make the partial derivatives of L to be in respect to the cordinates x, y, z, as well as λ to be equal to zero, then

L = xy +2(xz +yz) +λ(xyz -8788)

For x: we have

y+2z +λyz=0

For y we have

y: x +2z +λxz=0

For z we have 2x+2y +λxy=0............eqn(*)

For we have xyz -8788=0

If we simplify the partial derivative equation of y and x above then we have

λ = (y +2z)/(yz).

= 1/z +2/y............eqn(1)

λ = (x +2z)/(xz)

= 1/z +2/x.............eqn(2)

Set eqn(1 and 2) to equate we have

1/z +2/y = 1/z +2/x

x = y

From eqn(*) we can get z

λ = (2x +2y)/(xy) = 2/y +2/x

If we simplify we have

1/z +2y = 2/x +2/y

Then z = x/2

26/2 =13

Therefore,

x = y = 2z = ∛(2·8788)

X= 26

y = 26 cm

z = 13 cm

Answer:

We can use the cross products property.

11/8 = y / 13

8y = 11 * 13

y = 11 * 13 / 8 = 17.875

Answer:

y=17.875

Step-by-step explanation:

[tex]\frac{11}{8} = \frac{y}{13}[/tex]

11(13)=8y

143=8y

y=17.875

Answer:

The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].

Step-by-step explanation:

The standard equation of the ellipse is described by the following expression:

[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]

Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)

[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]

The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].

Answer:

5.35 more miles

Answer:

5.35 miles to the finish line

Step-by-step explanation:

Step one

13.1-7.75=

5.35

Answer:

The given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2). Hence, the value of x is 7.5.

Function is a type of relation, or rule, that maps one input to specific single output.

The given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2).

here x = 2

Substitute in the function;

F(x)=x^4-2x^3+3x^2 - ax+3

F(2) = 2^4-2(2)^3+3(2)^2 - a(2) +3

F(2) = 16 - 16 + 12 - 2a +3

F(2) = 15 - 2a

15 - 2a = 0

15 = 2a

a = 7.5

Hence, the value of x is 7.5

Learn more about function here:

https://brainly.com/question/2253924

#SPJ2

Answer:

(a) The value of a is 53.35.

(b) The value of a is 38.17.

(c) The value of a is 26.95.

(d) The value of a is 25.63.

(e) The value of a is 12.06.

Step-by-step explanation:

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{55-22}=\frac{1}{33}[/tex]

Here, 22 < X < 55.

(a)

Compute the value of a as follows:

[tex]P(X\leq a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.95\times 33=[x]^{a}_{22}\\\\31.35=a-22\\\\a=31.35+22\\\\a=53.35[/tex]

Thus, the value of a is 53.35.

(b)

Compute the value of a as follows:

[tex]P(X< a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.49\times 33=[x]^{a}_{22}\\\\16.17=a-22\\\\a=16.17+22\\\\a=38.17[/tex]

Thus, the value of a is 38.17.

(c)

Compute the value of a as follows:

[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.85=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.85\times 33=[x]^{55}_{a}\\\\28.05=55-a\\\\a=55-28.05\\\\a=26.95[/tex]

Thus, the value of a is 26.95.

(d)

Compute the value of a as follows:

[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.89=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.89\times 33=[x]^{55}_{a}\\\\29.37=55-a\\\\a=55-29.37\\\\a=25.63[/tex]

Thus, the value of a is 25.63.

(e)

Compute the value of a as follows:

[tex]P(1.83\leq X\leq a)=\int\limits^{a}_{1.83} {\frac{1}{33}} \, dx \\\\0.31=\frac{1}{33}\cdot \int\limits^{a}_{1.83} {1} \, dx \\\\0.31\times 33=[x]^{a}_{1.83}\\\\10.23=a-1.83\\\\a=10.23+1.83\\\\a=12.06[/tex]

Thus, the value of a is 12.06.

Answer:

x = 0,00375 mm

Step-by-step explanation:

a) El factor de ampliación es 400/1   es decir el tamaño real se verá ampliado 400 veces mediante el uso del microscopio

b) De acuerdo a lo establecido en la respuesta a la pregunta referida en a (anterior) podemos establecer una regla de tres, según:

Si al microscopio el tamaño de la célula es 1,5 mm, cual será el tamaño verdadero ( que es reducido 400 en relación al que veo en el microscopio)

Es decir     1,5 mm      ⇒    400

                    x (mm)    ⇒       1 (tamaño real de la célula)

Entonces

x  =  1,5 /400

x = 0,00375 mm

Answer:

x = 28.01t,

y = 10.26t - 4.9t^2 + 2

Step-by-step explanation:

If we are given that an object is thrown with an initial velocity of say, v1 m / s at a height of h meters, at an angle of theta ( θ ), these parametric equations would be in the following format -

x = ( 30 cos 20° )( time ),

y = - 4.9t^2 + ( 30 cos 20° )( time ) + 2

To determine " ( 30 cos 20° )( time ) " you would do the following calculations -

( x = 30 * 0.93... = ( About ) 28.01t

This represents our horizontal distance, respectively the vertical distance should be the following -

y = 30 * 0.34 - 4.9t^2,

( y = ( About ) 10.26t - 4.9t^2 + 2

In other words, our solution should be,

x = 28.01t,

y = 10.26t - 4.9t^2 + 2

These are are parametric equations

Answer:

Question 2

Step-by-step explanation:

2) The time when she woke up was -  3° C

During nature walk, temperature got 3° C warmer than when she woke up.

So, temperature during nature walk = - 3 + 3 = 0° C

Answer:

81.23 ft and 77.88 ft long

Step-by-step explanation:

The sum of the internal angles of a triangle is 180 degrees, the missing angle is:

[tex]a+b+c=180\\a+23+22=180\\a=135^o[/tex]

According to the Law of Sines:

[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}= \frac{C}{sin(c)}[/tex]

Let A be the side that is 147 feet long, the length of the other two sides are:

[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}\\B=\frac{sin(23)*147}{sin(135)}\\B=81.23\ ft\\\\\frac{A}{sin(a)}= \frac{C}{sin(c)}\\C=\frac{sin(22)*147}{sin(135)}\\C=77.88\ ft[/tex]

The other two sides are 81.23 ft and 77.88 ft long

Answer:

We conclude that the rate of inaccurate orders is greater than ​10%.

Step-by-step explanation:

We are given that in a study of the accuracy of fast food​ drive-through orders, one restaurant had 40 orders that were not accurate among 307 orders observed.

Let p = population proportion rate of inaccurate orders

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 10%     {means that the rate of inaccurate orders is less than or equal to ​10%}

Alternate Hypothesis, [tex]H_A[/tex] : p > 10%      {means that the rate of inaccurate orders is greater than ​10%}

The test statistics that will be used here is One-sample z-test for proportions;

                          T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of inaccurate orders = [tex]\frac{40}{307}[/tex] = 0.13

           n = sample of orders = 307

So, the test statistics =  [tex]\frac{0.13-0.10}{\sqrt{\frac{0.10(1-0.10)}{307} } }[/tex]  

                                    =  1.75

The value of z-test statistics is 1.75.

Also, the P-value of the test statistics is given by;

            P-value = P(Z > 1.75) = 1 - P(Z [tex]\leq[/tex] 1.75)

                          = 1 - 0.95994 = 0.04006

Now, at 0.05 level of significance, the z table gives a critical value of 1.645  for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 1.75 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the rate of inaccurate orders is greater than ​10%.

Answer:

[tex]\boxed{\sf \ \ \ x = 2 \ \ and \ \ y = 5 \ \ \ }[/tex]

Step-by-step explanation:

hello, we have two equation

(1) x + 4y = 22

(2) 2x + y = 9

let's multiply (1) by 2 and subtract (2)

2x + 8y - (2x + y) = 2*22 - 9 = 44 - 9 = 35

<=> 2x + 8y -2x -y = 35

<=> 7y = 35

<=> y = 35/7 = 5

we replace this value in (1) and it comes

x + 4*5 = 22

<=> x = 22 - 20 = 2

so the solution is

x = 2 and y = 5

hope this helps

Answer:

Step-by-step explanation:

Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...

  y = (300 -2x)/3

And the enclosed area is ...

  A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)

This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.

The maximum area is enclosed when the dimensions are ...

  50 ft by 75 ft

That maximum area is 3750 square feet.

_____

Comment on the solution

The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).