Solve x2 – 8x + 15 < 0. Select the critical points for the inequality shown. –15 –5 –3 3 5

Answer:

  y = 3x +5

Step-by-step explanation:

The equation of a perpendicular line can be formed by swapping the x- and y-coefficients, and negating one of them. The constant in the equation will be chosen to make the equation true at the given point.

The desired equation in the given standard form will be ...

  3x -y = c . . . . . . for some new constant c

Note that we have kept the x-coefficient positive, and have negated the y-coefficient.

The new constant will make the equation true at the point (-1, 2):

  3(-1) -(2) = c = -5

So, the standard-form equation is ...

  3x -y = -5

The answer form suggests you want to solve this for y. Adding y+5 to both sides will give the form you want:

  3x -y +(y+5) = -5 +(y+5)

  3x +5 = y

  y = 3x +5

Answer:

1/x - 3

Step-by-step explanation:

The number is x.

The reciprocal of the number is 1/x.

3 is subtracted from the reciprocal of a number.

1/x - 3

Step-by-step explanation:

a ) Solution,

[tex] = \frac{7}{8} \div \frac{9}{10} \\ [/tex]

[tex] = \frac{7}{8} \times \frac{10}{9} \\ [/tex]

[tex] = \frac{70}{72} \\ [/tex]

Change into lowest term....

[tex] = \frac{35}{36} \\ [/tex]

Answer:

94 hamburgers

Step-by-step explanation:

Let's solve this question through the use of equations.

Start by defining the variables used.

Let the number of hamburgers and cheeseburgers sold on Friday be h and c respectively.

Form 2 equations using the given information.

Given that the total sold is 376,

h +c= 376 -----(1)

The number of cheeseburgers sold was thrice the number of hamburgers sold.

c= 3h -----(2)

Solving by substitution:

Substitute (2) into (1):

h +3h= 376

Now that we have an equation expressed only in terms of h, we can find the value of h.

4h= 376

Divide both sides by 4:

h= 376 ÷4

h= 94

Thus, 94 hamburgers were sold on Friday.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Find the equation of the line, with the info given.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

The formula used in this problem is,

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[tex]\bf{y-(-1)=3(x-3)[/tex] | simplify

[tex]\bf{y+1=3(x-3)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                         [tex]\bf{=y+1=3(x-3)}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Answer:

x = 2 , y = 7

Step-by-step explanation:

Since

y-3x = 1

y = 3x+1 - equation 1

2y-x = 12 - equation 2

Since we are using substitution method,

we will substitute equation 1 into equation 2.

[tex]2(3x + 1) - x = 12 \\ 6x + 2 - x = 12 \\ 5x + 2 = 12 \\ 5x = 12 - 2 \\ 5x = 10 \\ x = \frac{10}{5} \\ = 2[/tex]

Now we substitute x into equation 1 to find y.

[tex]y = 3(2) + 1 \\ = 6 + 1 \\ = 7[/tex]

Therefore x = 2, y = 7.

2t + 4 < -8

2t < -12

t < -6

For the inequality to be true, t must be a number that is less than -6.

Hope this helps!

[tex]7x^2 = -12-5x\\\\7x^2 + 5x+12=0\\\\x=\frac{-5 \pm \sqrt{5^{2}-4(7)(12)}}{2(7)}\\\\\boxed{x=\frac{-5 \pm i \sqrt{311}}{14}}[/tex]

Answer:

1/36

Step-by-step explanation:

There is an 1/6 chance of rolling 1 the first time and 1/6 chance of rolling a 4 the second time. 1/6 * 1/6 = 1/36 chance of rolling a 1 then 4.

Answer: 112.5 square cm

Step-by-step explanation:

The area of the rectangle is [tex](20)(9)=180[/tex] square cm.

The area of the white triangle is [tex]\frac{1}{2}(9)(20-3-2)=67.5[/tex] square cm.

So, the area of the shaded region is [tex]180-67.5=112.5[/tex] square cm.

Step-by-step explanation:

Answer :- Amount (after 11 years) = $4522.11

Answer:

54

Step-by-step explanation:

the plot of land is an isosceles triangle, meaning two sides and angles are the same in value.

height (h)= 24

base (b)= 36

length (l)= 30

solution

find the area of triangle using area=half the product of the base and height.

A=1/2(36×24)

A= 216 square feet.

each tree needs 8 square feet

therefore using ratio and proportion,

1 tree= 8 square feet

x trees= 216 square feet

cross multiply and it'll be

216/8=x

therefore x= 54 trees

Answer:

Step-by-step explanation:

1) List the factors of each number.

Factors of 6 : 1, 2, 3, 6

Factors of 42 : 1, 2, 3, 6, 7, 14, 21, 42

Factors of 18 : 1, 2, 3, 6, 9, 18

2) Find the largest number that is shared by all rows above. This is the GCF.

GCF = 6

Answer:

a

Step-by-step explanation:

The midline is at y=2.

Also, since there is no horizontal shift amongst the remaining options, we know that since y=2 when x=0, this means it must be a sine curve.

This means the answer is a.

Hello!

Simplifying :

⇒ 4m + 4m + 4m + 4m

⇒ 4(4m)

None of the above

The amount that the designer will have to pay in FICA taxes is:$3,978.

FICA taxes comprises of:

Social Security tax= 6.2%

Medicare tax= 1.45%

Hence:

FICA taxes=($52,000×6.2%)+($52,000×1.45%)

FICA taxes=$3,224+$754

FICA Taxes=$3,978

Therefore the amount that the designer will have to pay in FICA taxes is:$3,978.

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Answer: horizontal

Step-by-step explanation: there going across sideways and not up and down

Answer:

6 yds^3

Step-by-step explanation:

I find these easiest if you put all of the dimensions into yards and then multiply

18 ft =  6 yds

36 ft = 12 yds

3 in = 3/36 yds    = 1/12 yds     now multiply them together

6 x 12 x 1/12 = 6 yds^3

Answer:

[tex]108 m^{2}[/tex]

Step-by-step explanation:

[tex]27\times4=108[/tex]

Answer:

27π cm² or 84.8 cm²

Explanation:

[tex]\sf Formula \ for \ area \ of \ sector = \dfrac{\theta}{360 } \ x \ \pi (radius)^2[/tex]

Shaded region angle: 360° - 90° = 270°

 Given radius: 6 cm

Applying formula:

[tex]\rightarrow \sf \dfrac{270}{360} \ x \ \pi (6)^2[/tex]

[tex]\rightarrow \sf 27\pi[/tex]

[tex]\rightarrow \sf 84.823 \ cm^2[/tex]

[tex]\rightarrow \sf 84.8 \ cm^2 \quad (rounded \ to \ nearest \ tenth)[/tex]

The value of (38)-2⁢(13⋅38)3⁢(13)4. is -154090

The expression is given as:

(38)-2⁢(13⋅38)3⁢(13)4.

Rewrite properly as:

(38) - 2 * ⁢(13 * 38) * 3 * ⁢(13) * 4.

Evaluate the products in the bracket

(38) - 2 * ⁢(494) * 3 * ⁢52

Further, expand

38 - 154128

Evaluate the difference

-154090

Hence, the value of (38)-2⁢(13⋅38)3⁢(13)4. is -154090

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Answer:

Step-by-step explanation:

[tex]y'' + \omega^2 y = 0[/tex]

has characteristic equation

[tex]r^2 + \omega^2 = 0[/tex]

with roots at [tex]r = \pm\sqrt{-\omega^2} = \pm|\omega|i[/tex], hence the characteristic solution is

[tex]y = C_1 e^{i|\omega|x} + C_2 e^{-i|\omega|x}[/tex]

or equivalently,

[tex]y = C_1 \cos(|\omega|x) + C_2 \sin(|\omega|x)[/tex]

With the given boundary conditions, we require

[tex]y(0) = 0 \implies C_1 = 0[/tex]

and

[tex]y'(\pi) = 0 \implies -|\omega| C_1 \sin(|\omega|\pi) + |\omega| C_2 \cos(|\omega|\pi) = 0[/tex]

With [tex]C_1=0[/tex], the second condition reduces to

[tex]|\omega| C_2 \cos(|\omega|\pi) = 0[/tex]

Assuming [tex]C_2\neq0[/tex] (because we don't want the trivial solution [tex]y=0[/tex]), it follows that

[tex]\cos(|\omega|\pi) = 0 \implies |\omega|\pi = \pm\dfrac\pi2 + 2n\pi \implies |\omega| = 2n\pm\dfrac12[/tex]

where [tex]n[/tex] is an integer. In order to ensure [tex]|\omega|\ge0[/tex], we must have [tex]n\ge1[/tex] if [tex]|\omega|=2n-\frac12[/tex], or [tex]n\ge0[/tex] if [tex]|\omega|=2n+\frac12[/tex].

Answer:

26

Step-by-step explanation:

(3a+2)/(a+4) = 8/3

(3a+2) = (8/3)(a+4)

(3a+2) = a*8/3 + 4*8/3

(3a+2) = 8a/3 + 32/3

3a - 8a/3 = 32/3 - 2

9a/3 - 8a/3 = 32/3 - 6/3

9a - 8a = 32 - 6

a = 26

Check:

(3*26 + 2) / (26+4) = 8/3

(78+2) / 30 = 8/3

80 / 30 = 8/3

Answer:

(19-12):12*100 =

(19:12-1)*100 =

158.33333333333-100 = 58.33

Answer:

84 degrees

Step-by-step explanation:

Angle A = 83 degrees

Angle B = x degrees

Angle C = 135 degrees

Angle CDE = 122 degrees

We know that the four inner corners of a quadrilateral should add up to 360 degrees. Two supplementary angles will add up to 180 degrees. Adjacent angles on a straight line will always be supplementary. Knowing this, just solve for <ADC and add that amount to <A and <C. Then, subtract that sum from 360 degrees.

<ADC = 180-122 = 58

58+83+135 = 276

360-276 = 84 degrees

The total number of pies they made altogether is 100.

In order to determine this value, add the number of blueberry pies with the number of apple pies.  Addition is the mathematical operation that is used to determine the sum of two or more numbers.

The total number of pies = 55 + 45 = 100 pies

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Answer:

  (d) Gauss-Jordan Elimination

  80 carnations; 50 roses; 70 daisies

Step-by-step explanation:

The given relations can be written as equations, which can be expressed as one matrix equation. Any of the methods listed can be used to solve the matrix equation.

If we let c, r, d represent numbers of carnations, roses, and daisies ordered, respectively, then the given relations can be written as ...

  c + r + d = 200 . . . . . . 200 flowers were ordered

  0c -r +d = 20 . . . . . . . . . . . . . 20 more daisies than roses were ordered

  1.50c +5.75r +2.60d = 589.50 . . . . . the total value of the order

Written as a matrix equation, it will be of the form ...

  AX = B

where A is the square matrix of variable coefficients, X is the column vector of variables, and B is the column vector of equation right-side constants. This is the matrix equation:

  [tex]\left[\begin{array}{ccc}1&1&1\\0&-1&1\\1.50&5.75&2.60\end{array}\right] \left[\begin{array}{c}c\\r\\d\end{array}\right] =\left[\begin{array}{c}200\\20\\589.50\end{array}\right][/tex]

The mathematical operations required to find the equation solution can be briefly described as ...

Inverse Matrices

The coefficient matrix is inverted and multiplied by the constant column vector:

  [tex]X=A^{-1}B[/tex]

The inversion operation requires computation of 10 determinants, of which 9 are of 2×2 matrices. That's a total of about 39 multiplications, 9 divisions, and 20 additions.

Cramer's Rule

Using Cramer's rule requires computation of 4 determinants of 3×3 matrices. The total number of operations comes to about 48 multiplications, 3 divisions, and 20 additions.

Gaussian Elimination

To obtain the upper triangular matrix that results from Gaussian Elimination requires about 11 multiplications, 11 additions, and 2 divisions. This finds the value of one variable, but the others must be found by substitution into the remaining two equations, requiring an additional 3 multiplications and 3 additions.

Gauss-Jordan Elimination

This method starts with an augmented matrix that appends column vector B to the square matrix A. The result of this is shown in the attachment. It is a diagonal matrix with the variable values a direct result of the matrix operations. The calculator's RREF( ) function performs matrix row operations to transform the augmented matrix to this Reduced Row-Echelon Form. About 6 multiplications, 6 additions, and 4 divisions are required.

Clearly, Gauss-Jordan Elimination is the method that requires the least computational work, so it would probably be used for this question.

The attachment shows the order to be ...

__

Additional comment

The estimates of computational load presented by each of the solution methods are not intended to be exact counts. For this specific problem, some of the operations can be avoided due to the fact that some coefficients are already 1. Also, some computations are not needed simply because they are intended to produce an outcome that is already known. The intention is to give an idea of the relative difficulty of using these different methods.

In some cases, computationally less-efficient methods may be preferred because they are simpler to describe.

A bisector is a line that divides either a given line or an angle into two equal parts. The answer to the given question is in the attachments to this answer.

The process of bisection implies dividing a given angle or line into two equal parts. Thus a bisector should be constructed.

The construction required is as given below:

For figure 1:

For figure 2:

For figure 3:

The required construction is as shown in the attachments to this answer.

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