Solve the following proportion.
х
42
35
10

9514 1404 393

Answer:

  (x, y, z) = (5, 11, 6)

Step-by-step explanation:

To solve this problem, you need to understand "row operations". The ones we're concerned with are multiplying a row by a scalar, and adding rows together.

You also need to understand what the solution looks like, and the usual way that is achieved. The solution will have the 3×3 matrix left of the vertical line be a diagonal of 1s (the identity matrix). Then the numbers to the right of the vertical line represent the solution.

__

In the following, we will use the notation [a]+b[c]⇒[d] to mean that row 'a' is added to the product of row 'c' and the scalar 'b' and that sum replaces row [d]. Multiplying a row by a scalar multiplies each element in the row by that scalar.

The first several operations look like this. Notice we have made the upper left 2×2 matrix an identity matrix. Steps will continue to take care of the 3rd column.

  [tex]\left[\begin{array}{ccc|c}1&1&1&22\\6&1&8&89\\-6&4&4&38\end{array}\right] \qquad\text{given}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&-5&2&-43\\0&5&12&127\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ 6[1]+[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ $-\frac{1}{5}$[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[1]-[2]$\rightarrow$[1]}[/tex]

Now, we normalize the third column.

  [tex]\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&1&6\end{array}\right] \qquad\text{$\frac{1}{14}$[3]$\rightarrow$[3]}\\\\\left[\begin{array}{ccc|c}1&0&0&5\\0&1&0&11\\0&0&1&6\end{array}\right] \qquad\text{$-\frac{7}{5}$[3]+1$\rightarrow$[1];\ $\frac{2}{5}$[3]+[2]$\rightarrow$[2]}[/tex]

This is the target of our row operations. It tells us the solution to the system of equations is ...

  (x, y, z) = (5, 11, 6)

_____

A number of online calculators and phone or tablet apps are available for putting a coefficient matrix into this "reduced row-echelon form." Many graphing calculators will do this, too.

In the end, this is not terribly different from ad hoc solution using "elimination" methods. That is precisely what we did when we created the zeros in the first two columns of row 3.

Answer:

amplitude = |-4| =4

period = 2 pi/3

phase shift = pi / 3

midline = 2

Step-by-step explanation:

f(x)=-4 cos (3x-pi)+2

The equation is in the form

f(x) = a cos (bx -c) +d  where |a| is the amplitude

period  is 2 pi /b

phase shift:  c/b

midline = d

amplitude = |-4| =4

period = 2 pi/3

phase shift = pi / 3

midline = 2

Answer:

Equation: y=2x-1

Slope: 2

y-intercept: -1

Step-by-step explanation:

Hi there!

We are given the points (-1, -3) and (-2, -5). We need to find the slope, equation of the line, and the y intercept of the line

First, let's find the slope

The formula for the slope (m) calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where ([tex]x_1[/tex],[tex]y_1[/tex]) and ([tex]x_2[/tex],[tex]y_2[/tex]) are points

We have everything we need for the formula, but let's label the values of the points to avoid any confusion

x1=-1

y1=-3

x2=-2

y2=-5

Now substitute into the formula (remember: the formula has SUBTRACTION):

m=[tex]\frac{-5--3}{-2--1}[/tex]

simplify

m=[tex]\frac{-5+3}{-2+1}[/tex]

add

m=[tex]\frac{-2}{-1}[/tex]

divide

m=2

So the slope is 2

Now let's find the equation of the line

The question asks for it to be in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We calculated the slope from earlier, so let's substitute that into the equation

y=2x+b

Now we need to find b

The equation will pass through both (-1, -3) and (-2, -5) so we can use either one of them to solve for b (doesn't matter which one)

Let's take (-1, -3) as an example

substitute -1 as x and -3 as y into the equation

-3=2(-1)+b

multiply

-3=-2+b

Add 2 to both sides

-1=b (the value of the y intercept!)

Substitute -1 as b into the equation

y=2x-1

We found everything needed for this problem

Hope this helps!

Angle 2 and Angle 4 are same-side interior angles, which are supplementary.

(2x + 10) + (4x + 80) = 180

6x + 90 = 180

6x = 90

x = 15

Hope this helps!

Answer:

X = 15

Step-by-step explanation:

Angle 2 = Angle 3 since they are alternate angles

Now, angle 3 and 4 should add up to 180 since they are on a straight line

∴ (2x + 10) + (4x + 80) = 180

   6x + 90 = 180

     6x = 180 - 90

     6x = 90

       x = 15

HOPE THIS HELPS

Answer:

Step-by-step explanation:

Answer:

The relative frequency is found by dividing the class frequencies by the total number of observations

Step-by-step explanation:

Relative frequency measures how often a value appears relative to the sum of the total values.

An example of how relative frequency is calculated

Here are the scores and frequency of students in a maths test

Scores (classes)              Frequency                Relative frequency

0 - 20                                10                               10 / 50 = 0.2

21 - 40                               15                               15 / 50 = 0.3

41 - 60                               10                               10 / 50 = 0.2

61 - 80                                5                                 5 / 50  = 0.1

81 - 100                             10                                10 / 50 = 0.2

                                          50                                               1

From the above example, it can be seen that :

Answer: Rs 25,000

Step-by-step explanation:

Given

Retailer sold an electric iron to a customer at a loss of 10%

Suppose the Cost price of iron is [tex]x[/tex]

So, selling price is [tex]0.9x[/tex]

This price must be equal to [tex]25425[/tex]+ VAT

[tex]\Rightarrow 0.9x=25425-0.13(0.9x)\\\Rightarrow 0.9x+0.117x=25425\\\Rightarrow 1.017x=25425\\\Rightarrow x=\text{Rs }25,000[/tex]

Thus, the cost price is [tex]Rs.25,000[/tex]

Answer:

5%

Step-by-step explanation:

First, find the amount of tax:

5250 - 5000

= 250

Divide this by the original price of $5000 to find the percent of import tax:

250/5000

= 0.05

So, the percent of import tax is 5%

Answer:

Independent means that one has no effect on the other. Exclusive means one cannot happen alongside the other. In simpler terms, independent events can be thought of as the chance it'll rain and how many people are flossing their teeth in the morning. Both happen, but neither one impacts the other.

Exclusive, on the other hand, means only one can happen. Lets say at nine in the evening your favorite show is on. However, you have an early morning and should be asleep by nine. You cannot both be asleep and watching your favorite show, and so these events are exclusive.

Answer:

x ≈ 63.27

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan49° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{EF}{DE}[/tex] = [tex]\frac{x}{55}[/tex] ( multiply both sides by 55 )

55 × tan49° = x , then

x ≈ 63.27 ( to the nearest hundredth )

Answer:

• Shanna had $10 in her piggy bank and earned $5 each week in allowance.

Step-by-step explanation:

Week 0 dollars = 10

This means Shanna had $10 her piggy bank before the week started

Week 2 dollars = 20

Her account has increased from 10 to 20 dollars in two weeks. This means she is earning

Amount earned per week = change in earnings / change in week

= 20 dollars - 10 dollars / Week 2 - week 1

= 10 dollars / 2 weeks

= 5 dollars per week

Amount earned per week = $5

Therefore,

• Shanna had $10 in her piggy bank and earned $5 each week in allowance

Answer:

option b

Step-by-step explanation:

cuz its the only one that makes sense

Answer:

9/16

Step-by-step explanation:

3/8 ÷ 2/3

Copy dot flip

3/8 * 3/2

Multiply the numerators

3*3=9

Multiply the denominators

8*2 = 16

Numerator over denominator

9/16

Answer:

-2 is an extraneous solution because it creates 0 in the denominator.

There is one acceptable solution to the equation

Step-by-step explanation:

x² + 5x + 6 = x² + 2x + 3x + 6

                  = x(x + 2) + 3(x + 2)

                  = (x + 2)(x + 3)

[tex]\frac{x}{x+2}+\frac{2}{x^{2}+5x+6}=\frac{5}{(x+3)}\\\\\frac{x}{x+2}+\frac{2}{(x+2)(x+3)}=\frac{5}{(x+3)}\\\\\frac{x*(x+3)}{(x+2)(x+3)}+\frac{2}{(x+2)(x+3)}=\frac{5*(x+2)}{(x+3)(x+2)}\\\\\frac{x^{2}+3x+2}{(x+2)(x+3)}=\frac{5x+10}{(x+3)(x+2)}\\\\[/tex]

x² + 3x + 2 = 5x + 10

x² + 3x - 5x + 2 - 10 = 0

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

x(x + 2) - 4(x + 2) = 0

(x + 2)(x - 4) = 0

x +2 = 0    or x - 4 = 0

x =  - 2    or x = 4

Answer:

10^-5

10^-5 = 1/100,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{1}{100000}=\frac{1}{10^{5}}=10^{-5}\\\\\\\frac{1}{a^{m}}=a^{-m}[/tex]

Answer:

320

Step-by-step explanation:

r = 4, so 2 x 4 = 8.

s = 6 and t = 3, so 6 x 3 = 18. 18 squared is 324.

u = 12, so 8 + 324 - 12, which equals 320.

Answer:

50/sin90=x/sin45

x=35.36cm

Answer:

158.33 minutes = 2.63 hours

Step-by-step explanation:

Sagot:

100 cm

Hakbang-hakbang na paliwanag:

Kung ganoon :

Distansya na sakop ng Ruben = 900 centimetri

Distansya na sakop ng Jamie = 10 metro

Pagko-convert sa centimeter:

100 cm = 1 m

x cm = 10 m

Paggamit ng multiplikasyon ng krus:

x = 100 * 10

x = 1000 cm.

Dahil dito Distansya ni Jamie = 1000 cm

Distansya sa pagitan ng Jamie at Ruben;

1000 cm - 900 cm = 100 cm

Answer:

I would say D is your answer

Step-by-step explanation:

Answer:

the fourth one

use mathaway its like my best friend for math!!!

Step-by-step explanation:

Answer:

b translation

Step-by-step explanation:

Dilation means that it gets bigger or smaller

translation means a shift

reflections means that it flips across a line of symmetry

rotation means that it rotates across a point

We shifted the figure down and to the right.  It appears to be the same size and shape

I would go with a translation

Answer:

[tex]a^{6} a^{9} = a^{15}[/tex]

Step-by-step explanation:

is this the question ///

Write the expression a^15 as a product of two exponents with the same base, one of which equals: a^6

if so ...

[tex]a^{6} a^{9} = a^{15}[/tex]

Graph exists as an illustration of any object or a physical format by dots, lines, etc.

The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could also describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists in a particular case of the graph of an equation.

A function is defined as a connection between a set of inputs containing one output each. In simple words, a function exists as an association between inputs where each input is connected to exactly one output. Every function includes a domain and codomain or range. A function exists generally represented by f(x) where x is the input.

From the given figure,

Graph 1 exists a function.

Graph 2 exists a function.

Graph 3 doesn't exist as a function.

Graph 4 exists a function.

Graph 5 doesn't exist as a function.

Graph 6 doesn't exist as a function.

Hence, Graph exists as a representative of any object or a physical design by dots, lines, etc.

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If 180° < θ < 270°, then 90° < θ/2 < 135°, which places θ/2 in the second quadrant so that sin(θ/2) > 0 and cos(θ/2) < 0.

Recall that

cos²(θ/2) = (1 + cos(θ))/2

==>   cos(θ/2) = -√[(1 + (-15/17))/2] = -1/√17

and

sin²(θ/2) = (1 - cos(θ))/2

==>   sin(θ/2) = +√[(1 - (-15/17))/2] = 4/√17

Then

tan(θ/2) = sin(θ/2) / cos(θ/2)

… = (4/√17) / (-1/√17)

… = -4

Answer:

cos A = 7/25

Step-by-step explanation:

Since we are given a right triangle, we can use trig functions

cos A = adj side/ hypotenuse

cos A = 7/25

Answer:

[tex]\boxed{\sf cos\ A =\frac{7}{25}}[/tex]

Step-by-step explanation:

We need to find out the value of cos A using the given triangle . Here we can see that the sides of the triangle are 7 , 25 and 24 .

We know that the ratio of sine is base to hypontenuse .

[tex]\sf\longrightarrow cos\theta =\dfrac{ base}{hypontenuse}[/tex]

Here we can see that the side along the angle A is 7 , therefore the base of the triangle is 7. And the side opposite to 90° angle is 25 . So it's the hypontenuse . On using the ratio of sine ,

[tex]\sf\longrightarrow cos \ A =\dfrac{ b}{h}=\dfrac{AB}{AC}[/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow \boxed{\blue{\sf cos \ A =\dfrac{7}{25}}}[/tex]

Hence the required answer is 7/25.

Answer:

It's C

X = -3

Step-by-step explanation:

Edge 2022

The equation represents the directrix is x=-3.

the correct option is (C).

A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix . The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.

given: y²=12x

y²=4*3*x

Here a=3

So, x+a=0

x+3=0

x=-3.

Hence, the directrix of parabola is: x=-3

Learn more about directrix here:

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