Proportions in similar triangles

Answer:

First, we write the augmented matrix.

⎡

⎢

⎣

1

−

1

1

2

3

−

1

3

−

2

−

9

|

8

−

2

9

⎤

⎥

⎦

[1−1123−13−2−9 | 8−29]

Next, we perform row operations to obtain row-echelon form.

−

2

R

1

+

R

2

=

R

2

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

3

−

2

−

9

|

8

−

18

9

⎤

⎥

⎦

−

3

R

1

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

0

1

−

12

|

8

−

18

−

15

⎤

⎥

⎦

−2R1+R2=R2→[1−1105−33−2−9|8−189]−3R1+R3=R3→[1−1105−301−12|8−18−15]

The easiest way to obtain a 1 in row 2 of column 1 is to interchange

\displaystyle {R}_{2}

R 2

and

\displaystyle {R}_{3}

R 3

.

Interchange

R

2

and

R

3

→

⎡

⎢

⎣

1

−

1

1

8

0

1

−

12

−

15

0

5

−

3

−

18

⎤

⎥

⎦

InterchangeR2andR3→[1−11801−12−1505−3−18]

Then

−

5

R

2

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

57

|

8

−

15

57

⎤

⎥

⎦

−

1

57

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

1

|

8

−

15

1

⎤

⎥

⎦

−5R2+R3=R3→[1−1101−120057|8−1557]−157R3=R3→[1−1101−12001|8−151]

The last matrix represents the equivalent system.

x

−

y

+

z

=

8

y

−

12

z

=

−

15

z

=

1

x−y+z=8 y−12z=−15 z=1

Using back-substitution, we obtain the solution as

\displaystyle \left(4,-3,1\right)

(4,−3,1)

Answer:

Step-by-step explanation:

Answer:

A.) Paul

B.) Plain

C.) Paul

Step-by-step explanation:

Paul: Shirt - Striped; Jumper - Spotted; Towel - Plain

Kerry: Shirt - Plain; Jumper - Striped; Towel - Spotted

Sandra: Shirt - Spotted; Jumper - Plain; Towel - Striped

Hope this helps! Have a nice dayy! :)

Answer:

The length if the garden is 21 meters.

The width of the garden is 5.25 meters.

If the scale changes to 1 cm : 9 meters, the new length of the garden is 63 meters and the new width of the garden is 15.75 meters.

The new length of the garden is 3 times as long as the original length of the garden.

Answer:

D/4 - 21

C/3 - 5.25

D/4 - 63

C/3 - 15.75

B/2 - 3

Step-by-step explanation:

Answer:

yes.

Step-by-step explanation:

it is correct

Answer: Yes, this is correct.

Answer: Thought I’d return the favor and help u with this question! But anyways, the axis of symmetry is at x = -3.

Explanatio: This can be found by looking at the basic form of vertex form:

y = (x - h)^2 + k

In this basic form the vertex is (h, k). By looking at what is plugged into the equation, it is clear that h = -3 and k = -4. This means the vertex is at (-3, -4).

It is a fact that the axis of symmetry is a vertical line of x = (vertex value of x). So we can determine that the axis of symmetry is at x = -3

i hope this helps u

Answer:

x ≈ 16.5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 70°

Opposite Leg = x

Adjacent Leg = 6

Step 2: Solve for x

Answer:

What is the slope of the line that is parallel to the given line and passes through the given point?

-1/4

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point?

y + 4 = -1/4(x + 2)

What is the y-intercept of the line that is parallel to the given line and passes through the given point?

-9/2

Step-by-step explanation:

Good lcuk for anyone who needs this<3

The equation of the line in point slope for is expressed as [tex]y - 2 = 3/2(x - 2)[/tex]

Since the line cross the y-axis at -1, hence the y-intercept of the line that is parallel to the given line and passes through the given point is (0, -1)

The equation of a line in point-slope form is expressed as:

y - y0 = m(x - x0)

m is the slope

(x0, y0) is any point on the line

Using the coordinate points (2, 2) and (-2, -4)

Determine the slope

Slope = -4-2/-2-2
Slope = -6/-4
Slope = 3/2

Using the point (2, 2), the equation of the line in point slope for is expressed as:

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

Since the line cross the y-axis at -1, hence the y-intercept of the line that is parallel to the given line and passes through the given point is (0, -1)

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Answer:

90 hours of training would you need to pay

Answer:

90hours

Step-by-step explanation:

Addition of 10 hours= Addition of 150$

an=a+(n-1)d

2450=1250+(n-1)(150)

120/15=n-1

8+1=n

n=9

and 9x10=90 (each n=10hours)

Thus:

B. 90 hours

Brianliest please

Answer: Graph A

Step-by-step explanation:

1) angle HJI

2) angle IJH

Answer:

82 kg

Step-by-step explanation:

To find the mean of a set of values, we must add them up and divide by the number of values.

Step 1, adding the values:

[tex]75+68+78+82+85+90+88+92+76=\\734[/tex]

Step 2, dividing by the # of terms:

There are 9 terms in total.

[tex]\frac{734}{9} =\\81.556[/tex]

To the nearest kilogram, we can round 81.556 into 82.

The mean mass of the 9 men was [tex]\fbox{82}[/tex] kg.

I hope this helps! Let me know if you have any questions :)

Answer:

Vertex: (1, 6)

Axis of symmetry: x = 1

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

I was stumped on this question too so I figured I might as well learn how to do it. All you have to do is divide the middle number (16x) by 2. Pretty easy! Hope this helps anyone who needs it!

Answer:

D = [tex]\sqrt{\frac{216W}{35L} }[/tex]

Step-by-step explanation:

From the given question, the expression showing the relationship among the weight, length and diameter of the metal bar is;

W [tex]\alpha[/tex] L[tex]D^{2}[/tex]

W = kL[tex]D^{2}[/tex]

where k is the constant of proportionality.

When W = 140, D = 4 and L = 54, then;

140 = k(54)[tex](4)^{2}[/tex]

      = 864k

k = [tex]\frac{140}{864}[/tex]

  = [tex]\frac{35}{216}[/tex]

k = [tex]\frac{35}{216}[/tex]

⇒ W = [tex]\frac{35LD^{2} }{216}[/tex]

So that;

35L[tex]D^{2}[/tex] = 216W

[tex]D^{2}[/tex] = [tex]\frac{216W}{35L}[/tex]

D = [tex]\sqrt{\frac{216W}{35L} }[/tex]

Answer:

PRQ = 86 degrees

Answer:

[tex]Area = 52\sqrt3 \ ft^2[/tex]

Step-by-step explanation:

Area of trapezoid

                         [tex](\frac{a+ b}{2}) \times h[/tex]      -----------( 1 )

We will split the trapezoid into Triangle and rectangle. To find the height and full length of base.

[tex]sin 60 = \frac{opposite}{hypotenuse}[/tex]   [tex][ opposite \ in \ the \ equation \ \ is \ the \ height \ of \ the \ trapezoid ][/tex]

[tex]\frac{\sqrt3}{2} = \frac{opposite }{ 8}\\\\\frac{\sqrt3}{2} \times 8 = opposite\\\\4\sqrt3 = opposite[/tex]

Therefore, h = 4√3 ft

[tex]cos 60 = \frac{adjacent}{hypotenuse}[/tex]    [tex]adjacent \ in \ the\ equation \ is \ the\ base \ of \ the \ triangle ][/tex]

[tex]\frac{1}{2} = \frac{adjacent}{hypotenuse}\\\\\frac{1}{2} \times 8 = adjacent\\\\4 = adjacent[/tex]

Therefore, a = 11 feet, b = 11 + 4 = 15 feet

Substitute the values in the Area equation :

                                                [tex]Area = \frac{11 + 15}{2} \times 4 \sqrt3 = \frac{26}{2} \times 4\sqrt3 = 13 \times 4\sqrt3=52\sqrt3 \ ft^2[/tex]

Answer:

[tex]8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3 = -6m^6 - mn^5 - 5m^3n^3 + 14m^2n^4 + 8mn^5 + n^6[/tex]

Step-by-step explanation:

Given

[tex]8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3[/tex]

Required

Correctly combine the like terms

We have:

[tex]8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3[/tex]

Collect like terms (in decreasing degrees of m)

[tex]- 2m^6 - 4m^6 - mn^5- m^3n^3 - 4m^3n^3+ 5m^2n^4 + 9m^2n^4 + 8mn^5 + n^6[/tex]

[tex]-6m^6 - mn^5 - 5m^3n^3 + 14m^2n^4 + 8mn^5 + n^6[/tex]

So:

[tex]8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3 = -6m^6 - mn^5 - 5m^3n^3 + 14m^2n^4 + 8mn^5 + n^6[/tex]

Answer:

The sequence converges to 1.

Step-by-step explanation:

Sequence 2/4, 3/5, 4/6, 5/7

This sequence can be summarized as:

[tex]\sum_{n=0}^{\infty} \frac{n+2}{n+4}[/tex]

To test if it converges, we can calculate the limite of [tex]\frac{n+2}{n+4}[/tex] as n goes to infinite.

Limit:

[tex]\lim_{n \rightarrow \infty} \frac{n+2}{n+4}[/tex]

Considering only the terms with the highest exponent in the numerator and the denominator:

[tex]\lim_{n \rightarrow \infty} \frac{n+2}{n+4} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1[/tex]

Thus, the sequences converges to 1.

Answer:

1

----------

x+1

Step-by-step explanation:

2x+12

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

2x^2 + 14x+12

Factor

2(x+6)

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

2(x^2+7x+6)

2(x+6)

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

2(x+6)(x+1)

Cancel like terms

1

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

(x+1)

Solve for y in the first equation.

Answer:

[tex]P =5x-260[/tex]

Step-by-step explanation:

Given

[tex]R = 3x^2 + 4x - 60[/tex] --- Revenue

[tex]C = 3x^2 - x + 200[/tex] --- Cost

Required

The expression for profit (P)

This is calculated as:

[tex]P =R - C[/tex]

So, we have:

[tex]P =3x^2 + 4x - 60 - (3x^2 -x+200)[/tex]

Open bracket

[tex]P =3x^2 + 4x - 60 - 3x^2 +x-200[/tex]

Collect like terms

[tex]P =3x^2 - 3x^2+ 4x +x- 60-200[/tex]

[tex]P =5x-260[/tex]

If the profit is the difference between the revenue and the cost, 5x – 260  expression represents the profit. Correct option is 3.

The profit is calculated by subtracting the cost from the revenue. In mathematical terms, the profit (P) can be represented as:

Profit (P) = Revenue - Cost

Among the given options:

1. 3x - 260

2. 3x + 140

3. 5x - 260

4. 5x + 140

We need an expression where the first term represents the revenue and the second term represents the cost, so that when we subtract the cost from the revenue, we get the profit.

Option 3, 5x - 260, fits this pattern:

- Revenue: 5x

- Cost: 260

When we subtract the cost from the revenue:

Profit (P) = Revenue - Cost = 5x - 260

So, option 3, 5x - 260, is the expression that represents the profit.

To know more about profit:

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Complete question is:

If the profit is the difference between the revenue and the cost, what expression represents the profit?

1. 3x – 260

2. 3x + 140

3. 5x – 260

4. 5x + 140

Answer:

You can use similar processes when converting from smaller to larger units. When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide.

Example look at the pic please 7,225 cm = ___ m

Meters are larger than centimeters, so you expect your answer to be less than 7,225.

Using the factor label method, write 7,225 cm as a fraction and use unit fractions to convert it to m.

Cancel similar units, multiply, and simplify.

7,225 centimeters = meters

Answer:

Sample Response: If you move from smaller to larger units, divide by a power of 10 or move the decimal to the left. If you move from larger to smaller units, multiply by a power of 10 or move the decimal to the right.

Answer: C, You can tell the trend line is incorrect since all of the points are below it. A trend line should be in-between all of the points to give the best estimate.

Step-by-step explanation:

Answer:

Distance rode = 6 miles

Step-by-step explanation:

distance from home = 2 miles

remaining distance =  4 miles

The distance rode = 4 + 2 = 6 miles

Answer:

Girls: 50

Boys: 36

A) 60°

Step-by-step explanation:

86-14=72

72÷2=36

Girls=36+14=50

Boys=36

115+115+70=300

360-300=60°

Answer:

36 boys and 50 girls

the remaining angle measures 60°

Step-by-step explanation:

x = boy count

x + 14 = girl

x + x + 14 = 86

2x + 14 = 86

2x = 72

x = 36

x + 14 = 50

36 boys and 50 girls

the 4 angles of a quadrilateral = 360°

115° + 115° + 70° + x = 360°

300 + x = 360°

x = 360 - 300

x = 60°

The remaining angle measures 60°

Answer:

b

Step-by-step explanation:

Answer:

b......................

Step-by-step explanation:

.

Question options:

A. The mean is the best comparison of the measures of center.

B. The juniors tended to have higher essay scores than the sophomores.

C. The medians of both data sets are equal.

D. The interquartile range is the best comparison of the measure of variability.

E. A histogram is the best way to show that both distributions are nearly symmetric.

Answer:

B. The juniors tended to have higher essay scores than the sophomores.

C. The medians of both data sets are equal.

E. A histogram is the best way to show that both distributions are nearly symmetric.

Explanation:

A histogram is used to represent data in a bar graph like manner. In a histogram, the bars lie along the x axis, each within the range of intervals while the y axis is used to count the frequency of occurrence that determines the area of each bar in the graph. Using a histogram, we can find B, C, and E from the options given above.

Answer:

28 cm

Step-by-step explanation:

The perimeter (P) is the sum of the sides

P = LE + EF + ( FG + HI + JK ) + ( GH + IJ + KL )

   = 8 + 6 + 8 + 6

   = 28 cm