Find the area of the triangle.

A. 27.8km^2
B. 32.8 km^2
C.14.9 km^2
D. 54.8km^2

Answer:

The third option with the right angle

Step-by-step explanation:

By creating a perpendicular line through the line of reflection (the orange dotted line) and the point "D" we can measure the distance of D from the line of reflection. Then draw "D'" using the distance of the "D" from the line of reflection.

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:

Perimeter of ΔPRS = 35.91 units

Step-by-step explanation:

From the figure attached,

By applying triangle sum theorem in the given triangle PRS,

m∠P + m∠R + m∠S = 180°

45° + m∠R + 60° = 180°

m∠R = 75°

By applying sine rule,

[tex]\frac{\text{sinP}}{RS}= \frac{\text{sinS}}{PR}=\frac{\text{sinR}}{PS}[/tex]

[tex]\frac{\text{sin}(45^{\circ})}{10}= \frac{\text{sin}(60^{\circ})}{PR}=\frac{\text{sin}(75^{\circ})}{PS}[/tex]

[tex]\frac{\text{sin}(45^{\circ})}{10}= \frac{\text{sin}(60^{\circ})}{PR}[/tex]

PR = 12.25 units

[tex]\frac{\text{sin}(45^{\circ})}{10}=\frac{\text{sin}(75^{\circ})}{PS}[/tex]

PS = 13.66 units

Perimeter of triangle PRS = PR + PS + RS

                                            = 12.25 + 13.66 + 10

                                            = 35.91

Answer:

18c - 30d + 36

Step-by-step explanation:

To apply the distributive property, we must "distribute" (multiply) the outer term by the terms in the parentheses. In this case, the outer term is 6, and the inner terms are 3c, 5d, and 6. Then, if there's any like terms, you must combine them.

6(3c - 5d + 6)

(6 · 3c) + (6 · -5d) + (6 · 6)

18c + -30d + 36

As you can see, there's no like terms in this expression, so the equivalent expression to 6(3c - 5d + 6) is 18c + -30d + 36.

Answer:

-1

Step-by-step explanation:

We can use the slope formula since we are given two points

m = (y2-y1)/(x2-x1)

    = (-16- -10)/(8-2)

   = (-16+10)/(8-2)

   = -6/6

   = -1

Hello!

Answer: C. x² - 64 - 0

Good luck! :)

Answer:

$425

Step-by-step explanation:

Let x represent the number of bracelets made and let y represent the number of necklace made.

Since the craftsman has 1000 beads to work with, hence:

10x + 20y ≤ 1000    (1)

Also, the craftsman has 1600 minutes, hence:

10x + 40y ≤ 1600   (2)

From ploting equations 1 and 2 on the geogebra online graphing, we can see that the solution to the problem is (40, 30).

Since the bracelet costs $5 and a necklace costs $7.50, hence the maximum revenue is:

Revenue = 5x + 7.5y = 5(40) + 7.5(30) = $425

Step-by-step explanation:

I don't have a calculator with me right now but I can give you the equation to work out your answer.

cos-1(35/38)

There should be a function of "cos-1" on you're calculator, not just "cos"

hope it helps :)

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 = 5

Step-by-step explanation:

△STR ≅ △LMN

This means the corresponding sides are equal.

SR and LN are corresponding sides.

SR and LN are equal.

The value of b is 5.

The value of SR is 43

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

△STR ≅ △LMN

This means the corresponding sides are equal.

SR = 7b + 8

LN = 11b − 12

SR and LN are corresponding sides.

SR and LN are equal.

So,

7b + 8 = 11b − 12

Subtract 7b on both sides.

8 = 11b - 7b - 12

Add 12 on both sides.

8 + 12 = 4b

20 = 4b

b = 20/4

b = 5

Now,

SR:

= 7b + 8

= 7 x 5 + 8

= 35 + 8

= 43

Thus,

The value of b is 5.

The value of SR is 43

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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

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:

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

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Answer:

The slope is undefined

Step-by-step explanation:

Since x doesn't have an existing value it leaves the slope as undefined.

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:

-55/3

Step-by-step explanation:

-3/11 x1/5

-3/55

Multiplicative inverse means Reciprocal of -3/55 [That means the numerator goes to the denominator and the denominator to the numerator]

=> -55/3

Answer:

sin X =35/37

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin X = opp side / hypotenuse

sin X =35/37

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:

The correct choice is (A)

Answer:  

A.

an=100 · (0.64)n−1a subscript n baseline equals 100 times left parenthesis 0.64 right parenthesis superscript n minus 1 baseline; about 10.74 cm

Step-by-step explanation:  I got it off of the internet

Step 1 of 1

In geometric sequence, the ratio between two consecutive terms is constant. This ration is called the common ratio.

Consider the following sequence:

Thus the common ratio of the sequence is .

...............................................................................................................................................

You drop a handball from a height of 1 meter. Each curved path has 64% of the height of the previous path.   A. A(n)= 100*(0.64)^n-1

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:

rs.6,300

Step-by-step explanation:

Simple Interest, S.I. = Rs. 1260 =  

100

PR×2

​  

 =    

50

PR

​  

          -(i)

Compound Interest, C.I. = Amount(A) - Principle(P)

=P(1+  

100

R

​  

)  

2

 - P = PR(R/10000+1/50)=Rs.1323         -(ii)

Dividing (ii) by (I),

200

R

​  

+1 =  

1260

1323

​  

⇒Rate,R=10%p.a.

Now,  

100

PRT

​  

=1260

⇒  

100

P×10×2

​  

=1260

The amount of money that we need to deposit in the bank to get RS 1225 is RS 1100.03.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount.

Suppose we need to deposit the P amount to get RS 1225

By compound interest formula,

1125 = P(1 + 0.05)^(9/2)

P = RS 1100.03

Hence "We need to deposit Rs. 1100.03 in the bank in order to receive Rs. 1225".

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Answer:

A reflection across the x axis

Step-by-step explanation:

Parallelogram ABCD was reflected across the x axis to create parallelogram A'B'C'D'

Answer:

158.33 minutes = 2.63 hours

Step-by-step explanation:

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:C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The proportional relationship is same

Step-by-step explanation:

Generally, we can get the unit rate by dividing the y-value by the x-value

This will be;

9/2 or 18/4 or 27/6 = 4.5

from what we have y = 4.5x

Now, as we can see, the proportional relationship is same