Is substitutions the best method to use when one variable is already known

see the attached figure

A(4,8)  B(0,7)  C(4,3)

the line of reflection is x=5

the reflection is (x,y)-------------------> (10-x,y)

therefore

A(4,8)-----------------> A1(10-4,8)------> A1(6,8)

B(0,7)-----------------> B1(10-0,7)------> B1(10,7)

C(4,3)-----------------> C1(10-4,3)------> C1(6,3)

a) Angles ACB in ∆ABC and ECD in ∆EDC are congruent, since they form a vertical angle pair.

Angles ABC and EDC are clearly congruent, since they are both right angles.

The legs AB and ED are parallel, so angles BAC and DEC are congruent alternating interior angles.

Then ∆ABC is similar to ∆CDE by the angle-angle-angle postulate.

b) Because they're similar, corresponding sides occur in a fixed ratio, which tells us that

CD/BC = ED/AB

p/(5 cm) = (4 cm)/(6 cm)

p = 10/3 cm

Answer:

99 m to nearest metre.

Step-by-step explanation:

Hypotenuse = 135,  opposite side = ?

- so we need the sine function

sin 47 = x / 135 were x is the height of the kite.

x = 135 * sin 47

= 98.73 m

Answer:

175 degrees.

Step-by-step explanation:

Supplementary angles add up to 180 degrees

Therefore the answer is:

180 - 5

= 175 degrees.

Hi Student!

The first step to almost any problem is that we must concentrate the important information that is given to us in the problem.  This problem gives us information including that the measure of an angle is 5 degrees and that this angle is part of a supplementary pair.  Let's define what a supplementary pair or angles are.

Now that we have our definitions and important information, we can move onto the next part which is actually finding the other angle.  This step is simple now that we know that supplementary angles add up to 180.  We can just create an equation that will help us determine our solution.

[tex]angle_1\ +\ angle_2 = 180\ degrees[/tex]

[tex]5\ degrees\ +\ angle_2 = 180\ degrees[/tex]

[tex]5\ degrees-5\ degrees\ +\ angle_2 = 180\ degrees-5\ degrees[/tex]

[tex]angle_2 = 175\ degrees[/tex]

Therefore, our final solution to the supplementary angle of 5 degrees is 175 degrees which can be found by subtracting the given angle from 180.

Answer:

188 feet

i know that the answer

nasa makatulong po

The volume of a cylinder, in cubic feet, is,

V = 2,034.7 feet³

We have to given that,

In a cylinder,

Height = 8 feet

And, Diameter = 18 feet

Hence, Radius of cylinder is,

r = 18/2

r = 9 feet

We know that,

Volume of cylinder is,

V = πr²h

Substitute all the values, we get;

V = 3.14 × 9² × 8

V = 2,034.7 feet³

Therefore, The volume of a cylinder, in cubic feet, is,

V = 2,034.7 feet³

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Answer:

9 weeks

Step-by-step explanation:

let the time when they will both have the same amount be x

since Maria is saving then her money is bound to increase

therefore amount she will have after x weeks=235+15x

Sergio is spending so his money is reducing

therefore amount he will have after x weeks=

685-35x

so

235+15x=685-35x

685-235=15x+35x

450=50x

x= 450/50

9weeks

Answer:

[tex] \frac{ - 2x - 2}{ {x}^{2} + 2x - 3 } [/tex]

is the answer

Answer:

1.2

Step-by-step explanation:

{2.8, 0.75, +1.2}

Median: 1.2

Answer:  4.75

Step-by-step Explanation

Answer:

36 dollars

Step-by-step explanation:

4.50 times 8 = 36 dollars

Answer:

8

Step-by-step explanation:

5 + 3 = 8

Answer: A - (5.196, -3)

Step-by-step explanation: correct on ed

Answer:

[tex]y = \frac{1}{2}x + \frac{3}{2}[/tex]

Step-by-step explanation:

Assuming this is a linear equation in the form of [tex]y = mx + b[/tex], we can first solve for the slope using [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex], for these points, the slope would be [tex]\frac{1}{2}[/tex]. Now we plug in the points to get the equation:

plugging in (7,5), we get [tex]5 = \frac{1}{2}[/tex] ×[tex]7[/tex] + [tex]b[/tex]

and solving for b, we get b = [tex]\frac{3}{2}[/tex]

therefore, the equation of the line passing through (7,5) and (1,2) is [tex]y = \frac{1}{2}x + \frac{3}{2}[/tex].

hope this helps!

The total amount of change, in cents, that was found is determined as 96 cents.

The total amount of change is calculated as follows;

let the total = T

there was at least one coin of each type

T = p + n + d + q

more than half of the coins were pennies

[tex]\frac{p+n + d + q }{2} \leq p[/tex]

more than half = pennies

next, we have; nickels + dimes + quarters

y(dimes) = $0.25

y(0.1) = 0.25

y = 0.25/0.1

y = 2.5 ≅ 3

dimes = 3 coins

since dimes = 3 coins, number of nickels is now calculated as;

x(0.05) = 3(0.1)

x = (0.3)/(0.05)

x = 6 coins

nickels = 6 coins

Total coins = nickels + dimes + quarters + pennies

Total coins = nickels + dimes + quarters + pennies

let pennies = 7

Total coins = 6 + 3 + 1 + 7

Total coins = 17

half of 17 = 8.5

7 is less than half (8.5), number of pennies cannot be 7, since more than half of the coins are pennies.

let pennies = 11

Total coins = 6 + 3 + 1 + 11

Total coins = 21

half = 10.5

more than half = number of pennies = 11

11($0.01) + 6($0.05) + 3($0.1) + 1($0.25) = $0.96 = 96 cents

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Answer:

C

Step-by-step explanation:

Points given are
(0,8) and (1, 16)
The first point given is the y-intercept, 8

The y-intercept of A is 2
The y-intercept of B is 16
The y-intercept of C is 8
the y-intercept of D is 16

The only one that works is C

Answer:

x = 20

y = √3 / 10

Step-by-step explanation:

The cosine ratio gives the ratio between the adjacent side and the hypotenuse.

The sine ratio gives the ratio between the opposite side and the hypotenuse.

Taking cosine ratio to find x :

cos 60° = 10/x

1/2 = 10/x

x = 20

Taking sine ratio to find y :

sin 60° = y/x

√3 / 2 = y/20

y = √3 / 10

Answer:

x= 20 ,  y= 10√3

Step-by-step explanation:

This question is clearly a trigonometry question

Please bare in mind :

Cos 60 = 1/2

Sin 60 = √3/2

Tan 60 = √3

Side x is the hypotenuse (h)

Side y is the Opposite (o)

And side with length of 10 is adjacent (a)

To find x, we have a, and we need h

So we use C = a/h

Cos 60 = 10/h

h = 10/Cos 60

h = 10/0.5

h = 20 ,  x=20

To find y, we can use pythagaros as we found the value of x :

10² + y² = x²

10² + y² = 20²

y² = 20²-10²

y² = 300

y = √300

y= √100×3   y=√100 × √3

y = 10√3

This is our y value

Another way to find y is trigonometry :

We have a and we need o so we use :

T = o/a

Tan 60  = o/10

o = 10×tan 60

o = 10×√3

o = 10√3 ,  y=10√3

Sorry for not being urgent but give brainliest please

Answer:

1 pack of pencils and 4 packs of pens

Step-by-step explanation:

Because, 1 pack of pencils has 16. And 1 pack of pens has 4. So...

1 pack of pencils = 16 and 4 packs of pens = 4 + 4 + 4 + 4 which equals 16 too.

Hope this helps! :)

Answer:

x = 104°

Step-by-step explanation:

The 142° and <DCE form a straight line, and a straight line measures 180°, do the two angles add up to it:

180° =  142° + m<DCE

m<DCE = 38°

The red symbol in <DCE and <CDE mean they are congruent, so m<CDE is the same as m<DCE, which is 38°.

The 142° angle is an exterior angle to triangle, DCE, an exterior angles are the sum of the remote interior angles, which are <CDE and <DEC. Therefore, we can write:

142° = m<CDE + m<DEC

And we can substitute the values we have:

142° = 38° + x

x = 104°

Answer:

c = 23.93

Angle ∠B = 21.22°

Angle ∠C = 41.779°

Step-by-step explanation:

Answer:

[tex](y {}^{2} - 3y - 5) - ( - {y}^{2} - 7y + 4) \\ {y}^{2} - 3y - 5 + {y}^{2} + 7y - 4 \\ 2 {y}^{2} + 4y - 9[/tex]

A is the correct answer

Answer:

Step-by-step explanation:

The probability of each number is same:

So P(7) is also 1/8.

Correct choice is B

The total ounces of water Diane brought are 576 ounces and  the fraction of a gallon of water did she start the hike with is 3/16.

The cost price per ounce is the amount of money required to buy one ounce of a brand or goods.

To find the cost price per ounce, divide the total amount of cost of the goods to the total number of goods.

1. There are 8 ounces in 1 cup and 16 cups in 1 gallon. Diane brought 4.5 gallons of water to a campout.  Let x ounces of water, did she bring. Thus,

[tex]x=4.5\times16\times8\\x=576\rm\; ounces[/tex]

Diane started a hike with 24 ounces of water in her backpack. The fraction of gallons in 24 ounces is,

[tex]n=\dfrac{24}{8\times16}\\n=\dfrac{3}{16}[/tex]

Thus, the total ounces of water Diane brought are 576 ounces and  the fraction of a gallon of water did she start the hike with is 3/16.

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Answer: A

Step-by-step explanation:

[tex]$$Solve for $x$ :$$(x+5)(2 x-7)=0$$Split into two equations:$$x+5=0 \text { and } 2 x-7=0$$Subtract 5 from both sides: $x=-5$ and $2 x-7=0$ \\Add 7 to both sides: $x=-5$ and $2 x=7$\\Divide both sides by 2:\\Answer:$$x=-5 \text { and } x=\frac{7}{2}$$[/tex]

Rounding up for 2nd zero = 7/2 = 3.5

Therefore, the zeroes of the function (rounded to whole numbers) are x = -5 and x = 4

Answer:

the answer is c

Step-by-step explanation:

to find the zeros set

f

(

x

)

=

0

(

3

x

−

5

)

(

2

x

+

7

)

=

0

equate each factor to zero and solve for x

2

x

+

7

=

0

⇒

x

=

−

7

2

3

x

−

5

=

0

⇒

x

=

5

3

Answer:

-4, -3,-3,1/2,3/4

Step-by-step explanation:

this should be right

Step-by-step explanation:

the slope of a line or linear equation is always the factor of the driving variable.

usually in the form of

y = ax + b

x is the variable, and a the slope.

but in our case the variable is called "n".

it does not matter, the same principle applies.

the slope is the factor of n : 1050.

and as the slope is always the ratio y/x, we are looking for a fraction form, and that would be 1050/1.

so, the third answer is correct.

Answer:

Step-by-step explanation:

5x is greater than -20 because if you look at the worst possible solution which is 5(0) it's still larger than -20 because of the number line 0 is greater than -20 so yes 5x is greater than -20

Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

Expand and rewrite both equations to make y the subject:

[tex]\begin{aligned}4(x-2y)-(5x+3y) & =30\\\implies 4x-8y-5x-3y & =30\\4x-5x-8y-3y & =30\\-x-11y & =30\\x+11y & = -30\\ 11y & = -x-30\\ y & = \dfrac{-x-30}{11}\end{aligned}[/tex]

[tex]\begin{aligned}3(3x+7y)-2(x+9y) & = 12\\\implies 9x+21y-2x-18y & = 12 \\9x-2x+21y-18y & = 12\\7x+3y & = 12 \\3y & = -7x+12\\ y & = -\dfrac{7}{3}x+4\end{aligned}[/tex]

Now solve for [tex]x[/tex] by substitution:

[tex]\begin{aligned}y & = y\\\\\implies \dfrac{-x-30}{11} & = -\dfrac{7}{3}x+4\\\\-x-30 & = 11\left(-\dfrac{7}{3}x+4\right)\\\\-x-30 & = -\dfrac{77}{3}x+44\\\\-x+\dfrac{77}{3}x & =44+30\\\\\dfrac{74}{3}x & = 74\\\\74x & = 222\\\\x & = \dfrac{222}{74}\\\\x & =3 \end{aligned}[/tex]

The function of F is defined by f(x) = x + 2, the value of f(n - 4) is given as f(n - 4) = n - 4 + 2 = n - 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

f(x) = x + 2

The value of f(n - 4) is given as:

f(n - 4) = n - 4 + 2 = n - 2

The function of F is defined by f(x) = x + 2, the value of f(n - 4) is given as f(n - 4) = n - 4 + 2 = n - 2

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Answer:

In Exercises 9 − 16, Ind the indicated measure in a LMNQ. Explain your reasoning. m ∠ L M N Answer m ∠ L M N = 80 ∘ View Answer Discussion You must be signed in to discuss. AS Ahin S. February 11, 2021 Find m?LMN in parallelogram LMNQ AS Ahin S. February 11, 2021 Watch More Solved Questions in Chapter 7 Problem 1 Problem 2 Problem 3 Problem 4

Step-by-step explanation:

By solving a little system of equations we will see that the two numbers are 12 and 31.

Let's define the two numbers as a and b.

We know that one of the numbers is 7 more than twice the other, so we have:

a = 2b + 7

We also know that the sum of the two numbers is 43, so we get:

a + b = 43

Replacing the first equation into the second one we get:

2b + 7 + b = 43

3b = 43 - 7 = 36

b = 36/3 = 12

Now that we know b, we can find a:

a = 2*12 + 7 = 31

So the numbers are 12 and 31.

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