Find ALL solutions for the photo given. Find all real solutions of the equation given

Answer:

Step-by-step explanation:

Given:

Angles QPR and TPR both are:

Verify if the remaining angles are same.

This is not same as ∠PTS:

This makes ∠PST ≠ ∠PRQ

Since corresponding angles are different, the triangles are not similar

Given two right triangles.

Verify the corresponding sides have same ratio.

Find the ratio of longer legs:

Find JN:

Find the ratio of shorter legs:

The triangles are similar by SAS since we have two sides similar and included angle is same (right angle)

[tex]\orange{\bigstar\underline{\underline {\pmb{\frak{ \purple{Required~Answer}}}}}}[/tex]

[tex] \\ [/tex]

To find value of x.

[tex] \\ [/tex]

⇢ (3x - 3)° = 60°

[tex] \\ [/tex]

Reason:-{

They both are alternate interior angles.

What is alternate interior angles.?

When two lines are cut by a third line, a transversal.}

[tex] \\ [/tex]

⇢ 3x - 3° = 60

⇢ 3x = 60° + 3°

⇢ 3x = 63°

⇢ x = 63°/3°

⇢ x = 21°

[tex] \\ [/tex]

Verification:

[tex] \\ [/tex]

⇢ (3x - 3)° = 60°

⇢ (3 × 21 - 3)° = 60°

⇢ 63° - 3° = 60°

⇢ 60° = 60°

LHS = RHS

HENCE VERIFIED!

[tex] \\ [/tex]

To find value of y.

[tex] \\ [/tex]

⇢(4y + 4)° + 60° = 180°

[tex] \\ [/tex]

Reason:-{

The lines are in linear pair.

What is linear pair?

A pair of adjacent angles that form angles when two lines intersect}

[tex] \\ [/tex]

⇢ (4y + 4)° + 60° = 180°

⇢ (4y + 4)° = 180° - 60°

⇢ 4y + 4° = 120°

⇢ 4y = 120° - 4

⇢ 4y = 116°

⇢ y = 116/4°

⇢ y = 29°

[tex] \\ [/tex]

Verification:

⇢ (4y + 4)° + 60° = 180°

⇢ (4 × 29 + 4)° + 60° = 180°

⇢(116 + 4)° + 60° = 180°

⇢ 120° + 60° = 180°

⇢ 180° = 180°

LHS = RHS

HENCE VERIFIED!

~WindyMint♡

By using the equivalence of the formed angles, the solution is x = 41.

Note that the angle that is at the right of the equation with x, is equivalent to the bottom right angle, which measures 60°.

Then we will have that:

(3x - 3)° + 60° = 180°

Now we can solve that for x:

(3x - 3)° = 180° - 60° = 120°

3x = 120 + 3

x = 123/3 = 41

The solution is x = 41

If you want to learn more about angles, you can read:

https://brainly.com/question/17972372

Answer:

3/2 cm/s

Step-by-step explanation:

speed = gradient of the line (slope)

To calculate the slope divide the change in y by the change in x:

(9 - 0) / (6 - 0) = 9/6 = 3/2 cm/s

Answer: c

Step-by-step explanation:

The answer Is C molecule

Answer:

  15

Step-by-step explanation:

Let 'a' represent Artaud's age. He notices the relationship ...

  -a +39 = 24

If we add a-24 to both sides, we get ...

  15 = a

Artaud is 15 years old.

Answer: 15 years old

Step-by-step explanation:

Let x be Artaud's age. Let the opposite of his age be -x

-x + 39 = 24

-x = 24-39

-x = -15 (multiply both sides by -1)

x = 15 years old

Answer:

The answer will be 96

Step-by-step explanation:

32×3=96

32

3

×

____

96

Answer:

96

Step-by-step explanation:

Answer:

438/5 and some corn starch = 1 cup

so 87.6 of wheat flour cups for one cake flour cup

Step-by-step explanation:

1 cake flour=x

x=438/5

x=87.6 and some corn starch but it's not mentioned how much so we can just say 87.6 wheat flour cups for 1 cake flour.

Each scenario can be used to simulate probability, and there are 3 correct scenarios and 2 incorrect scenarios in the list of options

From the question, we have the following parameters:

This means that the probability of hit is:

P(Hit) = 20/30

Simplify

P(Hit) = 2/3

Using the complement rule,

P(Miss) = 1/3

The above means that the simulation that represents the situation must have the following parameters:

Using the above highlights, the correct scenarios are:

Read more about probability at:

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Let's name the x-coordinates and y-coordinates

So, According to question

Abscicca of Point A = 2

Ordinate of Point B = -4

Point D = (-4,2)

Answer:

9 numbers

Step-by-step explanation:

10^2 + 10 = 110. This is also greater than 100.

Highest value of x is 9.

9^2 + 9 = 90.

Not sure if zero counts, but if it does, it'll be 10 numbers instead.

Hope this helps!

There are 9 positive integers x satisfy the inequality x² + x < 100.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have the inequality

x² + x < 100.

First take x= 1 then

1² + 1 = 2 < 100

Take x= 2

2² + 2 = 6 <100

Take x= 3

3² + 3 = 12 < 100

Take x = 4

4² + 4 = 20 < 100

Take x= 5

5² + 5 = 30 < 100

Take x =6, 7, 8, 9, 10 and 11

6² + 6<100

7² + 7<100

8² + 8<100

9² + 9 <100

10² + 10 > 100

So, there are 9 possible digits.

Learn more about Inequality here:

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Answer:

2 mm: 1 m

Step-by-step explanation:

That is, the same soccer field has different lengths in actual and in a map.

These scale and actual lengths must be related, and they are related to each other by what we call the scale ratio.

Scale ratio = dimensions in a drawing : actual dimensions

= 232mm : 116m

(we divide this by 116 to get 2)

= 2mm : 1m

Answer:

∠ECD = 82°

Step-by-step explanation:

Alternate Interior Angles Theorem : when two parallel lines are cut by a transversal, the alternate interior angles are congruent.  Alternate angles form a Z shape and are sometimes called "Z angles".

Therefore,

∠CDF = ∠GBC = 45°

∠CEF = ∠GAC = 53°

The sum of the interior angles of a triangle is 180°

⇒ ∠ECD + ∠CDF + ∠CEF = 180

⇒ ∠ECD + 45 + 53 = 180

⇒ ∠ECD = 180 - 45 - 53 = 82°

In ∆ABC

[tex]\\ \tt\longrightarrow x+53+45=180[/tex]

[tex]\\ \tt\longrightarrow x+98=180[/tex]

[tex]\\ \tt\longrightarrow x=180-98[/tex]

[tex]\\ \tt\longrightarrow x=82[/tex]

Now

m<ECD and m<ACB are opposite hence equal

Answer:

slope = 9/4

Step-by-step explanation:

Slope is a ratio (looks like a fraction) It tells you the steepness or flatness of a line.

To find slope you subtract the y's (that's the second number in the ordered pairs; here it's 10 and 1) put that on top. Then subtract the x's and put that on the bottom (here 9 and 5)

Slope = 10-1 / 9-5

=9/4

Now, parallel lines have the same slope, so if one of the lines has slope 9/4, then the other line does too!

Answer:

35v

Step-by-step explanation:

5(6v)+5v

[tex]5 \times 6v + 5v \\ 30v + 5 \\ combine \: the \: terms \\ = 35v[/tex]

Answer:

35v

Step-by-step explanation:

5 times 6v = 30v, then you add 5v which gives you 35v. Hope that helps :)

[tex]\cfrac{5}{8}\cdot \cfrac{8}{25}\implies \cfrac{5}{25}\cdot \cfrac{8}{8}\implies \cfrac{1}{5}\cdot 1\implies \cfrac{1}{5}[/tex]

Answer:

1100 dirham

Step-by-step explanation:

If one book is 55 dirham, then you multiply that by 20 to get the total cost.

(If you are supposed to go from dirham to something else, then I'm sorry I don't know)

Hope this helps!

Answer:

Make all of the +/-2 values into -3,+4

Step-by-step explanation:

This is because the x intercept values for a parabola are where the equation equals zero, by making the equations -3 and +4, the equations will give zero values at -4 and plus 3 when they are set equal to zero, I can specify further if need be.

Answer:

B

Step-by-step explanation:

$500 a week x 50 weeks in a year = $25,000 a year

$27,500 > $25,000

HOPE THIS HELPED

Answer:

    2

Step-by-step explanation:

   1 + 1 = 2

Answer:

1 + 1 = 2

Step-by-step explanation:

1 + 1 = 2

basic addition as

2 + 2 = 4

or like

3 + 2 = 5

or

2 + 1 = 3

Hey there!

8x - 3 + 4x + 3 = 180°

COMBINE the LIKE TERMS

(8x + 4x) - (3 + 3) = 180°

8x + 4x - 3 + 3 = 180°

12x + 0 = 180°

12x = 180°

DIVIDE 12 to BOTH SIDES

12x/12 = 180/12

CANCEL out: 12/12 because that gives you 1

KEEP: 180/12 because it helps solve for the x-value

NEW EQUATION: x = 180/12

SIMPLIFY IT!

x = 15

Therefore, your overall answer is: x = 15

The answer to your given question is:

12x + 0 = 180

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

35.93

Step-by-step explanation:

If the mean of 15 numbers is 41.6, the sum of these numbers must be (15)*(41.6) = 624

We n=know one of these numbers is the 117 that was entered by mistake.  Subtract that out and replace it with the correct number, 17.  In essence we are modifying the number by (-117+17) or -100.

524 is the corrected value.  Divide that by 15 to find the ciorrect mean:

(524)/15 = 34.93

Answer:

um yes to the opreations sjut ad

Answer:

a)c=20

b)b=16

c)a=-3

d)c=2•5

e)a=0•8

1)

x+10<-7

bring 10 to the other side

x<-10-7

x<-17

2)

-3x-4>5

bring -4 to the other side

-3x>9

divide -3 at the other side, since it is negative it changes to less than

x<-3

Answer:

  24.5 mi

Step-by-step explanation:

Each cm represents 9.8 miles, so 2.5 cm will represent a distance 2.5 times as far:

  (2.5)(9.8 mi) = 24.5 mi

From Old Faithful to West Thumb is 24.5 miles.

Answer:

Step-by-step explanation:

is between two numbers.

is less than or equal to a number.

is greater than or equal to a number.

It is meaningful to compute the probability that a continuous random variable when it is between two numbers.

Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.

Continuous random variable is is one which takes an infinite number of possible values.  A random variable is said to be continuous if it assumes a value that falls between a particular interval.

So, from the above mentioned statement we can assume that ;

The statement given in option [tex](c)[/tex] is correct .

Hence, we can say that it is meaningful to compute the probability that a continuous random variable when it is between two numbers.

To know more about Continuous random variable click here

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Answer:

8:5

Step-by-step explanation:

Answer:

45% increase

Step-by-step explanation:

The new number (87) is bigger than the original number (60), so this is a percent increase.

To find the percent of change, which in this case is a percent increase, take the change amount and divide by the original, then convert to a percent.

Subtract to find the change.

87 - 60 is 27.

27 is the amount of change.

change/original

= 27/60

= .45

Times by 100 to change to a percent.

.45 × 100

= 45%