GEOMETRY - FIND X ON THIS TRIANGLE

Boy is 22.5 feet high from the ground

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

The given question can be solved by sin, as value of perpendicular is to be evaluated and height and angle is provided. Let height from the ground be x

sin(22.5°) = x / 58

x = 58sin22.5 = 58(.38258)  =  22.5 feet high.

Thus the Boy is 22.5 feet high from the ground.

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Number of shirts = dependent variable

Cost of the purchases = independent variable

Answer:

6 cookies per day.

Step-by-step explanation:

if she is going to sell 18 cookies within 3 days, would divide that problem, (18 divided by 3) which will get you selling 6 cookies per day during that 3-day challenge.

Applying the definition of similar triangles, the value of x is determined as: 12.5.

In a triangle like the one shown above, the line that intersects the two sides of the triangle divides the two sides of the triangle to form similar triangles. Thus, their corresponding sides are proportional to each other.

Therefore, we would have:

(x + 5) / 5 = (10 + 4) / 4

(x + 5) / 5 = 14/4

4(x + 5) = 5(14)

4x + 20 = 70

4x = 70 - 20

4x = 50

x = 50/4

x = 12.5

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A bisector is a line that divides a given line or angle into two equal parts or measures. So that the required statements and reasons are given below:

              STATEMENT                                                 REASONS

1. BC bisects <ABD                                 Given

2. m<ABC = [tex]26^{o}[/tex]                                       Bisection property of an angle

3. 2(m<ABC) = [tex]52^{o}[/tex]                                   Sum of angles of a bisected angle

4. m<ABC = m<CBD                                Congruent parts of a bisected angle

5. <mABC + m<ABC =  [tex]52^{o}[/tex]     Sum of an individual angle of a bisected angle

6.  m<ABC + m<CBD = [tex]52^{o}[/tex]                      Sum of angles of a bisected angle

7. m<ABC + m<CBD = m<ABD          Sum of the angles of a bisected angle

The above statements and reasons are majorly centered on a bisector, the angles formed due to the bisection of a given angle, and the bisected angle.

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Answer:

1. BC bisects <ABD | Given

2.m<ABD=52 | Given

3.m<ABC = m<CBD | Definition of Bisector

4.m<ABC + m<CBD = m<ABD | Angle Addition Postulate

5.m<ABC + m<CBD =52 | Substitution Property

6.m<ABC + m<ABC =52 | Substitution Propery

7.2(m<ABC)=52 | Addition

8.m<ABC=26 | Division Property

Step-by-step explanation:

Edge 2022

It's B

Slope is negative, the other must be positive due to m1 x m2 = - 1

m1 = -2/5

The diagram shows a gradient of -2/5. So, the

reciprocal of this valve to make - 1 is 5/2 (which is the - 2/5 flipped upside down, but positive)

-2/5 x 5/2 = - 10/10 (or - 1)

Thus, the perpendicular line to this has a gradient of 5/2.

Hope this helps!

3x - 2y < 7

=============================================================

Explanation:

The dashed boundary line goes through (1, -2) and (3, 1)

Find the slope of this line using the slope formula.

[tex](x_1,y_1) = (1,-2) \text{ and } (x_2,y_2) = (3,1)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-2)}{3 - 1}\\\\m = \frac{1 + 2}{3 - 1}\\\\m = \frac{3}{2}\\\\[/tex]

The slope is 3/2 indicating we go up 3 and to the right 2.

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

Now use the point-slope template so we can determine the equation of the boundary line.

[tex]y - y_1 = m(x - x_1)\\\\y - (-2) = \frac{3}{2}(x - 1)\\\\y + 2 = \frac{3}{2}(x - 1)\\\\2(y+2) = 3(x-1) \ \ \text{ see note1 below}\\\\2y + 4 = 3x - 3\\\\2y - 3x = -3 - 4\\\\-3x+2y = -7\\\\3x-2y = 7 \ \ \text{ see note2 below}\\\\[/tex]

Note1: For this step, I multiplied both sides by 2 to clear out the fraction.

Note2: Multiply both sides by -1 so that the x coefficient is positive

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

The key thing to pull away from the previous section is that the boundary line equation is 3x - 2y = 7

The question from here is: "What do we replace the equal sign with?"

We need to pick either < or > since we have a dashed boundary. We won't have an "or equal to" portion.

Let's assume the inequality sign is <

3x - 2y = 7 turns into 3x - 2y < 7

To see if this works, we'll plug in the origin (0,0) to get...

3x - 2y < 7

3(0) - 2(0) < 7

0 < 7

The last inequality above is true, so 3x - 2y < 7 is also true when x = 0 and y = 0. It tells us that the origin is in the shaded region. This matches with what the graph shows.

Therefore, we have confirmed that 3x - 2y < 7 is indeed the case.

You could pick other test points. However the origin is the easiest to work with in my opinion. If the boundary went through the origin, then you'd have to pick another point like (0,1).

If you want to use technology to verify the answer, then Desmos and GeoGebra are two good options to go for. See the screenshots below.

Answer:

Que is talking about a syrup which contains 50% of sugar .

Que asked : amount of sugar syrup from X grams of sugar.

Explanation :

if a sugar syrup contains 50% of sugar , that means that the half of the solution contains sugar and half is solvent .

means , 2 × amount of sugar = solution (syrup)

now , we are given x grams of sugar

then , solution can be made with x grams of sugar = 2 × (X grams) = 2X gram of solution or sugar syrup.

.

.

Mark BRAINLIEST!

Answer: the amount of liters that would fill the glass tank's volume can not be found

Step-by-step explanation:

there is not enough information to find out how many liters could fill the glass tanks volume

The required volume of glass tank = Vb +Vw liters

Volume, is defined as the ratio of the mass of object to its density.

Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water.

Volume of pebbles = Vb
Volume of water = Vw
Volume of glass tank = Vg
Vg = Vb + Vw

Thus, the required volume of glass tank is = Vb + Vw liters

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Answer:

D

Step-by-step explanation:

this is because when multipled you get 0.3204 so u round and it becomes 0.320

Answer:

D

Step-by-step explanation:

0.04 x 8.01 = [tex]\dfrac{4}{100} . \dfrac{801}{100}[/tex]

[tex]=\dfrac{3204}{10000}\\\\\\0.3204[/tex]

Answer:

58%

Step-by-step explanation:

29 / 50  * 100% = 58 %    ( rather pathetic score, huh?)

Answer:

58%

Step-by-step explanation:

the boy gets 29 marks out of 50

Then

He gets 29 × 2 marks out of 50 × 2

Then

He gets 58 marks out of 100

Therefore

He scored 58%

Answer:

0.04

Step-by-step explanation:

30+5+0.1+0.009 is 35.109

35.149 - 35.109= 0.04

35.149 = 30+5+0.1+ ____ +0.009

= 30 + 5 + 0.1 + x + 0.009

= 35.109 + x

x is the unknown value, so what number add to the 35.109 gives 35.149? That's what we're after.

35.149 = 35.109 + x

- 35.109 both side

0.04 = 0 + x

Thus, x = 0.04

(35.109 - 35.109 cancles each other & we get x on its own because 0.04 - 0 gives you 0.04)

Hope this helps!

The formulas and the equivalent formulas are

W = X - Y                                    X = W +Y

W = X/Z - Y                                 X = Z(W + Y)

W = (X - Y)/Z                               X = WZ+Y

W = XY                                       X =W/Y

To do this, we simply make X the subject of the formula in expressions on the left.

So, we have:

W = X - Y

This gives

X = W + Y

W = X/Z - Y

This gives

X/Z = W + Y

X = Z(W + Y)

W = (X - Y)/Z

This gives

X - Y = WZ

X = WZ + Y

W = XY

This gives

X =W/Y

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Complete question

Match each formula on the left with an equivalent formula on the right.

W = X - Y                                     X =W/Y

W = X/Z - Y                                 X = Z(W + Y)

W = (X - Y)/Z                               X = WZ+Y

W = XY                                       X = W +Y

Answer:

43

Step-by-step explanation:

sequence: +5

∴ninth term of sequence = 38+5

                                          = 43

Hello!

We know the y-intercept (b) is 160. So let's find the slope!

Slope = rise / run

Slope = 120 - 160 / 1 - 0

Slope = -40/1 = -40

Forming the equation :

y = mx + b

y = -40x + 160

∴ The equation of the line in slope-intercept form is y = -40x + 160.

The probability that the sample will be rejected if five items from 1 lot is selected is 26/15504.

Given Industrial product is product in lots of 20. If sample contains more than one defective then the lot will be rejected.

Probability is the chance of happening an event among all the events possible. The probability lies between 0 and 1. The formula of calculating probability is as under:

Probability= number of items/ total items.

Sample from 1 lot =5

Samples in 1 lot=20

Lot will be rejected when 1 sample, 2 sample , 3 sample, 4 sample or all the samples are defective.

Probability that the lot will be rejected=[tex](5C_{2} +5C_{3} +5C_{4} +5C_{5})/20C_{5}[/tex]

=(10+10+5+1)/15504

=26/15504

Hence the probability that lot will be rejected if the lot is rejected if more than one defective is observed is 26/15504.

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Answer:

40   40   100°

Step-by-step explanation:

Is that TRIANGLE FGH?

    the angles add to 180

        180 / ( 4 + 4 + 10 ) = 10

then each angle is       4 x10       4 x 10     and  10 x10

Answer:

y=3x-4

Step-by-step explanation:

Answer:

  d.  102°

Step-by-step explanation:

We can use the relations ...

to write equations that let us find x and all of the angles in ∆PQR.

The congruence relation ∆ABC ≅ ∆PQR tells us that ∠P = ∠A. Using the given expressions for these angles, we have ...

  ∠P = ∠A

  8x +4 = 5x +16

  3x = 12 . . . . . . . . . subtract (5x+4)

  x = 4 . . . . . . . . . divide by 3

Then the measure of angle P is ...

  ∠P = 8x +4 = 8(4) +4 = 36 . . . . . degrees

Angle Q in ∆PQR is given as ...

  ∠Q = 10x +2 = 10(4) +2 = 42 . . . . . degrees

Then the measure of angle R needed to make the total of angles in ∆PQR be 180° is ...

  ∠R = 180° -36° -42° = 102°

Angle R is 102°.

__

In summary:

The amount of aspirin that would be in the patient's body is; 281.25.

A) The amount of aspirin in the patient's body after 2 hours can be evaluated as follows;

a = 500×(3/4)² = 4500/16 = 281.25.

B) The number 500 as used in the equation represents the amount of aspirin in the patient's body prior to taking the medicine, at time, t= 0.

C) The fraction 3/4 as used in the task content is the factor of change in aspirin content in the patient's body.

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Answer:

b - 140

Step-by-step explanation:

an angle bisector divides an angle in half

so

half of the angle is 70

the other half is 70

so

70 + 70 = 140

b is your answer

Answer: B. 140°

Step-by-step explanation:

Hi!

An angle bisector just cuts the angle in half.

Therefore, if one half is 70°, the other half is also 70°!

To find the measure of the angle just add them!

70° + 70° = ?

= 140°

So, your answer is B. 140°

Hope this helps and have a great day!

Using relations in a right triangle, it is found that:

The ratio of 8 to 15 is equals to tan B.

The relations in a right triangle are given as follows:

Researching the problem on the internet, we have that:

Hence the tangent of B is:

tan(B) = 8/15.

Which means that:

The ratio of 8 to 15 is equals to tan B.

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Answer:

(x - 5)(x + 5)

Step-by-step explanation:

x² - 25 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

x² - 25

= x² - 5²

= (x - 5)(x + 5)

Answer:

Step-by-step explanation:

(x-5) +(x+5)

Answer:

Step-by-step explanation:

y = 3 (x-1)(x+ 7 )    this graph will intercept the x axis  when y = 0

 0 = 3 ( x-1)(x+7)     so you can see this = 0   when x =1   or when x = -7

                                  these are the x-axis intercepts

         the vertex will be right in the middle between the intercepts found above    ....... at  x = -3    

          plug this value in to find the y coordinate   3 ( -3-1)(-3+7) = -48

                   vertex is   -3, -48

               the axis of symmetry is the value of the x coordinate of the vertex

                          x = - 3

        direction of opening will be upward.....

   see attached graph

The statements that are true about the intervals of the continuous function are Options 2, 4  and 5

Looking at the values given, the intervals which satisfies the condition are known to be:

f(x)<=0 over the interval [0,2]

f(x)>0 over the interval (-2,0)

f(x)>=0 over the interval [2,∞)

Because:

Since the table with x  and f(x) values, we have to examine analyze the table and see the each option that is in line with f(x) or not .

Examine the values of x that is from -3 to 3, the f(x) values are both positive and negative . hence f(x)>0 is false over the interval (-∞,3)

Looking at the the interval from 0 to 2, the f(x) values are 0 and negative. Hence, f(x)<=0 over the interval [0,2]

When you look over the interval (-1,1), the f(x) values are said to be both positive and negative and as such, f(x)<0 is false over the interval (-1,1)

When you look at the interval (-2,0) , the f(x)  is positive and as such, f(x)>0 over the interval (-2,0)

Looking at the interval  [2,∞), f(x) is positive and as such, f(x)>=0 over the interval [2,∞)

Therefore, Option 2, 4 and 5 are correct.

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Answer:

t is number of 2 dollars

f is number of 5 dollars

2t+5f=58

f+15=t

2(f+15)+5f=58

simplify

2f+30+5f=58

simplify

7f+30=58

subtract

7f=28

f=4

substitute

4+15=t

4 five dollars

19 2 dollars

Hope This Helps!!!

Answer:

(- 9, 2 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(9, 2 ) → (- 9, 2 )

Answer:

28 ft^2

Step-by-step explanation:

The room is in the shape of a square.  That means the base of the room (width and length) will have the same dimensions.

Length x Width = 49 ft^2

Length = Width

Length^2 = 49 ft^2

Length  = 7 feet

Width is also 7 feet

The height of the room is 4 feet, plenty for non-humans.  One wall area would be (7 ft)*(4 ft) = 28 ft^2