I have a lot of algebra problems. Someone help me even with this one please!

Given the 22 m. horizontal distance and the angles of elevation of 26°

and 31° gives the height of the building as approximately 2.49 meters.

Horizontal distance from the building = 22 m

Angle of elevation to the top of the roof = 26°

Angle of elevation to the top of the antenna = 31°

Height of his eyes from the ground = 1.53 m

Required:

The height of the antenna.

Solution:

In a right triangle, we have relative to an angle of the triangle, we have;

Opposite side = Adjacent side

Height of the building + Height of antenna = [tex]1.53 + 22 \times tan \left(31^{\circ} \right)[/tex] ≈ 14.75

Which gives;

Height of the building = [tex]1.53 + 22 \times tan \left(26^{\circ} \right)[/tex] ≈ 12.26

Therefore;

Height of the antenna ≈ 14.75 - 12.26 ≈ 2.49

Learn more about trigonometric tangent ratio here:

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Answer:

parallel

Step-by-step explanation:

Let's rewrite each equation into the slope-intercept form so that we can easily identify the slope of each line.

slope-intercept form: y= mx +c, where m is the gradient and c is the y-intercept.

9x +3y= 12

3x +y= 4 (÷3 throughout)

y= -3x +4 -----(1)

24x +8y= 35

8y= -24x +35 (-24x on both sides)

[tex]y = - 3x+ 4 \frac{3}{8} [/tex] -----(2)

Thus, the slopes of the lines are both -3. Since both lines have the same gradient, they are parallel to each other.

Notes:

• parallel lines have the same gradient

• the product of the gradients of two perpendicular lines is -1

• gradient and slope has the same meaning and can thus be used interchangeably

Answer:

Let's define the high temperature as T.

We know that:

"four times T, was more than 2*T plus 66°C"

(i assume that the temperature is in °C)

We can write this inequality as:

4*T > 2*T + 66°C

Now we just need to solve this for T.

subtracting 2*T in both sides, we get:

4*T - 2*T > 2*T + 66°C - 2*T

2*T > 66°C

Now we can divide both sides by 2:

2*T/2 > 66°C/2

T > 33°C

So T was larger than 33°C

Notice that T = 33°C is not a solution of the inequality, then we should use the symbol ( for the set notation.

Then the range of possible temperatures is:

(33°C, ...)

Where we do not have an upper limit, so we could write this as:

(33°C, ∞°C)

(ignoring the fact that ∞°C is something impossible because it means infinite energy, but for the given problem it works)

Answer:

There are 39 seats I think.

Step-by-step explanation:

548 divided by 14 is a decimal but rounded it to the nearest full number.

[tex] \frac{3}{8} \div \frac{4}{9} \\ = \frac{3}{8} \times \frac{9}{4} \\ = \frac{27}{32} [/tex]

Hope it helps!!!

Thanks!!!

Answer:

The population of Fun City after 171 years would be 214563.

Step-by-step explanation:

The statement depicts a case of exponential growth, whose model is described below:

[tex]p(t) = p_{o}\cdot r^{\frac{t}{T} }[/tex] (1)

Where:

[tex]p_{o}[/tex] - Initial population, no unit.

[tex]p(t)[/tex] - Current population, no unit.

[tex]r[/tex] - Growth rate, no unit.

[tex]t[/tex] - Time, in years.

[tex]T[/tex] - Growth period, in years.

If we know that [tex]p_{o} = 21000[/tex], [tex]r = 2[/tex], [tex]t = 171\,yr[/tex] and [tex]T = 51\,yr[/tex], then the population of the city after 171 years is:

[tex]p(t) = 21000\cdot 2^{\frac{171}{51} }[/tex]

[tex]p(t) = 214563[/tex]

The population of Fun City after 171 years would be 214563.

Answer:y=-5+1

Step-by-step explanation:

Answer:

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Step-by-step explanation:

The given expression to us is ,

[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]

Now take the LCM as ( x - 1 ) and Simplify , we have ,

[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]

Simplifying further , we get ,

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Hence the second option is correct .

Answer:

[tex] \frac{ \frac{3}{x - 1} - 4 }{2 - \frac{2}{x - 1} } \\ = \frac{ \frac{3 - 4(x - 1)}{x - 1} }{ \frac{2(x - 1) - 2}{x - 1} } \\ = \frac{3 - 4x + 4}{2x - 2 - 2 } \\ \frac{7 - 4x}{2(x - 2)} \\ option \: b \: is \: your \: answer \\ thank \: you[/tex]

k<28

Step 1: Simplify both sides of the inequality.

−k+28>0

Step 2: Subtract 28 from both sides.

−k+28−28>0−28

−k>−28

Step 3: Divide both sides by -1.

−k /−1  >  −28 /−1

k<28

Answer:

k < 28

Step-by-step explanation:

Given inequality :-

Last Option is correct .

Answer: 26.11

Step-by-step explanation:

73.18 - 5.23 × 90 = 73.18 - 47.07 = 26.11

Answer:

53:36

Step-by-step explanation:

53:36

265:180

The ratio of time Dhanu spent playing with model railway to the time riding bicycle is 53 : 35.

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

Time spent playing with the model railway = 4 hours 25 minutes.

Converting the time to minutes = (4 x 60) + 25 = 265 minutes

Time in minutes spent riding a bicycle = 60 x 3 = 180

Ratio of the minutes - 265 : 180

53 : 35

To learn more about ratios, please check: https://brainly.com/question/25927869

Answer:

[tex] ({x}^{2} + 4 )( {x}^{2} - 4) \\ 1)( {x}^{2} - 16) \\ = (x - 4)(x + 4) \\ 2)( {x}^{2} + 16) \\ = (x - 4)(x + 4) \\ 3) {x}^{2} + 8x + 16 \\ {x}^{2} + (4 + 4)x + 16 \\ {x}^{2} + 4x + 4x + 16 \\ x(x + 4) + 4(x + 4) \\ (x + 4)(x + 4) \\ 4) {x}^{2} - 8x - 16 \\ {x}^{2} - (4 + 4)x - 16 \\ {x}^{2} - 4x + 4x - 16 \\ x(x - 4) + 4(x - 4) \\ (x - 4)(x + 4)[/tex]

Answer:

18

Step-by-step explanation:

Let the number of employees with both cell and car be b. Using a Venn diagram shown above,

19 + 22 - b + 2 = 25

43 - b = 25

b = 18

Hello,

Imagine Algebra does not exist .

Let's suppose all tickets are children's tickets

The sum should be 5$*375=1875$

Not enough, we must have $2153: 2153-1875=278 ($) must be found.

Let's replace a children ticket with an adult one,

we get one dollar more.

We must thus exchange 278 tickets

There are 278 adult tickets and 375-278=97 children tickets

Proof:  278*6+97*5=2153

Answer:

(12, 2 )

Step-by-step explanation:

Given (x, y ) on the graph of f(x) , then on the inverse function

(x, y ) → (y, x ), then

(2, 12 ) → (12, 2 ) ← point on g(x) the inverse function

Answer: A.Spreads: The weights of the tigers are more spread out.

B.Centers:The leopards have a lower median weight than the tigers

Step-by-step explanation:

On analyzing the dot plots, we find that the weight of Leopards are more spread out and the weight of Leopards has a lower median than Tiger.

Median is a statistical measure that determines the middle value of a dataset listed in ascending order. The measure divides the lower half from the higher half of the dataset.

Median of Weight of Leopard = 50 kg

Median of Weight of Tiger = 125 kg

This implies that the Leopards have a lower median weight than Tigers.

What is spread of data?

Spread describes the variation of the data. One of the measures of spread is range.

Range of weight of Leopards= 40 kg

Range of weight of Tigers = 90 kg

This implies that the weight of Tigers are more spread out.

Learn more about median here

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Answer:

1 and 2.....then 3 is a different question

Answer:

1)  [tex]T_{(a, \, b)}[/tex] = f(x - a) + b

Coordinate change

(x, y) → (x + a, y + b)

2) RFy(x, y) = f(-x)

Coordinate change

(x, y) → (-x, y)

3) RFx(x, y) = -f(x)

Coordinate change

(x, y) → (-y, x)

4) RCCW90(x, y) = f⁻¹(-x)

Coordinate change

(x, y) → (-y, x)

5) RCCW180(x, y) = -(f(-x))

Coordinate change

(x, y) → (-x, -y)

6) A 270 degrees counterclockwise rotation gives;

RCCW270(x, y) = -(f⁻¹(x))

Coordinate change

(x, y) → (y, -x)

Step-by-step explanation:

1) Horizontal translation a units right = f(x - a)

The vertical translation b units up = f(x) + b

Therefore, we get; [tex]T_{(a, \, b)}[/tex] = f(x - a) + b

The coordinate change

(x, y) → (x + a, y + b)

2) A reflection across the y-axis = RFy(x, y) = f(-x)

The coordinate change

(x, y) → (-x, y)

3) A reflection across the x-axis gives RFx(x, y) → (x, -y)

Therefore, in function notation, we get;

RFx(x, y) = -f(x)

4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)

In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)

5) A 180 degrees counterclockwise rotation about the origin gives;

(x, y) → (-x, -y)

Therefore, we get;

In function notation RotCCW180(x, y)  = -(f(-x))

6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)

In function notation RotCCW270(x, y) = -(f⁻¹(x))

Given equation of the Circle is ,

[tex]\sf\implies x^2 + y^2 = 25 [/tex]

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]

Here we can see that the distance of point from centre is less than the radius.

Hence the point lies within the circle .

inside the circle

Step-by-step explanation:

we want to verify whether (-4,2) lies inside or outside or on the circle to do so recall that,

step-1: define h,k and r

the equation of circle given by

[tex] \displaystyle {(x - h)}^{2} + (y - k) ^2= {r}^{2} [/tex]

therefore from the question we obtain:

step-2: verify

In this case we can consider the second formula

the given points (-4,2) means that x is -4 and y is 2 and we have already figured out h,k and r² therefore just substitute the value of x,y,h,k and r² to the second formula

[tex] \displaystyle {( - 4 - 0)}^{2} + (2 - 0 {)}^{2} \stackrel {?}{ < } 25[/tex]

simplify parentheses:

[tex] \displaystyle {( - 4 )}^{2} + (2 {)}^{2} \stackrel {?}{ < } 25[/tex]

simplify square:

[tex] \displaystyle 16 + 4\stackrel {?}{ < } 25[/tex]

simplify addition:

[tex] \displaystyle 20\stackrel { \checkmark}{ < } 25[/tex]

hence,

the point (-4, 2) lies inside the circle

Answer:

1/2 + 2/3 + 5/4 = 29/ 12 = 2 5/  12  ≅ 2.4166667

Step-by-step explanation:

Add: 1/ 2  + 2/ 3  = 1 · 3/ 2 · 3  + 2 · 2/ 3 · 2  = 3/ 6  + 4/ 6  = 3 + 4/ 6  = 7/ 6

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 3) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - one half plus two thirds = seven sixths.

Add: the result of step No. 1 + 5/ 4  = 7/ 6  + 5/ 4  = 7 · 2/ 6 · 2  + 5 · 3/ 4 · 3  = 14/ 12  + 15/ 12  = 14 + 15/ 12 = 29/ 12

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 4 = 24. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - seven sixths plus five quarters = twenty-nine twelfths.

hope it helps...

correct me if I'm wrong...

Answer:

y=X²-4x+5

Step-by-step explanation:

substitute all the left side values to get the outputs..

y=(5)²-4(5)+5 =10

Answer:

A

Step-by-step explanation:

In fact, if we try to substitute, we have:

10 = 5^2 -4(5) +5

10 = 25 - 20 + 5

10 = 10 (ok)

17 = -2^2 - 4(-2) + 5

17 = 4 + 8 + 5

17 = 17 (ok)

and so on

Answer:

AB = DC So ∠A and ∠D are bigger then 90%

Answer:

E2020

Step-by-step explanation:

Given:

The statement is: If 2 angles are both right angles then they are congruent.

To find:

The converse of the given statement and then check whether it is true or not.

Solution:

We know that,

Statement: If p, then q.

Converse : If q, then p.

The statement is: If 2 angles are both right angles then they are congruent.

So, the converse of this statement is:

If 2 angles are congruent then both are right angles.

This statement is not true because if 2 angles are congruent then it is not necessary that the angles are right angles.

Therefore, the converse of this statement is not true.

Answer:

30

Step-by-step explanation:

Multiply by 2 to 18, x+6=36

subtract 6 x=30

x=30

Answer:

i) 2 + 2x

ii) 154 = 2(2 + 2x + x)

iii) Length = 52m

Breadth = 25m

Step-by-step explanation:

Perimeter of swimming pool = 154m

Breadth = x

Length = 2 + 2x

Formula for finding perimeter = P = 2(l + b)

Therefore,

154 = 2 ( 2 + 2x + x)

154 = 4 + 4x + 2x

154 = 4 + 6x

154 - 4 = 6x

150 = 6x

150/6 = x

25 = x

With the value of x,

we can fInd the length and the breadth

Breadth = x

= 25

Length = 2 + 2x

= 2 + 2(25)

= 2 + 50

= 52

Answer:

No

Step-by-step explanation:

Because 1 don't equal to 16

Answer:

no

Step-by-step explanation:

* means multiply

(2,1)

x = 2

y = 1

just plug in the numbers

1 = 8*2 ?

1 = 16? no

Answer:

Step-by-step explanation: