Tower A and B are 151 m apart.
From the top of tower A at 68 m above ground, the angle of elevation to the top of tower B is 23°.
How tall is tower B to the nearest metre?

Answer:

x =62

Step-by-step explanation:

The two angles form a straight line so they add to 180

x+118 = 180

Subtract 118 from each side

x = 180-118

x =62

Answer:

x = 62°

Step-by-step explanation:

These both angles are located at straight line.

So, the sum of both angles is 180 °.

x + 118 ° = 180 °

Subtract 118 ° from 180 °

x = 180 ° - 118 °

x = 62 °

Answer:

y = -1/6x - 1/2

Step-by-step explanation:

y = -1/6x + b

-1 = -1/6(3) + b

-1 = -1/2 + b

-1/2 = b

Answer:

$10,667.66

Step-by-step explanation:

The formula for calculating the compound interest is expressed as:

A = P(1+r/n)^nt

P is the principal = $9000

r is the rate = 3%

time t = 6years

n = 1/4

Substitute

A = 9000(1+0.03/(1/4))^6/4

A = 9000(1+0.03(4))^1.5

A = 9000(1+0.12)^1.5

A = 9000(1.12)^1.5

A = 9000(1.1853)

A = 10,667.67

Hence the amount after 6 years is $10,667.66

Answer:

[tex]y \: \alpha \: {(x + 2)}^{3} \\ y = k {(x + 2)}^{3} \\ k \: is \: a \: constant \\ when \: x = 0 \: \: y = 32 : \\ 32 = k {(0 + 2)}^{3} \\ 32 = k(8) \\ k = 4 \\ \therefore \: y = 4 {(x + 2)}^{3} \\ when \: x \: is \: 1 : \\ y = 4 {(1 + 2)}^{3} \\ y = 4 \times 27 \\ y = 108[/tex]

Answer:

y = (x+2) + 6

Step-by-step explanation:

Answer:

200-2 = 198

Step-by-step explanation:

If you have 200 apples and you eat two you have 198 apples

Answer:

[tex]n + 5 = 12[/tex]

Step-by-step explanation:

"A number increased by a 5 is 12".

The value of n.

[tex]n + 5 = 12[/tex]

[tex]n = 12-5[/tex]

[tex]n = 7[/tex]

Answer:

7

Step-by-step explanation:

subtract the sum, in this case 12. by 5 to get the answer. 12-5=7

Answer:

∠EFG=2×∠EHG

∠EFG=2×42

∠EFG=84°

so,m∠EFG=84°

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

hope it helps...

have a nice day!!

First let's calculate the exponents.

[tex]27^2 : 729 = 9-1\div \:2\div \:729\div \:3[/tex]

Now we should multiply and divide.

[tex]1\div2\div729\div3:\frac{1}{4374} = 9-\frac{1}{4374}[/tex]

Now we should add and subtract.

[tex]9-\frac{1}{4374} :\frac{39365}{4374} = \frac{39365}{4374}[/tex]

Convert the improper fractions into mixed numbers.

[tex]8\frac{4373}{4374}[/tex]

Answer :

[tex]8\frac{4373}{4374}[/tex]

Answer:

3

X is slope but the equation isnt set up proper

12x-4y=3

-12x -12x

-4y=-12x+3

/-4 /-4

y= 3x+3/-4

Answer:

3

Step-by-step explanation:

Answer:

-3.7 =z

Step-by-step explanation:

10.42= −2.6z+0.8

Subtract .8 from each side

10.42-.8= −2.6z+0.8-.8

9.62= −2.6z

Divide each side by -2.6

9.62 / -2.6 = -2.6z/-2.6

-3.7 =z

[tex]\sf\purple{The\:value\:of\:z\:is\:-3.7.}[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]10.42 = - 2.6 \: z + 0.8 \\ \\✒ \: 2.6 \: z = 0.8 - 10.42\\ \\ ✒ \: 2.6 \: z = - 9.62 \\\\ ✒ \: z \: = \frac{ - 9.62}{2.6} [/tex]

To remove the decimals, we multiply both numerator and denominator by 100.

[tex]✒ \: z \: = \frac{ - 962}{260} \\ \\ ✒ \: z = - 3.7[/tex]

[tex]10.42 = - 2.6 \times ( - 3.7) + 0.8 \\ \\✒ \: 10.42 = 9.62 + 0.8 \\ \\✒ \: 10.42 = 10.42 \\\\ ✒ \: L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

Answer:

The average rate of change of the function over the interval is 5.

Step-by-step explanation:

Average rate of change of a function:

The average rate of change of a function f(x) over an interval [a,b] is given by:

[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]

Interval -3 less-than-or-equal-to x less-than-or-equal-to 3

This means that [tex]a = -3, b = 3[/tex]

[tex]f(x) = x^2 + 3x + 6[/tex]

So

[tex]f(b) = f(3) = (3)^2 + 3(3) + 6 = 9 + 9 + 6 = 24[/tex]

[tex]f(a) = f(-3) = (-3)^2 + 3(-3) + 6 = 9 - 9 + 6 = 6[/tex]

Average rate of change

[tex]A = \frac{f(b)-f(a)}{b-a} = \frac{24+6}{3-(-3)} = \frac{30}{6} = 5[/tex]

The average rate of change of the function over the interval is 5.

Answer:

24/100

Step-by-step explanation:

Answer:

Step-by-step explanation:

I believe it is 26?

Answer:

26 cards

Step-by-step explanation:

Sam:

⅓=2+6

=8

Bill:

3/3=3×8

=24

3/3=½

24+2=26

Now ,Min have 26 cards.

hope it help

Answer:

$28.00

Step-by-step explanation:

1. The markup is 40% of the $20 cost, so the markup is:

(0.40)(20) = 8

2. Then the selling price, being the cost plus markup, is:

20 + 8 = 28

3. The CD set sold for $28.00

Step-by-step explanation:

sp=(100+p)% of cp

=100+40/100*20

=140/100*20

=28

Answer:

The x Intercepts of y=5x^2-15x is (1, 0) and (-1, 0)

Step-by-step explanation:

Answer:

(0,0) and (3,0)

Step-by-step explanation:

5x²-15x = 0

5x(x-3) = 0

5x=0;    x=0

x-3=0;   x=3

Answer:

48

Step-by-step explanation:

3 ⋅ 2^t

3 * 2^4

3*16

48

Answer:On the vertical axis, place frequencies. Label this axis "Frequency".

On the horizontal axis, place the lower value of each interval. ...

Draw a bar extending from the lower value of each interval to the lower value of the next interval.

Step-by-step explanation:

Answer:

Attached is a file of a sample histogram compiled by Social Science Statistics with the values in the question inputted.

Step-by-step explanation:

Histograms are bar graphs that represent a set of values. The vertical y-axis indicate how many values there are in a certain interval, and the horizontal x-axis indicates those intervals, usually in intervals of 10, but this depends on the range of your data.

A histogram with the following forty (40) values:

37, 22, 28, 25, 53, 29, 37, 41, 54, 29, 23, 30, 37, 41, 27, 26, 39, 24, 36, 48, 45, 31, 27, 40, 38, 41, 39, 37, 30, 44, 42, 46, 53, 43, 44, 43, 49, 51, 38, 32

Answer:

765 ml & 1800 ml

Step-by-step explanation:

[tex]3x + 8x = 2475\\\\11x = 2475\\\\x=225\\\\3(225)=765\\8(225)=1800[/tex]

Answer:

122 degrees

Step-by-step explanation:

A parallelogram has 360 degrees in total

360 - (58 + 58) = 244

244/2 = 122

I hope this helped you!

Answer:

x = 122

Step-by-step explanation:

Consecutive angles in a parallelogram are supplementary, sum to 180° , so

x + 58 = 180 ( subtract 58 from both sides )

x = 122

[tex]\begin{cases} h(x)=\sqrt{x}\\ g(x)=4x^2+4 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ g(\sqrt{a})=4(\sqrt{a})^2+4\implies g(\sqrt{a})=4\sqrt{a^2}+4\implies g(\sqrt{a})=\boxed{4a+4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ h(~~g(\sqrt{a})~~)\implies h\left( \boxed{4a+4} \right)=\sqrt{4a+4}\implies h(~~4a+4~~)=\sqrt{4(a+1)} \\\\\\ h(~~4a+4~~)=\sqrt{2^2(a+1)}\implies h(~~4a+4~~)=2\sqrt{a+1}[/tex]

Answer:

The answer is 10

Step-by-step explanation:

a + 5 =15

15-5=10

Answer:

Step-by-step explanation:

a+5=15

a=15-5

a=10

1.

[tex](3 {x}^{2} - 4x - 1) + (8 {x}^{2} - x + 6) \\ \\ combining \: the \: like \: terms,\:we\:have\\ \\ = 3 {x}^{2} + 8 {x}^{2} - 4x - x - 1 + 6 \\ \\ = 11 {x}^{2} - 5x + 5[/tex]

2.

[tex](6 {x}^{2} - x - 4) + ( 2{x}^{2} + 5x - 5) \\ \\combining \: the \: like \: terms, \: we \: have \\ \\= 6 {x}^{2} + 2 {x}^{2} - x + 5x - 4 - 5 \\ \\= 8 {x}^{2} + 4x - 9[/tex]

3.

[tex](4 {x}^{2} + 2x - 5) + (6 {x}^{2} - x - 5) \\ \\ combining \: th e\:l ike \: terms, \: we \: have \\ \\= 4 {x}^{2} + 6 {x}^{2} + 2x - x - 5 - 5 \\ \\= 10 {x}^{2} +x - 10[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

Answer:

7:20

Step-by-step explanation:

divide both by 5 to simplify

Answer:

n=-2,A

Step-by-step explanation:

15-3n=21

-3n=21-15

-3n=6

n=6/-3

=-2

Answer:

[tex]1 + cot^2 \theta[/tex]

Step-by-step explanation:

Given the expression;

[tex]\frac{tan^2\theta+1}{tan^2 \theta}[/tex]

Separating into partial fraction;

[tex]\frac{tan^2 \theta}{tan^2 \theta} + \frac{1}{tan^2 \theta}\\= 1 + \frac{1}{tan^2 \theta}\\\\[/tex]

Since [tex]\frac{1}{tan \theta} = cot \theta\\[/tex]

Hence the expression becomes;

[tex]1 + cot^2 \theta[/tex]

Answer:

yes it is

Step-by-step explanation: