A wire is attached to the top of a 45-foot telephone pole and anchored to the ground. The angle of elevation is 64 degrees. How long is the wire to the nearest foot?

Answer:

7:10 (boys to girls)

10:7 (girls to boys)

7:17 (boys to everyone combined)

10:17 (girls to everyone combined)

~

Answer:

30

Step-by-step explanation:

These are generally easier to evaluate by hand if they are simplified first.

... (4a^2)b -ab^2 -(3a^2)b +ab^2 -ab +6

... = (a^2)b(4 -3) + ab^2(-1 +1) -ab +6

... = a^2·b -ab +6

... = ab(a -1) +6

... = (-3)(2)(-3-1) +6

... = (-6)(-4)+6

... = 24 +6 = 30

Put the values of a = -3 and b = 2 to the expression

[tex]4a^2b-ab^2-3a^2b+ab^2-ab+6[/tex]

[tex](4)(-3)^2(2)-(-3)(2)^2-(3)(-3)^2(2)+(-3)(2)^2-(-3)(2)+6\\\\=(4)(9)(2)+(3)(4)-(3)(9)(2)-(3)(4)-(-6)+6\\\\=72+12-54-12+6+6\\\\=\boxed{30}[/tex]

The number 9.36×10-4 in standard form is 0.000936. You convert from scientific notation to standard form by moving the decimal point to the left by the number equivalent to the exponent when the exponent is negative.

Explanation:

When asked what is 9.36×10-4 in standard form, we are being asked to convert a number from scientific notation to its regular number format. Scientific notation is a method of writing numbers that are too big or too small to be conveniently written in decimal form. To convert this to standard form, we move the decimal point to the left if the exponent is negative (or to the right if the exponent is positive) as many times as the value of the exponent.

In this case, we have a negative exponent (-4), so we move the decimal four places to the left:

9.36 -> 0.936 -> 0.0936 -> 0.00936 -> 0.000936

Therefore, 9.36×10-4 in standard form is 0.000936.

Answer:

Length of Charlie's brother's room  = 8 2/5 feet

Area of Charlie's brother's room  = 60 9/10 feet²

Step-by-step explanation:

Width Charlie's room = 7 1/4 = (7 x 4 +1)/4 = 29/4  feet

Length Charlie's room =  10 1/2 = (10 x 2 +1)/2 = 21/2 feet

Length brother's room = 4/5 x 21/2 = (4 x 21)/(5 x 2) = 84/10 = 8 2/5 feet

Area = Length x Width = (42/5 x 29/4) feet² = 1218/20 feet² = 60 9/10 feet²

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

Point (1,8)  

Step-by-step explanation:

We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.

When a point divides any segment internally in the ratio m:n, the formula is:

[tex][x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}][/tex]

Let us substitute coordinates of point P and Q as:

[tex]x_1=-8[/tex],

[tex]y_1=-4[/tex]

[tex]x_2=4[/tex]

[tex]y_2=12[/tex]

[tex]m=3[/tex]

[tex]n=1[/tex]

[tex][x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}][/tex]

[tex][x=\frac{12-8}{4},y=\frac{36-4}{4}][/tex]

[tex][x=\frac{4}{4},y=\frac{32}{4}][/tex]

[tex][x=1,y=8][/tex]

Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.

Answer:

Step-by-step explanation:

1,8

The "rate of change" is presumed to refer to the rate at which the balance in the bank account changes as dues are collected from Art Club members. It increases by $15 for each new collection, so we can say ...

... the rate of change is $15 per member.

We further presume that the problem intends the "initial value" to refer to the fact that the 17 × $15 = $255 does not match the full amount of the current Art Club account balance ($300). So, there must have been some balance in the account before collection started. We can interpret that $45 "initial value" as ...

... the account balance before dues collection started is the initial value.

Answer:

{x = 1/7 ,y = 1

Step-by-step explanation:

Solve the following system:

{-5 y = -5 | (equation 1)

{7 x + 6 y = 7 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 6 y = 7 | (equation 1)

{0 x - 5 y = -5 | (equation 2)

Divide equation 2 by -5:

{7 x + 6 y = 7 | (equation 1)

{0 x+y = 1 | (equation 2)

Subtract 6 × (equation 2) from equation 1:

{7 x+0 y = 1 | (equation 1)

{0 x+y = 1 | (equation 2)

Divide equation 1 by 7:

{x+0 y = 1/7 | (equation 1)

{0 x+y = 1 | (equation 2)

Collect results:    Answer:    {x = 1/7 ,y = 1

Answer:

No

Step-by-step explanation:

Answer:

The correct answer would be A) (4, 49.6)

Step-by-step explanation:

In order to find the equation, we first have to start with the base form of direct variation.

y = kx

Now we input the k value.

y = 12.4x

Now that we have this, we can try the ordered pairs and look for which satisfies the equation.

y = 12.4x

49.4 = 12.4(4)

49.4 = 49.4

Since this is the true statement, this is the ordered pair that works.

Answer:

(4,49.6)

Step-by-step explanation:

Answer:

X = 37

Y = 29

Step-by-step explanation:

X + Y = 66

X - Y = 8

------

Solve second equation for X

X = Y + 8

Substitute for X in first equation

Y + 8 + Y = 66

2 * Y = 58

Y = 29

___

X - 29 = 8

X = 37

X = 37

Y = 29

Good Luck,

- I.A. -

Answer:

x = 37 and y = 29

Step-by-step explanation:

x + y = 66

x - y = 8

solve second equation for x

x = y + 8

substitute for x in first equation

y+8 +y = 66

2y = 58

y = 29

x - 29 = 8

x = 37

x = 37 and y = 29

Answer:

(A) y - 7 = 2(x -2)

(B) y = -x + 6; y - 5 = -1(x + 1)

(C) Consistent independent

(D) (1, 5)

Step-by-step explanation:

(A) Road 1

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁)     Insert the points  

 3 - 7 = m(0 - 2)

     -4 = m(-2)           Divide each side by -2

     m = -4/(-2)          Divide numerator and denominator by-2,

      m = 2

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 7 = 2(x₂ -2)

y - 7 = 2(x -2)

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

(B) Road 2

(a) Slope

y = mx + b

Choose point (3,3)

m = (3 - 5)/(3 - 1)

m = -2/2

m = -1

=====

(b) y-intercept

y = mx +b

Choose point (3,3).

3 = -3 + b      Add 3 to each side

b = 6

=====

(c) Equation of line (point-slope form)

y = mx + b

y = -x + 6

=====

(d) Equation of line (slope-intercept form)

y - 5 = -1(x - 1)

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

(C) Consistency

The two roads intersect.

There is only one point of intersection, so this is a consistent, independent system of equations

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

(D) Point of intersection

(1)      y - 7 = 2(x -  2)

(2)          y =   -x + 6     Substitute (2) into (1)

-x + 6 – 7 = 2(x – 2)    Remove parentheses

       -x - 1 = 2x – 4      Add 4 to each side

       -x +3 = 2x            Add x to each side

             3 = 3x            Divide each side by 3

             x = 1               Substitute into 2

=====

            y = -1 + 6

           y = 5

The point of intersection is (1, 5).

Answer:

Step-by-step explanation:

Numerical reasoning

If all questions were 2-point, the total score would be 80. It is 20 more than that. Each 4-point question that replaces a 2-point question will add 2 points to the score, so there must be 20/2 = 10 of them.

There are 10 4-point questions and 30 2-point questions.

_____

With an equation

Let x represent the number of 4-point questions. Then 40-x is the number of 2-point questions. The total number of points is ...

... 2(40-x) +4x = 100

... 2x +80 = 100 . . . . simplify

... 2x = 20 . . . . . . . . .subtract 80

... x = 10 . . . . . . . . . . divide by 2.

There are 10 4-point questions and 40-10=30 2-point questions.

Answer:

2.5 min

Step-by-step explanation:

The tortoise takes 1 min/3 m.

7.5 × 1/3  = 2.5 min

Answer:

D) 75%

Step-by-step explanation:

75% of 24 = 0.75 x 24 = 18

B. (5, -2)

Try the points in the inequalities and see what works. Here, we evaluate the point in the first inequality, and if that works, then the second inequality.

A. 2 ≤ -(-5) -5 . . . ⇒ . . . 2 ≤ 0 . . . false

B. -2 ≤ 5 -5 . . . true

... -2 ≥ -(5) -4 . . . true . . . . . . selection B is a viable choice

C. we know from A that the first inequality will be satisfied

... -2 ≥ -(-5) -4 . . . ⇒ . . . -2 ≥ 1 . . . false

D. 2 ≤ 5 -5 . . . . false

Answer:

Total tax paid by Bruce = $2477.62

Step-by-step explanation:

Bruce banner taxable income last year = $43,467

State's income tax rate = 3.9%

State's income tax = 43467*3.9% = 43467*0.039 = $1695.21

City income tax rate is = 1.8

City income tax = 43467*1.8% = 43467*0.018 =$782.41

Total tax = $1695.21 + $782.41

= $2477.62

Thank you.

Answer:

x = 2/5

Step-by-step explanation:

[tex]x^3=\dfrac{0.008}{0.125}=\dfrac{8}{125}=\dfrac{2^3}{5^3}\\\\x=\sqrt[3]{\dfrac{2^3}{5^3}}=\dfrac{\sqrt[3]{2^3}}{\sqrt[3]{5^3}}=\dfrac{2}{5}[/tex]

The value of x is 2/5.

Answer:

x = 2/5

Step-by-step explanation:

x^3 = .008/.125

Take the cubed root on each side

x^3 ^ (1/3)  = (.008/.125) ^ 1/3

Using ( a/b) ^c = a^c / b^c  and a^b^c = a^ (b*c)

x^(3 *(1/3))  = (.008) ^ 1/3 / (.125) ^ 1/3

x = (.008) ^ 1/3 / (.125) ^ 1/3

x = .2/.5

x = 2/5

The simplest form of 38 multiplied by 45 equals  to 1710.

To multiply 38 and 45, we'll use the long multiplication method:

  38

x 45

------

 190   (38 * 5)

+1520  (38 * 40, shift one position to the left)

------

1710

So, 38 multiplied by 45 equals 1710.

Another method is to break down 38 into its factors to simplify the multiplication:

38 = 2 * 19

Now, we can rewrite 38 * 45 as (2 * 19) * 45:

(2 * 19) * 45 = (2 * 45) * 19

             = 90 * 19

Now, we can multiply 90 by 19:

90

x 19

-----

180  (90 * 9, shift one position to the left)

+ 0   (90 * 1, with a zero placeholder)

-----

1710

Again, we get the result as 1710.

So, whether we use long multiplication directly or break down the numbers into factors, the result remains the same: 38 * 45 = 1710.

Answer:

Point

Step-by-step explanation:

If you are referring to geometry

Answer:

Question 39: False

Question 43: True

Step-by-step explanation:

Question 39

|-4| is a solution of x ≤ 4

|-4| ⇒ This mean the absolute value of 4. The sign s are neglected.

So, |-4| is not a  solution of x ≤ 4.

Question 43

The point (5, -1) is a solution of the equation: y = 2x − 11.

To prove this we are to substitute the point (5, -1) in the equation y = 2x − 11.

y = -1 and x = 5

y = 2x − 11   ⇒   -1 = 2(5) -11

                         -1 = 10 - 11

                         -1 = -1

Answer:

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.

Step-by-step explanation:

I like to call the numbers in the ratio 1 : 3 "ratio units".

That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).

_____

Coment on the answer wording

I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".

In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."

Answer:

[-5/2, 1/2] is the correct answer

Step-by-step explanation:

Subtract the left side to compare to zero:

... 4x^2 +8x -5 ≤ 0

... (2x +5)(2x -1) ≤ 0 . . . . factor

... x = -5/2 . . . or . . . x = 1/2 . . . . are the zeros

The factors will differ in sign (the product will be negative) when x is between the zero values. Hence the solution set is ...

... x ∈ [-5/2, 1/2]

_____

Check

When you normalize the leading coefficient of the quadratic to 1, it becomes ...

... x² +2x -5/4 ≤ 0

Now, you know the sum of zeros must be -2 and the product of zeros must be -5/4. The zeros associated with the answer given in your key have a sum of -4.5 and a product of -5/2. It cannot be right.

Answer:

ave rate of change = (-6)^(2+2) +3 -  (-6)^(-1+2) +3

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

                                      2+1

Step-by-step explanation:

To find the average rate of change

ave rate of change = f(x2) - f(x1)

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

                                   x2-x1

We know that x2 = 2 and x1 = -1

ave rate of change = f(2) - f(-1)

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

                                   2--1

ave rate of change = (-6)^(2+2) +3 -  (-6)^(-1+2) +3

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

                                      2+1

Answer:

ave rate of change = (-6)^(2+2) +3 -  (-6)^(-1+2) +3

Step-by-step explanation:

Attached pictures shows the answers in RED.

E. 168 sq units

The legs of this right triangle have length 24 and 14, so the area is ...

... A = (1/2)bh = (1/2)(24)(14) = 168 . . . . sq units

Answer:

Probability that a vehicle is white, given that the vehicle is a car :

0.2222

Step-by-step explanation:

A: vehicle is white

probability that a vehicle is white =P(A)= 0.25

B:vehicle is a car

probability that it is a car =P(B)= 0.36

A∩B:vehicle is a white car

P(A∩B)=probability that it is a white car = 0.08

A/B:vehicle is white,given that vehicle is a car

to find P(A/B)

baye's theorem says that

P(A∩B)=P(A/B)×P(B)

⇒   0.08=P(A/B)×0.36

⇒  P(A/B)=0.2222

Hence, probability that a vehicle is white, given that the vehicle is a car is :

0.2222

Answer: 0.22

Step-by-step explanation:

confirmed

B. 3x +y = 4

It is perhaps easiest to simply try the equations to see which one works.

For x=0, there are two different kinds of answers:

... A and C: -y = 4

... B and D: y = 4

Since we know y=4 when x=0 (from the point (0, 4)), we can eliminate choices A and C.

___

Using the point (1, 1), you can try choices B and D to see which works:

... B: 3·1 +1 = 4 . . . . true (put 1 where x and y are in the equation)

... D: -3·1 +1 = -2 = 4 . . . . false

The appropriate choice is the equation of B: 3x +y = 4.

_____

Derive the equation from the given points

There are several ways you can derive the equation. Since you have the y-intercept (the point with x=0), you can use the slope-intercept form to start.

The slope (m) is ...

... m = (change in y)/(change in x) = (4 -1)/(0 -1)

... m = -3

We know the y-intercept (b) is 4, so the slope-intercept form of the equation is ...

... y = mx +b

... y = -3x +4

Adding 3x puts this in standard form:

... 3x +y = 4

The equation of the line passing through points (1,1) and (0,4) is y = -3x + 4 or in standard form -3x + y = 4.

In the subject of mathematics, when it comes to identifying equations of the line in a graph, we consider the points it passes through. In this case, the line passes through the points (1, 1) and (0, 4). The equation of a line can be found using the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. The slope m between two points can be found using the formula: m = (y2 - y1) / (x2 - x1).

Let's substitute the given points into the slope formula and find the slope: m = (4 - 1) / (0 - 1) = -3.  Now, using the slope and one of the points (let's use (0,4)), we substitute into the line formula: y - 4 = -3(x - 0). This simplifies to y = -3x + 4, which aligns with answer D: −3x + y = 4.

https://brainly.com/question/33578579

#SPJ3

Answer:

b. 3x - (5y -7)

Step-by-step explanation:

Let x represent "a number". Let y represent "another number."

The "3 times a number" is represented by 3x.

And "5 times another number less 7" is represented by 5y -7.

The difference between these quantities is the second subtracted from the first:

... 3x - (5y -7) . . . . matches selection b.

Answer:

Step-by-step explanation:

We have been given an equation:

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

(a) Related equation means the equation that are equivalent to the given equation.

We can shift 3 on the right hand side of the equation:

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

We can solve the mixed fraction [tex]2\frac{1}{2}=\frac{5}{2}[/tex] we get.

(2)[tex]x=3+\frac{5}{2}[/tex]  

We can solve the right hand side of the equation [tex]x=3+\frac{5}{2}[/tex]    we get:

(3)[tex]x=\frac{11}{2}[/tex]

Hence, above three expressions are the related equations of the given equation.

(b) We have to find the related equations that isolates the variable and simplify.

So, basically we can solve for x.

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

[tex]x=1+3[/tex]

[tex]x=4[/tex].

Answer:

f(x)= -x²-4x-2

Step-by-step explanation (this way is not the shortest one):

1. for intercept (-2-√2;0): a(-2-√2)²+b(-2-√2)+c=0

for intercept (-2+√2;0): a(-2+√2)²+b(-2+√2)+c=0

for the point (-1;1): a(-1)²+b(-1)+c=1

2. using the three record written above, it is possible to make up the system of equations and calculate 'a', 'b' and 'c':

[tex]\left \{ \begin{array}{ccc}a-b+c=1\\a(-2- \sqrt2)^2+b(-2- \sqrt2)+c=0\\a(-2+ \sqrt2)^2+b(-2+ \sqrt2)+c=0\end{array}[/tex]

[tex]\left \{ \begin{array}{ccc}a=-1\\b=-4 \\c=-2\end{array}[/tex]

3. the required equation is: -x²-4x-2