The formula for the area of a triangle is A = 12bh, where b is the base of the triangle and h is the height of the triangle. What is the length of the base if the area is 32 cm2 and the height is 4 cm? A. 4 cm B. 8 cm C. 16 cm D. 18 cm

Answer:

If there are 1500 students in your school then 960 students would enjoy watching TV

Step-by-step explanation:

Step 1: We know that 64% of kids aged from 11 to 15 enjoy watching TV and there is 1500 students in your school

Step 2: We now want to find 64% of 1500, we can rewrite 64% as 0.64. We multiple 1500 by 0.64 to find out how many students enjoy watching TV

0.64 x 1500 = # of students who like watching TV

960 = # of students who like watching TV

Therefore out of 1500 students, 960 would enjoy watching TV

Answer:

Step-by-step explanation:

a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...

  m = -1/(5/6) = -6/5

Then the point-slope form of the desired line through (-3, 6) can be written as ...

  y = m(x -h) +k . . . . . line with slope m through (h, k)

  y = (-6/5)(x +3) +6

  y = -6/5x +12/5 . . . equation of line B

__

b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.

When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...

  d = |ax +by +c|/√(a² +b²)

The equation of line A can be written in general form as ...

  y = 5/6x -5/2

  6y = 5x -15

  5x -6y -15 = 0

Then the distance from P to the line is ...

  d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61

The length of segment PX is (66√61)/61.

__

c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...

  y = 5/6x -5/2

  y = -6/5x +12/5

Equating y-values gives ...

  5/6x -5/2 = -6/5x +12/5

Adding 6/5x +5/2 gives ...

  x(5/6+6/5) = 12/5 +5/2

  x(61/30) = 49/10

  x = (49/10)(30/61) = 147/61

  y = 5/6(147/61) -5/2 = -30/61

Then the point of intersection of the lines is X = (147/61, -30/61).

So, the midpoint of PX is ...

  M = (P +X)/2

  M = ((-3, 6) +(147/61, -30/61))/2

  M = (-18/61, 168/61)

Answer:

See below.

Step-by-step explanation:

In each case, you are looking for time. We know speed is distance divided by time. Lets start with the speed formula.

speed = distance/time

Now we solve it for time. Multiply both sides  by time and divide both sides by speed.

speed * time = distance

time = distance/speed

Time is distance divided by speed. In each problem, you have a speed and a distance. Divide the distance by the speed to to find the time.

1) speed = 44.1 km/h; distance = 150 km

time = distance/speed = 150 km/(44.1 km/h) =

= 3.401 hours = 3 hours + 0.401 hour * 60 min/hour = 3 hours 24 minutes

2) speed = 120 km/h; distance = 90 km

time = distance/speed = 90 km/(120 km/h) =

= 0.75 hours = 0.75 hour * 60 min/hour = 45 minutes

3) speed = 125 m/s; distance = 500 m

time = distance/speed = 500 m/(125 m/s) =

= 4 seconds

Answer:

(A)

Sin á = a/c

Cos ∅ = a/c

Tan á = a/b

(B)

Sin á = a/c

Cos á = b/c

Tan á = a/b

Therefore á=

(inverse sin) a/c

Or

(Inverse cos) b/c

Or

(Inverse tan) a/b

(C)

If b = 12 and c = 13

then a =√(c²-b²)

= 5

Hence 5/13 = a/c

Therefore sin á = cos ∅ = a/c = 5/13

Answer:

see explanation

Step-by-step explanation:

Since (k, 3) lies on each of the lines, the point satisfies the equations.

Substitute x = k, y = 3 into each and solve for k

y = 3x + 1

3 = 3k + 1 ( subtract 1 from both sides )

2 = 3k ( divide both sides by 3 )

k = [tex]\frac{2}{3}[/tex]

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

y = 4x - 2

3 = 4k - 2 ( add 2 to both sides )

5 = 4k ( divide both sides by 4 )

k = [tex]\frac{5}{4}[/tex]

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

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

3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )

k = 6

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

2x + 3y = 4

2k + 3(3) = 4

2k + 9 = 4 ( subtract 9 from both sides )

2k = - 5 ( divide both sides by 2 )

k = - [tex]\frac{5}{2}[/tex]

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

Explanation:

The translation notation T(-5, 3) looks like an ordered pair point, but it is not. Instead, it is a rule to tell you how to shift any point left/right and up/down. The first number is the left/right shifting as its done along the x axis. The negative value means we shift left, so we shift 5 units to the left. The positive 3 in the y coordinate place means we shift 3 units up.

We see this shifting happen when we go from

The translation notation T(-5, 3) is the same as writing [tex](x,y) \to (x-5, y+3)[/tex] which may be a more descriptive notation to use, and it would avoid confusion with ordered pair point notation.

Answer:

y=-x+2  

Step-by-step explanation:

it is linear equation y=mx+b two points (0,2),(1,1)

find m ( slope)=y2-y1/x2-x1 ⇒1-2/1-0⇒-1

y=mx+b choosea point from graph :(0,2)\when x =0 the y=b=2

y=-x+2  

Answer:

move to the left 3 more spaces

Step-by-step explanation:

you are at -8 already. Therefore, you (-3) more spaces, so you go to the left three more spaces. Use the saying keep change change to help with this.

Keep the first number sign, change the next sign, and the next sign.

Answer:

d

Step-by-step explanation:

Answer:

Sin

Step-by-step explanation:

Sin < = opposite/hypotenuse

Answer:

[tex]\frac{1}{9^4}[/tex].

Step-by-step explanation:

[tex]9^{-4}[/tex]

= [tex]\frac{1}{9^4}[/tex]

= [tex]\frac{1}{9 * 9 * 9 * 9}[/tex]

= [tex]\frac{1}{81 * 81}[/tex]

= [tex]\frac{1}{6561}[/tex]

= 0.0001524157903.

Hope this helps!

Answer:

The product renders: [tex]-9-7\,i[/tex]

Step-by-step explanation:

Recall that the product of the imaginary unit i by itself renders -1

Now proceed with the product of the two complex numbers using distributive property:

[tex](1-5\,i)\,(1-2\,i)=1-2\,i-5\,i+10\,i^2=1-7\,i-10=-9-7\,i[/tex]

the answer for this is A

Answer:

Correct option is A

Step-by-step explanation:

3x - 7

Three times a number x minus 7

Or

The difference of there times a number and 7

Answer:

None of the options are correct

Step-by-step explanation:

Let us assume point B is at (x, y) and the center of dilation is at (a, b). Therefore the distance between the two points is:

[tex]Distance =\sqrt{(b-y)^2+(a-x)^2}=11 \\\\\sqrt{(b-y)^2+(a-x)^2}=11[/tex]

If Triangle ABC is then dilated by 3/4, the new coordinate is B'(3/4 (x-a) + a, 3/4 (y - b) + b). The distance between B' and the center of dilation would be:

[tex]Distance =\sqrt{(b-[\frac{3}{4}( y-b)+b])^2+(a-[\frac{3}{4} (x-a)+a])^2}[/tex]

Therefore the distance cannot be gotten until the center of dilation is given

Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

a² = b² + c²

where a is the hypotenuse

From the question x is the hypotenuse

So we have

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

2 sqrt(41) =c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + 10^2 = c^2

64+ 100 = c^2

164 = c^2

take the square root of each side

sqrt(164) = sqrt(c^2)

sqrt(4*41) = c

2 sqrt(41) =c

Answer:

Rectangle

Explanation:

Rectangles can be oblong, and square is also a rectangle.

Answer:

Step-by-step explanation:

To find the percentage increase we use the formula

[tex]Percentage \: change = \frac{ change}{original \: quantity} \times 100[/tex]

To find the change subtract the smaller quantity from the bigger one

From the question

original price = $24,600

Current price = $ 25,338

Change = $25,338 - $ 24,600

Change = $ 738

So the percentage increase is

[tex] \frac{738}{24600} \times 100[/tex]

[tex] = \frac{3}{100} \times 100[/tex]

We have the final answer as

Hope this helps you

To get the area simply multiply the length by the width.

(3x^2+5x+10)(x^2-3x-1) = 3x^4 - 4x^3 - 8x^2 - 35x - 10

Answer:

the answer is A

Step-by-step explanation:

got it right on edge

Answer:

313/7

Step-by-step explanation:

Here, we are interested in turning the wordings of the statement to numeric values.

We take it one at a time.

Sum of 35 and 1/5(35) = 35 + 7 = 42

This is added to 1/7(11 + 8)

= 1/7(19) = 19/7

So we have;

42 + 19/7 = (294 + 19)/7 = 313/7

Answer:

11.6%

I hope this helps!

Answer: False. This expression is a monomial!

Answer:

false

Step-by-step explanation:

it is molonomial

Answer:

[tex]T.S.A = \pi r(r+l)\\l = 10mm\\r = 7mm\\\\T.S.A = 3.14 \times 7(7 + 10)\\= 21.98(17)\\T.S.A = 373.66\\\\T.S.A = 373.66[/tex]

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Let's solve your equation step-by-step.

[tex]3(x+7)-14=22[/tex]

Step 1: Simplify both sides of the equation.

[tex]3 ( x + 7 ) - 14 = 22\\(3)^(x) + (3) (7) + - 14 = 22[/tex] (Distribute)

[tex]3x + 21 + -14 = 22[/tex]

[tex]( 3x) + (21 + -14 ) = 22[/tex] (Combine Like Terms)

[tex]3x + 7 = 22\\3x + 7 = 22[/tex]

Step 2: Subtract 7 from both sides.

[tex]3x + 7 - 7 = 22 - 7 \\3x = 15[/tex]

Step 3: Divide both sides by 3.

[tex]\frac{3x}{3} = \frac{15}{3} \\x = 5[/tex]

So your answer would be : [tex]\boxed {x = 5}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer: A.14x + 6; the answer is a polynomial

Step-by-step explanation:

Since all of the variables have integer exponents that are positive this is a polynomial.

Answer:

Graphing Calculator

Step-by-step explanation:

Answer:

x = y/( ku-1)

Step-by-step explanation:

Here in this question, we are asked to solve for x.

we have;

Ux = x+ u/ k

cross multiply;

k * Ux = x + y

kUx = x + y

kUx- x = y

x(KU-1) = y

x = y/( ku-1)

Answer:

[tex]\Huge \boxed{\mathrm{61.22 \ m}}[/tex]

Step-by-step explanation:

A stone is thrown downward straightly with the velocity of 20 m/s and it reaches the ground at the velocity of 40 m/s. What will be the height of building? (Question)

The initial velocity ⇒ 20 m/s

The final velocity ⇒ 40 m/s

We can apply a formula to solve for the height of the building.

[tex](V_f)2 - (V_i)^2 =2gh[/tex]

[tex]V_f = \sf final \ velocity \ (m/s)[/tex]

[tex]V_i = \sf initial \ velocity \ (m /s)[/tex]

[tex]g = \sf acceleration \ due \ to \ gravity \ (m/s^2 )[/tex]

[tex]h = \sf height \ (m)[/tex]

Plugging in the values.

Acceleration due to gravity is 9.8 m/s².

[tex](40)^2 - (20)^2 =2(9.8)h[/tex]

Solve for [tex]h[/tex].

[tex]1600 - 400 =19.6h[/tex]

[tex]1200 =19.6h[/tex]

[tex]\displaystyle h=\frac{1200}{19.6}[/tex]

[tex]h= 61.22449[/tex]

The height of the building is 61.22 meters.

Answer:

The answer to this question can be defined as follows:

In option A, the answer is "- 357.14 miles per hour".  

In option B, the answer is "-0.98".

Step-by-step explanation:

Given:

[tex]\frac{dx}{dt} =- 300 \text{ miles per hour}[/tex]

[tex]\frac{dy}{dt} =- 400 \text{ miles per hour}[/tex]

find:

[tex]\frac{ds}{dt} =?[/tex] when

[tex]x= 150 \\y= 200\\s=x+y\\\\[/tex]

  [tex]= 150+200 \\\\=350[/tex]

[tex]\to s^2=x^2+y^2\\[/tex]

differentiate the above value:

[tex]\to 2s\frac{ds}{dt}= 2x \frac{dx}{dt}+2y \frac{dy}{dt}[/tex]

[tex]\to 2s\frac{ds}{dt}= 2(x \frac{dx}{dt}+y \frac{dy}{dt})\\\\\to \frac{ds}{dt}= \frac{(x \frac{dx}{dt}+y \frac{dy}{dt})}{s}\\\\[/tex]

        [tex]= \frac{(150 \times -300 +200 \times -400 )}{350}\\\\= \frac{-45000+ (-80000) }{350}\\\\= \frac{- 125000 }{350}\\\\= - 357.14 \ \text{miles per hour}[/tex]

In option B:

[tex]\to d=rt\\\\ \to t= \frac{d}{r}[/tex]

[tex]\to \ \ d= 350 \ \ \ \ \ \ r= -357.14\\[/tex]

[tex]\to t= - \frac{350}{357.14}\\\\\to t= - 0.98[/tex]

[tex] \LARGE{ \underline{ \boxed{ \orange{ \rm{Solution:)}}}}}[/tex]

☃️ Refer to the trigonometric table....

Then, proceeding

⇛ tan 60 ° = √3

⇛ tan 60° = tan (a + b)

⇛ 60° = a + b

Flipping it,

⇛ a + b = 60° --------(1)

And,

⇛ tan 30° = 1 / √3

⇛ tan 30° = tan (a - b)

⇛ 30° = a - b

Flipping it,

⇛ a - b = 30° ---------(2)

Now adding eq.(1) and eq.(2),

⇛ a + b + a - b = 60° + 30°

⇛ 2a = 90°

⇛ a = 90° / 2

⇛ a = 45°

Putting value of a in eq.(1),

⇛ 45° + b = 60°

⇛ b = 15°

☄ So, Our Required answers:

━━━━━━━━━━━━━━━━━━━━

Answer:

D: {x∈R | -2 ≤ x ≤ 2 }

R: {y∈R | 0 ≤ y ≤ 4 }

Step-by-step explanation:

The domain ranges between -2 and 2

The range ranges between 0 and 4

Answer:

7x - 7

Step-by-step explanation:

If PR, RS, and PS  are line segments then the equation below will work.

PR + RS = PS

(4x-2) + (3x-5) = 7x - 7