A bus leaves Riverside for Springfield and averages only 48 mph. Ten minutes later Smith leaves Riverside for Springfield traveling 64 mph in his car. How long before he overtakes the bus?

Answer:

a+b = 3

Step-by-step explanation:

a = b+4

a^2 = (b+4)(b+4) = b^2 + 8b +16=-b^2 = 12

8b=-4

b = - 1/2

a = 3.5

Answer:

[tex](2 \ sin 60)(3\ cos 60) +3\ tan 30\ =\ \frac{5\sqrt3}{2}[/tex]

Step-by-step explanation:

[tex](2 \ sin 60)(3 \ cos 60) + 3\ tan 30\\\\= (2 \times \frac {\sqrt3}{2}) (3 \times \frac{1}{2})+ (3 \times \frac{1}{\sqrt3})\\\\=(\sqrt{3}\ \times \frac{3}{2})+ \frac{3}{\sqrt3}\\\\=\frac{3\sqrt3}{2}+\frac{3}{\sqrt3}\\\\=(\frac{3\sqrt3}{2} \times \frac{\sqrt3}{\sqrt3})+(\frac{3}{\sqrt3} \times \frac{2}{2})\\\\=\frac{3\times (\sqrt3)^2}{2\sqrt3}\ + \ \frac{6}{2 \sqrt3}\\\\=\frac{3 \times 3}{2 \sqrt3} +\frac{6}{2 \sqrt3}\\\\=\frac{9+6}{2\sqrt3}\\\\=\frac{15}{2\sqrt3} \times \frac{\sqrt3}{\sqrt3}\\\\[/tex]

[tex]=\frac{15 \sqrt3}{2 \times (\sqrt{3})^2}\\\\=\frac{15 \sqrt 3}{2 \times 3}\\\\=\frac{5\sqrt3}{2}[/tex]

Answer:

20.485 Meters

Step-by-step explanation:

So first you wanna draw a diagram.  Start with the tower, then on the ground to the left (or right) draw a point.  The point will be labeled as 42 m away from the tower.  Now draw a line from that point to the top of the tower.  This makes your triangle, and that angle you just drew that touches the point is 26 degrees.

Now, since you have a right triangle you can use trig.  You know an angle and a side.  Specifically, relative to the 26 degree angle you know the adjacent angle and want the opposite, which is the tower.  So opposite and adjacent is tangent.  So you set up tan(26) = o/42 where o is the opposite side.  

So solving you get o = 20.485 meters

Answer:

1. m∠CGB=120

3. m∠AGD=90

5. m∠CGD=150

2. m∠BGE=60

4. m∠DGE=30

6. m∠AGE=120

Step-by-step explanation:

Sorry that they are out of order.

Answer:

1. m∠CGB=120°

2.m∠BGE=60°

3.m∠AGD=90°

4.m∠DGE=30°

5.m∠CGD=150°

6.m∠AGE=120°

Step-by-step explanation:

My work is scatterbrained so I'm not gonna be any help if I give an explanation.

Answer:

Area = 14.5

Step-by-step explanation:

Let's label the given coordinates A, B, C;

Thus;

A = (2, 3)

B = (-1, 0)

C = (2, -4)

From the coordinate geometry formula, the formula for area of a triangle with 3 vertices is;

Area = [Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2

Area = [2(0 - (-4)) + (-1)(-4 - 3) + 2(3 - (-4))]/2

Area = 29/2

Area = 14.5

Answer:

10*30 = 300, 300 is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The lines indicates that all side are 10 cm and the white shape is a rhombus

the biggest figure is a rectangle: its angles are 90 degrees

so the triangles have the angles : 90 30 60

so, we have that theeir side are

5 cm and 5√3 cm

perimeter = (10 + 5√3)* 2 + 10 = 20 + 10√3 + 10 = 30 + 10√3 = 10(3 + √3) cm

A = (10 + 5√3)* 5 = 50 + 25√3 = 25(2+√3) cm^2

Area of the two triangle = 5 * 5√3 = = 25√3 cm^2

if we want know the perimeter and the area of the white figure, we have

perimeter = 40 cm

area = 50 + 25√3 - 25√3 = 50 cm^2

Answer:

Step-by-step explanation:

On the day of the canteen, 800 coupons were sold, the price of each coupon was RM 30 and RM 50 respectively. The amount of money earned from the sale of coupons was RM30000. How many copies of RM30 and RM50 coupons were sold?

Let:

RM 30 = x

RM 50 = y

x + y = 800 - - - (1)

30x + 50y = 30000 - - - (2)

From (1)

x = 800 - y

Put x = 800 - y in (2)

30(800 - y) + 50y = 30000

24000 - 30y + 50y = 30000

24000 + 20y = 30000

20y = 30000 - 24000

20y = 6000

y =

Answer:

x = 3     y = 5

Step-by-step explanation:

     y=x+2

+    y=-x +8

2y = 10

y = 5

y = -x + 8

5 = -x + 8

x = 3

Answer:

(2x + y)(4x² - 2xy + y²)

Step-by-step explanation:

8x³ + y³ ← is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²) , then

8x³ + y³

= (2x)³ + y³

= (2x + y)((2x)² - 2xy + y²) , that is

(2x + y)(4x² - 2xy + y²)

7

Step-by-step explanation:

To solve this you need to use trigonometry:

1. Identify the sides. In this case, x is opposite and 10 is adjacent.

2. Identify which part of SOHCAHTOA you need to use. In this case, you need to use TOA.

3. Form your equation. In this case, x = tany x A

4. Substitute numbers into your equation. In this case, x = tan35° x 10

5. Calculate this equation using a scientific calculator. In this case the answer is 7.

Answer:

0.15

Step-by-step explanation:

first get three percent:

3/100 = 3%

then use of operation:

3% of 5;

= (3/100) * 5

Answer:

60%

Step-by-step explanation:

To change a fraction to a percentage, multiply the fraction by 100% , then

[tex]\frac{3}{5}[/tex] × 100% = [tex]\frac{3(100)}{5}[/tex] = [tex]\frac{300}{5}[/tex] = 60%

Given:

A figure of a circle.

To find:

The value of x.

Solution:

Central angle theorem: According to this theorem, the central angle on an arc is twice of the subtended angle on that arc.

Using the central angle theorem, we get

[tex]x=2\times 35^\circ[/tex]

[tex]x=70^\circ[/tex]

Therefore, the value of x is 70 degrees.

To find the inverse of a function, we switch out every x for a y and vice-versa.

Original: y = 4x + 8

Flipped: x = 4y + 8

Now, we solve for y again to put this equation into slope-intercept form.

x = 4y + 8

4y = x - 8

y = 1/4x - 2

h(x) = 1/4x - 2

Hope this helps!

Answer:

1241.99

Step-by-step explanation:

1241.993 grams is the original answer but rounded to the nearest hundred is 1241.99

Answer:

[tex]x=1[/tex]

[tex]y=2[/tex]

Step-by-step explanation:

[tex]y=x^2+3x-2[/tex] , [tex]y+3=5x[/tex]

Replace all occurrences of [tex]y[/tex] in [tex]y+3=5x[/tex] with [tex]x^2+3x-2.[/tex]

[tex](x^2+3x-2)+3=5x[/tex]

[tex]y=x^2+3x-2[/tex]

Add [tex]-2[/tex] and 3.

[tex]x^2+3x+1=5x[/tex]

[tex]y=x^2+3x-2[/tex]

Subtract 5x from both sides of the equation.

[tex]x^2+3x+1-5x=0[/tex]

[tex]y=x^2+3x-2[/tex]

Subtract 5x from 3x.

[tex]x^2-2x+1=0[/tex]

[tex]y=x^2+3x-2[/tex]

Rewrite 1 as [tex]1^2[/tex].

[tex]x^2-2x+1^2=0[/tex]

[tex]y=x^2+3x-2[/tex]

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

[tex]2x=2[/tex] · [tex]x[/tex] · [tex]1[/tex]

[tex]y=x^2+3x-2[/tex]

Rewrite the polynomial.

[tex]x^2-2[/tex] · [tex]x[/tex] · [tex]1[/tex] [tex]+[/tex] [tex]1^2=0[/tex]

[tex]y=x^2+3x-2[/tex]

Factor using the perfect square

trinomial rule [tex]a^2-2ab+b^2=(a-b)^2,[/tex]

where a = x and b = 1.

[tex](x-1)^2=0[/tex]

[tex]y=x^2+3x-2[/tex]

Set the [tex]x-1[/tex] equal to 0.

[tex]x-1=0[/tex]

[tex]y=x^2+3x-2[/tex]

Add 1 to both sides of the equation.

[tex]x=1[/tex]

[tex]y=x^2+3x-2[/tex]

Replace all occurrences of [tex]x[/tex] in

[tex]y=x^2+3x-2[/tex] with 1.

[tex]y=(1)^2+3(1)-2[/tex]

[tex]x=1[/tex]

[tex]y=2[/tex]

Answer:

The probability of picking 1 red candle followed by another red candle is 16.66%.

Step-by-step explanation:

Since Alfred draws candles randomly from a pack containing 4 colored candles of the same shape and size, and there are 2 red candles, 1 green candle, and 1 blue candle, and he draws 1 candle and then draws another candle without replacing the first one, to find the probability of picking 1 red candle followed by another red candle, the following calculation must be performed:

2/4 x 1/3 = X

0.5 x 0.333 = X

0.16666 = X

Therefore, the probability of picking 1 red candle followed by another red candle is 16.66%.

Answer:

1/6

Step-by-step explanation:

2/4 x 1/3 = 1/6

Answer:

true

Step-by-step explanation:

Because a logically equivalent is the same as biconditional statement

Step-by-step explanation:

hello the answer is true, you can check but it's obviously true

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Let integers be x and x-1

ATQ

[tex]\\ \sf\longmapsto 2x-1=1[/tex]

[tex]\\ \sf\longmapsto 2x=1+1[/tex]

[tex]\\ \sf\longmapsto 2x+2[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Now

[tex]\\ \sf\longmapsto x-1=1-1=0[/tex]

But

Integers can be x and 1-x as their sum is 1

[tex]\\ \sf\longmapsto x(1-x)=-12[/tex]

[tex]\\ \sf\longmapsto x- x^2=-12[/tex]

[tex]\\ \sf\longmapsto x^2-x-12=0[/tex]

[tex]\\ \sf\longmapsto x^2-4x+3x-12=0[/tex]

[tex]\\ \sf\longmapsto x(x-4)+3(x-4)=0[/tex]

[tex]\\ \sf\longmapsto (x-4)(x+3)=0[/tex]

[tex]\\ \sf\longmapsto x=4,-3[/tex]

Hey there!

To solve this problem, we will be using Trigonometric Ratio. Trigonometry is always helpful when it comes to finding a missing side with specific measure/angle.

1. Cosine Ratio

2. Adjacent and Hypotenuse

Hope you understand this topic! If not, feel free to ask!

3. Solve The Problem

Therefore, the equation for the problem is:

[tex] \large{cos62 \degree = \frac{x}{12} }[/tex]

*cos is the short form of cosine*

At this part, we need a calculator to find the value of cos62 degrees. That's because it is not a degree like 0, 30, 45, 60 and 90 which can be found without a calculator.

When we put cos62 in a calculator, make sure to put it in degree mode since a calculator has two modes which are degree and radian.

When we put cos62 in, we should get 0.46947156... Because you want a one decimal place, we round the value up to the nearest tenth as we get 0.5 because 6 is greater than 5 and should be rounded up and not down. That makes the equation to:

[tex] \large{0.5 = \frac{x}{12} }[/tex]

Oh well! Finally to the equation part. Whenever you have to solve the equation that has decimal numbers in it, the best way to deal with decimal numbers is to make them into a whole number or integer. But how? Simply multiply the whole equation by 10. Because 0.5×10 is 5 thus 0.5 becomes an integer after multiplying 10.

[tex] \large{0.5 \times 10 = \frac{x}{12} \times 10} \\ \large{5 = \frac{10x}{12} }[/tex]

10x/12 can be simplified again.

[tex] \large{5 = \frac{5x}{6} }[/tex]

Then we isolate x-value by multiplying 6 the whole equation.

[tex] \large{5 \times 6 = \frac{5x}{6} \times 6} \\ \large{30 = 5x} \\ \large{x = 6}[/tex]

Huh, that's awkward! We want the answer in a 1 decimal place but seems like the answer for this is 6. Why? Well that is not an exact answer, but more like an approximation. Because the value of cos62 degree is actually a repeating decimal and doesn't have exact value.

When we put the equation cos62 = x/12 in the equation and solve. It appears that the the answer is 5.63365875. Because we round up to nearest tenth, it gives an approximation to 5.63365875 instead.

Hence, the equation and value above is just a rounded to the whole number from 5.63365875.

Because you want a one place decimal. Hence,

4. Final Answer

Answer:

in 90 minutes he ran 30 laps

there is 60 minutes in a hour so the fraction would be

2/3 so we have to multiply this by 30

2/3*30=20

He can run 20 laps in a hour

Hope This Helps!!!

Hello,

The rational roots may be all divisors of 100

+1,-1,+2,-2,+4,-4,+5,-5,+10,-10,+20,-20,+25,-25,+50,-50,+100,-100

f(x)=x^4-29x^2+100

f(5)=5^4-29*5^2+100=0 : 5 is a root

f(-5)=(-5)^4-29*(-5)²+100=0 : -5 is a root

f(2)=2^4-29*2²+100=0 : 2 is a root

f(-2)=(-2^)^4-26*(-2)²+100= 0 : -2 is the last root.

Answer:

b

Step-by-step explanation:

[tex]\frac{x^4}{x^7} =x^4 \times x^{-7} =x^{4-7} =x^{-3}[/tex]

Answer:

b) 2 Km para o leste

Step-by-step explanation:

1. 2 km N

2. 2 km W

3. 1 km S

4. 4 km E

5. 2 km S

Sul e Norte:

(1.) 2 km N + (3.) 1 km S + (5.) 2 km S = 2 km - 1 km - 2 km = 0

Este e Oeste:

(2.) 2 km W + (4.) 4 km E = -2 km + 4 km = 2 km E

Veja imagem abaixo.

Answer:

Domain = ( -∞ , ∞ )

Range = ( ∞ , ∞ )

Step-by-step explanation:

A function is given to us and we need to find the domain and range of the given function .

The function :-

[tex]\rm \implies y = \dfrac{1}{4}x - 6 [/tex]

Definitions :-

In this case, there is no real number that makes the expression undefined. Therefore the domain will be :-

Domain :-

[tex]\rm Domain = ( -\infty , \infty ) [/tex]

or

[tex]\rm Domain = \{ x | x \in \mathbb{R} \}[/tex]

Range :-

[tex]\rm Range = ( -\infty , \infty ) [/tex]

or

[tex]\rm Range = \{ y | y \in \mathbb{R}\} [/tex]

Answer:

Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers.

Step-by-step explanation:

Answer:

Step-by-step explanation:

C looks right

as shown in the graphs  :P

Answer:

"85.7%" is the right answer.

Step-by-step explanation:

According to the question,

The total capacity of water tank will be:

⇒ [tex]v_1=A\times 14[/tex]

The total volume of water will be:

⇒ [tex]v_2=A\times 12[/tex]

Now,

The percentage of total capacity will be:

= [tex]\frac{100\times v_2}{v_1}[/tex]

= [tex]\frac{v_2}{v_1}\times 100[/tex]

By putting the values, we get

= [tex]\frac{A\times 12}{A\times 14}\times 100[/tex]

= [tex]85.7[/tex]%