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3 years ago

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50% of all the cakes Lucy bakes that week were party cakes 1-5 fruit cakes and remainder were sponge cakes what percentage of ca

kes were sponge cakes

1 answer:

Stells [14]3 years ago

4 0

30% were sponge cakes because you do 1/5=0.2 or20%+50%=70% and 100%-70%=30% so 30% is your answer.

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Line L passes through the points (0, --3) and (6,9).<br> (a) Find the equation of line L.

valentina_108 [34]

Step-by-step explanation:

Given points are :

$(0,\:-3)=(x_1,\:y_1) \:\&\: (6,\:9)=(x_2 ,\:y_2)$

Equation of line in two point form is given as:

$\frac{y -y_1 }{y_1 -y_2 } = \frac{x -x_1 }{x_1 -x_2 } \\ \\ \therefore \frac{y -( - 3)}{ -3 -9 } = \frac{x -0 }{0 -6 } \\ \\ \therefore \frac{y + 3}{ -12} = \frac{x }{ -6 } \\ \\ \therefore \frac{y + 3}{ 2} = \frac{x }{1} \\ \\ \therefore \: y + 3 = 2x \\ \\ \huge \red{ \boxed{\therefore \: 2x - y - 3 = 0}} \\ is \: the \: required \: equation \: of \: line.$

5 0

3 years ago

A triangle has base 2x+1 and height 6x-3. What value of x would give an area of 240m2?

GREYUIT [131]

Answer:

The values of x which would give an area of 240m² would be:

$x=-\frac{\sqrt{161}}{2},\:x=\frac{\sqrt{161}}{2}$

Step-by-step explanation:

Given

The base of triangle b = 2x+1

The height of triangle h = 6x-3

The Area of the triangle A = 240 m²

The Area of the triangle has the formula

A = 1/2 × b × h

substituting b = 2x+1, h = 6x-3 and A = 240

$240\:=\:\frac{1}{2}\:\left(2x+1\right)\:\times \left(6x-3\right)$

$480=\left(2x+1\right)\left(6x-3\right)$

$480=12x^2-3$

Subtract 480 from both sides

$12x^2-3-480=480-480$

$12x^2-483=0$

$3\left(4x^2-161\right)=0$

$3\left(2x+\sqrt{161}\right)\left(2x-\sqrt{161}\right)=0$

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

$2x+\sqrt{161}=0\quad \mathrm{or}\quad \:2x-\sqrt{161}=0$

solving

$2x+\sqrt{161}=0$

$2x=-\sqrt{161}$

Divide both sides by 2

$\frac{2x}{2}=\frac{-\sqrt{161}}{2}$

$x=-\frac{\sqrt{161}}{2}$

also solving

$2x-\sqrt{161}=0$

$2x=\sqrt{161}$

Divide both sides by 2

$\frac{2x}{2}=\frac{\sqrt{161}}{2}$

$x=\frac{\sqrt{161}}{2}$

Therefore, the values of x which would give an area of 240m² would be:

$x=-\frac{\sqrt{161}}{2},\:x=\frac{\sqrt{161}}{2}$

3 0

3 years ago

If the population of a particular country is growing at 1.5 % compounded continuously, how long will it take the population to

DIA [1.3K]

$e^{0.015t}=3$
Taking natural logs of both sides, we get
0.015t=ln 3
t = ln 3/0.015 = 73.24

The answer is 73.24 years.

5 0

3 years ago

What is -3(3y-7)=21-9y

Nina [5.8K]

Answer:

the equation is equivalent, y is any number

Step-by-step explanation:

-3(3y-7) = 21-9y

-9y + 21 = 21 - 9y

-9y = -9y

y=y

any number will satisfy y=y

6 0

3 years ago

Write an equation of a line in slope intercept from given (6,4) (5,2)

Oksana_A [137]

Answer:

y=2x-8

Step-by-step explanation:

<em>Slope-Intercept Form </em>

<em>y=mx+b where y and x are variables, m is the slope, and b is the y-intercept</em>

<u>1. Find slope using the slope formula </u> $\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

$\frac{2-4}{5-6} =\frac{-2}{-1} =2$

You now have

y=2x+b

<u>2. Plug in one of the given points into the equation and solve for b</u>

y=2x+b

2=2(5)+b

2=10+b

-8=b

<u>Final Answer:</u>

y=2x-8

5 0

2 years ago