8. Jess walked for 45 minutes at 3 km/h and then ran for half an hour at x km/h. At the end
of that time she was 6 km from the starting point. Find the value of x.

The x-intercepts of the parabola are (3, 0) and (7,0)

The given parameters are:

Vertex (h, k) = (5, -12)

Point (x, y) = (0, 63)

The equation of a parabola is:

y = a(x - h)^2 + k

Substitute (h, k) = (5, -12)

y = a(x - 5)^2 - 12

Substitute (x, y) = (0, 63)

63 = a(0 - 5)^2 - 12

Evaluate

63 = 25a - 12

Add 12 to both sides

25a = 75

Divide by 26

a = 3

Substitute a = 3 in y = a(x - 5)^2 - 12

y = 3(x - 5)^2 - 12

Set y to 0 to determine the x-intercepts

0 = 3(x - 5)^2 - 12

Add 12 to both sides

3(x - 5)^2 = 12

Divide by 3

(x - 5)^2 = 4

Take the square root of both sides

[tex]x - 5 = \pm 2[/tex]

Add 5 to both sides

[tex]x = 5 \pm 2[/tex]

Expand

x = (5 - 2, 5 + 2)

Evaluate

x = (3, 7)

Hence, the x-intercepts of the parabola are (3, 0) and (7,0)

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Based on the scatter plot on perishable and nonperishable items purchased by customers, the following is true:

Looking at the y-axis which shows the number of nonperishable items bought, the number of dots we find at 5 is 3 which means 3 people bought 5 nonperishable items.

The median of perishable items requires that we order the perishable items bought:

2, 2, 5, 6, 7, 8, 9, 10, 11

The median is 7 perishable items.

The number of people with the same number of perishable and nonperishables are 2 people.

One purchased 8 nonperishables and 8 perishables and the other purchased 9 of both items.

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Answer:

[tex]-\dfrac{463}{7}[/tex]

Explanation:

Given equation: 2x² - 6x - 7 = 0

In quadratic equation: ax² + bx + c

[tex]Sum \ of \ roots : \alpha + \beta = \dfrac{-b}{a}[/tex]

[tex]product \ of \ roots : \alpha \beta = \dfrac{c}{a}[/tex]

So, here given:

[tex]Sum : \alpha + \beta = \dfrac{-(-6)}{2} = 3[/tex]

[tex]Product : \alpha \beta = \dfrac{-7}{2} = - 3.5[/tex]

For finding value:

[tex]\dfrac{\alpha^3}{\beta } + \dfrac{\beta^3 }{\alpha }[/tex]

join fractions

[tex]\dfrac{\alpha^4+ \beta^4}{\alpha \beta }[/tex]

factor out

[tex]\dfrac{(\alpha^2 + \beta ^2)^2 -2\alpha ^2 \beta ^2 }{\alpha \beta }[/tex]

when factored more

[tex]\dfrac{((\alpha + \beta)^2 -2\alpha \beta )^2 -2(\alpha \beta)^2 }{\alpha \beta }[/tex]

insert values inside

[tex]\dfrac{((3)^2 -2(-3.5) )^2 -2(-3.5)^2 }{-3.5 }[/tex]

calculate for value

[tex]-\dfrac{463}{7}[/tex]

The coordinates of the vertex of the parabola are (-6,5).

The coordinates of a vertex of a parabolic equation are those x and y points for which the parabola crosses its axis of symmetry.

The vertex of an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

[tex]\mathbf{x_v = -\dfrac{2}{2(1/6)}}[/tex]

[tex]\mathbf{x_v = -6}[/tex]

From the equation:

[tex]\mathbf{y = \dfrac{1}{6}x^2+2x+11}[/tex]

[tex]\mathbf{y_v = \dfrac{1}{6}(-6)^2+2(-6)+11}[/tex]

[tex]\mathbf{y_v =5}[/tex]

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Answer:

b

Step-by-step explanation:

The distance in miles between our galaxy and the nearby galaxy is 5.99 * 10^12 miles

Given the following parameters

Distance that light travels = 5.9×10^12 miles

Distance in near galaxy = 5.1×10^6miles

Find the difference

Distance = 5.9×10^12 - 5.1×10^6

Distance = 5.99 * 10^12 miles

Hence the distance in miles between our galaxy and the nearby galaxy is 5.99 * 10^12 miles

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Answer:

h Tu to be a great day of school and

Step-by-step explanation:

great day of school and I have a great day of school and I have a great day of➡ school and I I have a great day of school and I have a great day of school and I have a great yy

Answer:

6 seconds after it is launched

Step-by-step explanation:

h(t) = -4t² + 16t + 48

The balloon is at ground level when it lands.

When it is launched, t = 0, and h(0) = 48

When it lands, at time t, h(t) = 0.

-4t² + 16t + 48 = 0

t² - 4t - 12 = 0

(t - 6)(t + 2) = 0

t = 6 or t = -2

The balloon will hit the ground 6 seconds after it is launched.

Using simpler trigonometric identities, the given identity was proven below.

Remember that:

[tex]sec(x) = \frac{1}{cos(x)} \\\\tan(x) = \frac{sin(x)}{cos(x)}[/tex]

Then the identity can be rewritten as:

[tex]sec^4(x) - sen^2(x) = tan^4(x) + tan^2(x)\\\\\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\[/tex]

Now we can multiply both sides by cos⁴(x) to get:

[tex]\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\\\\\cos^4(x)*(\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}) = cos^4(x)*( \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)})\\\\1 - cos^2(x) = sin^4(x) + cos^2(x)*sin^2(x)\\\\1 - cos^2(x) = sin^2(x)*sin^2(x) + cos^2(x)*sin^2(x)[/tex]

Now we can use the identity:

sin²(x) + cos²(x) = 1

[tex]1 - cos^2(x) = sin^2(x)*(sin^2(x) + cos^2(x)) = sin^2(x)\\\\1 = sin^2(x) + cos^2(x) = 1[/tex]

Thus, the identity was proven.

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The minimum length Starbucks must build the wheel chair ramp to meet the standards is 23.9ft.

A triangle in which one of the angles is 90 degrees is called a Right angled Triangle.

To find the angle of the ramp, Trigonometric Ratios will be used

As the ramp is forming a right triangle

sin x = 2/22

x = 5.21°

The angle the wheel chair ramp makes with the ground is 5.21°.

If the angle has to be less than 4.8°

Let the length of the wheel chair will be given by y

Then,

2/x < sin4.8

x > 2/sin 4.8

x > 23.9 ft

Therefore the minimum length Starbucks must build the wheel chair ramp to meet the standards is 23.9ft.

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The maximum height of the pie based on the information given is 124.

From the information given in the table, it can be seen that the time and the height of the pie was given in the table.

In this case, the maximum height of the pie based on the information given is 124. This can be seen at 4 seconds.

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The sum is given by -  f(y) = 4(y -1).

We have the following expression -

(y + 5) + (3y - 9)

We have to evaluate the above sum.

Now -

f(x) + g(x) = 3x + 9 - (6 - x)  

f(x) + g(x) = 3x + 10 - 6 + x

f(x) + g(x) =  4x + 4

f(x) + g(x) = 4(x + 1)

According to the question, we have -

(y + 5) + (3y - 9)

Assume that the sum is represented by the function f(y).

Solving, we get -

f(y) = y + 5 + 3y - 9

f(y) = y + 3y + 5 - 9

f(y) = 4y - 4

f(y) = 4(y - 1)

Hence, the sum is given by -  f(y) = 4(y -1).

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Answer:

Step-by-step explanation:

3/4 * 1/8 = 3*1 / 4*8

3 / 32 is the solution.

Step-by-step explanation:

[tex] \log(x) = - 1[/tex]

[tex] \log(y) = 6[/tex]

[tex] \log(z) = 2[/tex]

[tex] \: [/tex]

[tex] = \log( \frac{ {x}^{3}y }{ {z}^{2} } )[/tex]

[tex] = \log( {x}^{3} \times y \div {z}^{2} )[/tex]

[tex] = \log( {x}^{3} ) + \log(y) - \log( {z}^{2} )[/tex]

[tex] = 3 \log(x) + \log(y) - 2 \log(z)[/tex]

[tex] = 3.( - 1) + 6 - 2[/tex]

[tex] = - 3 + 6 - 2[/tex]

[tex] = 1[/tex]

Answer:

[tex]\frac{2\sqrt3}{3} = x[/tex]

Step-by-step explanation:

So you want to use PEMDAS to do the equation in order. This means that you'll start by adding 6 and 1 and then multiplying that value by 2

[tex]2(7)-|-10| = 3x^2[/tex]

[tex]14-|-10|=3x^2[/tex]

The absolute value can be defined as the "distance" from 0 which is going to be positive. You can think of it as the positive value of a number so if you have |-b| it will become b, and even if it's already positive, it will remain positive. so the absolute value of -10 is 10 but then it becomes negative again because of the subtraction

[tex]14-10=3x^2[/tex]

[tex]4=3x^2[/tex]

Now you want to solve for x by dividing both sides by 3 and taking the square root of both sides to isolate x

[tex]\frac{4}{3} = x^2[/tex]

[tex]\sqrt{\frac{4}{3}}=x[/tex]

You can distribute the square root across division since [tex](\frac{a}{b})^c = \frac{a^c}{b^c}[/tex] and the square root can be defined as [tex]x^{0.5}[/tex] since [tex]a^b * a^c = a^{b+c}[/tex] because if you spread it out it's really just [tex](a * a * a ... b\ amount \ of \ times) * (a * a * a ... c\ amount\ of\ times)[/tex] which can be simplified to (a * a * a... (b + c) amount of times) if that makes any sense. Anyways using this property you'll get [tex]a^{0.50} * a^{0.50} = a^{0.50 + 0.50} = a^1 = a[/tex]. If you look at it you'll notice a^0.50 multiplied by it self gives you a... sounds like the square root, which it is. So now the equation becomes

[tex]\frac{\sqrt{4}}{\sqrt{3}}=x[/tex]

[tex]\frac{2}{\sqrt3}[/tex]

Now if you look at the equation you'll notice there's a radical in the denominator, which can be rationalized by multiplying by sqrt(3)\sqrt(3) which is 1 except it makes the denominator 3 and keeps the original value

[tex]\frac{2}{\sqrt3} * \frac{\sqrt3}{\sqrt3}=x\\\frac{2\sqrt{3}}{3} = x[/tex]

To simplify a polynomial expression, we can expand parentheses by multiplying the terms within with the coefficient outside of them and add like terms.

[tex]3x(-2x + 7) - 5(x - 1)(4x - 3)[/tex]

⇒ Open up the parentheses

[tex]=(3x*(-2x) + 3x*7) - 5(x(4x - 3)-1(4x-3))\\=(-6x^2 + 21x) - 5(4x^2 - 3x-4x+3)\\=-6x^2 + 21x - 5(4x^2 - 7x+3)=-6x^2 + 21x - (20x^2 - 35x+15)\\=-6x^2 + 21x - 20x^2 + 35x-15\\=- 26x^2 + 56x-15[/tex]

[tex]- 26x^2 + 56x-15[/tex]

Answer:

10 (x+3/5)= 2y in slope intercept form

simplify

10x+6=2y

subtract by 2

y=5x+3

Hope This Helps!!!

The probability of picking a head and a number 4 is 0.25.

Your information is incomplete and the complete information wasn't found. An overview will be given.

A coin has a head and tail and the probability of choosing either is 1/2 or 0.5.

Let the 2 numbers be 1 and 4. The probability of picking either number will be 1/2 or 0.5 as well.

Here, let the probability of picking a head and a number 4 will be:

= 1/2 × 1/2

= 0.5 × 0.5

= 0.25

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Answer:

Milk and Eggs = 552

Step-by-step explanation:

First add all of the other percentages together. (70%), 100%-70%=30%. 30% of 1840 = 552.

Answer:

H.  552

Step-by-step explanation:

Circle graph information:

Total consumption = 1840 pounds per person

First, calculate the percentage of milk and eggs (the value of x).

Total percentages = 100%

⇒ x + 38 + 10 + 10 + 8 + 4 = 100

⇒ x + 70 = 100

⇒ x = 30

Therefore, 30% of food consumption is milk and eggs.

To calculate the number of pounds of milk and eggs the average American consumes each year, simply find 30% of the total consumption:

= 30% of 1840

= 30% × 1840

[tex]=\sf \dfrac{30}{100} \times 1840[/tex]

= 552

Therefore, the average American consumes 552 pounds of milk and eggs each year.

The value of x is 4.

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given:

In ΔCDB and ΔEAB

<CDB = <ABE    (alternate interior angle)

<DBC = <EAB    (alternate interior angle)

By AA similarity criteria

ΔCBD ~ ΔEAB

Now,

EB/ CD= EA/CB

6/x-1 = 4/x-2

6X-12= 4X-4

2x= 8

x=4

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The type of function is Exponential.

The function whose graph is in the linear straight line then that function is considered a linear function.

An example of this is 2x+3

An exponential function is a model or a relationship in which there is a constant change in the independent variable that gives the same change in proportionality.

The given function is not showing a linear growth which means there is no straight line so the function will be exponential.

When x increases by 1 unit then the growth factor will be 3/1 = 3

So the exponential growth factor is 3.

Exponential growth is like a pattern of data that shows a huge increase with passing time, and by creating the curve for an exponential function.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x)=5x+7

g(x)=-2x-4

g(f(x))=g(5x+7)=-2(5x+7)-4=-10x-14-4=-10x-18

=-10x+(-18)

Answer:

(a)  5165.42 rupees

(b)  $1.35

Step-by-step explanation:

Given information:

Part (a)

To find how many rupees $103.64 was worth, multiply the number of dollars by the number of rupees per dollar:

⇒ 103.64 × 49.84 = 5165.42 rupees (nearest hundredth)

Part (b)

To find how many dollars 67.36 rupees was worth, divide the number of rupees by the number of rupees per dollar:

⇒ 67.36 ÷ 49.84 = $1.35 (nearest hundredth)

The value of the investment after 2 years is K2400.00

The given parameters are:

Principal, P = K2,000.00

Rate, r = 10%

Time, t = 2 years

The value is then calculated as:

Amount = P + PRT

So, we have:

Amount = 2000 + 2000 * 10% * 2

Evaluate

Amount = 2400

Hence, the value of the investment after 2 years is K2400.00

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1/6 of the people are not elderly or men

The given parameters are:

Men = 1/2

Elderly = 1/3

The number of people that are not elderly or men are:

People = 1 - Men - Elderly

So, we have:

People = 1 - 1/2 - 1/3

Evaluate

People = 1/6

Hence, 1/6 of the people are not elderly or men

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In the case above, option b is correct: Marcelina spends the intended amount of money but she bought more than she did intended amount of corn

She  buy 50kg of corn in total

So the equation will be:

C= (20, 50) = 20 white, 50 yellow

But 30 while and 20 yellow is needed.

Since  C = 20 +50 = 70 corns

While 30 + 20 = 50 corns.

This implies that she spends the intended amount of money but she bought more than she did intended amount of corn and as such, option b is correct.

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Answer:

y=3/2x + 18

Step-by-step explanation:

So when two lines are perpendicular, that simple means the slope are reciprocals, and the signs are opposite. So for example if one equation had a slope of [tex]\frac{a}{b}[/tex], the equation that is perpendicular, would have a slope of [tex]-\frac{b}{a}[/tex]. So the first step would be to find the slope of 2x+3y=4. To find the slope we can convert it into slope-intercept form which is y=mx+b where m is the slope, and this is done by isolating y, as you can see the y is alone in the slope-intercept form.

Original equation:

2x + 3y = 4

subtract 2x from both equations:

3y = -2x + 4

Divide both sides by 3

y = -2/3x + 4/3

The y-intercept doesn't really matter in this case, what really matters is the slope, and the slope is the coefficient of x, since as x increases by 1, it will increase by the amount of the coefficient, because the slope is rise/run and since the run is 1, if you increase x by 1, the run is the slope, which is the coefficient. The slope in this case is -2/3. So the reciprocal of the slope is 3/2 (notice how the sign is the opposite as well). Now we have the equation

y=3/2x + b

To find the y-intercept, you simply use the point that was given (-2, 15). Plug in -2 as x, and 15 as y to find the value of b

Original equation

y=3/2x + b

Plug in known values:

15 = 3/2(-2) + b

Multiply the fraction:

15 = -6/2 + b

Simplify the fraction:

15 = -3 + b

Add 3 to both sides

18 = b

This gives you the equation

y=3/2x + 18