turning point of y=(x+3)(x-7)

The requried it takes 8.37 seconds for the object to hit the ground.

The polynomial 16T² - 1120 gives the height of the object in feet as a function of time T in seconds after it is dropped from a height of 1120 feet. When the object hits the ground, its height is zero. So we can set the polynomial equal to zero and solve for T:

16T² - 1120 = 0

T² - 70 = 0

T² = 70

T = ±√70

Since time cannot be negative, we can disregard the negative solution. Therefore, the object hits the ground after:

T = √70 ≈ 8.37 seconds

So it takes 8.37 seconds for the object to hit the ground.

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The values that go into the blanks are 19200 g, 3700 g, 8455 g, 800 g, 4450 g, 2.765 kg, 77 g, 12.508 kg, 30000 g and 7200 grams

From the question, we have the following parameters that can be used in our computation:

Statements 1 to 10

Evaluating the expressions, we have

Conversion

19 1/5 kg = 19 1/5  * 1000 g

19 1/5 kg = 19200 g

Sum

3.4 kg + 3/10 kg = 3.7 kg

3.4 kg + 3/10 kg = 3700 g

Difference

8.5 kg - 45 g = 8.455 kg

8.5 kg - 45 g = 8455 g

Dictionary and book

Heavier by = 1200 g - 0.4 kg

Heavier by = 800 g

Sum

1/2 kg + 50 g + 3.9 kg = 500 g + 50 g + 3900 g

1/2 kg + 50 g + 3.9 kg = 4450 g

Comparison

3 kg 15 g = ___ more than 1/4 kg

We have

Difference = 3 kg 15 g - 1/4 kg

Difference = 2.765 kg

So:

3 kg 15 g = 2.765 kg more than 1/4 kg

Sum

7/10 kg + 7/100 kg = 77 g

Sum

8 kg 8 g + 4 1/2 kg = 12.508 kg

Mr. Tan and Lisa

We have

Mr. Tan = 75 kg

Lisa = 2/5 of Mr. Tan

So, we have

Lisa = 2/5 of 75 kg

Lisa = 30000 g

Mass of 12 boxes

We have

Mass of 1 box = 0.6 kg

So, we have

Mass of 12 boxes = 0.6 kg * 12

Mass of 12 boxes = 7200 grams

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30x + 40y ≤ 240 and 2x + y ≥ 8 are the required system of inequalities and the graph is given in attachment

Let x be the number of pages printed with layout a, and let y be the number of pages printed with layout y.

We want to maximize the number of pictures printed subject to the cost constraint.

The cost constraint can be expressed as:

30x + 40y ≤ 240

We also have a constraint on the number of pictures:

4x + 2y ≥ 16

This inequality can be simplified to:

2x + y ≥ 8

We can graph these inequalities on the xy-plane:

First, graph the line 30x + 40y = 240 by finding its intercepts:

x-intercept: 30x + 40y = 240 -> x = 8

y-intercept: 30x + 40y = 240 -> y = 6

So the line passes through the points (8,0) and (0,6).

Next, graph the line 2x + y = 8:

x-intercept: 2x + y = 8 -> x = 4

y-intercept: 2x + y = 8 -> y = 8

So the line passes through the points (4,0) and (0,8)

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Answer:

3.14

Step-by-step explanation:

The value of pi to two decimal places is 3.14. It is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Pi is an irrational number, which means it cannot be expressed as a finite decimal or fraction. It is an important constant in many fields of mathematics and science, including geometry, trigonometry, and physics. The decimal representation of pi goes on infinitely without repeating, making it an interesting and challenging topic for mathematicians to explore.

The two points that have a distance of 3/8 between them are J and M.

We have,

The number line has 8 parts between 0 and 1.

This means,

One part = 1/8 units

Now,

The distance between two different points:

Between J and L:

= 2/8

Between J and M:

= 3/8

Between J and Q:

= 7/8

Between J and R:

= 1

Between L and M:

= 1/8

Between L and Q:

= 5/8

Between L and R:

= 6/8

Between M and Q:

= 4/8

Between M and R:

= 5/8

Between Q and R:

= 1/8

Thus,

The two points that have a distance of 3/8 between them are J and M.

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The probability of the spinner landing on blue is given as follows:

P(blue) = 0.45 = 45%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of trials for this problem is given as follows:

50 + 60 + 90 = 200 trials.

On 90 of these trials, the spinner landed on blue, hence the probability is given as follows:

p = 90/200 = 0.45 = 45%.

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The offset section of machine depicts.

Hence option (C) is correct.

In the given figure

If machine is cut according the given manner

Then the three part be cut accordingly

Since the cut mark divides the machine segment into equal parts.

So after cutting of machine

We get offset section of each subparts.

Hence it shows offset section of machine.

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Taking the difference between the length and the width we can see that it is it is 3g + 39 longer than wider.

To find this, we just need to take the difference between the length and the width, to do so, just take the length and subtract the width:

L - W

Here we know that:

L = 16g + 24

W = 13g - 15

The difference will give:

diff = 16g + 24 - (13g - 15)

diff = (16 - 13)g + 24 + 15

diff = 3g + 39

it is 3g + 39 longer than wider.

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If greenfield company has a piece of manufacturing equipment with a book value of $40,000 and a remaining useful life of four years.  the total increase or decrease in income by replacing the current equipment with the new equipment is:$22,000 decrease.

Here, we have,

to find the increase or decrease in income

Annual Savings $76,000

($19,000 × 4 years)

Add Proceeds from Sale of Machine $22,000

Total  $98,000

Total increase or decrease in income = $98,000 - $120,000

Total increase or decrease in income = $22,000 (Decrease)

Therefore the decrease in income is $22,000.

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complete question:

granfield company has a piece of manufacturing equipment with a book value of $40,000 and a remaining useful life of four years. at the end of the four years the equipment will have a zero-salvage value. granfield can purchase new equipment for $120,000 and receive $22,000 in return for trading in its current equipment. the current equipment has variable manufacturing costs of $39,000 per year. the new equipment will reduce variable manufacturing costs by $19,000 per year over its four-year life. the total increase or decrease in income by replacing the current equipment with the new equipment is:

Answer:

[tex]g(x) = {x}^{2} + 5[/tex]

The graph shows g(x), which is a translation of [tex]f(x) = x^2[/tex]. The function rule for g(x) is [tex]x^2 + 5[/tex]. Hence, g(x) = [tex]\underline{x^2 + 5}[/tex]

Given, g(x) is a translation of [tex]f(x) = x^2[/tex]

Let the equation of the function g(x) be

[tex]g(x) = a(x - h)^2 + k[/tex] ----------(1)

This curve passes through the points (1, 6), (-1, 6) and (2, 9), then their coordinates satisfy the equation:

[tex]6 = a(1 - h)^2 + k[/tex]----------(2)

[tex]6 = a(-1 - h)^2 + k[/tex]----------(3)

[tex]9 = a(2 - h)^2 + k[/tex]----------(4)

Subtract (2) from the first:

[tex]6 - 6 = a(1 - h)^2 + k - a(-1 - h)^2 - k[/tex]

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

As a [tex]\neq[/tex] 0,

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

[tex](1 - h)^2 = (-1 - h)^2[/tex]

[tex]1 - h = -1 - h[/tex],

or [tex]1 - h = 1 + h[/tex]

As, 1 = -1 is false

h = 0

Then, substituting h = 0 in (2) and (4),

[tex]6 = a(1 - 0)^2 + k[/tex]  ⇒ [tex]6 = a + k[/tex] ----------(5)

[tex]9 = a(2 - 0)^2 + k[/tex] ⇒ [tex]9 = 4a + k[/tex] ----------(6)

Solving (5) and (6) we get,

3a = 3

a = 1

Substituting a = 1 in (5),

6 = 1 + k ⇒ k = 5

Substituting a = 1, h = 0 and k = 5 in equation (1),

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

Therefore, the function rule for g(x) is [tex]x^2 + 5[/tex].

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The steps to conduct the steps of hypothesis testing on these data are:

The hypothesis will be:

Since we are comparing (GPAs) of three groups (students who check e-mail day by day, students  who check mail at least 2x a week, and students who check mail less than 2x a week), one can be able to make use of one-way analysis of variance (ANOVA) as the fitting test measurement.

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The calculated area of the plane figure is 467.61 sq ft

From the question, we have the following parameters that can be used in our computation:

The plane figure

The plane figure is a trapezoid

So, we start by calculating the height of the trapezoid as follows (using the pythagorean theorem)

h^2 = 18^2 - (33 - 25)^2

Evaluate

h^2 = 260

So, we have

h = √260

The area of the plane figure is then calculated as

Area = 1/2 * Sum of parallel sides * Height

So, we have

Area = 1/2 * (33 + 25) * √260

Evaluate

Area = 467.61

Hence, the area is 467.61 sq ft

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When we solve the system of equation, we notice that the small candles cost $10 and the large candles cost $15 each.

The system of equation, presented by the table can be expressed as;

12s + 16l = $360

7s + 22l = $400

Lets use the elimination method

(12s + 16l = 360) × 7

(7s + 22l = 400) × 12

The new equation becomes

84s + 112l = 2520

84s + 264l = 4800

We subtract the equation. E2 - E1

(84s + 264l) - (84s + 112l) = 4800 - 2520

(84 - 84) - (264l - 112l) = 2280

152l = 2280

l = 15

Since we know the price of the large candle, we can find the small candle

12s + 16l = 360

12s + 16($15) = 360

12s + 240 = 360

12s = 360 - 240

12s = 120

s = 10

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Answer:

Based on the illustration, it seems that the two materials used in the assembly are cast iron and aluminum (option E).

The calculated z-value of -2.93 is less than -1.96, we can reject the null hypothesis and conclude that there is enough evidence to suggest that the average amount in bottles is different from the standard 2 litres.

To test whether there is enough evidence that the average amount in bottles is different from the standard 2 litres, we can use a two-tailed hypothesis test with the following null and alternative hypotheses:

Null hypothesis: The population mean is equal to 2 litres.

Alternative hypothesis: The population mean is not equal to 2 litres.

We will use a z-test to compare the sample mean to the population mean. The test statistic is calculated as:

[tex]z = \dfrac{(x - \mu)} { \dfrac{\sigma} { \sqrt{n}}}[/tex]

where x is the sample mean, μ is the population mean (2 litres), σ is the population standard deviation (0.4 litres), and n is the sample size (200).

Plugging in the values, we get:

z = (1.97 - 2) / (0.4 / √200) = -2.93

The crucial values for a two-tailed test are -1.96 and 1.96 at a 5% level of significance. We may reject the null hypothesis and come to the conclusion that there is sufficient evidence to imply that the average amount in bottles is different from the typical 2 litres because the calculated z-value of -2.93 is smaller than -1.96.

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The Plot on the number line are shown in the image attached.

A number line is a pictorial representation of numbers on a straight line. The numbers increase as you move towards the right side of  horizontal number line and the numbers decrease as you move towards the left.

Looking at the number line, there are 10 divisions between two points e.g. 0 to 1.  

To know the value of  1 division, we divide the value of the distance between two points by the number of divisions:

= 1/10 = 0.1

1 2/5:

2/5 = 4 divisions

-1/2:

1/2 = 5 divisions

-2 1/10:

1/10 = 1 division

Thus, we can plot on the number line as shown in the image attached.

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Answer:

2000 ml or 2l

Step-by-step explanation:

Simplifying the given problem using laws of exponents is: 3∜(x⁶y⁴) - y∜x⁶

Some of the laws of exponents are as follows:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

We are given the expression:

∜(81x⁶y⁴) - y∜x⁶

Using laws of exponents, we can rewrite this as:

[81^(1/4) * x^(6/4) * y^(4/4)] - [y * x^(6/4)]

This gives us:

(3 * x^(6/4) * y) - y(x^(6/4))

= x^(6/4)(3y - y)

= 2yx^(6/4)

We can also write it as:

3∜(x⁶y⁴) - y∜x⁶

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The travelled distance of the traveller is equal to 195 kilometers.

According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:

x = d / 3

x + 65 = d / 2

Where:

Now we proceed to determine the travelled distance:

d / 3 + 65 = d / 2

d / 2 - d / 3 = 65

3 · d - d = 390

2 · d = 390

d = 195

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Answer:

B, false

Step-by-step explanation:

i just took this quiz online and the answer was b

The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is given as follows:

[tex]5.8 < \mu < 7.8[/tex]

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 41 - 1 = 40 df, is t = 1.6839.

The parameters for the interval in this problem are given as follows:

[tex]\overline{x} = 6.8, s = 3.7[/tex]

The lower bound of the interval is given as follows:

6.8 - 1.6839 x 3.7/sqrt(41) = 5.8.

The upper bound of the interval is given as follows:

6.8 + 1.6839 x 3.7/sqrt(41) = 7.8.

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The ratio of the number of baskets scored by team A to the number of baskets by team B is 2: 5. Then the correct option is B.

In a basketball game, team B scored 5 baskets for every 2 that team A scored.

The utilization of two or more additional numbers that compares is known as the ratio.

Assume that Team A scored two baskets while Team B netted five.

The problem statement states that for every two baskets Team A scored, Team B scored five. This may be expressed as the ratio shown below:

Ratio = 2x : 5x

Ratio = 2: 5

Thus, the correct option is B.

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Answer: they are not the same on a grid

Step-by-step explanation: to find the ordered paris the first one you count to the left and up so it would be 1 left, 2 up. the second one would be 2 left, one up

Null hypothesis: H0: mu <= 500 km

Alternative hypothesis: Ha: mu > 500 km

The decison rule is: If the calculated t-value is greater than 2.131, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

The test statistics

t = (x - mu) / (s / sqrt(n))

= (554 - 500) / (48.8 / sqrt(5))

= 3.01

The calculated t-value of 3.01 is greater than the critical t-value of 2.131. Therefore, we reject the null hypothesis.

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a fossil is usually found by digging underground

.

Answer: a fossil is usually found under layers and layers of rock. you can find one by digging deep enough

The value of x make the two expressions equal is -2.2

From the question, we have the following parameters that can be used in our computation:

(x+3)(x+8)= 3/5(x+8)

Divide both sides of the equations by x + 8

So, we have the following representation

x + 3 = 3/5

Multiply through the equation by 5

So, we have

5x + 15 = 3

This gives

5x = -12

Divide both sides by 5

x = -12/5

Evaluate the quotient

x = -2.2

Hence the value of x is -2.2

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Answer:

(x*0) (y*3)

Step-by-step explanation:

times 3

Answer: [tex]16\pi[/tex]

Step-by-step explanation:

The equation for the surface area of a cylinder is [tex]2\pi r^2 + 2\pi rh[/tex]

and the equation to find the radius (r) is diameter divided by 2 so [tex]\frac{d}{2}[/tex].

We know that...

so the full equation would be [tex]2\pi (2)^2 + 2\pi (2) (2) = 16\pi[/tex]

Answer:

$17.8

Step-by-step explanation:

C= 15.00 + 0.07(40)