find each side length. Round to the nearest tenth if necessary

If the function has a ∪ shape (opens up), then it only goes so low—has a minimum value.

Any even-degree function with a positive leading coefficient will open up, so have a minimum. Your function is degree 2 (even) and has a leading coefficient of 3 (positive).

_____

Comment on other polynomial functions

If the leading coefficient of an even-degree function is negative, it will have an inverted-U shape (∩), so will have a maximum.

Any odd-degree function will have a generally rising (/) or generally falling (\) shape, depending on the sign of its leading coefficient. If positive, then rising; if negative, then falling.

Answer:

a) $0.46 per bagel

Step-by-step explanation:

When you are looking for a unit price, you have to divide the price in this instance by the amount of items that you have. For example, here you just have to divide $2.76 by 6 to get $0.46.

Hope I could help! :)

Option B (cos 29° and sin 61°) contains equivalent trigonometric values, as the angles are complementary and adhere to the identity sin(90° - x) = cos(x).

The question asks us to identify equivalent trigonometric values out of the given pairs. The equivalent values will have the same numerical value if their angles are complementary (i.e., they add up to 90°) because of the identity sin(90° - x) = cos(x). Considering this, let's evaluate the provided pairs:

A: sin 17° and cos 17° are not complementary, so they are not equivalent.

B: cos 29° and sin 61° are complementary (29° + 61° = 90°), hence equivalent.

C: sin 78° and cos 102° are not complementary, and 102° is greater than 90°, so they are not equivalent.

D: cos 83° and cos 7° are not complementary, but they are both cosines of different angles, so they are not equivalent.

Thus, the pair with equivalent trigonometric values is B: cos 29° and sin 61°.

First, let's subtract 1 (100%) by 2/6:

1 - 2/6 = 4/6

Knowing that Conner gave his neighbor 1/4 of the remainder, we simply have to multiply 4/6 by 1/4:

4/6 * 1/4 = 4/24 = 1/6

Conner gave 1/6 of his pears to his neighbor.

Answer:

See below.

Step-by-step explanation:

The one that looks like the attachment.

It is vertically shortened from f(x) = x^2, so appears wider than f(x) = x^2 does. The vertex is still at (0, 0), it still opens upward, and it remains symmetrical about the y-axis.

[tex]f(x)=\dfrac{1}{2}x^2\\\\for\ x=0\to f(0)=\dfrac{1}{2}(0)=0\to(0,\ 0)\\\\for\ x=\pm1\to f(\pm1)=\dfrac{1}{2}(\pm1)^2=\dfrac{1}{2}(1)=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right);\ \left(1;\ \dfrac{1}{2}\right)\\\\for\ x=\pm2\to f(\pm2)=\dfrac{1}{2}(\pm2)^2=\dfrac{1}{2}(4)=2\to(-2,\ 2);\ (2,\ 2)\\\\for\ x=\pm4\to f(\pm4)=\dfrac{1}{2}(\pm4)=\dfraC{1}{2}(16)=8\to(-4,\ 8);\ (4,\ 8)[/tex]

Answer:

d = 8t

Step-by-step explanation:

To find a correlation, you need to find what numbers correlate and how.

Lets try multiplying the t value by 8 to get the value ( as one value is 1 and the other is 8 so it would seem suitable)

1 * 8 = 8

2 * 8 = 16

Both values match up which means that to get d, you multiply t by 8.

This means that your answer is d = 8t.

Answer:

3

Step-by-step explanation:

For a rectangular prism of dimensions L × W × H, pairs of opposite faces will have dimensions ...

These will be three different sets of dimensions if L, W, and H are all different lengths.

Answer:

The answer is option C i.e; y=0.9x-45

Step-by-step explanation:

When you substitute the values of x you have to get same values as given in the table

For example: substitute x=50 in the equation y=0.9x-45

Y= 0.9(50)-45

Y= 45-45

Y=0

Answer: The value of [tex]x^2+y^2[/tex] is 140

Step-by-step explanation:

We are given an expression:

[tex](x-y)^2=100[/tex]

And,

xy = 20

Using the identity:

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

Solving the expression:

[tex]x^2+y^2-2xy=100[/tex]

Putting the value of 'xy' in above equation, we get:

[tex]x^2+y^2-2(20)=100\\\\x^2+y^2=100+40\\\\x^2+y^2=140[/tex]

Hence, the value of [tex]x^2+y^2[/tex] is 140

Answer:

each person owe $10.26

Step-by-step explanation:

Six friends go out to lunch and decide to split the bill evenly. The bill comes to $61.56.

Total bill for 6 friends = $61.56

To find bill cost for 1 person we divide the total cost by 6

Bill for each person = [tex]\frac{61.56}{6}= $10.26[/tex]

So each person owe $10.26

Answer:

The very first line has an error.

Step-by-step explanation:

When you are solving the second system of equations for y, you need to subtract 3x from both sides and therefore it should be negative.

3x + y = -9

y = -3x - 9

Since the 3x isn't negative in the first line, there is an error.

You are referring to the thousandths spot.

1.00(0)000001

So, between any given number n to n.01 there are 10 numbers.

n.001, n.002, n.003, ..., n.01

Given : The Cost of Laptop in 2007 is $1250

Given : The Cost of Laptop in 2009 is $1100

Decrease in Price of Laptop from 2007 to 2009 : (1250 - 1100) =  $150

A) Percent Decrease in the Price of the Laptop from 2007 to 2009 is :

[tex]\mathsf{\implies \frac{Decrease\;in\;Price\;of\;Laptop\;from\;2007\;to\;2009}{Price\;of\;Laptop\;in\;2007} \times 100}[/tex]

[tex]\mathsf{\implies \frac{150}{1250} \times 100}[/tex]

[tex]\mathsf{\implies 12\%}[/tex]

Given : Decrease in Price of Laptop from 2009 to 2010 = $165

B) Percent Decrease in the Price of the Laptop from 2009 to 2010 is :

[tex]\mathsf{\implies \frac{Decrease\;in\;Price\;of\;Laptop\;from\;2009\;to\;2010}{Price\;of\;Laptop\;in\;2009} \times 100}[/tex]

[tex]\mathsf{\implies \frac{165}{1100} \times 100}[/tex]

[tex]\mathsf{\implies 15\%}[/tex]

The percent decrease in laptop prices, use the formula ((Original Price - New Price) / Original Price) x 100%. The percent decrease from 2007 to 2009 is 12%, and from 2009 to 2010 is 15% with a $165 decrease.

The cost of a laptop computer in 2007 was $1,250. In 2009, the price decreased to $1,100.

A.) To find the percent decrease from 2007 to 2009, you use the formula: Percent decrease = ((Original Price - New Price) / Original Price) x 100%

Substitute the values: ((1250 - 1100) / 1250) x 100% = 12%

Therefore, the percent decrease in the price of the laptop from 2007 to 2009 is 12%.

B.) To find the percent decrease from 2009 to 2010 with a $165 decrease, you apply the same formula: Percent decrease = ((Price in 2009 - Price in 2010) / Price in 2009) x 100%.

Substitute the values: ((1100 - (1100 - 165)) / 1100) x 100% = 15%

Therefore, the percent decrease in the price of the laptop from 2009 to 2010 is 15%.

Answer:

462 mi

Step-by-step explanation:

Gloria gets 420 mi/tank.

10 % of 420 is

420 × 0.10 = 42 mi

She will be able to drive an extra 42 mi.

420 + 42 = 462 mi

With her new tires, a tank of gas will take her 462 mi.

Answer:

462

Step-by-step explanation:

to find 10% of 420 you take

420 x .10 = 42

then add 42 to 420

420+42=462

Answer:

Step-by-step explanation:

Deposited amount initially (P) = $250.

Rate of interest(r) = 2.5% compounded monthly = 0.025

Number of years (t) = 4.

Number of months in an year (n) = 12.

Formula for compound interest:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex].

Plugging values in formula, we get

[tex]A= 250(1+\frac{0.025}{12})^{12\times 4}[/tex]

[tex]A= 250(1.00208)^{48}[/tex]

[tex]A= 250\times \:1.10506[/tex]

A=276.26.

Answer:

137.2 m³

Step-by-step explanation:

The ratio of volumes is the cube of the ratio of linear dimensions. The larger volume is ...

... V = (7/5)³ × 50 m³ = 2.744 × 50 m³

... V = 137.2 m³

The graph of [tex] f(x) [/tex] is a straight line, so it is a linear function.

The graph of [tex] g(x) [/tex] has the same shape of the graph of [tex] y=e^x [/tex] (for example), so it is an exponential function.

Answer:

f(x) is linear

g(x) is exponential

Step-by-step explanation:

exponential  -> It is a graph of half curve

quadratic  -> it is a graph of a U shaped curve

cubic  -> it is a graph of a full curve that goes top and bottom

linear -> It is a graph of a line

In the give graph f(x) is a line graph , so it is Linear

The graph g(x) is a curve that goes at the top not at the bottom. Its like a half curve. so it is an exponential

Answer:

200,000 m

Step-by-step explanation:

We will multiply the length of the ant by the number of ants to find out how long the line is.

10 million is 10 with 6 zeros

20 * 10 ^-3   move the decimal 3 places to the left

20. * 10 ^-3  = .02

.02 * 10000000

200000

Answer:

6

Step-by-step explanation:

Since the relationship is proportional, when y is increased by a factor of 3 from 7 to 21, so is x—from 2 to 2×3 = 6.

Answer:

[tex]Height=\sqrt{\frac{weight}{\text{body mass index}}}[/tex]

Step-by-step explanation:

We have BMI formula that is body mass index formula which is:

[tex]\text{Body mass index}=\frac{weight}{height^2}[/tex]

Now, we have to arrange the formula for height:

we will rearrange the terms and derive the formula for height in terms of weight and height.

[tex]Height^2=\frac{weight}{\text{body mass index}}[/tex]

Hence, the required result is:

[tex]Height=\sqrt{\frac{weight}{\text{body mass index}}}[/tex]

The point (3, 18) on the graph means the snail's position when the time is 3 units of time from the time reference is 18 units of distance from the the reference point for distance.

_____

We cannot conclude anything else. We don't know if the snail is moving (or has moved), or if there are any other points on the graph.

Answer: B) The snail traveled 18 ft in 3 h.

Step-by-step explanation: If you look at the graph they graphed (3, 18) the left side says distance (ft) and the dot is to the right of the 18 so it traveled 18 feet.  At the bottom it says time (h) and the dot above the 3 so it took to travel 8 feet.

Hope This Helped ^_^

Answer:

2500 total calories per day.

Step-by-step explanation:

Assuming that 3500 excess calories produces 1 pound gain, 7000 excess calories required for 2 pound gain

to be accomplished in 14 days

7000/14 = 500 excess calories per day

2000 required calories per day

2500 total calories per day.

Answer:

9×9×8×7×6= 27,216

Step-by-step explanation:

Your answer is :- 9×9×8×7×6= 27,216

Why did i multiply 9×9×8×7×6 ⤵️

Because we can fill each place of a five digit number with ten digits (0,1,2,3,4,5,6,7,8,9).

Now, let us assume the five digit number is abcde, where each alphabet represent a digit.

so according to our question a cannot be equal to 0 ( a≠0), because if a will be equal to zero then our number will be a four digit number. So a can be equal to 9 digits.

b digit can also be equal to 9 numbers. why??because we can place zero on the position of b and only one number will not be repeated which is a.

Now for c, d, e :- accordingly no number will be repeated so on the place of c, there can be 8 digits. On the place of d, there can be 7 digits. And on the place of e there can be 6 digits.

Therefore,

a×b×c×d×e=9×9×8×7×6=27,216

Answer:

.325

Step-by-step explanation:

If she had a quiz on 13 of the 40 days , the fraction is 13/40

13/40 = .325

Answer: The fraction of the days on which the quiz has been held expressed as a decimal is 0.325

Step-by-step explanation:

Decimal numbers are not considered as integers. They are rounded off to write an integer.

Fraction is present in the form of [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex]

We are given:

Number of days, the class had quiz = 13

Total number of days = 40

The fraction becomes: [tex]\frac{13}{40}[/tex]

Expression this as a decimal = 0.325

Hence, the fraction of the days on which the quiz has been held expressed as a decimal is 0.325

Answer:

BE:EC= 1/3

Step-by-step explanation:

Given ABCD is a parallelogram, Point K is such that it belongs to diagonal BD so that BK:DK=1:4.

If we make an extension of AK which meets BS at point E, then using ΔDKA and ΔEKB, we have

∠DKA=∠EKB (Vertically opposite angles)

∠KDA=∠KBE (Alternate interior angles)

∠DAK=∠BEK (Alternate interior angles)

Thus by AAA similarity,ΔDKA≅ΔEKB

⇒[tex]\frac{AD}{BE}[/tex]= [tex]\frac{DK}{BK}[/tex],

Since, AD= BC,therefore

[tex]\frac{AD}{BE}[/tex]= [tex]\frac{BC}{BE}[/tex]= [tex]\frac{4}{1}[/tex]

Now, BC= BE+EC, ⇒[tex]\frac{BE+EC}{BE}[/tex]= [tex]\frac{4}{1}[/tex]

⇒1+[tex]\frac{EC}{BE} = \frac{4}{1}[/tex]

⇒[tex]\frac{EC}{BE}= 3[/tex]

Reciprocating on both the sides, we get

[tex]\frac{BE}{BC} = \frac{1}{3}[/tex]

Final answer:

To find the length of QR, we used the Pythagorean theorem on triangle PNQ to find NQ, then added it to PR, resulting in QR measuring 53 inches.

Explanation:

To find the length of side QR in △PQR, we can apply the Pythagorean theorem to one of the right triangles formed by the altitude PN. The triangle we'll use is △PNQ, where NQ is part of QR, and PN is given as 15 in.

Firstly, we can calculate NQ using the Pythagorean theorem:

PN² + NQ² = PQ²

15² + NQ² = 39²

NQ² = 39² - 15²

NQ² = 1521 - 225

NQ² = 1296

NQ = √1296

NQ = 36 in

Since PR = 17 in, we can conclude that NR is the difference between PR and NQ:

NR = PR - NQ

NR = 17 - 36

NR = -19 in

The negative value indicates a mistake since lengths cannot be negative. Therefore, we should use the entire length of PQ instead:

QR = NQ + NR

QR = 36 + 17

QR = 53 in

Thus, side QR measures 53 inches.

The best way to plot them is by month.

170 - 110 = $60.

We are supposed to plot in months and the above calculation is in year, convert it into months

60/5 = $5 each month

So, the coordinates would be 0, 110 1, 115 2, 120 3, 125

The month will be in the x axis and your money will be the Y axis 

A suitable y-axis scale to plot spending habits ranging from $110 to $170 would start at $100 and go up to $180, while a good interval for the y-axis would be $10 to allow for clear plotting of values in whole dollars.

To answer the student's question about how to plot spending habits on a coordinate grid:

Answer:

B. (5,-2)

Step-by-step explanation:

Plug in X and Y, verify accuracy

To find the rate of change, find the difference of people at the park at each given hour and divide that by the total number of hours in the given time frame.

Early Time interval:

Hour 1 there was 55 people.

Hour 3 there was 135 people.

The rate of change is 135 - 55 / 3-1 = 80/2 = 40 people per hour.

Late time interval:

Hour 3 had 135 people.

Hour 5 had 175 people.

The rate of change is 175 - 135 / 5-3 = 40/2 = 20 people per hour

20 is less than 40, so the late time interval had the smallest rate change.