Norah brought home 2 pounds of grapes and ate 5⁄6 of the grapes that evening. How many pounds of grapes did Norah eat

The vertex of the parabola y = f(x + 1) is (1, -1).

To find the vertex of the parabola given by the equation y = f(x + 1), we need to determine the effect of the transformation on the vertex coordinates.

The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

In the given equation, y = f(x + 1), we can see that the transformation is a horizontal shift of 1 unit to the left. This means that the new vertex will be located 1 unit to the left of the original vertex.

Given that the original vertex is (2, -1), shifting 1 unit to the left would result in a new x-coordinate of 2 - 1 = 1. The y-coordinate remains the same.

Therefore, the vertex of the parabola y = f(x + 1) is (1, -1).

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Answer:

Circumference = (3.14)(15) = 47.1 in

Step-by-step explanation:

We know that 1000m = 1 km

37.5 km ^2 * 1000 m 1000m

------------ * ---------

1 km 1 km

The km will cancel

37.5 * 1000m * 1000m = 37500000 m^2

Answer:

The square root of 37 is approximately 6.0827. To determine which two integers it lies between, we can find the integers that are closest to the square root of 37.

The integer that is smaller than 6.0827 is 6, and the integer that is larger than 6.0827 is 7.

Therefore, the square root of 37 is between the integers 6 and 7.

In solving the given question, we can say that ∠ZEFI and ∠ZJIK are equal parallel lines  by  co-exterior angles property.

Geometry parallel lines are coplanar infinite lines that do not intersect anywhere. In a given three-dimensional space, parallel faces are faces that never intersect. Curves with a constant minimum distance between them and no tangents or intersections are said to be parallel. Two lines that lie in the same plane, are equally spaced, and never intersect are called parallel lines in geometry. Can be applied horizontally or vertically. Parallel lines are found in everyday objects such as railroad tracks, rows of books, and crosswalks.  

∠ZHIK and ∠ZEFI are equal by alternative angles property.

∠ZGFD and ∠ZEFD are equal by co-interior angles property.

∠ZGFD and ∠ZEFI are equal by interior alt. angles property.

∠ZEFI and ∠ZJIK are equal by  co-exterior angles property.

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Answer:

First answer: 3

Second answer: 6

Each square you see on the cube you add +1 to get 3

But in total the cube has 6 faces

Answer:

You can see 3 faces

There are 6 faces in a cube

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

The kilometers the bus travels between these two stops is 5.8 km

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

Speed = 23 km/h

Time = 13 : 40 - 13 : 25 = 15 minutes = 1/4 hr

The kilometers the bus travels between these two stops is calculated as

Distance = Speed * Time

Substitute the known values in the above equation, so, we have the following representation

Distance = 23 * 1/4

Evaluate

Distance = 5.8 km

Hence, the distance is 5.8 km

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Answer:

10

Step-by-step explanation:

\(11430\cdot 14 = 160020\) ounces

\(160020\div 16=10001.25\approx 10\) tons.

Hope this helps!

The required weight that the truck carried in ton is 5.

In the counting or finding data problem we first calculate the value of unity element then further add or multiply the next ones

Here we have given truck carry

11,430 bottles

If each bottle weight = 14 ounce

Therefore total weight of 11,430 bottles is = 11,430x14 = 160020 ounce

Also we have

1 ton = 32000 ounce

Or 1 ounce = \(\frac{1}{32000}\) ton

Therefore the required weight in ton of total weight 160020 ounce is

= \(\frac{160020}{32000}\)

= 5

This is the conclusion to the answer.

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Based on the given input and output values, we can conclude that the relationship is not linear.

No, the relationship between the given input values (1, 2, 3, 4) and output values (46, 39, 32, 25) is not a linear function. In a linear function, the relationship between the input and output values can be described by a straight line. However, if we plot the given points on a graph, we can observe that they do not form a straight line. Instead, they form a pattern that is not linear.

A linear function can be represented by the equation y = mx + b, where "m" is the slope of the line and "b" is the y-intercept. In this case, there is no constant slope that can be applied to the input values to obtain the corresponding output values. The difference between the consecutive output values is not constant, indicating a non-linear relationship.

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Answer:

11

Step-by-step explanation:

Since the y coordinates are the same, the distance is the values between the x coordinates

6 - -5

6+5

11

The right answer is 11 units.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

An open circle is used to represent x > 4 as we do not want to include 4 in our solution set.

Treat the <, ≤, >, or ≥  as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or. The xy plane is split along this line into two regions: one that fulfils the inequality and the other that does not.

Using the open instructions when we plot the inequality we see that x > 4 has an open circle at 4.

This indicates that we do not want to include 4 in our solution set.

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Answer:

2 and 3

Step-by-step explanation:

and integer is a positive or negative WHOLE NUMBER it is not a fraction or a decimal.

The Clara took 15.5 minutes more than usual to reach the farmers' market today, given that she walked leisurely.

Clara usually takes 22 minutes to walk briskly to the farmers' market. However, today she walked leisurely and it took her 6.5 minutes to reach the market. We need to find how much more time she took than usual to reach the market.

To find the difference in time, we need to subtract the usual time from the time she took today:

Time taken today - Usual time = Difference in time

Substituting the given values:

6.5 minutes - 22 minutes = Difference in time

Simplifying the expression:

-15.5 minutes = Difference in time.

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The coordinates of Q so that PQ is 7/9 of PR and if P is (-22,-32) and R is (5,4)​ is (-8, -2).

Suppose that there is a line segment \overline{AB} such that a point P(x,y) lying on that line segment \overline{AB} divides the line segment \overline{AB} in m:n, then, the coordinates of the point P is given by:

\((x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\)

where we have:

the coordinate of A is (x_1, y_1)

and the coordinate of B is (x_2, y_2)

We are given that;

PQ = 7/9 of PR.

P coordinate= (-22,-32)

R coordinates= (5,4)​

We can use the midpoint formula to find the coordinates of point Q, which is the midpoint of segment PR. Then, we can use the fact that PQ is 7/9 of PR to find the coordinates of Q.

The midpoint formula is:

((x1 + x2) / 2, (y1 + y2) / 2)

Using this formula with points P and R, we get:

(((-22) + 5) / 2, ((-32) + 4) / 2) = (-8.5, -14)

This gives us the coordinates of the midpoint of segment PR, which is the coordinates of point Q.

Let's do this for the x-coordinate of Q:

(xQ - (-22)) * (9/7) = 5 - (-22)

Simplifying this equation, we get:

xQ = -8

Now, let's do this for the y-coordinate of Q:

(yQ - (-32)) * (9/7) = 4 - (-32)

Simplifying this equation, we get:

yQ = -2

Therefore, the coordinates of point Q will be (-8, -2).

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Answer:

1/2 minute

Step-by-step explanation:

We can use a ratio to solve

1/3 bottle     1 bottle

------------   = --------------

1/6 minute    x minutes

Using cross products

1/3x = 1/6 *1

1/3 x = 1/6

Multiply each side by 3

3 * 1/3x = 3 * 1/6

x = 3/6

x = 1/2

1/2 minute

Answer:

30 seconds (1/2 minute)

Step-by-step explanation:

We are given that,

Amount of water filled in 1/6 minute = 1/3

Now, Let the time taken to fill the whole bottle with water be x

Hence,

Through the ratio method we get,

1/3:1/6 : : 1:x

Hence, we need to multiply the extremes and the means together and equalize them.

Hence,

x/3=1/6

x=(1/6)×3

x=(1/2) minute or 30 seconds

Answer:

15/8 cup or \(1\frac{7}{8}\) cup

Step-by-step explanation:

3/4 = 0.75

Ratios:

\(\frac{0.75}{12} =\frac{x}{30} \\\\12x=22.5\\x= 15/8\)

Answer:

\(\frac{15}{8}\) cup

This can also be expressed as the following:

\(1\frac{7}{8}\) cup

Step-by-step explanation:

This problem involved ratios. A ratio is a way of expressing one value compared to another when the two values being compared are of a different unit. The problem gives one the general ratio of the following,

\(sauce (cups) : people (number)\)

Substitute in the given values, since one knows the units, it is unnecessary to write it,

\(\frac{3}{4}:12\)

In this problem, the ratio of cups of sauce to people is constant, therefore one can say that the amount of sauce that (12) people need is proportional to the amount of sauce that (30) people need. Thus, set up an equation to solve for the unknown amount of sauce that (30) people need. Let parameter (x) represent the unknown amount of sauce.

\(\frac{3}{4} : 12 = x : 30\)

Use cross products to simplify,

\((12)(x)=(\frac{3}{4})(30)\)

Simplify,

\(12x=\frac{45}{2}\)

Inverse operations,

\(12x = \frac{45}{2}\)

Multiply both sides by (2)

\(24x=45\)

Divide both sides by (24),

\(x=\frac{45}{24}\)

Simplify,

\(x=\frac{15}{8}\)

Answer:

7.25

Step-by-step explanation:

36.25/5=7.25 simple

Step-by-step explanation:

cost of 5 scarf = 36.25

cost of one scarf = 36.25/5

= 725/100

= 7.25 $

so one scarf cost = 7.25$

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Answer:

a. $12,600

b. $21

c. $19

Step-by-step explanation:

a) The cost is $3000 plus $16 per book

For 600 books, we have

3000 + 16(600)

= 3000 + 9600 = $12,600

b) Cost per book will be;

12,690/600 = $21

c) for 1000

= 3000 + 16(1000)

= 3000 + 16,000 = 19,000

cost per book is 19,000/1000 = $19

Answer:

The zeros are -6 and -2

Step-by-step explanation:

factor the equation.

(x+2)*(x+6)

x+2=0

x+6=0

1. The graphs and table that represent functions include the following: B, C, and E.

2. The set of ordered pairs that does not represent a function are:

A. {(-4, 9), (-4, 7), (1, -5), (7, -7)}.

C. {(-2, 0), (0, -2), (1, 1), (2, 0)}.

D. {(-5, 4), (-3, 4), (-1, 4), (2, 4)}.

In Mathematics and Geometry, a function is used for defining and representing the relationship that exists between two or more variables in a relation, table, ordered pairs, or graph.

Part 1.

Based on the given graphs and tables, we can logically deduce that the graph of a circle represent a relation because it does not have an inverse function. Also, tables D and F does not represent a function because the input values (domain) are not uniquely mapped to the output values (range).

Part 2.

Based on the given set of ordered pairs, we can logically deduce that only set A represent a function because the input values (domain) its uniquely mapped to the output values (range).

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Answer:

5

Step-by-step explanation:

q = 6

r = 19

4q^2

= 4 x q^2

= 4 x 6^2

= 4 x 6 x 6

= 144

qr

= q x r

= 6 x 19

= 114

qr + 25

= 114 + 25

= 139

4q^2 - ( qr + 25 )

= 144 - 139

= 5

I think it's 28 units²

a) Since Todd and Amani started with the same initial deposit, they will never have the same amount in their accounts if they keep to their weekly savings plans because Todd's weekly savings are two times that of Amani.

b) An equation to represent the total amount in each of their accounts at any given time or weeks is as follows:

An equation is a statement of equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine values, variables, and numbers or constants without the equation symbol (=), which differentiates them from equations.

                                        Todd     Amani

Initial deposit in account  $10       $10

Weekly deposits               $4         $2

Let the number of weeks of deposits = w

Let the total deposit in Todd's account in w weeks = t

t = 10 + 4w

Let the total deposit in Amani's account in w weeks = a

a = 10 + 2w

For Todd's and Amani's account to be equal, 10 + 4w = 10 + 2w

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a) \(Calculation of 5 point DFT of x(n) is: X(k) = [28, -2 - 16j, -8, -2 + 16j, -2]\)On squaring the values of X(k),\(we getY(k) = X(k)²= [784, 68 - 80j, 64, 68 + 80j, 4]\)

Now we need to compute the inverse DFT of Y(k) which is given below:

\(Let us calculate the 5-point IFFT by using the circular convolution approach as: Y(k) = X(k)²[784, 68 - 80j, 64, 68 + 80j, 4] = x²(k)By using 5-point IFFT\),

\(we can obtain the values of y(n) as below:y(n) = [1960, -360 + 168j, 256, -360 - 168j, 16]b) Given x(n) = ejwon, 0≤n≤N - 1\)and zero otherwise.

We need to find the Fourier Transform X(w) of x(n) and N-point DFT X(k) of x(n).

\(The Fourier Transform X(w) of x(n) is:X(w) = Σx(n)ejwn = Σejwon ejwn = N∑(k=0) ej2πkn/N\)

The above expression is a Geometric series.

\(When the common ratio is |r|<1, the sum of the geometric series becomes:S = a(1 - r^n)/(1 - r)\)

\(Substituting r = ej2π/N and a=1, we get:S = 1(1 - ej2πn/N)/(1 - ej2π/N)\)

\(Hence, the Fourier Transform X(w) of x(n) is:X(w) = N(1 - ej2πn/N)/(1 - ej2π/N)\)

The N-point DFT of the finite length sequence x(n) is given by:\(X(k) = Σx(n)ej2πkn/N  , for 0 ≤ k ≤ N - 1\)

\(Here, the given sequence x(n) is:x(n) = ejwon, 0≤n≤N - 1\) and zero otherwise.

\(Substituting the given sequence in the above equation, we get:X(k) = Σej2πkn/Nfor 0 ≤ k ≤ N - 1 = Σcos(2πkn/N) + jsin(2πkn/N) for 0 ≤ k ≤ N - 1\)

\(Here, let us separate the real and imaginary parts as below:X(k) = Σcos(2πkn/N) + jsin(2πkn/N) for 0 ≤ k ≤ N - 1= Σcos(2πkn/N) + Σjsin(2πkn/N) for 0 ≤ k ≤ N - 1\)

\(On substituting the values of cos and sin in the above equation, we get: X(k) = Re(X(k)) + jIm(X(k)), for 0 ≤ k ≤ N - 1where, Re(X(k)) = Σcos(2πkn/N) for 0 ≤ k ≤ N - 1Im(X(k)) = Σsin(2πkn/N) for 0 ≤ k ≤ N - 1\)

Therefore, we can calculate the N-point DFT X(k) of x(n) by using the above expression.

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Answer:

-23\2h+3\2 i.e. option A is the answer