Henry has a recipe that calls for 1 1/2 cups of sugar. He wants to use 1/2 of that amount. How much sugar will Henry use?

Answer:

387 contains 80 and 8 x 10 = 80

The reason that the point (3, 5) is not a solution to the given inequality is given below.

We are given that;

y > 2x + 1

Now,

The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.

If we have (3,5) as a point, we can see that it lies on the boundary line

y = 2x + 1.

Since the inequality is strict (y >), points on this line are not solutions to the inequality

Therefore, by the inequality the answer will be given above.

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The equations that can be used to solve for y, the length of the room, are: y(y + 5) = 750, y² – 5y = 750, and y(y – 5) + 750 = 0.

It states that when multiplying a number by a group of numbers added together, you can multiply the number by each individual number in the group and add the products together to get the same answer.

In order to find the length of the room, we need to solve for y in each of the equations given.

First, let's solve for y in the equation y(y + 5) = 750. We can use the distributive property to expand the equation to y² + 5y = 750.

Then, we can subtract 750 from both sides of the equation to get y² + 5y - 750 = 0.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

Second, let's solve for y in the equation y² – 5y = 750.

To solve this equation, we can add 5y to both sides to get y² = 5y + 750. Then, we can divide both sides by y to get y = 5y + 750.

We can then subtract 5y from both sides to get y - 5y = 750. Finally, we can divide both sides by 5 to get y = 150.

Third, let's solve for y in the equation y(y – 5) + 750 = 0.

To solve this equation, we can use the distributive property to expand the equation to y² – 5y + 750 = 0.

Then, we can subtract 750 from both sides to get y² – 5y = -750.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

In conclusion, the equations that can be used to solve for y, the length of the room, are y(y + 5) = 750, y2 – 5y = 750, and y(y – 5) + 750 = 0. The solutions for y are y = -25 and y = 30.

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Answer:

Step-by-step explanation:It must be an equal ratio- 2:3:7 = n:n:112

Now, to find the other numbers (n) in the ratio, we have to find the relationship between the two proportions.

To get from 7 to 112, we must multiply by 16. This is the relationship.

So, we must multiply both, the walnut and raisin cookies by 16 also.

2 x 16 = 32 = Raisin

3 x 16 = 48 = Walnut

Already known: 112 = Pinwheel

Now that we have all the data, we can make the ratio.

Raisin : Walnut : Pinwheel

32 : 48 : 112

Hope this helps! :)

Answer: (a) (i)50.42 m/s (ii) 51.35 m/s (iii) 52.094 m/s (iv) 52.2614 m/s (v) 52.27814 m/s

(b) 54.14 m/s

Step-by-step explanation:

The average speed over the given time interval [a,b]: = \(\frac{y(b)-y(a)}{b-a}\)

Given: If an arrow is shot upward on Mars with a speed of 56 m/s, its height in meters t seconds later is given by \(y = 56t − 1.86t^2.\)

(a)

(i) average speed = \(\frac{y(2)-y(1)}{2-1}\)

\(=\frac{56(2)-1.86(2)^2-(56(1)-1.86(1)^2)}{1}\)

\(=50.42\) m/s

(ii) average speed = \(\frac{y(1.5)-y(1)}{1.5-1}\)

\(=\frac{56(1.5)-1.86(1.5)^2-(56(1)-1.86(1)^2)}{0.5}\)

\(=51.35\)m/s

(iii) average speed = \(\frac{y(1.1)-y(1)}{1.1-1}\)

\(=\frac{56(1.1)-1.86(1.1)^2-(56(1)-1.86(1)^2)}{0.1}\)

\(=52.094\)m/s

(iv) average speed = \(\frac{y(1.01)-y(1)}{1.01-01}\)

\(=\frac{56(1.01)-1.86(1.01)^2-(56(1)-1.86(1)^2)}{0.01}\)

\(=52.2614 \)m/s

(v) average speed = \(\frac{y(1.001)-y(1)}{1.001-01}\)

\(=\frac{56(1.001)-1.86(1.001)^2-(56(1)-1.86(1)^2)}{0.001}\)

\(=52.27814 \)m/s

(b) \(y(1)=56(1)-1.86(1)^2\)

\(=56-1.86\)

\(= 54.14\) m/s

Answer:

Below

Step-by-step explanation:

3.15 can be read as  3 and 15 hundredths =   3   15/100  = 3  3/20

Answer:  63/20

Step-by-step explanation:

Step-by-step explanation:

3(x-7) + 4 = 22

or,3x-21+4 = 22

or, 3x-17 = 22

or, 3x = 22+17

or, x = 39/3

    x = 13

Answer:

dwdaddaw

Step-by-step explanation:

ad plus devide

The probability that either event A or B will occur is 43/60

Using the parameters given

n(A) = 29

n(B) = 14

Total number of events = 29+17+14 = 60

The probability of each event :

P(A) = 29/60

P(B) = 14/60

P(A or B ) = P(A) + P(B)

P(A or B ) = 29/60 + 14/60

P(A or B ) = 43/60

Therefore, the probability of A or B is 43/60

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Answer:

Step-by-step explanation:

You want the perimeter of each of the figures defined by the coordinates of their vertices. You are told to use the distance formula as necessary.

The first attachment shows the graph of the triangle. The distance formula is needed only for the length of the diagonal segment:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((3 -(-2))² +(-3 -3)²) = √(5² +(-6)²) = √61 ≈ 7.81

The lengths of the horizontal and vertical legs of the triangle are the difference of their x- and y-coordinates, respectively.

  CB = 3 -(-2) = 5

  CA = 3 -(-3) = 6

The perimeter is the sum of the side lengths:

  P = CA +CB +AB = 6 +5 +7.81 = 18.81

The perimeter of the triangle is 18.81 units.

The second attachment shows the graph of the parallelogram. As with the triangle, we only need to use the distance formula for the length of the diagonal side. Here is the length of ML.

  d = √((4 -2)² +(1 -(-2))²) = √(2² +3²) = √13 ≈ 3.606

The length of the horizontal legs is the difference of their x-coordinates.

  KL = 4 -(-1) = 5

Opposite sides are congruent, so the perimeter is double the length of two adjacent sides.

  P = 2(3.606 +5) ≈ 17.21

The perimeter of the parallelogram is about 17.21 units.

Answer:

1.  18.81 units

2.  17.21 units

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.3 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}\)

Given vertices of ΔABC:

Plot the vertices on the given graph paper and join with line segments to create the triangle.

As points B and C share the same y-coordinate:

\(\implies BC = |x_B-x_C|=|3-(-2)|=5\:\: \sf units\)

As points A and C share the same x-coordinate:

\(\implies AC = |y_A-y_C|=|3-(-3)|=6\:\: \sf units\)

Use the distance formula to find the length AB:

\(\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(3-(-2))^2+(-3-3)^2}\\& =\sqrt{(5)^2+(-6)^2}\\& =\sqrt{25+36}\\& =\sqrt{61}\\\end{aligned}\)

The perimeter of a two-dimensional shape is the distance all the way around the outside.

\(\begin{aligned}\textsf{Perimeter of $ABC$} & = AB + BC + AC\\& = \sqrt{61}+5+6\\& = 11+\sqrt{61}\\& = 18.81\:\: \sf units\:(nearest\:hundredth)\end{aligned}\)

Given vertices of polygon KLMN:

Plot the vertices on the given graph paper and join with line segments to create the polygon.

As the y-coordinate of points K and L, and M and N are the same, KL and MN are parallel line segments.

As the difference between the x-coordinates of K and N, and L and M is 2 units, KN and LM are parallel line segments.

Therefore, the polygon is a parallelogram.

A parallelogram has two pairs of opposite sides that are equal in length.

Therefore, KL = NM and KN = LM.

As points K and L share the same y-coordinate:

\(\implies KL = |x_K-x_L|=|-1-4|=5\:\: \sf units\)

Use the distance formula to find the length KN:

\(\begin{aligned}KN & =\sqrt{(x_N-x_K)^2+(y_N-y_K)^2}\\& =\sqrt{(-3-(-1))^2+(-2-1)^2}\\& =\sqrt{(-2)^2+(-3)^2}\\& =\sqrt{4+9}\\& =\sqrt{13}\\\end{aligned}\)

The perimeter of a two-dimensional shape is the distance all the way around the outside.

\(\begin{aligned}\textsf{Perimeter of $KLMN$} & = 2\:KL + 2 \:KN\\& = 2 \cdot 5 + 2\cdot \sqrt{13}\\& =10 + 2\sqrt{13}\\& = 17.21\:\: \sf units\:(nearest\:hundredth)\end{aligned}\)

Answer:

D. -1/2

Step-by-step explanation:

When a line is perpendicular to another line the slope will be the exact opposite. For example line A = y = 3x + 5 the line perpendicular to it will be -1/3x.

So -1/2 is the slope of your perpendicular line.

The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

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complete question;

Find the values of x and y. Find value of x.

Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:

1 hour and 30 minutes

Step-by-step explanation:

I think this because it said his top speed was 20,000 and he flew 30,000 if you add another 20,000 to the 20,000 he flew in 30,000 you would get 40,000 which is 2 hours so 1 hour and 30 min. Hope it Helped!

The Euler path of the given graph is CDBFADF.

A path in a finite graph known as an Euler path is one that traverses each edge precisely once while yet allowing for the revisiting of vertices.

A similar Euler trace that begins and finishes at the same vertex is known as an Euler circuit or cycle. When Leonhard Euler found a solution to the Seven Bridges of Konigsberg puzzle in 1736, it was first brought up for discussion.

A path known as an Euler path is one that utilises every edge in the graph once and only once. It doesn't have to return to the starting point because it is a path.

A circuit that utilises every edge in the diagram once is known as an Euler circuit. As it is a circle, it should start and terminate at the same vertex

The euler path of the given graph is CDBFADF.

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Answer:

x-4y=4

Step-by-step explanation:

The equation of a straight line is in slope intercept form:

y = mx + b;

where y and x are variables, m is the slope of the line and b is the y intercept.

The standard form of a line is:

Ax + By = C

where A, B and C are constants, x and y are variables

The equation of a straight line passing through the points (x₁, y₁) and (x₂, y₂) is given by:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\)

Given that a line passes through the points (0, -1) and (4, 0), the equation of the line is given by:

\(y-(-1)=\frac{0-(-1)}{4-0} (x-0)\\\\y+1=\frac{1}{4} x\\\\y=\frac{1}{4} x-1\\\\4y=x-4\\\\x-4y=4\)

Answer:

Step-by-step explanation:

After considering all the given data we conclude that the area of the given figure is 80, under the condition that the given figure is a rhombus.

Let us name the rhombus as ABCD, now looking at the figure we can detect that there are two diagonals crossing each other making a point  E, this allows the  two  diagonals to split in four smaller lines that are congruent in value
Then
Line AE = 5ft and Line ED = 5ft (because of congruency)
Line CE = 8ft and Line EB = 8ft(because of congruency)
Therefore,
Now we know that the diagonals
AD = 10ft
CB = 18 ft
The area of a rhombus can be evaluated applying the formula
Area = (d1 × d2) / 2,
Here,
d1 and d2 = lengths of the diagonals.
For this case, the diagonals are 10 ft and 16 ft.
Then, the area of the rhombus is
(10 × 16) / 2
= 80
Then, the area of the given figure is 80.
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Answer: 3rd one

Step-by-step explanation:

Answer:

You have 7,167

Step-by-step explanation:

If this was to be converted into a whole number, it would be:

7,167

The tangent from the external point are equal, so the x value is 3 units.

7) The measure of the arc XW is 180-105=75

8) The measure of the arc VWY is 105+75+85 = 265

9) We know that, tangent from the external point are equal

In circle C, AB=AD

26=8x+2

8x=24

x=24/8

x=3 units

10) 9x-3=7x+5

9x-7x=5+3

2x=8

x=8/2

x=4

Therefore, the tangent from the external point are equal, so the x value is 3 units.

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Reason:

We cannot divide by zero. This means the denominator cannot equal zero. If it was zero, then,

2x+10 = 0

2x = -10

x = -10/2

x = -5

Follow that chain in reverse to see that x = -5 causes the denominator 2x+10 to be zero. This is why we kick -5 out of the domain. Any other x value is valid.

Answer:

from looking at this we can see

1*4=4

2*4=8

3*4=12

6*4=24

a

Hope This Helps!!!

The expression which is used to represents the statement "one-more than the quotient of a number x" and 4 is "x/4 + 1".

A "Quotient" is the result of a division operation between two numbers, where one number is divided by another. It represents the number of times one number is contained within another number.

An "Expression" is defined as "mathematical-phrase" which contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions and other mathematical symbols.

The quotient of a number"x" and 4 can be written as x/4.

So, one more than the quotient of a number x and 4 can be represented by the expression:

⇒ x/4 + 1,

Therefore, required mathematical expression is "x/4 + 1".

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The given question is incomplete, the complete question is

Write an expression to represent : One more than the quotient of a number x and 4.

Work Shown:

The set {A,B,C,1,2} has five items. There are four slots to fill.

So we have 5^4 = 5*5*5*5 = 625 different possible passwords where the characters can be repeated.

625 four-character passwords can be formed.

----------------------------

Each character of the password is independent of previous characters, which means that the fundamental counting principle is used to solve this question.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

----------------------------

Thus, the number of passwords is:

\(5 \times 5 \times 5 \times 5 = 5^4 = 625\)

625 four-character passwords can be formed.

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The Diameter of the cube would be 3 inches

What is Variation?

A variation is a relationship that exists between a set of values for one variable and a set of values for other variables.

Solution:

We know that,

Horse Power is directly proportional to RPM * Diameter

So, we can write

Horse Power = k * RPM * Diameter

here, k is any constant

From the first case given, we can find the value of k

16 = k * 2 * 120

k = 1/15

Putting the value of k in second case,

30 = 1/15 * 150 * Diameter

Diameter = 3 inches

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Answer: 2m^2n^3 x ( -5m^2 + 4n^2 -3n^2 )

Step-by-step explanation:

ok, so just let me, uh, make this a little easier on my eyes lol:

-10m^4n^3+8m^2n^6-6m^2n^6 ----> (-10m^4)(n^3) + (8m^2)(n^6) - (6m^2)(n^6)

I just put in parentheses. nothing changed. just parentheses.

Since the leading coefficients, -10 , 8 , and 6 are multiples of two,

we can take out 2 from each... [-10/2 = 5 , 8/2 = 4 , 6/2 = 3 ]

= 2 x [ (-5m^4)(n^3) + (4m^2)(n^6) - (3m^2)(n^6) ]

Looking at it now...

we can take out m^2 from each... m^4 , m^2 , and m^2

m^2 [m^2 , 1 , 1]

since    m^4 /m^2 = m^2 , m^2 /m^2 = 1 , m^2 /m^2 = 1

= 2(m^2) x [ (-5m^2)(n^3) + (4x1)(n^6) - (3x1)(n^6) ]

= 2(m^2) x [ (-5m^2)(n^3) + (4)(n^6) - (3)(n^6) ]

Finally, one more step...

we can take out n^3 from each term.... n^3 , n^6 , and n^6

n^3 [1 , n^2 , n^2] since n^3 /n^3 = 1 , n^6 /n^3 = n^2 , n^6 /n^3 = n^2

= 2(m^2)(n^3) [ (-5m^2)(1) + (4)(n^2) - (3)(n^2) ]

= 2m^2n^3 x [ (-5m^2) + (4n^2) - (3n^2) ]

= 2m^2n^3 x ( -5m^2 + 4n^2 -3n^2 )

ANSWER: 2m^2n^3 x ( -5m^2 + 4n^2 -3n^2 )

keep this parentheses. seriously.

practice harder and harder you will get what you want