Factorise completely:
4x² + 8xy - xy - 2y²
2

In the parallelogram ABCD

1. The value of y = 6

2. The value of AB = 24

A parallelogram is an object that has four sides with two of its sides parallel to each other

1. In the parallelogram CD and AB have side lengths y + 18 and 4y repsectively. To find y, we proceed as folows

Since CD = y + 18 and AB = 4y, we know that in any parallelogram, parallel sides are equal. So, CD = AB

So, y + 18 = 4y

Subtracting y from both sides of the equation, we have that

y + 18 = 4y

y - y + 18 = 4y - y

0 + 18 = 3y

18 = 3y

3y = 18

Dividing through by 3, we have

y = 18/3

y = 6

So, y = 6

2. To find AB, we proced as folows.

Given that AB = 4y and y = 6

Substituting this into the equation, we have that

AB = 4y

= 4(6)

= 24

So, AB = 24

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Answer:

hope this helps

Step-by-step explanation:

y-y=m(x-x¹)

y-(-1)=-3(x-1)

y+1=-3x+3

-1 -1

y=-3x+2

Answer:

  3n

Step-by-step explanation:

The number of raised fingers is 3 for each hand, so is 3 times the number of hands.

For n hands, the number of raised fingers is ...

  3n

Answer:

9

Step-by-step explanation:

if she has 14 and then spends 5 she will have 9. 4-5=9

If \(h^{-1}(x)\) is the inverse of \(h(x)\), then

\(h\left(h^{-1}(x)\right) = x\)

Given that \(h(x)=-(x-2)^2+7\), we have

\(h\left(h^{-1}(x)\right) = -\left(h^{-1}(x)-2\right)^2 + 7 = x\)

Solve for the inverse :

\(-\left(h^{-1}(x)-2\right)^2 + 7 = x \\\\ -\left(h^{-1}(x)-2\right)^2 = x-7 \\\\ \left(h^{-1}(x)-2\right)^2 = 7-x \\\\ \sqrt{\left(h^{-1}(x)-2\right)^2} = \sqrt{7-x} \\\\ \left|h^{-1}(x)-2\right| = \sqrt{7-x}\)

At this point, we have two possible solutions:

• If \(h^{-1}(x)\ge2\), then \(\left|h^{-1}(x)-2\right| = h^{-1}(x)-2\). Continuing with the equation, we have

\(h^{-1}(x) - 2 = \sqrt{7-x} \\\\ h^{-1}(x) = 2 + \sqrt{7-x}\)

• Otherwise, if \(h^{-1}(x)<2\), then \(\left|h^{-1}(x)-2\right|=-\left(h^{-1}(x)\right)=2-h^{-1}(x)\), in which case

\(2-h^{-1}(x) = \sqrt{7-x} \\\\ h^{-1}(x) = 2 - \sqrt{7-x}\)

Both solutions are simultaneously incompatible. For instance, when x = 0 we have \(h^{-1}(0)=2+\sqrt7\) using the first solution, and \(h^{-1}(0)=2-\sqrt7\) using the second one. Choosing one over the other depends on how you restrict the domain.

(A) If we want to stick with the first solution, we would required that x ≥ 2. In other words, we would have \(h(x)\) defined only when x ≥ 2; then \(h\left(h^{-1}(x)\right)\) is defined only when \(h^{-1}(x)\ge2\), so that ...

(B) ... the inverse is

\(\boxed{h^{-1}(x)=2+\sqrt{7-x}}\)

(C) The domain of the inverse is the same as the range of the original function, and vice versa.

• Domain: we have for all x that

\(-(x-2)^2 \le 0\)

so

\(-(x-2)^2 + 7 \le 7\)

which means the range of \(h(x)\), and hence the domain of \(y=h^{-1}(x)\), is

\(\left\{y \mid y \le 7\}\)

• Range: we get this immediately from the domain restriction we chose earlier,

\(\left\{x \mid x \ge 2\}\)

See the attached plot - \(h(x)\) is shown as a dashed orange curve; \(h(x)\) with the restricted domain is shown in blue; the inverse \(h^{-1}(x)\) corresponding to the restricted \(h(x)\) is shown in green; the other inverse is shown with a dashed red curve. You can see a geometrical properties of inverses: if you mirror the blue curve along the dotted line (y = x), you would get the green curve.

Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Answer:

there should be 14, 45 pound boxes

Step-by-step explanation:

1000-190= 810

810/45=14 boxes

Answer:

Answer vary :

Mike is paid $6.20 per 1 hour.

Step-by-step explanation:

honestly in my opinion that’s the answer.

‘what is happening is we need to find out how much he is paid for only one hour.

knowing that mike is paid 217 in 35 hours we divide

- 217 divided by 35 = 6.2

and that’s the answer to check if it’s right we multiple 6.2 by 35

- 6.2 times 35 = 217

wich shows it is correct.

and that is how I came to that solution.

The equation is y = 5x.

We are supposed to complete the given ordered pairs and then use the results to graph the solution set for the equation on paper.(1)

When x is 20, then y = 5(20) = 100.(2)

When x is 0, then y = 5(0) = 0.

Therefore, the two ordered pairs are (20, 100) and (0, 0).

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Answer:

x = -1

x = -9

Step-by-step explanation:

sqrt of 16 can be -4 and 4.

sqrt of (x + 5)² = x + 5

x + 5 = 4

x + 5 - 5 = 4 -5

x = -1

x + 5 = -4

x + 5 - 5 = -4 - 5

x = -9

Answer:

The answer is 1 1/4

Step-by-step explanation:

solve by making a ratio!

(2 1/4 cups)/ (1 4/5 hrs)

to find how many cups he can drink in 1 hr, divide both the numerator and denominator by 1 4/5.

(5/4 cups)/ (1 hr)

the question asks for a mixed number. convert 5/4 to a mixed number.

5/4= 1 1/4

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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According to the ideal gas law, The slope of the line of best fit for a plot of P versus 1/V is algebraically equal to nR/T.

According to the ideal gas law, the slope of a line of best fit for a plot of pressure (P) versus the inverse of volume (1/V) is algebraically equal to the product of the number of moles (n) and the gas constant (R) divided by the temperature (T).
Here's a step-by-step explanation:
Recall the ideal gas law formula: PV = nRT
Rearrange the formula to isolate P: P = (nRT)/V
Express the equation in terms of 1/V: P = nR(T * 1/V)
In this form, we can see that the slope of the line of best fit for a plot of P vs. 1/V is equal to nR/T.
Therefore, the slope of the line of best fit for a plot of P versus 1/V is algebraically equal to nR/T.

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Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

Divide each term in the bracket by 4:

=  

3

x

−

2

Explanation:

Multiplying by  

1

4

is the same as dividing by 4. - You are finding a quarter of something.

To find a quarter of the bracket, divide each coefficient by 4.

You will get two unlike terms so you will not be able to simplify them.

This is the reason why you cannot simplify inside the original bracket either.

Step-by-step explanation:

Answer:

x = 25°

Step-by-step explanation:

3x + 2x + x + 30° = 180°

6x + 30° = 180°

6x = 150°

x =25°

=> 3x = 25 * 3 = 75°

=> 2x = 25 * 2 = 50°

=> x + 30° = 25° + 30° = 55°

(a) The mode, median, first quartile, and third quartile of the data set is 24, 24, 12, and 43, respectively. There are no outliers.

(b) The data value corresponding to the 60th percentile is 33.8.

(c) The percentile rank of the age 40 is 70th percentile.

(a) The mode of the data set is 24, as it appears twice in the data set.
The median of the data set is 24, as it is the middle value when the data set is arranged in ascending order.
The first quartile (Q1) is 12, as it is the median of the lower half of the data set.
The third quartile (Q3) is 43, as it is the median of the upper half of the data set.
To check for outliers, we can use the interquartile range (IQR), which is Q3 - Q1 = 43 - 12 = 31.
The lower outlier boundary is Q1 - 1.5(IQR) = 12 - 1.5(31) = -34.5.
The upper outlier boundary is Q3 + 1.5(IQR) = 43 + 1.5(31) = 89.5.
Since all the values in the data set are within the outlier boundaries, there are no outliers.

(b) To find the data value corresponding to the 60th percentile, we can use the formula:
Percentile rank = (p/100)(n + 1)
where p is the percentile, and n is the number of data values.
In this case, p = 60 and n = 25, so the percentile rank is (60/100)(25 + 1) = 15.6.
Since the percentile rank is not a whole number, we can use interpolation to find the data value corresponding to the 60th percentile.
The data value corresponding to the 60th percentile is 32 + (0.6)(35 - 32) = 33.8.

(c) To find the percentile rank of the age 40, we can use the formula:
Percentile rank = (L + 0.5f)/n
where L is the number of data values less than 40, f is the frequency of 40, and n is the number of data values.
In this case, L = 17, f = 1, and n = 25, so the percentile rank of the age 40 is (17 + 0.5(1))/25 = 0.7 or 70th percentile.

(d) To draw a boxplot for the data set, we can use the values of the first quartile (Q1), median, and third quartile (Q3) that we found in part (a).
The boxplot would look like this:
[12]---[24]---[43]
    Q1    Median   Q3

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The final equation of the graph after translation and transformation is y=2(x + 1)2 -2.

a) To graph the function y=-0.5(x - 3)2 + 2 using translation and transformation, we will start with the graph of y = x2, which is a standard parabola. Then, we will apply the following transformations:

1. Horizontal translation: The graph of y=x2 is shifted 3 units to the right by adding (x-3) to the x-value.

2. Vertical reflection: The graph is reflected across the x-axis by multiplying the function by -0.5.

3. Vertical translation: The graph is shifted 2 units up by adding 2 to the y-value.

The final equation of the graph after translation and transformation is y=-0.5(x - 3)2 + 2.

Here are the steps to graph it:

1. Plot the vertex of the parabola at (3,2).

2. Since the coefficient of (x-3)2 is negative, the parabola will open downwards.

3. Mark the x-intercepts by solving -0.5(x - 3)2 + 2 = 0. This gives us x = 1 and x = 5.

4. Plot two more points on either side of the vertex, and then draw the curve through all the points to complete the graph.

b) To graph the function y=2(x + 1)2 -2 using translation and transformation, we will start with the graph of y = x2, which is a standard parabola. Then, we will apply the following transformations:

1. Horizontal translation: The graph of y=x2 is shifted 1 unit to the left by subtracting 1 from the x-value.

2. Vertical stretching: The graph is stretched vertically by a factor of 2 by multiplying the function by 2.

3. Vertical translation: The graph is shifted 2 units down by subtracting 2 from the y-value.

The final equation of the graph after translation and transformation is y=2(x + 1)2 -2.

Here are the steps to graph it:

1. Plot the vertex of the parabola at (-1,-2).

2. Since the coefficient of (x+1)2 is positive, the parabola will open upwards.

3. Mark the x-intercepts by solving 2(x + 1)2 - 2 = 0. This gives us x = -1 ± sqrt(1/2).

4. Plot two more points on either side of the vertex, and then draw the curve through all the points to complete the graph.

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a. The system of inequalities that models the situation is:

The equation for the cost is: C(x,y) = 0.2x + 0.4y.

b. The graph is given by the image at the end of the answer, and the vertices are (4,4), (10,4) and (10,7).

c. The number of clay beads and glass beads in a necklace that costs the least to make is: 4 clay beads and 4 glass beads.

The variables for the system are presented as follows:

Each necklace has no more than 10 clay beads and at least 4 glass beads, hence the constraints are listed as follows:

The numbers of each beads are countable amounts, meaning that they cannot assume negative values.

Four times the number of glass beads is less than or equal to 8 more than twice the number of clay beads, hence the final constraint is of:

4y ≤ 8 + 2x.

Each clay bead costs $0.20 and each glass bead costs $0.40, hence the cost function is given as follows:

C(x,y) = 0.2x + 0.4y.

Using the three constraints, the graph is given by the image at the end of the answer, and the vertices are as follows:

The minimum cost is at the vertex with the smallest numeric value of the cost function, hence the numeric values are listed as follows:

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Answer:

Step-by-step explanation:

I think its c

Answer:

x = 2

Step-by-step explanation:

\( \frac{x + 4}{3} = 2\)

\(x + 4 = 6\)

\(x = 6 - 4 = 2\)

Answer:

x=20

Step-by-step explanation:

Well just cross multiply if its easier

x(3)=3x

12*5=60

60=3x

x=20

Step-by-step explanation:

Two straightener angle are ∠1 and ∠2 , and also a number of straightener angle is 180°. We can make the equation into :

∠1 + ∠2 = 180°

KNOWN ∠2 = 115°

Prove that ∠1 = 65°

Using the equation before, to find ∠1

∠1 + ∠2 = 180°

∠1 +115° = 180°

∠1 = 180° - 115°

∠1 = 65° Proved

Answer:

5

Step-by-step explanation:

3 to the power of 0 is 1

Why? n to the power of 0 is 1 independent of n

2 to the power of 2 is 4

Why? 2 × 2 = 4

So it's 1 + 4 = 5

I hope this helps you :)

Answer:

The solution is v ≤ 81.
Graph it on a number line by writing a closed circle above the number 81 with a line moving to the left (sorry I'm bad at explaining, just comment if you don't get it)

Step-by-step explanation:

5/9v ≤ 45

Divide 5/9 on both sides

v ≤ 81

Answer:

r7

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Center:   (-3, 4)

radius = r = \(\sqrt{25}\) = 5

diameter = 2r = 10

Answer:

Center= (3,-4)   Radius=5   Diameter=10

Step-by-step explanation:

The numbers (3,-4) are the coordinates in the center of a circle. The radius is squared to get the end number so to get the radius, you have to find its square root- \(\sqrt{25\) =5. The diameter is 2 times bigger than the radius so 5 times 2= 10.

Answer:

198

Step-by-step explanation:

hope this helps