Given the points A(-2, 1) and B(3, 4), what are the coordinates of point C in the fourth
quadrant such that mZCAB= 90 degrees and AB = AC? Express your answer as an ordered pair.
degree

The value of (F - G)(-5) when F(x) = x² - 1 and G(x) = 3 - x is -13.

To find (F - G)(-5), we need to substitute -5 for x in both F(x) and G(x) and then subtract G(-5) from F(-5).
So, F(-5) = (-5)² - 1 = 24 and G(-5) = 3 - (-5) = 8.
Therefore, (F - G)(-5) = F(-5) - G(-5) = 24 - 8 = -13.
In order to find (F - G)(-5), we first need to determine what F(x) and G(x) are.

F(x) is given as x² - 1, so we can write F(x) as:

F(x) = x² - 1  

Similarly, G(x) is given as 3 - x, so we can write G(x) as:

G(x) = 3 - x

We now need to find (F - G)(-5), which means we need to evaluate F(-5) and G(-5) and then subtract G(-5) from F(-5).

Let's start by finding F(-5). To do this, we simply substitute -5 for x in F(x):F(-5) = (-5)² - 1F(-5) = 25 - 1F(-5) = 24

Now we need to find G(-5). To do this, we substitute -5 for x in G(x):G(-5) = 3 - (-5)G(-5) = 3 + 5G(-5) = 8

We now have F(-5) and G(-5), so we can find (F - G)(-5) by subtracting G(-5) from F(-5):

(F - G)(-5) = F(-5) - G(-5)(F - G)(-5) = 24 - 8(F - G)(-5) = -13

Therefore, (F - G)(-5) = -13.

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The NPV of the investment is approximately ₦938,619.28.

If the NPV is positive, it indicates that the investment is worth undertaking because the present value of the expected cash flows exceeds the initial cost.

To determine if the investment is worth undertaking, we need to calculate the net present value (NPV) of the investment. NPV takes into account the initial cost of the investment and the expected cash flows over a specified period, discounted at the appropriate rate.

Here's how we can calculate the NPV for this investment:

Calculate the present value (PV) of the expected cash flows:

PV = [tex]Cash Flow / (1 + Interest Rate)^n[/tex]

Where:

Cash Flow = ₦200,000 per annum for 10 years

Interest Rate = 11% per annum

n = number of years

PV = [tex]₦200,000 / (1 + 0.11)^1 + ₦200,000 / (1 + 0.11)^2 + ... + ₦200,000 / (1 + 0.11)^10[/tex]

Calculate the NPV:

NPV = PV - Initial Cost

Given that the initial cost is ₦405,000, we can now calculate the NPV.

NPV = PV - ₦405,000

Let's calculate the PV and NPV:

PV = [tex]₦200,000 / (1 + 0.11)^1 + ₦200,000 / (1 + 0.11)^2 + ... + ₦200,000 / (1 + 0.11)^10[/tex]

PV = [tex]₦200,000 / 1.11^1 + ₦200,000 / 1.11^2 + ... + ₦200,000 / 1.11^10[/tex]

PV ≈ ₦200,000 / 1.11 + ₦200,000 / 1.23 + ... + ₦200,000 / 2.470

Calculating the PV using the formula above, we find:

PV ≈ ₦1,343,619.28

Now, let's calculate the NPV:

NPV = PV - ₦405,000

NPV = ₦1,343,619.28 - ₦405,000

NPV ≈ ₦938,619.28

The NPV of the investment is approximately ₦938,619.28.

If the NPV is positive, it indicates that the investment is worth undertaking because the present value of the expected cash flows exceeds the initial cost. In this case, since the NPV is positive, it suggests that the investment is worth undertaking.

Please note that this calculation assumes a constant cash flow of ₦200,000 per annum over the 10-year period and an interest rate of 11% per annum.

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Answer:

56

Step-by-step explanation:

33 + 23 = 56

Answer:

x² + 7x + 10 = (x + 5)(x + 2)

Step-by-step explanation:

***********************************************************

Rule:

To factor a trinomial of the form

x² + ax + b,

find two numbers whose product is b and whose sum is a.

Call these numbers, if they exist, p and q.

Then the factorization is

(x + p)(x + q).

***********************************************************

Let's apply the rule to this problem.

To factor

x² + 7x + 10.

Here, a = 7, and b = 10, so we need to find two numbers that multiply to 10 and add to 7.

The numbers are 5 and 2 since 5 × 2 = 10, and 5 + 2 = 7.

The factorization is

(x + 5)(x + 2)

Answer: x² + 7x + 10 = (x + 5)(x + 2)

ANSWER:

STEP-BY-STEP EXPLANATION:

As per the given statement -

A right cylinder with ,

Volume of the cylinder can be calculated as :

here

Plugging the values in the above formula

[tex]396 = 3.14 \times (6)^2 \times h \\ \\ 396 = 3.14 \times 36 \times h \\ \\ 396 = 113.06 \times h \\ \\ h = \dfrac{396}{113.06 } \\ \\ { \pink{{ \boxed{h \approx 3.5 \: m}}}}[/tex]

In feet,

1 metre = 3.2808 feet

3.5 metre = 3.2808 ft × 3.5

= 11.48 feet (approximately)

Hence, The the height, in feet, of the cylinder is 11.48 feet

The expanded form of the series ∑ₙ=₀³(n² + 3) = (0 + 3) + (1 + 3) + (4 + 3) + (9 + 3)

A series is the sum of temrs of a sequence

Given the series ∑ₙ=₀³(n² + 3), we want to find it in expanded form. We proceed as follows.

Since we have  ∑ₙ=₀³(n² + 3), we start from n = 0 to n = 3 in n² + 3.

So, when n = 0,  

n² + 3 = 0 + 3

So, when n = 1,  

n² + 3 = 1² + 3

= 1 + 3

So, when n = 2,  

n² + 3 = 2² + 3

= 4 + 3

So, when n = 3,  

n² + 3 = 3² + 3

= 9 + 3

So, collecting them together, we have that

∑ₙ=₀³(n² + 3) = (0 + 3) + (1 + 3) + (4 + 3) + (9 + 3)

So, the expanded form is  (0 + 3) + (1 + 3) + (4 + 3) + (9 + 3)

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The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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The percentage strength of the ointment containing 1 g of medication in 100 g of total ointment is 1%.

The percentage strength of a w/w (weight/weight) ointment is calculated by dividing the weight of the active ingredient by the weight of the total ointment and multiplying by 100.

In this case, you have 1 gram of medication in 100 grams of total ointment. To calculate the percentage strength, you can use the following formula:

Percentage strength = (weight of medication / weight of total ointment) × 100

Substituting the values, we get:

Percentage strength = (1 g / 100 g) × 100

Simplifying this equation:

Percentage strength = 0.01 × 100

Therefore, the percentage strength of the ointment containing 1 g of medication in 100 g of total ointment is 1%.

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Answer:

x add y add z = 11

x sub 4 add 9= 11

x add 5= 11

x = ll sub 5

x= 6

The point that is three-fifths of the way from -3 to 3 on the number line is 0.6.

To find the point on the number line that is three-fifths of the way from -3 to 3, we can use the concept of the distance between two points and the idea of a fraction of that distance.

The distance between -3 and 3 is 3 - (-3) = 6.

To find three-fifths of this distance, we can multiply the distance by the fraction 3/5.

(6) * (3/5) = 18/5 = 3.6

So, three-fifths of the distance from -3 to 3 is 3.6.

To find the point that is three-fifths of the way from -3 to 3, we start at -3 and move 3.6 units to the right.

-3 + 3.6 = 0.6

Therefore, the point that is three-fifths of the way from -3 to 3 on the number line is 0.6.

In conclusion, the point 0.6 is three-fifths of the way from -3 to 3 on the number line.

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The number of likes Ali's photo received is 42 and it is three times the number of likes that Kate's photo received. Let x represent the number of likes Kate's photo received. The equation that represents this relationship is 3x = 42. Solving for x gives x = 14, which means Kate's photo received 14 likes. Kate’s photo got 14 likes.

To solve this problem, we can use a basic algebraic equation where we let x represent Kate’s likes and 3x represents Ali’s likes.

This is because Ali got 3 times as many likes as Kate. Since Ali’s latest photo got 42 likes, we can set 3x equal to 42. This gives us the equation: 3x = 42.

To solve for x, we can divide both sides of the equation by 3, which gives x = 14.

Thus, Kate's photo got 14 likes.
In summary, to find the number of likes that Kate’s photo got, we can use the equation 3x = 42, where 3x represents Ali’s likes and x represents Kate’s likes. Solving for x gives us x = 14, which means that Kate’s photo got 14 likes.

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Using probability mass function formula, the probability of having x success in the n independent trials is 0.143.

We can use probability mass function to determine the probability of x success in the n independent trials.

[tex]P(x) = (n C x) * (p^x) * ((1-p)^(^n^-^x^))[/tex]

Where:

- n is the number of trials

- p is the probability of success in a single trial

- x is the number of successes

Given:

- n = 32 (number of trials)

- p = 0.34 (probability of success)

- x = 10 (number of successes)

Calculating P(x = 10):

[tex]P(x = 10) = (32 C 10) * (0.34^1^0) * ((1 - 0.34)^(^3^2 ^- ^1^0^))[/tex]

P(x = 10) = 0.143

Therefore, the probability of having 10 successes in 32 independent trials, with a success probability of 0.34, is approximately 0.143.

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The value of the number is 64

We need to know that index forms are described as mathematical forms that are used to represent numbers or variables that are too large or too small in more convenient forms.

The rules of index forms are;

Add the exponents when multiplying numbers of like bases

Subtract the exponents when dividing numbers of like bases

From the information given, we have the index form as;

4⁴⁻¹

subtract the exponent, we get;

4³

Find the cube of 4, we have;

64

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The inequality 5m - 7 > 16 holds true for all numbers greater than 4.6 in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

To determine the numbers for which the inequality 5m - 7 > 16 holds true in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, we can solve the inequality by isolating the variable m.

Starting with the given inequality:

5m - 7 > 16

We can add 7 to both sides of the inequality:

5m > 16 + 7

5m > 23

Next, we divide both sides of the inequality by 5:

m > 23/5

To simplify, we divide 23 by 5:

m > 4.6

Now, we can analyze the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} to determine thenumbers for which m is greater than 4.6.

Looking at the set, we find that the numbers greater than 4.6 are: 5, 6, 7, 8, 9, 10.

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The arranged expressions from least to greatest are: 1, 203.69

To arrange the expressions from least to greatest, let's simplify them first:

Expression 1: (72 / 8) - 2 x 3 + 172 / (8 - 2) x 3 + 172 / (8 - 2) x 3 + 172 / (8 - 2) x (3 + 1)

Expression 2: 72 / 8 - 2 x (3 + 1)

Simplifying Expression 1:

(72 / 8) - 2 x 3 + 172 / (8 - 2) x 3 + 172 / (8 - 2) x 3 + 172 / (8 - 2) x (3 + 1)

= 9 - 6 + 172 / 6 x 3 + 172 / 6 x 3 + 172 / 6 x 4

= 9 - 6 + 28.67 x 3 + 28.67 x 3 + 28.67 x 4

= 9 - 6 + 86.01 + 86.01 + 114.68

= 9 - 6 + 200.69

= 3 + 200.69

= 203.69

Simplifying Expression 2:

72 / 8 - 2 x (3 + 1)

= 9 - 2 x 4

= 9 - 8

= 1

Now, let's arrange the expressions from least to greatest:

1 < 203.69

Therefore, the arranged expressions from least to greatest are:

1, 203.69

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Answer:

[tex]\textsf{a)} \quad (x+1)^2+(y-4)^2=36[/tex]

[tex]\textsf{b)} \quad (x-5)^2+(y+2)^2=64[/tex]

[tex]\textsf{c)} \quad (x-3)^2+(y-7)^2=130[/tex]

Step-by-step explanation:

To write the equation of a circle given its center and radius, we can substitute the values into the standard circle equation formula.

[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Given values:

Substitute the values into the circle equation formula:

[tex](x-(-1))^2+(y-4)^2=6^2[/tex]

Therefore, the equation of the circle is:

[tex]\boxed{(x+1)^2+(y-4)^2=36}[/tex]

[tex]\hrulefill[/tex]

Given values:

The diameter of a circle is twice its radius.

Therefore, if the diameter of the circle is 16, the radius is r = 8.

Substitute the values into the circle equation formula:

[tex](x-5)^2+(y-(-2))^2=8^2[/tex]

Therefore, the equation of the circle is:

[tex]\boxed{(x-5)^2+(y+2)^2=64}[/tex]

[tex]\hrulefill[/tex]

Given values:

Substitute the values into the circle equation formula and solve for r²:

[tex](-4-3)^2+(-2-7)^2=r^2[/tex]

           [tex](-7)^2+(-9)^2=r^2[/tex]

                      [tex]49+81=r^2[/tex]

                              [tex]r^2=130[/tex]

Therefore, the equation of the circle is:

[tex]\boxed{(x-3)^2+(y-7)^2=130}[/tex]

Answer:

Maximum= (-2,15)

Minimum= (2,-15)

The surface area of the smaller ornament to 1 d.p is 1952.0 cm²

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

Scale factor is expressed as;

scale factor = new dimension/original dimension

We can also say that the ratio of the corresponding sides of similar shapes is equal and it is the scale factor.

Scale factor = (area factor)²

scale factor = 220/55 = 4

area factor = 4² = 16

Therefore;

16= 31232/x

16x = 31232

Divide both sides by 16

x = 31232/16

x = 1952.0 cm²

Therefore the area of smaller ornament is 1952.0

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Answer: √35

Step-by-step explanation:

If two triangles are similar, then that means the ratios of the sides within each triangle will equal each other. Knowing this and that these triangles are similar, we can set the ratio of the known side and the unknown side of each triangle equal to each other.

Doing this, we get the equation [tex]\frac{5}{x} =\frac{x}{7}[/tex]. Notice that 5 is in the numerator while 7 is in the denominator. It could be flipped, but what's important is that they are not both in the numerator or denominator. We know they should not be as in the triangle on the right, 5 is the shorter non-hypotenuse side, whereas on the left, the 7 is the longest non-hypotenuse side, so they do not correspond to the same side.

From this equation, we can just solve for x. Solving for x by cross multiplying gives the answer [tex]x=\sqrt{35\\[/tex].

The equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The point-slope form of a line can be converted to the slope-intercept form of a line, y = mx + b, where b is the y-intercept.

The equation y - 5 = (4/3)(x - 6) can be rearranged into the point-slope form of a line by isolating the y-term and simplifying: y - 5 = (4/3)(x - 6)y - 5 = (4/3)x - 8y = (4/3)x - 3

Now, we have the point-slope form of the line with slope 4/3 and y-intercept -3.

To convert this to the slope-intercept form of a line, we simply rearrange the equation to solve for y:y = (4/3)x - 3 This is the slope-intercept form of the line, where the slope is 4/3 and the y-intercept is -3.

Thus, the equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

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Fill in the blanks with the correct number. (please spell out your solution using lower case lettering.)Mitosis results in  genetically identical cells.Meiosis results in  sex cells.

Answer:

[tex]1.6*10^{-5}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{0.02^2*0.01}{0.5^2}\\\\=\frac{0.0004*0.01}{0.25}\\\\=\frac{0.000004}{0.25}\\\\=\frac{4*10^{-6}}{2.5*10^{-1}}\\\\=\frac{4}{2.5}*10^{-6-(-1)}\\\\=1.6*10^{-5}[/tex]

Hope this helped!

Answer:

n = 16

Step-by-step explanation:

median = 2320

n is even, so the median is the mean of the two middle numbers.

Let x and y be the two middle numbers, with y > x.

The median is 2320, and the number of numbers is even, so the median is (x + y)/2. Since x and y are not equal to 2320, then x < 2320, and y > 2302.

There must be 7 more numbers less than 2320, so you have:

a, b, c, d, e, f, g, x, y, i, j, k, l, m, n, o

The total number of numbers is 16.

n = 16

A fertilizer covers 5/6 square foot in 1/4 hour. The unit rate is 31/3 square feet per hour.

To find the unit rate in this problem, we need to determine the amount of square feet covered per hour. The given information tells us that the fertilizer covers 5/6 square foot in 1/4 hour.

To calculate the unit rate, we can divide the amount covered by the time it takes. In this case, we divide 5/6 square foot by 1/4 hour.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, we have:

(5/6 square foot) ÷ (1/4 hour) = (5/6) * (4/1)

Now, we can multiply the numerators (top numbers) together and the denominators (bottom numbers) together:

(5/6) * (4/1) = (5 * 4) / (6 * 1) = 20/6

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

(20/6) ÷ 2/2 = 10/3

The resulting fraction, 10/3, represents the unit rate. However, the question asks us to express it as a mixed number.

To convert an improper fraction (a fraction with a numerator greater than the denominator) to a mixed number, we divide the numerator by the denominator and express the remainder as a fraction.

In this case, 10 divided by 3 is 3 with a remainder of 1.

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If a + 2b + 3 = 0, then the statement could imply that the expression evaluates to zero.

If a + 2b + 3 > 0, then the statement could indicate that the expression is greater than zero.

If a + 2b + 3 = c, then the statement could suggest that the expression is equal to some value c.

If a + 2b + 3, then the statement is incomplete. It does not provide any specific condition or outcome that follows the "then" part of the statement.

A conditional statement typically follows the form "If [condition], then [outcome]." In this case, we have the expression a + 2b + 3, but it is not clear what condition or outcome is being referred to.

To complete the conditional statement, we need additional information to specify the condition and the corresponding outcome. For example:

If a + 2b + 3 = 0, then the statement could imply that the expression evaluates to zero.

If a + 2b + 3 > 0, then the statement could indicate that the expression is greater than zero.

If a + 2b + 3 = c, then the statement could suggest that the expression is equal to some value c.

Without further context or specific instructions, it is not possible to determine the exact completion of the conditional statement.

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Answer:

∠ ABC = 48°

Step-by-step explanation:

∠ ABH and ∠ CBH form ∠ ABC , that is

∠ ABC = ∠ ABH + ∠ CBH

given that BH bisects ∠ ABC , then

∠ ABH = ∠ CBH = 24°

∠ ABC = 24° + 24° = 48°

The correct statement regarding the graph of the function f(x) = (x + 2)(x + 6) is given by:

The function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to look at the graph of the function relative to the x-axis, as follows:

Hence, for function f(x) = (x + 2)(x + 6), we have that:

Therefore, the correct statement for the signal of the function is given as follows:

Hence, the correct option is B.

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The angles ∠1 and ∠2 are right angles.

In the figure, | lines and m are perpendicular. Therefore, let's describe the relationship between angle 1 and angle 2 as follows;

Perpendicular lines are lines that intersect at a 90 degrees angle.

In other words, a perpendicular lines are two lines that intersect each other and the angle formed between the two lines should be equal to 90 degrees .

Therefore, the ∠1 and ∠2 are right angles.

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Tiffani finished in the 18th position, and Betsy finished in the 13th position.

Mithra finished 16th.

Tiffani finished 18th.

Betsy finished 13th.

Based on the given information, we know the following:

Mithra finished 16th in the baking competition.

Tiffani finished two places in front of Mithra.

Betsy finished 3 places behind Mithra.

From this, we can determine the positions of Tiffani and Betsy as follows:

Since Tiffani finished two places in front of Mithra, her position is 16th + 2 places = 18th.

Since Betsy finished 3 places behind Mithra, her position is 16th - 3 places = 13th.

Tiffani finished in the 18th position, and Betsy finished in the 13th position.

Mithra finished 16th.

Tiffani finished 18th.

Betsy finished 13th.

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When an elevator ascends at a constant pace, its floor number can be described by a linear equation using time x as a variable. The equation can be represented as f(x) = mx + b, where m is the slope or rate of change and b is the y-intercept.

In this case, since the elevator is moving upward, the slope m of the line will be positive. To find the slope of the equation using x to represent time, we must divide the change in y or floor by the change in x or time. The rate of change is constant, which means that the slope will remain constant as the elevator moves up.

Therefore, the equation using x to represent time that best represents the floor number of an elevator ascending at a steady rate is f(x) = mx + b, where m is a positive constant representing the rate of ascent, and b is the floor number where the elevator began its journey.

For example, if the elevator started at floor number 3 and ascended at a rate of 2 floors per minute, the equation would be f(x) = 2x + 3, where x represents the time in minutes elapsed since the journey began. After 5 minutes, the equation would give us a floor number of f(5) = 2(5) + 3 = 13.

Thus, the floor number of the elevator can be easily calculated using this equation.

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