Use the quadratic formula to find the exact solutions of x2 − 5x − 2 = 0. x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a x equals 5 plus or minus the square root of 33, all over 2 x equals negative 5 plus or minus the square root of 33, all over 2 x equals 5 plus or minus the square root of 17, all over 2 x equals negative 5 plus or minus the square root of 17, all over 2

Answer:

Step-by-step explanation:

zachary climed 9.5 m

erin climed 8.8m

to 2 dp

zachary-9.51

erin-8.76

Answer:

To find the linear function with the given properties, we need to determine the slope and y-intercept of the function.

We can use the slope-intercept form of a linear function, which is:

y = mx + b

where m is the slope and b is the y-intercept.

First, we can find the slope using the two given points:

slope = (y2 - y1) / (x2 - x1)

slope = (4 - (-12)) / (-7 - (-3))

slope = 16 / (-4)

slope = -4

Now that we have the slope, we can use one of the given points to find the y-intercept. Let's use the point (-3, -12):

y = mx + b

-12 = (-4)(-3) + b

-12 = 12 + b

b = -24

Therefore, the linear function that satisfies the given properties is:

f(x) = -4x - 24

Answer:

-7 in binary is -0b111.

-5 in binary is -0b101.

Step-by-step explanation:

Answer:

-111

-101

Step-by-step explanation:

Binary uses powers of 2.

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

7 = 4 + 2 + 1

7 = 1 × 2^2 + 1 × 2^1 + 1 × 2^0

7 in binary is 111

-7 in binary is -111

5 = 4 + 1

5 = 1 × 2^2 + 0 × 2^1 + 1 × 2^0

5 in binary is 101

-5 in binary is -101

Answer:

Step-by-step explanation:

x

x  - 1

(x - 1 ) × 3

(x - 1 ) × 3 =

3x - 3

Answer: Let's call the base of the triangle "b" and the height of the triangle "h". We are given that the sum of the base and the height is 22 cm, so we can write:

b + h = 22

We want to find the dimensions for which the area of the triangle is a maximum. The formula for the area of a triangle is:

A = (1/2)bh

We can use the equation b + h = 22 to solve for h in terms of b:

h = 22 - b

We can substitute this expression for h into the formula for the area:

A = (1/2)b(22 - b)

Simplifying this expression, we get:

A = 11b - (1/2)b^2

To find the value of "b" that maximizes the area, we can take the derivative of this expression with respect to "b" and set it equal to zero:

dA/db = 11 - b = 0

Solving for "b", we get:

b = 11

Substituting this value of "b" back into the equation b + h = 22, we get:

h = 22 - b = 22 - 11 = 11

Therefore, the dimensions for which the area of the triangle is a maximum are:

base = 11 cm

height = 11 cm

And the maximum area is:

A = (1/2)bh = (1/2)(11 cm)(11 cm) = 60.5 square cm

Step-by-step explanation:

Answer: 1945

Step-by-step explanation:

Answer:

Harriet Tubman was born in 1820.

Step-by-step explanation:

Showing how brave and resourceful she was in running such a dangerous operation. A black woman operating in slave territory could be highly noticeable. It is a testament to her courage, brains, and fortitude that she was successful. Also, kudos to the many white persons who manned the stations along the Underground Railroad who coordinated with her.

Her impact on America—demonstrating an individual with struggle can accomplish much and correct wrongful structures in our land.

Answer:

x ≈ 10.4

Step-by-step explanation:

using the tangent ratio in the right triangle

tan41° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{x}[/tex] ( multiply both sides by x )

x × tan41° = 9 ( divide both sides by tan41° )

x = [tex]\frac{9}{tan41}[/tex] ≈ 10.4 ( to the nearest tenth )

Answer:

x=10.34

Step-by-step explanation:

tanФ=opposite ÷ adjacent

tan41°=9/x

0.87=9/x

x=9/0.87

 =10.34

Answer:

X= 135°

Step-by-step explanation:

Let y be equal to x

45° + y = 180°

Y = 180 - 45

Y = 135°

Therefore y = X

Answer:

two are supplementary. the measure of one of these angles is 12 degrees less than one-third the measure of the other.what is the measure of each angle

Let's call the measures of the two angles x and y, where x is the larger angle. We know that the two angles are supplementary, which means they add up to 180 degrees:

x + y = 180

We also know that one of the angles (let's say y) is 12 degrees less than one-third the measure of the other angle (x):

y = (1/3)x - 12

Now we can substitute the second equation into the first equation to solve for x:

x + (1/3)x - 12 = 180

Multiplying both sides by 3 to get rid of the fraction, we have:

3x + x - 36 = 540

Combining like terms, we get:

4x - 36 = 540

Adding 36 to both sides, we get:

4x = 576

Dividing both sides by 4, we get:

x = 144

Now we can use the first equation to solve for y:

144 + y = 180

Subtracting 144 from both sides, we get:

y = 36

Therefore, the measures of the two angles are 144 degrees and 36 degrees.

The sum of the sides of a regular polygon is 96ft, find the measure of it side.

Let's say that the regular polygon has n sides, and each side has length s. The formula for the sum of the sides of a regular polygon is:

sum of sides = n * s

We know that the sum of the sides is 96ft, so we can write:

96 = n * s

We want to find the length of each side, so we need to isolate s on one side of the equation. We can do this by dividing both sides by n:

s = 96/n

Now we can substitute this expression for s into the formula for the perimeter of a regular polygon:

Perimeter = n * s

Perimeter = n * (96/n)

Simplifying this expression, we get:

Perimeter = 96

We know that the perimeter of a regular polygon is the sum of the lengths of all its sides, so we can divide the perimeter by the number of sides to find the length of each side:

s = Perimeter / n = 96 / n

Therefore, the length of each side of the regular polygon is 96/n feet. We cannot determine the value of n from the given information in the problem.

Answer:

Step-by-step explanation:

Let the profit in 2020 be P.

The profit in 2021 would then be 1.20P (20% increase).

The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).

We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).

Therefore, the higher profit was in 2020.

The solution is, the higher profit was in 2020.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Let the profit in 2020 be P.

The profit in 2021 would then be 1.20P (20% increase).

The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).

We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).

Therefore, the higher profit was in 2020.

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Answer:

£6.8

Step-by-step explanation:

to make 1 litre of drink juice and lemonade are in the ratio

= 1: 4

juice costs £6 per litre

lemonade costs 50p per litre

to make 1 litre lemonade will cost 4 * 50p = 200p

1£ = 250p

thus, 200p = £.8

thus, cost to make 1 litre of the fruit drink is £6.8

The complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C is [tex]\frac{-4\pi i}{a}[/tex] if a < 1, and 0 if a > 1.

From the question, we are to evaluate the given complex integral when a <1 and a > 1

We can evaluate the complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C using the residue theorem. Since the function has a pole of order 2 at z = a, we need to compute the residue of the function at that point.

If a < 1, then the point a is inside the unit circle C. To compute the residue at z = a, we can expand the function in a Laurent series centered at z = a:

[tex]\frac{zdz}{(z-a)^2}= (\frac{1}{(z-a)})^2 d(z-a)[/tex]

= (1/(z-a))^2 dz - (2/(z-a))^1 da + ...

[tex](\frac{1}{(z-a)})^2dz -(\frac{2}{(z-a)})^1 da + ...[/tex] (Laurent series expansion)

The residue of the function at z = a is given by the coefficient of the [tex](z-a)^{-1}[/tex] term in this expansion, which is:

[tex]Res[z=z0] \frac{z dz}{(z-a)^2} = \frac{-2}{(a - 0)^1} = \frac{-2}{a}[/tex]

Therefore, by the residue theorem, the value of the integral is given by:

[tex]\oint \frac{c zdz}{(z-a)^2} = 2\pi i \times \frac{-2}{a} = \frac{-4\pi i}{a}[/tex]

If a > 1, then the point a is outside the unit circle C. Since the function is holomorphic on and inside the unit circle, it has no singularities inside C and the integral is zero:

[tex]\oint \frac{c zdz}{(z-a)^2} = 0[/tex]

Hence, the complex integral is [tex]\frac{-4\pi i}{a}[/tex] when a < 1, and 0 if a > 1.

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Answer:

Sin 60°

Sin 60°

Cos 30°

Cos 30°

The trigonometry equations when evaluated are ∅ = 82π/125 and ∅ = 28π/23

Equation 1

Given that

cos ∅ = -8/17, π/2 < ∅ < π

Take the arc cos of both sides of the equation

So, we have the following

∅ = 82π/125

Equation 2

The trigonometry equation from the question is given as

tan ∅ = 2/5

The domain of the function is given as

π < ∅ < 3π/2

This means that the definition of the function is

tan ∅ = 2/5, π < ∅ < 3π/2

Take the arc tan of both sides of the equation

So, we have the following

∅ = tan⁻¹(2/5), π < ∅ < 3π/2

Express fraction as decimal

This gives

∅ = tan⁻¹(0.4), π < ∅ < 3π/2

Evaluate the arc tan

∅ = 28π/25

Hence, the measure of the angle is approximately 28π/23

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Answer:

i don't know

Step-by-step explanation:

good luck bro

(alright I'm just here for the points so yeah bye)

[tex]\cfrac{\sqrt[5]{1024h^{-8}s^5}}{\sqrt[5]{h^{-5}s^9}}\implies \sqrt[5]{\cfrac{1024h^{-8}s^5}{h^{-5}s^9}}\implies \left( \cfrac{2^{10}h^{-8}s^5}{h^{-5}s^9} \right)^{\frac{1}{5}}\implies \left( \cfrac{2^{10}}{h^{-5}h^8s^{-5}s^9} \right)^{\frac{1}{5}}[/tex]

[tex]\left( \cfrac{2^{10}}{h^{8-5}s^{9-5}} \right)^{\frac{1}{5}}\implies \left( \cfrac{2^{10}}{h^3 s^4} \right)^{\frac{1}{5}}\implies \cfrac{2^{10\cdot \frac{1}{5}}}{h^{3\cdot \frac{1}{5}}s^{4\cdot \frac{1}{5}}} \\\\\\ \cfrac{2^2}{h^{\frac{3}{5}}s^{\frac{4}{5}}}\implies {\Large \begin{array}{llll} \stackrel{k ~ ~~ ~ r ~~~ t }{4h^{-\frac{3}{5}}s^{-\frac{4}{5}}} \end{array}}[/tex]

When a is equal to -2, the ordered pair is an equational solution.

The places where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation is the solution set of the system of linear equations.

y=3x+7

Ordered pair (-3,a)

introducing x=-3 as a value in the equation

y=3(-3)+7

y=-9+7

y=-2

Hence,value of a is -2 that makes the ordered pair a solution of the equation.

y=3x+7 represents the equation of a straight line. So, it can satisfy infinite ordered pair.

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Answer: The range is the best measure of variability for the given data set and its value is 500.

The range is the difference between the maximum and minimum values in a data set, and in this case, the maximum value is 1100 and the minimum value is 600, so the range is 1100-600=500. The range gives us an idea of how spread out the data is, but it can be affected by outliers. In this case, it seems like a reasonable measure of variability since there are no extreme values that would greatly affect the range.

Step-by-step explanation:

From the data of the number of meters swam by students , range is the best measure of variability and equals 500

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the data set be represented as A

Now , the value of A is

A = { 600, 750, 800, 850, 900, 1100 }

The appropriate measure of variability for the given data is the range. The range is the difference between the largest and smallest values in the data set.

And , range = 1100 - 600

R = 500

Hence , the range of the data set is R = 500

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Answer:

Ivanna takes 9.6 minutes per mile.

To find out, you can divide the total time by the total distance:

time per mile = total time ÷ total distance

time per mile = 96 minutes ÷ 10 miles

time per mile = 9.6 minutes/mile

Step-by-step explanation:

The equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).

The slope refers to the measure of the steepness of a line or a curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or the curve.

The equation of a line can be written as with the help of slope intercept form is given by:

y = mx + b

Where "b" is the y-intercept and "m" is the line's slope of the line.

In the equation y = (-2/3)x + 6, we can see that the slope 'm' is -2/3, which means that for every unit increase in x, the y-value decreases by 2/3 of a unit. This tells us that the line represented by this equation is decreasing (i.e., sloping downwards) from left to right.

The y-intercept 'b' is 6, which means that the line intersects the y-axis at the point (0, 6). This is the starting point of the line, where the value of y is 6 when x is 0.

Therefore, the equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).

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Answer:321.125 and i think the R that you are trying to say stands for remainder

Step-by-step explanation:

The symbolic quantified statement is given as:

For all real integers x and y, if x³ = y³, then x = y.

Using quantifiers, this can be written as:

∀x,y∈ℝ, (x³ = y³) → (x = y)

The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.

The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.

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Answer:

no sé talvez sería

bueno no sé jajaja

Answer:

See graph

Step-by-step explanation:

The transformation is as follows

The transformation of h(x) to -h(x) - 4 is a combination of two transformations

1. A reflection around the x -axis. Every point(x, y) in h(x) becomes (x', y') where x' = x and y' = -y so (x, y) → (x, -y)

2. A translation of each reflected point 4 units down; x value does not change but y values are shifted down so the new y is y'-4 = -y -4

The result of both transformations is:
every coordinate (x, y) in h(x) will be transformed to (x, -y -4)

Seeing as the graph consists of two straight lines meeting at the origin, all we need to do is take any 3 points in h(x), find the transformed coordinates and connect them with straight ilnes

h(x0              -h(X) - 4

(-2, 4)    ⇒      (-2, -4-4) = (-2, -8)

(0, 0 )   ⇒       (0, -0 - 4) = (0, -4)

(4, 2)    ⇒       (4, -2 -4)   = (4, -6)

take these three points and plot

The statement "Square both sides twice and then solve the resulting linear equation." describes the correct process to solve √(3x+4)=√3x+4

Given equation:

[tex]\sqrt{3x} + 4= \sqrt[]3{x} + 4[/tex]

Square both sides :

[tex]3x+4=3x + 16+8\sqrt{3x}[/tex]

= [tex]8\sqrt{3x} =-12[/tex]

Square both sides again

[tex]64[/tex] × [tex]3x[/tex][tex]=144[/tex]

=  x=3\4

Linear equations are mathematical expressions that describe a straight line on a coordinate plane. They are used to model relationships between variables that have a constant rate of change or a constant slope.

Linear equations are fundamental and essential in many areas of mathematics, science, and engineering, and are used extensively in algebra, geometry, calculus, statistics, and physics.

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Complete question:

Which statement describes how to solve √(3x+4)=√3x+4?

The commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.

A mathematical method called linear programming is used to maximise a linear objective function under the restrictions of linear equality and inequality. Finding choice variable values that maximise or decrease the objective function while meeting the limitations is required.

Let us suppose the number of advertisement run on television = x.

Let us suppose the number of advertisement run on radio = y.

Let us suppose the number of advertisement run on online = z.

Then,

140,000x + 18,000y + 30,000z

The constraints on the ads run on are as follws:

1,500x + 200y + 550z <= 24,100 (budget constraint)

x <= 15 (television usage limit)

y <= 19 (radio usage limit)

z <= 12 (online usage limit)

y <= 0.45(x+y+z) (radio usage limit as a percentage of total usage)

x >= 0.15(x+y+z)

Using the linear programming model we have:

x = 15, y = 7 and z = 12.

Substitute the value of x, y, and z:

140,000(15) + 18,000(7) + 30,000(12) = 2,910,000

Hence, the commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.

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Answer: 2/7 as a decimal rounded to the nearest thousandth is 0.286.

Answer: To satisfy the given condition, we need to place the numbers in the boxes in a way that the sum of any three adjacent boxes is divisible by 3.

We can divide the boxes into three groups as follows:

Group 1: Boxes {1, 4, 7}

Group 2: Boxes {2, 5, 8}

Group 3: Boxes {3, 6, 9}

For any three boxes in a group, the sum of their contents must be divisible by 3. We can place any multiple of 3 in the middle box of each group, and the other two boxes will have to be filled accordingly.

Step-by-step explanation:

For Group 1:

If we place 3 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 1.

If we place 6 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 5}, {1, 8}, {4, 5}, {4, 8}, {7, 5}, {7, 8}. This gives us another 6 possible ways to fill the boxes in Group 1.

For Group 2:

If we place 3 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 2.

If we place 6 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 8}, {1, 5}, {4, 8}, {4, 5}, {7, 8}, {7, 5}. This gives us another 6 possible ways to fill the boxes in Group 2.

For Group 3:

If we place 3 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 9}, {2, 6}, {5, 9}, {5, 6}, {8, 9}, {8, 6}. This gives us 6 possible ways to fill the boxes in Group 3.

If we place 6 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 6}, {2, 3}, {5, 6}, {5, 3}, {8, 6}, {8, 3}. This gives us another 6 possible ways to fill the boxes in Group 3.

Therefore, the total number of ways to fill the boxes is:

6 x 6 x 6 x 6 = 1296.

Thus Bian can write the integers 1 to 9 in these ways.

hope it helps...