What are the roots of the equation x² - 10x +34 = 0 in simplest
a + bi form?

Answer:

a. 4

b. -2

Step-by-step explanation:

coordinate: (2,0), (0,4)

gradient = 4 - 0 / 0 - 2

 = -2

Answer:

0.16 btw thanks for the points

Answer: 0.16

Step-by-step explanation:

put 16 over 100 and divide it. Then you get your answer 0.16.

Y=4x-1

The equation of a line is:

Y=mx+c

We are told that the slope is 4 which is also gradient, meaning that M=4

Now we are left with:

Y=4x+c

There are two ways to get C:

1. We know that C represents the y-intercept so immediately we can conclude that C=-1

2. You can work it out by substituting the coordinate for the X and Y value:

-1=4(0)+c

-1=C

So in conclusion, the equation of the line is:

Y=4x-1

The surface area of a regular square pyramid is 332.64 square cm

We know that the surface area of pyramid is nothing but the sum of the areas of its lateral faces and its base.

surface area of pyramid

= areas of lateral faces of pyramid + area of base of pyramid

We know that the formula for the lateral surface area of regular pyramid is:

A = ½ × P × l

where P is the perimeter of the base and l is slant height

Here, a base of regular square pyramid with has sides of 13. 2 cm

a = 13.2 cm and slant height of 6 cm i.e., l = 6 cm

Using the formula of area of square, the base area of pyramid would be,

B = (13.2)²

B = 174.24 sq.cm.

the perimeter of base is:

P = 4 × 13.2

P = 52.8 cm

So, using the above formula of lateral surface area of pyramid the lateral surface area would be

A1 = 1/2 ×  52.8 × 6

A1 = 158.4 sq. cm.

So, the surface area of the pyramid is:

A = A1 + B

A =  158.4 + 174.24

A = 332.64 square cm

Therefore, the surface area of the pyramid = 332.64 square cm

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The system of equations .5(5x + 4) = 17.5x + 14 have Infinite solutions.

We know two simultaneous equations have a unique solution when they intersect at a point,

when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.

Given, A system of equation 3.5(5x + 4) = 17.5x + 14.

17.5x + 14 = 17.5x + 14.

As the LSH and RHS are equal the equation of the two lines is the same and hence they coincide and have an infinite number of solutions.

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The factory can make 744 quarts of ice cream per day.

To find out how many quarts of ice cream could be made in 48 hours, we can use the principle of proportionality. Since the factory makes 310 quarts of ice cream in 10 hours, we can set up a proportion:

310 quarts / 10 hours = x quarts / 48 hours

To solve for x, we can cross multiply:

310 quarts * 48 hours = 10 hours * x quarts

x = (310 quarts * 48 hours) / 10 hours = 1480 quarts

So the factory could make 1480 quarts of ice cream in 48 hours.

To find the rate per day, we need to divide the number of quarts made per hour by the number of hours in a day. Since there are 24 hours in a day, we can calculate the rate per day as:

rate per day = (310 quarts / 10 hours) * 24 hours = (31 quarts/hour) * 24 hours = 744 quarts/day

So the factory can make 744 quarts of ice cream per day.

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This hurricane would be classified as a Category 2 hurricane on the Saffir-Simpson Hurricane Wind Scale.

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A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is (0.2301, 0.2759).

(0.2301, 0.2759).

This interval is calculated using the following formula:

(sample proportion - margin of error, sample proportion + margin of error)

Where the sample proportion is the number of favorable voters (100) divided by the sample size (432), and the margin of error is calculated using the standard error and a critical value from a normal distribution table.

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Answer: 108000

Step-by-step explanation: Here's how I got my answer:

So, first, we need to know something. Whenever there's a fraction, you need to do this. I'll show you the numbers for this problem:

(60^3) / 2

So, the numerator goes in parentheses, and the denominator is what we are dividing by. So, 60^3 is the same as 60 x 60 x 60. You'd get 216000. Then, divide by 2 to get 108000. I hope this helps!

TIP: do NOT turn 3/2 into an improper fraction; 1 1/2. You would get a completely different answer.

The dy for the given values of x and dx is dy = 0.5632, and their difference to the nearest thousandth is 0.0005.

The difference between dy and Δy can be determined by subtracting dy from Δy and taking the absolute value. In this case, dy approximates Δy to the nearest thousandth with a difference of 0.0005. This is a very small difference, indicating that dy is an accurate approximation for Δy.

The accuracy of dy can be attributed to the fact that the function f(x) = ln(1 + x^2) is a smooth function, meaning that the rate of change at a point (i.e., the derivative) is nearly constant. This allows dy to accurately approximate the change in y, Δy, over a small interval of x. Furthermore, the choice of dx = 0.2 is a small enough value that it does not significantly affect the accuracy of the approximation.

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The total weight of the loaves of bread remaining is 1.5 lbs

From the problem it can be deduced that'

There are 3.5 loaves of bread

each weighing 1.5 lbs

Anton's family eats 2.5 loaves of bread

the total weight of the loaves of bread that are left = ?

The loaves of bread that are left

= 3.5 loaves - 2.5 loaves

= 1 loaf

Since 1 loaf weighs  1.5 lbs the weight of the left over bread is 1.5 lbs

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Answer:35° being the smallest interior angle of the triangle, the exterior angle attached to it is the largest. It measures 180° - 35° = 145°.p.

Step-by-step explanation:

If William spends a winter day recording the temperature once every three hours for science class. If  the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. The temperature at 6pm is: -11.1°F

Between 9am and noon, the temperature rose 16.2°F, so the temperature at noon will be:

Temperature at noon  = -12.2 + 16.2

Temperature at noon  = 3.0°F

Between noon and 3pm, the temperature dropped 9.1°F, so the temperature at 3pm will be:

Temperature at 3pm = 3.0 - 9.1

Temperature at 3pm = -6.1°F

Between 3pm and 6pm, the temperature dropped 5°F, so the temperature at 6pm was:

Temperature at 6pm =-6.1 - 5

Temperature at 6pm = -11.1°F

Therefore the temperature at 6pm is  -11.1°F.

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Answer:

18b^6

Step-by-step explanation:

3b⁴ x 6b²

The sum of the three sides of the triangle is 24.

The sum of three sides of a triangle is calculated using the formula S = a + b + c, where a, b, and c are the lengths of each side of the triangle.

To calculate the sum of three sides of a triangle, first measure the lengths of each side and assign a value for each side. For example, if the lengths of the sides are 6, 8, and 10 respectively, then the values for each side would be a = 6, b = 8, and c = 10.

Next, plug in the values of the sides into the formula S = a + b + c to calculate the sum:

S = 6 + 8 + 10

S = 24

Therefore, the sum of the three sides of the triangle is 24.

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Answer: The Answer is false!

Step-by-step explanation:

The area of a rectangle is found by multiplying the length by the width.

Answer:

To find the number of three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed, we can use the formula for permutations:

Step-by-step explanation:

Number of permutations = (number of choices for the first digit) x (number of choices for the second digit) x (number of choices for the third digit)

In this case, we have 6 choices for each digit, since we are allowed to repeat the digits. Using the formula, we get:

Number of permutations = 6 x 6 x 6 = 216

Therefore, there are a total of 216 three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed.

However, not all of these will be even. For a number to be even, the last digit must be even, so the last digit can only be 2, 4, or 6. This means that there are 3 choices for the last digit.

Therefore, the total number of even 3-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 is 366=108.

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Answer:

The fixed cost to insure jewellery is $0.602.

Step-by-step explanation:

We can use the information provided to set up a system of two equations in two variables, and then use the system to solve for the fixed cost of insuring the jewellery. Let x be the fixed cost and y be the percentage of the value of the jewellery. Then we can write the following two equations:

1000x + 1000y = 32 (1) (cost equation for insuring $1000 worth of jewellery)

3500x + 3500y = 44.5 (2) (cost equation for insuring $3500 worth of jewellery)

We can use either of these equation to solve for the fixed cost(x), to do that we can first solve for y from either of the equation, and then substitute it in other equation.

From equation (1)

y = (32 - 1000x) / 1000

then substitute this in equation (2)

3500x + 3500((32-1000x) / 1000) = 44.5

3500x + 32 - 3500x =44.5 - (1000x)

-20x = -12.05

x = 0.602 $

So, the fixed cost to insure jewellery is $0.602.

That means you have to pay $0.602 as a fixed cost, in addition to 0.01(y) as a percentage of the value of jewellery to insure it.

Answer:

25

Step-by-step explanation:

Given expression:

[tex]5^{1125} \times 0.2^{1123}[/tex]

Rewrite 0.2 as a fraction:

[tex]\implies 5^{1125} \times \left(\dfrac{1}{5}\right)^{1123}[/tex]

[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]

[tex]\implies 5^{1125} \times \dfrac{1^{1123}}{5^{1123}}[/tex]

Simplify the numerator by applying the exponent rule a¹ = a:

[tex]\implies 5^{1125} \times \dfrac{1}{5^{1123}}[/tex]

[tex]\textsf{Apply the fraction rule} \quad a \times \dfrac{b}{c}=\dfrac{ab}{c}:[/tex]

[tex]\implies \dfrac{5^{1125} \times1}{5^{1123}}[/tex]

[tex]\implies \dfrac{5^{1125}}{5^{1123}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 5^{1125-1123}[/tex]

Simplify the exponent:

[tex]\implies 5^{2}[/tex]

Simplify:

[tex]\implies 5 \cdot 5[/tex]

[tex]\implies 25[/tex]

The given problem has been proved below using the rules of Congruence.

The given problem can be solved easily if we apply the basic rules of Congruence on the question properly as they are required. Congruence is when two given figures have the same shape and size.

Given that,

3AB=7AD

3AC=7AE

So, by re-arranging them we get the same ratio that is,

AB/AD=7/3

AC/AE=7/3

Hence, we can conclude that,

AB/AD=AC/AE

Also, we can show that ∠BAC and ∠DAE by the property of vertical angles.

But ∠BAC ≌ ∠DAE is also true by the vertical angle theorem in this diagram.

So, SAS property ∆ABC~∆ADE is proved in the end.

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The result of (x-3)(4x+2) using FOIL method is 4x^2 -6x +2x -6.

The FOIL method is a technique used to multiply two binomials. It stands for "First, Outer, Inner, Last" and follows these steps:

First: Multiply the first term of the first binomial by the first term of the second binomial

Outer: Multiply the first term of the first binomial by the second term of the second binomial

Inner: Multiply the second term of the first binomial by the first term of the second binomial

Last: Multiply the second term of the first binomial by the second term of the second binomial

Applying FOIL method to (x-3)(4x+2) we get:

First: 4x * x = 4x^2

Outer: 4x * -3 = -12x

Inner: -3 * 4x = -12x

Last: -3 * 2 = -6

So the result of (x-3)(4x+2) is 4x^2 -12x -12x -6 = 4x^2 -24x -6.

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The volume of a right square pyramid PABCD is 50.91 cubic units

Let l be the side length of right squared pyramid and h be the height.

We know that the formula for the volume of the right squared pyramid.

V = a²h / 3

And the formula for the height of right squared pyramid.

h = (1/√2)a

Here, the side length (a) = 6 units

So, using above formula of height,

h = (1/√2) × 6

h = 6/√2

h = 3√2 units

Now using the formula for the volume of the right squared pyramid, the volume of pyramid PABCD would be,

V = (6² × 3√2) / 3

V = 6² × √2

V = 36√2

V = 50.91 cubic units

Therefore, the volume of PABCD is 50.91 cubic units

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Answer:

simply do 70 divided by 12, then that divided by 3, in total it should take 1, 2, or 3 hours to read 3 books a month

Step-by-step explanation:

Using the Pythagoras Theorem the third side c of the right-angled triangle is obtained as 6.5 units.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

The data given is -

Assume a, b and c are sides of right-angled triangle.

Then, two adjacent sides of right-angled triangle are -

a^2=29.25 squared units

b^2=13 squared units

The unknown side c is taken to be x.

Find the length of c using Pythagoras Theorem -

c^2=a^2+b^2

where, c is the hypotenuse, a is the perpendicular and b is the base.

Plugging the values in the equation -

x^2=29.25+13

x=√(29.25+13)

x=√42.25

x=6.5

Therefore, the third side measures x=6.5 units.

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The station of PT is 12305.58 ft

The station of PT can be determined using the formula:

PT = PI + R * (central angle in radians)

To use this formula, we first need to convert the central angle from degrees to radians. We can do this by multiplying the central angle by (π/180)

Next, we need to determine the radius (R) of the curve. We can use the formula:

R = L / (central angle in radians)

Where L is the tangent length.

Finally, we can substitute the values into the formula for PT:

PT = 105 00 + (1200 / (29.86 * (π/180)))

PT = 105 00 + (1200 / (0.5236))

PT = 105 00 + 2295.58

PT = 12305.58

It's important to note that this calculation assumes that the degree of curvature is a circular curve and that the PI is at the tangent point of the curve.

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The scale factor 5/2 takes hexagon J to hexagon K.

From the given two Hexagon's K and L, the Hexagon K is copy to Hexagon K.

The scale factor = the ratio of edges

Scale factor = 20/8 = 30/12 = 5/2

Hence, the scale factor 5/2 takes hexagon J to hexagon K.

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To complete stain the bottom rectangular prism, he needs to cover 624 square inches.

A solid object's surface area is a measurement of the overall space that the object's surface takes up.

Given that:

Bottom rectangular prism:

Length = 22 in

Width = 8 in

Height = 6 in

The surface area of the rectangular prism is:

SA = 2( lh + wh + lw)

SA = 2((22)(6) + (8)(6) + (22)(6))

SA= 624 square inches.

To complete stain the bottom rectangular prism, he needs to cover 624 square inches.

Square:

Side = 4 in

The surface area of the cube is:

[tex]SA = 6a^2[/tex]

[tex]SA = 6 (4)^2\\\\SA= 96[/tex]square inches.

To completely stain two squares, he needs to cover 96 * 2 = 196 square inches.

Top rectangular prism:

Length = 18 in

Width = 5 in

Height = 2 in

The surface area of the rectangular prism is:

SA = 2( lh + wh + lw)

SA = 2((18)(2) + (5)(2) + (18)(5))

SA = 136 square inches

Hence to completely stain top rectangular prism, he needs to cover 136 square inches.

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The value of x is 0

Now, According to the question:

Let's know:

How to find the value of 'x'

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

The given equation is:

9x - 7 = -7

To solve the value of 'x'

9x - 7 = -7

Add 7 on both sides:

9x - 7 + 7 = -7 + 7

9x = 0

x = 0/9

x = 0

Hence, The value of x = 0

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The complete question is this:

How do you solve 9x - 7 = -7