[tex]x^{2}-6x+1=0[/tex]

Solve the quadratic equation using the quadratic formula.
Show exact answers in simplified radical form; no rounded decimals.

The blanks in this two-column proof should be completed (filled) as follows:

Statements                                             Reasons_______________

m∠RST = 5x° and m∠UVW = 7x°                Given

∠RST and ∠UVW are supplementary

m∠RST = 5x° + m∠UVW = 180           definition of supplementary angles

5x + 7x = 180                                       substitution property of equality

12x = 180                                              addition property of equality

x = 15                                                    division property of equality

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this context, we can logically deduce that the sum of angles RST and UVW are supplementary angles:

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Answer: b

Step-by-step explanation:

Answer:

He will save 1 cent per pound if he buys the Sweet Sugar brand

1) Probability that exactly 4 flights are selected is; P(X = 4) = 0.11469

2) The probability that at most 3 flights are on time is; P(X ≤ 3) = 0.99533

3) The probability that at least 6 flights are on time is; P(X ≥ 6) = 0.57672

The formula for binomial probability distribution is;

P(r) = nCr * p^(r) * (1 − p)^(n − r)

Where;

n = Number of events

r = Number of successful events in the trials

p = Probability of success in the single trial of the events

We are given;

p = 80% = 0.8

n = 7

1) Probability that exactly 4 flights are selected is;

P(X = 4) = ⁷C₄ * 0.8⁴ * (1 − 0.8)^(7 − 4)

P(X = 4) = ⁷C₄ * 0.8⁴ * 0.2³

P(X = 4) = 0.11469

2) The probability that at most 3 flights are on time is;

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Solving using online binomial calculator gives;

P(X ≤ 3) = 0.99533

3) The probability that at least 6 flights are on time is;

P(X ≥ 6) = P(X = 6) + P(X = 7)

P(X ≥ 6) = 0.57672

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The value of 9 pounds of blueberries is $24.75.

The value of 5 pounds of blueberries is $13.75.

The fact that the Blueberry Farm sells 6 pounds of blueberries for $16.50 implies that the cost per pound will be:

= $16.50 / 6

= $2.75

Therefore, 9 pounds of blueberries cost:

= Cost per pound × 9

= $2.75 × 9

= $24.75

5 pounds of blueberries will cost:

= 5 × $2.75

= $13.75

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Answer:

3

Step-by-step explanation:

9-2/3x=7

We know that 9-2=7 so 2/3x must be 2

2/3x=2

You have to multiply each side by 3/2

x=3

The number is 3

The original amount of nuts, x, in the recipe is 103

The equation for the original amount is 2x + 2x = 412

An algebraic expression can be defined as an expression made up of terms, factors, constants, coefficients, and variables.

These expressions are also known to be made up of mathematical operations such as;

From the information given, we have that;

Beverly doubles the amount of nuts and peanut butter chips

Total number = 412

This is represented as;

2x + 2x = 412

collect like terms

4x = 412

Make 'x' the subject of formula

x = 412/ 4

x = 103

Hence, the value is 103

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Answer:

A

Step-by-step explanation:

∠ A and ∠ B are vertically opposite angles and are congruent. that is

∠ A and ∠ B are vertical angles

The statement which could be true for the function, g as required in the task content is; Choice C; g(0) = 2.

It follows from the task content that the statement which could be true about the function g is to be identified.

Since the given function instances are; g(0) = -2 and g(-9) = 6.

Since the function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

Hence, the statement which could be true about the function, g is; Choice C; g(0) = 2.

This is so because, 0 is in the domain of the function and 2 is in the range of the function.

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The likelihood of their next third child having additional digits of (six fingers on each hand and six toes on each foot) is 1/2.

For the given condition,

Because the father has the dominant feature as well as the mother is now in normal condition, there is a 50% chance that this deformity will be passed down to children.

Thus, the likelihood of their next (third) child having additional digits is 1/2.

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The area of wallpaper required is 0.98 [tex]m^{2}[/tex]

Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures. 

Mensuration is a subject of geometry. Mensuration deals with the size, region, and density of different forms both 2D and 3D. Now, in the introduction to Mensuration, let’s think about 2D and 3D forms and the distinction between them.

d = 0.26m

h = 1.2m

s = pi * d * h

 = 0.98 square meter

the area of wallpaper required is 0.98 [tex]m^{2}[/tex]

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Answer:

0.98 m²

Step-by-step explanation:

I got it right hope this helps.

Step-by-step explanation:

the equation

y = -8/5 x + 6

tells us 2 things :

-8/5 is the slope of the line, 6 is the y-intercept (the y value when x = 0).

a parallel line has the same slope (just a different y-intercept) : -8/5

a perpendicular line (intercepts at 90°) turns the original slope upside-down and flips the sign : 5/8

we the use the given point as x and y values and calculate the y-intercepts.

parallel :

3 = -8/5 × 5 + y-intercept = -8 + y-intercept

11 = y-intercept

y = -8/5 x + 11

perpendicular :

3 = 5/8 × 5 + y-intercept = 25/8 + y-intercept

(3×8)/8 = 24/8 = 25/8 + y-intercept

-1/8 = y-interceot

y = 5/8 x - 1/8 = 1/8 × (5x - 1)

VZW=64

Step-by-step explanation:

Since the lines are straight the angles are equal. 2x+32=3x+16

Solve this for x.

32=x+16

16=x

Put the value for x (16) in to one of the angle equations

2(16) + 32 = 32 + 32 = 64

Answer: Width = 7 inches, Length = 14 inches

Step-by-step explanation:

Let the width be [tex]w[/tex]. Then, the length is [tex]2w[/tex].

Using the formula for the perimeter of a rectangle,

[tex]2(w+2w)=42\\\\w+2w=21\\\\3w=21\\\\w=7\\\\\implies 2w=14[/tex]

The factors of the number 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100. If you add them up, you will get the total of 217

Answer: $195.70

Step-by-step explanation:

Answer:

90 degrees is the amount of degrees in a right angle

x = -1 is the solution to the given inequality |x| - 2 ≤ -3.

The five steps to resolving inequalities are as follows?

When addressing an inequality, we can:

Isolate the variable on one side of the inequality and place all other constants on the other. To achieve this, alter the inequality by performing opposing procedures. First, multiply each side by two to isolate the x. Any action you take toward one side must also be taken toward the other.

C) If x = -1,

|x| - 2 ≤ -3

|-1| - 2 ≤ -3.

1 - 2 ≤ -3.

-1 ≤ -3 which is true.

Hence, x = -1 is the solution to the given inequality |x| - 2 ≤ -3.

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The correct answer is Option B. Parameters are defined as a group of numerical characteristics of a population.

Parameters are generally the numbers or values that represent the whole population's numerical characteristics. There is a difference between Statistics and Parameters.

Statistics is generally defined as the numerical characteristics of a sample. For example, a sample of standard mean or a sample of standard deviation is an example of statistics.

Parameters are the numerical representation of the characteristics of a population. For example, Population mean or Population standard deviation are examples of Parameters. These represent the data or the characteristics of the population in numerical.

Hence, the correct answer is Option B.

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The correct answer is Parameters are described as a group of numerical characteristics of a population.

In general, Parameters are the numerical values that represent the entire population's numerical characteristics. There is a variation between Statistics and Parameters. Statistics are defined as the numerical characteristics of a sample. A sample of standard mean deviation or a sample of standard deviation are examples of statistics.

               Parameters are the numerical portrayal of the characteristics of a population.  Population mean deviation or Population standard deviation are examples of Parameters. These depict the information or the characteristics of the population in a numerical way.

Hence, the correct answer is Parameters are described as a group of numerical characteristics of a population.

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1. The angles measures are larger than the original angle measures is a false statement.

2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.

3. The final angle measure are the same as the original angle measure is false statement.

4. The original figure and the final figure may not be congruent is true statement.

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Answer:

f(x) = |x-3| + 5

Answer:

both a and b

Step-by-step explanation:

It is because in the elimination method it does not matter whether you eliminate x or y so if you use option a which multiplies -2 by 1st equation so it will become:

-4x+6y=40

4x+6y=8

so the -4x and 4x cancels and a is a valid option.

If you use the b which multiplies the second with 3 it becomes:

2x-3y=-10

4x+3y=24

so -3y and 3y cancel which also makes this a valid option.

Answer: both a and b

The locations of the destinations given by the angles formed between parallel lines and their common transversal in the question are;

1) US Capitol

2) CIA Building

3) US Capitol

4) US Treasury

5) Walmart

The relationship between the angles formed are;

1) The location that is at a corresponding angle to the White House is the Supreme Court

The location at the vertical angle to the Supreme Court is the Smithsonian Institute

The location that is at the angle right adjacent to the Smithsonian Institute is the US Capitol

2) The location that is vertical angles to the FBI Building is the National Zoo

The same side interior angle to the National Zoo is the National Coffee shop

The location at the alternate interior angle to the National Coffee Shop is the CIA Building

3) The location at the alternate exterior angles to Lincoln Memorial is Walmart

The adjacent location that is a right angle to Walmart is the White House Gardens

The location that is at the corresponding angle to the White House Gardens is the US Capitol

4) The location that is at the corresponding angle location to the Smithsonian Institute is the National Zoo Gift Shop

The location that is at the same side interior angle to the national gift shop is the US Capitol

The location that is at the vertical angle location to the US Capitol is the US Treasury

5) The location that is at alternate interior angle location to the Ford's theater is the US Capitol.

The location that is supplementary with the Vietnam War Memorial and the National Zoo is the National Coffee Shop

The location at the angle that is vertical from the National Coffee Shop is the Lincoln  Memorial

The location that is at alternate exterior angle with the Lincoln Memorial is Walmart

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Graph for the equation ( y = -300x +  1200 ) below

y-intercept = ( 0, 1200 )

x-intercept = ( 4, 0 )

Hope this helps! :)

The y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

y=-300x+ 1200

Now, for y- intercept put x=0

y= 1200

and, for x- intercept put y= 0

0 = -300x +1200

x= 4

Hence, the y-intercept is ( 0, 1200 ) and the x-intercept is ( 4, 0 ).

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Answer:

74 square yards

Step-by-step explanation:

Area of rectangular garden:

                 l = 20 yds

                 w = 15 yds

     Area of the rectangular garden = l *w

                                                          = 20 * 15

                                                          = 300 square yards.

Area of the outer rectangle (rectangular garden and the sidewalk):

             length = 20 + 1 + 1 = 22 yds

            width   = 15 + 1 + 1  = 17 yds

       Area of outer rectangle = 22 * 17

                                               = 374 square yards

To find the area of the sidewalk, subtract the area of rectangular garden from the outer rectangle.

Area of the sidewalk = area of outer rectangle - area of sidewalk

                                  = 374 - 300

                                  = 74 square yards

For the given triangle, the value of x would be 12.

What is the geometric mean theorem of a triangle?

According to the geometric mean theorem, the length of an altitude drawn from a triangle's right angle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

For the given triangle, we can apply the geometric mean theorem,

                      By the geometric mean theorem, we can write

                                      6² = 3 * x

                                      36 =  3 * x

                                  ⇒ x = 36/3

                                  ⇒ x = 12.

Hence, for the given triangle, the value of x would be 12.

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Answer:123

Step-by-step explanation:

7328x3424

Steven battling average for the whole season he played was 0.45

An equation is an expression showing the relationship between two or more numbers and variables.

Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season.

Hence:

Batting average = (total number of time he hit the ball in both season half) / (total number of balls thrown)

Therefore:

Battling average = (12 + 6)/ (26 + 14) = 18 / 40 = 0.45

Steven battling average was 0.45

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