Let A (0,0), B= (2,-1),C= (6,4), and D-= (4, 5). Plot these points. Prove that ABCD is a parallelogram. Draw a diagram.

Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

The addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.

Adding the polynomial

(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)

= x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9

= x⁴ + x³ + 4x² - 3x - 2x + 1 + 8 - 9

= x⁴ + x³ + 4x² - 5x

Therefore, the addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.

Learn more about polynomial:

https://brainly.com/question/1401895

#SPJ1

Answer:

X=11

Step-by-step explanation:

Step 1: Subtract 2x from both sides.

3x−5−2x=2x+6−2x

x−5=6

Step 2: Add 5 to both sides.

x−5+5=6+5

x=11

Hoped  I helped-

Sleepy~

The value of x from the given equation is 11.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 3x-5 = 2x + 6.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 3x-5=2x+6

3x-2x=6+5

x=11

Therefore, the value of x from the given equation is 11.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

The equation of the line that passes through (4, 3) and (-4, -1) is y = -x/2 + 5. So, correct option is A.

To find the equation of the line that passes through two given points, we use the slope-intercept form of a linear equation, which is:

y = mx + b

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

First, we need to find the slope of the line using the two given points. The formula for finding slope between two points is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given points into the formula, we get:

m = (-1 - 3) / (-4 - 4) = -4/8 = -1/2

Now we know the slope, we can use one of the given points (4, 3) and substitute the slope into the slope-intercept form of the equation and solve for b.

y = mx + b

3 = (-1/2)(4) + b

3 = -2 + b

b = 5

Therefore, the equation of the line that passes through (4, 3) and (-4, -1) is:

y = -x/2 + 5

So, correct option is A.

To learn more about equation click on,

https://brainly.com/question/29255626

#SPJ1

Complete question is:

What is the equation of the line that passes through (4, 3) and (-4, -1)?

Choices:

y = -x/2 + 5

y=2x+7

y=x/2 +1

y= -x/2 +7

Answer:

(x-3)^2+(y+1)^2=16 Hope this helps

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

5.33 inches

Step-by-step explanation:

Mean is another term for average. Therefore, we add up all precipitation items from Column B and divide by the total number of items (9):

\(5.98+6.05+7.59+5.27+3.11+7.18+2.95+7.22+2.61=47.96\)

\(47.96\div{9}\approx{5.33}\)

We can see that the dot plot is seen below.

We can see here that An example of a graphical representation of data is a dot plot. It is a number line with dots above each value to indicate the frequency or count of that value.

Depending on the type of data being shown, the dots are often arranged either horizontally or vertically.

Dot plots are known to be useful for showing the distribution of data, particularly for small data sets.

Learn more about dot plot on https://brainly.com/question/15853311

#SPJ1

The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

Learn more about quadrilateral here:

https://brainly.com/question/23935806

#SPJ1

The measure of ∠A is 4° greater than the measure of ∠B. The two angles are complementary. thus, m∠A = 47° and m∠B = 43°.

Since the right angle is considered to be a full angle, complement originates from the Latin word completum, which means "finished." If two angles sum to 90 degrees, they are said to be complimentary angles. That is to say, a right angle is formed when two complimentary angles are combined (90 degrees).

When two angles' measurements sum up to 90 degrees, they are said to be complimentary. When two angles sum up to 180 degrees, they are called supplementary. They are referred to be complimentary angles when the total of two angles is 90 degrees. For instance, the angles of 30 degrees and 60 degrees complement one another.

Two angles are said to be complementary angles if the sum of the measure of angles is 90 degree.

As per the statement:

The measure of A is 4 degrees greater than the measure of B

⇒  m∠A = 4° + m∠B     .....[1]

It is given that:  The two angles are complementary

By definition of complementary angles;

⇒ m∠A + m∠B = 90°      .......[2]

Substitute equation [1] into [2] we have;

⇒  4° + m∠B + + m∠B = 90°

⇒  4° + 2 m∠B = 90°

Subtract 4 degree from both sides we have;

Divide both sides by 2 we have:

2 m∠B = 86°

Substitute in [1] we have:

m∠B = 43°

Therefore, measure of each angles are:

m∠A = 4° + 43° = 47°

and m∠B = 43°

To know more about complementary angles refer to:

https://brainly.com/question/16281260

#SPJ1

The exact value of the tan(75°), found using trigonometric identities for the tangent of the sum of two angles, indicates that the exact value of tan(75°) is (1+√3/3)/(1 - √3/3))

Trigonometric identities are equalities of expressions that includes trigonometric functions which are valid for all values of the argument, or the domain of the function.

The exact value of tan(75°) can be found from the formula for the tangent of the sum of two angles as follows;

tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)•tan(B))

tan(75°) = tan(45° + 30°)

tan(45° + 30°) = (tan(45°) + tan(30°))/(1 - tan(45°)•tan(30°))

tan(30°) = √3/3

tan(45°) = 1

tan(45° + 30°) = (1 + √3/3)/(1 - √3/3)

tan(75°) = (1 + √3/3)/(1 - √3/3)

The correct option is therefore option B

\(tan(75 ^{ \circ } ) = \dfrac{1 + \frac{ \sqrt{3} }{3} }{1 - \frac{ \sqrt{3} }{3} } \)

Learn more about trigonometric identities here:

https://brainly.com/question/14421002

#SPJ1

The area and arc length of each piece can be found using the

relationship between a circle and a sector of the circle.

Responses (b, c, and d are approximated):

a. 120°

b. 10.6 square inch

c. 28.3 in.

d. Area: 15.8 in.², Central angle: 89.1°

Given:

Diameter of the pan, d = 9-inch

Number pie pieces cut from the apple pie = 6

The pie pieces are sectors of a circular pie.

a. The central angle of one pie pieces = \(\dfrac{360^{\circ}}{6}\) = 60°

Therefore;

b. Area of circular pie = π·r²

Where;

\(r = \mathbf{\dfrac{d}{2}}\)

Therefore;

\(r = \dfrac{9}{2} = \mathbf{ 4.5}\)

\(The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}\)

c. The circumference of a circle = 2·π·r

The circumference of the original pie = 2 × π × 4.5 in. ≈ 28.3 in.

d. Let the arc length of the pie piece = 7 inches

\(\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8\)

\(The \ central \ angle \ of \ the \ pie \ piece = \dfrac{7}{2 \cdot \pi \cdot 4.5} \times 360^{\circ} \approx \underline{ 89.1^{\circ}}\)

Learn more about circumference, area and sector of a circle here:

https://brainly.com/question/12985985

The range of the given relation is:   range = { 3, 9, 10}

Range is the out come of the event is know as y.

Here, the given relation:

               R = {(0,3), (8,9), (16,10)

Now, range = { 3, 9, 10}

Thus, the range of the given relation is: range = { 3, 9, 10}

Learn more about Range from:

https://brainly.com/question/15697193

#SPJ1

Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

Answer:

John pay:449.65

Step-by-step explanation:

(391×15)÷100=58,65

391+58,65=449,65

Answer:

8

Step-by-step explanation:

If you match up the pieces then you would find that the missing side/green blank is 8

Answer:

C. bar graph
bar graph  is the best type of graph for comparing the hours that two students work as babysitters each week. The x-axis can represent the two students and the y-axis can represent the number of hours worked. Each student's bar can be a different color to make it easy to differentiate between them.

C. bar graph

bar graph  is the best type of graph for comparing the hours that two students work as babysitters each week.

Answer:

Who was the first president of United States?

A Benjamin Franklin

B George Washington

C Abraham Lincoln

D John Adams

Answer:

290.87 miles

Step-by-step explanation:

336 miles - 67 hours

x miles - 58 hours

Cross multiply

67x = 336 x 58

67x = 19488.

Divide both sides by 67

x = 19488/67

x = 290.87 miles

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

For more such questions on graphing visit:

https://brainly.com/question/19040584

#SPJ8

Answer: Irrational

Step-by-step explanation:

Two pie is the same as saying 2 x π

This means that 2π is an irrational number

The type of number of 2 π is Irrational number.

In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.

It is an irrational number. A number is rational if it can be expressed as a quotient of 2 integer numbers. Number π 2 cannot be expressed as a quotient of integers, so it is an irrational number.

Hence, The type of number of 2 π is Irrational number.

Learn more about Irrational number here:
https://brainly.com/question/17450097
#SPJ3

The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

for such more question on matching expressions

https://brainly.com/question/12270624

#SPJ8

She should use 4 grams of fat, and 2 calories per half cup serving

This is a group of equations which may have none, one or more solutions.

From the question, we have the following system of equations

\(13x+8y=68\)

\(145x+330y=1240\)

Where:

x represents the grams of fats, and y represents the number of calories

Next, we plot the graph of both equations (see attachment)

From the attachment, the solution to the system is:

(x,y) = (4,2)

Hence, she should use 4 grams of fat, and 2 calories per half cup serving

Read more about system of equations at:

https://brainly.com/question/13729904

If the initial velocity is 75 feet per second, it will take approximately 5.125 seconds for the ball to hit the ground.

The given formula h= -16t²+vt+s represents the height (h) of an object thrown vertically in the air at time (t), with initial velocity (v) and initial height (s). In this case, we are given that the initial height of the softball is 4 feet and the initial velocity is 75 feet per second.

We want to find out how long it will take for the ball to hit the ground, which means we want to find the time (t) when the height (h) is 0.

Substituting the given values into the formula, we get:

0 = -16t² + 75t + 4

This is a quadratic equation in standard form, which we can solve using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Where a=-16, b=75, and c=4. Substituting these values into the formula, we get:

t = (-75 ± √(75² - 4(-16)(4))) / 2(-16)

t = (-75 ± √(5625 + 256)) / (-32)

t = (-75 ± √(5881)) / (-32)

We can simplify the expression under the square root as follows:

√(5881) = √(49121) = 711 = 77

So we have:

t = (-75 ± 77) / (-32)

Simplifying further, we get two possible solutions:

t = 0.5 seconds or t = 5.125 seconds

Since the softball player hits the ball when it is 4 feet above the ground, we can disregard the solution t=0.5 seconds (which corresponds to when the ball is at its maximum height) and conclude that it will take approximately 5.125 seconds for the ball to hit the ground.

To learn more about velocity click on,

https://brainly.com/question/3699894

#SPJ1

Answer:

The minimum exam score to be awarded an A is about 8.52.

Step-by-step explanation:

Let X represent the scores on a common final exam.

It is provided that X follows a normal distribution with mean, μ = 71 and standard deviation, σ = 9.

It is provided that according to the department policy is that the top 10% of students receive an A.

That is, P (X > x) = 0.10.

⇒ P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The corresponding z-score is:

z = 1.28

Compute the value of x as follows:

\(z=\frac{x-\mu}{\sigma}\\\\1.28=\frac{x-71}{9}\\\\x=71+(1.28\times 9)\\\\x=82.52\)

Thus, the minimum exam score to be awarded an A is about 8.52.

Answer:

can you take a picture of you problem

The equation of the line that passes through the point (3,2) and has a slope of 4 is; y = 4x - 10

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Point (3,2)

Then Slope m = 4

Now Write the equation as;

y - 2 = 4(x - 3)

y = 4x - 10

Hence, The equation of the line is; y = 4x - 10

Learn more about equations here;

brainly.com/question/25180086

#SPJ1

9514 1404 393

Answer:

  >180° (more than 180°)

Step-by-step explanation:

Angles are classified as ...

It seems that we're looking at definitions:

  obtuse : >90° :: reflex : >180°