Calculate the unknown angle of x

According to the statement if One x-intercept for a parabola is at the point (-4,0)  of the equation the other x-intercept for the parabola is (2, 0).

A parabola is an U-shaped mirror-symmetrical planar curve. It matches a variety of seemingly dissimilar mathematical formulations, all of which identify the same curves. A point and a line are two ways to describe a parabola.

Apollonius, who discovered numerous features of conic sections, is credited with the name "parabola." It signifies "application," referring to the "application of regions" notion, which, as Apollonius demonstrated, has a connection with this curve. Pappus is responsible for the focus-directrix attribute of the parabola as well as other conic sections.

given equation:  y=X² -2x+8

on solving the equation:

y==X² -2x+8

X² + 4x -2x -8

x(x - 4) -2(x - 4)

-1(x-2)(x+4)

According to the statement if One x-intercept for a parabola is at the point (-4,0)  of the equation the other x-intercept for the parabola is (2, 0).

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Answer:

the numbers lie on the number line from left to right: c, b, a

Step-by-step explanation:

a > b > c

bigger numbers are to the right on the number line

The distance from the given point to the given line is d = 13/5 units.    

Given:

To find:

So,

Let us define line L as follows:

Choose A as the fixed point on line L with the coordinates ( m, k ).

The line L now gives the coordinates of any point (x, y):

That was accomplished by subtracting the coordinates (x,y) from (m,k).

The dot product of constants (a, b) to vector coordinates between points (x,y) to (m,k):

For the above expression to be true, the dot product of two orthogonal vectors must be zero.

As a result, vector (a, b) is always perpendicular to every vector pointing in the direction of line L.

The vector is:

It could be the line connecting the points (x_1, y_1) and (m, k).

The magnitude of the scalar projection of v onto a gives the distance d from the point P 1: (x_1, y_1) to the line L because the latter is the duration of the side of a right triangle with two vertices being P_1 and (m, k), and the other vertex lying on L.

So:

In which point A (m,k) is on the line;

Then,

Given a point P (-2,3) and a line L, the equation is 3x - 4y + 5 = 0.

Where.

Now, calculate:                  

Therefore, the distance from the given point to the given line is d = 13/5 units.    

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The correct question is given below:
Use scalar projection to show that the distance from a point P1(x1,y1) to the line ax+by+c=0 is |ax1+by1+c|/underfoot(a^2 +b^2)

Use this formula to find the distance from the point (-2,3) to the line 3x-4y+5=0

Answer:

-20

Step-by-step explanation:

By checking the piecewise function and evaluating it at x = 1, the result of the piecewise function is equal to - 4.

Piecewise functions are functions formed by several expressions constrained by intervals in the real set. In this case we find a piecewise functions consisting in two expressions constrained by two intervals in the real set. The piecewise function is defined by these expressions:

Then, we need to evaluate the piecewise function at x = 1. By direct inspection, we conclude that the value according to the piecewise function evaluated at x = 1 is equal to - 4.

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As we first choose a cluster of the store before surveying all of the customers present in the store, they employed cluster sampling in this instance.

A population is divided into several clusters that are representative of homogeneous traits and have an equal chance of being included in the sample using the sampling technique known as cluster sampling.

Cluster sampling using a single stage: As the name implies, sampling only happens once.

Two-stage cluster sampling: In this case, a small number of individuals are chosen from each group by means of systematic or simple random sampling rather than the entire cluster.

Multiple stage cluster sampling: Compared to two stage sample, multiple stage cluster sampling goes one or more steps beyond. Complex clusters must be formed in order to conduct effective research across several geographies, and this can only be done by employing the multiple-stage sampling technique.

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The answer to the question is 3+x

and the probability of blue balls is 3/3+x

We are required to find out the total number of balls that is the sum of blue and yellow balls

so the total number of balls in the bag​ is 3+x

The concept here used is probability.

Probability is the quantitative relation of rangethe amount|the quantity} of outcomes in  thorough set of equally possible outcomes that manufacture a given event to the whole number of doable outcomes

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

probability of blue balls=blue balls/total balls

=3/3+x

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Hey your question is incomplete, the complete question is

A bag contains 3 blue balls and x yellow balls.Write down the total number of balls in the bag.If a ball is drawn from the bag, write down the probability that it is blue.

Answer: A=-1/12

Step-by-step explanation:

[tex]\displaystyle\\\frac{1}{2}+(-\frac{5}{6} )+\frac{1}{4}=\\\\\frac{1*6-5*2+1*3}{12} =\\\\ \frac{6-10+3}{12}= \\\\\frac{-1}{12}= \\\\-\frac{1}{12}[/tex]

Answer:

Equations

expression

inequality

equation

expression

equation

Step-by-step explanation:

An expression does not have an equal sign.

An equation does have an equal sign

Inequality has a > or< symbols

The total length of the bridge built is less than the total length of the bridge.

We are given;

Length of bridge to be built per day = 54 feet

Number of days they built the bridge = 9 days

Thus, to find the total length that the bridge will span, we multiply the length built each day by the number of days. Thus;

Total Length of bridge = (54 * 9)

Total Length of bridge = 486 ft

Since we want to find if the bridge is at least 490 feet long. Thus, the total length of the bridge built is less than the total length of the bridge.

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The correct sequence of the steps required to construct the bisector of [tex] \angle{A}[/tex] is presented as follows;

The game given steps and their number of appearance in the question photo are;

1. Label the intersection of the arcs in the interior of the angle as point D.

2. Without changing the opening of the compass, place the point of the compass at point C and draw another arc in the interior of the angle

3. Place the point of the compass on point B and draw an arc in the interior of the angle

4. Use the straight edge to draw [tex] \overrightarrow{AD}[/tex]

5. Place the point of the compass at point A and draw an arc that intersects the sides of [tex] \angle{A}[/tex]. Label the points of intersection as points B and C.

The correct order of the steps required to construct the bisector of [tex] \angle{A}[/tex] is as follows;

Step 5 → Step 3 → Step 2 → Step 1 → Step 4

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The total balance remaining on Joshua's game card is $4.5. So, the correct option is (A).

In the Question, It is given that Joshua purchase a game card for $18 which makes the Balance Bal = $18 on his card.

Now, He played 2 rounds of Basketball hoop and each costs $3.25 which makes total for Basketball B = 2*3.25 => B = $6.25

And, He played 4 rounds of Air Hockey each game cost $1.75 which makes the total for Air Hockey A = 4*1.75  => A = $7

To calculate the remaining balance on his card we need to subtract these games' costs from the balance on his card :

=> T = Bal - B - A, Where T = Total, Bal = Balance on card, B = Basketball, A = Air Hockey

=> T = 18 - 6.25 - 7    => T = $4.5

Hence, the Total balance remaining on his card T = $4.5

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The area of a Dragon's kite with the given dimensions is 6 square feet.

Given that, team Dragon's kite is 4 feet long and 3 feet across.

We need to find how much fabric it takes to make their kite.

The area of a kite can be defined as the amount of space enclosed or encompassed by a kite in a two-dimensional plane. Like a square, and a rhombus, a kite does not have all four sides equal.

The area of a kite is half the product of the lengths of its diagonals. The formula to determine the area of a kite is Area = ½ × d1 × d2. Here d1 and d2 are long and short diagonals of a kite.

Now, the area of Dragon's kite = 1/2 × 4 × 3=6 square feet.

Therefore, the area of a Dragon's kite with the given dimensions is 6 square feet.

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Step-by-step explanation:

(a)

First:

Get AE using Pythagoras

[tex] {ae}^{2} = {6}^{2} + {8}^{2} [/tex]

[tex] {ae}^{2} = 100[/tex]

AE =10

Connect OM to form Traingle AOM.

AM=5cm (AE is 10 and AM=ME meaning that they are divided into two equal parts)

AM^2=OM^2+AO^2

5^2=OM^2+4^2

OM^2=5^2-4^2

OM=3

(B) OM is parallel to BE because of midpoint theorem

The Theorem states that The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

(C) AOM is a right angled triangle at O because angle AOM is 90°. Because OM is a perpendicular Line that bisects the chord of AB

a) He will start 900 feet from the edge

b) 16 Round trips are needed to cover the field.

Because Mr. Johns intends to check a wheat field 960 feet wide for weeds so he will distribute a 60-foot wide strip using a high clearance sprayer that has two 30-foot booms.

a) 960 foot - 60 foot = 900 foot

Therefore, he should start 900 feet from the edge.

b) 960 foot / 60 foot = 16 Trips.

Therefore, 16 round trips are needed to cover the field.

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The pharmaceutical company uses the quantitative variable to conducts an experiment.

Variables:

A variable is a characteristic of an object. Their values may occur more than once for a set of data. We consider just two main types of variables in this course.

Quantitative Variables - Variables whose values result from counting or measuring something.

Qualitative Variables - Variables that are not measurement variables. Their values do not result from measuring or counting.

Given,

A pharmaceutical company conducts an experiment in which a subject takes 75 mg of a substance orally.

And  the researchers measure how many seconds it takes for one quarter of the substance to exit the bloodstream.

Here we need to find the kind of variable is the company​ studying.

Here the company uses the Qualitative Variable because here they measure the effects of the medicine not the measurement.

So, the experiment uses the Qualitative Variable.

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It can be concluded that only 2 birds of species A make alarm calls and 10 do not. For species B, there are no alarm calls.

Now,

Hence, It can be concluded that only 2 birds of species A make alarm calls and 10 do not. For species B, there are no alarm calls.

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The smallest sample observation that can increase 8.1 without changing the sample median's value is 4.4.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set. Simply expressed, the sample median is the middle value after sorting the observations in ascending order if the sample size is odd. The sample median is the average of the two middle values if the sample size is equal. The data set's median value is the value that falls in the middle, ordered by magnitude. The sample median is the average of the two middle terms when the number of samples in the data set is even. When the data set is symmetrically distributed, the sample mean serves as a reliable indicator of the central tendency.

The median can be calculated as (12.5+12.6)/2=12.55.

The incremented least observed value is 12.5-8.1=4.4, and the difference is that.

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Answer: It would take the bug 26min to clime the pole

Step-by-step explanation: For me I drew a pole and labeled it like a number line.

1. use or make a number line and plot 0-10 on it.

2. jump 2 points from 0 on the number line

3. Jump backwards once to make the equation accurate

4. plot the times it takes along the way to find the answer until you get to 10

I hope

Jack can use 3 3/14 feet of Barb wire used for each foot when he has 150 feet of barb wire which needs to be put on 35 3/4 feet of fencing.

We are given that:

Jack has 150 feet of Barb wire.

The fencing is:

35 3/4 feet that is equal to

= 140 / 3 feet

For each foot the Barb wire will be calculated by dividing the total Barb wire by the wire required for fencing.

So, we get that:

Barb wire used for each foot = 150 ÷ 140 / 3

Barb wire used for each foot = 450 / 140

Barb wire used for each foot =  = 45 / 14

Barb wire used for each foot = 3 3/14 feet.

So, Jack can use 3 3/14 feet of Barb wire used for each foot when he has 150 feet of barb wire which needs to be put on 35 3/4 feet of fencing.

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Answer:

8/45m² + 2/35m

Step-by-step explanation:

...........................

The equation that models the path of the ball is y =  -0.05·x² + 5·x.

Given,

The distance where the football landed from where it was kicked = 100 feet

The maximum height that the football reached =  125 feet

We have to write an equation that models the path of the ball while it was in the air.

The path may be parabola.

So, equation is like:

y = a·(x - h)² + k

Where;

(h, k) = The coordinate of the vertex (which is the coordinates of the highest point reached by the ball)

Therefore, taking the x-coordinate of the highest point reached by the ball as midpoint of the horizontal distance moved by the ball, we have;

The x-coordinate of the midpoint of the horizontal distance moved by the ball = (50, 0)

We have;

The coordinate of the highest point reached by the ball = (50, 125)

Therefore;

(h, k) = (50, 125)

Substituting the above values in the equation of the parabola gives;

y = a·(x - 50)² + 125

At x = 100, y = 0, which gives;

0 = a·(100 - 50)² + 125 = a·2500 + 125

0 = a·2500 + 125

a = -125/2500 = -0.05

Therefore, we have;

y = a·(x - h)² + k = y = -0.05 × (x - 50)² + 125 = -0.05·x² + 5·x - 125 + 125

y  = -0.05·x² + 5·x - 125 + 125 = -0.05·x² + 5·x

y =  -0.05·x² + 5·x

The equation that models the path of the ball is y =  -0.05·x² + 5·x.

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Answer:

108cm^2

Step-by-step explanation:

Find the areas of the rectangle and the two triangles. Then add all three areas together. See image.

Answer:

D and E

Step-by-step explanation:

In order for the equations to have infinite amount of solutions, they have to be equal to each other.

A: 3x-1 doesn't equal 3x+1

B: 2x-1 is not equal to 1-2x since they negate each other.

C: 3x-2 doesn't equal 2x-3

D: 3(x-1)=3x-1*3=3x-3 ==> D is an answer.

E: 2(x+1)=2x+1*2=2x+2 ==> E is an answer

F: 3(x-2)=3x-6. However, 2(x-3)=2x-6. 3x-6 doesn't equal 2x-6.

Hence, 3(x-2) doesn't equal 2(x-3).