When sketching a parabola, use ______ to make both sides even and avoid extra calculations.
A. Completing the square
B. FOIL
C. Symmetry
D. Factoring
E. End behaviors

Answer:

w=2

Step-by-step explanation:

Simplifying

4w + -9(6 + -5w) = 44

4w + (6 * -9 + -5w * -9) = 44

4w + (-54 + 45w) = 44

Reorder the terms:

-54 + 4w + 45w = 44

Combine like terms: 4w + 45w = 49w

-54 + 49w = 44

Solving

-54 + 49w = 44

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '54' to each side of the equation.

-54 + 54 + 49w = 44 + 54

Combine like terms: -54 + 54 = 0

0 + 49w = 44 + 54

49w = 44 + 54

Combine like terms: 44 + 54 = 98

49w = 98

Divide each side by '49'.

w = 2

Simplifying

w = 2

Answer:

w has multiple forms

exact w = 53/5

decimal w = 10.6

mixed number w = 10 3/5

5 x 53/5 - 9 = 44

The x-coordinate for the center of gravity is 16.1, and the y-coordinate is 15.4 which is determined using average.

To find the center of gravity (also known as the centroid), we need to calculate the weighted average of the x and y coordinates using the given data points and their respective weights. The weights are represented by the "dc coordinates demand a" value for each data point.

Let's calculate the x-coordinate first:

x-coordinate = (1040 + 2525 + 830 + 1120 + 25*6) / (40 + 25 + 30 + 20 + 6) = 16.1

Now let's calculate the y-coordinate:

y-coordinate = (1240 + 3025 + 1530 + 2011 + 6*25) / (40 + 25 + 30 + 20 + 6) = 15.4

Therefore, the center of gravity is located at approximately (16.1, 15.4) in terms of x and y coordinates.

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Answer: 3 hours

Step-by-step explanation: 65x4=260 455-260=195 195/65=3

The time taken by Jacob's family on the second day will be 3 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

The time is calculated as:-

For 4 hours of driving at an average speed of 65 miles per hour, the distance covered is,

d = 65 x 4 = 260 miles

Miles remaining for the second day is,

455 - 260 = 195 miles

Time taken to cover 195 miles second day is,

T = 195 / 65 = 3 hours

Therefore, the time taken by Jacob's family will be 3 hours.

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Both teams can complete the search in a time period of 4 hours.

Distance is a measurement of how far apart two points or objects are from one another. Time is a unit used to describe how long it takes for an object to travel between two points. Speed is a unit used to describe how quickly or slowly an item or a point moves.  

Here we have

Two search-and-rescue teams leave base camp at the same time,
looking for a lost child.

The first team, on horseback, heads north at 3 mph,  

The second team, on foot, heads south at 2.5 mph.

Let both teams complete searching in 'x' mins

The distance traveled by 1st team in 'x' mins = 3 × x  

= 3x  m

The distance traveled by 2nd team in 'x' mins = 2.5 × x  

= 2.5x m    

As we know total distance = 22 miles

=> 3x + 2.5x = 22 miles

=> 5.5x = 22 miles

=> x = 4 hrs  

Therefore,

Both teams can complete the search in a time period of 4 hours.

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Answer:  February is the month that serves as the counterexample.

Step-by-step explanation: February has 28 days most years, 29 days in a leap year. So it is an an example that disproves the statement that all months have at least 30 days.

Answer:

question isn't clear could you post a clear pic some digits aren't visible

Answer:

The equation of the straight line in point - slope form

y +1 = -2 ( x-2)

Step-by-step explanation:

Step(i):-

Given points are C( 2,-1) and D(1,1)

Slope of the line

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

   m = -2

Step(ii):-

Equation of the straight line passing through the point ( 2,-1) and having slope

m =-2

y - y₁ = m ( x- x₁)

y - (-1) = -2 ( x-2)

y +1 = -2 ( x-2)

Final answer:-

The equation of the straight line

y +1 = -2 ( x-2)

Answer:

42

Step-by-step explanation:

substitute x = 7 into f(x)

f(x) = 6x = 6 × 7 = 42

42 lightbulbs are needed for 7 chandeliers

The vector \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \) is perpendicular to none of the above.

Given,

vector \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \).

We are to check among the given vectors, which one of the following vectors is perpendicular to the vector \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \).

We know that, two vectors are perpendicular if their dot product is zero.

So, we need to find the dot product of vector \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \) with the given vectors.

Let's calculate dot product of vector \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \) with vector \( 5 \hat{a}_{x}+2 \hat{a}_{y}+2 \hat{a}_{z} \).

Dot product of vectors \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \) and \( 5 \hat{a}_{x}+2 \hat{a}_{y}+2 \hat{a}_{z} \) is\( \vec{A}.(5 \hat{a}_{x}+2 \hat{a}_{y}+2 \hat{a}_{z})=(2 \hat{a}_{x}-5 \hat{a}_{z})\cdot (5 \hat{a}_{x}+2 \hat{a}_{y}+2 \hat{a}_{z})=2\cdot5-5\cdot0+2\cdot0=10 \)

As the dot product is not zero. So, vector \( 5 \hat{a}_{x}+2 \hat{a}_{y}+2 \hat{a}_{z} \) is not perpendicular to vector \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \).

Let's calculate dot product of vector \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \) with vector \( 5 \hat{a}_{x}+2 \hat{a}_{y} \).

Dot product of vectors \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \) and \( 5 \hat{a}_{x}+2 \hat{a}_{y} \) is\( \vec{A}.(5 \hat{a}_{x}+2 \hat{a}_{y})=(2 \hat{a}_{x}-5 \hat{a}_{z})\cdot (5 \hat{a}_{x}+2 \hat{a}_{y})=2\cdot5-5\cdot0+2\cdot0=10 \)

As the dot product is not zero. So, vector \( 5 \hat{a}_{x}+2 \hat{a}_{y} \) is not perpendicular to vector \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \).

Therefore, none of the given vectors is perpendicular to vector \( \vec{A}=2 \hat{a}_{x}-5 \hat{a}_{z} \).Hence, option (d) None of the above is the correct answer. The correct option is (d).

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Step-by-step explanation:

ABC and ADE are similar triangles.

that means they have the same angles, and there is one scaling factor for all sides from one triangle to the other.

so, we see that AB = 2, AD = 2+1 = 3

the scaling factor f from AB to AD is then

AB × f = AD

2 × f = 3

f = 3/2

the same scaling factor now applies between BC and DE (= x).

BC × f = x

1 × 3/2 = x

x = 3/2 = 1.5

Answer:

  3 tents hold 2 campers

Step-by-step explanation:

The given relations can be expressed as a single equation in the number of 2-camper tents.

__

Let x represent the number of 2-camper tents. Then the number of 4-camper tents is 6-x, and the total number of campers in tents is ...

  2x +4(6 -x) = 18

  -2x +24 = 18

  -2x = -6 . . . . . . subtract 24

  x = 3 . . . . . . . divide by -2

Exactly 3 tents hold 2 campers.

_____

Additional comment

The other 3 tents hold 4 campers.

Another way to consider this is to assume that all tents hold 2 campers, and then realize there are 18 -6×2 = 6 campers left over. If these are placed 2 per tent, then there will be 6/2 = 3 tents with 4 campers. The remaining 3 tents will have 2 campers.

Answer:

Step-by-step explanation:

Given the expression  5 p + 6 = 7, to know the value of variable p. we need to make p the subject of the formula as shown;

Given  5 p + 6 = 7

Step 1: Subtract 6 from both sides

5p+6-6 = 7-6

5p = 7-6

Step 2: We will then divide both sides by the coefficient of p i.e 5 to have;

5p/5 = (7 - 6)/5

p =  (7 - 6)/5

Hence, the correct expression of variable p is p = (7 - 6)/5

Answer:

Step-by-step explanation:

Thus if you are not allowed to repeat a digit the number of possible 4 digit numbers you can construct from 1,2,3,4 is 4 3 2 1 = 24.

The number of 4-digit numbers can you write if you can use only digits 1 and 2 is 16.

Given that, using only digits 1 and 2 form 4-digit numbers.

Digits are the single symbols used to represent numbers in Maths. For example, in number 89, 8 and 9 are two digits. Hence, the numerals such as 0, 1, 2, 3,4, 5,6,7,8,9, and 0 are the form of digits which are used to represent a combination of numbers and do arithmetic operations in our day to day life.

Here,

For the first digit you are picking from 2 digits.

For the second digit you are picking from 2 digits.

For the third digit you are picking from 2 digits.

For the fourth digit you are picking from 2 digits.

2×2×2×2=16

4-digit numbers

1111, 2111, 1211, 1121, 1112, 1221, 2112, 1122, 2211, 1212, 2121, 2221, 1222, 2122, 2212 and 2222.

Therefore, the number of 4-digit numbers can you write if you can use only digits 1 and 2 is 16.

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The sample size is too small, the sample is not representative of the population and the wording of survey question influences the response self-selected sample are potential limitations for a research study.

The sample size being too small can limit the accuracy and precision of the results and reduce the power of statistical tests.

A sample not being representative of the population can result in sampling bias, which can affect the validity of the results.

The wording of a survey question can influence the response, which can result in biased results. A self-selected sample, where participants voluntarily participate in a study, can also result in biased results because only those who are interested or motivated to participate will do so.

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Answer:

b

Step-by-step explanation:

you can take the rectagel and you x the rectagel

Answer:

33:21

Step-by-step explanation:

The way I look at it is that 11:7 is 18 parts of 54. So I divide 54 by 18 and get 3 per. Then multiply, 11 * 3 is 33 and 7 * 3 is 21.

The expression is 12 x 2 / 7 will be 24/7. And the number 54 into the ratio 11:7 will be 33 and 21.

The utilization of two or more additional numbers that compares is known as the ratio.

The expression is given below.

⇒ 12 x 2 / 7

⇒ 24 / 7

Divide 54 into the ratio 11:7.

⇒ 54 x 11 / (11 + 7)

⇒ 594 / 18

⇒ 33

⇒ 54 x 7 / (11 + 7)

⇒ 378 / 18

⇒ 21

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The height of a Doric Column that has a base diameter of 5 feet is 4/3 feet greater than the height of a Doric column that has a base diameter of 2 feet.

The height of a Doric Column that has a base diameter of 5 feet is 10 feet greater than the height of a Doric column that has a base diameter of 2 feet.

To calculate the difference in height, we need to use the fact that the height of a column is proportional to its diameter.

The ratio of the height to the diameter of a Doric column is approximately 4:9.

This means that for every 4 units of height, there are 9 units of diameter.

To find the difference in height between a Doric column with a base diameter of 5 feet and one with a base diameter of 2 feet, we can use the following equation:

Difference in height = (Height of larger column) - (Height of smaller column)

Let's find the height of the two columns using the ratio we just mentioned.

Height of a Doric column with a base diameter of 5 feet = 4/9 * 5 feet = 20/9 feet

Height of a Doric column with a base diameter of 2 feet = 4/9 * 2 feet = 8/9 feet

Now, we can calculate the difference in height:

Difference in height = 20/9 - 8/9= 12/9 = 4/3 feet

So, the height of a Doric Column that has a base diameter of 5 feet is 4/3 feet greater than the height of a Doric column that has a base diameter of 2 feet.

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The percentage can be seen on a graph of the normal curve by shading the area under the curve between the corresponding z-scores for the given interval.

For the ostrich population, the given interval of 4.5 to 5.25 meters represents one standard deviation above the mean (4.5 + 0.75 = 5.25) and includes 34% of the population.

Therefore, we can conclude that the mean stride length of the ostrich population is 4.5 meters, and the standard deviation is 0.75 meters.

To find a similar interval for the emu population, we can use the empirical rule for normal distributions.

This rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Using this rule, we know that approximately 68% of the emu population has stride lengths within one standard deviation of the mean, which is 3 meters ± 0.5 meters.

Therefore, a similar interval to the one given for the ostriches (4.5 to 5.25 meters) would be 3.5 to 4.25 meters for the emus.

The percentage of the ostrich population with stride lengths between 4.5 and 5.25 meters can be seen on a graph of the normal curve by shading the area under the curve between the corresponding z-scores. We can find the z-scores for the interval using the formula:

z = (x - μ) /

where x is the value of the upper or lower bound of the interval, μ is the mean, and σ is the standard deviation.

For the given interval of 4.5 to 5.25 meters for the ostrich population:

z1 = (4.5 - 4.5) / 0.75 = 0

z2 = (5.25 - 4.5) / 0.75 = 1

We can then use a standard normal distribution table or calculator to find the area under the curve between z = 0 and z = 1, which is approximately 0.34 or 34%.

To see this visually, we can plot the normal curve with the mean and standard deviation marked, and shade the area between the z-scores corresponding to the interval of interest.

A similar graph can be used to show the percentage of the emu population within a given interval.

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After solving the equation for n and b we find out that Lin bought 1 necklace and 4 bracelets.

We can set up the following system of equations based on the given information: n = number of necklaces, b = number of bracelets

4n + b = 20 (Lin spends $20 on necklaces and bracelets)

where 4n represents the cost of n necklaces and b represents the cost of b bracelets. This system of equations can be used to solve for n and b. we can solve for n and b using the system of equations:

n + 1b = 5

4n + 1b = 20

We can use the first equation to solve for n in terms of b: n = 5 - b

Substitute this expression for n into the second equation: 4(5 - b) + b = 20

Simplifying this equation, we get: 20 - 4b + b = 20

Solving for b, we get: b = 4

Substituting this value of b back into n = 5 - b, we get: n = 1

Therefore, Lin bought 1 necklace and 4 bracelets

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Complete Question

At a local fair , Lin purchases necklaces and bracelets. Necklaces cost $4 each and bracelets cost $1 each, Lin spends $20 on these items. Let n represent the number of necklaces Lin buys and b represent the number f bracelets Lin buys. Find the number of necklaces and bracelets Lin purchased.

Answer:

C

Step-by-step explanation:

3x - 9y = 9 → (1)

- 2x +2y = 8 ( subtract 2y from both sides )

- 2x = - 2y + 8 ( divide through by - 2 )

x = y - 4

substitute x = y - 4 into (1)

3(y - 4) - 9y = 9

3y - 12 - 9y = 9

- 6y - 12 = 9 ( add 12 to both sides )

- 6y = 21 ( divide both sides by - 6 )

y = \(\frac{21}{-6}\) = - \(\frac{7}{2}\)

(a) The independent variable is age (a) and the dependent variable is population (P).

(b) P(20) = 6.38 million. This means that 6.38 million Americans were 20 years or older in 2015.

(c) P(0) = 363.804 million. This means that 363.804 million Americans were 0 years or older in 2015.

Answer:

35 Degrees

Step-by-step explanation:

Given in figure.

Happy to help :)

The solution is, the value of the angle ADF = 35° .

Here, we have,

from the given diagram, we get,

ABCD is a trapezium.

EBC is a straight line.

F is the point on AB so that DFE is a straight line.

Angle BEF = 45°

Angle FBC = 100°

now, we have,

angle FBE = 180 - 100

                 = 80 degrees

now, from triangle BEF , we get,

Angle EFB = 55 degrees

again, as AFB is vertically opposite angle,

so, angle AFB = Angle EFB = 55 degrees

finally from triangle ADF , we get,

Angle ADF = 180 - 90 - 55

                  = 90 - 55

                  = 35 degrees

so, the value of the angle ADF = 35° .

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Answer:

The first answer is $1050000

The second answer is $1500000

The third one is $450000

Hope this helps:)

Answer:

Isosceles Right

Step-by-step explanation:

The triangle has two sides with equal lengths, making it an isosceles triangle.

The triangle also has a 90° angle, making it a right triangle.

So, the triangle would be an isosceles right triangle.

Hope that helps.

Precalculus is an example here, since x=−2 is a vertical type line, there is no  y-intercept as well as the slope is undefined.

The slope is undefined and all of the factors on the road have an x-coordinate of that (a few number). For example, if x = -2, then all factors alongside this line can have an x-coordinate of -2, making it a vertical line. y=−2 is a flat line crossing the factor at (0,−2) consequently the gradient is 0 and the the y intercept is -2.

A terrible slope approach that variables are negatively related; that is, whilst x increases, y decreases, and whilst x decreases, y increases. Graphically, a terrible slope approach that as the road on the road graph movements from left to right, the road falls. The x-coordinate -2 is represented throughout. This is NOT a function.

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A straight line PPF indicates constant opportunity costs in production is TRUE.

The Production-Possibility Frontier (PPF) is a graphical representation of the maximum amount of two goods that can be produced given a certain number of resources.

If the PPF is a straight line, then the opportunity cost of producing an additional unit of one good is the same regardless of how much of that good is already being produced. This means that the resources used to produce the two goods are perfectly substitutable and there are no increasing opportunity costs.

However, if the PPF is a curved line, then the opportunity cost of producing an additional unit of one good increase as more of that good is produced. This is because the resources used to produce the two goods are not perfectly substitutable and there are increasing opportunity costs.

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Answer:

To convert 2 Bigha into Kattha:

If 1 Bigha = 20 Kattha:

2 Bigha = 2 * 20 Kattha = 40 Kattha

If 1 Bigha = 16 Kattha:

2 Bigha = 2 * 16 Kattha = 32 Kattha

A linear equation to represent the line shown on the graph is given as:

y = 2x - 2.

General point-slope form is:

y = mx + c

(x1, y1) = (3, 2)

y intercept = -2

m = (2 + 2)/(2 - 0)

m = 2

y = 2x + (-2)

y = 2x - 2

Thus,  a linear equation to represent the line shown on the graph is given as: y = 2x - 2.

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The correct question is-

Write a linear equation to represent the line shown on the graphs shown by question 7.

Answer:

15a

Step-by-step explanation:

Multiply  

3

by  

5

=

15

a

Answer:

• First pic

\({ \tt{4x + 65 \degree + x = 180 \degree}} \\ \dashrightarrow \: { \sf{ \{angles \: on \: straight \: line \}}} \\ \\ { \tt{5x + 65 \degree = 180 \degree}} \\ \\ { \tt{5x = 180 \degree - 65 \degree}} \\ \\ { \tt{x = (\frac{115}{5} ) \degree}} \\ \\ \dashrightarrow \: { \boxed{ \tt{ \: \: x = 23 \degree \: \: }}}\)

• Second pic:

\({ \tt{(180 \degree - 124 \degree) + 2x = 6x}} \\ \dashrightarrow \: { \sf{ \{interior \: angle \: sum equivexterior \: angle \} }} \\ \\ { \tt{56 \degree = 6x - 2x}} \\ \\ { \tt{4x = 56 \degree}} \\ \\ { \tt{x = ( \frac{56}{4} ) \degree}} \\ \\ \dashrightarrow \: { \boxed{ \tt{x = 14 \degree}}}\)