What quadratic equation could be solved to find any solutions to the system of equations?
y = -5x + 6
y = x^2 + 7x - 11
Replace the values of a, b, and c, in the equation to formulate the correct equation.
0 = ax² + bx + c

The angles are vertical and the value of x  from the angles (4x -25) and 75 can be expressed as 25.

A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees. When two lines join to form an angle, say X=45°, the opposite angle is also 45°, for instance.

From the fiqure we can see that the angles the vertically opposite angles, base on this condition we can form the equation as;

(4x-25)=75

4x=(75+25)

4x=100

x=100/4

x=25

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The calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.

As a result, we must reject the null hypothesis.

A manager of a sports club maintains data about the main sport in which members participate and their ages.

To verify if there is a connection between the age of a member and their sport preference, a test of independence is performed on 651 sports club members who were randomly selected at a 5% level.200 Words:

Test of independence: Test of independence is a statistical method that helps to determine if there is a connection between two groups, and if there is, what is the magnitude of the relationship.

A test of independence is performed using the chi-square statistic.

The null hypothesis in this test is that there is no relationship between the two group S.

We will use a chi-square test to determine whether there is a connection between the age of the member and the sport in which they participate.

Hypotheses:

Null hypothesis: There is no link between the age of a member and the sport in which they participate.

Alternate hypothesis: There is a relationship between the age of a member and the sport in which they participate.

Level of significance = 5%.

Step 1: Prepare the contingency table for observed values

Age  Basketball  Football  Hockey  Soccer  Other Under 20 years  25  30  20  10  15 20-29 years  20  50  35  30  25 30-39 years  15  40  40  35  30 40-49 years  10  35  25  25  20 Over 50 years  5  15  10  15  10

Step 2: Calculate the marginal frequencies.

Age  Basketball  Football  Hockey  Soccer  Other Total Under 20 years  25  30  20  10  15 100 20-29 years  20  50  35  30  25 160 30-39 years  15  40  40  35  30 160 40-49 years  10  35  25  25  20 115 Over 50 years  5  15  10  15  10 55 Total 75  170  130  115  100 651

Step 3: Compute the expected frequencies.

The predicted frequency for each group is (row total) * (column total) / total number of observations.

Age  Basketball  Football  Hockey  Soccer  Other Under 20 years  11.5  26.1  19.9  17.7  15 20-29 years  30.9  70.1  53.4  47.5  40.1 30-39 years  30.9  70.1  53.4  47.5  40.1 40-49 years  21.3  48.2  36.8  32.7  27.6 Over 50 years  9.4  21.4  16.4  14.6  12.3

Step 4: Calculate the test statistic:

We will use a chi-square test statistic to determine whether the null hypothesis should be accepted or rejected.

Chi-square test formula is:χ2 = Σ (Observed frequency – Expected frequency)2 / Expected frequency.

Degrees of freedom = (Number of rows – 1) * (Number of columns – 1)

χ2 = (25-11.5)2 / 11.5 + (20-30.9)2 / 30.9 + (15-30.9)2 / 30.9 + (10-21.3)2 / 21.3 + (5-9.4)2 / 9.4 + (30-26.1)2 / 26.1 + (50-70.1)2 / 70.1 + (40-70.1)2 / 70.1 + (35-48.2)2 / 48.2 + (15-21.4)2 / 21.4 + (20-19.9)2 / 19.9 + (35-53.4)2 / 53.4 + (40-53.4)2 / 53.4 + (25-36.8)2 / 36.8 + (10-16.4)2 / 16.4 + (15-14.6)2 / 14.6 + (15-32.7)2 / 32.7 + (25-27.6)2 / 27.6 + (10-12.3)2 / 12.3χ2 = 15.16

Degrees of freedom = (5-1) * (4-1) = 12

Step 5: Determine the p-value:

The p-value is determined by looking up the chi-square value and the degrees of freedom in the chi-square table.

The p-value is the probability of obtaining a result as extreme as or more extreme than the calculated value if the null hypothesis is true.

We will use a 5% level of significance.

Since the calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.

As a result, we must reject the null hypothesis.

There is evidence to suggest that the age of a member is related to the sport in which they participate.

In other words, the age of a member and their sport preference are not independent.

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Answer:

15

Step-by-step explanation:

The factors of 15 are 1,3,5,15

The factors of 30 are 1,2,3,5,6,10, 15, 30

The largest factor that both of these numbers share is 15

Answer:

x = 4, y = -14

Step-by-step explanation:

1. x + y = -10 and -3x - y = 2

2. y= -10 - x > plug in for y > -3x - (-10 - x) = 2

3. solve for x > -3x + 10 + x = 2

-2x + 10 = 2 > -2x = -8 > x= 4

4. plug x into original equation > 4 + y = -10 > y = -14

The probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

This is a binomial distribution problem, where we have n = 15 trials and the probability of success (a patient having hyperextending joints) is p = 0.2.

A. To find the probability that exactly 5 of the 15 patients have hyperextending joints, we can use the formula for the binomial probability mass function:

P(X = 5) = (15 choose 5) * 0.2^5 * 0.8^10

where (15 choose 5) is the number of ways to choose 5 patients out of 15. Using a calculator, we get:

P(X = 5) = 0.188

So the probability that exactly 5 of the 15 patients have hyperextending joints is 0.188, or about 18.8%.

B. To find the probability that no more than 7 of the 15 patients have hyperextending joints, we need to add up the probabilities of having 0, 1, 2, ..., 7 patients with hyperextending joints. We can use the cumulative distribution function (CDF) of the binomial distribution:

P(X ≤ 7) = Σ(P(X = k)) for k = 0 to 7

Again, using a calculator, we get:

P(X ≤ 7) = 0.985

So the probability that no more than 7 of the 15 patients have hyperextending joints is 0.985, or about 98.5%.

C. To find the probability that more than 7 of the 15 patients have hyperextending joints, we can use the complement rule:

P(X > 7) = 1 - P(X ≤ 7)

We already know from part (B) that P(X ≤ 7) = 0.985, so:

P(X > 7) = 1 - 0.985 = 0.015

Therefore, the probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.

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The possible triangle whose vertices are given by the lattice points with positive integer coordinates less than 5 is 20.

To solve this, we apply principles of permutation and combination to count the number of possible triangles that can be formed from the given set of lattice points.

Here are the different ways of arranging the lattice points with lattice point coordinates less than 5:

If we want to choose any three lattice points, we can pick the first point from the 20 given in the table above.

Then, we can pick the second point from those lattice points that lie strictly above and strictly to the right of the first point.

For the third point, we can only pick lattice points lying above and to the right of the line segment connecting the first two points.

So, there are 20 possible triangles whose vertices are positive integer coordinates less than five.

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Answer:

5.2 feet

Step-by-step explanation:

436.8/7/12 feet

Answer: Yes

Step-by-step explanation:

1.4691 is more than 1.465, and less than 1.472

Answer:

first find constant term

y=kx

32=k(4)

32/4=4k/4

k=8

find value of y when x=5

y=kx

y=8×5

y=40

In linear equation, 6499 ft CD, the height of the plane from the ground, to the nearest foot.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Part A) Find BC, the distance from Tower 2 to the plane, to the nearest foot.

in the triangle ACD

sin16=CD/(7600+BD)--------> CD=sin16*(7600+BD)---------> equation 1

in the triangle BCD

sin24=CD/BD-----------> CD=sin24*BD---------------> equation 2

equation 1=equation 2

sin16*(7600+BD)=sin24*BD-----> sin16*7600+sin16*BD=sin24*BD

sin24*BD-sin16*BD=sin16*7600----> BD=[sin16*7600]/[sin24-sin16]

BD=15979 ft

in the triangle BCD

cos24=BD/BC---------> BC=BD/cos24-------> 15979/cos24-------> 17491

BC=17491 ft

    =  BC is 17491 ft

Part 2) Find CD, the height of the plane from the ground, to the nearest foot.

CD=sin24*BD        ( remember equation 2)

BD=15979 ft

CD=sin24*15979 -----------> CD=6499 ft

     =  CD is 6499 ft

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Step-by-step explanation:

According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n complex zeros (counting multiplicities).

The degree of the polynomial f(x) = 5x^6+2x^3−4x + 1 is 6, which means that it is a sixth-degree polynomial. Therefore, it has exactly 6 complex zeros (counting multiplicities).

Note that the zeros may be real or complex, and they may not all be distinct. To find the exact number of zeros and their values, we would need to use additional methods such as factoring, the rational zeros theorem, or numerical methods.

Answer:

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root. In the case of the polynomial function f(x) = 5x^6+2x^3−4x + 1, it is a sixth-degree polynomial function, which means it has at most six complex roots. However, the Fundamental Theorem of Algebra does not tell us the exact number of roots, nor does it tell us whether the roots are real or complex.

To determine the number of real roots of the function f(x), we can use the Intermediate Value Theorem or graph the function to find the number of times it crosses the x-axis. However, determining the number of complex roots requires more advanced techniques, such as the use of the Fundamental Theorem of Algebra in combination with the Factor Theorem, Rational Root Theorem, or other methods.

Therefore, based on the Fundamental Theorem of Algebra alone, we can say that the function f(x) = 5x^6+2x^3−4x + 1 has at least one complex root, but we cannot determine the exact number or nature of the roots without additional analysis.

Answer:

v<-4/35. If you want interval notation it is (-infinity, -4/35)

Step-by-step explanation:

The rectangular prism's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula:

SA = 2lw+2lh+2hw.

A face is just a flat surface in the geometric sense, and edges are formed where surfaces meet. Pyramids and prisms are both examples of polyhedra. A pyramid, however, is not a prism.

Method to find surface area:

Thus, the rectangular prism's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula:

SA = 2lw+2lh+2hw.

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Surface Area = (width×length  +  height×length  +  height×width) × 2

—————

Please remember to revise this and make it in your own words if you want! I tried making this as simple as possible! I hope this helps you. -Doodle

—————

Answer:42.8571429%

Step-by-step explanation:

His GPS tracker got 7 miles while he actually ran 10. 10 - 7 = 3. Then you divide 3 by 7 which is [tex]\frac{3}{7}[/tex] and that is around 42.8571429%.

An angle measurement, m∠BOC = 60° degrees where O is the center of the corcle.

What is an angle?

Since the ΔABC has three similar sides, we know that it is an equilateral triangle, meaning that all three angles are equal and each angle measures 60°.

Since A, B, and C are points on a circle with O as the center, we know that each of the distances OA, OB, and OC is equal to the radius of the circle.

Let's call this radius r.

Since ΔABC is equilateral, we know that each side has length r. We can also draw radii from the center O to points A, B, and C to form three congruent triangles AOB, BOC, and COA, each with two sides of length r and one angle of 60°.

Since the sum of the angles in a triangle is 180° degrees, each of the other two angles in each of these congruent triangles must measure 60° as well.

Thus, we see that ∠BOC is one of the angles in the isosceles ΔBOC, which has two angles of 60° and a third angle x, which we want to find.

We can use the fact that the sum of the angles in a triangle is 180° to find x:

x + 60 + 60 = 180

Simplifying, we get:

x = 60

Therefore, angle BOC measures 60°

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Complete question is:  m∠BOC = 60° degrees where O is the center of the corcle.

The bank made $100 in profit from the loan.

What is simple interest?

Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on.

If John had to pay back $321 in total and the original loan was $221, then the bank made $100 in interest from John.

Interest = Amount John had to pay - Original Loan

Interest = 321 - 221

Interest = $100

So, the bank made $100 in profit from the loan.

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The radius of the circle is 9 units. The center of the circle is at (5, 0).

The given equation is (x – 5)²y² = 81.

To identify the radius and center of this circle, we can rewrite the equation in standard form.

First, let's divide both sides by 81 to get (x – 5)²y²/81 = 1.

Next, we can take the square root of both sides to eliminate the squared terms.

This gives us the equation (x – 5)/9 · y/3 = 1.

The standard form of a circle is (x – h)² + (y – k)² = r², where (h, k) is the center of the circle and r is the radius.

Comparing this form to our equation, we can see that (x – 5)/9 and y/3 correspond to (x – h) and (y – k), respectively.

Therefore, we can solve for h and k by setting (x – 5)/9 = 0 and y/3 = 0, respectively.

This gives us h = 5 and k = 0, so the center of the circle is (5, 0). Finally, we can solve for the radius r by noting that the

distance from the center (5, 0) to the edge of the circle is 3 units in the x-direction and 9 units in the y-direction.

Therefore, the radius of the circle is 9 units, and we can express our final answer as:

The radius of the circle is 9 units. The center of the circle is at (5, 0).

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Answer:

a) v.h=v*cos(63)=7.26 m/s

b) v.v=v*sin(63)=14.26 m/s

c) t=v.v/g=14.26/9.8=1.46 s since time the body takes to go upward is defined by the acceleration due to gravity and the vertical component of the speed

d) h=1/2*gt^2=7.15 m

e) T=2t=2.92 s

f) R=v.h*t=7.26*1.46=10.6 m since horizontal displacement is defined by the horizontal component of the speed only.

Step-by-step explanation:

Hope this helps! =D

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The measure of diagonal DB in the given square is 5√2.

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles.

Using Pythagoras theorem of right triangle

DB² = DC² + BC²

Here given that

DC = BC

Then

DB² = DC² + DC²

DB² = 5² + 5²

DB² = 25 + 25

DB² = 50

DB = √50

DB = 5√2

Thus, the measure of diagonal DB in the given square is 5√2

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To calculate the amount of money Joe will have in 3 years, we can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the amount of money Joe will have in 3 years

P = the principal amount = $2500

r = the annual interest rate = 9% = 0.09 (expressed as a decimal)

n = the number of times the interest is compounded per year (assuming annual compounding, n = 1)

t = the number of years = 3

Plugging in these values, we get:

A = $2500(1 + 0.09/1)^(1*3)

= $2500(1.09)^3

= $2500(1.29503)

= $3237.58 (rounded to two decimal places)

Therefore, Joe will have $3237.58 in 3 years.

A house with value at 210000 correct to 2 significant figures. The lowest possible value of the house is equals to the £205000.

The second significant figure of a number is the digit after the first significant figure. This is true even in case of the digit is zero. We have a house is valued at £210000 correct to 2 significant figures. So, it is bounded question. Since, two significant figures is correct then there is error in 10000 range in £210000. The rounded up value is £2.10 × 10⁵. Steps to determine these bounds

here x = £210000, y = 10000

Since 2 significant digits are correct,

is about 10,000 of £210,000. The lowest possible number rounded to 2 significant digits in the £210,000 range is £205,000, because anything below that looks like £204....that doesn't round up to £21. Hence required value is £205000.

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The coordinates of the point where the food bag is hung are (2.5, 7, 6.5).

The center of the coordinate system (where the lines intersect) is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0). An ordered pair contains the coordinates of one point in the coordinate system.

The coordinates of the point on the first tree where the rope is attached are (10, 6, 8), and the coordinates of the point on the second tree where the rope is attached are (-5, 8, 5).

To find the distance between the points, we can use the distance formula:

distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

Plugging in the coordinates from part 1, we get:

distance = √((-5 - 10)² + (8 - 6)² + (5 - 8)²)

distance = √(225 + 4 + 9)

distance = √(238)

Therefore, the distance between the points is √(238).

Since the food bag is hung at a point exactly halfway along the length of the rope, we can find its coordinates by taking the average of the coordinates of the points where the rope is attached.

The x-coordinate of the midpoint is: (10 + (-5)) / 2 = 2.5

The y-coordinate of the midpoint is: (6 + 8) / 2 = 7

The z-coordinate of the midpoint is: (8 + 5) / 2 = 6.5

Therefore, the coordinates of the point where the food bag is hung are (2.5, 7, 6.5).

To determine whether the food is safe from bears, we need to compare the height of the food bag to the maximum height that bears can reach. The food bag is hung at a height of 6.5 feet, and bears can reach a height of 7.5 feet when standing. Therefore, the food is not completely safe from bears, as they may be able to reach it if they stand up on their hind legs. However, hanging the food bag at this height does make it more difficult for the bears to reach, and may deter them from trying to get to it. It is also important to note that proper food storage techniques in bear country should involve using bear-resistant containers, in addition to hanging food bags.

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The median provides Farrah with an understanding of the central value in her data set, which can help her analyze the overall distribution of the data points.

The median is a measure of central tendency that tells Farrah the middle value of her data when it is arranged in ascending order.

To find the median, Farrah should follow these steps:
1. Arrange her data in ascending order (from smallest to largest).
2. If there is an odd number of data points, the median is the middle value.
3. If there is an even number of data points, the median is the average of the two middle values.

It is less affected by outliers or extreme values than the mean, making it a more reliable representation of the center of her data.

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The measures of angles in a rhombus are m∠2=130, m∠3=50 and m∠4=50.

Angle measure is a term used in geometry to describe the size of an angle. It is usually expressed in degrees, which is a unit of measurement for angles. A degree is defined as 1/360th of a complete revolution around a circle.

In the rhombus, m∠1 =130

In a rhombus, opposite angles are congruent.

The angle opposite to angle 1 is angle 2.

so m∠1 =m∠2

m∠2= 130 degrees

Other pair of opposite angles are also congruent.

so m∠3=m ∠4

We know that the sum of 4 angles = 360

m∠1+m∠2+m∠3+m∠4=360

130+130+m∠3+m∠4=360

260+m∠3+m∠4=360

m∠3+m∠4=360-260

m∠3+m∠3=100

2m∠3=100

m∠3=50

Now, m∠3=50

m∠4=50

Therefore, m∠2=130, m∠3=50 and m∠4=50

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Answer:

x = 11

Step-by-step explanation:

3x + 5x + 2 =90

(3x + 5x) + (2) = 90

8x + 2 = 90

8x + 2 -2 = 90 -2

8x = 88

8x/8 = 88/8

x = 11

The work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is 200 foot-pounds.

Given, The weight of the chain per foot = 2 pounds

Total length of the chain = 20 feet

The chain is hanging from a winch 20 feet above ground level.

The work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is to be determined.

The force required to lift the chain is equal to the weight of the chain. Therefore, the force needed is F = 2 × 20 = 40 pounds. The work done is the product of force and distance.

Therefore, Work done = force × distance= 40 × (20 − 10)= 400 foot-pounds

Thus, the work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is 200 foot-pounds.

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Therefore, the estimated population of great white sharks that have migrated from Mexico to Hawaii is 2,500.

Shark population estimation is the process of determining the size and trends of shark populations in a given area. It involves collecting and analyzing data on shark abundance, distribution, behavior, and other factors to understand their population dynamics.

There are different methods used to estimate shark populations, including mark-recapture studies, aerial surveys, acoustic tracking, and genetic analysis. These methods allow researchers to estimate the number of sharks in a given area, monitor changes in their population over time, and identify potential threats to their survival.

To estimate the population of great white sharks that have migrated from Mexico to Hawaii, we can use the capture-recapture method, also known as the Lincoln-Petersen index.

Let:

The Lincoln-Petersen index formula is:

[tex]N = (n_1 * n_2 * n_3) / (m_1 * m_2 * m_3)[/tex]

Plugging in the given values, we get:

[tex]N = (45 * 20 * 20 * 20) / (3 * 2 * 4)[/tex]

[tex]N = 60,000 / 24[/tex]

[tex]N = 2,500[/tex]

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The equation of the polynomial function in standard form is P(x) = x³ + 6x² - 7x - 60

Given that we have the following

zeros = -5,-4,and 3

The polynomial function in standard form is calculated as

P(x) = (x - zeros)

So, we have

P(x) = (x + 5)(x + 4)(x - 3)

Opening the brackets, we have the following equation

P(x) = x³ + 6x² - 7x - 60

Hence, the polynomial is P(x) = x³ + 6x² - 7x - 60

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The sum of the ages of the family seven years ago is given as follows:

45 years.

The sum of the ages of the family is obtained applying the proportions in the context of the problem.

Each year, the age of each person increases by one, hence, considering a family of five, the yearly increase in the age of the family is given as follows:

5 x 1 = 5 years.

The two youngest are 6 and 8, meaning that seven years ago, the youngest was not yet born.

The ages of a family of five sum to 80, hence the sum seven years ago was given as follows:

80 - 5 x 7 = 45 years.

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