Find the area of the triangle. A drawing of a triangle with base of 12 and a half feet and height of 4 feet.

The solution of the system of equations is (4, 5).

Here we have the system of equations:

3x + y = 17

2x - y = 8

We would want tosolve this using matrices, then we need to solve:

[tex]\left[\begin{array}{ccc}3&1\\2&-1\end{array}\right] *\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}17\\8\end{array}\right][/tex]

If we add the first and second equations (or the rows of the first matrix) then we will get:

[tex]\left[\begin{array}{ccc}3&1\\5&0\end{array}\right] *\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}17\\25\end{array}\right][/tex]

Then we have:

5y = 25

y = 25/5

y = 5

And now that we know the value of y we can input it in any of the equations to find x.

3x + y = 17

3x + 5 = 17

3x = 17 - 5 = 12

x = 12/3 = 4

The solution is (4, 5).

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The intersection of A and B' is an empty set because there are no elements that are in both A and B'. The correct answer is (option E) the empty set.

What is a set ?

A set is a collection of distinct objects, called elements or members, that are well-defined and unordered.

We can start by finding the complement of set B, which consists of all the elements in U that are not in B:

B' = {r, t, v, x, z}

Then, A ∩ B' consists of all the elements that are in A and also in B':

A ∩ B' = {u, w, y} ∩ {r, t, v, x, z} = { }

Therefore, The intersection of A and B' is an empty set because there are no elements that are in both A and B', the correct answer is (option E) the empty set.

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The team scored 2 field goals, 2 safeties, and 4 touchdowns.

A statement proving the equality of two mathematical expressions is known as an equation. The goal is frequently to ascertain the values of the variables that make the equation true, and it may have one or more variables.

The football team scored 8 times and a total of 38 points.

Let T be the number of touchdowns, F be the number of field goals, and S be the number of safeties.

We know, T = F + S and F + S = 4

Substituting, T = F + S into the equation for total points,

we get, 7T + 3F + 2S = 38

Solving for F and S, we get F = 2 and S = 2.

Therefore, the team scored 2 field goals, 2 safeties, and 4 touchdowns.

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Solve for F and S then get F = 2 and S = 2.

The team scored 4 touchdowns, 2 field goals, and 2 safeties.

The football group scored 8 times, totaling 38 points.

Let,

T is the no.of touchdowns,

F is the no.of field goals, and

S is the no.of safeties.

Touchdown: The ball is in possession of a runner who has moved from the field of play into the end zone and is on, above, or behind the plane of the opposing goal line (extended).

Field Goal: a three-point goal in football obtained by kicking the ball over the crossbar during normal play.

Safeties: NFL defences can score a safety, worth two points, by tackling the offensive player with the ball behind his own goal line or forcing him to run or throw the ball out of bounds behind his own goal line.

We know that,

T = F + S and

F + S = 4

For total points, put T = F + S into the equation.

We get,

7T + 3F + 2S = 38

Solve for F and S,

we get,

F = 2 and S = 2.

As a result, the team tallied 2 field goals, 2 safeties, and 4 touchdowns.

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Answer:

The arc length of this quarter-circle is 7π/4.

Step 1: Isolate x/5 by subtracting 9 from both sides:

  x/5 + 9 -9 = 11 -9

             x/5 = 2

Step 2: Isolate x by multiplying both sides by 5:

        5 · x/5 = 2 · 5

                 x = 10

The solution is 10.

Answer:

5/2

Step-by-step explanation:

substitute the values into the cosine rule:

(2[tex]\sqrt{7}[/tex])² = ((2x - 1)² + (2x + 1)²) - 2(2x - 1)(2x + 1)cos(60))

work out each part separately:

(2[tex]\sqrt{7}[/tex])² = 28

(2x - 1)² = 4x² - 4x + 1

(2x + 1)² = 4x² + 4x + 1

(2x - 1)² + (2x + 1)² = (4x² - 4x + 1) + (4x² + 4x + 1) = 8x² + 2

2((2x - 1)(2x + 1)cos(60)):

(2x - 1)(2x + 1) = 4x² - 1

cos(60) = √1/2 = 1/2

2(4x² - 1)(1/2) = 4x² - 1

substitute back in:

28 = (8x² + 2) - (4x² - 1)

28 = 4x² + 3

25 = 4x²

25/4 = x²

x = √(25/4)

x = 5/2

Answer:

To find the volume of a rectangular prism, we need to know the length, width, and height of the prism. However, the height is not given in the problem, so we cannot calculate the volume.

We can use the surface area and given dimensions to set up an equation to solve for the height. The surface area of a rectangular prism is given by:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively. We are given that the surface area is 62 square feet, and the width and length are 2 and 5 feet, respectively. Substituting these values into the surface area equation, we get:

62 = 2(2)(5) + 2(5)h + 2(2)h

62 = 20 + 14h

42 = 14h

h = 3

Now that we have found the height of the rectangular prism, we can calculate its volume. The volume of a rectangular prism is given by:

V = lwh

Substituting the given dimensions and calculated height, we get:

V = (5)(2)(3)

V = 30

Therefore, the volume of the rectangular prism is 30 cubic feet.

Step-by-step explanation:

Answer:

[tex]30ft^3[/tex]

Step-by-step explanation:

Surface area of a rectangular prism is A = 2(wl +hl +hw)

Volume, height, and Width is given now we can solve for l, v

[tex]A = 2(wl + hl + hw)\\62ft^2 = 2(2ft * l + 5ft * l + 5ft * 2ft)\\62ft^2 = 2(2lft + 5lft + 10ft^2)\\62ft^2 = 2(7lft + 10ft^2)\\62ft^2 = 14lft + 20ft^2\\14lft = 42ft^2\\l = 3ft[/tex]

Now that we have the length, we can solve for the volume

Volume of a rectangular prism = Length x Width x Height

[tex]V = 3ft * 2ft * 5ft\\ = 30ft^3[/tex]

Hope this helps!

Brainliest is much appreciated!

The table below shows the number of hybrid vehicles and the total number of vehicles in the parking lot for each day of the weekend:

Day Hybrids Total

Fri x y

Sat x y

Sun x y

Since the ratios for the three days were equivalent, this means that the fraction of hybrid vehicles to total vehicles was the same for each day. In other words:

x/y = x/y = x/y

Therefore, the values of x and y must be the same for each day. This means that the number of hybrid vehicles and the total number of vehicles in the parking lot were the same for each day of the weekend.

In conclusion, the table should be completed with the same values of x and y for each day, as shown below:

Day Hybrids Total

Fri x y

Sat x y

Sun x y

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Therefore , the solution of the given problem of triangle comes out to be DE = 15, EF = 20, and m∠D = 35, so the solution is A.

A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.

Here,

We must demonstrate that the respective sides and angles of two triangles are proportional in order to establish their similarity.

We are aware of the lengths of two of the sides and one of the angles in the triangular ABC. The third side's length can be determined using the Law of Cosines:

=> BC² = AB² + AC² - 2ABACcos(35°)

=> 9² + 12² - 2912*cos(35°) = BC²

=> BC ≈ 8.455

The edges of triangle ABC are therefore AB = 9, AC = 12, and BC 8.455.

=> A. DE=15, EF=20, and m=35

The angle measurement is 35 degrees, which corresponds to the angle in the triangular ABC. If the ends are proportionate, we can verify this:

=> DE/AB = 15/9 = 1.67

=> EF/AC = 20/12 ≈ 1.67

This collection of measurements meets the requirements for the triangles to be similar because the ratios are equal.

=> DE = 15, EF = 20, and m∠D = 35, so the solution is A.

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Answer:

True

Step-by-step explanation:

A factorial means a number multiplied by all of the positive integers before it. That means both n+3! and n! have a common factor of n!. When you take out this factor of N, the fraction (n+3)!/n! ‘s denominator would be one, and the numerator would have all of the positive integers before n+3 and also being greater than n. Thus, (n+1)(n+2)(n+3)

The possible distances from the Earth to Venus at the time of an elongation of 39.4 degrees are 0.709 AU and 1.333 AU.

The elongation of a planet is the angle formed when the planet, Earth, and Sun are in a straight line. At a certain time, the elongation of Venus was found to be 39.4 degrees. To find the possible distances from the earth to Venus at that time in Astronomical Units (AU), the Law of Cosines can be used.

The Law of Cosines states that for a triangle with sides a, b, and c and angles A, B, and C, c2 = a2 + b2 - 2abcosC.

In this case, a is the distance from the sun to Venus (0.723 AU), b is the distance from the Earth to Venus, and C is the elongation (39.4 degrees).

Therefore, b2 = 0.7232 + b2 - 2(0.723)(b)cos39.4.

Solving for b, we get b = 0.709 AU and b = 1.333 AU, so the possible distances from the Earth to Venus are 0.709 AU and 1.333 AU.

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Given:-

To find:-

Solution:-

Here the sum of the two unknown angles will be 90° as they are the angles which make up 90° . So that;

[tex]\implies x^o + 42^o + 3x^o = 90^o \\[/tex]

[tex]\implies 4x^o = 90^o - 42^o \\[/tex]

[tex]\implies 4x^o = 48^o \\[/tex]

[tex]\implies x =\dfrac{48}{4} \\[/tex]

[tex]\implies \boxed{ x = 12} \\[/tex]

Hence the value of x is 12 .

and we are done!

Step-by-step explanation:

Your debt ratio is the ratio of the credit limit you have spent.

Your debt ratio is the amount you have spent on the credit card/ the limit

You have spent $9000- $3200 = $5800

Debt ratio = 5800/9000

=58/90 = 29/45

2. Acceptable ratio is less than 43%

Is 29 out of 45 less than 43%

Convert 29/45 to percentage

29/45 /100/1 = 64.44%

You have exceeded acceptable ratio at 64.4%

Answer:

Your debt ratio is the percentage of your credit limit that you have spent.

spent $9000- $3200 = $5800

Debt to income ratio = 5800/9000 = 58/90 = 29/45

2. A satisfactory ratio is less than 43%.

Is 29 percent of 45 less than 43%?

29/45 converted to a percentage 29/45 /100/1 = 64.44%

Step-by-step explanation:

Brainliest pls

In September 1998, the population of the country of West Goma in millions was modeled by f(x)=16.9e0.001x. The population of East Goma in millions was modeled by g(x)=13.8e0.019x. In both formulas, x is the year, where x=0 corresponds to September 1998.

To find the year when the population of West Goma will equal the population of East Goma, we will use the following method:

$$f(x)=g(x)$$

$$16.9e^{0.001x} = 13.8e^{0.019x}$$

Taking natural logarithms of both sides we have,

$$\ln(16.9) + 0.001x = \ln(13.8) + 0.019x$$

$$0.018x = \ln(16.9) - \ln(13.8)$$

$$x = \frac{1}{0.018}(\ln(16.9) - \ln(13.8))$$

$x \approx 41.06$, which corresponds to September 2039.

Therefore, the year when the population of West Goma will equal the population of East Goma is September 2039. Option E. 2039 is the correct answer.

Note: The growth rate of West Goma is smaller than that of East Goma, hence it will take a longer time to equalize.

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Check the picture below.

center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1

The dimensions of the given ellipse are major axis 12 units long and parallel to the y-axis, minor axis 8 units long, and the center is located at (-2,5).Let us find the standard form equation of the ellipse. The standard form equation of an ellipse is given by:(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1Where (h, k) is the center of the ellipse, a is the distance from the center to either the x-axis or the y-axis, and b is the distance from the center to the other axis. Therefore, for the given ellipse, the equation of the ellipse in standard form is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1Thus, the standard form equation of the ellipse whose major axis is 12 units long and parallel to the y-axis, minor axis 8 units long, and center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1.

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The expected value of X is given byE(X) = 1/p= 1/(1/4) = 4

To obtain either h, h, h or t, t, t, let's consider the sequence h, h, h, t, t, t. The probability of obtaining h, h, h or t, t, t is (1/2)^3 + (1/2)^3 = 1/4. Also, the probability of the first head or tail occurring on the nth flip is (1/2)^n-1. If X denotes the number of flips of a coin required to get h, h, h or t, t, t, then X has a geometric distribution with parameter p = 1/4. Hence, the expected value of X is given byE(X) = 1/p= 1/(1/4) = 4The expected number of flips of a coin, which comes up heads with probability 0.5, that are necessary to obtain either h, h, h or t, t, t is 4.

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9 Is the value of x in   linear equation.

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. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

2x-5y=1  ..............1

-3x+7y=-3  ..................2

Multiply by 3 in (1) and by 2 in (2)

   6x - 15y = 3

   -6x + 14y  = -6

after substtuting

    y = 3

put value of y in 1

  2*x - 5*3 = 1

   2x = 1 + 15

     2x = 16

       x = 8

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Answer:

9) 15

10)22

11)25

Step-by-step explanation:

9)

[tex]area=\frac{bh}{2} \\30=\frac{(2x+1)4}{2} \\\\30=4x+2\\\\28=4x\\x=7\\[/tex]

substitute:

=2x+7

=2(7)+1

=15

10)

[tex]area=\frac{bh}{2} \\114=\frac{12(3x-2)}{2} \\114=18x-12\\126=18x\\7=x[/tex]

substitute:

=3x-2

=3(7)+1

=22

11)

[tex]area=h\frac{b1+b2}{2} \\\\69=\frac{4x-2}{2} \\\\69=\frac{24x-12}{2} \\\\69=12x-6\\75=12x\\x=6.25\\\\=4x\\=4(6.25)\\=25[/tex]

The correlation coefficient for the SAT math score and the GPA of the students is given as follows:

r=0.94668.

A correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It is represented by the symbol "r" and ranges from -1 to 1.

The value of the correlation coefficient indicates the strength of the linear relationship between the variables. The closer the value of "r" is to -1 or +1, the stronger the linear relationship between the variables. A value of 0 indicates that there is no linear relationship between the variables.

The correlation coefficient is calculated inserting the points of the data-set into a correlation coefficient calculator.

The points from the graph are given as follows:

(595, 3.4), (520, 3.2), (715, 3.9), (405, 2.3), (680, 3.9), (490, 2.5), (565, 3.5).

Inserting these points into a calculator, the coefficient is given as follows:

r = 0.94668.

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Option C requires the examination of the data on bowling scores to find out what Molly's mean score is, and this constitutes a statistical inquiry that can be resolved with the information that has been gathered.

The statistical question that can be answered from the data is: C) What was Molly's average bowling score?

Option A is not a statistical question because it only concerns Molly's personal feeling towards one of her bowling scores.

Option B is a factual question that does not require statistical analysis.

Option D is also a factual question that does not require statistical analysis.

However, option C involves analyzing the bowling scores data to determine Molly's average score. This is a statistical question that can be answered using the collected data.

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Complete question:

Molly joined an after-school bowling club. The club members go bowling once a week throughout the school year. The bowling scores are recorded for each game so that they can be analyzed at the end of each week. Which of these is a statistical question that can be answered from the data?

A) Which bowling score made Molly the proudest?

B) How many times did the bowling club meet?

C) What was Molly's average bowling score?

D) On what day did the bowling club begin?

Answer:

When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant. The slope is another name for the constant rate of change.

Step-by-step explanation:

The constant would be 2.

The midpoint of the line segment joining the points C and D is M = (-4, 0).

The coordinates of the midpoint M of the line segment joining the points C = (0, 8) and D = (-8, -8) can be found using the midpoint formula:

M = ((x1 + x2)/2, (y1 + y2)/2)

So, for C = (0, 8) and D = (-8, -8), we have:

M = ((0 + (-8))/2, (8 + (-8))/2)

M = (-4, 0)

Therefore, the midpoint of the line segment joining the points C and D is M = (-4, 0).

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The container holds 99.223 grams of tablets.

One-sixteenth of a pound is represented by the weight measurement called an ounce (oz). A slice of bread and a pencil are two items that weigh about one ounce. One fluid ounce is the same as one-eighth of a cup in terms of volume. A medication cup has a volume of roughly one liquid ounce.

To convert ounces to grams, we can use the conversion factor 1 oz = 28.3495 g.

So, the container holds:

[tex]$3.5\ \text{oz} \times 28.3495\ \frac{\text{g}}{\text{oz}} = 99.223\ \text{g}$[/tex]

Therefore, the container holds 99.223 grams of tablets.

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1. 6:15 has a ratio of 2:5

2. 10:40 has a ratio of 1:4

3. 6:28 has a ratio of 3:14 but it would be 12:56 based on the answer choices

4. 15:25 has a ratio of 3:5 but it would be 15:25 based on the answer choices

Answer:

Step-by-step explanation:

To solve this system of equations, we can use either substitution or elimination method.

Let's use the elimination method to eliminate y.

Multiplying the first equation by 2 and the second equation by 5, we get:

14x - 10y = 76

10x + 50y = -60

Now, we can add the two equations to eliminate y:

(14x - 10y) + (10x + 50y) = 76 - 60

Simplifying the left side and right side, we get:

24x = 16

Dividing both sides by 24, we get:

x = 2/3

Now that we have the value of x, we can substitute it back into either of the original equations to find y.

Let's substitute it into the first equation:

7x - 5y = 38

7(2/3) - 5y = 38

Simplifying and solving for y, we get:

-5y = 38 - 14/3

-5y = 100/3

y = -20/3

Therefore, the solution to the system of equations is (x, y) = (2/3, -20/3).

Answer:

  C, E

Step-by-step explanation:

You want to identify the true statements about the end behavior, symmetry, domain, and range of g(x) = -5x² and f(x) = 5x-10.

The function g(x) is of even degree (the exponent is 2), and the function f(x) is of odd degree (the exponent is 1). An even-degree function cannot have the same end behavior as an odd-degree function.

The range of any odd-degree polynomial function is (-∞, +∞).

Any even-degree polynomial function will have a global maximum or minimum so cannot have the same range. The range of g(x) is (-∞, 0].

The domain of any polynomial function is "all real numbers." Both f and g have the same domain.

An even-degree function may have an axis of symmetry. An odd-degree function cannot be symmetrical about any line. The functions cannot have the same symmetry.

Two polynomial functions may have a number of points of intersection equal to the highest degree. That means a degree-1 and a degree-2 function may have up to 2 points of intersection. These two functions intersect twice, as the graph in the attachment shows.

Answer:

dghcŕhĝt5dfg9yd6grdy6cjbjbknygug4ximpohyvug5h7h6g6

Answer:

h(t)=−16t²+v

0  t+h 0

for each situation presented. For each situation, determine how long, in seconds, it takes the thrown object to reach maximum height. Initial velocity: 32 ft/s; initial height: 20 ft

Step-by-step explanation:

The probability that the next patient arrives during the following 20 minutes is approximately 0.776.

(a) The probability that exactly 7 patients will arrive during a 90-minute period can be found by using the Poisson distribution formula.Poisson distribution formula:P(X = x) = (e-λ * λx) / x!Where: λ is the average number of events per unit of time or space, x is the number of occurrences, e is the exponential constant equal to 2.71828.x! means x factorial that is x(x − 1)(x − 2)⋯(2)(1).Here, λ = 9/60 = 0.15 (since there are 9 arrivals in one hour, there would be 9/60 arrivals in 1 minute)We are to find the probability of exactly 7 patients arriving in 90 minutes.The time period is 90/60 = 1.5 hours. Hence, λ = 0.15 × 1.5 = 0.225P(X = 7) = (e-λ * λ7) / 7! = (e-0.225 * 0.2257) / 7! = 0.085 ≈ 0.09Therefore, the probability that exactly 7 patients will arrive during a 90 minutes period is approximately 0.09(b) We can calculate the probability of at least 30 minutes passing until the next patient arrives by using the cumulative distribution function (CDF) of the exponential distribution.Exponential distribution formula:f(x) = λe-λxwhere λ is the rate parameter, x is the time period, and e is the exponential constant equal to 2.71828.The mean waiting time between two successive arrivals is 60/9 = 6.67 minutes.Hence, λ = 1/6.67 = 0.15The probability of at least 30 minutes passing until the next patient arrives can be calculated as follows:P(X > 0.5) = 1 - P(X ≤ 0.5) = 1 - (1 - e-λx) = e-λx = e-0.15×0.5 ≈ 0.776Therefore, the probability that at least 30 minutes will pass until the next patient arrives is approximately 0.776.(c) The probability that the next patient arrives during the following 20 minutes can be calculated as follows:P(X > 1) = 1 - P(X ≤ 1) = 1 - (1 - e-λx) = e-λx = e-0.15×1/3 ≈ 0.776Therefore, the probability that the next patient arrives during the following 20 minutes is approximately 0.776.

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