What is the answer.

Answer:

a) no solutions

Step-by-step explanation:

in both equations actually the parts of the x and y terms are the same. but when aligned they say they are equal to different numbers.

but the same expression cannot be equal to different values at the same time. so, this is a contradicting system of equations without any solution.

-4x + 2y = -14

y = 2x + 8 | ×2

2y = 4x + 16

-4x + 2y = 16

16 is NOT -14. so, this is a contradiction, and there cannot be a solution.

Answer:

Step-by-step explanation:

You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.

Newton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...

  T = 36 -26·(22/26)^(t/2)

At times of t=4 and t=9, the temperature readings will be ...

__

Additional comment

The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Plan A has the majority of votes.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given this,  the school board in Wichita Falls, Texas, began planning for new and renovated high school facilities.

thus we can say the total number of members who voted is 7.

Therefore, 4 votes are required for the majority.

Therefore, there is no plan that receives a majority of votes.

1st choice votes to A=3

1 choice votes to B=3 1st choice votes to C=1

So, C is to be eliminated and his 1 vote is to be transferred to A (as A is the next choice after C in column 3 of the table)

First choice vote to A = 3 + 1 = 4

First choice vote to B = 3

Since A gets the majority of votes A is the winner

Thus, Plan A has the majority of votes.

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Complete question:

Based on the information, the Stafford loan will have a lower balance by $527.14 at the time of repayment

Using the formula for compound interest, the total cost of the loan can be calculated as follows:

Total cost of Stafford loan = $11,650 x (1 + 0.0595/12)^(12*0.5) = $12,652.14

Total cost of PLUS loan = $12,436.41 x (1 + 0.0655/12)^12 = $13,179.28

Therefore, the Stafford loan will have a lower balance at the time of repayment by $527.14 ($13,179.28 - $12,652.14).

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The time interval between the first two instants when this element has a position of y = 0. 175 m is 21 ms.

The time interval between the first two instants when this element has a position of y = 0. 175 m is calculated as;

y (x, t) = ( 0.35 m sin[1.25 rad/m)x  + (99.6 rad/s)t]

x = 0

y(0,t) =  0.35 sin(1.25 rad/m)0 + 99.6t ) = 0.175

0.35 sin(99.6t) = 0.175

sin (99.6t) = 0.175/0.35

sin (99.6t) = 0.5

99.6t = sin⁻¹ (0.5)

99.6t = (π/6 ) or ( π - π/6) = 5π/6

time, t₁ = ( π/6 ) / ( 99.6 ) = 5.257 x 10⁻³ s

time, t₂ = ( 5π/6 ) / ( 99.6 ) = 26.28 x 10⁻³ s

time interval = t₂ - t₁

= 26.28 x 10⁻³ s - 5.257 x 10⁻³ s

= 21 x 10⁻³ s

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The complete question is below:

A transverse wave on a string is described by the equation

y (x, t) = ( 0.35 m) sin[1.25 rad/m)x  + (99.6 rad/s)t]

Consider the element of the string at x = 0.

What is the time interval between the first two instants when this element has a position of  y = 0. 175 m?

The steps to graph and the graph of the first linear equation are provided.

Here we want to graph some linear equations, so let's do that with the first one, which is:

y = (-1/4)*x + 2

To graph it, just evaluate it in two different values of x, such that:

for x = 0

y = (-1/4)*0 + 2 = 2

So we have the point (0, 2)

for x = 4

y = (-1/4)*4 + 2 = -1 + 2 = 1

So we have the point (4, 1).

Now you just need to graph these two points on a coordinate axis and then connect them with a line. The graph of that line can be seen below.

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Answer:

The gcf of 16,48,72 is 4,12,18

Answer:

Answer:

Step-by-step explanation:

\(\frac{\pi r^2}{2 \pi } \times \theta=32\\\frac{1}{2} r^2 \times \theta=32\\r^2=\frac{32 \times 2}{\theta} \\r^2=\frac{64}{\theta} \\r=\frac{8}{\sqrt{\theta} }\)

substitute the value of θ and solve ,you get the value of radius r

Answer: 24

Step-by-step explanation:

To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.

Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.

The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.

Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19

Radius of the circle = 4.19/60 = 0.07

Angle of sector = 360 - 60 = 300 degrees

Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041

The area of the triangle can be found using the formula:

Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24

Therefore, the total area of the composite figure is:

0.0041 + 24 = 24.0041

Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.

The median will be greater than the mean in a left-skewed distribution

We have,

In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.

A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.

When the data is skewed left, it means that the distribution is being pulled towards the left side.

This is because there are a few extreme values on the left side that are pulling the mean in that direction.

In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.

For a left-skewed distribution,

The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.

In a data distribution that is skewed left, the mean will be less than the median.

This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.

Therefore,

The median will be greater than the mean in a left-skewed distribution

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Answer:

  9x -4y = -44

Step-by-step explanation:

You want the equation of the line through (-4, 2) and perpendicular to the line through (-4, 6) and (5, 2).

The equation of a line through (h, k) and perpendicular to the line through (x1, y1) and (x2, y2) can be written as ...

  (x2 -x1)(x -h) +(y2 -y1)(y -k) = 0

Using the given points, this becomes ...

  (5 -(-4))(x -(-4)) +(2 -6)(y -2) = 0

  9(x +4) -4(y -2) = 0

Expanding this gives the general form equation:

  9x -4y +44 = 0

Subtracting the constant gives the standard form equation:

  9x -4y = -44

Answer:

\(\frac{51}{22}\)

\(2\frac{7}{22}\)

Step-by-step explanation:

Answer:

2 7/22

Step-by-step explanation:

(−12 3/4) ÷ (−5 1/2)

(−12 3/4) = -51/4

(−5 1/2) = -11/2

-51/4 ÷ -11/2

= 51 × 2 / 4 × 11

= 51/22

= 2 7/22

Answer:

We know that:

Jocelyn started with $0, this is represented with the point (0, $0)

After 8 weeks, she had $60, this is represented with the point (8, $60)

Jocelyn assumes that she saved money at a constant rate, so we can represent this with a linear relationship.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

In our case, y is the amount of money that she has saved, x is the number of weeks since she started saving, the slope is the amount of money that she saves each week, and the y-intercept is the initial amount of money that she had saved.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, our two points are:

(0, $0) and (8, $60), then the slope will be:

a = ($60 - $0)/(8 - 0) = $60/8 = $7.5

our equation is:

y = $7.5*x + b

To find the value of b, just replace both values in one of the points in the equation, for example, the point (0, $0)

$0 = $7.5*0 + b

$0 = b

Then our equation is:

y = $7.5*x     for 0 ≥ x ≥ 8

Where i added a restriction in the domain because this is described only for the first 8 weeks after she started saving money.

Answer:

7606.62

Step-by-step explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)

Now just equate this to a time 0 payment at the same rate

\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.

Answer:

--------------------------------------

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer:

Total number of children = 70

Step-by-step explanation:

Given:

Number of kids buy popcorn = 42

Percent of kids buy popcorn = 60% = 0.6

Find:

Total number of children

Computation:

Total number of children = Number of kids buy popcorn / Percent of kids buy popcorn

Total number of children = 42 / 0.6

Total number of children = 70

The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

Step-by-step explanation:

x - 12 ≤ 3 - 2x

3x ≤ 15

x ≤ 5

To graph this, just draw a VERTICAL line passing through x = 5, then shade the area to the LEFT

\(\bold{\huge{\green{\underline{ Solution}}}}\)

\(\bold{\underline{ Given :- }}\)

\(\bold{\underline{ To \: Find :- }}\)

\(\bold{\underline{ Let's \: Begin :- }}\)

In the given right angled triangle, we have

Now, By using trigonometric ratios

\(\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}\)

\(\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}\)

\(\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}\)

According to the question :-

\(\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}\)

\(\bold{ 1/√2= }{\bold{\frac{2}{m}}}\)

\(\bold{\red{ m = 2√2 \: units }}\)

Therefore,

Let the unknown angle be x

\(\sf{ 45° + x + 90° = 180° }\)

\(\sf{ x = 180° - 135 ° }\)

\(\sf{ x = 45° }\)

Now,

\(\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}\)

\(\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}\)

\(\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}\)

\(\bold { n = 2√2/√2 }\)

\(\bold{\red{ n = 2\: units }}\)

Thus, The value of m = 2√2 and n = 2

\(\sf{\blue{ Hence, \: option \: D \: is \: Correct }}\)

Answer:

16

Step-by-step explanation:

71.91 ~ 72

56.423 ~ 56

72-56=16

Answer:

Since 7 and 11 are both rational, the sum and difference are rational.

Step-by-step explanation: It's A

Answer:

Since 7 and 11 are both rational, the sum and difference are rational.Step-by-step explanation: A

Answer:

  46

Step-by-step explanation:

You want to evaluate the expression t²u+s for t=-2, u=9, s=10.

Put the numbers in the places of the corresponding variables, and do the arithmetic.

  (-2)²·9 +10 = 4·9 +10 = 36 +10 = 46

The value of the expression is 46.

Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}\)