PLS HELP ILL GIVE U POINTS :)

Explain how you know the following system of equations has at most 2 solutions.
Solve the system algebraically. Show your work.
Solve the system by graphing.


y= 2x-1
y= x^2-9

6 feet 7 inches

1 feet = 12 inches

6 feet = 6(12) = 72 inches

6 feet 7 inches = 72 + 7 = 79 inches

Answer:

79 inches

Answer:

1133.98

almost 1134 grams :)

Step-by-step explanation:

multiply by 28.35 to get the answer :)

Answer:

1133.98

Step-by-step explanation:

Hope it helps and have a nice day!!!!! :)

BRAINIEST IS APPRECIATED!!!

Answer:

6

Step-by-step explanation:

4 marbles we have to take out (without looking) to be sure that we have at least two marbles of the same color.

There are 4 black, 4 red, and 4 white marbles in a box.

So, in order to have atleast two marbles of the same color we must take out atleast four marbles.

That is 1 black, 1 red, and 1 white of each color and the fourth one may be of any color. So we have atleast two marbles of the same color.

Therefore we have to rake out atleast 4 marbles in order to have at least  two marbles of the same color.

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The directional derivative of f at point (3,4) in the direction of the unit vector determined by the angle θ = 2π/5 is approximately -29.13

To find the directional derivative of f(x,y) = -2x^2 + 4y^2 at point (3,4) in the direction of the unit vector determined by the angle θ = 2π/5, we need to first find the unit vector u in the direction of θ.

The unit vector u can be found as:

u = (cos θ, sin θ) = (cos (2π/5), sin (2π/5))

Using the formula for directional derivative, the directional derivative of f at point (3,4) in the direction of u can be calculated as:

D_u f(3,4) = ∇f(3,4) · u

where ∇f(3,4) is the gradient of f at point (3,4), which can be found as:

∇f(x,y) = (-4x, 8y)

So, ∇f(3,4) = (-12, 32)

Substituting these values, we get:

D_u f(3,4) = (-12, 32) · (cos (2π/5), sin (2π/5))

Using a calculator, we can evaluate this dot product as:

D_u f(3,4) ≈ -29.13

Therefore, the directional derivative of f at point (3,4) in the direction of the unit vector determined by the angle θ = 2π/5 is approximately -29.13

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The probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/10.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is the sum of the probabilities of the two events occurring together for the outcomes where the pointer is on 1, 2, or 4 and the coin is heads up. From the table, we see that this occurs for the outcomes (H, 1), (H, 2), and (H, 4), which have a total probability of:

P(H and 1 or 2 or 4) = P(H and 1) + P(H and 2) + P(H and 4)

= 1/10 + 1/10 + 1/10

= 3/10

Therefore, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/10.

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Answer: I believe he could wear 768 outfits

Step-by-step explanation: I had a similar question consisting of the same numbers.

The temperature at a given chirp rate can be determined from a linear regression model as follows;

a. The linear regression model is; T = 4.1484·C - 166.1

b. At 72 °F the chirp rate is approximately 57 chirps per minute

At 90 °F the chirp rate is approximately 62 chirps per minute

A linear regression model, models a relationship between variables using a linear approach

a. The data given the values of the temperatures at a  given chirp rate per minute is used to create the attached scatter plot.

From the scatter plot, a trend line is drawn using the Add Chart Element, within the Chart Tools, Design Menu.

From the Format Trendline window, The Display Equation on chart check box is selected, to show the trend line equation.

The trendline equation that is the linear regression model for chirp rate as a function of time is; y = 4.1484·x - 166.1

Where, y = T, and x = C, we have; T = 4.1484·C - 166.1

b. If the temperature, T, is 72 °F, we have;

T = 72 °F

72 = 4.1484·C - 166.1

\(C = \dfrac{72+166.1}{4.1484} \approx 57\)

If the temperature is 90 °F, the chirp rate is calculated as follows;

T = 90 = 4.1484·C - 166.1

\(C = \dfrac{90+166.1}{4.1484} \approx 62\)

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The missing side lengths are x = y =  2sqrt(2) units.

In a 45-90-45 degree triangle, the two legs are congruent. Therefore, if one leg has length x, the other leg must also have length x.

Using the Pythagorean Theorem, we can write:

x^2 + y^2 = (hypotenuse)^2

Substituting the given values, we get:

x^2 + y^2 = 4^2

x^2 + y^2 = 16

We know that the two legs of the triangle are congruent, so we can write:

x = y

Substituting this into the equation above, we get:

x^2 + x^2 = 16

2x^2 = 16

x^2 = 8

x = sqrt(8) = 2sqrt(2)

So the missing side length (base) is 2sqrt(2) units.

To find the perpendicular length (y), we can use the fact that x = y. Therefore:

y = x = 2sqrt(2) units

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The given question is incomplete, the complete question is:

Find the missing side lengths. Leave your answers as radicals in simplest form

6 weeks from now, you will have $215 in your bank account

The given parameters are:

b = 60 + (20+6)w

When the account balance is $215, we have

60 + (20+6)w = 215

Subtract 60 from both sides

(20+6)w = 155

This gives

26w = 155

Divide both sides by 26

w = 5.96

Approximate

w = 6

Hence, 6 weeks from now, you will have $215 in your bank account

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There are 15,504 ways to randomly select a team of 5 people from a group of 20 people

If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:

C(20, n) = 20! / (n! * (20 - n)!)

where C(20, n) represents the number of ways to select n people from a group of 20 people.

For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:

C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504

Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.

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The given property “If AB=CD then CD=AB” is known as the symmetric property. Symmetric property is a type of equivalence relation in mathematics that states that if the relation between two elements is in the form of "if A is related to B, then B is related to A," then this type of relation is symmetric.

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Based on the cost of filling of the car, we can infer that Mr. Johnson does not have enough to spend on gas.

The car can take 25 gallons of gas and already has 4 liters inside it. The quantity of gas Mr. Johnson has to buy is:

= 25 - 4

= 21 gallons

The price of a gallon is $3.04. The price of 21 gallons would be:

= Price of gas x Number of gallons

= 3.04 x 21

= $63.84

In conclusion, Mr. Johnson does not have enough to spend on gas because he has only $50 yet the gas will cost $63.84.

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Answer:

23/72 is the answer in simplest form

Step-by-step explanation:

The Engel curve for good q2 represents the relationship between income (Y) and the quantity demanded of good q2. To find Sally's Engel curve for q2, we need to express her income (Y) in terms of the prices of q1 (p1) and q2 (p2), and the quantities of q1 (q1) and q2 (q2).

Given Sally's utility function U = 6(q1)^0.5 + q2, we can assume that she maximizes her utility subject to her budget constraint.
Her budget constraint can be expressed as: p1*q1 + p2*q2 = Y

Since we are interested in finding Sally's Engel curve for q2, we need to solve the budget constraint for Y.
p1*q1 + p2*q2 = Y

Rearranging the equation to solve for Y:
Y = p1*q1 + p2*q2

Now we can substitute the utility function U into the budget constraint equation:
6(q1)^0.5 + q2 = p1*q1 + p2*q2

To isolate q2, we can move the terms involving q2 to one side of the equation:
q2 - p2*q2 = p1*q1 - 6(q1)^0.5

Factoring out q2:
q2(1 - p2) = p1*q1 - 6(q1)^0.5

Now, divide both sides of the equation by (1 - p2):
q2 = (p1*q1 - 6(q1)^0.5) / (1 - p2)

This equation represents Sally's Engel curve for good q2. It shows how the quantity demanded of q2 (q2) changes with changes in income (Y), the price of q1 (p1), and the price of q2 (p2).

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Answer: $1640

Step-by-step explanation:

Since the salesperson's commission rate is 4%, therefore the commission from the sale of $41,000 worth of furnaces will be calculated as follows:

= 4% × $41000

= 4/100 × $41000

= 0.04 × $41000

= $1640

Therefore, the commission is $1640.

Answer:

6 1/8

Step-by-step explanation:

to find how long she spent on the boat you have to subtract 7 by the time that she spent hiking and swimming

7-3/8=6 5/8

6 5/8 - 1/2 = 6 1/8

she spent 6 1/8 on the boat which is a long time lol

After answering the provided question, we can conclude that This is the equation in slope-intercept form.

The slope-intercept form of a linear equation in mathematics is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point at which the line meets the y-axis. The slope-intercept form is a handy approach to represent a line's equation because it allows you to quickly see the line and determine its slope and y-intercept. The slope indicates how steep the line is, while the y-intercept indicates where the line intersects the y-axis.

Based on the information provided, we can conclude that the pontoon boat rental fee is $25 per hour.

A one-time cleaning fee is charged, which is not mentioned in the problem. As a result, we cannot draw any conclusions about this fee.

Friends of the Williams family rented the same boat for 6 1/2 hours, which is equivalent to 6.5 hours.

Their friends paid the rental and cleaning fee of $237.50.

We can use the point-slope formula to find the equation in slope-intercept form: y - y1 = m(x - x1), where m is the slope, (x1, y1) is a point on the line, and y is the total cost of renting the boat.

x1 = 6.5

y1 = 237.50

y - 237.50 = 25(x - 6.5)

y = 25x - 112.50

This is the equation in slope-intercept form.

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Answer:

crcrc4cc4crfc

Step-by-step explanation:

Answer:

You can use scale factor

Step-by-step explanation:

Null hypothesis: The valve performs to the specifications, i.e., the mean pressure produced by the valve is 5.7 lbs/square inch.

Alternative hypothesis: The valve does not perform to the specifications, i.e., the mean pressure produced by the valve is not equal to 5.7 lbs/square inch.

To test these hypotheses, we can use a one-sample t-test. Given that the sample size is large (220 engines) and the standard deviation is known (0.6), we can calculate the test statistic using the formula:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

Substituting the given values:

t = (5.8 - 5.7) / (0.6 / sqrt(220))

Calculating this expression yields:

t = 1.73205

Now, we need to compare this t-value with the critical t-value at a significance level of 0.02 and the degrees of freedom (sample size - 1). If the calculated t-value exceeds the critical t-value, we reject the null hypothesis.

However, without the critical t-value, we cannot make a final determination. Please provide the critical t-value or the degrees of freedom to complete the hypothesis test and draw a conclusion regarding the valve's performance.

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Answer:

Step-by-step explanation:

Given that 1cm=500000cm

Then using unitary law, we get

Actual distance=2.5cm=2.5×500000=12,50,000cm

The equation of the hyperbola that satisfies the given conditions is x^2 / 4 - y^2 / 16 = 1. This equation represents a hyperbola with its center at the origin (0, 0), foci at (0, ±8), and vertices at (0, ±2).

To find the equation of a hyperbola given its foci and vertices, we can start by determining the key properties of the hyperbola. The foci and vertices provide important information about the shape and orientation of the hyperbola.

Given:

Foci: (0, ±8)

Vertices: (0, ±2)

Center:

The center of the hyperbola is located at the midpoint between the foci. In this case, the y-coordinate of the center is the average of the y-coordinates of the foci, which is (8 + (-8))/2 = 0. The x-coordinate of the center is 0 since it lies on the y-axis. Therefore, the center of the hyperbola is (0, 0).

Transverse axis:

The transverse axis is the segment connecting the vertices. In this case, the vertices lie on the y-axis, so the transverse axis is vertical.

Distance between the center and the foci:

The distance between the center and each focus is given by the value c, which represents the distance between the center and either focus. In this case, c = 8.

Distance between the center and the vertices:

The distance between the center and each vertex is given by the value a, which represents half the length of the transverse axis. In this case, a = 2.

Equation form:

The equation of a hyperbola with the center at (h, k) is given by the formula:

((x - h)^2 / a^2) - ((y - k)^2 / b^2) = 1

Using the information we have gathered, we can now write the equation of the hyperbola:

((x - 0)^2 / 2^2) - ((y - 0)^2 / b^2) = 1

Simplifying the equation, we have:

x^2 / 4 - y^2 / b^2 = 1

To find the value of b, we can use the distance between the center and the vertices. In this case, the distance is 2a, which is 2 * 2 = 4. Since b represents the distance between the center and either vertex, we have b = 4.

Substituting the value of b into the equation, we get:

x^2 / 4 - y^2 / 16 = 1

Therefore, the equation of the hyperbola that satisfies the given conditions is:

x^2 / 4 - y^2 / 16 = 1

This equation represents a hyperbola with its center at the origin (0, 0), foci at (0, ±8), and vertices at (0, ±2).

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Given:

A figure of a parallelogram.

The vertex angles are \((12b+8)^\circ,(5b+2)^\circ,2a^\circ\).

To find:

The values of a and b.

Solution:

We know that the pairs of consecutive angles of a parallelogram are supplementary angles. It mean their sum is 180 degrees.

\((12b+8)^\circ+(5b+2)^\circ=180^\circ\)       (Supplementary angles)

\((17b+10)^\circ=180^\circ\)

\(17b+10=180\)

Subtract 10 from both sides.

\(17b=180-10\)

\(17b=170\)

Divide both sides by 17.

\(b=\dfrac{170}{17}\)

\(b=10\)

Now,

\((5b+2)^\circ=(5(10)+2)^\circ\)

\((5b+2)^\circ=(50+2)^\circ\)

\((5b+2)^\circ=52^\circ\)

And,

\((5b+2)^\circ+2a^\circ=180^\circ\)       (Supplementary angles)

\(52^\circ+2a^\circ=180^\circ\)

\(2a^\circ=180^\circ-52^\circ\)

\(2a^\circ=128^\circ\)

Divide both sides by 2.

\(a^\circ=\dfrac{128^\circ}{2}\)

\(a^\circ=64^\circ\)

\(a=64\)

Therefore, the value of a is 64 and the value of b is 10.

Answer:

12

Step-by-step explanation:

Answer:

Growth

Rate of growth is 77%

Initial amount is 22

Step-by-step explanation:

Generally, the exponential equation can be written as;

F(x) = I(1 + r)^n

where I is the initial value, r is the rate is percentage

From the question, we can see that the initial value is 22

Kindly recall that we can write 1.77 as 1+ 0.77

Now 0.77 is same as 77/100 which simply imply77%

Thus, we have 77% as the rate

Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

The optimizing function of the printed area is  while dimensions that maximize the printed area is 80 by 12 cm

Assume the dimensions of the poster be w and h, where:

w represents the width.

h represents the height.

So, the area of the poster is:

a= hw

The area is given as 960.

So, we have:

hw = 960

w = 960/h

When the height is reduced by 10 cm and the width by 6 cm.

The printed area (P) becomes

p =(w-12)(h-20)

p =(960/h-12)(h-20)

p = (960-12h/h)(h-20)

p =960h - 19200-12h²+240h

p = -12h²+1200h-19200

p = 80,20

w = 960/h

w = 960/80 = 12

Consequently, 80 by 12 cm are the dimensions that maximize the printed area.

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We start by rearranging the given differential equation into the standard form of a separable differential equation:

\(\frac{dh}{dt} = (\frac{-R}{v}) (\frac{h}{R+h})\)

=> \((\frac{v}{R+h)} \frac{dh}{h} = \frac{-R}{v} dt\)

Integrating both sides with respect to their respective variables, we get:

\(ln|h+R| - ln|R| = (\frac{-R}{v}) t + C\)

where C is the constant of integration. Simplifying, we have:

\(ln|h+R| = (\frac{-R}{v})t + ln|CR|\)

where CR is a positive constant obtained by combining R and the constant of integration.

Taking the exponential of both sides, we get:

\(|h+R| = e^{(\frac{-R}{v}) t} + ln|CR|)\)

=> \(|h+R| = e^{(\frac{-R}{v}) t} CR\)

We take cases for h+R being positive and negative:

Case 1: h+R > 0

Then we have:  \(|h+R| = e^{(\frac{-R}{v}) t} CR\)

\(h = (e^{(\frac{-R}{v}) t} CR) - R\)

Case 2: h+R < 0

Then we have:

\(|h+R| = e^{(\frac{-R}{v}) t} CR\)

=>\(h =- ((e^{(\frac{-R}{v}) t} CR)+R\)

Therefore, the general solution to the given differential equation is:

\(h(t)=e^{(\frac{-R}{v}) t} CR)-R\) if h+R > 0,

\(- (e^{\frac{-R}{v} }t ) CR)+R\)if h+R < 0}

where CR is a positive constant determined by the initial conditions.

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