How many times does the graph of the function below intersect touch the x-axis? y= -3x^2 + x + 4

Answer/Step-by-step explanation:

3. By substitution method, let's substitute [tex] \frac{2}{3}x- 4 [/tex] for y in the first equation.

Thus,

[tex] \frac{1}{3}x + 2(\frac{2}{3}x- 4) = 1 [/tex]

Solve for x

[tex] \frac{x}{3} + \frac{4x}{3} - 4 = 1 [/tex]

Add 4 to both sides

[tex] \frac{x}{3} + \frac{4x}{3} - 4 + 4 = 1 + 4 [/tex]

[tex] \frac{x}{3} + \frac{4x}{3} = 5 [/tex]

[tex] \frac{x + 4x}{3} = 5 [/tex]

[tex] \frac{5x}{3} = 5 [/tex]

Multiply both sides by 3

[tex] \frac{5x}{3}*3 = 5*3 [/tex]

[tex] 5x = 15 [/tex]

Divide both sides by 5

[tex] x = 3 [/tex]

Now, substitute 3 for x in the equation.

[tex] y = \frac{2}{3}x- 4 [/tex]

[tex] y = \frac{2}{3}(3) - 4 [/tex]

[tex] y = 2 - 4 [/tex]

[tex] y = -2 [/tex]

The solution of the equation is x = 3, y = -2

4. Solving by elimination, let's try to eliminate the x-variable by adding both equation together.

[tex] 3x - 2y = 11 [/tex]

[tex]-3x - y = 4[/tex]

            [tex] -3y = 15 [/tex]  => [tex] (-3x +(-3x) = 0; -2y +(-y) = -3y; 11 + 4 = 15) [/tex]

Divide both sides by -3 to solve for y

[tex] \frac{-3y}{-3} = \frac{15}{-3} [/tex]

[tex] y = -5 [/tex]

Substitute -5 for y in the first equation to find x

[tex] 3x - 2(-5) = 11 [/tex]

[tex] 3x + 10 = 11 [/tex]

Subtract 10 from both sides

[tex] 3x + 10 - 10 = 11 - 10 [/tex]

[tex] 3x = 1[/tex]

Divide both sides by 3

[tex] \frac{3x}{3} = \frac{1}{3} [/tex]

[tex] x = \frac{1}{3} [/tex]

The solution is [tex] x = \frac{1}{3}, y = -5 [/tex]

Answer:  see below

Step-by-step explanation:

Multiply the coefficient by the exponent and reduce the coefficient by 1.

1) f'(x) = 10

2) f'(x) = 12x³ + 4x - 5

3) f'(x) = 6x² + 7

4) f'(x) = 20x + 20

5) f'(x) = 20x + 23

Answer:

C.

Step-by-step explanation:

The dotted line means it is not "equal to" and since its shaded BELOW the line, its less than.

[tex]y < \frac{-1}{5} x+1[/tex] inequality is represented by given graph.

" Inequality is defined as the relation between two variables using sign of inequality such as >, <, ≤, ≥ ."

According to the question,

From the given graph,

(0,1) and (5,0) are excluded points in the graph of the inequality .

value of y < 1 for x = 0, value of x < 5 for y =0 represents open interval.

Option (A) and (B) represent Close interval , therefore both are not correct option.

Option(D) y >1 for x=0 , x>5 for y=0 , it is not correct option.

Option (C) [tex]y < \frac{-1}{5} x+1[/tex]

y <1 for x = 0 and x<5 for y = 0 represent the graph inequality.

Hence, Option(C) is the correct answer.

Learn more about inequality here

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Answer:

The coordinates of point P are (-7/2, 5/4)

Step-by-step explanation:

Here, we want to give the coordinates of the point P that divide CD in the given ratio

To do this , we shall be making use of a mathematical formula;

Let’s say the ratio 1:3 represents a:b, our formula those becomes

{(bx1 + ax2)/(a + b) ,( by1+ay2)/a+b}

From the question, we can identify that

(x1,y1) = (-6,-1)

(x2,y2) = (4,8)

a = 1 and b = 3

Plugging these values into the formula we have

3(-6) + 1(4)/(1+3) , 3(-1) + 1(8)/(1+3)

= (-18 + 4)/4 , (-3+ 8)/4

=-14/4, 5/4

= (-7/2, 5/4)

Answer:

x = -3, y = -7

Step-by-step explanation:

You can set the equations equal to each other, so the set becomes:

2x - 1 = 3x + 2

-x = 3

x = -3

y = 2(-3) -1 = -7

Answer:

x = -3

y = -7

Step-by-step explanation:

y = 2x - 1

y = 3x + 2

Set the equations equal to each other

2x-1 = 3x+2

Subtract 2x from each side

2x-1-2x = 3x+2-2x

-1 =x+2

Subtract 2 from each side

-1-2 = x+2-2

-3 =x

Now find y

y = 2x-1

y = 2(-3) -1

y = -6-1

y = -7

Answer:

I believe it is  -1+1=0

Step-by-step explanation:

Answer:

D. A reduction with a scale factor of [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We know for sure it is a reduction because the image, W'X'Y'Z', is smaller than the pre-image WXYZ. Because it is a reduction, the scale factor must be less than 1, so the only option can be D. Both B and C say enlargement and A says it is a scale factor of 2.

Hope this helps and I am sorry no one has answered your question until now.

I will be happy to answer any of your other questions if you want.

Have a good day! :)

Answer:

Range y≥-3

Step-by-step explanation:

Answer:

D. Range: y ≥ -3.

Step-by-step explanation:

(x - 4)^2 - 3

= x^2 - 4x - 4x + 16 - 3

= x^2 - 8x - 13

Since this is a parabola, there are no limits to the x-values, but there is a limit on the y-values: the y-values cannot exceed the highest or lowest point of the parabola, the vertex.

To find the vertex...

-b / 2a

8 / 2 = 4

(4 - 4)^2 - 3

= 0 - 3

= -3

So, your answer is D. Range: y ≥ -3.

Hope this helps!

Answer:

  your mark is correct

Step-by-step explanation:

The marked answer choice is correct.

(2, -18) is not a global minimum, because there are function values that are lower.

(0, -6) is not a global maximum, because there are function values that are higher.

A global maximum is also a local maximum.*

_____

* More correctly, a global maximum is either a local maximum or the end point of an interval. No intervals are involved in this question.

Answer:

Assuming this is a linear problem, the equation would look like this:

C(m)=Mx

Step-by-step explanation:

Because you don't have any other details, this as much of an answer I can give you. The cost for the company depends on how many mugs they produce. If the cost for making a mug is 3 dollars, then m would be that value, and x would be the amount of mugs you're trying to make.

The relationship between the number of mugs and the cost for company A will be c = nm.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Write an equation to represent the relationship between the number of mugs and the cost for company A.

The cost for company A is directly proportional to the number of mugs.

c ∝ m

c = nm

Where 'n' is the cost of each mug.

The relationship between the number of mugs and the cost for company A will be c = nm.

More about the linear equation link is given below.

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Answer:

the probability that they find enough subjects for their​ study is 0.9515

Step-by-step explanation:

From the given information:

Let X be the random variable that follows a normal distribution.

Therefore:

X [tex]\sim[/tex]Binomial(n=733,p=0.04)

[tex]\mu = np[/tex]

[tex]\mu = 733*0.04[/tex]

[tex]\mu = 29.32[/tex]

[tex]\sigma = \sqrt{np(1-p)}[/tex]

[tex]\sigma = \sqrt{29.32(1-0.04)}[/tex]

[tex]\sigma = \sqrt{29.32(0.96)}[/tex]

[tex]\sigma = \sqrt{28.1472}[/tex]

[tex]\sigma = 5.305[/tex]

The probability of P(X ≥ 21) lies in the region between 20.5 and 21.5 by considering a discrete contribution of a continuous normal distribution. Eventually, X > 20.5

∴

P(X >20.5)= P(Z > z)

Using  standard normal z formula:

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{20.5-29.32}{5.305}[/tex]

[tex]z = \dfrac{-8.82}{5.305}[/tex]

[tex]z = -1.662582[/tex]

z = -1.66

P(X >20.5)= P(Z > -1.66)

From the standard z tables ;

P(X >20.5)= 1 - 0.0485

P(X >20.5)= 0.9515

Answer:

95.45%

Step-by-step explanation:

To go about this, what we do is to calculate the z-scores of the values in the range given.

Mathematically;

z-scores = (x-mean)/SD

Here in this case , mean is 3 and standard deviation is 0.25

So for 2.5 minutes, we have ;

z-score = (2.5-3)/0.25 = -0.5/0.25 = -2

For 3.5 minutes, we have;

z-score = (3.5-3)/0.25 = 0.5/0.25 = 2

The required probability we want to calculate according to the range is thus;

P(-2<z<2)

We can calculate this value by the use of the standard normal table

Mathematically, we can have the above as;

P(-2<z<2) = P(z<2) - P(z<-2)

We proceed using the table and we have the values as follows;

P(-2<z<2) = 0.97725 - 0.02275 = 0.9545

Now the value 0.9545 in percentage would be 95.45%

Answer:

THe standard form of equation for a line is -2x+y=6

Step-by-step explanation:

THe standard equation has a form of Ax+ By=C, where A, B and C are constants.

12x-y=-6 is not a standard form of a line equation, because the value near you is negative, but should be positive. It would be this form if we would change it a little bit to the form:

-12x=y=6

x=−0.23240812,−1.43425854

Answer:

Step-by-step explanation:

let the plane intersects the join of points in the ratio k:1

let (x,y,z) be the point of intersection.

[tex]x=\frac{3k+2}{k+1} \\y=\frac{5k+4}{k+1} \\z=\frac{-4k+16}{k+1} \\\because ~(x,y,z)~lies~on~the~plane.\\2(\frac{3k+2}{k+1} )-3(\frac{5k+4}{k+1} )+\frac{-4k+16}{k+1} +6=0\\multiply~by~k+1\\2(3k+2)-3(5k+4)+(-4k+16)+6(k+1)=0\\6k+4-15k-12-4k+16+6k+6=0\\-7k+14=0\\k=2\\x=\frac{3*2+2}{2+1} =\frac{8}{3} \\y=\frac{5*2+4}{2+1}= \frac{14}{3} \\z=\frac{-4*2+16}{2+1} =\frac{8}{3}[/tex]

point of intersection is (8/3,14/3,8/3)

and ratio of division is 2:1

Answer:

12

Step-by-step explanation:

3(4 - 2)^2

Parentheses first

3 ( 2) ^2

Then exponents

3 *4

Then multiply

12

Answer:

All three are rational numbers.

Step-by-step explanation:

I used Desmos (a graphing calculator online) and the roots were all able to be written with fractions.

Answer:

Cantidad que Lupe dejó en casa con inicialmente = 127.5 soles.

Amount that Lupe left home with initially = 127.5 soles.

Step-by-step explanation:

Pregunta correcta

Lupe va al mercado y compra abarrotes con los 2/5 de su dinero ; luego va a la seccion de carnes y compra con los 1/3 de lo que le queda ; si gasta 3 soles en pasaje de ida y vuelta ; ¿con cuanto dinero salio de su casa si llega de regreso a su casa con 48 soles?

Solución

Deje que la cantidad de dinero que Lupe dejó en casa sea x soles.

Lupe compra comestibles con 2/5 de su dinero. Es decir, Lupe gasta (2/5) × x = (2x/5)

En este punto, Lupe se queda con

x - (2x/5) = (3x/5) soles.

Lupe luego gasta 1/3 de lo que queda en la carne

(1/3) de lo que queda = (1/3) × (3x/5) = (x/5)

Lo que significa que Lupe gasta (x/5) soles en la sección de carne.

Cantidad restante después de la sección de carne = (3x/5) - (x/5) = (2x/5)

Lupe gasta 3 soles en el viaje de ida y vuelta al mercado y se queda con 47 soles después de todo.

(2x/5) - 3 = 48

(2x/5) = 48 + 3 = 51

2x = 5 × 51 = 255

2x = 255

x = (255/2) = 127.5 soles

¡¡¡Espero que esto ayude!!!

English Translation

Lupe goes to the market and buys groceries with 2/5 of her money; then he goes to the meat section and buys with 1/3 of what he has left; if you spend 3 soles on a round trip ticket; How much money did you leave your home with if you arrive home with 48 soles?

Solution

Let the amount of money Lupe left home with be x soles.

Lupe buys groceries with 2/5 of her money

That is, Lupe spends (2/5) × x = (2x/5)

At this point, Lupe is left with

x - (2x/5) = (3x/5) soles.

Lupe then spends 1/3 of what is left on meat

(1/3) of what is left = (1/3) × (3x/5) = (x/5)

Meaning that Lupe spends (x/5) soles at the meat section.

Amount left after the meat section = (3x/5) - (x/5) = (2x/5)

Lupe spends 3 soles on round ticket trip to market and is left with 47 soles after everything.

(2x/5) - 3 = 48

(2x/5) = 48 + 3 = 51

2x = 5 × 51 = 255

2x = 255

x = (255/2) = 127.5 soles

Hope this Helps!!!

Answer:

The expression of the ellipse is: [tex]\frac{x^2}{4} + y^2 = 1[/tex]

Step-by-step explanation:

The equation of a ellipse can be written by the following expression:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

Where 2a is the length of the major axis and 2b is the length of the minor axi. Since we were given the length of the minor vertex, then:

[tex]2b = 2\\b = 1[/tex]

The length of the major axis is the distance between the two vertices.

[tex]2a = \sqrt{[2 - (-2)]^2}\\2a = \sqrt{(2 + 2)^2}\\2a = \sqrt{4^2}\\2a = 4\\a = 2[/tex]

Therefore the expression of the ellipse is:

[tex]\frac{x^2}{2^2} + \frac{y^2}{1^2} = 1\\\\\frac{x^2}{4} + y^2 = 1[/tex]

Answer:

Multiply the first equation by -4

Step-by-step explanation:

Equation A: 3c = d − 8

Equation B: c = 4d + 8

We want to eliminate variable d

Multiply the first equation by -4

-4( 3c = d − 8)

-12c = -4d +32

Add this to the second equation

-12c = -4d +32

c = 4d + 8

================

-11c = 0d + 40

Answer:

A : Multiply equation A by −4

Step-by-step explanation:

3c = d - 8

Multiply the equation by -4.

-12c = -4d + 32

-12c = -4d + 32

c = 4d + 8

Add equations.

-11c = 0d + 40

-11c = 40

The d variable is eliminated.

Answer:

The diagrammatic representation of speed of each person's trip can be given by a column graph per second where the height of the column represents the total distance covered and the position of the column represents the time

The difference in speed is seen in the difference in the height of the column per unit time with the higher column representing the higher speed

The above graph can be combined with the distance time graph where the slope of the line graph is the speed with which the person is riding the bike.

The difference in speed is seen in the difference in slope with the steeper slope representing the higher speed

Step-by-step explanation:

Answer:

Side LM is congruent to side RQ

Angle MNO is congruent to angle RST

Side ON is congruent to side ST

Angle LMN is congruent to angle QRS

Step-by-step explanation:

A way to solve this is to use parchment paper or draw the same shape next to each other, as you will get these:

Side LM is congruent to side RQ

Angle MNO is congruent to angle RST

Side ON is congruent to side ST

Angle LMN is congruent to angle QRS

The correct answer is A. T = 0.25k + 0.97t

Explanation:

For an equation to be correct it needs to include all important values and use the appropriate mathematical symbols to show how the values relate. In the case presented, it is known the total bill (T) is the result of both the electricity (k) and gas (t) consumed. According to this, the two values need to be added to find the total (T). This means T = k + t.

Besides this, it is specified a kilowatt or unit of electricity costs $0.25, this means the correct expression for finding the total paid for electricity is 0.25k as the number of kilowatts consumed need to be multiplied by the cost of a kilowatt. Similarly, the cost of the gas requires multiplying the number of therms by the cost of one therm, which is $097. According to this, the correct equation is T = 0.25k + 0.97t

Answer:

6 possible integers

Step-by-step explanation:

Given

A decreasing geometric sequence

[tex]Ratio = \frac{m}{7}[/tex]

Required

Determine the possible integer values of m

Assume the first term of the sequence to be positive integer x;

The next sequence will be [tex]x * \frac{m}{7}[/tex]

The next will be; [tex]x * (\frac{m}{7})^2[/tex]

The nth term will be [tex]x * (\frac{m}{7})^{n-1}[/tex]

For each of the successive terms to be less than the previous term;

then [tex]\frac{m}{7}[/tex] must be a proper fraction;

This implies that:

[tex]0 < m < 7[/tex]

Where 7 is the denominator

The sets of [tex]0 < m < 7[/tex] is [tex]\{1,2,3,4,5,6\}[/tex] and their are 6 items in this set

Hence, there are 6 possible integer

Answer:

$320

Step-by-step explanation:

Let the total sum of money be $x.

Therefore,

12 1/2% of x = 40

25/2% * x = 40

0.125 * x= 40

x = 40/0.125

x = $320

Thus, total sum of money is $320.

Answer:

579 pastries

Step-by-step explanation:

You can write an equation to solve this problem.

(3 * 147) + 138

(441) + 138 = 579

They sold 579 pastries in total.

Answer:

Option C is the correct option

Step-by-step explanation:

Let the points be A and B

A ( 4 , 5 ) ------> ( x1 , y1 )

B ( 10 , 13 ) ------> ( x2 , y2 )

Now, let's find the distance between these points:

[tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

plug the values

[tex] = \: \sqrt{(10 - 4) ^{2} + {(13 - 5)}^{2} } [/tex]

Calculate the difference

[tex] = \sqrt{ {(6)}^{2} + {(8)}^{2} } [/tex]

Evaluate the power

[tex] = \sqrt{36 + 64} [/tex]

Add the numbers

[tex] = \sqrt{100} [/tex]

Write the number in exponential form with. base of 10

[tex] = \sqrt{ {(10)}^{2} } [/tex]

Reduce the index of the radical and exponent with 2

[tex] = 10 \: units[/tex]

Hope this helps..

Best regards!!

Answer:

The slope is 1/3 and the y intercept is 6

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

3y -x =18

Add x to each side

3y = x+18

Divide each side by 3

3y/3 = x/3 +18/3

y = 1/3x +6

The slope is 1/3 and the y intercept is 6

We need to solve for y (y = mx + b):

3y - x = 18

~Add x to both sides

3y = 18 + x

~Divide 3 to everything

y = 6 + x/3 or y = 6 + 1/3/x

So... 1/3 is the slope and 6 is the y-intercept.

Best of Luck!