a piece of rope 11/12 yd long is cut into two pieces.  One piece is 4/7 yd long.  How long is the other piece?​

Answer:

A root of f(x) is x=5

Step-by-step explanation:

If (x-5) is a factor of f(x), then 5 is a root.

If (x+5) is a factor of f(x), then -5 is a root.

So we are only given that (x-5) is a factor of f(x), so we only know that x=5 is a root.

This is by factor theorem. It says if (x-c) is a factor then f(c)=0 which means c is a root of f(x) because it makes the expressions equal to 0.

Answer:

0

Step-by-step explanation:

Quadratic equation

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

The discriminant is the part of the quadratic formula within the square root symbol: [tex]{b^{2}-4*a*c}[/tex].  The discriminant indicates if there are two solutions, one solution, or none.

The discriminant can be positive, zero or negative which determines how roots exist for the given quadratic equation.

So, a positive discriminant tell us that the quadratic has two different real solutions.

A discriminant of zero tell us that the quadratic has two real and equal solutions.

And a negative discriminant tell us that none of the solutions are real numbers.

In this case: 25x^2-10x+1=0

We can see that

a= 25    b=-10   c=1

Using:  [tex]{b^{2}-4*a*c}[/tex]

We have  [tex]-10^{2}-4* 25*1 =100-100=0[/tex]

the answer is zero, so the quadratic has two real and equal solutions

Answer:

What is the value of the discriminant of f?

0

How many x-intercepts does the graph of f?

1

Step-by-step explanation:

I promise you i just got this question and this is the answer

The simplified form of the fraction 11/5 is determined as 2 1/5.

Simplification refers to the process of reducing an expression, equation, or fraction into its simplest or most concise form.

Fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). This reduces the fraction to its simplest form.

The given fraction expression;

11/5

This expression is simplified as follows;

11/5 = 2 remainder 1

The final expression becomes;

11/5 = 2 1/5

Thus, the simplified form of the expression 11/5 is determined as 2 1/5.

Learn more about simplification here: https://brainly.com/question/28008382

#SPJ6

[tex]4x^2-12x+29=20 \\4x^2-12x+9=0\\(2x-3)^2=0\\2x-3=0\\2x=3\\x=\dfrac{3}{2}[/tex]

With these kind of equations you want to use the quadratic formula. These problems take time, so don't fret you'll get there! :)

Quadratic formula:

-b +- √b^2-4(a)(c)  

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

2(a)

Next find your a, b, and c!

a= 4

b=12

c=29

Time to plug those answers in.

12 +- √(-12)^2-4(4)(9)

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

2(4)

Next solve everything in the radical first! Then the bottom.

12 +- √144-144

----------------------- ~ x=12/8 ~ x=3/2

8

You get: x=3/2!

Answer:

C). This is an example of causation

Step-by-step explanation:

Causation : It can be defined as the one event is the result of the other event. It is simply the cause and its effect. There is a causal relation between the two events.

Correlation : It can described the direction of the relation between two or more events or variables.

The conclusion of the experiment is that the plant that received more than two hours of sunlight in each day grew more than the plants that received less than two hours of sunlight in each day.

This is the cause of one event and its effect on the other event.

So option C is correct because sunlight causes plants to grow.

So option C). This is an example of causation.

Answer:

C( This is an example of causation

Answer:

Attached

Step-by-step explanation:

The equation for the graph is

c(x)=3x+2

rewrite as

y=3x+2.............................................(1)

Then graph equation to visualize as attached.

Let the x-axis to represent minutes and the y-axis to represent cost

Answer:

The graph of required function is shown below.

Step-by-step explanation:

The given function is

[tex]c(x)=3x+2.00[/tex]

In this function c(x) is the cost for a taxi ride and x is the number of minutes.

It means, in the graph of cost function x-axis represents the time in minutes and y-axis represents the cost.

Time can not be negative. So, the function is defined for all non-negative values of x.

Table of values:

x            c(x)

0            2.00

1             5.00

2            8.00

3            11.00

Plot any two points from these points on a coordinate plane and connect them by  straight line.

Therefore, the graph of required function is shown below.

Answer:

22 cm, 24 cm, and 24 cm.

Step-by-step explanation:

Isosceles Triangle is a type of triangle in which two of the three sides are equal in length. The perimeter is 70 cm. Therefore, in this question, since the sides are unknown, we can assume that:

Length of the shorter side = x cm.

Length of the other sides = y cm.

The relationship between x and y is given by:

x = (2y - 26) cm (because it is mentioned that the shortest side is 26 cm less than twice as long as the other sides).

Perimeter of a triangle = sum of all sides.

Since its an isosceles triangle, therefore:

Perimeter of the triangle = x + 2y.

Substituting the values in the perimeter formula gives:

Perimeter of the triangle = 2y - 26 + 2y.

70 = 4y - 26.

4y = 96.

y = 24 cm.

Substituting y = 24 in the equation x = 2y - 26 gives x = 2(24) - 26 = 22 cm.

So in the ascending order, the lengths are 22 cm, 24 cm, and 24 cm!!!

Answer:

The patient must take [tex]2\frac{1}{2}\ tablets[/tex] per day

Step-by-step explanation:

we know that

12 1/2 grains (gr) of aspirin is equal to 12.5 grains

using proportion

Let

x -----> the number of aspirin tablets

[tex]\frac{1}{5} \frac{tablet}{gr} =\frac{x}{12.5} \frac{tablets}{gr} \\ \\x= 12.5/5\\ \\x=2.5\ tablets[/tex]

Convert to mixed number

[tex]2.5=2\frac{1}{2}\ tablets[/tex]

Answer:

Option A. 93.5°

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

∠C=(1/2)[83°+2(52°)]

∠C=(1/2)[83°+104°]

∠C=(1/2)[187°]

∠C=93.5°

Answer:

The turns of a graph is represented by the number of maximum or minimum that the function has.

If we differenciate f(x) we get:

f'(x)=4x^3+6x

f'(x)=2x(2x^2 + 3)

Therefore f'(x) =0, when x=0. Given that negative roots are not defined.

Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.

Attached you find the graph of the function which confirms the number of turns.

If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!

Answer: 10

Step-by-step explanation:

if we know a-b=5, to get the answer of 2(a-b) multiply 5 by 2.

Answer:

10

Step-by-step explanation:

a-b=5

Multiply each side by 2

2(a-b) = 2*5

2 (a-b) = 10

Answer:

Part 1) The solution of the absolute value is  (-∞,-6)∪ (2,∞)

Number line with open circles on negative 6 and 2, shading going in the opposite directions

Part 2) The graph in the attached figure

Step-by-step explanation:

we have

[tex]\left|2x+4\right|>8[/tex]

we know that

The absolute value has two solutions  

step 1

Find the positive case

[tex]+(2x+4)>8[/tex]

[tex]2x>8-4[/tex]

[tex]2x>4[/tex]

[tex]x>2[/tex]

The solution is the interval ----> (2,∞)

All real numbers greater than 2

step 2

Find the negative case

[tex]-(2x+4)>8[/tex]

Multiply by -1 both sides

[tex](2x+4)<-8[/tex]

[tex]2x<-8-4[/tex]

[tex]2x<-12[/tex]

[tex]x< -6[/tex]

The solution is the interval ----> (-∞,-6)

All real numbers less than -6

therefore

The solution of the absolute value is

(-∞,-6)∪ (2,∞)

Number line with open circles on negative 6 and 2, shading going in the opposite directions

step 3

using a graphing tool

see the attached figure

Answer:

10 squared units

Step-by-step explanation:

This triangle is pretty easy since it creates a right triangle.  So the base length and height length are pretty easy to identify.

The area of a triangle is .5*base*height.

The base length after drawing the points is a horizontal so just count it or do 4-0=4.

The height length after drawing the points is a vertical so just count it or do 4-(-1)=4+1=5.

So the area of the triangle is .5*4*5=.5(20)=10 units squared.

Now if you didn't fill like drawing it and you knew how to find the determinant.

You just compute

.5 times det|  0   -1     1  |

                   |  0   4      1  |

                   |   4  -1      1  |

.5[  0 det| 4     1  |          -   -1 det|  0   1 |          +    1 det | 0   4 |      ]

              |  -1    1  |                        |  4   1 |                         |  4  -1 |

.5[ 0                           - -1(0-4)                      +   1(0-16)]

.5[  0                         -4                               -16]

.5[-20]

-10

And if you get a negative just take the absolute value of it giving you 10.  

Answer:

-16 cents

Step-by-step explanation:

We are given that on  three rolls of a single​ die, you will lose ​$19 if a 3 turns up at least​ once, and you will win ​$5 otherwise.

We are to find the expected value of the game.

P (at least one 5 in three rolls) = 1 - P (no. of 3 in three) = [tex]1-(\frac{3}{6} )^2[/tex] = 0.875

P (other results) = 1 - 0.875 = 0.125

Random game value = -19, +5

Probabilities: 0.875, 0.125

Expected game value (X) = 0.875 × (-19) + 0.125 × (5) = -16 cents

Therefore, every time you play the game, you can expect to lose 16 cents

Answer:

It is expected to lose 5.10 dollars

Step-by-step explanation:

The probability of getting a 3 by throwing a die once is 1/6.

By throwing it 3 times the probability of not getting a 3 is:

[tex]P=(\frac{5}{6}) ^ 3 =0.5787[/tex]

Then the probability of obtaining a three at least once in the 3 attempts is:

[tex]P'=(1-0.5787)=0.421[/tex]

So if X is the discrete random variable that represents the amount gained in a single move of this game, the expected gain E(X) is:

[tex]E(X)=P'*(X') + P*(X)[/tex]

[tex]E(X) =0.421'*(-19) + 0.5787*(5)\\\\E(X) =-\$5.10[/tex]

Step-by-step explanation:

The expected value is the sum of each outcome times its probability.

E = (0.70)(50000) + (0.05)(0) + (0.25)(-3500)

E = 34125

The store is expected to gain $34,125.

To calculate the expected gain or loss for the new store, we multiply each possible outcome by its probability, then sum these values. This results in an expected gain of $34,125 for the store.

The problem requires calculating the expected value of the coffee franchise's new store opening. We use probability and finance to estimate the expected gains or losses.

The expected value (EV) is calculated as follows:

Multiply each outcome by its respective probability.

Sum these products to get the EV.

So, the expected value is:

EV = (0.70 imes $50,000) + (0.05 imes $0) + (0.25 imes -$3,500)

EV = $35,000 + $0 - $875

EV = $34,125

This implies an expected gain of $34,125 for the new store.

Answer:

x=-7

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

40 + x+57 + 90 =180

Combine like terms

187 +x = 180

Subtract 187 from each side

187-187 +x = 180-187

x = -7

Answer:

g(x) is option 1 or g(x) = (x + 7)^2 + 5

A quadratic equation has the general form of:

y=ax² +bx + c

It can be

converted to the vertex form in order to determine the vertex of the parabola.

It has the standard form of:y =a(x+h)² + k

where hand k represents the vertex, h represent the point in the x axis and k is thepoint in the y axis. Therefore, from the details given in the problem, the equation that represents

g(x) is option 1 or g(x) = (x + 7)^2 + 5

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=adjacent\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ \sqrt{61^1-11^2}=a\implies \implies \sqrt{3600}=a\implies 60=a[/tex]

Answer:

The farthest Left

Step-by-step explanation:

The second equation, y<x+1, means that every y value will be less than the x value +1. Since it is less than, and not less than or equal to, the graph is represented by the dotted line and not a solid line. Moving on to the next problem, we have to get it in slope-intercept form. We start with x-4y is less than or equal to 4. We need to separate the x and y, so we add 4u to the negative 4y, cancelling it out, but what we do to one side, we have to do to the other, so we add 4y, making our equation x is less than or equal to 4y + 4. Next, we need to get the y by itself, so we subract 4 from the y side, cancelling it out and subtract it from the other side, which leaves us with x-4 is less than or equal to 4y. 4y is just 4 times y so we divide it by four on both sides to get y is greater than or equal to 1/4x-1. Since the solution can be equal to, we make the line solid and when we plot both lines, we get the graph furthest to the left.

Answer:

The x-term inside the radical has a negative coefficient

Step-by-step explanation:

The argument of a square root should be ALWAYS greater or equal to zero. If the domain of the function is x<7, rearranging, we have: 0<x-7

Therefore the argument is: x-7, and the function is: y = √(x-7)

The statement "The x-term inside the radical has a negative coefficient" is the right answer.

Answer:

Yes

Step-by-step explanation:

To be a solution of the system, it has to satisfy both the equations.

Let's check first one:

3x - 2y = -1

3 (1) - 2(2) = 3 - 4 = -1

So correct (satisfies).

Now, 2nd one:

y = -x + 3

y = -(1) + 3

y = -1 +3

y = 2

Yes, this is satisfied.

Hence, (1,2) IS A SOLUTION OF THE SYSTEM

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=\dfrac{5}{2}x+2&(1)\\2y=5x+8&(2)\end{array}\right\\\\\text{substitute (1) to (2)}:\\\\2\left(\dfrac{5}{2}x+2\right)=5x+8\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)\left(\dfrac{5}{2}x\right)+(2)(2)=5x+8\\\\5x+4=5x+8\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\4=8\qquad\bold{FALSE}\\\\\text{The system of equations has no solution.}[/tex]

Answer: 3347.005 users but you cant divide people in half so its 3347 people

Answer0< x<10

Step-by-step explanation: it says reasonable so this is one of the few time it’s not all positive integers cause it’s a real world question and it’s from 2000 to 2010 so 10 years is the REASONABLE domain for this problem

Answer:

-1/3 is the slope perpendicular

Step-by-step explanation:

When we have 2 points, we can use the formula

m = (y2-y1)/(x2-x1) to find the slope

m = (1-7)/(3-5)

   =-6/-2

    =3

The slope is 3

We want a slope perpendicular

Remember that is the negative reciprocal

- (1/3)

-1/3

Two lines are perpendicular when,

[tex]a_1=-a_2^{-1}[/tex]

Now solve for [tex]a_2[/tex] to get [tex]a_2=-a_1^{-1}[/tex]

First we calculate the slope [tex]a_1[/tex] from the given points [tex]E(x_1,y_1),F(x_2,y_2)\longrightarrow E(5,7),F(3,1)[/tex].

[tex]a_1=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-7}{3-5}=\dfrac{-6}{-2}=3[/tex]

Now use the first formula and insert the data in it to find the value of the second slope [tex]a_2[/tex],

[tex]a_2=-3^{-1}=\boxed{-\dfrac{1}{3}}[/tex]

And that's it.

Hope this helps.

r3t40

Answer:

Option D (r(t) = 3.50t +25 ; r(8) = 53)

Step-by-step explanation:

The fixed cost to rent the kayak $25. This is the cost which remains fixed irrespective of the usage of the kayak. The variable cost of using the kayak is the cost which depends on the usage of the kayak. It is mentioned that the kayak is used for 4 hours and the company charges $3.5 for every half hour. The cost function is given by:

r(t) = 25 + 3.5t ; there r is the total cost of using the kayak and t is the number of half-hours the kayak is used.

4 hours means that there are 8 half-hours. Therefore, t=8. Put t=8 in r(t).

r(8) = 25 + 3.5*(8) = 25 + 28 = 53.

Therefore, Option D is the correct answer!!!

Answer:

The Answer would be D.

r(t) = 3.50t +25

r(8) = 53

Step-by-step explanation:

The Rental Company charges a fixed price of $25 to rent the kayak, as well as an additional $3.50 for each half hour. So the only variable we are looking at would be the amount of time the kayak was rented. We can model this question with the following equation.

[tex]f(x) = 25 + 3.50x[/tex]

with x being the time the kayak was rented in 30 min intervals. Since the kayak was rented for 4 hours we can multiply this by 2 to get 8 (30 min intervals). Now we can plug this into the formula and solve it.

[tex]f(8) = 25 + 3.50(8)[/tex]

[tex]f(8) = 25+  28[/tex]

[tex]f(8) = 53[/tex]

So to rent the kayak for 4 hours it would cost $53

Answer:

A Secant is a line in the plane of a circle that intersects the circle at exactly two points

Step-by-step explanation:

A line intersecting in two points is called a secant line, in one point a tangent line and in no points an exterior line. A chord of a circle is the line segment that joins two distinct points of the circle. A chord is therefore contained in a unique secant line and each secant line determines a unique chord.

G -1/6= 1/6

Move -1/6 to the other side

sign changes from -1/6 to 1/6

G-1/6+1/6=1/6+1/6

G = 2/6

Reducing: divide by 2 for 2/6

2/2= 1

2/6= 3

Answer : G= 2/6= 1/3