9x^2-64I need help solving

It sounds like you're asked to find c such that f(x), defined by

\(f(x)=\begin{cases}cx^2+8x&\text{for }x<5\\x^3-cx&\text{for }x>5\end{cases}\)

is continuous at x = 5.

With the strict inequalities given in the definition, this is not possible. So you probably meant to use ≤ or ≥ in one of the pieces of the definition.

In order for f(x) to be continuous at x = 5, the limit from either side as x approaches 5 must be the same.

We have

\(\displaystyle\lim_{x\to5^-}f(x)=\lim_{x\to5}(cx^2+8x)=25c+40\)

and

\(\displaystyle\lim_{x\to5^+}f(x)=\lim_{x\to5}(x^3-cx)=125-5c\)

Then

\(25c+40=125-5c\implies30c=85\implies c=\dfrac{85}{30}=\boxed{\dfrac{17}6}\)

According to the equation does the graph of the systems of equations solve is B.

1/3x+1=2x-4 is correct.

A graph is a structure consisting of a group of items, some of which are "linked." The objects are mathematical abstractions known as vertices, and each pair of connected vertices is known as an edge.

It is evident from the graph that the two lines intersect at the location:

(3, 2).

To put it another way,

at x =3, y = 2

The point where two lines intersect is:

(x, y) = (3, 2) (3, 2).

Now,

x = 3 is the point  of the x-coordinate

y = 2 is the point of the y-coordinate

Now, examine the equation, 1/3x+1=2x-4, to see if it contains the correct x-coordinate value.

(1/3)x + 1 = 2x -4

subtracting 1 from both side:

(1/3)x + 1 -1  = 2x -4 -1

We get:

(1/3)x = 2x -5

subtract 2x from both sides:

(1/3)x -2x = 2x -5 -2x

We get:

-(5/3)x = -5

on simplifying the equation we get:

x = 3

the value of x = 3

this show that the 1/3x+1=2x-4 is correct.

To know more about graph visit:

https://brainly.com/question/17267403

#SPJ9

Answer:

The mean is 56.6, the median is 53, modes are 41, 43, and 63, the range is 56, and the IQR is 20.

Step-by-step explanation:

The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.

Average = Sum / Count

= 849 / 15

= 56.6

Step-by-step explanation:

i think c is your answer

The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

For more questions on number of visible arcs:

https://brainly.com/question/31336038

#SPJ8

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3\)

Answer:

236 ft^3

Step-by-step explanation:

Base radius = 5 ft

Height = 3 ft

Volume =   πr^2h

              =  π × 5^2 × 3

              =  75π

               =  235.61944901923 feet^3

Nearest Cubic Foot = 236 ft^3

Nearest Cubic Foot:

Hence Answer is:

236 ft^3

Hope this helps!

When two angles are called "Complementary Angles" it means their measures add up to 90 degrees.

Hence, if angle a and angle b are complementary angles,

Answer:

(-1,-1),(1,-4)

Step-by-step explanation:

it is the wright answer

Answer: 2656 bacteria after 996 minutes

Step-by-step explanation:

This has to do with exponential growth-

996/332=3, which means we must think about it in terms of doubling the bacteria numbers three times over the course of 996 minutes.

1st: 332*2=664

2nd: 664*2=1328

3rd: 1328*2=2656 bacteria after 996 minutes

Answer:3016

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The z score is a score used to determine the number of standard deviations by which the raw score is above or below the mean, it is given by the equation:

\(z=\frac{x-\mu}{\sigma} \\\\\mu=mean, \sigma=standard\ deviation,x=raw\ score\\\\for\ a\ sample\ n:\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }\)

Given that μ = 650, σ = 50. To find the probability that 5 students who have a mean of 490, we use:

\(z=\frac{x-\mu}{\sigma/\sqrt{n} } =\frac{490-650}{50/\sqrt{5} } =-7.16\)

From the normal distribution table, P(x < 490) = P(Z < -7.16) = 0.0001 = 0.01%

Since only a small percentage of people score about 490, hence the local newspaper editor should write a scathing editorial about favoritism

Answer:

\(A:E:M = 6:4:5\)

Step-by-step explanation:

Given

Abam =N3.00 when Emeka = N2.00

Emeka = N4.00 when Madu = N5.00

Required

Determine their ratios

Represent their ratios with the first letter of their names:

From the first statement

\(A:E = 3:2\) ---- (1)

From the second

\(E:M = 4:5\) ----- (2)

Multiply the ratio in (1) by 2

\(A:E = 3 * 2: 2 * 2\)

\(A:E = 6: 4\) ---- (3)

Notice that the value of E in both cases is the same i.e E = 4

(1) and (3) can be merged to give:

\(A:E:M = 6:4:5\)

Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

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

Step-by-step explanation:

The equation of a parabola in vertex form is:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

\(-3 = a(1 - (-2))^2 + 6\)

\(-3 = a(3)^2 + 6\)

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

\(y = -1(x + 2)^2 + 6\)

This equation can also be written as:

\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)

Answer:

f(2) = -3

Step-by-step explanation:

Let x= 2

What value is y when x=2

Y = -3 when x =2

f(2) = -3

The smallest number of students who go to one of these clubs is 21.

A stem-and-leaf diagram is a quantitative assessment of a collection of data in which the data values are divided into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).

Based on the given stem and leaf diagram, the smallest number of students who go to one of these clubs is represented by the leaf value "1" in the stem "2."

Therefore, the smallest number of students who go to one of these clubs is 21.

To learn more about the stem-and-leaf diagram click here:

https://brainly.com/question/8450114

#SPJ1

Answer:

the answer is "d" because the x region is negative 2 and the y region is a positive1

Answer:

20cm it's is the answers

Step-by-step explanation:

5*4=20

Answer:

1/6

Step-by-step explanation:

you divide 24 pieces into 4 different bags, which is 6.

The volume is the amount of space thus the volume of the given prism will be 204.7 cm³ thus option (B) is correct.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

Volume has units of cube example meter³,cm³, etc.

The volume of the given prism will be the area of the front triangle with a length of 12 cm.

The form triangle has been attached below,

The length x will be,

x = √(6² - 3.5²) = 4.87 cm.

The area of from triangle = (1/2) × 7 × 4.87

A = 17.06 cm²

The volume of the prism = A × length (12 cm)

Volume = 17.06 × 12 = 204.68 cm².

Hence "The volume is the amount of space thus the volume of the given prism will be 204.7 cm³".

To learn more about volume,

https://brainly.com/question/1578538

#SPJ1

The complete question has been attached below ;

The corporate team-building event will cost $1224 if there are 72 attendees.

Given, the corporate team-building event will cost $833 if it has 49 attendees.

We have to find the cost if there are 72 attendees,

So, according to the question

49 attendees = $833

1 attendee = 833/49

72 attendees = 72×833/49

72 attendees = 1224

Hence, the corporate team-building event will cost $1224 if there are 72 attendees.

Learn more about Unitary Method here https://brainly.com/question/28627316

#SPJ9

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

Given,

The points which the line passes, (x₁, y₁) = (7, 6)

Slope of the line, m = 0

We have to find the equation of the line:

We know that,

y - y₁ = m(x - x₁)

So,

y - 6 = 0(x - 7)

y - 6 = 0

y = 6

That is,

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

Learn more about equation of line here:

https://brainly.com/question/25789778

#SPJ1

Answer:

let the number be x

then

4x-3= x+24

4x-x=24+3

3x=27

x=3

Step-by-step explanation:

The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

For more such questions on interior angles

https://brainly.com/question/24966296

#SPJ8

The numerical value of x in the similar pair of triangle is 10.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

From the diagram,

Side A of the small triangle = 10

Side B of the small triangle = x + 2

Side A of the Big triangle = 10 + x

Side B of the big triangle = x + 14

Hence;

Ratio of Side A to Side B of the small triangle = 10 / x + 2

Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14

Since the triangle area similar, equate the two ratio and solve for x.

10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )

Cross multiply

10( x + 14 ) = ( 10 + x )( x + 2 )

Expand using FOIL method

10x + 140 = 10x + 20 + x² + 2x

10x + 140 = x² + 12x + 20

x² + 12x + 20 = 10x + 140

x² + 12x + 20 - 10x - 140 = 0

x² + 2x - 120 = 0

Factor the left side of the equation

( x - 10 )( x + 12 ) = 0

Hence;

x - 10 = 0 and x + 12 = 0

x = 10 and x = -12

Since the dimension of the triangle cannot be negative,

x = 10

Therefore, the value of x is 10.

Learn more about FOIL Method here: brainly.com/question/28527940

#SPJ1

Answer:

Angle A = 17°, Angle B = 73°

Step-by-step explanation:

Angle A & Angle B are complementary angles (given) so they will form 90°.

Let's take,

Angle A = x

Angle B = 4x +5 (angle B is five degrees more than four times angle A)

Measure of each angle=?

Angle A + Angle B = 90°

x + 4x + 5 = 90

5x + 5 = 90

5x = 90 - 5

5x = 85

x = 85 ÷ 5

x = 17°

Angle A = x = 17°

Angle B = 4x + 5 = 4(17) + 5 = 68 + 5 = 73°

•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•

Answer:

13

Step-by-step explanation:

Use sin = opposite/hypotenuse

Setup an equation. I'm going to use x to represent the hypotenuse.

\(sin44=\frac{9}{x}\)

Now move the x to the other side by multiplying. We want to solve for x.

\(x(sin44)=(\frac{9}{x})x\)

The x cancels on the right side. Now divide both sides by sin44. To get  by itself on the left.

\(\frac{x(sin44)}{sin44} = \frac{9}{sin44}\)

\(x = \frac{9}{sin44}\)

Use your scientific calculator, make sure it is on degrees, and divide 9 by sin44.

\(x = 12.9560088566\)

Round to the nearest whole number

\(x = 13\)

Answer:

-10

Step-by-step explanation:

when a number Inside of parentheses is close to another number (like being near a fireplace trying to say warm) it means to multiply :3 !

Example: (3)2=6           6(6)=36

in our case it is (-5)2        So was ist -5 x 2? -10

hope this helped!

for some extra practice to check your knowledge, what is (-3+-2)2 ?

Answer:

80 months

Step-by-step explanation:

If the present monthly heating costs average $300, but the insulation is expected to reduce heating costs by 10%, then there will be a monthly saving of 10%:

\(\implies \rm Monthly\;saving=10\%\;of\;\$300 =\dfrac{10}{100} \times \$300=\$30\)

To calculate how many months it will take to recover the cost of the insulation, divide the cost of installing the insulation by the monthly saving:

\(\implies \rm Number\;of\;months=\dfrac{\$2400}{\$30}=80\)

Therefore, it will take 80 months to recover the cost of the insulation.

Answer:

80 months

Step-by-step explanation:

The expected monthly savings from the insulation are: $300 × 10% = $30.

So, the number of months required to recover the cost of the insulation, $2400, is $2400/$30 = 80 months.

Answer:

d=rt

d=8(6)

d=48 miles

Step-by-step explanation: