Math worksheet lesson 10

The equation is r(x) = 10x - 0.025x² where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.

For maximum r, r'(x) = 0

It becomes: r'(x) = [tex]10-0.025\times2x=0[/tex]

= [tex]10-0.5x=0[/tex]

[tex]x=\frac{10}{0.05}[/tex]

x= 200

Hence, r(200) = [tex]10\times200-0.025\times200^{2}[/tex]

Solving it we get,

r(200) = 1000

Hence, maximum revenue is $1000.

The slope-point form of a line:

[tex]y-y_0=m(x-x_0)[/tex]

We have

[tex]m=\dfrac{3}{4}\\\\(4,\ 1)\to x_0=4,\ y_0=1[/tex]

Substitute:

[tex]y-1=\dfrac{3}{4}(x-4)[/tex]

The slope-intercept form:

[tex]y=mx+b[/tex]

Solve for y:

[tex]y-1=\dfrac{3}{4}(x-4)\qquad|\text{use distributive property}\\\\y-1=\dfrac{3}{4}x-3\qquad|\text{add 1 to both sides}\\\\y=\dfrac{3}{4}x-2[/tex]

Answer: D.

in 40 minutes it will be 12:10

You seem to be missing some information here.

Complex conjugate example:

2 - 16i >> 2 + 16i

Are you sure this is the entire question?

For this case we have a complex number of the form:

[tex]a + (b) (i)\\[/tex]

Where:

Thus, given 1-8i, its complex conjugate is given by:

[tex]1 + 8i\\[/tex]

On the other hand, the product of both is given by:

[tex](1 + 8i) (1-8i) =\\\\(1 ^ 2-8i + 8i-64 (i ^ 2)) =\\\\1-64 (-1) =\\\\1 + 64 = 65\\[/tex]

Answer:

Conjugate complex: [tex]1 + 8i\\[/tex]

Product: 65

  11 = -3k - 22 - 8k

  11 = -11k - 22         added like terms (-3k and -8k)

+22         +22

33 = -11k

[tex]\frac{33}{-11} = \frac{-11k}{-11}[/tex]

 -3 = k

Answer: k = -3

Answer: 10 & 16

Step-by-step explanation:

When dividing a positive number by a negative number, the result is negative.

A better estimation would be -3.

Solution:

As the two numbers [tex]15 \frac{1}{3} {\text{and} -4\frac{2}{3}[/tex] are mixed fractions.

[tex]15 \frac{1}{3}= \frac{46}{3} \\\\ -4\frac{2}{3}= \frac{-14}{3}[/tex]

Now,  [tex]\frac{ \frac{46}{3}}{\frac{-14}{3}}[/tex] = - 3

Ankur's answer= 3

The mistake he has committed , while dividing two fractions , he must have forgot that one of the fraction which is in the denominator bears negative sign  before it.

So, [tex]\frac {+}{-}= -[/tex].

Ankur forgot to put negative sign before 3.

So, The correct option which describes ankur's error is : Ankur found that the quotient of a positive number and a negative number is positive.

Option 3 is right choice.

Construction of an angle congruent to a given angle.

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.

For two angles to be congruent their measurements must be equal.

Therefore, we can conclude that the construction above is angle congruent to a given angle.

Learn more about congruent angles here

https://brainly.com/question/28262429

#SPJ4

An angle congruent to a given angle construction is illustrated in the figure. Option B is the right choice.

Congruent angles share an identical measure, establishing equality between their angular dimensions.

In the realm of geometry, the fundamental criterion for angles to be considered congruent is that their measurements are precisely equal. This equality in angular magnitude implies that the angles exhibit indistinguishable orientations and positions.

Consequently, when engaging in geometric constructions, if a constructed angle aligns in measurement with a given angle, it is deemed congruent to the specified angle.

This fundamental concept is pivotal in geometric reasoning and problem-solving, providing a basis for establishing equivalences between angles and facilitating precise angular constructions. In summary, congruent angles signify an equality in measurement, forming a cornerstone in geometric analyses and constructions.

Option B is the right choice.

For similar question on congruent

https://brainly.com/question/29789999

#SPJ3

Answer:

The graph in option (c) is the correct answer.

Step-by-step explanation:

The line corresponding to the inequality [tex]x+y<1[/tex] represents the dashed line and the line corresponding to the inequality [tex]2y\geq x-4[/tex] represents the solid line.

In order to figure out the correct shaded region, we test one point from each of the four possible regions and figure out the point at which both the inequalities bold true. The region containing that point would be the correct shaded region.

Let us test the point (0,0).

First inequality [tex]0+0<1[/tex], that is, [tex]0<1[/tex] holds true.

The second inequality [tex]2(0)\geq 0-4[/tex] that is, [tex]0\geq -4[/tex] as well holds true.

Since both the inequalities hold true at point (0,0), therefore, region  containing origin is the correct answer. Thus, the correct answer is forth option. Since the options are not labeled, I have attached the correct graph with my solution in order to make sure you get the correct answer.

The correct answer would be A.  13/3 Divided by -5/6

The total answer would be negative 5 1/5

because you do 4x3+1=13 over the denominator that is already there so 13/3 then you do KCF a.k.a keep change and flip you keep 13/3 change the division sign into multiplication sign then you flip the -5/6 to -6/5 then multiply straight across and reduce this is the way my teacher taught me how to remember - to positive kind of things:

when a negative thing or bad thing happens to a good person is that good or bad in this case thats bad because if you think about it if a bad thing happend to someone you care about that would be bad. then that same idea goes for each pattern another example could be a good thing (+) happens to a good person (+) it is good (+)

(+) (+)=+

(-) (-)=+

(+) (-)= -

(-) (+)= -

Hope this helps. Have a good day! :)

For this one, I would go with D.

D makes the most sense, giving that there is two sets of each and, that it is just a shorter way to say "add all the sides."  

B and C would only give us half or part of the perimeter and then A does not make much sense.

D would be the answer through process of elimination.

And Whats the question here?!?!

Answer: The correct statements are 0.75 (x,y) = (0.75x, 0.75y) , LM is parallel to L'M' and "the vertices of the image are closer to the origin than those of the preimage".

Explanation:

It is given that the triangle ABC was dilated according to the rule DO,0.75 (x,y)

DO, 0.75(x,y) represents the rule of dilation. Where both x- and y-coordinates are multiplied by 0.75 the dilation is about the origin has a scale factor of 0.75. The  notation for this dilation would be,

[tex](x,y)\rightarrow (0.75x,0.75y)[/tex]

Therefore, the first statement is true.

Since both x- and y-coordinates are multiplied by 0.75, therefore the sides of image and preimage are parallel but the sides of image are 0.75th of the side of preimage.

Therefore, the second statement "LM is parallel to L'M'" is true but the third and fifth statement is false.

The scale factor is 0.75 which is less than 1, so the vertices of the image are closer to the origin than those of the pre-image.

Therefore, the forth statement "The vertices of the image are closer to the origin than those of the pre-image"  is true.

Answer: 124

Step-by-step explanation:

It is 165 degrees celcius

37 and 38

consecutive integers have a difference of 1 between them

let n and n + 1 be the consecutive integers, then

n + n + 1 = 75 ( subtract 1 from both sides )

2n = 74 ( divide both sides by 2 )

n = [tex]\frac{74}{2}[/tex] = 37

the integers are 37 and 37 + 1 = 38

Answer: [tex]\frac{4}{15}[/tex]

Step-by-step explanation:

First pick (blue)     and        Second pick (red)

             [tex]\frac{6}{10}[/tex]                  x                    [tex]\frac{4}{9}[/tex]

= [tex]\frac{6(4)}{10(9)}[/tex]

= [tex]\frac{2(2)}{5(3)}[/tex]

= [tex]\frac{4}{15}[/tex]

Answer:

The answer is 4/15 hopefully this helps!

Always remember (y2-y1)/(x2-x1) for finding slope

So (-3)-4 / 1-1=

-7 / 0

So undefined

y = -x - 6

the equation of a line in ' slope- intercept form ' is

y = mx + c ( m is the slope and c the y-intercept )

y = - x is in this form with m = - 1 and c = 0

note that parallel lines have equal slopes thus

the partial equation is y = - x + c

To find c substitute ( - 8, 2 ) into the partial equation

2 = 8 + c ⇒ c = 2 - 8 = - 6

y = - x - 6 ← is the equation of the parallel line

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have

[tex](r,\ 6),\ (5,\ -4)\\\\m=\dfrac{5}{7}[/tex]

Substitute

[tex]\dfrac{-4-6}{5-r}=\dfrac{5}{7}\\\\\dfrac{-10}{5-r}=\dfrac{5}{7}\qquad|\text{cross multiply}\\\\5(5-r)=(-10)(7)\qquad|\text{use distributive property}\\\\25-5r=-70\qquad|-25\\\\-5r=-95\qquad|:(-5)\\\\\boxed{r=19}[/tex]

You multiply fractions simply by multiplying numerators and denominators with each other:

[tex] -\dfrac{1}{4} \times \left(-\dfrac{6}{11}\right) = \dfrac{1 \times 6}{4 \times 11} = \dfrac{6}{44} = \dfrac{3}{22} [/tex]

Answer:

Stacy made a blanket using some fabric, she had 3 yards left over and decided to use the leftover pieces to make pot holders. She cut each piece into 8 inches long. Stacy had enough fabric to create 4.5 pieces.

Step-by-step explanation:

we find that 13 full pieces of fabric, each 8 inches long, can be cut from three yards of fabric.

The question asks how many pieces of fabric, each measuring 8 inches in length, can be cut from a total length of three yards of fabric. To begin with, we need to convert yards to inches, because the unit of measurement for the fabric pieces is in inches, not yards. We know that 1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches, hence 3 feet x 12 inches/foot = 36 inches). Therefore, three yards of fabric is 3 x 36 inches, which equals 108 inches.

Now, if each piece is to be 8 inches long, we divide the total number of inches by the length of one piece to find out how many pieces can be made:
108 inches / 8 inches/piece = 13.5 pieces.

However, since we cannot have half a piece of fabric, we can only make 13 full pieces, with a small remaining piece that would be less than 8 inches long.

Answer:

Step-by-step explanation:

(g/h)(t) = g(t) / h(t)

              =( t³-5t² ) /(t+5) we cannot simplify this further so

(g/h)(t) = ( t³-5t² ) /(t+5)

               =

Answer:

The awnser is C and trust me

Step-by-step explanation:

The slope:

[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

Look at the picture.

6 units down → -6

2 units right → 2

[tex]m=\dfrac{-6}{2}=-3[/tex]

answer:  [tex] \frac{3}{-1} x[/tex]

explanation:

slope-intercept formula ==> [tex]y = mx + b[/tex]

[tex]m[/tex] is slope , and [tex]b[/tex] is y-intercept

to find the slope you need to start at the y intercept and go 3 units up and 1 unit left. and if you repeat it again, until you reach the top of the graph and that would make partial of the line.

so, the slope is [tex]\frac{rise}{run}[/tex], so if you plug it in it would look like this

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

A D D I T I O N A L  I N F O

then you find the y-intercept which would be where the line intersects at the y axis, which is -10. plug the number into the equation

[tex]y = \frac{3}{-1} x - 10[/tex]

and that would make our final answer.

hope this helps! correct me if there is anything wrong ❤ from peachimin

Answer: C

Step-by-step explanation:

(x - y)²

we want (8)², so need: x - y = 8

There are many options that satisfy x - y = 8  but of the options provided to you, 10 - 2 is the only one that works.

A) 2 - 6 = -4

B) 64 - 0 = 64

C) 10 - 2 = 8

D) 8 - 64 = -56

ANSWER

The possible rational roots are [tex]\pm3[/tex]  and [tex]\pm\frac{1}{3}[/tex]

EXPLANATION

According to  the rational roots theorem, the possible rational roots of

[tex]9x^3+14x^2-x+18=0[/tex]

is given by all the possible factors of [tex]18[/tex] which are

[tex]\pm1,\pm2,\pm3,\pm6,\pm9,\pm18[/tex]

expressed over all the possible factors of the coefficient of the highest degree of the polynomial which is  [tex]9[/tex] which are

[tex]\pm1,\pm3,\pm9[/tex]

in their simplest form.

One of this possible ratios are [tex]\pm9[/tex] from the factors of 18, over [tex]\pm3[/tex] from the factors of 9.

This will give us

[tex]\frac{\pm9}{\pm3} =\pm3[/tex].

Another possible rational root is

[tex]\pm \frac{1}{3}[/tex].

Hence the correct options are

A and C.

Secrete: Check if the denominator is a factor of 9 and the numerator is also a factor of 18, then these are the correct answers.

The possible rational roots of the polynomial 9x^3+14x^2-x+18=0, according to the Rational Root Theorem, are ±3 and ±1/3. The other given options, ±1/18 and ±1/2, do not meet the criteria set by the theorem.

The question asks for the possible rational roots of the polynomial 9x^3+14x^2-x+18=0 according to the Rational Root Theorem. The Rational Root Theorem states that if a polynomial has a rational root p/q, where p and q are integers and q is not zero, then p is a factor of the constant term and q is a factor of the leading coefficient.

The constant term here is 18 and its factors are ±1, ±2, ±3, ±6, ±9, and ±18. The leading coefficient is 9 and its factors are ±1, ±3, and ±9. According to the theorem, we divide each factor of the constant term by each factor of the leading coefficient to determine the potential rational roots:

±1/1, ±1/3, ±1/9

±2/1, ±2/3, ±2/9

±3/1, ±3/3, ±3/9

±6/1, ±6/3, ±6/9

±9/1, ±9/3, ±9/9

±18/1, ±18/3, ±18/9

Out of the list, the values that match the options given in the question are ±3 and ±1/3. The other options, ±1/18 and ±1/2, are not rational roots because 1/18 is not a factor of 9 (leading coefficient), and 2 is not a factor of 18 (constant term) when considering the reduced form.

Answer:

24 dozen chocolate chip

14 dozen peanut butter

Step-by-step explanation:

x = number of dozen chocolate chip cookies

y = number of dozen peanut butter cookies

Total number of cups of flour is:

2x + 3y ≤ 90

Total number of eggs is:

x + 4y ≤ 80

Total profit is:

P = x + 1.5y

Since this is multiple choice, one method would be to calculate the profit for each option, then choose the one that's largest.

But let's try solving this algebraically.  x and y are positive integers, and we want them to be as large as possible.

Let's start by assuming the solution is on the line 2x + 3y = 90.

x + 4y ≤ 80

2x + 8y ≤ 160

90 − 3y + 8y ≤ 160

5y ≤ 70

y ≤ 14

If y = 14, x = 24, and P = 45.

Now let's assume the solution is on the line x + 4y = 80.

2x + 3y ≤ 90

2 (80 − 4y) + 3y ≤ 90

160 − 8y + 3y ≤ 90

70 ≤ 5y

14 ≤ y

Therefore, to maximize the profit, they should bake 24 dozen chocolate chip cookies and 14 dozen peanut butter cookies.