Give the function f(x)= 0.5lx - 4| -3, for what values of x is f(x) = 7

Answer:

7 [tex]\frac{37}{55}[/tex]

Step-by-step explanation:

In order to solve an equation like this, you'll need to find a common denominator for your Fraction.

7 [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{11}[/tex]

7 [tex]\frac{22}{55}[/tex] + [tex]\frac{15}{55}[/tex]

7 [tex]\frac{37}{55}[/tex]

Answer:

  A)  f'(c) = 3

Step-by-step explanation:

The mean value theorem says that if f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists some c such that ...

  a < c < b

  f'(c) = (f(b) -f(a))/(b -a)

__

We are told that f(x) is differentiable on the closed interval [-1, 4], so we know it meets the requirements of the mean value theorem. Then we can conclude that there is some c such that ...

  f'(c) = (12 -(-3))/(4 -(-1)) = 15/5

  f'(c) = 3 . . . . for some c in the interval -1 < c < 4

Answer:

Plan A = 1000 dollars to be invested in an account that pays 100 dollars per year. (1000 + 100 = 1100 dollars in a year)

Plab B = 1000 dollars to be invested in an account that pays 5% interests per year  (1000 * .05 = 50 => 1000 + 50 = 1050 dollars per year)

The correct answer is Plan A will be worth more than plan B after two years.

Step-by-step explanation:

Plan A = 1000 dollars to be invested in an account that pays 100 dollars per year. (1000 + 100 = 1100 dollars in a year)

Plab B = 1000 dollars to be invested in an account that pays 5% interests per year  (1000 * .05 = 50 => 1000 + 50 = 1050 dollars per year)

Plan A will be worth more than plan B after two years.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now, WE get;

For Plan A,

1000 dollars to be invested in an account that pays 100 dollars per year.

Hence, We get;

(1000 + 100 = 1100 dollars in a year

For Plan B;

1000 dollars to be invested in an account that pays 5% interests per year

So, WE get;

(1000 x 0.05 = 50

Hence, Total in a year,

= 1000 + 50

= 1050 dollars per year)

Thus, the correct answer is,

⇒ Plan A will be worth more than plan B after two years.

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Answer:

C. Scalene

F. Obtuse

Step-by-step explanation:

The triangle is scalene because all 3 sides are different lengths.

The triangle is obtuse because 1 angle is bigger than 90° (132°).

Answer:

scalene

obtuse

Step-by-step explanation:

All the sides are different length, so it is a scalene triangle

The 132 degree angle is greater than 90 degrees and less than 180 so it is obtuse

Answer:

The numbers at 13 and 13

Step-by-step explanation:

The two numbers in question are equal, and if their sum is 26, then they must be 13 and 13.

The two numbers are (13, 13).

Given that,

The sum of the two numbers is 26.

And the sum of their square is minimum.

We have to determine,

The two numbers are.

According to the question,

Let, the first number be x,  

and the second number be y.

The sum of the two numbers is 26.

[tex]x + y = 26[/tex]

And The sum of their squares is a minimum.

[tex]x^2 + y^2 = h[/tex]

Solving both the equation,

[tex]x + y = 26\\\\x = 26-y[/tex]

Substitute the value of x in equation 2,

[tex]x^2 + y^2 = h\\\\(y-26)^2 + y^2 = h \\\\y^2 + 676 -52y + y^2 = h\\\\2y^2 -52y + (676-h) = 0[/tex]

Then, The vertex of the parabola is,

[tex]\dfrac{-b}{2a} = \dfrac{-(-52)}{2(2)} = \dfrac{52}{4} = 13[/tex]

The minimum value of the parabola is 13, which is also the sum of squares.

Therefore, The two number is x = 13 and y =13.

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Answer:

f(x) = 2(x+3)^4

Step-by-step explanation:

I graphed the functions on the graph below so you can see how I got my answer.

Answer:

g(x)=2x^4+3

Step-by-step explanation:

Answer:

(4y7+7x4)(−4y7+7x4)

Step by Step:

Factor 49x8−16y14

−16y14+49x8

=(4y7+7x4)(−4y7+7x4)

The factor of the expression 49x⁸ − 16y¹⁴ is (7x⁴ - 4y⁷) and (7x⁴ + 4y⁷) after using the identity.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

49x⁸ − 16y¹⁴

As we know the polynomial identity:

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

a² - b² = (a - b)(a + b)

The expression 49x⁸ − 16y¹⁴ can be written as:

= (7x⁴)² − (4y⁷)²

After using the identity: a² - b² = (a - b)(a + b)

= (7x⁴ - 4y⁷)(7x⁴ + 4y⁷)

Thus, the factor of the expression 49x⁸ − 16y¹⁴ is (7x⁴ - 4y⁷) and (7x⁴ + 4y⁷) after using the identity.

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Answer:

A

Step-by-step explanation:

3^5 x 3^4

=3^5 + 4

=3^9

so the answer is option A

Answer:

C

Step-by-step explanation:

1÷2×8×3=12

Answer:

The two sides of the triangle are equal so by the property that : If  opposite sides of a triangle are equal then the opposite angles are also equal .

Area of triangle = 1/2 multiplied by base and also multiplied by height

A =1/2*b*h

So, we can conclude that the opposite angles are 90 + 90 degrees = 180 degrees (as the angles are equal)

Therefore, c)1/2 *8*3  is right

Answer:

1458/3456 = 27/64 (simplification)

cube root of 27/64 = 3/4

square of 3/4 = 9/16

9/16 multplied by 1024 = 576.

THIS IS THE REAL WORKING AND ANSWER

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The surface area of the smaller container is 576 cm²

Two shapes or solids are similar if their corresponding sides are in the same proportion and their corresponding angles are equal.

Given that, The two containers are mathematically similar in shape, the larger container has a volume of 3456 cm³ and a surface area of 1024 cm². The smaller container has a volume of, 1458 cm³.

We know, that the cube of scale factor is equal to ratio of volumes of given shape and ratio of surface area is equal to square of scale factor.

1458/3456 = 27/64

∛27/64 = 3/4

Therefore, the scale factor = 3/4

(3/4)² = 9/16

9/16x1024 = 576.

Hence, The surface area of the smaller container is 576 cm²

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Answer:

the letter in the green box should be 3.

i believe the full equation should be y= -3/2 x+1

Step-by-step explanation:

the y side keeps decreasing by 1 1/2 which in improper fraction form is -3/2. the x side keeps increasing by 1.

Answer:

Hey there!

Eight years ago, Manuel's age was 36/2, or 18.

Now, his age is 18+8, or 26 years old.

So, he is 26 years old now.

Hope this helps :)

Answer: After 210 seconds they with next flash at the same time.

Step-by-step explanation:

Given: Ardem has two lights.

One flashes every 15 seconds the other flashes every 42 seconds.

If they started flashing at the same time, then the number of seconds after that they with next flash at the same time = LCM (15, 42)   [LCM - Least common multiple]

Prime factorization of 15 = 3 x 5

Prime factorization of 42 = 2 x 3 x 7

Then, LCM (15, 42) = 2 x 3 x 5 x 7 = 210

i.e. After 210 seconds they with next flash at the same time.

Answer:

17 nickels

Step-by-step explanation:

To be able to find the answer, you can say that the sum of the value of each coin multiply for its quantity is equal to 10.08, which you can express as follows:

quarters= 0.25

dimes= 0.10

nickels= 0.05

pennies= 0.01

(0.25*19)+(0.10*39)+(0.05*x)+(0.01*58)=10.08, where

x= the quantity of nickels

Now, you can solve for x:

4.75+3.9+0.05x+0.58=10.08

0.05x=10.08-4.75-3.9-0.58

0.05x=0.85

x=0.85/0.05

x=17

According to this, the answer is that there are 17 nickels in the cup holder.

Answer:

[tex]x = 2, 12[/tex]

Your correct answer is D, since I don't see a -12.

Step 1: Subtracting 2 from both sides

Since we have to find the value of x, we have to factor the equation. To do so, we first have to subtract the two from both sides of the equation so all the values are on one side of the equation.

[tex]x^2-10x-22(-2)=2(-2)\\x^2-10x-24=0[/tex]

Step 2: Factoring the equation

Part 1

After subtracting 2 from both sides of the equation, we have to factor the polynomial to be able to get it into two sets of parentheses, so in order to do that, we will ignore the equal sign and the 0 for now. We are now left with:

[tex]x^2-10x-24\\[/tex]

First, we find the multiples of the first term, [tex]x^2\\[/tex], and the last term, -24. Since there is an invisible 1 before the first term, we are basically finding the multiples of [tex]1x^2[/tex], which is [tex]1x[/tex] and [tex]1x[/tex], or x and x. Now we have to find the correct set of numbers for -24. Do do that, we have to make sure that when we multiply the first set of numbers (x, x) with the second set (?, ?) and add them together, then we would get the number in the middle (-10x). So: Two of the most obvious multiples for 24 are 6 and 4, 12 and 2, and 3 and 8. But, this is a negative 24, so we have to work ahead to find out which pair we use first. If we multiply 8 and 3 with x and x, we get 8x and 3x. When we add them together, we do not get 10x, but instead, we get 11x, so it is the wrong pair. If we do the same thing to 6 and 4, we would get 10x, but since 24 is negative, it is not correct because we would need one of the numbers to be negative. In this case, they equal to 10x, but one of the numbers would have to be negative because (if 6 was the negative):

[tex]-6 * 4=-24\\[/tex]

But:

[tex]4-6\neq 10\\[/tex]

So this is not the correct set either. Our last set is 12 and 2, and when we multiply by x (12x and 2x) and we set one of the numbers to be a negative (-12) and subtract them, we get -10x, so, therefore, this is the correct number pair.

[tex]-12*2=-24\\2-12=-10[/tex]

Part 2

With all that done, we now have to factor the numbers. We take the first numbers (x and x), and we place them in front of each of the two parentheses.

[tex](x,?)(x,?)[/tex]

Now, we place -12 and 2 in those places.

[tex](x,-12)(x,2)[/tex]

To find x, we have to plug in the equal sign and 0 from the beginning.

[tex](x,-12)(x,2)=0[/tex]

Since they both have to equal to 0, then that means there would be two different answers because, for example: 12 - 12 = 0, but 12 - 2 ≠ 0.

To find both solutions, we treat the numbers in each of the parentheses as its own equation, and we solve it from there.

x - 12 = 0

12 - 12 = 0

x - 2 = 0

2 - 2 = 0

12 and 2 are our solutions! Hope this helps :)

Answer:

12  and 2

Step-by-step explanation:

factor the euqation x^2-10x-22=2 and you get (x,-12)(x,2)=0 and when you solve that you get 12 and 2

Answer:

[tex]\sqrt{37}[/tex]

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A(- 2, 9) and (x₂, y₂ ) = B(4, 8)

d = [tex]\sqrt{(4+2)^2+(8-9)^1}[/tex]

   = [tex]\sqrt{6^2+(-1)^2}[/tex]

   = [tex]\sqrt{36+1}[/tex]

    = [tex]\sqrt{37}[/tex] ≈ 6.1 ( to 1 dec. place )

Answer: The answer is B

Step-by-step explanation:

Answer:

Option B is correct

Step-by-step explanation:

cos (3pi/4) = -cos(pi - 3pi/4) = -cos(pi/4) = -sqrt(2)/2

=> Option B is correct

Answer: Option C

Step-by-step explanation: When we count all bases of the squares present

in the triangle,( do not count the number of boxes just the base of the squares) we notice that all of them covers 4 base of the squares, except option c where it covers 5 bases.

Answer:

0.15 or 15%

Step-by-step explanation:

Since lengths are uniformly distributed, the probability that a class period runs between a two exact times is:

[tex]P(x_1\leq x \leq x_2)=\frac{x_2-x_1}{b-a}[/tex]

In this case, a = 47.0 and b = 52.0 minutes.

The probability that a given class period runs between 50.25 and 51.0 minutes is:

[tex]P(50.25\leq x \leq 51.0)=\frac{51.0-50.25}{52-47} \\P(50.25\leq x \leq 51.0)=0.15=15\%[/tex]

The probability is 0.15 or 15%.

Answer:

y = - 9.1768x2 + 122.2567x + 14.9091

Step-by-step explanation:

Given the following :

Month (x) Daily Rental Price (y) 1 $154 2 $205 3 $266 4 $358 5 $403 6 $425 7 $437 8 $430 9 $381 10 $285 11 $211 12 $195

Using the online regression equation graphing tool ; The quadratic model obtained in the form,

y = Ax^2 + Bx + C is :

y = - 9.1768x2 + 122.2567x + 14.9091

Attached below is a picture of the quadratic regression curve.

Answer:

Slope =  [tex]\frac{-3}{4}[/tex]

Step-by-step explanation:

(5 , -2)   ; (-3, 4)

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{4-[-2]}{-3-5}\\\\=\frac{4+2}{-3-5}\\\\=\frac{6}{-8}\\\\=\frac{-3}{4}\\\\[/tex]

Answer:

360 degrees

Step-by-step explanation:

The sum of all exterior angles in any convex polygon is 360 degrees.

Answer:

360 degrees.

Step-by-step explanation:

The sum of exterior angles of every polygon is 360 degrees so the What is the sum of the exterior angles of a 14-gon is also equal to 360 degrees.

Answer:

D. 1800°

Step-by-step explanation:

The given polygon has 12 sides.

The formula for finding the sum of the interior angles of an n-sided polygon is given as, ( n − 2 ) × 180.

Where n is the number of sides of the polygon.

Thus, the sum of the interior angles of the 12 sided polygon given above is:

(12 - 2) × 180

= 10 × 180 = 1800°

Sum of the measures of the interior angles of the 12-sided polygon is D. 1800°

Answer:

Step-by-step explanation:

a) 500,000+300,000+150000+80000+0.02x+0.03x+0.08x=1030000+0.13x

b)1030000*(0.13*200)=26780000

there are two different power : power and exponent

exponent :    5⋅5⋅5=5^3

power 4^2 it is read as 4 to the second power or 4 squared 4 ∙ 4

"Like terms" are terms whose variables are the same example : x,7x,2x tey all have the same variable x

i hope it helps

Answer: 10 rows

Step-by-step explanation:

Given:

Seats on each row = 199.

Population of student attending = 1990.

no of students from same school = 39.

Therefore;

If the students from same school must seat in same row determine the number of rows that most be reserved for these students.

1. At most 39 students from same school

= total population of all students/ students from same school

= 1990 / 39

= 51 schools would be attending the event

2. No of students a row can accommodate

= Seats on each row / no of students from each school

= 199/39

= 5

3. No of rows to that most be reserved

= 51 / 5

= 10

So 10 rows must be reserved.

Answer:

x = Rs 20,833.33

the value of x is Rs 20,833.33

Step-by-step explanation:

Let x,y and z represent the price of the item initially, after one month and after two months respectively.

Given that;

after one month its label price is reduced by 20%

y = x - 20% of x

y = x - 0.20x

y = 0.80x ........1

after 2 months its reduced price is further reduced by 10% and then sold it for Rs 15000.

z = y - 10% of y

z = y - 0.10y

z = 0.90y ........2

Substituting equation 1 into 2;

z = 0.90(0.80x)

z = 0.72x

Also z = Rs 15000

So,

z = 0.72x = Rs 15000

0.72x = Rs 15000

x = Rs 15000/0.72

x = Rs 20833.33333333

x = Rs 20,833.33

the value of x is Rs 20,833.33

Answer:

[tex](x+2)^2} +(y-1)^2}=5[/tex]

Step-by-step explanation:

[tex](x-h)^2} +(y-k)^2}=r^2[/tex]

r=[tex]\sqrt{5}[/tex]

h=-2

k=1

Plug in

[tex](x+2)^2} +(y-1)^2}=5[/tex]

Answer:

d on edginuity

Step-by-step explanation:

i know for a fun fact

Answer: the monthly​ payment is $192

Step-by-step explanation:

The cost of the new home entertainment system is $14230.

If the down payment is ​$2300, then the balance to be paid would be

14230 - 2300 = $11930

We would apply the periodic interest rate formula which is expressed as

P = a/[{(1+r)^n]-1}/{r(1+r)^n}]

Where

P represents the monthly payments.

a represents the amount of the balance

r represents the annual rate.

n represents number of monthly payments. Therefore

a = $11930

r = 0.05/12 = 0.0042

n = 72 months

Therefore,

P = 11930/[{(1+0.0042)^72]-1}/{0.0042(1 + 0.0042)^72}]

11930/[{(1.0042)^72]-1}/{0.0042(1.0042)^72}]

P = 11930/{1.352 -1}/[0.0042(1.352)]

P = 11930/(0.353/0.0056784)

P = 11930/62.125

P = $192

Answer:

(2, -2) are the coordinates of the point which divides BA into ration 2:4.

Step-by-step explanation:

The given two co-ordinates of A are (-2, 6) and B is (4, -6).

Let P be the point that divides the line BA into ratio 2:4.

to find coordinates of a point P on the line segment BA dividing it in a ratio 2:4, we can use segment formula.

[tex]x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}[/tex]

Where (x,y) is the co-ordinate of the point P which  

divides the line segment joining the points [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] in the ratio m:n.

Please refer to the attached image.

As per the given values :

[tex]x_{1} = 4\\x_{2} = -2\\y_{1} = -6\\y_{2} = 6\\[/tex]

Putting the given values in above formula :

x-co-ordinate of P:

[tex]x = \dfrac{4 \times 4 -2 \times 2}{4+2}\\\Rightarrow \dfrac{12}{6}\\\Rightarrow x = 2[/tex]

y-co-ordinate of P :

[tex]y = \dfrac{4 \times -6 +2 \times 6}{4+2}\\\Rightarrow \dfrac{-24+12}{6}\\\Rightarrow \dfrac{-12}{6}\\\Rightarrow y = -2[/tex]

So, answer is P(2, -2).