Shreya took 1/2 of a cake and shweta took 1/4 of the cake. What portion of the cake is left

Answer:

Domain: [tex]x > -5[/tex] or [tex](-5,\infty)[/tex]

Range: [tex]y\geq -3[/tex] or [tex][-3,\infty)[/tex]

Step-by-step explanation:

The domain is essentially the set of x-values in a given graph. In this graph. we see that the lowest x-value is an unfilled dot when x=-5. The unfilled dot means that the function [tex]f(x)[/tex] doesn't include -5. We then see that the x-value goes to positive infinity. This means that [tex]x[/tex] must be greater than -5. It is not greater or equal to -5 because the dot is not filled.

Therefore, we have that [tex]x > -5[/tex]. To convert to interval notation we can take the lower value (-5) and put it on the left side and put the higher value ([tex]\infty[/tex]) and put it on the right side. Since the graph doesn't include -5, we can put parentheses around both values to get [tex](-5,\infty)[/tex].

Note: We always put parentheses around both [tex]\infty[/tex] and [tex]-\infty[/tex].

The range is basically the same as the domain but with the y-value. We can see that the lowest y-value is y=-3. This includes -3 since the line fills the point in. Then we see that the highest y-value is once again positive infinity. This means that [tex]y\geq-3[/tex].

Now when we convert to interval notation, we have -3 and [tex]\infty[/tex]. This time since y=-3 is included in the function, we put a hard bracket around -3. Thus, we get [tex][-3,\infty)[/tex].

Hope this helps!

Answer:

Image 2: a segment from -4 to 4 with the endpoints excluded (with empty circles).

Step-by-step explanation:

|x| < 4 means "the distance from x to 0 is less than 4". That means that any number bigger than -4 and smaller than 4 matches the inequality from the question.

Side note: Please start analyzing the absolute values as "distance from 0" and you'll be able to solve those questions yourself with less effort.

Each part of the question is plotted on the number line as an image with the solution.

How are rational numbers represented on the number line?

(1)      [tex]\frac{-3}{8} , 1\frac{1}{5} = \frac{6}{5} = 1.2 , \frac{-3}{4}[/tex]  are plotted on the number line as an image with the solution.

(2) -13+15+(-8) = -6 is plotted on the number line as an image with the solution.

(3) [tex]\frac{3-(-14)}{7} = \frac{17}{7} = 2.429, \frac{-36+58}{-11} = -2[/tex] are plotted on the number line as an image with the solution.

Learn more about number line here:

https://brainly.com/question/24644930

#SPJ9

The  linear inequality will have a solution of (0,0) is y<-2x and y>-3x.

Option (A) and (D) is correct.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.

According to given question we have

a. y<-2x

To put the value of x any y (0,0) we get

=0<-2*0

=0<0

b. y<-3x+4

To put the value of x any y (0,0) we get

=0<-3*0+4

=0<0+4

=0<4

c. y>-2x+6

To put the value of x any y (0,0) we get

=0>-2*0+6

=0>0+6

=0>6

d. y>-3x

To put the value of x any y (0,0) we get

=0>-3*0

=0>0

Therefore, the  linear inequality will have a solution of (0,0) is y<-2x and y>-3x.

Learn more details about inequality here:

https://brainly.com/question/20383699

#SPJ1

Answer: x=0.5, y=1

Step-by-step explanation:

-4x+3y=1

6x-y=2

6x-2=y

-4x+3(6x-2)=1

-4x+18x-6=1

-4x+18x=7

14x=7

x=0.5

6x-y=2

6(0.5)-y=2

3-y=2

y=1

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Answer:

4/5

Step-by-step explanation:

8/10

=4/5

Answer:

8/9!!

all credit goes entirely to the person in comments for giving us all the right answer.

Quadratic equations are all those equations that can be reformulated in a standard format (αx² + bx + c(=0) where the value of x is unknown and the values of the coefficients (a, b and c) are unknown.

These equations can always be solved using the quadratic formula, although sometimes it is also possible to use factorization or isolation of variables.

Expand squared

It is distributed

Combine like terms.

Move terms to the left

Subtract the numbers

Use the quadratic formula.

                        [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a} \end{gathered}$}[/tex]

In standard form we identify "a", "b" and "c" from the original equation and add to the quadratic formula.

                      [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-(-14)\pm\sqrt{(-14)^{2}-4\cdot1\cdot41 } }{2\cdot1} \end{gathered}$}[/tex]

Simplify

                                         [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14\pm4\sqrt{2} }{2} \end{gathered}$}[/tex]

Separate equations

To solve for the unknown variants, we split the equation into two: one with a plus sign and the other with a minus sign.

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14+4\sqrt{2} }{2} \end{gathered}$}[/tex]

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{14-4\sqrt{2} }{2} \end{gathered}$}[/tex]

Solve

Order and isolate the variant to find each solution.

                                            [tex]\large\displaystyle\text{$\begin{gathered}\sf x=7+2\sqrt{2} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x=7-2\sqrt{2} \end{gathered}$}[/tex]

                            [tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\blue{Answer \ \ \longmapsto \ \ x=7\pm2\sqrt{2} }} \end{gathered}$}}}[/tex]

Answer: To the right

Step-by-step explanation:

The negatives on a number line are on the left side and the positives on the right.

Step-by-step explanation: educated guess

The modified equation is expressed as g(x) = x^2 - 6

Translation is the process of changing the position on an x-plane.

Given the function of a graph expressed as y=x^2

If the function is shifted 6 units to the left, hence the resulting function is given as;

g(x) = x^2 - 6

Hence the modified equation is expressed as g(x) = x^2 - 6

Learn more on translation here; https://brainly.com/question/12861087

#SPJ1

Step-by-step explanation:

photo please ......................

Answer:

Step-by-step explanation:

need to see the graph

Step-by-step explanation:

It's simple in the following diagram ( 13x + 45)° + (19x +3)° won't be equal to 180° as they are vertically opposite angle...... and are vertically opposite to each other...

So to find the value of x :

13x + 45° = 19x + 3°

13x - 19x = 3 - 45

-6x = - 42

x = -42 / -6

x = 7°

☘☘☘...

Functions and their domains of all the subparts are:

So,

(A) (fog)(x) and domain:

[tex](f \circ g)(x)=f(g(x))=(g(x))^2+g(x)=\left(x^2+14 x+2\right)^2+x^2+14 x+2\\=x^4+28 x^3+200 x^2+56 x+4+x^2+14 x+2=x^4+28 x^3+201 x^2+70 x+6[/tex]

The domain of (fog)(x) is the collection of domain values for g(x) with range values in the domain of f(x).

Because both functions are polynomials, the domain is [tex](-\infty, \infty)[/tex].

(b) (gof)(X) and domain:

[tex](g \circ f)(x)=g(f(x))=(f(x))^2+14(f(x))+2=\left(x^2+x\right)^2+14\left(x^2+x\right)+2\\=x^4+2 x^3+x^2+14 x^2+14 x+2=x^4+2 x^3+15 x^2+14 x+2[/tex]

The domain name is [tex](-\infty, \infty)[/tex] because this is a polynomial composition.

(c) (fof)(x) and domain:

[tex]\begin{aligned}&(f \circ f)(x)=f(f(x))=(f(x))^2+f(x)= \\&\left(x^2+x\right)^2+x^2+x=x^4+2 x^3+x^2+x^2+x=x^4+2 x^3+2 x^2+x\end{aligned}[/tex]

Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].

(d) (gog)(x) and domain:

[tex](g \circ g)(x)=g(g(x))=(g(x))^2+14(g(x))+2=\left(x^2+14 x+2\right)^2+14\left(x^2+14 x+2\right)+2\\=x^4+28 x^3+200 x^2+56 x+4+14 x^2+196 x+28+2=x^4+28 x^3+214 x^2+252 x[/tex]

Because this is a polynomial composition, the domain is [tex](-\infty, \infty)[/tex].

Therefore, functions and their domains of all the subparts are:

Know more about functions here:

https://brainly.com/question/25638609

#SPJ4

The complete question is given below:
Find the functions and their domains. (enter the domains in interval notation.)

[tex]f(x)=x^2+1 x, g(x)=x^2+14 x+2[/tex]

(a) (fog)(x) and domain

(b) (gof)(X) and domain

(c) (fof)(x) and domain

(d) (gog)(x) and domain

The values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1

The functions are given as:

f(x) = 2x^2 - 9x - 5

g(x) = x - 5

The composite function (f.g)(x) is calculated as

(f.g)(x) = f(x) * g(x)

This gives

(f.g)(x) = (2x^2 - 9x - 5) * (x - 5)

Evaluate the product

(f.g)(x) = 2x^3 - 9x^2 - 5x - 10x^2 + 45x + 25

Evaluate the like terms

(f.g)(x) = 2x^3 - 19x^2 + 40x + 25

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

This gives

(f/g)(x) = (2x^2 - 9x - 5)/(x - 5)

Factorize the numerator

(f/g)(x) = (2x + 1)(x - 5)/(x - 5)

Evaluate the quotient

(f/g)(x) = 2x + 1

Hence, the values of the composite functions are (f.g)(x) = 2x^3 - 19x^2 + 40x + 25 and (f/g)(x) = 2x + 1

Read more about composite functions at

https://brainly.com/question/13502804

#SPJ1

Solving a system of equations we can see that we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

Let's define the variables:

We know that we want to make 200ml, then:

x  + y = 200

And the concentration of these 200ml must be of 68%, then the concentrations in the left side and in the rigth side must give the same value, so we can write:

x*0.5 + y*0.8 = 200*0.68

(the concentrations are written in decimal form)

Then we have the system of equations:

x  + y = 200

x*0.5 + y*0.8 = 200*0.68

To solve it we start by isolating x in the first equation:

x = 200 - y

Replacing that in the other equation we get:

(200 - y)*0.5 + y*0.8 = 200*0.68

Now we can solve this for y, we will get:

100 - y*0.5 + y*0.8 = 136

y*0.3 = 136 - 100 = 36

y = 36/0.3 = 120

So we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

The surface area and the volume of the triangular prism are 26.88 square cm and 7.68 cubic cm.

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

It is given that:

The triangular prism is given in the picture:

The surface area = 4x2 + 2x2.4 + 3.2x2 + 2(1/2)3.2x2.4

The surface area = 8 + 4.8 + 6.4 + 7.68

The surface area = 26.88 square cm

The volume = (1/2)x3.2x2x2.4

The volume 7.68 cubic cm

Thus, the surface area and the volume of the triangular prism are 26.88 square cm and 7.68 cubic cm.

Learn more about triangular prisms here:

brainly.com/question/16909441

#SPJ1

Answer:--------X=3/13---------

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

Every fifth car would be 1/5 or 20%

Answer:

x² + (y + 3)² = 25

Step-by-step explanation:

the centre (C) of the circle is at the midpoint of the diameter.

using the midpoint formula

midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

with (x₁, y₁ ) = P (3, 1 ) and (x₂, y₂ ) = Q (- 3, - 7 )

C = ( [tex]\frac{3-3}{2}[/tex] , [tex]\frac{1-7}{2}[/tex] ) = ( [tex]\frac{0}{2}[/tex] , [tex]\frac{-6}{2}[/tex] ) = (0, - 3 )

the radius r is the distance from the centre to either P or Q

using the distance formula

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

with (x₁, y₁ ) = C (0, - 3 ) and (x₂, y₂ ) = P (3, 1 )

r = [tex]\sqrt{(3-0)^2+(1-(-3)^2}[/tex]  

 = [tex]\sqrt{3^2+(1+3)^2}[/tex]

 = [tex]\sqrt{3^2+4^2}[/tex]

 = [tex]\sqrt{9+16}[/tex]

 = [tex]\sqrt{25}[/tex]

 = 5

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (0, - 3 ) and r = 5 , then

(x - 0 )² + (y - (- 3) )² = 5² , that is

x² + (y + 3)² = 25

The mean of the data is 30 and the median of the data is 27.5.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data. The mean of the data will be calculated by adding all the numbers and dividing it by the quantity of the numbers.

The median of the data generally refers to the middle most value of the series. The median of the data is calculated by arranging the numbers in increasing order and getting the middle value of the numbers.

Given data is 26, 29, 27, 28, 29, 27, 27, 53, 25, 29 arrange all the numbers in increasing order.

25,26,27,27,27,28,29,29,29,53

Mean = Sum of all the numbers / Total numbers

Mean =  (25 + 26 + 27 + 27 + 27 + 28 + 29 + 29 + 29 + 53 ) / 10

Mean = 300 / 10

Mean = 30

Median = ( 27 + 28 ) / 2 = 27.5

Therefore, the mean of the data is 30 and the median of the data is 27.5.

To know more about mean and median follow

https://brainly.com/question/6281520

#SPJ4

Answer: 125

Step-by-step explanation:

The total number of matches played is 552.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

The given parameters are as;

Teams = 24

Matches against each other = 2

Therefore, the total number of matches played is;

Total = Teams * (Teams - 1)

This gives;

Total = 24 * (24 - 1)

Evaluate;

Total = 552

Hence, the total number of matches played is 552.

Read more about combination at:

brainly.com/question/11732255

#SPJ2

Answer:$976

Step-by-step explanation:

If the quadratic is y = a*x^2 + b*x + c

the coordinates of the vertex are:

x = -b/2a

y = (1/2a)*( -0.5*b^2 + c)

For a quadratic equation in standard form:

y = a*x^2 + b*x + c

The x-value of the vertex is given as:

x = -b/2a

Once we get the x-value of the vertex, we can get the y-value by evaluating the quadratic equation in x = -b/2a, we will get:

y = a*(-b/2a)^2 + b*(-b/2a) + c

y = b^2/(4a) - b^2/2a + c = (1/2a)*(b^2/2  - b^2 + c)

y = (1/2a)*( -0.5*b^2 + c)

Then the coordinates of the vertex are:

x = -b/2a

y = (1/2a)*( -0.5*b^2 + c)

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

Answer:

1013

Step-by-step explanation:

(6)(7)(8−0)(3)+5

=42(8−0)(3)+5

=(42)(8)(3)+5

=(336)(3)+5

=1008+5

=1013

Answer:

D. 491.52

Step-by-step explanation:

Answer: -4 because 2(-6)2 = -24 and 5(2)2 = 20 so -24 + 20 is -4.

Answer:-4

Step-by-step explanation:

2(-6)2

2 x -6 x 2=-24

5 x 2 x 2=20

-24+20=-4

The population density of Singapore in residents per square kilometer is 8266.12 per square kilometer

What is Population Density ?

The given parameters are

Number of people = 21400 residents

Area = 1 mi²

Convert the square mile to square kilometer

1 x 1.609² = 2.588881 Km²

Population density = Number of residents ÷ area

Population density = 21400 ÷ 2.588881

Population density = 8266.12 per square kilometer

Therefore, the population density of Singapore in residents per square kilometer is 8266.12 per square kilometer

Learn more about Population Density

brainly.com/question/1581160

#SPJ4

Answer:

¹/₄

Step-by-step explanation:

Given:

The dessert is the "whole", i.e. equal to 1.

To find how much of the dessert was left, subtract all the given portions from 1:

[tex]\begin{aligned}\textsf{Dessert left for Sara} & = 1-\dfrac{1}{8}-\dfrac{1}{4}-\dfrac{3}{8}\\\\& = \dfrac{8}{8}-\dfrac{1}{8}-\dfrac{2}{8}-\dfrac{3}{8}\\\\& = \dfrac{8-1-2-3}{8}\\\\& = \dfrac{2}{8}\\\\& = \dfrac{1}{4}\end{aligned}[/tex]

Therefore, ¹/₄ of the dessert was left for Sara.

Answer:

2/8 (or) 1/4

Step-by-step explanation:

The amount of desert she served is,

→ 1/8 + 1/4 + 3/8

→ (1 + 2 + 3)/8

→ 6/8

Then amount of desert left for Sara is,

→ 1/1 - 6/8

→ (8 - 6)/8

→ 2/8 (or) 1/4

Hence, she was left with 2/8 of desert.

Answer:

Step-by-step explanation:

first let : x = 3 and y = 5

so x-3 means 3-3 = 0

and 2y means 2 * 3 = 6

therfore x-3 > 2y means 0 > 6, false