is {1, ...} a defined set

[tex]\\ \sf\longmapsto 1-(2x+4)=-4x+5[/tex]

[tex]\\ \sf\longmapsto 1-2x-4=-4x+5[/tex]

[tex]\\ \sf\longmapsto -2x-3=-4x+5[/tex]

[tex]\\ \sf\longmapsto -2x+4x=5+3[/tex]

[tex]\\ \sf\longmapsto 2x=8[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{8}{2}[/tex]

[tex]\\ \sf\longmapsto x=4[/tex]

Step-by-step explanation:

[tex]\Large \boldsymbol {} \sf 1-(2x+4)=-4x+5 \\\\1-2x-4=-4x+5 \\\\4x-2x=5+3 \\\\2x=8 \\\\\boxed{\sf x=4}[/tex]

Here we have a quadratic function and we want to find the value of a constant with a given restriction.

We will find that c = 8.

So we have the function:

[tex]f(x) = -2c + cx - x^2[/tex]

We know that:

[tex]f(5)^{-1} = -1 = \frac{1}{-2c + c\cdot 5 - (5)^2}[/tex]

Notice that the above equation means that:

[tex]-2c + c\cdot5 - (5)^2 = -1[/tex]

Then we just need to solve the above equation for c:

[tex]-2c + 5c - (5)^2 = -1\\\\(-2 + 5)\cdot c - 25 = -1\\\\3\cdot c = -1 + 25\\\\3\cdot c = 24\\\\c = 24/3 = 8[/tex]

So we found that the value of c is 8.

This means that the function is:

[tex]f(x) = -16 + 8\cdot x - x^2[/tex]

You can see the graph below:

If you want to learn more, you can read:

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In the diagram, ∠5 is adjacent to ∠EHD.

Angle

Angles are formed when two rays intersect at a point. An angle is also formed when to lines intersect each other, thereby the two lines share a common endpoint.

Adjacent angles are two angles that have a common side and a common vertex (corner point). They are placed side by side to each other.

In the diagram, ∠5 is adjacent to ∠EHD.

Find out more on Angle at: https://brainly.com/question/25770607

Answer:

10/27

Step-by-step explanation:

3^x = 10

We want to find 3^(x-3)

Rewriting

We know that a^(b-c) = a^b * a^ (-c)

3^x * (3^-3)

We know that 3^-3 = 1/3^3

3^x * 1/27

10 * 1/27

10/27

==========================================================

Explanation:

Average = (sum of scores)/(number of scores)

We can turn that equation into symbolic form to say

A = S/n

We're told that "18 students had an average of 80" (paraphrased) which means,

A = S/n

80 = S/18

80*18 = S

S = 1440

Those 18 students' scores add up to 1440.

For the other group of 40-18 = 22 students, their scores add to

S = A*n

S = 70*22

S = 1540

Overall, everyone's scores add up to 1440+1540 = 2980

Divide this over the number of people in class (40) to get the final answer

2980/40 = 74.5

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

Here's an alternative way to compute the answer

(18/40)*80 + (22/40)*70 = 74.5

This works because 18/40 of the class got an average of 80 while the remaining 22/40 of the class got an average of 70.

Answer:

15:4

Step-by-step explanation:

Multiply the fractions to get a common denominator. Multiply 3/4 by 5 and your get 15/20 and multiply 1/5 by 4 and you get 4/20. The numerators represent the ratio.

Answer:

[tex] {(x - y)}^{2} \\ = (x - y)(x - y)[/tex]

open the brackets:

[tex] = ( {x}^{2} - xy - xy + {y}^{2} ) \\ = {x}^{2} - 2xy + {y}^{2} [/tex]

Answer:

Step-by-step explanation:

The easiest way to explain this is to use slope and then writing equations for lines. The reason for that is because we are told that the production uniformly increases. That "uniform increase" is the rate of change, and since the rate of change is constant, we are talking about the slope of a line, where the rate of change is constant throughout the whole length of the line.

Create coordinates from the info given:

In the third year, 600 units were made. Time is always an x thing, so the coordinate is (3, 600). Likewise for the other bit of info. Time is always an x thing, so the coordinate is (7, 700). Applying the slope formula:

[tex]m=\frac{700-600}{7-3}=\frac{100}{4}=25[/tex]  which means that 25 units per year are produced. Write the equation to find the number of units produced in any year. I used the point-slope form of a line to do this:

y - 600 = 25(x - 3) and

y - 600 = 25x - 75 so

y = 25x + 525

If we want to know the number of units in the first year, we will replace x with 1 and do the math:

y = 25(1) + 525 so

y = 550 units, choice C.

Answer:

x=5

Step-by-step explanation:

-2(-3+ x) = -4

Distribute

-2 * -3 + (-2) *x = -4

6 -2x = -4

Subtract 6 from each side

6 -2x-6 = -4-6

-2x = -10

Divide each side by -2

-2x/-2 = -10/-2

x = 5

Answer:

5

Step-by-step explanation:

-2(-3+x)=-4

Use distributive property (Multiply -2 by -3 which gives you 6vand multiply -2 by x which gives you -2x )

6-2x=-4

Bring the 6 over to the other side

-2x=-4-6

-2x=-10

Divide both sides by -2 to get x by itself

x=5

Answer:

x=1

Step-by-step explanation:

log2( x^2 -x+2) = 1+2log2(x)

Rewriting 1 as log2(2)

log2( x^2 -x+2) = log2(2)+2log2(x)

We know that a log b = log a^b

log2( x^2 -x+2) = log2(2)+log2(x^2)

we know log a + log b = log (ab)

log2( x^2 -x+2) = log2(2*x^2)

Since the bases are the same the terms inside must be equal

x^2 -x+2 = 2x^2

Subtract 2x^2 from each side

-x^2 -x+2 = 0

Multiply by -1

x^2 +x-2 = 0

Factor

(x+2)(x-1)=0

Using the zero product property

x+2 = 0  x-1=0

x=-2  x=1

Checking the solutions

log2( x^2 -x+2) = 1+2log2(x)

X cannot be negative because 2 log2(x) cannot be negative

log2( 1^2 -1+2) = 1+2log2(1)

x=1

[tex]\\ \rm\Rrightarrow log_2(x^2-x+2)=1+2log_2x[/tex]

[tex]\\ \rm\Rrightarrow log_2(x^2-x+2)=log_22+2log_2x[/tex]

[tex]\\ \rm\Rrightarrow log_2(x^2-x+2)=2log_2(2x)[/tex]

[tex]\\ \rm\Rrightarrow log_2(x^2-x+2)=log_2(2x^2)[/tex]

[tex]\\ \rm\Rrightarrow x^2-x+2=2x^2[/tex]

[tex]\\ \rm\Rrightarrow x^2+x-2=0[/tex]

[tex]\\ \rm\Rrightarrow (x+2)(x-1)=0[/tex]

log is always positive so x=1

Laws used

2a , 1st exp= a2 + ab

= a(a+b)

2nd exp = a2-b2

= (a+b) (a-b)

HCF = (a+b)

b, 1 st exp= (a+b)2

= (a+b)(a+)

2 nd exp = a2-b2

= (a+b) ( a-b)

HCF = (a+b)

c, 1 st exp= (a-1)2

= (a+1) (a-1)

2nd exp= a2-1

= (a+1)(a-1)

HCF = (a-1)

d, 1st exp= (x-2)(x-3)

= x(x-3)-2(x-3)

= x2 - 3x - 2x + 6

= x2- 5x+ 6

= x2 - (3+2)x + 6

=x2 -3x-2x+ 6

= x(x-3) -2(x-3)

=(x-3)(x-2)

2 nd exp = (x+2) (x-3)

= x( x-3) + 2 (x-3)

= x2 - 3 x+ 2x -6

= x(x-3) + 2(x-3)

=(x-3) ( x+ 2)

HCF = (x-3)

Answer:

She is three years old.

Step-by-step explanation:

If she is 3, then six years from now she will be nine.

3 * 3 = 9

Answer:

C - 60

Step-by-step explanation:

4x^2 = 144

x = 6

p=10*6

P=60

Answer:

hi, thanks for asking! the answer to this question is, 108.

Step-by-step explanation:

first, you must think how much it adds up to if u add the numbers toghether. then, boom!

hope this helps<3

Answer:

4/6

Step-by-step explanation:

Im pretty sure***

but if a dice has 6 sides, and you have to get something less than 5, which is 1-4, which is 4 numbers, so 4 out of 6 total is 4/6

Answer:

sinF = [tex]\frac{11}{61}[/tex]

Step-by-step explanation:

sinF = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{EG}{FE}[/tex] = [tex]\frac{11}{61}[/tex]

The ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].

In a right angled triangle, the sine of an angle is the length of the side opposite the angle divided by the length of the hypotenuse.

sin θ = opposite side w.r.t θ / hypotenuse

According to the given question

We have

A right angle triangle EFG, in which

∠G = 90 degree

EG = 11

FE = 61

and,  GF = 60

Now, the opposite side with respect to ∠F is GE

and the hypotenuse is EF

Therefore, sine of ∠F = side which is opposite w.r.t ∠F/ hypotenuse

⇒ [tex]sinF=\frac{GE}{EF}[/tex]

⇒ [tex]SinF=\frac{11}{61}[/tex]

Hence, the ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].

Learn more about sine of an angle here:

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Answer:

Option C. bar graph is the answer.

Answer:

B

Step-by-step explanation:

The 2 triangles are similar, so the corresponding sides are in proportion, that is

[tex]\frac{DE}{XY}[/tex] = [tex]\frac{FD}{ZX}[/tex] , substitute values

[tex]\frac{DE}{9}[/tex] = [tex]\frac{8}{12}[/tex] ( cross- multiply )

12 DE = 72 ( divide both sides by 12 )

DE = 6 → B

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the amount invested at 3%. Then (x -500) is the amount invested at 2%, and 4x is the amount invested at 4%. The total interest income is ...

  0.02(x -500) + 0.03x + 0.04(4x) = 179

  0.21x -10 = 179 . . . . . simplify

  0.21x = 189 . . . . . . . . add 10

  x = 900 . . . . . . . . . . . divide by 0.21

  x -500 = 400

  4x = 3600

$400 is invested at 2%; $900 is invested at 3%, $3600 is invested at 4%.

Here Mass is constant

Using Newtons s law

[tex]\\ \sf \longmapsto F=ma[/tex]

[tex]\\ \sf \longmapsto \dfrac{F}{a}=m[/tex]

[tex]\\ \sf \longmapsto \dfrac{F_1}{a_1}=\dfrac{F_2}{a_2}[/tex]

[tex]\\ \sf \longmapsto \dfrac{8}{4}=\dfrac{F_2}{3}[/tex]

[tex]\\ \sf \longmapsto F_2=\dfrac{24}{4}[/tex]

[tex]\\ \sf \longmapsto F_2=6N[/tex]

Answer:

F = 6N

Step-by-step explanation:

Equation

F = ka

F - force

k - constant of proportionality

a - acceleration

Step 1 - find k  

8N=k*4m/s^2

k=2

Step 2 - find F

F=2*3m/s^s

F=6

Answer:

Card picked=2

P(factors of 28)={1,2,4,7,14,28}

total cards=4

in percentage=4 x 20 + 20

80+20=100

Therefore 2 in percentage will be

2 x 20 + 20

=40+20=60%

Answer:  5.8 (choice B)

=================================================

Explanation:

To find the length of the median, we add up the parallel sides and divide by 2. In other words, we're averaging the parallel sides to get the length of the midsegment shown.

FE = (WX + VY)/2

FE = (4.5 + 7.1)/2

FE = 11.6/2

FE = 5.8

Answer:

x>22

Step-by-step explanation:

Answer:

x > 22

Step-by-step explanation:

Given

52 - 3x < - 14 ( subtract 52 from both sides )

- 3x < - 66

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

x > 22

================================================

Explanation:

We'll step through the grade levels in increasing order

The teacher starts with 700 sour worms total. Then 2/7 of that is given to the Kindergartners

2/7 of 700 = (2/7)*700 = 200

So Ms. Mitchell handed out 200 worms to the Kindergartners.

This means she has 700-200 = 500 left over.

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

Now onto the 1st graders.

The teacher hands out 7/25 of the remaining total (500) to the first graders

7/25 of 500 = (7/25)*500 = 140

She hands out 140 worms to the first graders and has 500-140 = 360 worms left.

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

Now the 2nd graders

"Of the remaining worms, she gives 4/9 to the 2nd graders" tells us that

4/9 of 360 = (4/9)*360 = 160 worms are given to the second graders

This leaves 360-160 = 200 worms left

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

Now the 3rd graders

37/50 of 200 = (37/50)*200 = 148

The teacher hands out 148 worms to the 3rd graders

There are 200 - 148 = 52 worms left.

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

Finally, we're at the 4th graders

Each 4th grader gets the same number of worms (aka the amount is distributed equally). Since there are 52 worms left, and 13 fourth graders, this means each fourth grader gets 52/13 = 4 worms. It's a slightly interesting coincidence that the number '4' matches up with the grade level. It's possible your teacher adjusted the numbers to make this an intentional goal.

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

To recap everything, we found these worm counts for each grade level

Note how those values add back up to 700, ie 200+140+160+148+52 = 700. This helps confirm the answer.

Then once we see that 52 worms are left, each fourth grader gets 52/13 = 4 worms a piece.

So this is why the final answer is 4.

Answer:

Yes

Step-by-step explanation:

This equation does not factorise, so quadratic equation will be useful. It is easier than other methods that can be applied to this equation.

Answer:

Step-by-step explanation:

The length of the edge = x

Surface area:

Make note of the coefficients in the first and fourth equations. They've been conveniently picked so that subtracting one equation from the other eliminates every variable but t. We have

(3r + 2s + t + 2u + 3v) - (3r + 2s + 3t + 2u + 3v) = 7 - 17

-2t = -10

t = 5

Answer:

7.2

Step-by-step explanation:

Since the angle is equal, 24/(x+8.7)=13.1/8.7. x=7.2

Answer:

x ≈ 7.2

Step-by-step explanation:

Δ MNO and Δ MKL are similar, so the corresponding sides are in proportion, that is

[tex]\frac{MN}{MK}[/tex] = [tex]\frac{MO}{ML}[/tex] , substitute values

[tex]\frac{13.1}{13.1+10.9}[/tex] = [tex]\frac{8.7}{8.7 +x}[/tex]

[tex]\frac{13.1}{24}[/tex] = [tex]\frac{8.7}{8.7+x}[/tex] ( cross- multiply )

13.1(8.7 + x) = 208.8 ← distribute left side

113.97 + 13.1x = 208.8 ( subtract 113.97 from both sides )

13.1x = 94.83 ( divide both sides by 13.1 )

x = [tex]\frac{94.83}{13.1}[/tex] ≈ 7.2 ( to the nearest tenth )

Answer:

table:

.1, .25, .35, .2, .1

p(x=4) = .1

p(x<2) = .35

p(3≤x≤4)= .55

1.95, 1.12

Step-by-step explanation:

this is kind of hard to read, but i think i've got it

mean:

0*.1+1*.25+2*.35+3*.2+4*.1= 1.95

The second moment:

0²*.1+1²*.25+2²*.35+3²*.2+4²*.1= 5.05

the variance is the second moment minus the first moment squared (first moment is the mean) and then the standard deviation is the square root of the mean

5.05-1.95²= 1.2475 √1.2475= 1.1169 or 1.12