A family is comparing different car seats. One car seat is designed for a child up to and including 26 lb. Another car seat is designed for a child between 18 lb and 40 lb. A third car seat is designed for a child between 25 lb and 75 ​lb, inclusive. Model those ranges with compound inequalities. Which car seats are appropriate for a ​33-lb ​child? The inequality for a child up to and including 26 lb is ________.

Answer:

The sum of all internal angles of this polygon is: [tex]900^o[/tex]

Step-by-step explanation:

Recall that the formula for the number of diagonals of a polygon with n-sides is given by the formula:

[tex]diagonals=\frac{n\,(n-3)}{2}[/tex]

and since Lucero noticed that the number of digonals was 7 more that the number of sides, then, these two quantities (n + 7) and the number of diagonals must be equal. we can set an equation stating such, and solve for "n" (number of sides of the polygon):

[tex]n+7=\frac{n\,(n-3)}{2} \\2(n+7)=n(n-3)\\2\,n+14=n^2-3\,n\\n^2-3\,n-2\,n-14=0\\n^2-5\,n-14=0\\(n-7)\,(n+2)=0\\[/tex]

therefore n = 7 or n = -2

The only answer with meaning is the first one (7 sides), since a polygon must have a positive number of sides.

Now that we know the number of sides of the polygon, we can find what the sum of its internal angles should give, based on the equation;

Addition of internal angles of a polygon is = [tex](n-2)\,180^o[/tex]

Which in our case renders:

[tex](n-2)\,180^o=(7-2)\,180^o= 5\,(180^o) = 900^o[/tex]

Answers:

Step-by-step explanation:

A linear function must be straight. It can have a slope, but it must not curve.

___________________________________________________________

Answer: 1.41421356237 in a short answer it would be 1.4

Step-by-step explanation:

Answer:

2.54 and 0.393 :))))))

Answer:

✔ 1 3/32 in

inches

✔ 2.78 cm

centimeter

Step-by-step explanation:

edge 2023

Answer:

u + c = 6

Step-by-step explanation:

u² - c² ← is a difference of squares and factors as

u² - c² = (u - c)(u + c) = 36 , thus

6(u + c) = 36 ( divide both sides by 6 )

u + c = 6

Step-by-step explanation:

Odd numbers from the list are 75, 189, and 315.

75, 189, and 315, are composite numbers.

Prime factorization of 75 = 3 × 5 × 5

Prime factorization of 189 = 3 × 3 × 3 × 7

Prime factorization of 315 = 3 × 3 × 5 × 7

315 is an odd number, and a composite number that is divisible by 3 different prime numbers.

The correct answer would be Option D 315

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into other numbers. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Numbers that have more than two factors are called composite numbers.

Given here: The number must be odd and has three prime factors

In option D 315 its prime factorization is 315=3²×5×7

It has 3 different prime factors 3,5,7 and thus option D is the correct answer.

Hence, The correct answer would be Option D 315

Learn more about prime numbers here:

https://brainly.com/question/4184435

#SPJ2

Answer:

29 ml

Step-by-step explanation:

Vcube = 1cm×1cm×1cm = 1 cm³

1 cm³ = 1 ml

If this cube is dropped into a 28ml of water the new reading will be 29 ml.

hope this helped :)

Answer:

50°

Step-by-step explanation:

Transformation is the movement of one point from its initial location to a final location. If an object is transformed, all its points are transformed. Types of transformation is reflection, dilation, rotation and translation.

If an object is translated, it maintains its shape and size as well as the length of its sides and angles, only the location changes.

If polygon LMNP with ∠M of 50° is translated 5 units right and 4 units down to a new point, M' has the same angle measure. Hence ∠M' = 50°

Answer:

Step-by-step explanation:

Given the average low temperature by month in Nashville is represented by the function  f(x)=-1.4x² + 19x +1.7, where x is the month, the average rate of change is expressed as d[f(x)]/dx = 2(1.4x) + 19

d[f(x)]/dx  = 2.8x + 19

Since the number of months between March and August is 5 months and x is in months, hence we will substitute x = 5 into the resulting function to get  the average rate of change from March to  August as shown;

d[f(x)]/dx  at x = 5

= 2.8(5)+ 19

= 14 + 19

= 33

Hence the average rate of change from March to August is 33

Solution:

The point C' of the image coincides with point E of the preimage and D' of the image coincide with the point F of the preimage.

Explanation:

The regular hexagon have 6 corner points ABCDEF.

The complete angle about the center  because it is a close figure as shown in given figure. It means the line from two consecutive vertices to the center of hexagon make an angle of  because 6 lines from the vertices to the center divides the center angle in 6 equal parts.

It is given that the hexagon is rotated at  counterclockwise about the center, therefore the image of vertices shifts 4 places counterclockwise.

In figure first hexagon show preimage and second hexgon shows image. From figure it is noticed that the point C' of the image coincides with point E of the preimage and D' of the image coincide with the point F of the preimage.

therefore, the point C' of the image coincides with point E of the preimage and D' of the image coincide with the point F of the preimage.

Answer:

E = First Blank

F= Second Blank

Answer:43

Step-by-step explanation:

Answer:

The best option is the first one. It provides a higher present value.

Step-by-step explanation:

Giving the following information:

Option 1:

Receive $15,000,000 today.

Option 2:

Receive $1,000,000 for 30 years.

Discount rate= 7% compounded annually

To compare both options, we need to calculate the present value of Option 2. The option with the higher present value is the most convenient.

Option 2:

First, we need to determine future value:

FV= {A*[(1+i)^n-1]}/i

A= annual cash flow

FV= {1,000,000*[(1.07^30) - 1]} / 0.07

FV= $94,460,786.32

Now, the present value:

PV= FV/(1+i)^n

PV= 94,460,786.32 / (1.07^30)

PV= $12,409,041.18

The best option is the first one. It provides a higher present value.

Answer:

4n+13

Step-by-step explanation:

Answer:

4n+13

Step-by-step explanation:

group all the like terms together to get 5n-4n+3n= n+3n= 4n, and group 3+10 together to get 13. the finished answer should be 4n+13

Answer:

[tex]\frac{1}{3} x-2[/tex]

Step-by-step explanation:

Answer:

y=1/3x-2

Step-by-step explanation:

HOPE THIS HELPS!!!! :)

<3333333333

Answer:

answer is 25

Step-by-step explanation:

x+2+153=180

x+155=180

x=180-155

x=25

hope this helps :)

Answer:

x=-13

Step-by-step explanation:

divide each term by -7 and simplify I think I hope that works let me know if it's not right

Answer:

x = 23

y = 157

Step-by-step explanation:

3x  = x + 46 (outside angle of triangle theorem)

x + y = 180 (same side interior angles theorem)

<=>

2x = 46

x + y = 180

<=>

x = 23

y = 157

Answer:

The notation "f(x)" is exactly the same thing as "y"

Step-by-step explanation:

The effect of using f(x) instead of y is that it allows us to talk about f.

If we have an equation relating X to Y then that's a relationship between rwo nimbers.

For example if you have that y=

[tex]y = {x}^{3} [/tex]

...then that means that X and Y are some numbers obeying that equation

Answer:

Solution : Option A and Option C

Step-by-step explanation:

To find the values of x that are not present in the domain, we can start by making the denominator equal to 0. This would make the fraction undefined, and hence will solve for the value(s) of x that do not belong to the function -

x² - 3x - 10 = 0,

(x + 2)(x - 5) = 0,

x = - 2 and x = 5

Domain {x | x ≠ - 2 ≠ 5 }

Hence our solution(s) are option a and option c

Answer:

[tex]\huge \boxed{x=5 \ \mathrm{and} \ x=-2}[/tex]

Step-by-step explanation:

The domain of a function are all possible values for x.

To find the domain of a rational function, we set the denominator equal to 0, and solve for x. Those values of x are not included in the domain, since the denominator of 0 would make the rational function undefined.

[tex]x^2-3x-10 =0[/tex]

Factoring left side of the equation.

[tex](x+2)(x-5)=0[/tex]

Setting the factors equal to 0.

[tex]x+2=0 \\ \\ x=-2 \\ \\ \\ \\ x-5=0 \\ \\ x=5[/tex]

The values of x that are not in the domain of the rational function are x = -2 and x = 5.

Answer:

5.48

Step-by-step explanation:

big number - little number

Answer:

5.48

Step-by-step explanation:

32.45 - 26.97

Answer:

[tex](-1,2,-1)[/tex]

Step-by-step explanation:

we already know that c= -1

we can substitute in 4b + c =7

[tex]4b+(-1)=7\\\\4b-1=7\\\\4b=7+1\\\\4b=8\\\\b=2[/tex]

we can substitute in a + b -5c = 6

[tex]a+(2)-5(-1)=6\\\\a+2+5=6\\\\a+7=6\\\\a=6-7\\\\a=-1[/tex]

so it is

[tex](-1,2,-1)[/tex]

Answer:

The Domain should be (10,+infinity) as x>10

Step-by-step explanation:

Answer:

55.

Step-by-step-explanation:

In a velocity/time graph like this the total displacement is the area of the body.

This is the area of (from left to right) of triangle OBF + area of the 2 rectangles + area of triangle CDE

Here this is 1/2 * 2 * 5 + 5 *4 + 5 * 4 + 1/2 * 5 * 4

= 5 + 20 +  20 + 10

= 55.

Answer:

55

Step-by-step explanation:

The displacement is the area under the line

The are comprises of

So the area is:

Answer:

Option D

Step-by-step explanation:

A function is a relation where each domain is assigned to exactly one range value.

In the relation given, the value of '-2' is repeated and assigned with two range numbers.

Therefore, the relation is not a function because -2 is paired with two range values.

Answer:

plane WRT

Step-by-step explanation:

Answer:

5a  

2

+4ab+5b  

2

Step-by-step explanation:

step  1. (((0-(4•(a2)))+3ab)+(12•(b2)))+(((9•(a2))+ab)-7b2)

 step 2. (((0-(4•(a2)))+3ab)+(12•(b2)))+((32a2+ab)-7b2)

step 3.(((0-(4•(a2)))+3ab)+(22•3b2))+(9a2+ab-7b2)

step 4. (((0-(4•(a2)))+3ab)+(22•3b2))+(9a2+ab-7b2)

step 5. 5.1    Factoring    5a2 + 4ab + 5b2

Answer: 14 gallons of the 64% acid solution is needed

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

Work Shown:

x = amount, in gallons, of the 64% acid solution

0.64x = amount of pure acid from the stuff we're adding in

0.38*12 = 4.56 = amount of pure acid from 38% solution

In total, we have 0.64x+4.56 gallons of pure acid out of x+12 gallons total

Dividing the two amounts will give us the decimal form of the percentage. Set this equal to 0.52 and solve for x

-----------

(0.64x+4.56)/(x+12) = 0.52

0.64x+4.56 = 0.52(x+12)

0.64x+4.56 = 0.52x+6.24

0.64x-0.52x = 6.24-4.56

0.12x = 1.68

x = 1.68/0.12

x = 14 gallons is the amount of the 64% acid solution we need to add in

Answer:

Step-by-step explanation: