Factor the polynomial 3x4 – 2x2 15x2 – 10 by grouping. which product is the factored form of the polynomial? (–x2 – 5)(3x2 2) (x2 – 2)(3x2 5) (x2 5)(3x2 – 2) (3x2 – 5)(x2 2)

Answer:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

option ( c ) [tex]\huge\pink{1 \frac{2}{5} }[/tex]

step by step explanation -

well , the question asks us to find the difference between the two terms given as mixed fractions ~

tho it's not that difficult to simplify a problem in mixed fraction , but solving the problem by first converting it to an improper fraction reduces the risk of mistakes ! so let's do the question by that way ~

[tex]4 \frac{4}{5} - 3 \frac{2}{5} \\ \\ converting \: into \: improper \: fraction \: we \: get \\ \\ \implies \: \frac{5 \times 4 + 4}{5} \: \: - \: \: \frac{5 \times 3 + 2}{5} \\ \\ \implies \: \frac{24}{5} \: \: - \: \: \frac{17}{5} \\ \\ since \: the \: denominators \: are \: same \: we \: can \: simply \: subtract \: the \: terms \\ \\ \implies \: \frac{7}{5} [/tex]

we're done with our solution tho , but since the options given are in mixed fraction , so let's convert the improper fraction , obtained as the answer , into a mixed fraction !

[tex] \frac{7}{5} = 1 \frac{2}{5} \\ [/tex]

hope helpful :D

Answer:

1 2/5

Step-by-step explanation:

subtract it and then add it and u will have your answer

Answer:

a rotation followed by a translation

Step-by-step explanation:

i did it

The rotation is followed by a translation.

We have given that,

a glide reflection

a rotation followed by a translation

a rotation followed by a reflection

reflection followed by a translation

We have to determine the tessellation below, and what transformation(s) maps Brick A onto Brick B.

Rotation is the circular movement of an object around an axis of rotation. A three-dimensional object may have an infinite number of rotation axes.

Therefore the rotation is followed by a translation.

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Answer:

8:18

Step-by-step explanation:

Answer:

Step-by-step explanation:

Trignomentary - real life problem.

We can find the height of the tower without measuring it. WE can find the height  of the tower when we know,

1.  A point which at a distance 'x' from the foot of the tower.

2. The angle of elevation is known  

Eg: A tower stands vertically on the ground. From a point on the ground which is 15 m away from the foot of the tower, the angle of elevation  of the top of the tower is 60°. Find the height of the tower.

AB - tower

We know the adjacent side of 60°  and we have to fing the opposite side of 60°. So, we have to use

[tex]\sf \ Tan \ 60^\circ=\dfrac{Opposite \ side \ of \ 60^\circ}{Adjacent \ side \ of \ 60^\circ}[/tex]

[tex]1.732 = \dfrac{AB}{BC}\\\\1.732=\dfrac{AB}{15}\\\\1.732*15=AB[/tex]

AB = 25.98 m

Height of the tower ≈ 26 m

Answer:

>

Step-by-step explanation:

1 mile =1760 yards

so 3 mile= 1760x3=5280yard

so, 5280 yards is more than 5000 yards

Answer:

357.5ft^3

Step-by-step explanation:

solve for bottom reticular prism

8 * 10 * 4

320ft^3

solve for top triangular prism

((3*5)/2)*5

37.5ft^3

add top and bottom  

320+37.5

357.5ft^3

Answer: 268ft^3

Step-by-step explanation: To solve, find the area of each side and add them all together.

8*4=32*2=64

10*4=40*2=80

10*5=50*2=100

8*3/2=12*2=24

64+80+100+24=268

Hope I helped <3

Answer:

5

Step-by-step explanation:

70% is 0.7, multiply 0.7×50=35 points on Jenny's test. Hannah scored 0.8×50=40 points on the test. Subtract 40-35 for the answer of 5

Answer:

  (-1.570796, 0.666239) ∪ (1.570796, 2.475353)

Step-by-step explanation:

A graphing calculator can give you the numerical values that limit the intervals of the solution. The attachment shows this solution.

__

We can multiply by cos(x) and solve the resulting quadratic inequalities. Two cases arise:

  tan(x) -cos(x) < 0 . . . . . . subtract cos(x)

  sin(x) -cos(x)² < 0 . . . . . . . for cos(x) > 0

  sin(x) -cos(x)² > 0 . . . . . . . for cos(x) < 0 (inequality is reversed)

Replacing cos(x)² with (1 -sin(x)²) gives quadratic equations in sin(x). (We're using <> to mean "could be greater than; could be less than, depending on cos(x)".)

  sin(x) -(1 -sin(x)²) <> 0

  sin(x)² +sin(x) -1 <> 0 . . . . put in standard form

  (sin(x)² +sin(x) +1/4) -1 -1/4 <> 0 . . . . complete the square

  (sin(x) +1/2)² -5/4 <> 0 . . . . . write as a square

  ((sin(x) +1/2)-√(5/4))·((sin(x) +1/2) +√(5/4)) <> 0 . . . . factor

Note that the second factor is always positive, so it has no impact on the intervals of solution.

__

The zeros of the first factor are located at ...

  sin(x) = 1/2(-1 +√5)

  x ≈ 0.666239 radians, and π - 0.666239 radians ≈ 2.475353 radians

The sine function will be positive between these angle values.

__

However, the intervals of solution to the inequality depend on the cosine function. Effectively, the solution space is where  (sin(x) +(1-√5)/2) and cos(x) have opposite signs.

The cosine function is positive for -π/2 < x < π/2, so one of the intervals of solution will be ...

  -π/2 < x < arcsin((√5 -1)/2), approximately (-1.570796, 0.666239)

The cosine function is negative for -π < x < -π/2 and for π/2 < x < π. The other interval of solution will be ...

  π/2 < x < (π -arcsin((√5 -1)/2)), approximately (1.570796, 2.475353)

_____

Additional comment

In the above, we have used α=arcsin( ) to mean the values of angle in the principal branch: -π/2 ≤ α ≤ π/2. That is why we have to subtract it from π to find the other end of the interval of interest.

Answer:

anwer 9$ and hour

Step-by-step explanation:

9×8=72

9+5=14

14×3=42

42+72=114

Answer:

x^2 + 14x + 57 = 0

Step-by-step explanation:

(x+5)^2+4(x+5)+12 = 0

x^2 +10x + 25 + 4x + 20 + 12 = 0

x^2 + 14x + 57 = 0

I think it’s -2(-2x + 3y) but I am unsure because I got -4 instead of 4

Step-by-step explanation:

Answer:

Yo espero yo ayuda tu résolve estes équations

Step-by-step explanation:

a) x=8

b) x=-7

c) x=5,1

d) x=5/4

e) x=-3

f) x=5

Lo siento, mi español no son muy bien.

The equation of the function which is graphed on the right is specified by: Option C: y = 2^{x-2} + 3

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

Since there is no graph available, we will work with the image attached below.

The function, as visible is tending to output 3 and x goes more and more negative.

That means:

[tex]\lim_{x\rightarrow -\infty}f(x) = 3[/tex] (assuming the predicted pattern is true).

Checking this for all the options:

Case 1: [tex]y = f(x) = 2^{x+3} - 2[/tex]

[tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x+3} -2 = -2[/tex]
Thus, the graph doesn't belong to this function.

Case 2: [tex]y = f(x) = 2^{x-3} + 2[/tex]

[tex]\lim_{x\rightarrow -\infty} f(x) = \lim_{x\rightarrow -\infty}2^{x-3} + 2 = 2[/tex]
Thus, the graph doesn't belong to this function.

Case 3: [tex]y = f(x) = 2^{x-2} +3[/tex]

[tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x-2} +3 = 3[/tex]
Thus, the graph may belong to this function. (we are still not sure since the last option may also have same limit, which if is found to be true, then additional findings would've to be done too).

Case 4: [tex]y = f(x) = 2^{x-2} - 3[/tex]

[tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x-2} -3 = -3[/tex]
Thus, the graph doesn't belong to this function.

Thus, assuming at least one option is true, the graph of the considered function on the right is of the function [tex]y = f(x) = 2^{x-2} +3[/tex]

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Answer:

c

Step-by-step explanation:

Answer:

A.

Divide each dimension by scale factor of 5

Big Δ dimensions : Small Δ dimensions

35 : 7

30 : 6

15 : 3

a = 7 in

b = 6 in

c = 3 in

Hope this helps and God bless!

Answer: 6x^2

Step-by-step explanation:

Answer:

The answer is 10 and i know because im smart

Step-by-step explanation:

because im smart

Answer:

24

Step-by-step explanation:

add 8 and 12 and 4 and its 24

Answer:

[tex]c + c \: + 40 + 12 = 100 \\ 2c + 52 = 100 \\ 2c = 100 - 52 \\ 2c = 48 \\ c = \frac{48}{2} \\ c = 24cm[/tex]

Answer: 24

Explanation: 12+40 is 52, perimeter is adding up all the sides. since perimeter is 100, then you have to see what numbers you add to get 100. 100-52 is 48. since there are 2 sides, you divide 48 by 2, which is 24.

I hope this is helpful xx

Answer:

L=93

Step-by-step explanation:

So basically you need to know the formula beforehand the formula to find the length of a rectangle what is P=2(l+w) so to find for L the equation will be L=P/2-W=294-54=93 Therefore 93 is L

The expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

We're given that:

Then we have:

y = time on math homework + history homework

y = 2 +2 +2 ... (x times) + 20 minutes

[tex]y = 2x + 20[/tex]

x is "number of math problems". Thus, x can be 0,1,2,... These numbers are called non-negative integers(or integers greater or equal to 0) or whole numbers.

y is the time taken, but we see that

y = 2 times (non-negative integer) + 20

y = positive integer times non-negative integer + positive integer

Thus, we have:

y = non-negative integer + positive integer = positive integer

Thus, y assumes positive integral values only (in minutes).

Also, y is always going to be at least 20 (as history homework is going to take 20 minutes, even if math homework is nill ).

Thus, the expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20

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Answer:

40/3

Step-by-step explanation:

-0.6X=-8

X=-8/-06

X=40/3

Answer:

it is A the meidian is the middle number in a orderd set

Answer:

25.5

Step-by-step explanation:

the sum of an infinite geometric series with first term a and common ratio r<1 is given by a/(1-r).

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

the sum of a given infinite geometric series is 200, and the common ratio is 0.15. What is the second term of this series?

Solve:

a/(1-r) = 200

a/0.85 = 200

a = 170 (that is the 1st term)

----

2nd term: a*r = 170*0.15 = 25.5

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

Answer:

Starting with 0, the difference in the corresponding terms in the two patterns increases by 2.

Step-by-step explanation:

P Q Difference

1 40 40 0

2 38 36 2

3 36 32 4

4 34 28 6

5 32 24 8

6 30 20 10

7 28 16 12

8 26 12 14

9 24 8 16

10 22 4 18

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

Answers are:

Excluding the first term, a term in Pattern P is always 2 greater than its corresponding term in Pattern Q.

Excluding the first term, a term in Pattern Q is always 4 greater than its corresponding term in Pattern P.

Starting with 0, the difference in the corresponding terms in the two patterns decreases by 4.

Answer: A

Step-by-step explanation: 27+9 = 36

[tex]\frac{1}{2} (n+8) + \frac{3}{4} [/tex]

[tex]\frac{1(n+8)}{2} + \frac{3}{4} [/tex]

[tex]\frac{n+8}{2} + \frac{3}{4} [/tex]

[tex]\frac{2(n+8)}{4} + \frac{3}{4} [/tex]

[tex]\frac{2(n+8) + 3}{4} [/tex]

[tex]\frac{2n + 16 +3}{4} [/tex]

[tex] \frac{2n + 19}{4} [/tex]

Answer:

64 textbooks

Step-by-step explanation:

the first two teachers had 21 students each that's 21+21=42

the other teacher had 22 students so apparently all the textbooks handed to the students are,21+21+22=64

Answer:

20x

Step-by-step explanation:

The approximate area of the sketch for the new lamp is : A = 70 [tex]in^{2}[/tex]

A trapezium is one pair of parallel sides and one pair of non-parallel sides.

from the diagram we can extract the necessary information needed to find the area of the trapezium.

for the first trapezium (lamp shade)

a = 4 in

b = 6 in

h = 6 in

[tex]A_{1}[/tex] = [tex]\frac{a + b}{2}[/tex] * h

[tex]A_{1}[/tex] = [tex]\frac{4 + 6}{2}[/tex] * 6

[tex]A_{1}[/tex] = [tex]\frac{10}{2}[/tex] * 6

[tex]A_{1}[/tex] = 5 * 6 = 30[tex]in^{2}[/tex]

For the area of the second trapezium (lamp base)

a = 4 in

b = 6 in

h = 4 in

[tex]A_{2}[/tex]  = [tex]\frac{a + b}{2}[/tex] * h

[tex]A_{2}[/tex]  = [tex]\frac{4 + 6}{2}[/tex] * 4

[tex]A_{2}[/tex]  = [tex]\frac{10}{2}[/tex] * 4

[tex]A_{2}[/tex]  = 5 * 4 = 20[tex]in^{2}[/tex]

For the area of the third trapezium (lamp base)

a = 6 in

b = 4 in

h = 4 in

[tex]A_{3}[/tex]  =  [tex]\frac{a + b}{2}[/tex] * h

[tex]A_{3}[/tex]  =  [tex]\frac{6 + 4}{2}[/tex] * 4

[tex]A_{3}[/tex]  =  [tex]\frac{10}{2}[/tex] * 4

[tex]A_{3}[/tex]  =  5 * 4 = 20[tex]in^{2}[/tex]

The total Area of the trapezium (lamp)

A = [tex]A_{1}[/tex]  +  [tex]A_{2}[/tex]  +  [tex]A_{3}[/tex]

A = 30 + 20 + 20

A = 70 [tex]in^{2}[/tex]

Inconclusion The approximate area of the sketch for the new lamp is : A = 70 [tex]in^{2}[/tex]

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Answer:

Step-by-step explanation:

20, 30, 70