Given: F(x) = 3x2+ 1, G(x) = 2x - 3, H(x) = x

F(3) + G(4) - 2H(5) =

Answer:

x = 5 ,  x = - 6

Step-by-step explanation:

First we factor using factorisation method :

We need 2 numbers that multiply to give +1 and add to give -30 :

To find these numbers we write out all the factors of 30 :

1, 30

2 , 15

3 , 10

5 , 6    ----> These must be the numbers as -5+6 = 1

Now we split +x into -5x and +6x :

x² -5x + 6x -30 = 0

Factor the first 2 terms together and the last two terms :

x(x-5) + 6(x-5) = 0

Keep 1 bracket and terms outside the brackets collect them into one:

(x-5)(x+6) = 0

We know that 1 of these brackets must be equal to zero as anything multiplied by zero = 0

Either x - 5 =0      OR x + 6 = 0

So x = 5                x = - 6

These are our final answers

Hope this helped and have a good day

Answer:

(x-5) (x+6)

x=5

X=-6

Step-by-step explanation:

x²+x-30=0

factorizing

x²-5x+6x-30=0

x(x-5)+6(x-5) =0

(x-5)(x+6)=0

now solve individually

x-5=0

send 5 to the other side

x=5

x+6=0

send 6 to the other side

x=-6

hope you understand the procedure

Two ares are congruent if they have the same measure and lengths

The statement is given as:

Two ares are congruent if they have the same measure and ?

The conditions for congruent shapes in geometry are;

This means that the angle and the length must be equal

Hence, the term that completes the blank is length

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The limit for the given piecewise function does not exist(DNE).

4th option is correct.

In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time.

Unique real numbers are limits in mathematics.

According to the question,

Left hand limit of the function= -5(3)+4 = -15+4 = -11

Right hand limit of the function= (3)(3)+2 = 11

As the left and right-hand limits are not equal. Thus, the limit of the function does not exist.

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Answer:

278 square centimeters

Step-by-step explanation:

You need to use the Pythagorean Theorm. If you're pyramid is a perfect square, then to the middle the length is 5. Because 10/2 is 5. You then use the Pythagorean Theorm  (a^2 + b^2 =c^2) to find the side length of the traingle. When you square the hypotenuse and subtract the bottom leg sqaured, you are left with 3.46274054 after square rooting it. (c^2-a^2=b^2) Plug these into the equation for a right, rectangluar pyramid. You then get 277.9, rounded, is 278.

Hope this helps!

Answer:

$592.92

Step-by-step explanation:

Bills:

47 ones = 47*1 = $47

22 fives = 22*5 = $110

9 tens = 9*10 = $90

17 twenties = 17*20 = $340

Total Bills: 47+110+90+340 = $587

Coins:

67 pennies = 67*1 = $0.67

12 nickels = 12*5 = $0.60

9 dimes = 9*10 = $0.90

15 quaters = 15*25 = $3.75

Total Coins: 0.67+0.6+0.9+3.75 = $5.92

Total: $587+$5.92 = $592.92

Answer:

10

Step-by-step explanation:

Answer:

10 apples

Step-by-step explanation:

20% of 50 = 10

10 apples

Answer:

The surface area (SA) of the given triangular prism is 120m.

Step-by-step explanation:

Greetings !

B/c, SA=bh+(b₁+b₂+b₃)l

Answer:

SA = 120 m2

Step-by-step explanation:

one 9×5 rectangle = 45 m2
one 4×9 rectangle = 36 m2
one 9×3 rectangle = 27 m2

two (4×3)/2 triangles = 6 + 6 = 12 m2

Add the areas:

surface area = 45 + 36 + 27 +12 = 120 square meters

Hope this helps

Answer:

Brock or separate is located nearly Westside to centure in gives best direction from the central only

Answer:

watch oreimo..

The equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]

The natural logarithm equation is given as:

ln 5 = y

Rewrite as:

ln(5) = y

Take the exponent of both sides

[tex]e^{ln(5)} = e^y[/tex]

Evaluate the expression

[tex]5 = e^y[/tex]

Rewrite as:

[tex]e^y = 5[/tex]

Hence, the equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]

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The area of the circular manufactured good is given by:

[tex]A = 1.8146 \times 10^{16} \text{m}^2[/tex]

The area of a circle of radius r is:

[tex]A = \pi r^2[/tex].

In this problem, the radius in meters is:

[tex]r = 7.6 \times 10^7[/tex]

Hence the area in m² is:

[tex]A = \pi (7.6 \times 10^7)^2 = 181.46 \times 10^{14} = 1.8146 \times 10^{16} \text{m}^2[/tex]

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The number of bats are expected to be in the colony after 11 years if the colony continues to grow at the same rate is 69,632

Let

exponential function;

y = ax^t

When t = 3

272 = ax³

when t = 5

1088 = ax^5

272/1088 = ax^3 / ax^5

1/4 = x^3-5

1/4 = x^-3

1/4 = 1/x²

1 × x² = 4 × 1

x² = 4

x = 2

Substitute x = 2 into

272 = ax³

272 = a × 2³

272 = a × 8

272 = 8a

a = 272/8

a = 34

Number of bat expected at the colony after 11 years

y = ax^t

= 34 × 2^11

= 34 × 2048

y = 69,632 bats

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Since the function is h(t) = −5t² + 15t, the domain of the function h(t) is  0 ≤ t ≤ 3

The domain of a function is the range of input values that make the function have real values.

Now given the function h(t) = −5t² + 15t, it will have real values when

h(t) ≥ 0

So, h(t) ≥ 0

⇒  −5t² + 15t ≥ 0

Factorizing, we have

-5t(t - 3) ≥ 0

5t(t - 3) ≤ 0

t(t - 3) ≤ 0

t ≤ 0 and t - 3 ≤ 0

t ≤ 0 and t ≤ 3

For t ≤ 0, say -1, t(t - 3) = -1(-1 - 3) = -1(-4) = 4 ≥ 0

For 0 ≤ t ≤ 3, say 2, t(t - 3) = 2(2 - 3) = 2(-1) = -2 ≤ 0

For t ≥ 3, say 4, t(t - 3) = 4(4 - 3) = 4(1) = 4 ≥ 0

Since we require  t(t - 3) ≤ 0, the domain of t is thus 0 ≤ t ≤ 3

So, the domain of the function h(t) is  0 ≤ t ≤ 3

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Considering the similarity of triangles, the corresponding sides are:

[tex]\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}[/tex].

If two triangles have the exact same angles, they are called similar, and the corresponding sides, that is, the sides adjacent to the same angles, have proportional lengths.

In this problem, the corresponding sides have equal ratios given as follows:

[tex]\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}[/tex].

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The function P(x), for the price of the materials for the pen is 4.18(800/x + x) + 38.

Based on the information, the function P(x), for the price of the materials for the pen will be:

P(x) = 4.18 (2 × 400/x + x) + 38

= 4.18(800/x + x) + 38.

The dimensions will be:

We'll differentiate the function which will give 20✓2. Therefore, the value for x will be 20✓2 which is 28.28 feet and that of y will be 10✓2 which is 14.14 feet.

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Answer:

See below    

Step-by-step explanation:

Remember... when you square a negative number, you get a positive result

  AND you cannot divide by zero AND you cannot have the sqrt of a negative number  so:

-2 > x > 2     (looks like 'D'   but there is a negative sign missing)

you need 628 square feet of sand.

Here we need to find the volume of the sand needed.

The volume filled with sand will be a cylinder of diameter of 20ft, and a height of 2 inches.

First, the radius is half of the diameter, then:

R = 20ft/2 =10ft

Remember that:

1ft= 12in

Then:

R = 10ft = 10*(12 in) = 120 in

And remember that the volume of a cylinder of radius R and height H is:

[tex]V = pi*R^2*H[/tex]

Where pi = 3.14

Then we have:

[tex]V = 3.14*(120 in)^2*2in = 90,432 in^2[/tex]

To get that in feets, we need to divide by 12 squared, then:

[tex]90,432 in^2 = 90,432ft^2/(12^2) = 628 ft^2[/tex]

So you need 628 square feet of sand.

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Answer:

Multiples of 4:4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …

Multiples of 6:6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …

Answer: The least common denominator of 1/4 and 1/6 is 12.

Prime factorisations of 8= 2 × 2 × 2.

Prime factorisations of 12= 2 × 2 × 3.

More items...

Hi! ⋇

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   To find the least common denominator of [tex]\sf{\frac{1}{2}}[/tex] and [tex]\sf{\frac{5}{6}}[/tex], we should first find the least common multiple of 2  and 6, which is 6:

 Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16... ∞

 Multiples of 6: 6, 12, 18, 24... ∞

(all common multiples are in bold-face; all multiples of 6 are in bold-face because all multiples of 6 are also multiples of 2)

· In both sets, 6 is the least common multiple, and it's also the least common denominator.

Hope this made sense to you !!

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The polynomial function is P(x) = x^3(x + 1)^3(x -1)

The zeros of the polynomial and the multiplicities are given as:

The degree is given as

Degree = 7

The polynomial is represented as:

P(x) = (x - zero)^multiplicity

Using the above format, we have

P(x) = (x + 1)^3(x - 0)^3(x -1)

This gives

P(x) = x^3(x + 1)^3(x -1)

Hence, the polynomial function is P(x) = x^3(x + 1)^3(x -1)

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Answer:

Median

Explanation:

Real estate prices are virtually usually biased to the right. If we estimate the price of a typical home in a city at $500,000. We would have no trouble locating properties for $2 million and $3 million, and perhaps even some $5 or $6 million residences. However, you won't find houses for under $1.5 million. Because of this, the mean value is pulled toward the high end more than the median value.

Answer:

5 points

Step-by-step explanation:

Subtracting their scores, we get (-3)-(-8)=5

Based on the information given about the equation, y will be 0.5x + 2.

From the information given, it should be noted that the equation of the line it represents was given and the y intercept is = (0, 2).

The function to represent y will be:

y = mx + b

y = (1/2)x + 2

y = 0.5x + 2

In conclusion, y = 0.5x + 2.

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The trigonometric form of the complex number given in the task content is; 18(isin(π/2)).

If follows from the task content that the complex number whose trigonometric representation is to be determined is; 18i.

Hence, It follows that the trigonometric form is;

= 18(cos(π/2) + isin(π/2)). where; cos(π/2) = 0.

Hence, we have;

= 18(isin(π/2)).

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Factorization implies the obtaining of the common factors in an expression.

The term factorization implies the obtaining of the common factors in an expression.

The factors of the expressions are as follows;

1) (x−1)(x+7)

2) (x−2)(x−3)

3) (x+1)(x−7)

4) (x−1)(x+6)

5) (x−3)(x+4)

6) (x+2)(x−4)

7) (x+1)(x−5)

8) (x−1)(x+3)

9) (x+4)(x−4)

10) (x+3)(x−4)

11) (x−3)(x−6)

12) (x+2)(x−7)

13) (x−2)(x−5)

14) (x−3)(x−8)

15) (x+5)(x−6)

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The area of the square is given by the  quadratic expression:

[tex]A = 9x^2 - 6xy + y^2[/tex]

If we have a square whose side measures S, the area of said square is given by the equation:

[tex]A = S^2[/tex]

In this case, we know that the side length of our square is given by:

[tex]S = 3x - y[/tex]

Replacing that in the area equation we get:

[tex]A = (3x - y)^2[/tex]

Now we just need to expand that product, we will get:

[tex]A = (3x - y)^2 = (3x)*(3x) + (3x)*(-y) + (-y)*(3x) + (-y)*(-y) \\\\A = 9x^2 - 6xy + y^2[/tex]

Then we can see that the correct option is the last one.

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Answer:

95.7 cm by 126.5 cm

Step-by-step explanation:

To use the scale factor of 0.55, we multiply 174 and 230 by 0.55: 174*0.55 = 95.7,  230*0.55 = 126.5

Answer:

C is 27 and d is 16

Step-by-step explanation:

count how many cubes are on the first level and multiple but how many it goes up too

Answer:

Step-by-step explanation:

Comment

The formula used to figure out the costs is

C(x) = 2885 + 30x

2885 is the total of the fixed costs -

Now the problem gets sort of complicated. If the company could print an unlimited amount of pages, the 2885 remains the same, no matter what.

But x gets larger and larger. and so C(x) gets larger and larger.

Answer

Therefore the average cost would approach infinity.

A