Determine which polynomial is a perfect square trinomial. 4x2 − 12x + 9 16x2 + 24x − 9 4a2 − 10a + 25 36b2 − 24b − 16

Answer:

Step-by-step explanation:

The pulling force

Answer:

F = -52.8 N

Step-by-step explanation:

Given :

Inclination angle : 25°

Weight, W = 400 lb

The force N will push the box against the ramp.

Therefore, Force F will prevent the box from sliding down the ramp.

F = W sin 25°

  = 400 x (-0.132)

  = -52.8 N ( negative sign shows that the force applied in the opposite direction )

Answer:

$11,340

Step-by-step explanation:

1 month: 630

18 months: 18×630=11,340

Anna pays a total of $11,340 in rent over the course of 18 months by multiplying her monthly rent of $630 by 18.

To find out how much rent Anna pays over the course of 18 months, we need to multiply her monthly rent by the number of months. Anna pays $630 each month, so over 18 months, she would pay:

$630 times 18 = $11,340.

Therefore, Anna pays a total of $11,340 in rent over the course of 18 months.

Answer:

Option D is correct.

Step-by-step explanation:

The length of 2 sides of triangle are given i.e 10 cm and 16 cm.

We need to find the range of the values of length of the third side.

Sum of 2 sides of triangle is greater than the 3rd side

so, 10+16 = 26

So, the length of third side should be less than 26

and we know that the length of third side should be greater than the absolute difference of other two sides

16-10 = 6

So, the length of third side should be greater than 6

Combining both we get 6<x<26

Hence Option D is correct.

The range of possible values for the third side of the triangle is 6 < x < 26

10 + 16 = 26 cm

Difference = 16 cm - 10cm

= 6 cm

Therefore, the range of value of the third side is x is greater than 6cm less than 26cm

6 < x < 26

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Answer:

[tex]\displaystyle \boxed{-\frac{1}{2}}[/tex]

Step-by-step explanation:

Slope formula:

     ↓

[tex]\displaystyle \frac{Y_2-Y_1}{X_2-X_1}[/tex]

[tex]\displaystyle Y_2=5\\\displaystyle Y_1=3\\\displaystyle X_2=(-2)\\\displaystyle X_1=2\\[/tex]

[tex]\displaystyle \frac{5-3}{(-2)-2}=\frac{2}{-4}=\frac{2\div2}{-4\div2}=\frac{1}{-2}=-\frac{1}{2}[/tex]

Therefore the slope is -1/2.

-1/2 is the correct answer.

Hope this helps!

Answer:

SAS

Step-by-step explanation:

we know that

Triangles are congruent by SAS, if any pair of corresponding sides and their included angles are equal in both triangles

so

In this problem

we have that

the pair of corresponding sides AB with DC and AD with DA and their included angles  ∠ BAD with ∠CDA are equal

therefore

Triangle ABD is congruent with triangle DCA by SAS congruency theorem

Answer:

sas

Step-by-step explanation:

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Answer:

x-10

Step-by-step explanation:

we know that

(-x+10) subtracted from 0 is equal to

0 minus (-x+10)

so

0-(-x+10)=0+x-10

=x-10

Answer:

x-10

Step-by-step explanation:

Answer:

b. 3

Step-by-step explanation:

In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].

30°-60°-90° Triangles

x√3 → long side

x → short side

2x → hypotenuse

45°-45°-90° Triangles

x → two legs

x√2 → hypotenuse

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Hi.

Answer:

[tex]\boxed{x>17}\checkmark[/tex]

The answer should have positive sign but not negative.

Step-by-step explanation:

First, you add by 8 from both sides.

[tex]6x-8+8>4x+26+8[/tex]

Then, simplify.

[tex]6x>4x+34[/tex]

Next, you do is subtract by 4x from both sides.

[tex]6x-4x>4x+34-4x[/tex]

Simplify.

[tex]2x>34[/tex]

Therefore, you divide by 2 from both sides.

[tex]\frac{2x}{2}>\frac{34}{2}[/tex]

Finally, you solve and simplify.

[tex]34/2=17[/tex]

[tex]x=17\checkmark[/tex]

X=17 is the correct answer.

Hope this helps you!

Have a nice day! :)

Answer:

The solution for the inequality is x>17

Step-by-step explanation:

Consider the provided inequality.

[tex]6x - 8 > 4x + 26[/tex]

Subtract 4x to both the sides.

[tex]6x -4x- 8 > 4x-4x + 26[/tex]

[tex]2x- 8 > 26[/tex]

Add 8 to the both sides.

[tex]2x- 8+8 > 26+8[/tex]

[tex]2x > 34[/tex]

Divide both the sides by 2.

[tex]x > 17[/tex]

Hence, the solution for the inequality is x>17

Final answer:

Maggie needs to practice at least 1.5 hours on each of the two remaining days.

Explanation:

To determine the minimum number of hours Maggie needs to practice on each of the two remaining days, we can set up an inequality based on the given information. Maggie needs to spend at least six hours each week practicing the piano, and she has already practiced three hours. Let's let x represent the number of hours she needs to practice on each of the remaining two days. The inequality can be written as:

3 + 2x ≥ 6

Solving for x, we subtract 3 from both sides of the inequality:

2x ≥ 3

Then, we divide both sides by 2 to solve for x:

x ≥ 1.5

Therefore, Maggie needs to practice at least 1.5 hours on each of the two remaining days.

Maggie must practice for at least [tex]$\dfrac{3}{2}$[/tex] hours each of the last two days.

Let x equal the number of hours Maggie practices each of the last two days. Since she Needs to practice at least 6 hours per week, and she already practiced 3 hours this week, she must practice for at least 6 - 3 = 3 more hours.

Splitting this time evenly between the two days means she practices x hours each day.

This can be expressed in the following inequality: [tex]$x + x \geq 3$[/tex] which combines the information about the minimum number of hours needed and the fact that she splits the remaining time evenly.

Simplifying the left side of the inequality gives [tex]$2x \geq 3$[/tex]. Dividing both sides by 2 gives [tex]$x \geq \dfrac{3}{2}$[/tex].

Thus, Maggie must practice for at least [tex]$\dfrac{3}{2}$[/tex] hours each of the last two days.

Answer:

d

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

To evaluate (f ￮ g)(x)

Substitute x = g(x) into f(x)

f(x² + 14) = x² + 14 - 14 = x² → C

The value of (fog)(x) = x^2. So, option C is correct.

The functions f(x) and g(x) are composite functions then,

(fog)(x) = f(g(x)).

Given that,

f(x) = x - 14

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

Then,

(fog)(x) = f(g(x))

           = ([tex]x^2+14[/tex]) - 14

           = x² + 14 - 14

           = x²

Therefore, the value of (fog)(x) = x².

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Answer:

y = -2x²

Step-by-step explanation:

The set of ordered pairs is:

(x₁, y₁) = (2, -8)

(x₂, y₂) = (3, -18)

(x₃, y₃) = (4, -32)

(x₄, y₄) = (5, -50)

First let's check if this is linear.  For even increments of x, Δy is:

Δy₂₁ = y₂ − y₁ = -18 − -8 = -10

Δy₃₂ = y₃ − y₂ = -32 − -18 = -14

Δy₄₃ = y₄ − y₃ = -50 − -32 = -18

Δy isn't constant, so this isn't linear.  However, the difference of the differences is constant:

Δy₃₂ − Δy₂₁ = -14 − -10 = -4

Δy₄₃ − Δy₃₂ = -18 − -14 = -4

So this is a quadratic.

y = ax² + bx + c

To find the coefficients of a, b, and c, we can either plug in three points from the set and solve the system of equations:

-8 = a(2)² + b(2) + c

-18 = a(3)² + b(3) + c

-32 = a(4)² + b(4) + c

Or, if it's simple, we can use a little trial and error.

-8 = -2 (2)²

-18 = -2 (3)²

-32 = -2 (4)²

So the function is:

y = -2x²

Answer:

Part 1) [tex]A=96\ cm^{2}[/tex]

part 2) [tex]A=40.8\ ft^{2}[/tex]

Step-by-step explanation:

Part 1)

we know that

The area of a trapezoid is equal to

[tex]A=(1/2)[b1+b2]h[/tex]

In this problem we have

[tex]b1=12\ cm[/tex]

[tex]b2=6+12+2=20\ cm[/tex]

[tex]h=6\ cm[/tex] ----> perpendicular distance between the two bases

substitute

[tex]A=(1/2)[12+20](6)[/tex]

[tex]A=96\ cm^{2}[/tex]

Part 2)

we know that

The area of a kite is equal to

[tex]A=(1/2)[D1*D2][/tex]

we have

[tex]D1=10.2\ ft[/tex]

[tex]D2=8\ ft[/tex]

substitute

[tex]A=(1/2)[10.2*8][/tex]

[tex]A=40.8\ ft^{2}[/tex]

Answer:

25) 96 cm²

26)  40.8 ft ²

Step-by-step explanation:

25) To find the area of trapezoid

Area of trapezoid = h(a + b)/2

Here a = 6 + 12 + 2 = 20 cm

b = 12 cm and h = 6

Area =  h(a + b)/2

 = 6(20 + 12)/2

 = 96 cm²

26) To find the area of kite

Area of kite = pq/2

Where p and q are the two diagonals

Here p = 10.2 ft and q = 8 ft

Area = pq/2

 = (10.2 * 8)/2 = 40.8 ft²

Answer:

C) a+3

Step-by-step explanation:

We are given the following data:

Tom's Age:  10  11  12  a

Kim's Age:   13  14  15  

We have to evaluate Kim's age when Tom's age is a.

We have to build a relationship between Tim's age and Kim's age. If we look at their ages carefully we can see a pattern and their relation can be described as:

[tex]\text{Kim's age = Tim's age + 3}[/tex]

Thus, when Tim's age is a, we can compute Kim's age as:

[tex]\text{Kim's age = a + 3}[/tex]

[tex]\bf 2x^2+10x+12\implies 2(x^2+5x+6)\implies 2(x+3)(x+2)[/tex]

recall that 3 * 2 = 6, and 3x + 2x = 5x.

Answer:

Step-by-step explanation:

It is a little easier if you take out the two.

2*(x^2 + 5x +6)

The numbers that multiply to 6 and adds to 5 are 3 and 2

2*(x + 3)(x + 2)

So that's how the trinomial factors.

Answer:

86%

Step-by-step explanation:

64.97/ 75 = 0.8662...

0.8662 x 100 = 86%

but it weighted so:

0.8662 x actual weighted % =  % got out of weighted %

example:

Test is Weighted 25% out of 100%

0.8662 x 25% = 21 %

this case you got 21% out of 25% for the test

there were D. 1163 books left on the shelves or in circulation.

///////////////////////////////////////////////////////////////////////////

let us count the number of books that are NOT on the shelves now.

1st step: 32 + 24 = 56

2nd step: the total number of books minus the amount of books that are damaged or out:  1,219 - 56 = 1163

Answer:

C. 1,163

Step-by-step explanation:

Total books = books on shelves + books lost + books out for repair

What do we know

1219 =  books on shelves + 32 + 24

1219 = books on selves + 56

Subtract 56 from each side

1219-56 = books on shelves - 56

1163 = books on shelves

The answer to your question is 0.55555555555

Solution: You simply divide 5 by 9 to get your whole number. In other words, 5/9 =0.55555555555

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The fraction 5/9 cannot be converted into a whole number because it results in a decimal number (approximately 0.55) upon division.

In Mathematics, we have different types of numbers - whole numbers, fractions, decimals, etc. Here, you are asked to convert a fraction 5/9 into a whole number. However, it's essential to understand, that 5/9 cannot be converted into a whole number because it is less than 1.

For general understanding, a whole number can only be a non-negative number without any fractional or decimal parts, such as 0, 1, 2, 3, 4, and so forth. A fraction like 5/9 implies division, and when you divide 5 by 9, you get a decimal number (approximately 0.55), which is not a whole number.

Thus, the fraction 5/9 cannot be precisely converted into a whole number without rounding it off.

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Answer:

295261.98 or just 295.2962 (rounded).

Step-by-step explanation:

You have to figure out how many ml are in a gallon. Then multiply that by 3.9 gallons.

Answer:

[tex]\large\boxed{-\dfrac{5}{4}=-1\dfrac{1}{4}}[/tex]

Step-by-step explanation:

[tex]\text{Put the values of x = -1 and y = -5 to the expression}\ \dfrac{x^2y}{4}:\\\\\dfrac{(-1)^2(-5)}{4}=\dfrac{(1)(-5)}{4}=\dfrac{-5}{4}[/tex]

Answer:

[tex]\large\boxed{(f+g)(x)=5x+3}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=2x-6,\ g(x)=3x+9\\\\\text{Substitute:}\\\\(f+g)(x)=(2x-6)+(3x+9)\\\\=2x-6+3x+9\qquad\text{combine like terms}\\\\=(2x+3x)+(-6+9)\\\\=5x+3[/tex]

Answer:

295.01

Step-by-step explanation:

Use A = Pe^(rt)

$294.88 is the worth of the investment after 4 years.

percentage, a relative value indicating hundredth parts of any quantity.

Given that  $190 is invested at an interest rate of 11% per year and compounded continuously.

We need to find the worth of the investment after 4 years.

[tex]A=Pe^{rt}[/tex]

A is the final amount

p is the principal amount

r is the rate of interest

t is the time.

[tex]A=190e^{0.11(4)}[/tex]

[tex]A=190e^{0.44}[/tex]

A=190×1.552

A=294.88

Hence, $294.88 is the worth of the investment after 4 years.

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The correct answer: D

Answer: 1:2 ratio

Step-by-step explanation:

Total-red roses=pink roses

24-16=8

8:16

GCF: 8

16/8=2

8/8=1

1:2 ratio

pink:red

The ratio of pink to red roses 1:2 ratio

Total-red roses=pink roses

24-16= 8

8:16

GCF: 8

16/8=2

8/8=1

1:2 ratio

pink : red

A ratio indicates how many times one number contains another.

The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.

Ratios can be reduced (as fractions are) by dividing each quantity by the common factors of all the quantities. As for fractions, the simplest form is considered that in which the numbers in the ratio are the smallest possible integers.

Thus, the ratio 40:60 is equivalent in meaning to the ratio 2:3, the latter being obtained from the former by dividing both quantities by 20. Mathematically, we write 40:60 = 2:3, or equivalently 40:60∷2:3. The verbal equivalent is "40 is to 60 as 2 is to 3."

Ratios may also be established between incommensurable quantities (quantities whose ratio, as the value of a fraction, amounts to an irrational number). The earliest discovered example, found by the Pythagoreans, is the ratio of the length of the diagonal d to the length of a side s of a square, which is the square root of 2, formally.

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Answer:

[tex]\displaystyle 64 = y[/tex]

Step-by-step explanation:

[tex]\displaystyle y = 8[3] + 40; y = 24 + 40; 64 = 24 + 40[/tex]

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Answer:x^1/2

Step-by-step explanation:

x^1/6*3=

x^3/6=

x^1/2

Answer:

3x-14xy+13y+4

Step-by-step explanation:

3x – 10xy + 13y – 4xy + 2x2

= 3x-14xy+13y+4

Simplification of the expression  [tex]3x - 10xy + 13y - 4xy + 2x^{2}[/tex]  is  [tex]3x - 14xy + 13y + 2x^{2}[/tex] .

Given expression is  [tex]3x - 10xy + 13y - 4xy + 2x^{2}[/tex]

Grouping the like terms from the expression, results -

= [tex]3x - (10xy - 4xy) + 13y + 2x^{2}[/tex]

Simplification of the expression is -

= [tex]3x - 14xy + 13y + 2x^{2}[/tex]

Thus, simplification of the expression  [tex]3x - 10xy + 13y - 4xy + 2x^{2}[/tex]  is  [tex]3x - 14xy + 13y + 2x^{2}[/tex] .

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Answer:

[tex]\large\boxed{y\leq8\to\{y\ |\ y\leq8\}\to y\in(-\infty,\ 8]}[/tex]

Step-by-step explanation:

[tex]-1+4y\leq31\qquad\text{add 1 to both sides}\\\\-1+1+4y\leq31+1\\\\4y\leq32\qquad\text{divide both sides by 4}\\\\\dfrac{4y}{4}\leq\dfrac{32}{4}\\\\y\leq8[/tex]

Answer:

C:  x = 1/2

Step-by-step explanation:

Set the divisor, 2x - 1, equal to zero and solve for x:  2x = 1, so x = 1/2.  Statement C is true.

Answer:

The correct option is C.

Step-by-step explanation:

If a function f(x) is completely divisible by (x-a), it means (x-a) is a factor of f(x) and x=a is a root of that polynomial.

The given polynomial is

[tex]P(x)=2x^2+9x-5[/tex]

It is given that when David divide the above polynomial by (2x-1), then he get

[tex]Quotient=x+5[/tex]

[tex]Remainder=0[/tex]

Since the remainder is zero it means P(x) is completely divisible by (2x-1) or (2x-1) is a factor of P(x).

[tex]2x-1=0[/tex]

Add 1 on both the sides.

[tex]2x=1[/tex]

Divide both sides by 2.

[tex]x=\frac{1}{2}[/tex]

It means [tex]\frac{1}{2}[/tex] must be a root of the polynomial [tex]2x^2+9x-5[/tex].

Therefore, the correct option is C.

Answer:  The required product is [tex]4x^5\sqrt[3]{3x}[/tex]

Step-by-step explanation:  We are given to find the following product :

[tex]P=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}.[/tex]

We will be using the following property of exponents :

[tex](i)~\sqrt[b]{x^a}=x^\frac{a}{b}\\\\(ii)~x^a\times x^b=x^{a+b}\\\\(iii)~x^a\times y^a=(xy)^a.[/tex]

The required multiplication is as follows :

[tex]P\\\\=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}\\\\=(16x^7)^\frac{1}{3}\times (12x^9)^\frac{1}{3}\\\\=(16\times12\times x^{7+9})^\frac{1}{3}\\\\=(192x^{16})^\frac{1}{3}\\\\=192^\frac{1}{3}x^\frac{16}{3}\\\\=(64\times3)^\frac{1}{3}x^\frac{16}{3}\\\\=4^{3\times\frac{1}{3}}3^\frac{1}{3}x^{5+\frac{1}{3}}\\\\=4\times 3^\frac{1}{3}x^5\times x^\frac{1}{3}\\\\=4x^5\sqrt[3]{3x}.[/tex]

Thus, the required product is [tex]4x^5\sqrt[3]{3x}.[/tex]