Which polynomial identity will prove that 64+27=91?

A. Difference of Squares
B. Difference of Cubes
C. Sum of Cubes
D. Square of a Binomial

Answer:

The correct answer option is P (both green) = 91 / 435

Step-by-step explanation:

We are given that in a jar containing 30 marbles, 10 are red, 6 are black and 14 are green.

Two marbles are drawn and the second one is drawn without returning the first marble and we are to find the probability of getting green marbles both time.

P (both green) = [tex] \frac { 1 4 } { 3 0 } \times \frac { 1 3 } { 2 9 } [/tex] = 91 / 435

ANSWER

D. 25 feet

EXPLANATION

The height of the wall,h, the taut wire and the distance from the base of the pole to the point on the ground, formed a right triangle.

According to the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.

Let the hypotenuse ( the length of the ) taught wire be,l.

Then

[tex] {l}^{2} = {h}^{2} + {b}^{2} [/tex]

[tex]{l}^{2} = {20}^{2} + {15}^{2} [/tex]

[tex]{l}^{2} = 400 + 225[/tex]

[tex]{l}^{2} = 625[/tex]

[tex]l= \sqrt{625} = 25ft[/tex]

Answer:

25

Step-by-step explanation:

Answer:

The answer is d

Step-by-step explanation:

A line segment is a portion of an infinite line separated by two end points

The mean altitude will be -54 per minute

We are given with altitude change as -378 feet over 7 minutes

Now

We need feet per minute

So -378 / 7 will give us the altitude change per minute

-378 / 7 = -54

Therefore the mean change of altitude in feet per minute is -54 per minute

Answer:

38.4

Step-by-step explanation:

1. Pythagorean Theorem: 4.5²+ x²= 12²→  20.25 + x² = 144→ 144-20.25= 123.75

2. Square root 123.75, number wont be perfect, just round. (11.1)

3. Use inverse cos, sin, or tan. Answer will be the same.

in short, we simply split the total amount by the given ratio, so we'll split or divide 1020 by (15 + 2) and then distribute accordingly.

[tex]\bf \cfrac{petunias}{geraniums}\qquad 15:2\qquad \cfrac{15}{2}~\hspace{7em}\cfrac{15\cdot \frac{1020}{15+2}}{2\cdot \frac{1020}{15+2}}\implies \cfrac{15\cdot \frac{1020}{17}}{2\cdot \frac{1020}{17}} \\\\\\ \cfrac{15\cdot 60}{2\cdot 60}\implies \cfrac{900}{120}\implies \stackrel{petunias}{900}~~:~~\stackrel{geraniums}{120}[/tex]

The total number of geraniums in the greenhouse is 120. This was determined by calculating the value of each 'part' in the provided petunia to geranium ratio and then multiplying the number of geranium 'parts' by this value.

The question provides a ratio of petunias to geraniums in the greenhouse, which is 15:2. This is the same as saying for every 15 petunias, there are 2 geraniums. If you combine the parts of the ratio, you get a total of 17 parts (15 petunias + 2 geraniums). We know that the total number of flowers in the greenhouse is 1020.

Now, we'll figure out what each 'part' is equal to in the real world. To do that, we divide the total number of flowers by the total number of parts, so 1020 ÷ 17 = 60. This tells us each 'part' in our ratio is equal to 60 flowers.

From there, since we need to find the number of geraniums, we multiply the number of geranium 'parts' by the value of each 'part'. So, the number of geraniums in the greenhouse is 2 (The geranium 'parts') x 60 = 120 geraniums.

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Answer:

See below  

Step-by-step explanation:

14)

 14² =   8² + TV²

196 = 64  + TV²

TV² = 132

TV =√132 = √(4 × 33) = 2√33

sinA = TV/AT   = (2√33)/14 = √33/7

cosA = AV /AT = 8/14          = 2/7

tanA = TV/AV   = (2√33)/8  = √33)/4

sinT = AV/AT   = 8/14          = 4/7

cosT = TV/AT   = (2√33)/14 = √33/7

tanT = AV/TV   = 8/(2√33)   = (4√33)/33

16)

  6² = 3² + GT²

 36 = 9   + GT ²

GT² = 27

GT  = √27 = √(9 × 3) = 3√3

sinA = GT/AT  = (3√3)/6 = √3/2

cosA = AG/AT = 3/6        = ½

tanA = GT/AG = (3√3)/3 = √3

sinT = AG/AT = 3/6        = ½

cosT = GT/AT = (3√3)/6 = √3/2

tanT = AG/GT = 6/(3√3) = (2√3)/3

18)

 13² =   8² + TX²

169 = 64  + TX²

TX² = 105

TX  = √105

sinA = TX/AT  = (√105)/13

cosA = AX/AT = 8/13

tanA = TX/AX  = (√105)/8

sinT = AX/AT  = 8/13

cosT = TX/AT  = (√105)/13

tanT = AX/TX  = 8/(√105) = (8√105)/105

Answer: option c

Step-by-step explanation:

By definition, you can calculate the slope of  line by applying the formula shown below:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Then:

You can see that in the option C the equation of the slope is applied correctly:

[tex]\frac{9-(-3)}{1-(-2)}[/tex]

Where:

[tex]y_2=9\\y_1=-3\\\\x_2=1\\x_1=-2[/tex]

Then, you obtain the following value of the slope of the line:

[tex]m=\frac{9-(-3)}{1-(-2)}=4[/tex]

Answer: Your correct answer should be C, [tex]\frac{(9 - (-3))}{(1 - (-2))}[/tex]

Step-by-step explanation:

Recall the slope equation is: (y2 - y1)/(x2 - x1) or [tex]\frac{(y2 - y1)}{(x2 - x1)}[/tex]. You need two points: point one (x1, y1) and point two (x2, y2).

* The first answer choice is flawed because not only is it in a different formula (xs are in the numerator instead of the denominator area), but it says 1 - 2 when it should be 1 - (-2) or 1 + 2.

* The second answer choice is flawed because it is in a different formula (this time, x1 - x2/y3 - y2) and 2 - 1 is suppose to be -2 - 1.

* The last answer is flawed because it should be -3 - (-) 11 and -2 - (-)4, or -3 + 11 and -2 + 4.

Note: If you had a negative operation and a negative number behind it, you can either formulate the equation like x - (-) y or drop the negative sign from said number and change the minus operation sign to the plus one (x + y).

The only answer choice that checks out and is not flawed is C.

Answer:

Step-by-step explanation:

2  on  top goes  to  last  on  the  bottom  or  b  goes  to  d

1st one one top goes to the 2nd one on bottom or a goes to b

last one on top goes to the third one on bottom or d goes to c

The last two witch are 3rd on top and first one together

Hope this helped it took me a long time :)

The x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

A unit circle refers to a circle with unit radius (r = 1 unit) and positioned at center ( coordinates of origin = (h,k) = (0,0))

Thus, the equation of unit circle would be:

[tex]x^2 + y^2 =1[/tex]

Getting expression for y in terms of x,

[tex]x^2 + y^2 =1\\\\y = \pm \sqrt{1 - x^2}[/tex]

Using this equation to evaluate x for all given y:

[tex]\pm \dfrac{\sqrt{5}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{5}{9} = 1 - x^2\\\\x^2 = \dfrac{4}{9}\\\\x = \pm \dfrac{2}{3}[/tex]

From the options available, the fourth block seems valid.

Thus, we get:

[tex]y = \pm \dfrac{\sqrt{5}}{{3}} \rightarrow \left(\dfrac{2}{3}, y\right)[/tex]

[tex]\pm \dfrac{\sqrt{7}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{7}{9} = 1 - x^2\\\\x^2 = \dfrac{2}{9}\\\\x = \pm \dfrac{\sqrt{2}}{3}[/tex]

From the options available, the fourth block seems valid.

Thus, we get: [tex]y = \pm \dfrac{\sqrt{7}}{{3}} \rightarrow \left(\dfrac{\sqrt{2}}{3}, y\right)[/tex]

[tex]\pm \dfrac{3}{5} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{9}{25} = 1 - x^2\\\\x^2 = \dfrac{16}{25}\\\\x = \pm \dfrac{4}{5}[/tex]

From the options available, the fourth block seems valid.

Thus, we get: [tex]y = \pm \dfrac{3}{5} \rightarrow \left(\dfrac{4}{5}, y\right)[/tex]

[tex]\pm \dfrac{2\sqrt{2}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{8}{9} = 1 - x^2\\\\x^2 = \dfrac{1}{9}\\\\x = \pm \dfrac{1}{3}[/tex]

From the options available, the fourth block seems valid.

Thus, we get: [tex]y = \pm \dfrac{2\sqrt{2}}{{3}} \rightarrow \left(\dfrac{1}{3}, y\right)[/tex]

Thus, the x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.

Learn more about equation of a circle here:

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Answer:

x+3

Step-by-step explanation:

Factor x² + 6x + 9 = (x+3)(x+3)

Factor x² + 5x + 6 = (x+3)(x+2)

We can see that (x+3) is the LCM since it goes into  x² + 6x + 9 and

x² + 5x + 6

Answer:

87777777777777777777777777

Step-by-step explanation:

Answer:

B. -12

Step-by-step explanation:

The given limit are;

[tex]\lim_{x \to -11} f(x)=-3[/tex] and [tex]\lim_{x \to -11} g(x)=4[/tex]

We want to find;

[tex]\lim_{x \to -11} (fg)(x)=\lim_{x \to -11} f(x)\times \lim_{x \to -11} g(x)[/tex]

We substitute the given limits to obtain;

[tex]\lim_{x \to -11} (fg)(x)=-3\times 4[/tex]

[tex]\lim_{x \to -11} (fg)(x)=-12[/tex]

Answer:

B

Step-by-step explanation: EDGE 2020

Dana’s waking rate in miles per hour is 3 mph.

I did 3/4 x 4 = 3 because she walked 1/4 a mile and I needed to figure out the miles per one whole hour.

I hope this made sense and helped you.

Answer:

[tex]I=\frac{13xr}{1,200}[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Simple interest Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal form

t is Number of Time Periods in years

in this problem we have

[tex]t=(13/12)\ years\\ P=\$x\\r=(r/100)[/tex]

substitute in the formula above

[tex]I=x(r/100)(13/12)[/tex]

[tex]I=\frac{13xr}{1,200}[/tex]

Final answer:

To calculate simple interest for x dollars at an rate of r percent over 13 months, convert r percent to a decimal and time to years, then use the formula I = x × (r/100) × (13/12). For example, $100 at 5% interest for 13 months would earn approximately $5.42 in simple interest.

Explanation:

The calculation of simple interest for a principal of x dollars at a rate of r percent over 13 months involves a few straight-forward steps. The formula for the simple interest is given by:

I = P × r × t

Where I represents interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time the money is invested or borrowed for, in years.

To convert the rate r percent to a decimal, divide by 100. Then, convert the time of 13 months to years by dividing by 12.

Thus, the simple interest formula for this question becomes:

I = x × (r/100) × (13/12)

For example, if you deposit $100 into a savings account with a simple interest rate of 5% for 13 months, the interest earned would be calculated as follows:

I = 100 × (5/100) × (13/12)

This results in:

I = 100 × 0.05 × 1.08333

I = $5.42 (approximately)

The simple interest earned, in this case, would be approximately $5.42.

The correct answer would be A.

A.

You can distribute the 8

Distribute 8 to a and multiply them = 8a

Distribute 8 to -6 and multiply them = -48

= 8a-48

[tex]\bold{Hey\ there!}[/tex]

[tex]\bold{Good\ luck\ on\ your\ assignment\ \& enjoy\ your\ day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

The answer is c 226.9 m2

Step-by-step explanation:

Hope this helps

Answer:

It's A.

Step-by-step explanation:

5x2 + 60x = 0

5x is the GCF so:

5x(x + 12 ) = 0

5x = 0, x + 12 = 0

x =0, x = -12.

Answer:

The correct option is 1.

Step-by-step explanation:

The given quadratic equation is

[tex]5x^2+60x=0[/tex]

Taking out the common factors.

[tex]5x(x+12)=0[/tex]

Using zero product property, equate each factor equal to 0.

[tex]5x=0\Rightarrow x=0[/tex]

[tex]x+12=0\Rightarrow x=-12[/tex]

The solutions of the given equations are x=0 and x=-12.

Therefore the correct option is 1.

[tex]f'(x)\ge0[/tex] for all [tex]x[/tex] in [-3, 0], so [tex]f(x)[/tex] is non-decreasing over this interval, and in particular we know right away that its minimum value must occur at [tex]x=-3[/tex].

From the plot, it's clear that on [-3, 0] we have [tex]f'(x)=-x[/tex]. So

[tex]f(x)=\displaystyle\int(-x)\,\mathrm dx=-\dfrac{x^2}2+C[/tex]

for some constant [tex]C[/tex]. Given that [tex]f(0)=7[/tex], we find that

[tex]7=-\dfrac{0^2}2+C\implies C=7[/tex]

so that on [-3, 0] we have

[tex]f(x)=-\dfrac{x^2}2+7[/tex]

and

[tex]f(-3)=\dfrac52=2.5[/tex]

Answer:

$38.50/mo

Step-by-step explanation:

Rate of change = change in balance/time.

Change in balance = $731 - $500 = $231

Rate of change = $231/6 mo = $38.50/mo  

Answer:

31.60%

Step-by-step explanation:

(731−500)÷731=0.3160

0.3160×100=31.60%

Hope it helps!

Answer:

see attachment.  

Step-by-step explanation

see attachment

ANSWER

y=7

EXPLANATION

The horizontal asymptote of an exponential function

[tex]f(x)= a {(b)}^{x} + c[/tex]

is y=c.

The given exponential function is

[tex]f(x)= 4 {(52)}^{x} + 7[/tex]

When we compare to

[tex]f(x)= a {(b)}^{x} + c[/tex]

c=7, therefore the horizontal asymptote is y=7.

Answer:

Step-by-step explanation:

[tex]sin (\frac{\pi}{2} - x) = cos x \\\\ sin (a - b) = sin a.cos b - sin b.cos a \\\\ sin (\frac{\pi}{2} - x) = sin \frac{\pi}{2}.cos x - sin x.cos \frac{\pi}{2} \\\\ sin \frac{\pi}{2} = 1; cos \frac{\pi}{2} = 0 \\\\ sin (\frac{\pi}{2} - x) = 1.cos x - sin x.0 \\\\ sin (\frac{\pi}{2} - x) = cos x[/tex]

I hope I helped you.

By substituting a = π/2 and b = x into the trigonometric subtraction formula and considering that sin(π / 2) equals 1 and cos(π / 2) equals 0, we can verify the identity sin((π / 2) – x) = cos x

The question asks us to use the trigonometric subtraction formula for sine to verify the identity: sin((π / 2) – x) = cos x. From the trigonometric subtraction formulas, we know that sin(a - b) = sin a cos b - cos a sin b.

In this case, a = π/2 and b = x. Substituting these values into the formula, we ge: sin((π / 2) - x) = sin(π / 2) cos x - cos(π / 2) sin x.

Since sin(π / 2) equals 1 and cos(π / 2) equals 0 (from the Unit Circle in trigonometry), our equation simplifies to:  sin((π / 2) - x) = 1 * cos x - 0 * sin x, which further simplifies to sin((π / 2) - x) = cos x.

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Answer:

The 3 angles are 36.87, 53.13 and 90 degrees.

Step-by-step explanation:

This right  triangle ABC  has sides 3, 4 and 5 units.

To find the angles:

sin A - 3/5  gives m <  A =  36.87 degrees

sin B = 4/5 gives m < B = 53.13 degrees.

1 yard = 3 feet.

Multiply the length of the truck by 3 to get total feet:

6 x 3 = 18 feet.

Subtract the length of the truck from the length of the parking space:

20 - 18 = 2 feet

1 foot = 12 inches.

Multiply 2 feet by 12:

2 x 12 = 24 inches longer.

Answer:

35° and 85°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Since one angle = 60° then the sum of the other 2 angles = 120°

Sum the parts of the ratio 7 + 17 = 24 parts, hence

[tex]\frac{120}{24}[/tex] = 5° ← value of 1 pat of the ratio, hence

7 parts = 7 × 5° = 35°

17 parts = 17 × 5° = 85°

note that 60° + 35° + 85° = 180°

Answer:

length of base is 10

Step-by-step explanation:

The area of the entire firgure is 1600 cm^2.  There are 4 equal sized pennants, so each pennant is 1600/4 = 400

the bottom pennant has area 400 and is triangular shaped.  the area of a triangle is 1/2 b h.  

A = 1/2 b h       given height is 80 and area is 400.  plug these values in

400 = 1/2 b (80)

400 = 40 b       divide both sides by 40

b = 10

Answer: 233/23

Step-by-step explanation:

QUESTION 1

The given logarithm is

[tex]\log_{243}(27)[/tex]

Let [tex]\log_{243}(27)=x[/tex].

We rewrite in exponential form to get;

[tex]27=243^x[/tex]

We rewrite both sides of the equation as an index number to base 3.

[tex]3^3=3^{5x}[/tex]

Since the bases are the same, we equate the exponents.

[tex]3=5x[/tex]

Divide both sides by 5.

[tex]x=\frac{3}{5}[/tex]

[tex]\therefore \log_{243}(27)=\frac{3}{5}[/tex]

QUESTION 2

The given logarithm is

[tex]\log_{25}(\frac{1}{5} )[/tex]

We rewrite both the base and the number as power to base 5.

[tex]\log_{5^2}(5^{-1})[/tex]

Recall that: [tex]\log_{a^q}(a^p)=\frac{p}{q} \log_a(a)=\frac{p}{q}[/tex]

We apply this property to obtain;

[tex]\log_{5^2}(5^{-1})=\frac{-1}{2}\log_5(5)=-\frac{1}{2}[/tex]

Answer: first option

Step-by-step explanation:

To form an arithmetic sequence, you have that for the sequence [tex]7,6k,22[/tex]:

[tex]6k-7=22-6k[/tex]

Therefore, to calculate the value of k to form an arithmetic sequence, you must solve for k, as following:

- Add like terms:

[tex]6k+6k=22+7\\12k=29[/tex]

- Divide both sides by 12. Then you obtain;

[tex]k=\frac{29}{12}[/tex]

Answer:

[tex]k=\frac{29}{12}[/tex]

Step-by-step explanation:

The given sequence is 7, 6k, 22.

For this to be an arithmetic sequence, there must be a common difference.

[tex]6k-7=22-6k[/tex]

Group similar terms;

[tex]6k+6k=22+7[/tex]

Simplify;

[tex]12k=29[/tex]

Divide by 12

[tex]k=\frac{29}{12}[/tex]