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Identify the radical expression of 51/^3.

Answer:

angle of elevation to the sun is 15.52°

Step-by-step explanation:

basketball goal 10 ft high casts a shadow 36 ft long

This forms a right angle triangle. the diagram is attached below

We need to find out angle A

We know opposite side = 10ft and adjacent side = 36 ft

We use tan formula

[tex]tan(A) = \frac{opposite}{adjacent}[/tex]

[tex]tan(A) = \frac{10}{36}[/tex]

To find A we move tan to the other side, it becomes tan^-1

[tex]A =tan^{-1}(\frac{10}{36})[/tex]

A = 15.52

So angle of elevation to the sun is 15.52°

Answer:

first answer is -10

second answer is 10

third answer is -2

fourth answer is 2

Step-by-step explanation:

Explanation to get the answers:

you plug in the b c d and a

depending on what your abc and d are will depend on how the equation goes

like for example if the equation is

a x (c) - (-d) + b

and a=5, b=8, c=10, d=15

then you plug 5 where a is

plug in 10 where c is

plug 15 where d is as a negative

and lastly plug 8 where b is

if you have a calculator/graphing calculator i would use it to help answer these equations

a graphing calculator solves it for you without doing all the extra work like you would on a regular calculator

i use the graphing calculator to help solve equations like this specific one and it works very well

i hope my answers and explanation helps you :)

Answer:

b≤15

Step-by-step explanation:

If he only has 15 birdhouses in stock, then he can only sell 15 or less birdhouses. He cant sell more birdhouses, simply because he doesnt have more than 15.

Final answer:

The inequality representing the number of birdhouses Jason can sell, given he has 15, is b≤15 since he cannot sell more than he has.

Explanation:

The inequality that represents the number of birdhouses, b, Jason can sell at a craft fair, given he has 15 birdhouses, is b≤15. This is because the number of birdhouses he can sell cannot exceed the number he has, which is 15. The inequality b≤15 means that Jason can sell no more than 15 birdhouses, he could sell exactly 15, or he could sell less, depending on the demand at the craft fair.

This constraint ensures that Jason operates within the bounds of his available stock, preventing him from overselling. It implies that Jason can sell up to 15 birdhouses, including the possibility of selling exactly 15 or selling fewer, depending on the demand at the craft fair. This inequality serves as a practical guideline for Jason to manage his sales effectively, aligning his offerings with the limitations of his inventory.

Answer:

[tex]6^{\frac{1}{5} }=\sqrt[5]{6}[/tex]

[tex]6^{\frac{7}{5} }=\sqrt[5]{6^7}[/tex]

[tex]6^{\frac{1}{6} }=\sqrt[6]{6}[/tex]

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

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

[tex]6^{\frac{9}{2} }=\sqrt[2]{6^9}[/tex]

Step-by-step explanation:

A radical is the root operation for n roots such as square root or cuberoot in the form [tex]\sqrt[n]{x}[/tex]. A fraction exponent [tex]x^{m/n}[/tex] can be converted to the radical form.

[tex]6^{\frac{1}{5} }=\sqrt[5]{6}[/tex]

[tex]6^{\frac{7}{5} }=\sqrt[5]{6^7}[/tex]

[tex]6^{\frac{1}{6} }=\sqrt[6]{6}[/tex]

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

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

[tex]6^{\frac{9}{2} }=\sqrt[2]{6^9}[/tex]

Answer:

$60

Step-by-step explanation:

$120/2(half) = $60

Answer: The amount given by his grandfather to him = $60.

Step-by-step explanation:

Given : Andrei's grandfather offered to give him a gift at 50% of the amount of money he saved in one year.

The amount saved by Andrei = $ 120

Then, the amount given by his grandfather to him will be

50% of ( amount saved by Andrei )

= (0.50) x ($120) [When we convert a percent into decimal we divide it by 100]

= $60

Therefore , the amount given by his grandfather to him = $60.

The required expression that has a solution of 56 is 7r. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
In order to determine the expression that has a solution of 56 when r = 8, lets inverse the expression, to determine the exact expression,
Now,
Let the constant value be x,

xr = 56
Put x = 8
8x=56
x = 56/8
x = 7

So the expression can be given as 7r = 56

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[tex]a_1=2;\ a_2=-6;\ a_3=18;\ a_4=-54;\ a_5=162;\ ...[/tex]

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

A recursive rule for a geometric sequence:

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\r=\dfrac{-6}{2}=-3[/tex]

Therefore [tex]\boxed{a_1=2;\qquad a_n=-3a_{n-1}}[/tex]

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

The exciplit rule:

[tex]a_n=a_1r^{n-1}[/tex]

Substitute:

[tex]a_n=2(-3)^{n-1}=2(3)^n(3)^{-1}=2(3)^n\left(\dfrac{1}{3}\right)\\\\\boxed{a_n=\dfrac{2}{3}\left(-3)^n}[/tex]

Answer:

[tex]m=\frac{-10}{4}[/tex], [tex]\frac{-5}{4}=m+\frac{-15}{4}[/tex] and [tex]m+2=-0.5[/tex]

Step-by-step explanation:

We solve for m in the equation to find the value.

[tex]\frac{3}{4}+m=\frac{-7}{4}  \\\frac{3}{4}-\frac{3}{4}+m=\frac{-7}{4}-\frac{3}{4}\\m=\frac{-10}{4}[/tex]

We now look for expressions which are [tex]m=\frac{-10}{4}=-2.5[/tex] or whose expressions solve to the same.

The following are equivalent [tex]m=\frac{-10}{4}[/tex], [tex]\frac{-5}{4}=m+\frac{-15}{4}[/tex] and [tex]m+2=-0.5[/tex].

Answer:

3rd one for lesson: Translations of the Square Root Function

Step-by-step explanation:

It should be a parabola that opens upward and is shifted 2 units downward.

The graph of the quadratic function y = x² - 2 typically looks like.

The graph of the quadratic function y = x² - 2 is a parabola. Specifically, it's a upward-opening parabola because the coefficient of the x² term (which is 1) is positive.

- The vertex of the parabola is at the point (0, -2).

- The parabola opens upward, so it does not intersect or cross the x-axis.

- It reaches its minimum value at the vertex, which is -2.

The graph that represents an upward-opening parabola with a vertex at (0, -2) and does not intersect the x-axis. It should be a parabola that opens upward and is shifted 2 units downward.

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Answer: ∠ A = ∠B= 48° and ∠ C = 84°

Step-by-step explanation:

Here, m∠ADE: m∠ADB = 2:9

Let m∠ADE = 2x and m∠ADB = 9x

Where x is any value.

By joining the points D and E (construction)

Since, Here DE ║ AB.

⇒ ∠DAB = 2 x

⇒ ∠ A = 4x ( because AD is the angle bisector so, ∠DAB=∠DAE = 2x )

Now,  Let O is the intersection point of angle bisectors AD and BE.

Then, By the property of angle bisctor.

O is the circumcenter of the triangle ABC.

Therefore, OA = OB

⇒ ∠DAB = ∠EBA = 2 x

But BE is the angle bisceor,

Therefore, ∠EBA = ∠EBC=2 x

But, ∠B = ∠EBA + ∠EBC

⇒ ∠B = 4x

Now, since BD is the same transversal on the parallel lines AB and ED,

⇒ ∠B = ∠ EDC

⇒ ∠ EDC = 4x

Since, ∠ADB + ∠ADE + ∠EDC = 180°

⇒ 9x + 2x + 4x = 180°

⇒ 15x = 180°

⇒ x = 12°

Thus, the measures of the angles of ΔABC are,

∠ A = 4x =4×12 = 48°

∠ B = 4x =4×12= 48°

⇒ ∠ C = 180° - 48°- 48°= 84°

The question is about finding the angles of a triangle given certain conditions. We use the Angle Bisector Theorem and other geometric principles related to angle bisectors. We set up an equation based on these principles and solve for the angles.

The given scenario is about triangle ABC, with AD and BE acting as angle bisectors of ∠A and ∠B respectively. Also, provided is the ratio of m∠ADE to m∠ADB, which is 2/9. Given these conditions, we are to find the measures of the angles of ΔABC.

First, we can make use of the Angle Bisector Theorem, which states that an angle bisector of an angle of a triangle divides the opposite side in a ratio equal to the ratio of the other two sides. From this theorem, we see that m∠ADE / m∠ADB = AD / DB.

We know from the given that m∠ADE/m∠ADB = 2/9.

Since DE is parallel to AB, angle ∠ADE is equal to angle ∠BAC and angle ∠ADB is equal to angle ∠ABC by the corresponding angles postulate.

As ∠ADE and ∠ADB are part of a straight angle ∠ADA, then ∠ABC + ∠BAC = 180° - ∠ADB. We can use these relationships to create an equation, solve for the angles, and find the measures of the angles of ΔABC.

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Answer:

x=3

Step-by-step explanation:

Since this is an isosceles trapezoid

The angles at the top have to equal each other

112 = 30x + 11y

The sides also have to equal each other.

12 = 2x+3y

Divide each side by 3

12/3 = 2x/3 + 3y/3

4 = 2/3 x +y

Subtract 2/3 x from each side

4 -2/3 x =y

Substitute this into the first equation

112 = 30x + 11y

112 = 30x +11(4-2/3x)

112 = 30x +44 -22/3 x

Subtract 44 from each side

112-44 = 30x +44-44 -22/3 x

68 = 30x -22/3 x

Get a common denominator on the right of 3

68 = 90/3x -22/3 x

68 = 68/3 x

Multiply each side by 3/68

68 * 3/68 = 68/3 * 3/68 x

3 =x

Answer:

The experimental probability of red is 20%.

Step-by-step explanation:

When calculating out the experimental probability, you ignore the actual probability of the action taking place. In this case, you only look to what actually did take place. In this case it was 2 out of 10 times, so we complete that math.

2/10 = 20%

Answer:

The experimental probability of it landing on red is 2/10 or 1/5

Step-by-step explanation:

engenuity 2020

Answer:

324 minutes or 5 hours 24 minutes

Step-by-step explanation:

On Tuesday, Saima rode her bike for 52 miles. If it takes Saima 6 minutes to ride each mile, then it takes her

[tex]52\cdot 6=312[/tex]

minutes to ride all 52 miles.

Before she rides her bike, Saima warms up for 12 minutes.

Therefore, it takes Saima

[tex]12+312=324[/tex]

minutes to warm up and ride her bike on Tuesday.

Step-by-step explanation:

On Tuesday, Saima rode her bike for 52 miles. If it takes Saima 6 minutes to ride each mile, then it takes her

minutes to ride all 52 miles.

Before she rides her bike, Saima warms up for 12 minutes.

Therefore, it takes Saima

minutes to warm up and ride her bike on Tuesday.

[tex]\dfrac{a^b}{a^c}=a^{(b-c)}[/tex]

An exponent represents repeated multiplication. For example, ...

... x^3 = x·x·x

... x^2 = x·x

If we divide these, the x's in the denominator cancel an equal number in the numerator:

... (x·x·x)/(x·x) = x

If we represent the repeated multiplication using exponents, we can represent the cancellation by subtraction:

... (x^3)/(x^2) = x^(3-2) = x^1 = x

Once we have this idea in mind that division can be done by subtracting denominator exponents, we can use it regardless of the magnitude or sign of the exponents involved.

Answer:

B) -2/√5

Step-by-step explanation:

see attached

Jim and John drank a combined total of 7/10 of their water bottles, with Jim drinking 2/5 (converted to 4/10 for the common denominator) and John drinking 3/10.

To determine how much water Jim and John drank from their water bottles, we can add the fractions of the water they each drank. Jim drank 2/5 of his water bottle, while John drank 3/10 of his. To add these fractions, we need a common denominator, which in this case is 10. Convert 2/5 to 4/10 by multiplying the numerator and denominator by 2. Now, we can add 4/10 (Jim's consumption) and 3/10 (John's consumption) together.

The total amount of water drank by both boys is: 4/10 + 3/10 = 7/10

Thus, together, Jim and John drank 7/10 of their water bottles combined.

Answer: D) 4

Step-by-step explanation:

x⁴ - x³ - 9x² + 7x + 14 = 0

possible rational roots are: ±{1, 2, 7, 14}

Try x = -1

-1  |   1   -1   -9   7   14

   |   ↓  -1     2   7   -14

       1   -2    -7   14   0 ← remainder is 0 so x = -1 is a root

Let's try x = 2 with the factored polynomial

2  |  1   -2   -7   14

   |  ↓    2   0   -14

       1    0   -7    0  ← remainder is 0 so x = 2 is a root

Factored polynomial x² - 7 can be factored to:

(x - √7) (x + √7)

⇒ x = √7   and x = -√7

The roots are x = {-1, 2, √7, -√7) which are all real numbers.

The Apex Savings Bank was required to keep a reserve of 4.5% of the deposit. The bank was free to loan out the remaining 95.5% which equaled $12,128.50.

The reserve rate is the percentage of the deposit that the bank must keep, in this case, Apex Savings Bank. To calculate the reserve rate, we divide the reserve by the deposit and multiply by 100%. Therefore, ($571.50 / $12,700) * 100% = 4.5%. This means the bank had a reserve rate of 4.5% at that time.

Moving on towards the second question about how much Apex Savings Bank was free to loan out. Since the bank must keep 4.5% of the deposit, it is free to loan out the rest, which is 100% - 4.5% = 95.5%. By applying this percentage to the deposit, we see that Apex Savings Bank was free to loan out 95.5% of $12,700, or $12,128.50.

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Answer:

48, 11, and 90 from top to bottom

Step-by-step explanation:

Hi! You again!

so for every adult, there are 6 children

8+8+8+8+8, or 8x6, is 48

15+15+15+15+15+15, or 15x6 is 90

and the middle is where it's a bit tricky, since we have to divide instead of multiply.

we're trying to find out what times 6 is 66.

11+11+11+11+11+11 is 66.

Answer:

8-48

11-66

15-90

Step-by-step explanation:

make a table start from 1 and work your way down.

Answer:

Value of D=73

D is positive that means  the roots are real and distinct.

Step-by-step explanation:

We have been given a quadratic equation:

[tex]2x^2-3x+8[/tex]

We have to find its dicsriminant which is [tex]D=b^2-4ac[/tex]

Here, a=-2 , b=-3 and c=8 on comparing with the general equation [tex]ax^2+bx+c=0[/tex]

On substituting the values in the formula of discriminant we get:

[tex]D=(-3)^2-4(-2)(8)[/tex]

[tex]\Rightarrow D=9+64=73[/tex]

Value of D=73

If D is positive that means  the roots are real and distinct.

Answer: 33 and 28

Step-by-step explanation:

so, all we know is ? + ? = 61

if the larger number is 5 more than the smaller number, we can assume that..

33 + 28 = 61

The mean distance ran by all four of them is 30.

Given is that sum of two numbers is 61 . The larger number is 5 more than the smaller number.

We can write the equations as -

x + y = 61                                               .... Eq{ 1 }

y = x + 5                                                  .... Eq{ 2 }

Now, we can write -

x + y = 61

x + x + 5 = 61

2x = 56

x = 28

and

y = 33

Therefore, the mean distance ran by all four of them is 30.

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The lengths of the sides of triangle DEF are DE = 0.75 cm, EF = 1.125 cm, and DF = 1.5 cm.

Triangles ABC and DEF are similar, which means their corresponding angles are equal. In similar triangles, the ratio of the lengths of corresponding sides is constant. To find the lengths of the sides of DEF, we can use the ratio of the corresponding sides of ABC and DEF.

Let x be the length of DE in triangle DEF. Since DE corresponds to AB, we have the ratio x/2 = 1.5/4, which simplifies to x = 0.75 cm. Similarly, for EF corresponding to BC, y/3 = 1.5/4, giving y = 1.125 cm. Finally, for DF corresponding to CA, z/4 = 1.5/4, yielding z = 1.5 cm.

Therefore, the lengths of the sides of triangle DEF are DE = 0.75 cm, EF = 1.125 cm, and DF = 1.5 cm. This result is consistent with the idea that in similar triangles, the ratio of corresponding sides remains constant.

The calculation involved setting up and solving simple proportions based on the given lengths of the sides of triangle ABC and using them to find the lengths of the sides of triangle DEF.

Answer:

The base is greater than 1, making it an exponential growth function.

Step-by-step explanation:

The student's mistake is that an exponential decay function can only have the base as less than 1, but because 1/0.5 = 2, it's an exponential growth function.

Answer:

Step-by-step explanation:

f(x)=(1/0.5)^x

Lets simplify what is in the parentheses

1 / .5 = 2

f(x)=(2)^x

Since 2 > 1

 This function grows

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]m[/tex] - slope

[tex](x_1,\ y_1)[/tex] - point

We have the point [tex](3,\ -2)\to x_1=3,\ y_1=-2[/tex] and the slope [tex]m=\dfrac{2}{3}[/tex]

Substitute:

[tex]y-(-2)=\dfrac{2}{3}(x-3)\\\\\boxed{y+2=\dfrac{2}{3}(x-3)}[/tex]

Answer: C

Step-by-step explanation:

The general form of the equation is: g(x) = a|x - h| + k  ;

4 units left means h = 4

2 units up means k = 2

--> g(x) = |x - 4| + 2

Option: C is the correct answer.

                C.   [tex]g(x)=|x+4|+2[/tex]

The parent function f(x) is given by:

             [tex]f(x)=|x|[/tex]

Now, we know that for any parent function f(x) the transformation of the type:

 f(x) → f(x+k)

is a translation of the function f(x) k units to the right if k<0

and k units to the left if k<0

and the transformation of the type:

           f(x) → f(x)+k

is a translation of a function f(x) k units upward if k>0

and k units downward if k<0

Now here it is given that:

The function f(x) is shifted 4 units left and 2 units up.

Hence, the transformed function g(x) is given by:

[tex]g(x)=f(x+4)+2\\\\i.e.\\\\g(x)=|x+4|+2[/tex]

Answer:

[tex]\overline{AM}\cong \overline{AM}[/tex]

Step-by-step explanation:

Given that triangle TAM is congruent to the triangle HAM.

We know that corresponding sides of congruent triangles are equal so we can write:

TA = HA

AM = AM

TM = HM

comparing these with given choices we see that, (AM = AM) is the only matching answer.

Hence final answers is the first choice  [tex]\overline{AM}\cong \overline{AM}[/tex].

Answer:

Height is 18 inches.

Base is 36 inches.

Step-by-step explanation:

Let the base of the triangular table top be x inches.

The height will be [tex]\frac{1}{2}[/tex]x inches.

The area of the triangular table top is 324 inches²

Area of a triangle = [tex]\frac{1}{2}[/tex] × Base × Height

342 inches² = [tex]\frac{1}{2}[/tex] × x × [tex]\frac{1}{2}[/tex]x

[tex]\frac{x^2}{4}[/tex] = 324

Finding the square root on both sides gives;

[tex]\frac{x}{2}[/tex] = 18

Therefore x (the base) = 36 inches

And [tex]\frac{1}{2}[/tex] (the height) = 18 inches.

Final answer:

The height of the triangular table top is 18 inches, and the base is 36 inches, using the formula for the area of a triangle and given that the base is twice the height with an area of 324 square inches.

Explanation:

The question requires finding the height and base of a triangular table top given that the area is 324 square inches and the base is twice as long as the height. To find these dimensions, we can use the formula for the area of a triangle, which is Area (A) = [tex]\frac{1}{2}[/tex] × base (b) × height (h). Given that the base is twice the height, we can express the base as 2h.

Now, we can set up the equation using the given area: 324 = [tex]\frac{1}{2}[/tex] × 2h × h. Simplifying gives us 324 = h², so the height (h) would be the square root of 324, which is 18 inches. The base (2h) is therefore 36 inches. So, the dimensions of the tabletop are a base of 36 inches and a height of 18 inches.

An equation is formed of two equal expressions. The number is 4/3.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the unknown number be represented by x.

The given phrase can be written in the form of an expression "The sum of 1/2 and four times a number is equal to 5/6 subtracted from five times the number" as,

Now, we can write the equation by equating the expressions together and then solving it for x,

(1/2) + 4x = 5x - (5/6)

(1/2) + (5/6) = 5x - 4x

x = (1/2) + (5/6)

x = (3/6) + (5/6)

x = 8/6

x = 4/3

Hence, the number is 4/3.

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