Two geometric means are inserted between 4 and 864 so the four numbers form a geometric sequence. What are these two numbers ?

B is the correct answer , it is incorrect.

Answer:

(b) is incorrect

Step-by-step explanation:

Applying Pythagoras' theorem to the right triangle.

The square on the hypotenuse (t ) is equal to the sum of the squares on the other 2 sides, that is

t² = r² + s² ( subtract r² from both sides )

t² - r² = s² ← is a correct equation → (a)

Answer:

98

Step-by-step explanation:

Substitute the given values into the expression

u + xy

= 18 + (10 × 8 ) ← multiply before adding

= 18 + 80

= 98

Answer: [tex]\frac{7}{16}hour[/tex]

Step-by-step explanation:

You know that the total time was: 7/8 hour

You also know that they spent 1/2 of the time at the beach.

Therefore, to calculate the time  Zach and his dog spend at the beach (which you can call x) , you must multiply both fractions (7/8 and 1/2).

Then, you obtain the following result:

[tex]x=\frac{7}{8}hour*\frac{1}{2}\\\\x=\frac{7}{16}hour[/tex]

Zach and his dog spent 7/16 of an hour at the beach. This was calculated by multiplying the total walking time of 7/8 of an hour by 1/2, which represents the proportion of the total time spent at the beach.

The question is asking for the amount of time that Zach and his dog spent at the beach. We know that they spent 1/2 of their total walking time, which was 7/8 hour, at the beach. To find this, we simply need to multiply those two fractions together. Multiply the numerators (top numbers) together to get the numerator of the product, and multiply the denominators (bottom numbers) together to get the denominator of the product. 1 * 7 equals 7, and 2 * 8 equals 16, so the product is 7/16 of an hour. This is the amount of time they spent at the beach.

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Answer:

Part A : 9x^2 - x - 3

Part B : 5x^2 - 9x + 9

Part C : -5x^2 + 9x - 9

Answer:

  see the attachment for a graph

Step-by-step explanation:

A graphing calculator is a useful tool for this.

___

The x- and y-intercepts are -2, so you can plot those points and draw the line through them.

Answer:

A. $7,764.62

Step-by-step explanation:

The amount you will have after 10 years if you invest $2,500 into an account that pays 12% per year, compounded annually is given by

[tex]A=P(1+r\%)^t[/tex]

where [tex]t=10[/tex] years

[tex]r\%=0.12[/tex]

and P=$2,500

We substitute these values into the formula to obtain;

[tex]A=2500(1+0.12)^{10}[/tex]

This will give us;

[tex]A=2500(1.12)^{10}[/tex]

[tex]A=7764.6205[/tex]

We round to the nearest hundredth to obtain;

[tex]A=7,764.62[/tex]

The correct choice is A.

Answer:

Option A

Step-by-step explanation:

We must use the compound interest formula:

[tex]A = P(1 + r)^t[/tex]

Where

P is the initial amount = 2500

r is the annual interest rate =0.12

t is time in years = 10

A is the final amount

Then we substitute these values in the formula:

[tex]A = P(1 + r)^t\\\\A = 2500(1+0.12)^10\\\\A = 7,764.62[/tex]

Answer:

8 boxes of pencils and 2 boxes of erasers

Step-by-step explanation:

2 times 4 equals 8, which is the part where she needs to buy 4 times as many pencils as erasers.

8 times 2 is 16 and 1 times 2 is 2 add both 16 and 2 together and you get 18 so she spends all $18

Answer:

90°

Step-by-step explanation:

Arc a subtends and angle of 45° to the circumference of the circle

We know that;

An angle subtended by an arc to the center of a circle is twice the angle subtended by the same chord to the center of the circle.

Therefore, if arc a subtends and angle of 45° to the circumference of the circle then;

a will be = 45 × 2

              =  90°

Answer:

He used formula C).

Step-by-step explanation:

The correct formula for the slant height is given by

x^2 = 3^2 + 7^2

x =  7.62 cm.

To get 9.2 he must have used

x^2 = 6^2 + 7^2 = 85

as  √85 = about 9.2.

Answer:

the green at the top means i got it right

Step-by-step explanation:

The answer is: [tex]f(t)=-4t^{2}+t+3[/tex]

Since we are given a quadratic function, we need to write it using the standard form of quadratic function (parabola).

The given function is:

[tex]f(t)=3-2t.2t=+t[/tex]

The standard form of a parabola is:

[tex]f(t)=a^{2}+bx+c[/tex]

Where,

a is equal to the quadratic variable coefficient

b is equal to the linear variable coefficient

c is the constant number

So, writing the function in the standard form will be:

[tex]f(t)=3-2t*2t+t=3-4t^{2}+t=-4t^{2}+t+3[/tex]

[tex]f(t)=-4t^{2}+t+3[/tex]

Where,

[tex]a=-4\\b=1\\c=3[/tex]

Have a nice day!

no. No results should be presented in a fair and objective manner.

Answer:

Assume that, as a newspaper reporter, you must graph data showing that LED light bulbs are more environmentally friendly than traditional light bulbs. Given that the environment is important to everyone, is it ethical to construct a graph that exaggerates the environmental benefits?  

No, it is not important that people buy LED light bulbs.

Yes, the environment is important to everyone.

Yes, it is important to make sure that people buy LED light bulbs.

No, results should be presented in a fair and objective manner.

Step-by-step explanation:  

It is not ethical at all to lie and exaggerate things, but to be objective and say things as they really are.

The answer is: No, the results must be presented in a fair and objective manner.

8.5 would be more consistent

Answer:

4.2 would be more consistent.

Step-by-step explanation:

Answer:

C. 4%

Step-by-step explanation:

If x=6 and y=3 is 9_______________________________________

Answer:

x = 2

Step-by-step explanation:

The product of the external part times the entire secant of one secant is equal to the external part times the entire secant of the other secant, that is

(x + 4)(x + 5) = (x + 1)(x + 12) ← distribute factors on both sides

x² + 9x + 20 = x² + 13x + 12 ( subtract x² from both sides )

9x + 20 = 13x + 12 ( subtract 13x from both sides )

- 4x + 20 = 12 ( subtract 20 from both sides )

- 4x = - 8 ( divide both sides by - 4 )

x = 2

Answer:

212.5

Step-by-step explanation:

10=85

212.5=25

Gavin can drive 8.5 miles with 1 gallon of gas. Therefore, he can drive 212.5 miles with 25 gallons of gas.

The question asks how many miles Gavin can drive on 25 gallons of gas, given that he has driven 85 miles on 10 gallons of gas. This requires the use of proportions to calculate. First, you find out how many miles Gavin can drive on 1 gallon of gas, which is 85 miles / 10 gallons = 8.5 miles/gallon. Then, using this value, we can multiply it by 25 gallons to get the total miles Gavin can drive on 25 gallons, which is 8.5 miles/gallon * 25 gallons = 212.5 miles. Therefore, Gavin can drive 212.5 miles on 25 gallons of gas.

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Answer:

Yes

Step-by-step explanation:

A circle can be circumscribed around the four vertices of a quadrilateral if and only if,

both pair of opposite angles inscribed in the quadrilateral are supplementary to each other. By supplementary to each other we mean that their sum is equal to 180°.

In this case we have opposite interior angles supplementary to each other hence we can circumscribe a circle around it. Such Quadrilateral are called cyclic quadrilateral.

Answer:

The answer is True

Step-by-step explanation:

I just got it correct.

Answer:

B) x = 1

C) x = 4

Step-by-step explanation:

Given:

f(x) = 2x

g(x) = 2^x

We have to find at what value of x, the above two functions are equal in value.

Now we have to check with the each options.

When x = 0, f(0) = 2(0) = 0 ; g(0) = 2^0 = 1 [Anything power 0, is 1]

When x = 1, f(1) = 2(1) = 2 ; g(1) = 2^1 = 2.

when x = 2, f(2) = 2(2) = 4; g(2) = 2^2 = 4

when x = 3, f(3) = 2(3) = 6, g(3) = 2^3 = 8

when x = 4, f(4) = 2(4) = 8, g(4) = 2^4 = 16

The two functions are equal in value when x = 1 and x = 2.

Final answer:

The value(s) of x for which the equation f(x) = 2x and g(x) = 2ˣ are equal are x = 1 and x = 2, as those are the points where the two functions have the same value.

Explanation:

The student seems to be asking for which value(s) of x the equations f(x) = 2x and g(x) = 2ˣ are equal. To find the solution, we need to identify the point where the two functions intersect, by setting them equal to each other and solving for x.

So we set up the equation 2x = 2ˣ and look for solutions. At first glance, it seems there are two obvious solutions:

When x = 1, f(x) = 2 x 1 = 2 and g(x) = 2¹ = 2, so the statement f(x) = g(x) is true.

When x = 0, f(x) = 2 x 0 = 0 and g(x) = 2⁰ = 1, so the statement f(x) = g(x) is not true.

Testing the other provided options similarly, you'll find that:

For x = 2, f(x) = 4 and g(x) = 4, hence f(x) = g(x) is true.

For x = 3, f(x) = 6 and g(x) = 8, hence f(x) = g(x) is not true.

For x = 4, f(x) = 8 and g(x) = 16, hence f(x) = g(x) is not true.

The correct answers are x = 1 and x = 2, where the equation f(x) = g(x) holds true.

Answer: [tex]3b^2-9bat^2+6a^2t^4[/tex]

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Apply the Distributive property.

- Remember that, according the exponents properties, when you multiply two powers with equal base, you must add the exponents.

- Add the like terms.

Therefore, you obtain that the product is the following:

[tex](b-2at^2)(3b-3at^2)=3b^2-3bat^2-6bat^2+6a^2t^4=3b^2-9bat^2+6a^2t^4[/tex]

Answer:

width=6cm, lenth is 7cm

Step-by-step explanation:

Let width of rectangle be x cm

Twice width=2x cm

length=2x-5 cm

Area of the rectangle= L× W =42cm²

(2x-5) × x =42

x(2x-5)=42

2x²-5x-42=0

solving the quadratic equation

x=6cm

width=6cm

length= (2×6)- 5 =7cm

Answer:

The answer is 15 m.

Step-by-step explanation:

Answer:

b = 15

Step-by-step explanation:

Using Pythagoras' theorem on the right triangle, that is

20² + b² = 25²

400 + b² = 625 ( subtract 400 from both sides )

b² = 225 ( take the square root of both sides )

b = [tex]\sqrt{225}[/tex] = 15

Figure 1: find the surface area: [(3 x 2 1/4) x 2] for the top and bottom. [(4 1/2 x 2 1/4)x 2] for the left and right squares. [(3 x 4 1/2) x 2] for the front and back. Which should be 20 1/4 + 27 + 13 1/2 = 60 3/4 m. The area is 4 1/2 x 3 x 2 1/4 = 30 3/4 m.

The area of the pattern is calculated by finding the area of the circle, semicircles, and quarter-circles separately and then adding them together. The area of the pattern is approximately 1005.31 cm^2.

To find the area of the pattern, we need to calculate the area of the circle, semicircles, and quarter-circles separately. The area of a circle is found using the formula A = πr^2, where r is the radius. So, the area of the circle is A = π(8)^2 = 64π cm^2. The area of a semicircle is half the area of a circle, so it is 32π cm^2. The area of a quarter-circle is a quarter of the area of a circle, which is 16π cm^2. To find the total area of the pattern, we add the areas of the circle, semicircles, and quarter-circles: 64π + 4(32π) + 8(16π) = 64π + 128π + 128π = 320π cm^2. Rounding to the nearest hundredth, the total area of the pattern is approximately 1005.31 cm^2.

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Finding the areas of the circles, semicircles, and quarter-circles separately and combining them together yields the pattern's overall area. The pattern's estimated area is 1005.31 cm^2.

To determine the area of the pattern, individual areas of the circle, semicircles, and quarter-circles are computed separately.

Utilizing the formula

A = πr^2

for a circle with a radius (r) of 8 cm, the circle's area is 64π cm^2.

The semicircles, constituting half the circle's area, total 32π cm^2 each.

Quarter-circles, representing a quarter of the circle's area, contribute 16π cm^2 each.

Combining these, the pattern's total area is calculated as 64π + 4(32π) + 8(16π) = 320π cm^2.

Rounded to the nearest hundredth, the total area is approximately 1005.31 cm^2.

This comprehensive approach ensures the accurate summation of all constituent shapes within the intricate pattern.

Answer:

[tex]\large\boxed{\dfrac{16a^4b^2c}{2abc}=8a^3b}[/tex]

Step-by-step explanation:

[tex]\dfrac{16a^4b^2c}{2abc}=\dfrac{16}{2}\cdot\dfrac{a^4}{a}\cdot\dfrac{b^2}{b}\cdot\dfrac{c}{c}=8a^3b[/tex]

Answer:

6g

Step-by-step explanation:

add all G's

The equivalent expression of g + g + g + g + g + g is 6g

The expression is given as:

g + g + g + g + g + g

Factor out g

g + g + g + g + g + g = g(1 + 1 + 1 + 1 + 1 +1)

Evaluate the sum

g + g + g + g + g + g = g * 6

Evaluate the product

g + g + g + g + g + g = 6g

Hence, the equivalent expression of g + g + g + g + g + g is 6g

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Answer:

1100 in²

Step-by-step explanation:

Find the area of the boxes separately and add them

first you have to add the -4 to the -2 and you get 2. so 2x=2 then you divide 2 by 2x and get x=1

The measure of one interior angle of a 42 sided regular polygon is given by A = 171.428°

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the interior angle of the polygon be represented as A

Now , let the number of sides of the polygon be n = 42 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

On simplifying , we get

42θ = 180 ( 42 - 2 )

42θ = 180 ( 40 )

Divide by 42 on both sides , we get

A = 180 ( 40 ) / 42

A = 171.428°

Therefore , the value of A is 171.428°

Hence , the measure of one angle is  171.428°

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Answer:

c

Step-by-step explanation:

Notice that there are two variables-- gender and preference-- this is where the two in two-way

Answer:

C)

Step-by-step explanation:

Answer:

Step-by-step explanation:

(2x-1)²=x²+4²

4x²-4x+1=x²+16

3x²-4x-15=0

a=3   b=-4   c= -15

D=b²-4ac

=16-4*3*(-15)=196

x1=-b+√D/2a=4+14/6=3

x2=-b-√D/2a=4-14/6=-10/6=-5/3

Answer:

x = 3

Step-by-step explanation:

Using Pythagoras' theorem on the right triangle, then

(2x - 1)² = 4² + x² ← expand parenthesis on the left side and simplify

4x² - 4x + 1 = 16 + x² ( subtract 16 + x² from both sides )

3x² - 4x - 15 = 0 ← in standard form

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × - 15 = - 45 and sum = - 4

The factors are - 9 and + 5

Use these factors to split the x- term

3x² - 9x + 5x - 15 = 0 ( factor the first/second and third/fourth terms )

3x(x - 3) + 5(x - 3) ← factor out (x - 3)

(x - 3)(3x + 5) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - [tex]\frac{5}{3}[/tex]

However, x must be greater than zero

Hence x = 3 cm

Answer:

X=56/9

Step-by-step explanation:

7x+2(x-5)46

7x+2x-10=46

9x-10=46

9x=46+10

9x=56