Write the fractions as mixed number. Answers please for each

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:

Multiply by 2

Step-by-step explanation:

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°

8.5 would be more consistent

Answer:

4.2 would be more consistent.

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

For this case we have that the order of algebraic operations must be carried out in the following way, according to the PEMDAS method:

P

Parenthesis first

E

Exponents (powers and square roots, etc.)

MD

Multiplication and Division (from left to right)

AS

Addition and Subtraction (from left to right)

We have two expressions:

[tex]8 * 3 ^ 2 + 3 =\\8 * 9 + 3 =\\72 + 3 =\\75[/tex]

The second expression is:

2^2 * 8÷2 + 2 =

4 * 8÷2 + 2 =

32÷2 + 2 =

16 + 2 =

18

ANswer:

75 and 18

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.

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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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.

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:

45 mph ≠ 40 mph

Step-by-step explanation:

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:

X=56/9

Step-by-step explanation:

7x+2(x-5)46

7x+2x-10=46

9x-10=46

9x=46+10

9x=56

Answer:

1100 in²

Step-by-step explanation:

Find the area of the boxes separately and add them

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.

An atom containing two more electrons than protons has a net charge of negative two (-2), as determined by the difference in number of positive protons and negative electrons.

An atom which has two more electrons than protons has a charge of -2. The charge of an atom is determined by the difference between the number of protons and electrons. Protons have a charge of +1 and electrons have a charge of -1. Hence, if the atom has two more electrons than protons, it will have a charge of -2 because electrons contribute a negative charge. For instance, for an atom with 2 protons (+2 charge) and 4 electrons (-4 charge), the overall charge would be -2.

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An atom with 2 more electrons than protons will have a net charge of -2.

An atom is the basic unit of matter, consisting of a nucleus containing protons and neutrons, surrounded by electrons. Elements are defined by the number of protons in their atoms. An atom's charge is determined by the difference between the number of electrons and the number of protons. If an atom has 2 more electrons than protons, it will have a net charge of -2.

For example, let's consider the element oxygen (O). Oxygen normally has 8 protons and 8 electrons, resulting in a neutral charge. If we add 2 more electrons to oxygen, it will then have 10 electrons and still 8 protons, giving it a net charge of -2.

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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:

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:

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

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!

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:

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:

-3 143/1000

Step-by-step explanation:

To write -3.143 in its equivalent fraction form, multiply the whole number part by the place value of the decimal and add it to the decimal part multiplied by the place value. The resulting fraction is -3143/1000.

To write the decimal number -3.143 in its equivalent fraction form, we first need to determine the place value of each digit. The number -3.143 has three digits after the decimal point, so the fraction's denominator will be ten, raised to the power of three, which is 1000. The fraction's numerator will be the whole number part of the decimal (in this case, -3) multiplied by 1000, plus the decimal part (0.143) multiplied by 1000.

Therefore, the equivalent fraction form of -3.143 is:

-3.143 = (-3 * 1000 + 0.143 * 1000) / 1000 = -3143 / 1000

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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

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:

Part A : 9x^2 - x - 3

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

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

Answer:

A:  6x - 7

Step-by-step explanation:

You may find it helpful to rearrange these two quantities vertically:

Add:

  (4x-3)

 +(2x-4)

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

    6x - 7

This corresponds to the first possible answer listed:  A.

The simplified expression is 6x - 7.

Hence the correct option is A.

Given is an expression (4x-3) + (2x-4), we need to perform addition operation to simplify the expression.

You must combine like terms in the provided expression, (4x-3) + (2x-4), to make it simpler.

Similar terms are those that share a variable and an exponent.

Group terms that are similar together.

(4x - 3) + (2x - 4)

Add the like terms' coefficients.

(4x + 2x) + (-3 - 4)

Add the coefficients together.

6x - 7

Therefore, the simplified expression is 6x - 7.

Hence the correct option is A.

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Answer:

the third graph

The correct graph is Graph 3.

We are given a modulus function f(x) by:

       [tex]f(x)=2|x|[/tex]

We will go through the following graphs by checking the value of the graph at some value of x and see whether the value on the graph at that x matches the value of f(x) at that particular x.

when x=1 we have:

[tex]f(x)=2\times |1|\\\\f(x)=2[/tex]

Graph 1:

When x=1

we have:

[tex]f(x)=0.5\neq 2[/tex]

Hence, Graph 1 does not represent the given function.

Graph 2:

when x=1 we have:

[tex]f(x)=1\neq 2[/tex]

Hence, Graph 2 is not the answer.

Graph 4:

when x=1 we have:

[tex]f(x)<2[/tex]

Hence, graph 4 is not the correct graph to represent f(x).

Hence, we are left with Graph 3.

When we plot the function f(x) we see that it matches the graph 3.

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:

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:

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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