How to solve radicals

The expressions with a product less than 2/3 are:

2/3 × 2/3 and 5/6 × 2/3 ⇒ 2nd and 4th

Step-by-step explanation:

Let us revise some fact about the product of two numbers

We need to select all the expressions with a product less than 2/3

∵ 4 and 1/8 × 2/3

- 4 and 1/8 means mixed number [tex]4\frac{1}{8}[/tex]

∵ [tex]4\frac{1}{8}[/tex] > 1

- That means the product of it and 2/3 will be greater than 2/3

   as the first fact above

∴ [tex]4\frac{1}{8}[/tex] × [tex]\frac{2}{3}[/tex] > [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{2}{3}[/tex] is between 0 and 1

- That means the product of it and 2/3 will be less than 2/3

   as the second fact above

∴ [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] < [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{2}{3}[/tex] × 2

∵ 2 > 1

- That means the product of it and 2/3 will be greater than 2/3

   as the first fact above

∴ [tex]\frac{2}{3}[/tex] × 2 > [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{5}{6}[/tex] × [tex]\frac{2}{3}[/tex]

∵ [tex]\frac{5}{6}[/tex] is between 0 and 1

- That means the product of it and 2/3 will be less than 2/3

   as the second fact above

∴ [tex]\frac{5}{6}[/tex] × [tex]\frac{2}{3}[/tex] < [tex]\frac{2}{3}[/tex]

The expressions with a product less than 2/3 are:

2/3 × 2/3 and 5/6 × 2/3

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Only the expressions 2/3 x 2/3 and 5/6 x 2/3 have products less than 2/3, with products of 4/9 and 5/9 respectively.

To determine which expressions have a product less than 2/3, each expression must be evaluated separately:

4 and 1/8 x 2/3 = 33/8 x 2/3

2/3 x 2/3 = 4/9

2/3 x 2 = 4/3

5/6 x 2/3 = 10/18 or 5/9

After simplifying, the expressions that yield a product less than 2/3 are:

2/3 x 2/3 = 4/9, as 4/9 is less than 6/9 (2/3)

5/6 x 2/3 = 5/9, which is also less than 6/9 (2/3)

The expressions 4 and 1/8 x 2/3 and 2/3 x 2 are both greater than 2/3.

Answer:

8a+5

Step-by-step explanation:

Like terms and yea

Answer: 8a + 5

Step-by-step explanation:

Combining like terms makes you add 5a + 3a and +7 - 2

The question is incomplete. Here is the complete question:

During ski season,the owner of ski shop has determined that the number of customers in a day is greater than or equal to 50 more then the temperature(Fahrenheit) . Write an inequality for the problem and determine the constraints on the variables.

Answer:

[tex]N\geq T+50[/tex]

Step-by-step explanation:

Let the number of customers be 'N' and the temperature in Fahrenheit be 'T'.

Given:

Number of customers is related to temperature in Fahrenheit as:

Number of customers is greater than or equal to 50 more than the temperature in Fahrenheit. This means,

[tex]N\geq T+50[/tex]

Now, since 'N' represents number of customers and number can never be a negative quantity. So, the only constraint for this inequality is that the number of customers must be greater than or equal to 0.

So, [tex]N\geq 0[/tex]

Mai made 12 successful free throws.

Step-by-step explanation:

Given,

Free throws made by Mai = 49 free throw

Successful throws = 25%

Number of successful throws = 25% of free throws

Number of successful throws = [tex]\frac{25}{100}*49[/tex]

Number of successful throws = [tex]\frac{1225}{100} = 12.25[/tex]

Rounding off to nearest whole number;

Number of successful throws = 12

Mai made 12 successful free throws.

Keywords: percentage, division

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Votes received by Wayne is 112

Solution:

To find: votes received by Wayne

Let the vote received by Wayne be "x"

Juan received 4 times as many votes as Wayne

Therefore,

Juan votes = 4 times as many votes as Wayne

Juan votes = 4x  ---- eqn 1

Neal received twenty less votes than Juan

Neal votes = twenty less votes than Juan

Neal votes = Juan votes - 20

Neal votes = 4x - 20 ---- eqn 2

Kerry got half as many votes as Neal

Kerry votes = half of neal votes

Kerry votes = [tex]\frac{4x - 20}{2}[/tex]  ---- eqn 3

The total votes cast in the election was 1,202

Wayne votes + Juan votes + Neal votes + Kerry votes = 1202

Plug in eqn 1 , eqn 2, eqn 3

[tex]x + 4x + 4x - 20 + \frac{(4x - 20)}{2} = 1202\\\\2x + 8x + 8x - 40 + 4x - 20 = 1202 \times 2\\\\22x - 60 = 2404\\\\22x = 2404 + 60\\\\22x = 2464\\\\x = 112[/tex]

Therefore votes received by Wayne is 112

Answer:

2x - 4

Step-by-step explanation:

Write out the equation:

(2 * x) - 4

Simplify

2x - 4

:)

Answer:

y = - 7x + 73

Step-by-step explanation:

y = mx + b   m: slope       b: y intercept

m = (y-y') / (x-x') = (31-3) / (6-10) = 28 / - 4 = -7

b = y - mx = 3 - (-7) x 10 = 73

equation: y = -7x + 73

check: 31 = -7 x 6 +73 = -42 + 73 = 31      (6,31)

The half-life h is calculated to be approximately 2.41.

To determine the half-life h from the given half-life function:

[tex]\[ Q(t) = 28550 \cdot \left( \frac{3}{4} \right)^{\frac{t}{h}} \][/tex]

we need to solve for h in the equation:

[tex]\[ \left( \frac{3}{4} \right)^h = \frac{1}{2} \][/tex]

To solve for  h , we take the natural logarithm (ln) of both sides of the equation:

[tex]\[ \ln \left( \left( \frac{3}{4} \right)^h \right) = \ln \left( \frac{1}{2} \right) \][/tex]

Using the logarithmic property [tex]\(\ln(a^b) = b \ln(a)\)[/tex], we get:

[tex]\[ h \ln \left( \frac{3}{4} \right) = \ln \left( \frac{1}{2} \right) \][/tex]

Now, solve for h :

[tex]\[ h = \frac{\ln \left( \frac{1}{2} \right)}{\ln \left( \frac{3}{4} \right)} \][/tex]

Calculate the natural logarithms:

[tex]\[ \ln \left( \frac{1}{2} \right) = \ln(0.5) \approx -0.6931 \\\[ \ln \left( \frac{3}{4} \right) = \ln(0.75) \approx -0.2877 \][/tex]

Now, divide these values to find  h :

[tex]\[ h = \frac{-0.6931}{-0.2877} \approx 2.41 \][/tex]

So, the half-life  h  is approximately:

[tex]\[ h \approx 2.41 \][/tex]

Therefore, the half-life  h  rounded to the nearest hundredth is:

h = 2.41

Answer:

A. 10%

Step-by-step explanation:

Let events A nad B be:

A = an employee is a female

B = an employee is under the age of 30.

Use formula

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

There are 200 employees, 150 of them are female, then

[tex]P(A)=\dfrac{150}{200}=\dfrac{3}{4}=0.75[/tex]

There are 200 employees, 40 of them are under the age of 30, then

[tex]P(B)=\dfrac{40}{200}=\dfrac{1}{5}=0.2[/tex]

The probability of randomly selecting an employee who is a female or under the age of 30 is 85%, then

[tex]P(A\cup B)=0.85[/tex]

Thus,

[tex]0.85=0.75+0.2-P(A\cap B)\\ \\0.85=0.95-P(A\cap B)\\ \\P(A\cap B)=0.95-0.85=0.1[/tex]

Therefore, the probability of randomly selecting an employee who is a female and under the age of 30 is 0.1 or 10%.

Answer:

[tex]\frac{7}{3}[/tex]

Step-by-step explanation:

Im going to assume a faction greater than one means an improper fraction.

Converting [tex]2 \frac{2}{6}[/tex] gets [tex]\frac{14}{6}[/tex] which simplified is [tex]\frac{7}{3}[/tex]

Answer:

get the $429 with 20% off cuz its really only $343.2

Step-by-step explanation:

100%-20%=80%

80%=0.8

429x0.8=343.2

Answer:

The last is the correct option

"all real values except x not-equals 7 and the x for which f (x) not-equals negative 3"

Step-by-step explanation:

Domain and Range of Functions

Given the function f(x), the domain of f is the set of all the values that x can take such f(x) exists. The range of f is the set of all the values that f takes.

We have a problem where we have to find the domain of a composite function. Let's recall that being f and g real functions, then

[tex]g\circ f=g(f(x))[/tex]

is the composite function of f and g.

We know the domain of f is the set of all real values except 7, and the domain of g is the set of all real values except –3.

Since f is the innermost function, the domain of the composite function is directly restricted by the domain of f. So, x cannot be 7.

Now, g takes f as its independent variable, and we know the domain of g excludes -3. It can be found that f(x) cannot be -3 because it will cause g not to exist.

Thus, the domain of [tex]g\circ f[/tex] is

All real numbers except x=7 and those where f(x)=-3

The last is the correct option

Answer:

Question 3:  [tex]4x^3+x^2-12x-3[/tex]

Question 4:  [tex]\frac{1}{2x}, x\neq 0[/tex]

Step-by-step explanation:

Question 3

g(x) * h(x) means to multiply both the functions given.

Also note the distributive property:

[tex](a+b)(n+p)=an+ap+bn+bp[/tex]

Now, lets multiply:

[tex]g(x)*h(x)=(4x+1)(x^2-3)\\=(4x)(x^2)-3(4x)+1(x^2)-1(3)\\=4x^3-12x+x^2-3\\=4x^3+x^2-12x-3[/tex]

The 2nd answer choice is right

Question 4

[tex](\frac{f}{g})(x)[/tex]  means to divide both the functions and simplify, if possible. Lets do this:

[tex](\frac{f}{g})(x)=\frac{6x-3}{12x^2-6x}=\frac{3(2x-1)}{6x(2x-1)}=\frac{3}{6x}=\frac{1}{2x}[/tex]

This is the correct answer.

The restriction on the domain is any x value that we CANNOT PUT IN THE FUNCTION.

We know we cannot divide by 0, so what makes this fraction division by 0??

If we put x = 0, the function is undefined. So x CANNOT be 0.

Third answer choice is right.

Answer:

x^2(5x-4)

Step-by-step explanation:

5x^3-4x^2=x^2(5x-4)

The solution is x = 4

Step-by-step explanation:

The given equation is a linear equation so it will have only one equation

Given equation is:

[tex]5x+3=2x+15​[/tex]

Subtraction property of equality:

[tex]5x+3-3 = 2x+15-3\\5x = 2x+12[/tex]

Subtraction property of equality:

[tex]5x-2x = 2x-2x+12\\3x = 12[/tex]

Division Property of Equality:

[tex]\frac{3x}{3} = \frac{12}{3}\\x = 4[/tex]

Hence,

The solution is x = 4

Keywords: Linear equation, variables

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Answer:

y-8=5/6(x-12)

Step-by-step explanation:

y-y1=m(x-x1)

y-8=5/6(x-12)

The required equation of the line is [tex]\rm y = \dfrac{5}{6}x-2[/tex].

Given that,

The equation of the line is,

[tex]\rm y = \dfrac{5}{6}(x-10)[/tex]

It passes through the point (12, 8).

We have to determine

The equation of the line is parallel to the given line.

According to the question,

The equation of the line is,

[tex]\rm y = \dfrac{5}{6}(x-10)[/tex]

The slope of the line [tex]\rm m_1[/tex] is 5/6.

If the two lines are parallel to each other then the slope of these lines is the same.

[tex]\rm m_1 = m_2\\\\\dfrac{5}{6} = \dfrac{5}{6}[/tex]

Therefore,

The equation of line passes through the point (12, 8) is,

[tex]\rm( y -y_1) = m (x-x_1)\\\\(y-8) = \dfrac{5}{6} (x-12)\\\\6 (y-8) = 5(x-12)\\\\6y-48=5x-60\\\\6y = 5x-60+48\\\\6y = 5x-12\\\\y = \dfrac{5}{6}x- \dfrac{12}{6}\\\\y = \dfrac{5}{6}x-2[/tex]

Hence, The required equation of the line is [tex]\rm y = \dfrac{5}{6}x-2[/tex].

For more details refer to the link given below.

https://brainly.com/question/9351049?

Answer:

52.33 inches

Step-by-step explanation:

Multiply the length of one side by the square root of 2.

In this case: 37, you would divide that by the square root of 2.

Hope this helps!

Answer:

[tex]f(5)=10[/tex]

Step-by-step explanation:

A sequence is defined by the recursive formula [tex]f(n+1)=f(n)-2[/tex]

If [tex]f(1)=18,[/tex] then

for [tex]n=1: f(2)=f(1+1)=f(1)-2=18-2=16[/tex]

for [tex]n=2: f(3)=f(2+1)=f(2)-2=16-2=14[/tex]

for [tex]n=3: f(4)=f(3+1)=f(3)-2=14-2=12[/tex]

for [tex]n=4: f(5)=f(4+1)=f(4)-2=12-2=10[/tex]

Answer:

10!

Step-by-step explanation:

Answer:

[tex]m=\frac{3}{4}[/tex]

Step-by-step explanation:

This equation is in the form of y=mx+b

In this equation, m is the slope. m is the coefficient of x.

In the equation, [tex]y=\frac{3}{4} x-7[/tex]

[tex]m=\frac{3}{4}[/tex], which is the slope.

Answer:

m = 3/4

Step-by-step explanation:

This equation is in the form of y=mx+b

In this equation, m is the slope. m is the coefficient of x.

In the equation, y=\frac{3}{4} x-7

m=\frac{3}{4}, which is the slope.

Answer:

Area =  [tex]2w^2+12w+16[/tex]

Step-by-step explanation:

We let the width of the pool be "w"

We know the length is twice as long as width, so the length is:

2w

So,

Width = w

Length = 2w

Since a sidewalk with 2 feet width goes around the pool completely, the area enclosed by pool + sidewalk would have 2 feet around it, so its length and width would be:

Width = w + 2 + 2 = w + 4

Length = 2w + 2 + 2 = 2w + 4

The area of a rectangular region is always length * width, so the expression for area of pool and sidewalk would be:

[tex](w+4)(2w+4)\\=2w^2+4w+8w+16\\=2w^2+12w+16[/tex]

If we let the width of the swimming pool be "w", the expression for the area of pool and sidewalk is:

Area =  [tex]2w^2+12w+16[/tex]

Answer:C: x = the quantity of 1 plus or minus the square root of 17 all over 2

Step-by-step explanation:

Answer:

The answer is option C: x = the quantity of 1 plus or minus the square root of 17 all over 2

Step-by-step explanation:

The general form of the quadratic equation is ax² + bx + c = 0

The general solution of the quadratic equation is:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

The given equation is x² − x − 4 = 0

So, a = 1 , b = -1 and b = -4

Substitute with a , b and c at the formula of the general solution.

The solution of the given equation = [tex]\frac{-(-1) \pm \sqrt{(-1)^2 - 4 * 1 * (-4)} }{2*1}= \frac{1\pm \sqrt{1 +16} }{2}=\frac{1\pm \sqrt{17} }{2}[/tex]

Comparing the solution with the given options

So, the answer is option C: x = the quantity of 1 plus or minus the square root of 17 all over 2

Answer: 40:8 and 20:4

Step-by-step explanation :It matches up if you multiply both top and bottom with 8 to get 40:8 and multiply with 4 to get 20:4 .

Answer:

A and E

Step-by-step explanation:

Answer:

x ≥ 25

Step-by-step explanation:

In the seventh grade, fifty students are trying for sports supplies to raise at least $2000. They already have $750.

Let us assume that each student has to raise $x more to meet the goal.

Then, a total of 50 students will raise $50x more.

Therefore, the inequality to solve for x will be  

750 + 50x ≥ 2000

⇒ 50x ≥ 1250

⇒ x ≥ 25 (Answer)

Final answer:

Each seventh grade student should raise at least $25 in order to collectively meet the goal of raising $2000 for their sports supplies after having already raised $750.

Explanation:

The goal amount for the seventh grade sports supplies fundraiser is $2000. They have already raised $750, leaving them with $1250 still needed to reach their goal. If there are 50 students working on the fundraiser, we can set up an inequality to determine how much money each student should raise minimally to meet the goal of $2000. Here's the inequality:

Let x be the amount each student needs to raise.

50x + $750 ≥ $2000

To solve for x, we subtract $750 from both sides of the inequality:

50x ≥ $2000 - $750

50x ≥ $1250

Now divide both sides by 50 to find the amount each student should raise:

x ≥ $1250 / 50

x ≥ $25

Therefore, each seventh grade student should raise at least $25 to meet the $2000 goal.

Answer:

m∠1 = 50°

m∠2 = 88°

Step-by-step explanation:

Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.

Answer:

2.) m/_1 = 50

3. )m/_2=88

Step-by-step explanation:

2.) the line that the exterior angle 140 is on is a straight line. this means it is 180 degrees. 180 - 140 = 40. the box in the left corner means it is a right angle or 90 degrees. evey triangle is 180 degrees so add 40 and 90 to get 130 and then subtract 130 from 180 to get 50 which is the angle number 1.

3.)the line 120 is on is a straight line so we do 180 minus 120 to get the angle inside. it is 60. 60 +32 = 92. 180 - 92 is 88 degrees.

Answer:

6x+2y+3

Step-by-step explanation:

5x+3+2y+x

6x+2y+3

Answer:

Do you know the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

67.6 oz cost $ 1.89

unit rate is : 1.89 / 67.6 = 0.027....rounds to 3 cents per oz

12 twelve oz cans.....thats (12 * 12) = 144 oz....for 2.99

2.99 / 144 = 0.0207....rounds to 2 cents per oz

the better bargain would be the 12 twelve oz cans because u save one penny more per oz then when ur buying the 2 liter bottle

Answer:

10

Step-by-step explanation:

n is the number of selections and k the number selected, that is

n = 5 and k = 2

note that n! = n(n - 1)(n - 2) ..... × 3 × 2 × 1, thus

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

= [tex]\frac{120}{2(1)3(2)(1)}[/tex]

= [tex]\frac{120}{2(6)}[/tex]

= [tex]\frac{120}{12}[/tex]

= 10

Answer:

10 cups

Step-by-step explanation:

First, we need to find the unit rate. 24/8 equals to 3. 3 is the amount of flour per cupcake. 24 + 3= 27 + 3= 30. You added twice to get to 30. 8+2=10

Answer:

The inequality is [tex]l\times (3.25)\leq 107.25[/tex]

Step-by-step explanation:

Given: Area of volleyball net= [tex]107.25 ft^{2}[/tex]

          Width of Volleyball net= [tex]3.25 \ ft[/tex]

Considering the volleyball net is in rectangular shape and l and w is length and width respectively.

Area of rectangle= [tex]l\times w[/tex]

Now, using formula to form inequality

⇒ [tex]l\times (3.25)\leq 107.25[/tex]

Next, using the inequality to find length of Volleyball net.

∴  [tex]l\times (3.25)\leq 107.25[/tex]

Dividing both side by 3.25

⇒ [tex]l= \frac{107.25}{3.25} = 33\ ft[/tex]

∴ l= 33 ft

The possible length of Volleyball net is 33 ft.

Answer:

b

Step-by-step explanation:

Answer:

That would be about 11.667

The number that is 2/3 of the way from 7 to 13 on a number line is 11. This is found by calculating 2/3 of the distance between the two numbers and adding it to the starting number.

To find the number that is 2/3 of the way from 7 to 13 on a number line, you first calculate the distance between the two numbers, which is 13 - 7 = 6. Then you take 2/3 of that distance, which is 2/3 * 6 = 4. Lastly, you add this result to the starting number, in this case, 7, giving you 7 + 4 = 11. Therefore, the number that is 2/3 of the way from 7 to 13 is 11.