4. Simplify the radical expression.

Answer:

x=1

Step-by-step explanation:

3x−1+2=4

Add −1 and 2 to get 1.

3x+1=4

Subtract 1 from both sides.

3x=4−1

Subtract 1 from 4 to get 3.

3x=3

Divide both sides by 3.

x=

3

3

​

Divide 3 by 3 to get 1.

x=1

Answer: C

Step-by-step explanation:

This is the definition of a negative exponent.

===================================================

Work Shown:

[tex]\frac{n^2+n-6}{n-2}\\\\\frac{(n+3)(n-2)}{n-2}\\\\n+3[/tex]

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

Explanation:

Often when simplifying, it's a good idea to factor and see what cancels (if anything does cancel).

To factor the numerator, think of two numbers that

Through trial and error, you should find the two numbers to be 3 and -2

So that's how [tex]n^2+n-6[/tex] factors to [tex](n+3)(n-2)[/tex].

After this point, the (n-2) terms cancel leaving n+3 behind

We can say [tex]\frac{n^2+n-6}{n-2}=n+3 \ \ \text{when } n \ne 2[/tex]

The [tex]n \ne 2[/tex] is to avoid a division by zero error.

1/2 is the factor which converts right angled triangles ΔRPQ to ΔVAQ

Triangle: A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane

Both the triangles are right angled triangles at ΔVAQ and ΔRPQ

side AV=3 units and AQ=4 units

side RP=6 units and PQ=8 units

AV is half of RP and AQ is half of PQ

AV=1/2(RP) and AQ=1/2(PQ)

1/2 factor converts ΔRPQ to ΔVAQ

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Answer:

b

Step-by-step explanation:

because you need ti 2x +

By using distributive property, [tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

In order to quickly solve equations, a number is distributed across the integers in the brackets. When using the distributive property of multiplication, for instance, to resolve the expression 4(2 + 4), we would do so as follows: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24.

We have,

[tex]-3\left(7x^{2}+3x\right)[/tex]

Using Distributive Property, A(B+C) = AB+AC

[tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]

Hence, [tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]

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To maximize the number of circular tables, he must thus employ 9 circular tables and 3 square tables.

Combinatorics is a branch of math focused on the arrangements of objects.

Estimates of the number of operations needed by a computer algorithm can be created using combinatorial approaches.

It is given that the number of persons in each circular table and the square table will be 10 and 4 respectively.

We now need to determine the largest multiple of 10 in order to maximize the number of circular tables.

Now, if we take 100, there will only be 2 seats left. However, 4 people are needed for square tables. Therefore, 100 is incorrect.

The circular tables utilized would be if we choose 90 as a multiple of 10 is,

= 90 / 9

= 10

Number of guests left,

=102 - 90

= 12

12 is a multiple of 4 as a result 3 square tables may therefore fit 12 people,

=4 × 3

=12

Thus, to maximize the number of circular tables, he must thus employ 9 circular tables and 3 square tables.

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The total mass of sugar used is 1.7 kg.

The mass of sugar he has left is 0.3 kg.

In mathematics, a fraction is a numerical value that represents a portion of a whole. The entire can be any number, a specific value, or an item. Fractions are written as p/q.

Given:

Total mass of sugar Mr tan has = 2 kg

Fraction of sugar used to make dessert = 1/4 kg

Fraction of sugar used to bake some cakes = 3/5 kg

The total mass of sugar used is calculated as,

= Mass of sugar used to make dessert + Mass of sugar used to bake some cakes

Mass of sugar used to make dessert = (1/4 of 2) kg = 1/2 kg

Mass of sugar used to bake some cakes = (3/5 of 2) kg = 6/5 kg

Total mass of sugar used = (1/2 + 6/5) kg = 17/10 = 1.7 kg

Mass of sugar left =  Total mass of sugar - Total mass of sugar used

                             = 2 kg - 1.7 kg  = 0.3 kg

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The Point-slop form for X is X = 5Y+15, and the Point-slop form for Y is [tex]\frac{X-5}{5}[/tex],  for the line with a slope 1/5 and passing through the point ​(-4​, -5​).

Finding the slop form using the formula  [tex]m=\frac{Y_{1} - Y_{2} }{X_{1} -x_{2} }[/tex]

The equation for x.

Here m=1/5.

∴  [tex]\frac{1}{5}=\frac{Y-(-4)}{X-(-5)}[/tex]

[tex]\frac{1}{5}[/tex] × X-(-5) = Y-(-4)

[tex]\frac{1}{5}[/tex] × X+5 = Y+4

X+5= 5Y+2O

X=5Y+20-5

X=5Y+15

∴Point-slop for X is X=5Y+15.

Solving for Y.

[tex]\frac{1}{5}=\frac{Y-(-4)}{X-(-5)}[/tex]

Simplifying and Solving.

[tex]\frac{1}{5}[/tex] × X-(-5) = Y-(-4), Taken  0n  X-(-5) the right side.

       [tex]\frac{1}{5}[/tex] × X+5 = Y+4

X+5= 5Y+2O

X+5-20=5Y

X-15=5Y

Taking 5 0n the right side.

[tex]\frac{X-15}{5}[/tex] = Y

∴ Point-slop form for Y is [tex]\frac{X-5}{5}[/tex]

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Step-by-step explanation:

it is a rectangle.

the area is a rectangle is

length × width

in our case

length × width = 55 ft²

length = 3×width + 4

we use that in the first equation :

(3×width + 4)×width = 55

3×width² + 4×width - 55 = 0

the general solution to a quadratic equation like

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

so,

width = (-4 ± sqrt(4² - 4×3×-55))/(2×3) =

= (-4 ± sqrt(16 + 660))/6 = (-4 ± sqrt(676))/6 =

= (-4 ± 26))/6

width1 = (-4 + 26)/6 = 22/6 = 11/3 = 3 2/3 ft

width2 = (-4 - 26)/6 = -30/6 = -5

negative numbers for the size of a physical object don't make sense, so

11/3 = 3 2/3 ft is our solution.

length = 3×width + 4 = 3×11/3 + 4 = 11 + 4 = 15 ft

so,

the length = 15 ft

the width = 3 2/3 ft (or 11/3 ft)

[tex] = 9( - 6 + 8i) - 3i( - 6 + 8i) \\ = - 54 + 72i + 15i - 24 {i}^{2} \\ = - 54 + 87i - 24 {i}^{2} [/tex]

ATTACHED IS THE SOLUTION

The correct option is A, the system of inequalities is:

On the graph, we can see two lines.

One is a dashed line (so we need to use the symbols > or < ) and it is horizontal, such that the line is:

y = -3

And the shaded region is above that line, so the inequality is:

y > -3.

The other inequality is below a line y = -x, and we can see that the line is solid (so we use the symbols ≤ or ≥).

Then here the inequality is.

y ≤ -x

Then the system of inequalities is:

y > -3.

y ≤ -x

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Answer:

10

Step-by-step explanation:

486-466 = 20

1/2 x 20 = 10

:]

Answer:

an expression that equals 10

Step-by-step explanation:

486 - 466 = 20

1/2 of 20 is 10

You don't list choices.

You need an expression that equals 10.

The number of times the value 1.5 exceeds the value 0.15 is 10, which is obtained by dividing both values.

We divide a by b to find how many times greater a number is than b; thus, to calculate how many times greater a number is, we use a division operation.

To determine how many times greater a number is than b, we compare them, i.e. divide them.

As an example:

50/10 = 5, indicating that 50 is five times greater than ten.

We must determine how many times the value 1.5 is greater than the value 0.15.

For this , let us divide 1.5 by 0.15

Number of times the value is greater = 1.5/0/15

                                                              = 10

Therefore, the number of times the value 1.5 is greater than the value 0.15 is 10.

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Answer:

1. How much did the 2 lb of the first type of candy cost the owner?

2x

2. How much did the 3 lb of the second type of candy cost the owner?

3*1.5 = 4.5

3. How much did the two types of candy cost the store owner in total?

2x + 4.5

4. How much money will the store owner get if she sells all of the new mixture?

(2 + 3)*2.5 = 12.5

5. Write an equation to find the cost per pound of the first candy

2x + 4.5 = 12.5

6. Solve the equation to find the owners cost of the first candy per pound

2x + 4.5 = 12.5

2x = 8

x = 4

We are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.

Given that, n=550 (Sample size, Number of trials), p=0.6 (Sample proportion) and 1−α=0.9 (Confidence level).

The confidence interval is one of the most used for estimating population parameters in statistics. It is common to perform an interval with a known confidence level to find a range of values that show us information about the population.

Using the standard error of the sample proportions [tex]ME=z_{\alpha /2}.\sqrt{\frac{p(1-p)}{n} }[/tex]

[tex]=z_{0.9/2}.\sqrt{\frac{0.6(1-0.6)}{550} }[/tex]

[tex]=z_{0.45}.\sqrt{\frac{0.6(0.4)}{550} }[/tex]

= 0.1736 × √(0.24/550)

= 0.1736 × 0.0208

= 0.00361

Confidence interval = 0.6±0.00361

= (0.6+0.00361, 0.6-0.00361)

= (0.6036, 0.5963)

Therefore, we are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.

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Answer:

Perimeter

P = 24.2

Step-by-step explanation:

Perimeter

P = 9 + √(6^2 + 6^2) + √(3^2 + 6^2) = 24.2

[tex]5 \div 6 \times 2100 = 1750[/tex]

[tex] \frac{4}{5} (w + z) \\ = \frac{4}{5} (12 + 43) \\ = \frac{4}{5} (55) \\ = 4(11) \\ = 44[/tex]

ATTACHED IS THE SOLUTION

The probability that x is less than or equal to 38 is 0.9861.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 38

μ = mean = 5

σ = standard deviation = 15

z-score = (38 - 5) / 15

z-score = 33 / 15

z-score = 2.2

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score =  2.2

probability = 0.9861

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The approximate height of the door is 84in

A rectangle is a polygon with 4 sides and 4 right angles.

It has 2 lines of symmetry and one of that lines is called a diagonal.

Rectangles are cut into two to form right angled triangles.

The rectangle is divided into two right angled triangles

with a diagonal of 94 inches, base = 42 inches.

The height of the rectangle, the base and the diagonal form a right angled triangle.

By Pythagoras,

[tex](94)^{2}[/tex] = [tex](42)^{2}[/tex] + [tex](height)^{2}[/tex]

8836 = 1764 + [tex](height)^{2}[/tex]

[tex](height)^{2}[/tex] = 8836 - 1764 = 7072

height = [tex]\sqrt{7072}[/tex] = 84 inches

In conclusion, the height of the rectangular door is 84 inches approximately.

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Answer: B is the answer to the question

Step-by-step explanation:

Answer:

52 yards across

Step-by-step explanation:

Hakim drew a scale drawing of a neighborhood park. he used the scale 5 inches : 2 yards. a soccer field in the park is 130 inches wide in the drawing. how wide is the actual field?

130/5 = 26

26*2 = 52 yards across

When the result of one function is utilized as the input for another, this is known as a composite function. If f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7 then the value of h(x) = x³.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function exists essentially applied to the output of another function.

Function composition is an operation used in mathematics that takes two functions, f and g, and creates a function, h = g ° f, such that h(x) = g. The function g is applied in this operation on the outcome of applying the function f to x.

Let the two functions be f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7.

f(x) = (h° g)(x)

⇒ f(x) = (h(g(x))

If f(x) = (h° g)(x) (6x³ - 7)³ = (h(g(x)) then h(x) = x³.

The complete question is:

Let f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7. Given that f(x) = (h° g)(x), find h(x).

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Answer:

h(x) = x³

Step-by-step explanation:

Given:

  [tex]f(x)=(6x^3-7)^3[/tex]

  [tex]g(x)=6x^3-7[/tex]

  [tex]f(x)=(h \circ g)(x)[/tex]

The relationship between f(x) and g(x) is that function f is function g cubed:

[tex]f(x)=(g(x))^3[/tex]

(h o g)(x) means we replace the x-variable of function h(x) with function g(x). So:

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

If (h o g)(x) equals f(x), then h(x) must be h(x) = x³.

Check by replacing the x-variable of function h(x) with the function g(x) and comparing it to f(x):

[tex]\begin{aligned}(h \circ g)(x)&=h(g(x))\\&=(g(x))^3\\&=(6x^3-7)^3\\&=f(x)\end{aligned}[/tex]

Hence proving that h(x) = x³.

Answer: 2.7 kg

1 kilogram (kg) = 2.204623 pounds (lb)

[tex]\frac{6 lb}{1}[/tex] × [tex]\frac{1 kg }{2.204623 lb}[/tex] = 2.721553753 kg

You place 1 kg over 2.204623 lb since they are equal. In the above equation, the pounds (lb) cancel out since one is in the numerator (the number on top of the fraction) and one is in the denominator (the number on the bottom of the fraction). You multiply 6 by the 1 in the numerator and multiply the 1 in the denominator by 2.204623. This turns the equation into:

[tex]\frac{6 kg}{2.204623}[/tex] =2.721553753 kg

You divide 6 by 2.204623 to get 2.721553753

To round to the tenths place, you include only the first number to the right of the decimal, which is 7. Since the number to the right of the 7 is less than five, it stays 7. If it were five or bigger, 7 would turn into 8.

The answer: 2.7 kg

Given:

The lengths of time spent in the store are normally distributed and are represented by the variable X

The survey indicates that for each trip to a supermarket, a shopper spends an average of 43 minutes with a standard deviation of 12 minutes in the store.

so, the mean = μ = 43

And the standard deviation = σ = 12 minutes

We will find the probability that supermarkets between 31 and 58 minutes

We will use the following formula to convert to the z-scores

So, we will find Z when x = 31 and When x = 58

So, we will find the probability of P (-1 < z < 1.25)

From the tables of the z-score:

omg what is the......................

Answer: 7.3 < 12

Step-by-step explanation:

The value of the given monomial, -8[tex]m^{4}n^{4}[/tex], when m = 0.5 and n = 2 is -8.

According to the question,

We have the following monomial:

-8[tex]m^{4} n^{4}[/tex]

We have m = 0.5 and n = 2.

Now, putting these values of m and n in the monomial:

-8 [tex](0.5)^{4} (2)^{4}[/tex]

(Please note that when a power is there on a number then it means that to solve the expression we have to multiply the base as many times as the given power. For example, in this case, we will multiply 2 four times and the result will be 16. This concept is applicable to every expression we are solving whether the base is in decimal or in fraction or a integer.)

-8*0.0625*16

-128*0.0625

-8

Hence, the value of the given monomial is -8.

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