Choose the correct simplification of (3x3y4z4)(2x3y4z2).

Answer:

[tex]\sqrt[3]{x}[/tex]

Step-by-step explanation:

we have

[tex](x^{\frac{1}{15}})^{5}[/tex]

Simplify

Multiply the exponents

[tex](x^{\frac{1}{15}})^{5}=x^{\frac{1}{15}*5}=x^{\frac{5}{15}}=x^{\frac{1}{3}}=\sqrt[3]{x}[/tex]

Answer:

[tex]\sqrt[3]{x}[/tex].

Step-by-step explanation:

We have been given an expression [tex](x^{\frac{1}{15}})^5[/tex]. We are asked to simplify our given expression.

We will use power rule of exponents [tex](a^b)^c=a^{b\cdot c}[/tex] to simplify our given expression as:

[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{15}\times 5}[/tex]

[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{3}\times 1}[/tex]

[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{3}}[/tex]

Using fractional exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex], we can write our expression as:

[tex](x^{\frac{1}{15}})^5=\sqrt[3]{x}[/tex]

Therefore, the simplified form of our given expression would be [tex]\sqrt[3]{x}[/tex].

Answer:

Domain: -∞ < x < ∞

Range: f(x) < 0

Step-by-step explanation:

[tex]f(x)=-2(\frac{1}{4})^x[/tex]

We need to sketch the graph and identify domain and range of the function f(x).

The graph is attached in the figure below.

Domain:

The domain of the function is all the values of x that gives the real values for f(x).

So, in our case all values of x gives real values for f(x). So domain is:

-∞ < x < ∞

Range:

The range of the function is the resulting f(x) values when we put all the values of x.

In our case the value of f(x) will always be less than zero because of the negative sign.

Range is:

f(x) < 0

When evaluating the expression [tex]b^2c - 1[/tex] for b = -4 and c = 2, we calculate b squared as 16, multiply by c to get 32, and subtract 1 to obtain the answer 31.

To evaluate the expression b2c - 1 for b = -4 and c = 2, we need to follow the order of operations, often referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, we calculate b², which is (-4)² = 16.

Next, we multiply this result by c, which gives us 16 * 2 = 32.

Finally, we subtract 1 from this product, resulting in 32 - 1 = 31.

Therefore, the evaluated expression [tex]b^2c - 1[/tex] is 31 when b = -4 and c = 2.

C' ( 0, 3)

A' ( 2 , 1)

C'A' = CA

C'A' = √(2^2 + 2^2) = √8 = 2√2

C'A' = CA = 2√2

The distance between the points (2, 1) and (-2, 2) is √17, which is approximately 4.123 units.

We have,

The coordinates of point A =(2, 1)  and C = (-2, 2)

Now,

To find the distance between two points, (x₁, y₁) and (x₂, y₂), we can use the distance formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Given the points (2, 1) and (-2, 2), we can substitute the values into the formula:

Distance = √[(-2 - 2)² + (2 - 1)²]

Distance = √[(-4)² + 1²]

Distance = √[16 + 1]

Distance = √17

Therefore,

The distance between the points (2, 1) and (-2, 2) is √17, which is approximately 4.123 units.

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Answer:

x = 80, y = 140 and z = 20

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles in the triangle with x and equate to 180

x + 60 + 40 = 180

x + 100 = 180 ( subtract 100 from both sides )

x = 80

40° and y form a straight angle and are supplementary, hence

40 + y = 180 ( subtract 40 from both sides )

y = 140

Sum the 3 angles in the triangle with z and equate to 180

z + y + 20 = 180, that is

z + 140 + 20 = 180

z + 160 = 180 ( subtract 160 from both sides )

z = 20

Answer:

it would be D

Step-by-step explanation:

Answer:

The number line D)

Step-by-step explanation:

Carly withdraws $18 from her bank account.

We assume that Carly has $x in her account. She withdraws $18 from her bank account.

So we have to subtract $18 from $x amount.

Which is $x - 18.

So we are subtracting $18 from her account.

It should be represented by an integer -18.

Now we have to identify the which number line represents -18.

It is D)

Answer:

It is A.

Step-by-step explanation:

To solve for b, use the 45-45-90 triangle theorem, in which each of the legs is x, so the legs would be 8. The hypotenuse would therefore be 8√2.

So without further solving the answer is A, since it's the only one with 8√2.

However, I will still solve for A and C. Using the 30-60-90 theorem, we have the sides as x, x√3, and 2x. The second longest side is b. Using this, we find a = 4√6 and c to be 4√2

Answer:

[tex]\boxed{\text{3.0 T}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}M + T + W + Th + F & = & \text{Total}\\2.4 + 4.4 + 1.8 + 2.8 + F & = & 14.4\\11.4 + F & = & 14.4\\F & = & 3.0\\\end{array}\\\text{Friday's sales of chlorine were }\boxed{\textbf{3.0 T}}[/tex]

Answer: There are 3 tons of chlorine sold on Friday.

Step-by-step explanation:

Since we have given that

Number of tone of chlorine on Monday = 2.4

Number of tone of chlorine on Tuesday = 4.4

Number of tone of chlorine on Wednesday = 1.8

Number of tone of chlorine on Thursday = 2.8

Total number of week's sales = 14.4 tons

So, we need to find the number of tone of chlorine on Friday.

According to question we get that

[tex]14.4=2.4+4.4+1.8+2.8+x\\\\14.4=11.4+x\\\\x=14.4-11.4\\\\x=3[/tex]

Hence, there are 3 tons of chlorine sold on Friday.

Answer:

41.03 square feet

Step-by-step explanation:

The area of a sector is given by the formula:

[tex]A=\frac{1}{2}r^2\theta[/tex]

Where A is the area, r is the radius and [tex]\theta[/tex] is the angle in radians.

Given the values, we plug into the formula and solve:

[tex]A=\frac{1}{2}r^2\theta\\A=\frac{1}{2}(5.6)^2(\frac{5\pi}{6})\\A=41.03[/tex]

Answer:

Part 1)  shaded area at left of x=8 (close circle) ---> [tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]  

Part 2) shaded area at left of x=-5 (close circle) ---> [tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]

Part 3) shaded area at left of x=-6 (close circle) ---> [tex]\frac{3x}{2}+105 \leq 96[/tex]

Part 4) shaded area at left of x=7 (close circle) ---> [tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]

see the attached figure

Step-by-step explanation:

Part 1) we have

[tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]  

Multiply by -10 both sides

[tex]x-2 \leq 6[/tex]

Adds 2 both sides

[tex]x \leq 6+2[/tex]

[tex]x \leq 8[/tex]

The solution is the interval -----> (-∞,8]

All real numbers less than or equal to 8

In a number line the solution is the shaded area at left of x=8 (close circle)

Part 2) we have

[tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]

Multiply by -6 both sides

[tex]100x+11 \leq -489[/tex]

Subtract 11 both sides

[tex]100x \leq -489-11[/tex]

[tex]100x \leq -500[/tex]

Divide by 100 both sides

[tex]x \leq -5[/tex]

The solution is the interval -----> (-∞,-5]

All real numbers less than or equal to -5

In a number line the solution is the shaded area at left of x=-5 (close circle)

Part 3) we have

[tex]\frac{3x}{2}+105 \leq 96[/tex]

Multiply by 2 both sides

[tex]3x+210 \leq 192[/tex]

Subtract 210 both sides

[tex]3x \leq 192-210[/tex]

[tex]3x \leq -18[/tex]

Divide by 3 both sides

[tex]x \leq -18/3[/tex]

[tex]x \leq -6[/tex]

The solution is the interval -----> (-∞,-6]

All real numbers less than or equal to -6

In a number line the solution is the shaded area at left of x=-6 (close circle)

Part 4) we have

[tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]

Multiply by -18 both sides

[tex]13x-10 \leq 81[/tex]

Adds 10 both sides

[tex]13x \leq 91[/tex]

Divide by 13 both sides

[tex]x \leq 91/13[/tex]

[tex]x \leq 7[/tex]

The solution is the interval -----> (-∞,7]

All real numbers less than or equal to 7

In a number line the solution is the shaded area at left of x=7 (close circle)

Final answer:

To verify a proportion solution, substitute the answer back into the original equation, check that the units are consistent, and ensure the answer's reasonableness in terms of magnitude, sign, and units.

Explanation:

To verify that a solution to a proportion is correct, one effective method is to perform a check by substituting the solution back into the original proportion equation. Here's how you can ensure the correctness of the solution step by step:

The correct equation representing the situation where Nancy's mother added candies to the 16 candies already in the bag is 16 + c = 32. Subtracting 16 from both sides gives the result c = 16, which is the number of candies her mother added.

The subject of this question is mathematics and it belongs to the middle school level. Nancy began with 16 candies and ended up with 32 candies after her mother added some. Nancy wants to find out how many candies her mother added.

To solve this problem, we need to use a simple addition equation. The equation that correctly represents the situation is 16 + c = 32. This equation says that Nancy's original amount of candies (16) plus the candies her mother added (c) equals the new total amount of candies (32).

To solve for c (the number of candies her mother added), we simply subtract 16 from both sides of the equation. Therefore, c = 32 - 16, which leads to c = 16, which is the number of candies her mom put in the bag.

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Final answer:

The correct equation for Nancy's chocolate candies is 16 + c = 32, solving for c reveals that 16 candies were added. Jenny initially had 14 chocolates before eating two and giving half of the remainder to Lisa.

Explanation:

The question asks to identify the correct equation to solve for the number of chocolate candies, c, that Nancy's mom put in the bag. Nancy originally had 16 chocolate candies, and her mother added some candies to the bag, increasing the total to 32 candies. The equation that represents this situation is 16 + c = 32. This equation can help Nancy find out how many candies her mother added to the bag.

To solve for c, we need to perform a subtraction operation:

This calculation gives us the number of candies Nancy's mother added, which means c = 16 candies.

Jenny's Chocolate Question

If Jenny has some chocolates, eats two, and gives half of what is left to Lisa, resulting in Lisa having six chocolates, then we must work backward to find the initial amount. Since Lisa received half of the remainder, Jenny must have had 12 chocolates after eating two. This means Jenny started with 14 chocolates as:

The correct answer for Jenny's beginning number of chocolates is 14.

Answer:

3 1/2 ; 3 19/20 ; 3 39/40

Step-by-step explanation:

Find common denominators. Change all mixed fraction to improper fractions before finding common denominators.

3 1/2  = 6/2 + 1/2 = 7/2

3 19/20 = 60/20 + 19/20 = 79/20

3 39/40 = 120/40 + 39/40 = 159/40

Find the common denominators. The smallest common denominators is 40. Remember that what you do to the denominator you do to the numerator:

3 1/2 = (7/2)(20/20) = 140/40

3 19/20 = (79/20)(2/2) = 158/40

3 39/40 = (159/40) = 159/40

Least to Greatest:

3 1/2 ; 3 19/20 ; 3 39/40

~

ANSWER

[tex]y = 3x[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + x + 1[/tex]

To find the gradient function, we find the first derivative;

[tex]f'(x) = 2x+ 1[/tex]

To find the gradient at (1,3), we put x=1 into the gradient function to get;

[tex]f'(1) = 2(1)+ 1 = 3[/tex]

The equation of the tangent line is

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

We substitute the point and the slope to get,

[tex]y-3=3(x-1)[/tex]

This simplifies to

[tex]y = 3x - 3 + 3[/tex]

[tex]y = 3x[/tex]

Answer:bsdaosdfhaodsifhaosdfaidfhaoif

have a nice time reading and understanding his:)

Step-by-step explanation:

considering APB as the triangle

AP is the tangent to the circle.

∴ OA ⊥ AP  (Radius is perpendicular to the tangent at the point of contact)

⇒ ∠OAP = 90º  

In Δ OAP,

sin ∠OPA = OA/OP = r/2r [Diameter of the circle]

∴ sin ∠OPA = 1/2 = sin 30º

⇒ ∠OPA =  30º

Similarly, it can he prayed that ∠OPB = 30

How, LAB = LOP + LOB = 30° + 30° = 60°  

In APB,  

PA = PB [lengths &tangents drawn from an external point to circle areequal]  

⇒ ∠PAB = ∠PBA --- (1) [Equal sides have equal angles apposite to them]  

∠PAB + ∠PBA + ∠APB = 180° [Angle sum property]  

∠PAB + ∠PBA + ∠APB = 180° - 60° [Using (1)]  

⇒ 2∠PAB = 120°

⇒ ∠PAB = 60°  

From (1) and (2)  

∠PAB = ∠PBA = ∠APB = 60°

APB is an equilateral triangle.

Answer:

Step-by-step explanation:

A horizontal line has an equation: y = a  (a - any real number).

Each point on a horizontal line y = a, has coordinates (x, a)    (x - any real number).

We have the point (-7, 5) → y = 5

Answer:

5:5 (first box, pencils to pens)

7:3 (second box, coloured pencils to crayons)

The probability of picking a pen (1st box): 5/10

The probability of picking a crayon (2nd box): 3/10

Probability of picking both: 5/10*3/10 = 15/100

Answer:

Where   is the figure????

Step-by-step explanation:

Final answer:

The situation with a constant rate of change is the length of a bead necklace compared with the number of identical beads, as it represents a linear relationship with a constant slope.

Explanation:

The situation that is most likely to have a constant rate of change is option C, which describes the length of a bead necklace compared with the number of identical beads.

In this scenario, each bead added to the necklace increases its length by a consistent amount. This defines a linear relationship, where the rate of change, also known as the slope in a linear equation, remains constant.

For example, if one bead adds one centimeter to the necklace, then ten beads will add ten centimeters, indicating that the rate of change is one centimeter per bead.

This can be depicted graphically as a straight line when you plot the number of beads against the length of the necklace.

Given the functions

(a) f(x) = x³ + 5x² + x

(b) f(x) = x² + x

(c) f(x) = -x

Function (a)

f(-x) = (-x)³ + 5(-x)² + (-x)  

      = -x³ + 5x² - x

      = -(x³ - 5x² + x)

The function is neither even nor odd.

Function (b)

f(-x) = (-x)² + (-x)

       = -(-x² + x)

The function is neither even nor odd.

Function (c)

f(-x) = -(-x)  

      = x

      = -f(x)

Because f(-x) = -f(x) the function is odd.

Answer: f(x) = -x is an odd function.

Final answer:

The equation of a circle with center (2,7) and a radius of 5 is (x - 2)² + (y - 7)² = 25.

Explanation:

To find the equation of a circle with its center at (2,7) and a radius of 5, we use the standard form of the equation for a circle which is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.

Plugging in the given values for our circle we have:

(x - 2)² + (y - 7)² = 5²

Expanding the right side of the equation gives us:

(x - 2)² + (y - 7)² = 25

This is the desired equation of the circle. It represents a circle with a radius of 5, centered at the point (2,7).

Answer:

In step 1, he substituted into the volume formula incorrectly.

Step-by-step explanation:

James calculated the height of a cylinder that has a volume of 324 cubic inches.

radius = 12 inches.

The formula for volume is = [tex]\pi r^{2} h[/tex]

So, James calculated wrongly by using the wrong formula.

The step 1 is wrong.

Answer:

In step 1, he substituted into the volume formula incorrectly.

Step-by-step explanation:

Answer:

6x^2 -4x +8

Step-by-step explanation:

(6x^2 + 5) - (4x - 3)

Distribute the negative sign

(6x^2 + 5) - 4x + 3

Combine like terms

6x^2 -4x +5+3

6x^2 -4x +8

Answer:

Step-by-step explanation:

[tex]h(x)=x-7,\ g(x)=x^2\\\\(g\circ h)(x)=g\bigg(h(x)\bigg)-\text{exchange x to x - 7 in}\ g(x):\\\\(g\circ h)(x)=(x-7)^2\\\\(g\circ h)(5)-\text{put x = 5 to the equation}\\\\(g\circ h)(5)=(5-7)^2[/tex]

Answer:

V looking graph

(absolute value function)

Step-by-step explanation:

We are looking for a relation that passes the vertical line test.

Basically if you can play a vertical line on your graph and it touches more than once on that vertical line (your graph) then it isn't a function.

The only one that is a function here is the V looking graph.

The graph in the shape of a V (absolute value function)

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Answer:

B 48

Step-by-step explanation:

it is b I know because I got it correct

Answer:

Its b

Step-by-step explanation:

You have to estimate the numbers so b is the best answer

[tex]\bf \begin{cases} f(x) = x\\ g(x) = 2x+7 \end{cases}~\hspace{7em}g(x)=11\implies \stackrel{g(x)}{11}=2x+7 \\\\\\ 4=2x\implies \cfrac{4}{2}=x\implies \implies \boxed{2=x} \\\\[-0.35em] ~\dotfill\\\\ f[90x]\implies f\left[90\left( \boxed{2} \right)\right]\implies f(180)=\stackrel{x}{180}[/tex]

Answer:

48 sq. units

Step-by-step explanation:

The area of a trapezoid is given by half sum of the bases multiplied by the height

[tex]=\frac{1}{2} (a+b)h[/tex]

where a and b are the two parallel sides of the trapezoid and h is the height or amplitude of the trapezoid

But you are aware that, the median of a trapezoid is equal to half the sum of the bases, thus the first part of the formulae  is covered by the median

[tex]Median=\frac{1}{2} (a+b)[/tex]

Hence area, A, of a trapezoid is simplified to product of median and amplitude

[tex]A=amplitude*median\\\\A=6*8=48sq.units[/tex]

Answer:

=48 sq. units.

Step-by-step explanation:

Area of a trapezoid =h× (a+b)/2

(a+b)/2 is the median ( half of the sum of the two parallel sides also called the bases.

Median=8 inches

Altitude is the distance between the two parallel sides= 6 inches

A=6 inches×8 inches

=48 sq. units.

Answer:

C

Step-by-step explanation:

If there is an expression such as:

[tex]\frac{A*B}{A*C}[/tex]

we can cancel out A from top and bottom and that will leave us with [tex]\frac{B}{C}[/tex]

Note: Let A, B, C, be any algebraic expression

For the problem given, we can simply cut (x+1) from top and bottom by rules of algebra. So the remaining terms are:

[tex]\frac{(x-1)}{(x+7)}[/tex]

This is option C

Answer:

C)

Step-by-step explanation:

When you have a*b/c*a, a crosses out, simplifying to b/c:

(x+1)(x-1)/

(x+1)(x+7)

When "crossing out", you are really just simplifying it to 1/1:

1*(x-1)/

1*(x+7)

Which is the same as:

(x-1)/(x+7)

Therefore, C is the correct answer

Answer:

29/12

Step-by-step explanation:

In an isosceles triangle, two sides are equal.

Therefore:

25/6+25/6+u = 10 3/4

50/6+u=43/4

u=43/4-50/6

u=43/4-25/3

u=129/12-100/12

u=29/12