Someone please explain (:

Answer:

[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]

Step-by-step explanation:

We have the following limit

[tex]\lim_{x \to 0}\ x^2 -2[/tex]

To solve this limit using direct substitution to substitute the value that tends x into f(x) and simplify.

In this case x tends to zero, then we substitute x = 0 in the function and simplify

[tex]\lim_{x \to 0}\ x^2 -2= (0)^2 -2= -2[/tex]

Therefore

[tex]\lim_{x \to 0}\ x^2 -2 = -2[/tex]

When x approaches 0 then f(x) it tends to -2

100 - 70% = 30

0.30 × p (p=45)

0.30 × 45 = 13.5

the sale price is $13.50

Answer:

The red line is g(x)

Step-by-step explanation:

* To solve this problem you must to know some fact about

  transformation

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

- A vertical stretching is the stretching of the graph away from

 the x-axis

• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically

 stretched by multiplying each of its y-coordinates by k.

- A vertical compression is the squeezing of the graph toward

 the x-axis.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed

 by multiplying each of its y-coordinates by k.

• if k should be negative, the vertical stretch or compress is

 followed by a reflection across the x-axis.  

* Now lets solve the problem

- g(x) = -1/2f(x + 2)

# x + 2 ⇒ means the graph moved 2 units to the left

# -1/2 ⇒ means the graph has vertical compressed followed

 by a reflection across the x-axis, then multiply

 each y-coordinate by -1/2

- The graph of f(x) intersects x-axis at point (3 , 0)

∴ The point will be (1 , 0) on g(x)

- The graph of f(x) intersects y-axis at point (0 , -6)

∴ The point will be (-2 , 3) on g(x)

* Look to the graph

# The red line is g(x)

# The blue line is f(x)

- To check your answer

# The equation of f(x) is f(x) = 2x - 6

∵ g(x) = -1/2f(x + 2)

∴ g(x) = -1/2[2(x + 2) - 6] = -1/2[2x + 4 - 6] = -1/2[2x - 2] = -x + 1

* g(x) intersect x-axis at point (1 , 0) and y-axis at point (0 , 1)

Simplifying the expression requires expanding the brackets, combining like terms, and applying algebraic rules including distribution. The resulting simplified form is – 35x2 + 8x – 8 after properly eliminating unnecessary terms and ensuring the solution is valid.

To simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2, we need to apply standard algebraic techniques such as distribution, combining like terms, and simplifying polynomial expressions.

Firstly, distribute the 3x across the parentheses: 3x×(x – 12x) becomes 3x2 – 36x2.

Then, expand the square: – 2(x – 2)2 becomes – 2(x2 – 4x + 4).

Next, we can simplify the expression by combining like terms and further distributing where necessary:

Combine like terms:

Eliminate terms wherever possible and check to see if the simplified expression is reasonable. We are using multiplication, distribution, and combination of like terms to simplify the algebraic expression.

Answer:

top question is not correct

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

Answer:

That would be sina.

Step-by-step explanation:

sin(a+b) = sinacosb + cosasinb

sin(a-b) = sinacosb -  cosasinb

Adding we get  sin(a+b) + sin(a-b) = 2sinaccosb

so sinacosb = 1/2sin(a+b) + sin(a-b)

Answer:

sina

Step-by-step explanation:

We have

          sin(a+b) = sina cosb + cosa sinb ---------------------eqn 1

           sin(a-b) = sina cosb - cosa sinb ---------------------eqn 2

eqn 1 + eqn 2

          sin(a+b) + sin(a-b) = sina cosb + cosa sinb + sina cosb - cosa sinb

          sin(a+b) + sin(a-b) = 2sina cosb

          [tex]sina\times cosb =\frac{1}{2}(sin(a+b) + sin(a-b))[/tex]

So answer is sina

Answer:  1. A- (0.1 0.2 0.3)

2.a-(3,4,5)

3.A-(-2,-1,0,+1)

4.a-(0123)

5.a-( 1/4 1/2 3/4

Step-by-step explanation:

I'm sorry you had to wait a whole year to get your answer :)

The exercise involves matching the terms decimal fractions, whole numbers, integers, natural numbers, and rational numbers to their respective sets of numbers. The correct matches are: decimal fractions {0.1, 0.2, 0.3}, whole numbers {0,1,2,3}, integers {-2, -1, 0, +1}, natural numbers {3,4,5}, and rational numbers {1/4,1/2, 3/4}.

The goal here is to

match

the given

description

or term to the given sets of numbers according to their properties. Let's start.

So, we have successfully made a

matching

for each description.

https://brainly.com/question/36757679

#SPJ2

Answer:

1.5 dollars/miles

Step-by-step explanation:

Given function [tex]y=3.75 + 1.5(x-1)[/tex] can be used to determine cost in dollars for a taxi ride of x miles.

Now we need to find about what is the rate of change of the cost in dollars with respect to the number of miles.

First we need to rewrite [tex]y=3.75 + 1.5(x-1)[/tex] in y=mx+b form

[tex]y=3.75 + 1.5(x-1)[/tex]

[tex]y=3.75 + 1.5x-1.5[/tex]

[tex]y=2.25 + 1.5x[/tex]

[tex]y=1.5x + 2.25[/tex]

comparing with y=mx+b, we get m=1.5

Hence rate of change of the cost in dollars with respect to the number of miles is 1.5.

the answer for this question is the dilation is reduction

The statement which is true about these rectangles is:

          The dilation is an enlargement.

Dilation Transformation--

Here we see that each of the sides of the original figure is multiplied by "1.5" to obtain a larger rectangle.

This means that the dilation is a enlargement.

( since the scalar is strictly greater than one )

Answer:

Option B is the correct answer.

Step-by-step explanation:

This would be linear growth because the y values are increasing, but not at an exponential rate.

Answer:

[-7,5]

Step-by-step explanation:

The range is all the permitted values of y in the function. The lowest to the highest.

Looking at the function, the lowest y value is -7

and

the highest y value is 5

So we can say the range is [-7,5], the last choice

Answer:

THE ANSWER IS 7

Step-by-step explanation:

CAUSE UR MOM IS A TRASHIE                 i'm sorry i meant YO MAMA

Final answer:

Kate can make 4 small flags from 2/3 yards of fabric since each flag requires 1/6 yards of fabric.

Explanation:

Kate has 2/3 yards of fabric and each small flag requires 1/6 yards of fabric. To find out how many flags Kate can make, you divide the total amount of fabric by the amount needed for one flag:

2/3 yards \/ 1/6 yards = 4 flags.

Here's the step-by-step calculation:

First, recall that dividing by a fraction is the same as multiplying by its reciprocal. In this case, the reciprocal of 1/6 is 6/1.

So, multiply 2/3 by the reciprocal of 1/6:

2/3 × 6/1 = 12/3 = 4.

Thus, Kate can make 4 small flags from the fabric she has.

Solution:

Given :

So, We have to find the Base of Triangle .

Area of triangle = 1/2*b×h, Where represents

Step : Substitute those value in Formula;

Area of triangle = 1/2 × b × h

10 = 1/2 × b × 11

20 = 11 × b

b = 20/11

b = 1.81 ft

Therefore, Base of Triangle is 1.81 ft

Final answer:

To find the base of a triangle with an area of 10 sq ft and a height of 10 ft, use the formula 1/2 × base × height. By rearranging the formula and substituting the known values, the base is calculated to be 2 feet.

Explanation:

The question is asking to find the length of the base of a triangle when the area is 10 square feet and the height is 10 feet. The formula for the area of a triangle is 1/2 × base × height. In this case, we know the area (10 sq ft) and the height (10 ft), and we need to solve for the base.

Inserting the known values into the formula gives us:

Area = 1/2 × base × height
10 = 1/2 × base × 10

To solve for the base, we rearrange the formula:

base = 2 × Area / height
base = 2 × 10 / 10
base = 2 feet

Therefore, the length of the base of the triangle is 2 feet.

Answer:

[tex]\large\boxed{L.A.=168\pi\ in^2}\\\boxed{S.A.=232\pi\ in^2}[/tex]

Step-by-step explanation:

The formula of a lateral area of a cone:

[tex]L.A.=\pi rl[/tex]

r - radius

l - slant height

The formula of a surface area of a cone:

[tex]S.A.=\pi r^2+\pi rl[/tex]

We have r= 8in and l = 21in. Substitute:

[tex]L.A.=\pi(8)(21)=168\pi\ in^2[/tex]

[tex]S.A.=\pi(8^2)+168\pi=232\pi\ in^2[/tex]

(x-8)^2+y^2=225 I'm not able to factor it

1. If AB is tangent to the circle, then

[tex]18^2=(2\cdot7.2)^2+10.8^2[/tex]

We have

[tex]18^2=324[/tex]

[tex](2\cdot7.2)^2+10.8^2=324[/tex]

so AB is indeed tangent to the circle.

2. The unlabeled leg is another radius of the circle so it has length 8. Then if AB is tangent to the circle,

[tex](10+8)^2=8^2+15^2[/tex]

but we have

[tex](10+8)^2=324[/tex]

[tex]8^2+15^2=289[/tex]

so that cannot be a right triangle and AB is not tangent to the circle.

Answer:

D- (3, 1).

Step-by-step explanation: Add the first equation so you can figure out what x equals. Then, plug the value into your next equation in order to find y. Hope this helps. :)

For this case we have the following system of equations:

[tex]2x + 4y = 10\\3x-4y = 5[/tex]

We solve by the method of elimination, then:

We add both equations:

[tex]2x + 3x = 10 + 5\\5x = 15\\x = \frac {15} {5}\\x = 3[/tex]

We find the value of y:

[tex]3 (3) -4y = 5\\9-4y = 5\\9-5 = 4y\\4 = 4y\\y = \frac {4} {4}\\y = 1[/tex]

Answer:

(3,1)

Option D

Answer:

4.4 inches

Step-by-step explanation:

To work out the length of each side of the cube you would need to cube root of the volume as seen below:

[tex] \sqrt[3]{85.184} [/tex]

And this gives the answer 4.4 inches.

Answer:

Volume = Length * Width * Height

A cube has equal length, width, and height values.

[tex]\sqrt[3]{85.184}[/tex] is 4.4

So the length of each side is 4.4 units

Answer:

123480

Step-by-step explanation:

We have to choose:

1. 2 cellists from 8 can be chosen in

[tex]C_8^2=\dfrac{8!}{2!(8-2)!}=\dfrac{8!}{2!6!}=\dfrac{6!\cdot 7\cdot 8}{2\cdot 6!}=28[/tex]

different ways.

2. 4 violonists from 7 can be chosen in

[tex]C_7^4=\dfrac{7!}{4!(7-4)!}=\dfrac{7!}{4!3!}=\dfrac{4!\cdot 5\cdot 6\cdot 7}{4!\cdot 2\cdot 3}=35[/tex]

different ways.

3. 4 musicians from 9 can be chosen in

[tex]C_9^4=\dfrac{9!}{4!(9-4)!}=\dfrac{9!}{4!5!}=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9}{5!\cdot 2\cdot 3\cdot 4}=126[/tex]

different ways.

In total, there are [tex]28\cdot 35\cdot 126=123480[/tex] differnt ways to fill all vacancies.

Answer:

84 m^2

Step-by-step explanation:

We can break the polygon into a rectangle and a triangle

The rectangle at the bottom is 12 by 4

A = 12*4 = 48

The triangle at the top has a base of 12 and a height of (10-4) = 6

A = 1/2 (12) *6 = 36

The total is the sum of the two areas

A = 48+36 =84 m^2

I think the answer might be 2

because

in the data given above all the numbers are between 12-19 they are all bigger than 10

and then there's 2 which is very far from 12 or any other numbers there and it is also less than 10

which makes more sense for it to be an outlier.

Hope this helps

Answer:

[tex]\large\boxed{1.\ 38\ and\ 22}\\\boxed{1'.\ 42\ and\ 30}[/tex]

Step-by-step explanation:

[tex]1.\\x,\ y-the\ numbers\ (x>y)\\\\\text{We have the system of equations:}\\\\\underline{\left\{\begin{array}{ccc}x-y=16\\x+y=60\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=76\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=38}\\\\\text{Put the value of x to the second equation.}\\\\38+y=60\qquad\text{subtract 38 from both sides}\\\boxed{y=22}[/tex]

[tex]1'.\\x-larger\ part\\x-12-smaller\ page\\\\x+(x-12)=72\\x+x-12=72\qquad\text{add 12 to both sides}\\2x=84\qquad\text{divide both sides by 2}\\\boxed{x=42}\\\boxed{x-12=30}[/tex]

Answer:

The answer is B. 12+17x

Step-by-step explanation:

Twelve more stands for +12 and the product of seventeen and a number is equal to 17*x or 17x.

Answer: OPTION B.

Step-by-step explanation:

You need to remember that a product is the result of a multiplication.

Let be the number mentioned in the problem "x", "the product of seventeen and a number" means that:

[tex](17)(x)=17x[/tex]

 Now "twelve more than the product of seventeen and a number" indicates that you need to add 12 to [tex]17x[/tex].

Therefore, you can write the phrase in the following mathematical expression:

[tex]17x+12[/tex] or  [tex]12+17x[/tex]

This matches with the option B.

Answer:

A

Step-by-step explanation:

Given a function f(x) = x^2, we can say:

The negative sign in front says that G(x) is flipped over the x-axis with respect to F(x). Also, the 2 in front tells us that it is a vertical stretch of the function F(x), since a > 1.

Hence, answer choice A is right.

Answer:

it is answer A

Step-by-step explanation:

Ap*x

The statistical question that could be answered by the data is "maximum cost of toys".

The graph shown is a line graph which is a type of chart that displays data points connected by a line. It's a common way to visualize how a particular quantity changes over time or across different categories.

Line graphs makes it easy to determine statistical measures including minimum and maximum values of a category or data.

Here, the maximum cost of toys is 10 and the minimum is 5.

Answer: 10.5

Step-by-step explanation:Find the perimeter of the figure. Use 3.14 for the pie and round your answer to one decimal.

This looks like a square with a line going from the right corner slanted down to the bottom left, but there is a half circle there so it doesnt actually touch the bottom left. on the right half of the line is 13 in.

A construction of the line plot for the length, in inches, of several nails is shown in the image attached below.

In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would make use of an online graphing calculator (tool) to graphically represent the given length (in yards) of several nails on a line plot as shown in the image attached below;

Length        Frequency

1/2                     2

5/16                   4

1/8                     2

3/8                     1

3/16                    1

In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 5/16 because it has the highest frequency of 4.

Complete Question;

This table shows the length, in inches, of several nails.

Length (in) 1/2, 5/16, 1/8, 1/2, 3/8, 5/16, 5/16, 3/16, 5/16, 1/8.

Create a line plot to display this data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.

Answer:

860.55 mm²

Step-by-step explanation:

The surface area of an hexagonal prism, also known as an octahedron, is given by the following formula (since we have the apothem):

S= 6*b*(a+h)

where b = is the side of the base, a is the apothem length, and h = the height

S = 6 * 8 * (4√3 + 11) = 48 * 17.92812 = 860.55 sq mm

Could have also have used another formula without the apothem:

S =3 * √3 * b² + 6 * b * h

S = 3 * √3 * 8² + 6 * 8 * 11 = 3√3 * 64 + 528 = 332.55  + 528 = 860.55 sq mm

Answer:

3131x+1

Step-by-step explanation:

Make equation simple

5x times 5x times 5x times 5x times 5x +x+1

Solve

5 times 5 times 5 times 5 times 5 = 3125

x times x times x times x times x times x = 5x

3125+5x=3130x

Now you might be thinking you cant add x but here your can because it is just broken apart

now add x+1

3131x+1