For the following functions, (a) describe the domain and range, and (b) sketch the graph.

f(x)=(1/2)^x(-3)

The slope of the equation x + 2y = 4, is -1/2 and y-intercept of the equation is 2.

When any equation is represented in the y = m x +c form, it is called the slope intercept form of the equation.

Here m is slope and c is constant.

The given equation of line,

x + 2y = 4,

To find the slope,  represent the equation in slop intercept form,

Simplify the equation,

x + 2y = 4

2y = -x + 4

y = -(1/2)x + 2

The slope of the equation is -1/2.

To find y-intercept, substitute x = 0,

y = -(1/2). 0 + 2

y = 2

The y-intercept of the equation is 2.

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Answer: C) 1

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One way is to graph the function f(x) = ln(x)/(x-1) and you'll see the curve slowly approach y = 1 when x approaches 1 from either side. Check out the attached image labeled "figure 1" for this graph.

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You can use a table to see this in action. See figure 2 (attached below as well).

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Another alternative is to use L'Hospital's rule. This is because we get the indeterminate form 0/0 after plugging x = 1 into the original function.

if y = ln(x), then dy/dx = 1/x

If y = x-1, then dy/dx = 1

So f(x) = ln(x)/(x-1) becomes (1/x)/1 = 1/x

If you plug in x = 1, you get 1/x = 1/1 = 1.

Regardless of which method you use, the limiting value is 1

So the first thing we need to do is set up an equation (using x to represent the number). Then, we'll solve it to get the answer.

Step 1: Translate the word problem into an equation

Word problem: The sum of nine and six-tenths and a number is thirteen and two-tenths.

Equation: [tex]9 \frac{6}{10}[/tex] + x = [tex]13 \frac{2}{10}[/tex]

Step 2: Isolate x by subtracting [tex]9 \frac{6}{10}[/tex] from each side

[tex]9 \frac{6}{10}[/tex] + x -  [tex]9 \frac{6}{10}[/tex] = [tex]13 \frac{2}{10}[/tex] -  [tex]9 \frac{6}{10}[/tex]

Step 3: The numbers on the left cancel out, leaving x alone

x =  [tex]3 \frac{6}{10}[/tex]

Step 4: Convert the answer to decimals

x = 3.6

Answer:

its B

Step-by-step explanation:

A scale factor of 1/2 makes the triangle half the size of the original.

The original is 4 units tall, so 1/2 scale makes the new one 2 units tall.

It is 6 units long, so 1/2 would be 3 units long.

Now since the scale factor is centered at (-1,3) fine the midpoint between The top left corner of the triangle and the center point:

Midpoint ( -1-5/2 , 3+7/2)

Midpoint = (-6/2 , 10/2)

Midpoint = -3,5

This is where the top left corner of the scaled triangle would be.

See attached picture:

The equation of line in the slope intercept form is c = 1.5 ( t ) + 12 where t is the number of toppings and c is the total cost

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the total cost of pizza with toppings be = c

Let the number of toppings be = t

Let the initial cost of the pizza be = $ 12

Let the cost of each toppings be = $ 1.50

So , the total cost of the pizza with toppings c =  ( cost of each toppings x number of toppings ) + initial cost of the pizza

Substituting the values in the equation , we get

Total cost of the pizza with toppings c = 1.50 ( t ) + 12

Therefore , the value of A is c = 1.50 ( t ) + 12

Hence , the equation is c = 1.50 ( t ) + 12  with slope m = 1.50 and y intercept as 12

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Final answer:

The equation in slope-intercept form for the total cost C of a pizza with t toppings when a pizza costs $12 and each additional topping costs $1.50 is C = 1.50t + 12.

Explanation:

To find the equation in slope-intercept form for the total cost C of a pizza with t toppings at a pizza parlor that charges $12 for a large cheese pizza and $1.50 for each additional topping, we can establish a relationship between the number of toppings and the total cost. Let's use the slope-intercept form of the linear equation, y = mx + b where y is the total cost, m is the cost per topping, x is the number of toppings, and b represents the base price of the pizza without toppings.

The base price of the pizza is $12, which is the y-intercept, and the additional cost per topping is $1.50, which is the slope. Therefore, the equation that represents the total cost C of the pizza with t toppings is:

C = 1.50t + 12

[tex]a_n=n^2-n\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}.\\\\n=1\to a_1=1^2-1=1-1=0\\\\n=2\to a_2=2^2-2=4-2=2\\\\n=3\to a_3=3^2-3=9-3=6\\\\n=4\to a_4=4^2-4=16-4=12\\\\n=5\to a_5=5^2-5=25-5=20\\\\Answer:\ \boxed{0,\ 2,\ 6,\ 12,\ 20}[/tex]

Answer: -1, 2, 7, 14, 23

Step-by-step explanation:

aₙ = n² - 2

for n=1

a₁ = 1² - 2 = 1-2= -1

for n=2

a₂ = 2² - 2 = 4-2 =2

for n= 3

a₃ =3² - 2 = 9-2=7

for n=4

a₄= 4² - 2 = 16-2=14

for n=5

a₅= 5² - 2=25-2=23

Therefore, the first five terms of the sequence are; -1, 2, 7, 14 and 23

Answer:

Perimeter = 32.44 unit

Area of triangle = 30 unit²

Step-by-step explanation:

By distance formula distance between (a,b) and (c,d) is [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]

So, we have

      [tex]AB=\sqrt{(16-2)^2+(2-8)^2}=15.23\\\\BC=\sqrt{(16-6)^2+(2-2)^2}=10\\\\AC=\sqrt{(2-6)^2+(8-2)^2}=7.21[/tex]

Perimeter = 15.23 + 10 + 7.21 = 32.44 unit

We have [tex]s=\frac{15.23+10+7.21}{2}=16.22[/tex]

Area of triangle[tex]=\sqrt{s(s-AB)(s-BC)(s-AC)}=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}=30[/tex]

Area of triangle = 30 unit²

Answer: 27 grams

Step-by-step explanation:

m(x) = 64(0.75)ˣ

m(3) = 64(0.75)³

      = 64(.421875)

      = 27

Answer:

This means the function touches the x-axis at -1 but does not cross.

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

This means the function touches the x-axis at -1 but does not cross.

Answer:

1) Translation

2) Rotation

3) Reflection  

Step-by-step explanation:

To make ΔDEF ≅ ΔD'E'F' , we will carry on the following steps:

Step 1: Translate ΔD'E'F' in upward direction, the figure will remain same but it will shift a little in upwards direction.

Step 2 : Rotate ΔD'E'F' about 180°. The figure obtained will be reflection of the original image ΔDEF.

Step 3 : Reflect ΔD'E'F'.

This implies that ΔDEF≅ΔD'E'F'.  

Answer:

C

Step-by-step explanation:

The lines drawn have the following features:

Since the equation of a line has the form y=mx+b where b is y-intercept and m is the slope, we can write

y=-2x+1

y=2x-3

This is the system of equations and is answer choice C.

Answer: C

Step-by-step explanation:

Slope-Intercept form of an equation is y = mx + b

Red line:

It crosses the y-axis at -3 so b = -3

Now count the rise over run from the b (0, -3) to another point (I chose (1, -1) because it was the next point on a lattice line). The rise is 2 and the run is 1. So. rise over run is 2/1  ⇒ m = 2

Equation: y = 2x - 3

Yellow line:

Follow the same steps as the Red line to get b = 1 and m = -2

Equation: y = -2x + 1

[tex]A_{\triangle}=\dfrac{1}{2}bh\\\\\text{We have}\ b=7cm,\ h=4cm\\\\\text{Substitute:}\\\\A_{\triangle}=\dfrac{1}{2}(7)(4)=\dfrac{28}{2}=\boxed{14\ cm^2}[/tex]

Answer:

area = 6m + 51 feet²

Step-by-step explanation:

area = length × width = 3(2m + 17) = 6m + 51

Answer:

∠NET = 63°

Step-by-step explanation:

We are given a figure with a circle A and a line ET which is tangent to the circle at the point T. Also, the measure of the angle TNG is given to be 27° and we are to find the measure of angle NET.

If we recall the point of tangency, we will remember that the point where a tangent touches the radius of a circle is always a right angle.

That makes the angle NTE to be 90°.

Putting the sum of these angles equal to 180 to get:

90 + 27 + ∠NET = 180

∠NET = 180 - 90 - 27

∠NET = 63°

Answer: B: 56

Step-by-step explanation: First find f(g(x)). Where f(x) = -3x-4 and

g(x) = 2x-6. Replace X in f(x) with the equation for g(x)

f(g(x)) = -3(2x-6) -4. Then use the foil method and simplify.

= -6x+18-4

=-6x+14

Now sub. in the value of x with -7 and evaluate.

=-6(-7)+14

=42+14

=56

Answer:

angle(ADB)=angle(CBD)

ADC+DCB=180

AE=CE

Step-by-step explanation:

we will verify each options

option-A:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

and alternate interior angles are always equal

so,

angle(ADB)=angle(CBD)

so, this is TRUE

option-B:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

so, we get

ADC+DCB=180

so, this is TRUE

option-C:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

[tex]angle(DEC)\neq angle(DEA)[/tex]

so, this is FALSE

option-D:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

so, this is TRUE

option-E:

Since, AC and DB are diagonals of parallelogram

so, they can not be equal

so, this is FALSE

We know that : Sin²θ + Cos²θ = 1

Given : Sinθ [tex]\bf{= \frac{4}{7}}[/tex]

[tex]\bf{\implies (\frac{4}{7})^2 + Cos^2(\theta) = 1}[/tex]

[tex]\bf{\implies Cos^2(\theta) = 1 - \frac{16}{49}}[/tex]

[tex]\bf{\implies Cos^2(\theta) =(\frac{49 - 16}{49})}[/tex]

[tex]\bf{\implies Cos^2(\theta) =(\frac{33}{49})}[/tex]

[tex]\bf{\implies Cos(\theta) = (\pm)(\frac{\sqrt{33}}{7})}[/tex]

Given : θ lies in Quadrant II

We know that : Cosθ is Negative in Quadrant II

[tex]\bf{\implies Cos(\theta) = (-)(\frac{\sqrt{33}}{7})}[/tex]

Option 3 is the Answer

Answer: sqrt(19)/10

Step-by-step explanation:

sinx=0.9

x=arcsin(0.9)

Insert x for cos(x):

cos(arcsin(0.9)=

Use identify [tex]cos(arcsin(x))=\sqrt{1-x^{2} }[/tex], so

[tex]\sqrt{1-(\frac{9}{10})^{2}} =\sqrt{\frac{19}{100} } =\frac{\sqrt{19}}{10}[/tex]

Sorry if this is confusing.

Final answer:

To find cos X given sin X = 0.9, use the Pythagorean identity, solve for cos2 X, take the square root, and round to the nearest thousandth to get cos X ≈ 0.436.

Explanation:

To calculate the value of cos X when sin X= 0.9, we can use the Pythagorean identity which states that sin2X + cos2X = 1. First, square the sine value: (sin X)2 = 0.92 = 0.81. Then, we subtract this value from 1 to find (cos X)2: 1 - 0.81 = 0.19. Finally, we take the square root of 0.19 to find the value of cos X. Since sin X is positive and assuming X is an angle in the first quadrant, cos X will also be positive. So, cos X = √0.19 ≈ 0.436.

Therefore, the value of cos X, rounded to the nearest thousandth, is 0.436.

Answer:

Let x represents the ounces of first spice.

From the given statements, you draw a table as shown below:

                           ounces of spice         Percentage           ounces of salt

First spice                 x                              3%                            0.03x

Second spice           175                            6%                          175(0.06)

Final  mixture          x+ 175                         5%                        (x+175)(0.05)

Now, to solve for x;

Final spice = First spice + second spice

[tex]0.03x+175(0.06) = (x+175)(0.05)[/tex]

[tex]0.03x + 10.5 = 0.05x + 8.75[/tex]

Subtract 10.5 on both sides we have;

[tex]0.03x + 10.5 -10.5= 0.05x + 8.75-10.5[/tex]

Simplify:

[tex]0.03x= 0.05x -1.75[/tex]

Subtract 0.05x on both sides;

[tex]0.03x - 0.05x= 0.05x -1.75-0.05x[/tex]

Simplify:

[tex]-0.02x= -1.75[/tex]

Divide both sides by -0.02, we get;

x = 87.5 ounces

Therefore, 87.5 ounces of spices i.e 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt

Answer:

None of the Above

Step-by-step explanation:

As it is given that

cosФ= 3/2

and Ф lies in quadrant 4

Now in quadrant 4 we know that by the rules of trigonometry that

cos Ф is positive in 4th quadrant also in 4th quadrant

and sinФ is negative in 4th quadrant

also we know that by simple rules of trigonometry in a right angled triangle

cos Ф=[tex]\frac{Base}{Hypotenuse}[/tex] =[tex]\frac{3}{2}[/tex]

now from the law of trigonometry

cos²Ф+sin²Ф=1

From this we derive the value of sinФ

solving the equation

sin²Ф=1-cos²Ф

Putting in the values of cos Ф

sin²Ф=1-[tex](\frac{3}{2})^{2}[/tex]

sin²Ф=1-[tex](\frac{9}{4})[/tex]

solving the fraction

sin²Ф=[tex](\frac{4-9}{4})[/tex]

sin²Ф=[tex](\frac{-5}{4})[/tex]

so taking square root of both sides

[tex]\sqrt{sin^{2}\alpha}=\sqrt{\frac{-5}{4} }[/tex]

here

[tex]\alpha[/tex]=Ф

so it becomes

sin Ф=[tex]\frac{\sqrt{-5} }{2}[/tex]

as we know that in imaginary numbers

[tex]\sqrt{-1}[/tex] = ι

so the given becomes

sin Ф=[tex]\frac{{-5ι} }{2}[/tex]

Which is the value of sin Ф

And in the given values we can see that it is none of the values

Also seeing the question we can see that the question is absurd because

cos Ф= base / hypotenuse

in our question we can see that base =3 and hypotenuse = 2

but in real geometry this is the rule that hypotenuse can never be smaller then base either it is equal to base or greater then base

the formula for finding value of finding hypotenuse is

hypotenuse ² = base ² + perp ²

so this formula shows that if perp is 0 then hypotenuse will be equal to base

in other cases it would be greater then base

Answer:

- 1/ 2

Step-by-step explanation

-1\ 2

Use the Pythagorean identity, sin2Θ + cos2Θ = 1 to get sinΘ = ±1 - cos2Θ, then solve for sinΘ.

Answer:

F(-4) = -3313

Step-by-step explanation:

To solve this, let x=-4

f(x) = 3x^5 + 4x^3-x+11

f(-4) = 3(-4)^5 + 4(-4)^3 -(-4) +11

     = 3(-1024) +4 (-64) +4+11

    = -3072 - 256+15

     = -3313

Answer:the answer is D. All of the above

Step-by-step explanation:

Answer:

D) ALL OF THE ABOVE

Explanation:

In today's world, banks offer various variety of services at door-steps to attract customers However, some basic today's services offered by the banks to its customers are discussed below:

1. Home banking:

Home banking is the procedure of finishing financial affairs from an individual's own home as opposed to using a branch of a bank. It compromises actions such as transferring money, applying for loans, paying bills, making financial inquires and directing deposits.

2. Online banking:

Online banking is one of the famous service offered by banks nowadays that allows customers to access their account data by using the internet. Online banking is also known as “Internet banking”.

3. Priority banking:

Priority banking may include various services, but some of the famous services include online bill pay, financial consultation, free checking of account amount and information.

Answer:

5. 20

6. 30

7. 22

Step-by-step explanation:

5. The median is indicated by the line (and dot) in the middle of the box.

6. The maximum value is indicated by the extreme right end of the whisker.

7, The upper quartile is indicated by the right end of the box.

Answer:

5. 20

6. 30

7. 22

Step-by-step explanation:

5. The median is indicated by the line (and dot) in the middle of the box.

6. The maximum value is indicated by the extreme right end of the whisker.

7, The upper quartile is indicated by the right end of the box.

Step-by-step explanation:

[tex]4csc(2x) = 2csc^2(x) tan(x)[/tex]

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

[tex]4 \frac{1}{sin(2x)}[/tex]

Also we use identity

sin(2x) = 2 sin(x) cos(x)

[tex]4 \frac{1}{2sin(x)cos(x)}[/tex]

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

[tex]2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}[/tex]

[tex]2\frac{sin(x)}{sin^2(x)cos(x)}[/tex]

[tex]2\frac{1}{sin^2(x)} \frac{sin(x)}{cos(x)}[/tex]

We know that sinx/ cosx = tan(x)

Also  1/ sin(x)= csc(x)

so it becomes 2csc^2(x) tan(x) , Right hand side

Hence verified

The value of x is -101/4 or the simplified form of the expression can be given as -1/2x = 101/8

This question relates to equation in mathematics and all we need to do is solve for x. But this requires some step by step process which are

The given equation is

[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\[/tex]

[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\\\(\frac{2}{2}x-10)-(\frac{3}{2}x-\frac{21}{8}) \\x- 10 -\frac{3}{2}x-\frac{21}{8}\\[/tex]

[tex]x-\frac{3}{2}x-10-\frac{21}{8}=0\\-\frac{1}{2}x =10+\frac{21}{8}\\-\frac{1}{2}x=101/8\\[/tex]

We have to divide through by coefficient of x

[tex]-\frac{1}{2}x =\frac{101}{8}\\(-1/2x)/(-1/2)=(101/8)/(-1/2)\\x=\frac{-101}{4} \\[/tex]

from the above calculation, the value of x is -101/4. The simplified form of the expression is -1/2x = 101/8

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Answer:

60 percent

Step-by-.step explanation:

You need to convert 3/5 to a percentage.

This is 3*100 / 5

= 300 / 5

= 60 per cent

Final answer:

Roasted beans retain 3/5 of their initial weight, which is equivalent to 60% when converted to a percent.

Explanation:

To convert this fraction to a percentage, we follow the steps outlined in the explanation: dividing the numerator by the denominator to get a decimal value, and then multiplying by 100 to express it as a percentage. In this case, 3 divided by 5 equals 0.60, which when multiplied by 100 gives 60%.

The roasted beans retain approximately 3/5 of their initial weight after roasting. To determine what percentage of their initial weight they retain, we convert the fraction 3/5 to a percent. To do this:

Therefore, roasted beans retain 60% of their initial weight.

Answer:

1. 29/4

2. 5

3. 6

4. 14/3

5. 29/27

Step-by-step explanation:

Answer: You the answer

Step-by-step explanation: cause your fine

Answer:

[tex]\$164.5[/tex]

Step-by-step explanation:

Bonnie deposits $70.00 into a new savings account.

The account earns 45% simple interest per year.

She neither added or removed from the savings account for 3 years.

We know that,

[tex]i=\dfrac{P\cdot r\cdot r}{100}[/tex]

here,

i = interest,

P = principal = $70,

r = rate of interest = 45%,

t = time = 3 years,

Putting the values,

[tex]i=\dfrac{70\cdot 45\cdot 3}{100}=\$94.5[/tex]

So the total amount will be,

[tex]=\text{Principal}+\text{Interest}[/tex]

[tex]=70+94.5[/tex]

[tex]=\$164.5[/tex]

Answer:

its 4.5 not 45

Step-by-step explanation: