Which statements about the graph of the exponential function f(x) are TRUE?The x-intercept is 1.The y-intercept is 3.The asymptote is y = -3The range is all real numbers greater than -3The domain is all real numbers.f(x) is positive for all x-values greater than 1As x increases, f(x) approaches, but never reaches, -3.

Answers

Answer 1

1 The x-intercept is the value of x where the graph intersects the x-axis. The graph crosses the x-axis at x = 1. This statement is true.

2 The y-intercept is the value of y where the graph intersects the y-axis. The graph crosses the y-axis at y = -2. This statement is false.

3 The horizontal asymptote is the value of y to which the graph approaches but never reaches. This value seems to be y = -3, thus this statement is true.

4 The range is the set of values of y where the function exists. The graph exists only for values of y greater than -3. This statement is true.

5 We can give x any real value and the function exists, i.e., any vertical line would eventually intersect the graph. This statement is true.

To find the domain of a function when we are given the graph, we use the vertical line test. This consists of drawing an imaginary vertical line throughout the x-axis. If the line intersects the graph, that value of x is part of the domain.

This imaginary exercise gives us the centainty that there is no value of x that won't intercept the graph, thus the domain is the set of all the real values.

6 We can see the graph is positive exactly when the function has its x-intercept, thus This statement is true.

7 As x increases, y goes to infinity. The value of -3 is not a number where f(x) approaches when x increases, but when x decreases. This statement is false.

Related Questions

Find LM if LN = 137mm.

Answers

[tex]\begin{gathered} \text{M is the mid point of LN, so } \\ LM=\frac{LN}{2}=\frac{137}{2}=68.5\text{ mm} \end{gathered}[/tex]

Alyssa will correctly label the numbers 48.4, 48482, 48.09, and 48on the number line below.

Answers

Answer:[tex]48\frac{3}{5}[/tex]Explanations:

The numbers under consideration are:

[tex]48.4,\text{ 48}\frac{1}{2},\text{ 48.09, 48}\frac{3}{5}[/tex]

Converting all the numbers to decimal:

[tex]\begin{gathered} 48\frac{1}{2}=\text{ 48+0.5 = 48.5} \\ 48\frac{3}{5}=\text{ 48 + }0.6\text{ = 48.6} \end{gathered}[/tex]

Therefore, the numbers can be written as:

48.4, 48.5, 48.09, and 48.6

Out of these numbers, only 48.6 is closest to 49

[tex]48\frac{3}{5}\text{ is closest to 49}[/tex]

This not a test btw ! But can you please help me with this !

Answers

[tex]\begin{gathered} A\colon6x-3y=-4 \\ B\colon_{\text{ }}-4x-y=5 \end{gathered}[/tex]

Using elimination:

[tex]\begin{gathered} (A)-3(B)\colon \\ 6x+12x-3y+3y=-4-15 \\ 18x=-19 \end{gathered}[/tex]

Therefore, the answer is:

B) Multiply A by 1 and B by -3

I need some help with this! I know about the trig identitys and stuff like that, but I just get a little confused on how to apply sometimes.

Answers

we have that

Let

x ------> the distance in miles from a point on the ground (the red line)

In the right triangle of the figure

sin(6.5)=7,000/x

solve for x

x=7,000/sin(6.5)

using a calculator

x=61,835.70 ft

Convert to miles

Remember that

1 mile=5,280 ft

61,835.7 ft=61,835.7/5,280=11.71 miles

therefore

the answer is 11.71 miles

Find the sum of the arithmetic series 31+37 +43 +49 +... where n=8,OA. 416B. 1668OC. 832D. 834Reset Selection

Answers

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given details

[tex]\begin{gathered} a_1=31 \\ n=8 \\ d=37-31=6 \end{gathered}[/tex]

STEP 2: Write the formula for finding sum of arithmetic series

STEP 3: Find the sum of the series

By substitution,

[tex]\begin{gathered} S_8=\frac{8}{2}[2(31)+(8-1)6] \\ S_8=4(62+42) \\ S_8=4(104)=416 \end{gathered}[/tex]

Hence, the sum is 416

15% of $764.69rounded to the nearest cent.

Answers

Percentage is expressed in terms of 100. To find 15% of 764.69, we would multiply ratio of 15% to 100% by 764.69. Thus, we have

15/100 * 764.69

= 114.7035

Which equation has at least one solution? Mark all that app A. 2x-1= 2 B. 3 y + 1) = 3y 1 C. 5p - (3 + p) = 6p + 1 D. 4/5m=1-1/5m E. 10 +0.5w =1/2w - 10 F. 4a + 3(a - 2) = 8a - (6 + a) Answer Choices:

Answers

Let's check the options

2x - 1 = 2

2x= 3

x= 3/2=1.5

option A has atleast one solution

3y+ 1 = 3y

option B has no solution

5p - (3 + p) = 6p + 1

5p - 3 - p = 6p + 1

4p - 6p = 1 + 3

-2p = 4

p =-2

option C has atleast one solution

4/5 m = 1- 1/5 m

4/5 m + 1/5m = 1

1m = 1

m = 1

Option D has atleast one solution

10 + 0.5w = 1/2w - 10

0.5 w - 1/2 w = -10 - 10

option E has no solution

4a + 3(a-2) = 8a - (6+a)

4a +3a - 6 = 8a -6 - a

7a -6 = 7a - 6

option F has many solution. Hence it also has atleast one solution

Therefore;

option A, C, D and F has atleast one solution

-10 is no less than 2 times a number plus 14

Answers

Let the number be x.

Then according to the question,

[tex]\begin{gathered} -10\ge2x+14 \\ -10-14\ge2x \\ -24\ge2x \\ x\ge-12 \end{gathered}[/tex]

Thus, the number should be greater than or equal to -12.

What is the first step for finding the quotient of 3x^3 z^5/5y * x^2 z^6/20y^3

Answers

The initial expression is:

[tex]\frac{3x^3z^5}{5y}\text{ / }\frac{x^2z^6}{20y^3}[/tex]

So the first step is to multiply the numerator of the second fraction with the denominator of the first franction and the denominator of the second fraction by the numerator of the first fraction so:

[tex]\frac{3x^3z^6}{5y}(\frac{20y^3}{x^2z^6})[/tex]

So is option C)

NEED ASAP ILL GIVE BRAINLIEST IF CORRECT

Answers

it’s the first option .

answer: 8 square root(y^5)
because your base in the fraction is y and so you can subtract the exponents.

numerator exponent - denominator exponent so it’s:

7/8 - 1/4 that gives you 5/8 and so it’s
y^(5/8) and if you write that in the radical form it’s numerator as exponent and denominator as your radical base. therefore the final answer would be:

8 square root(y^5) . so your first option at the top

What is the equation of the line below in slope-intercept form?(4 Points)x-3y = 6y =- 2y = 3x - 2y = - ** - 2y = -3x - 2

Answers

[tex]x-3y=6[/tex]

Let's make y the subject of the equation.

[tex]\begin{gathered} x-6=3y \\ y=\frac{x-6}{3} \\ y=\frac{1}{3}x-\frac{6}{3} \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]

The correct option is A

A boat is heading towards a lighthouse, whose beacon-light is 140 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 10∘∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.

Answers

see the figure below to better understand the problem

we have that

tan(10∘)=140/x -----> by TOA

solve for x

x=140/tan(10∘)

x=794 ft

therefore

The answer is 794 feet

Answer:

Step-by-step explanation:

tan 10=140/x

x=140 / tan 10

x=794

what is the answer to a negative 4 divided by a positive 6?

Answers

The expression given as negative 4 divided by a positive 6 has a value of -2/3

How to evaluate the expression?

From the question, the expression is given as

negative 4 divided by a positive 6

Rewrite the expression properly

This is rewritten as follows

-4 divided by +6

This can be represented as

-4/6

There are no like terms in the above expression

So, we have the following equation

-4/6 = -4/6

Divide 4 and 6 by a common factor

The common factor is 2

So, we have

-4/6 = -2/3

The expression cannot be further simplified

So, we have the following equation

-4/6 = -2/3

Hence, the value of the expression is -2/3

Answers

Based on the substitution method, the solution of the system of the equation is x = 3 and y = 17.

Substitution method:

Substitution method is the way of finding the value of any one of the variables from one equation in terms of the other variable.

Given,

Here we have the system of equations

x + y = 20

y = 3x + 8

Now we need to find the solutions for these equation using the substitution method.

From the given details we know that the value of y is defined as 3x + 8.

So, we have to apply these value on the other equation in order to find the value of x,

x + (3x + 8) = 20

4x + 8 = 20

4x = 20 - 8

4x = 12

x = 3

Now apply the value of x into the other equation in order to find the value of y,

y = 3(3) + 8

y = 9 + 8

y = 17

Therefore, the solution of the equation is x = 3 and y = 17.

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There is $1.90 in a jar filled with quarters, dimes, and nickels. There are 2 more quarters than dimes and there are 2 more nickels than quarters. How many of each coin are there? quarters dimes [ ) nickels Enter the number that belongs in the green box.

Answers

Answer:

5 quarters, 3 dimes, 7 nickels

Explanations:

Let the number of quarters in the jar = q

Let the number of dimes in the jar = d

Let the number of nickels in the jar = n

1 quarter = $0.25

1 dime = $0.1

1 nickel = $0.05

The jar is filled with quarters, dimes, and nickels, totaling $1.90

This can be represented mathematically as:

0.25q + 0.1d + 0.05n = 1.90.........(1)

There are two more quarters than dime:

q = d + 2..............(2)

There are two more nickels than quarters

n = q + 2..............(3)

make d the subject of the formula in equation (2)

d = q - 2............(4)

Substitute equations (3) and (4) into equation (1)

0.25q + 0.1(q - 2) + 0.05(q + 2) = 1.90

0.25q + 0.1q + 0.05q - 0.2 + 0.1 = 1.90

0.4q - 0.1 = 1.90

0.4q = 1.90 + 0.1

0.4q = 2.0

q = 2.0/0.4

q = 5

n = q + 2

n = 5 + 2

n = 7

d = q - 2

d = 5 - 2

d = 3

There are 5 quarters, 3 dimes, 7 nickels

how do I know where which choices below go into the correct blanks for number 1-4?

Answers

For 1, we have the following triangle:

Using the cosine function to get the hypotenuse we get:

[tex]\begin{gathered} \cos (45)=\frac{7}{h} \\ \Rightarrow h=\frac{7}{\cos(45)}=\frac{7}{\frac{1}{\sqrt[]{2}}}=7\cdot\sqrt[]{2} \\ h=7\cdot\sqrt[]{2} \end{gathered}[/tex]

Now that we have the hypotenuse, we can find the remaining side using the pythagorean theorem:

[tex]\begin{gathered} h^2=7^2+x^2 \\ \Rightarrow x^2=h^2-7^2=(7\cdot\sqrt[]{2})^2-7^2=49\cdot2-49=49 \\ \Rightarrow x^2=49 \\ x=7 \end{gathered}[/tex]

Therefore, the value of the remaining side is 7.

Given the exponential decay function below:Determine the intervals of increase and decrease.

Answers

Given the equation of exponential decay function:

[tex]y=(\frac{1}{3})^x-3[/tex]

The given function always decreases overall the domain

so, the answer will be the intervals of decrease is:

[tex](-\infty,\infty)[/tex]

ok my question is math algebra. consider the linear equation y-1=0 and grapthe two points

Answers

To find:

We need to find two points on the linear equation y-1=0 and to plot those points on graph.

Step by step solution:

We know that:

General coordinate of any two points on line y = 1:

= (x, 1)

So let us assume any two random points on the line:

= (1,1) and (2,1)

We will now mark them on the graph:

Question 17
2(h - 6) + 20 = -4

Answers

The answer is h= -6

Drag the measurements to the containers to show equal length

Answers

The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft

What is meant by measurements?

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.

An equation exists an expression that indicates the relationship between two or more numbers and variables.

1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.

Hence:

15 yd = 15 yd × 36 in per yd = 540 in

195 ft = 195 ft × 12 in per ft = 2340 in

5280 yd = 5280 yd * 3 ft per yd = 15840 ft

The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft.

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help meeeeeeeeeeeeeeeeeeeeeee

Answers

(f o g)(x) = radical -2x + 3

4. Which inequality is represented by the graph?8642S-6428X4-6laO4x - 2y > 12O4x - 2y < 12O4x + 2y > 12O4x + 2y < 12

Answers

Hello there. To solve this question, we'll have to remember some properties about inequalities and its graphs.

First, we have to determine the equation of the line. For this, we have to find, by inspection, two points contained in that line:

We can easily find the points (0, -6) and (2, -2).

With this, we can find the equation of the line using the point-slope formula:

[tex]y-y_0=m\cdot(x-x_0)[/tex]

Where (x0, y0) is a point of the line, as well as (x1, y1) and the slope m is given by:

[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]

Plugging the coordinates of the points, we get:

[tex]m=\frac{-2-(-6)}{2-0}=\frac{-2+6}{2}=\frac{4}{2}=2[/tex]

Such that:

[tex]\begin{gathered} y-(-6)=2\cdot(x-0) \\ y+6=2x \end{gathered}[/tex]

Rearranging it in the ax + by = c form,

[tex]2x-y=6[/tex]

Multiply both sides of the equation by a factor of 2

[tex]4x-2y=12[/tex]

Finally, notice that the values of y in the shaded region are greater than the values in the line, which means that the inequality we're looking for is:

[tex]4x-2y>12[/tex]

All the point (x, y) satisfying this inequality are contained in the shaded region.

HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST

Answers

the rational number :

-1 ³/₄ is located as point 1

14/8 is located as point 5

1.125 is located as point 6

-0.875 is located as point 4

What is number line ?

Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.

Here,

the rational number -1 ³/₄ is located as point 1, as -1 ³/₄ is greater then -1 and less then -2 on number line and is 3/4 of the gap between -1 and -2.

the rational number 14/8 is located as point 5, as 14/8 is greater then 0 and less then 1 on number line and is 3/4 of the gap between 0 and 1.

the rational number 1.125 is located as point 6, as 1.125 is greater then 1 and less then 2 on number line and is 1/8th of the gap between 1 and 2.

the rational number -0.875 is located as point 4, as -0.875 is greater then 0 and less then -1 on number line and is 1/8 th of the gap between -1 and 0.

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Zach can buy a dozen pencils for $1.89, 24 pencils for $3.60, or 36 pencils for $5.49. What is the best buy?

Answers

To know which one is the best option we have to divide the cost in the number of pencils so:

[tex]\frac{1.89}{12}=0.16[/tex]

the second option is:

[tex]\frac{3.60}{24}=0.15[/tex]

the thert option is:

[tex]\frac{5.49}{36}=1.16[/tex]

So the best option is the second option

which ordered pair is a solution of 6X + 7 < 21

Answers

Substitute 2 for x and 1 for in the inequality to verify that ordered pair satisfy the inequality or not.

[tex]\begin{gathered} 6\cdot2+7\cdot1<21 \\ 12+7<21 \\ 19<21 \end{gathered}[/tex]

The inequality is trus so point (2,1) satisfy the inequality.

Substitute 4 for x and 1 for y in the inequality to verify that ordered pair satisfy the inequality or not.

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Question 6 of 10
Assume that two chords in a given circle are the same distance from the
center of the circle. Which of the following must also be true?
O
A. They must be perpendicular.
B. They must be parallel.
C. They must be diameters.
D. They must be congruent.
SUBMIT

Answers

The true statement is the same distance from the center of the circle is they must be perpendicular.

We have given that,

Two chords in a given circle are the same distance from the center of the circle.

What prerequisites must be met for the chords to be in harmony?

The two chords must be equally spaced apart from the circle's center if they are congruent.

A is disregarded because it's possible that the chord won't travel through the circle's center.

Because the chords are not required to be parallel, B is rejected.

Because the chords do not have to be perpendicular, C is rejected.

A chord is any line segment that joins two points on the circle's circumference. While a circle's radius connects the center to the circle's point. As a result, we can conclude that radius is not a chord based on the definitions of both terms.

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2. Given: ZMOP is a right angle RP I OP Prove: MO || RP

Answers

Given that;

[tex]\begin{gathered} \measuredangle MOP\text{ is a right angle.} \\ \measuredangle MOP=90^0 \end{gathered}[/tex]

And;

[tex]\vec{RP}\perp\vec{OP}[/tex]

Since line RP is perpendicular to line OP, Angle RPO must be a right angle.

[tex]\measuredangle RPO=90^0[/tex]

Recall that for two parallel lines intersected by a straight line, Same side interior angles are supplementary.

[tex]A+B=180^0[/tex]

So, for line MO to be parallel to line RP, the sum of angle MOP and angle RPO must be equal to 180 degree.

[tex]\measuredangle MOP+\measuredangle RPO=90+90=180^0[/tex]

Since the sum of angle MOP and angle RPO is equal to 180 degree, then line MO is parallel to line RP.

[tex]\begin{gathered} \text{ Since} \\ \measuredangle MOP+\measuredangle RPO=180^0 \\ \text{Then;} \\ MO\Vert RP \end{gathered}[/tex]

Proved

A bakery makes and sells hot cocoa bombs during the holidays. The first 12 hot cocoa bombs of an order cost is $4.00 each. Each of the next 6 hot cocoa bombs cost $3.50 each. For orders exceeding 18, the cost drops to $3 each. The function C(x) represents the bakery's pricing.

Answers

Solution

Step 1

Given data for C(x), the bakery's pricing

[tex]\begin{gathered} F\text{or this range 0}\leq x\leq12ofhotcocoabombs\text{ we use C(x) =4x} \\ \text{For this range }1218,ofhotcocoabombs\text{ we useC(x) = }3x+15 \end{gathered}[/tex]

Required

Step 1

To find the cost of 8 hot cocoa bombs

[tex]\begin{gathered} C(8)\text{ lies in the range 0}\leq x\leq12 \\ \text{Hence we use 4x where x = 8} \\ \text{The cost of 8 hot cocoa bombs = 4(8) = \$32} \end{gathered}[/tex]

Step 2

To find the cost of 18 hot cocoa bombs

[tex]\begin{gathered} C(18)\text{ lies in the range 12}Step 3

To find the C(30)

[tex]\begin{gathered} C(30)\text{ lies in the range x}\ge18 \\ \text{Hence we use 3x +15, where x = 30} \\ C(30)\text{ = 3(30) + 15 = 90 + 15 = \$105} \\ \end{gathered}[/tex]

Step 4

What C(30) represents.

C(30) represents the cost of ordering 30 hot cocoa bombs which is $105

A reflection across which line(s) carries the trapezoid onto itself?

Answers

If we reflect about x =2, it is a mirror image on each side ( left and right). There is no other line where we can have a mirror image on each side.

A school bus with the football team left Jefferson HighSchool and drove at an average speed of 48 mph. A schoolbus with the cheerleading squad left 2 hours later and wasable to catch up to the football team after 6 hours. Whatwas the speed of the bus carrying the school's cheerleadingsquad?

Answers

Given data

A school bus with the football team from Jefferson High School drove at an average speed of 48mph

Another school bus with the cheerleading squad left 2 hours later and caught with the football team after 6 hours.

Required

To find the speed of the bus carrying the Cheerleading squad.

Step 1

Determine the distance the bus carrying the football team had travelled in the first 2 hours

Speed is given as

[tex]\begin{gathered} \text{speed =}\frac{dis\tan ce}{time} \\ \text{where sp}eed\text{ = 48mph} \\ \text{time = 2 hours} \\ \text{distance = sp}eed\text{ x time} \\ \text{distance = 48 x 2 =96miles} \end{gathered}[/tex]

Step 2

Determine of the distance covered by the bus with the football team in the next 6 hours and find the total distance in 8 hours

[tex]\begin{gathered} \text{Distance = sp}eed\text{ }\times\text{ time} \\ where \\ \text{speed = 48mph} \\ \text{time = 6 hours} \\ \text{Distance = 48 }\times\text{ 6 = 288 miles} \end{gathered}[/tex]

The total distance in 8 hours covered by the bus = 288 + 96 = 384miles

Step 3

Determine the speed of the bus carrying the Cheerleaders

The total distance to be covered by the Cheerleaders is 384 miles

The total time of their journey to catch with the bus carrying the Football team is 6hours

Hence the speed of the bus required is given as

[tex]\begin{gathered} \text{Speed = }\frac{dis\tan ce}{time} \\ \text{speed = }\frac{384}{6} \\ \text{speed = 64mph} \end{gathered}[/tex]

Therefore, the speed of the bus carrying the school's Cheerleaders squad is 64mph

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