ANSWER
The ordered pair is not a solution to the equation.
EXPLANATION
We want to find out if (-6, -2) is a solution to the equation:
r - s = 4
Using alphabetical order for the substitution, we have that for the ordered pair:
r = -6 and s = -2
To find if it is a solution, we will substitute the value of r and 6 from the ordered pair into the equation and then, check if both sides of the equation are actually equal.
That is:
-6 - (-2) = 4
-6 + 2 = 4
-4 = 4
Since both sides of the equation are not equal, the ordered pair is not a solution to the equation.
Given this graph and f(x)=<0 what are the values of x?
ANSWER
[tex]3\leq x\leq11[/tex]EXPLANATION
We want to find the interval on the domain of the function where:
[tex]f(x)\leq0[/tex]The graph of a function is less than or equal to 0 when the graph lies on and below the x-axis (horizontal axis).
From the given graph, we see that between x = 3 and x = 11, the graph of the function is on and below the x-axis.
Hence, the interval for the given condition is:
[tex]\begin{gathered} x\ge3\text{ and }x\leq11 \\ \\ 3\leq x\leq11 \end{gathered}[/tex]
That is the answer.
Complete the square to write f(x) = x2 + 6x + 14 in vertex form. a. f(x) = (x + 3)2 + 5 b. f(x) = (x - 3)2 + 14 C. f(x) = (x + 3)2 + 23 d. f(x) = (x + 6)2 + 14
f(x) = x^2 + 6x + 14
Equation is written in ax^2 + bx + c form
where:
a= 1
b= 6
c=14
Consider the vertex:
a (x+d) ^2 + e
d= b/2a = 6 / 2 (1) = 3
e = c- b^2/4a = 14 - [6^2/4(1) ] = 5
Substitute d and e in the vertex form:
f(x)= 1 (x + 3 ) ^2 + 5
f(x) = (x+3)^2 + 5
option a
A cheetah ran 300 feet in 2.4 seconds. What was the cheetah's average speed in feet per second?
The given data is,
Cheetah ran 300 feet in 2.4 sec.
Then the asking in the question averagae speed,so
Average speed=300/2.4
=125 ft/sec
This is distance travels by the cheetah in each second.
Which table or graph shows the value of y going up as the value of x goes up? ОА. ху 120 2 17 3 14 Ов. х у 1 5 2 4 3 3 42 7 6 Ос. 5
the only graph that increases in y as a function of the increase in x is option D
what is the value of this expression 2/3-2/4
The given expression is
[tex]\frac{2}{3}-\frac{2}{4}[/tex]To solve this we use the least common factor 12.
[tex]\frac{2}{3}-\frac{2}{4}=\frac{8-6}{12}=\frac{2}{12}=\frac{1}{6}[/tex]Therefore, the answer is 1/6.Is the number in the following statement an exact quantity or a measured quantity?You are told that a car gets 35 miles per gallon.measured quantityexact quantity
The problem states that a certain car travels 35 miles per gallon of fuel. This statement has a certain level of uncertainty, because the fuel consumption varies with how the car is manuvered, therefore the correct answer is measured quantity.
explain how the percent relates proportional quantities. Drag the words to complete the explanation Each word may be used once or not at all. part variable whole constant A percent is a of proportionality describing the of the
Given data:
A percent proportion is an equation in which percent is equal to the ratio.
Solve using the quadratic formula x^2 - 6x +32 = 7 or
The general form of a quadratic equation is expressed as
ax^2 + bx + c
The given equation is
x^2 - 6x + 32 = 7
x^2 - 6x + 32 - 7 = 0
x^2 - 6x + 25 = 0
By comparing with the given equation,
a = 1, b = - 6, c = 25
We would solve the equation by applying the quadratic formula which is expressed as
[tex]x\text{ = }\frac{-b+-\sqrt[]{b^2-4ac}}{2a}[/tex]We would substitute the given values into the equation. It becomes
[tex]\begin{gathered} x\text{ = }\frac{-\text{ - 6 +-}\sqrt[]{-6^2-4(1\times25)}}{2\text{ }\times1} \\ x\text{ = }\frac{6+-\sqrt[]{36-100}_{}_{}}{2} \\ x\text{ = }\frac{6\text{ +-}\sqrt[]{-64}}{2} \end{gathered}[/tex]Recall that the root of a negative number is a complex root. It would be written in form of complex numbers. It becomes
[tex]\begin{gathered} x\text{ = }\frac{6\text{ +-8i}}{2} \\ x\text{ = }\frac{6\text{ + 8i}}{2}\text{ or x = }\frac{6\text{ - 8i}}{2} \\ x\text{ = 3 + 4i or x = 3 - 4i} \end{gathered}[/tex]The length of a rectangle is 4 inches longer than it is wide. If the area is 192 square inches, what are the dimensions of the rectangle?
Lets draw a picture of our problem:
where x denotes the wide of the rectangle.
Since the area of a rectangle is wide times length, we have that
[tex]A=x(x+4)[/tex]since A=192 square inches, we get
[tex]\begin{gathered} 192=x(x+4) \\ or\text{ equivalently,} \\ x(x+4)-192=0 \end{gathered}[/tex]By distributing the variable x into the parenthesis, we have the following quadratic equation:
[tex]x^2+4x-192=0[/tex]which we can solve it by applying the quadratic formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{where},\text{ in our case,} \\ a=1 \\ b=4 \\ c=-192 \end{gathered}[/tex]then, by substituting these values, we have
[tex]x=\frac{-4\pm\sqrt[]{4^2-4(1)(-192)}}{2}[/tex]which gives
[tex]\begin{gathered} x=\frac{-4\pm\sqrt[]{16+768}}{2} \\ x=\frac{-4\pm\sqrt[]{784}}{2} \\ x=\frac{-4\pm28}{2} \end{gathered}[/tex]so, the two solutions are:
[tex]\begin{gathered} x_1=\frac{-4+28}{2}=\frac{24}{2}=12 \\ \text{and} \\ x_2=\frac{-4-28}{2}=\frac{-32}{2}=-16 \end{gathered}[/tex]But a negative solution is not allowed because the dimensions are always positive numbers. Then, the searched variable x is 12. Then, the wide and length are, respectively,
[tex]\begin{gathered} \text{ wide=x=12 inches} \\ \text{ length=x+4=12+4=16 inches} \end{gathered}[/tex]that is, the dimension of the rectangle are: wide is 12 inches and length is 16 inches.
Ben has a rectangular area 9 meters long and 6 meters wide. He wants a fence that will go around it as well as grass sod to cover it. How many meters of fence will he need? How many square meters of grass sod will he need to cover the entire area?
Length(L) = 9 meters
Width (W)=6 meters
To calculate how many meters of fence he will need, we have to calculate the perimeter of the rectangle:
perimeter of a rectangle (P) = 2L+2W
Replacing with the values given:
P= 2(9)+2(6)=18+12= 30 meters of fence
The grass needed to cover the entire area can be calculated by calculating the area of the rectangle:
Area of a rectangle (A)= W x L
A = 6 x9 = 54 square meters of grass
Simplify the expression. 2 4 12+(-4) - 51-5+5 12 + (-4)- 51-5+5= 150 2
the given expression is,
12 + (-4) - 2/5j -4/5j +5
now
= 12-4 + 5 -6/5j
= 17 - 4 - 6/5j
= 13 - 6/5j
thus, the answer is 13 - 6/5j
What is the sum of the first eight terms of the series 3 - 12+48-192+ ...
Given the series:
3 - 12 + 48 - 192 + ...
It can be identified as a geometric series because the common ratio is constant:
[tex]r=\frac{-12}{3}=-4[/tex]Now calculate the following terms:
a5 = (-192) * (-4) = 768
a6 = 768 * (-4) = -3072
a7 = -3072 * (-4) = 12288
a8 = 12288 * (-4) = -49152
The sum of the first eight terms is:
3 - 12 + 48 - 192 + 768 - 3072 + 12288 - 49152 = -39321
Sum = -39321
The sum of the first eight terms of the series 3 - 12+48-192+ ... will be -39321.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that the series is, 3 - 12+48-192+...
Given that the common ratio is constant, it is obvious that this series is geometric:
The common ratio for the sequence is,
r= -12/3
r= -4
The sum of the n term of the geometric sequence is,
Sₙ=a(rⁿ-1)/(r-1)
S₈=3((-4)⁸-1)/(-4-1)
S₈= -39321
Thus, the sum of the first eight terms of the series 3 - 12+48-192+ ... will be -39321.
Learn more about the sequence here:
brainly.com/question/21961097
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Subtract polynomials ( x^3 - 2x^2y) - ( xy^2 - 3y^3) - ( x^2y - 4xy^2)
We are given the following operation of polynomials:
[tex]\mleft(x^3-2x^2y\mright)-(xy^2-3y^3)-(x^2y-4xy^2)[/tex]First, we will apply the distributive property on the parenthesis. This means that we will change the sign of the terms inside each of the parenthesis that have a minus sign on the left side, like this:
[tex]x^3-2x^2y-xy^2+3y^3-x^2y+4xy^2[/tex]Now, we associate like terms. This means the terms that have the same variables elevated at the same exponents, like this:
[tex](x^3)+(-2x^2y-x^2y)+(-xy^2+4xy^2)+(3y^3)[/tex]Now, we add the coefficients of the like terms:
[tex]x^3-3x^2y+3xy^2+3y^3[/tex]Since we can't simplify any further this is the final answer.
A car dealership decides to select a month at random for its annual sale find the probability that it will be July or October Answer the following problems using either addition rule make sure to reduce your fraction
Probability formula:
[tex]\text{ P(E) = }\frac{\text{ N(Required outcome)}}{\text{N}(\text{Total outcome)}}\text{ }[/tex]Total number of months in a year = 12
[tex]\begin{gathered} \text{P(July) = }\frac{1}{12} \\ \text{P}(\text{October) =}\frac{1}{12} \end{gathered}[/tex][tex]\begin{gathered} \text{ P(July or October) = P(July) + P(October)} \\ =\frac{1}{12}+\frac{1}{12}=\frac{2}{12} \end{gathered}[/tex][tex]\frac{2}{12}=\frac{1}{6}[/tex]Therefore, the probability that it will be July or October is 1/6
Use this to find the equation of the tangent line to the parabola y = 4x ^ 2 - 4x + 2 at the point (3, 26) . The equation of this tangent line can be written in the form y = mx + b
Let's find the derivative
[tex]\begin{gathered} f^{\prime}(4x^2\text{ -}4x+2)=8x\text{ -}4 \\ f^{\prime}(3)=8(3)\text{ - }4=24\text{ - }4=20 \end{gathered}[/tex]The slope of the tangent line at the point x=3 is 20
[tex]\begin{gathered} y=mx+b \\ 26=20(3)+b \\ b=26\text{ - }60=\text{ -}34 \\ \\ So\text{ }y=20x\text{ -}34 \end{gathered}[/tex]Given the sum of the reciprocal of two numbers is 1/6 and the product of these two numbers is -48. What are those two numbers
Given:
the sum of the reciprocals of two numbers is 1/6
Let the numbers are (x) and (y)
so,
[tex]\frac{1}{x}+\frac{1}{y}=\frac{1}{6}\rightarrow(1)[/tex]And, the product of these two numbers is -48
so,
[tex]x\cdot y=-48\rightarrow(2)[/tex]from equation (2):
[tex]\begin{gathered} y=-\frac{48}{x} \\ \\ \frac{1}{y}=-\frac{x}{48}\rightarrow(3) \end{gathered}[/tex]substitute with (1/y) from equation (3) into equation (1) then solve for (x):
[tex]\begin{gathered} \frac{1}{x}-\frac{x}{48}=\frac{1}{6} \\ \frac{48-x^2}{48x}=\frac{1}{6} \end{gathered}[/tex]Using the cross product:
[tex]\begin{gathered} 48x=6(48-x^2)\rightarrow(\div6) \\ 8x=48-x^2 \\ x^2+8x-48=0 \\ (x-4)(x+12)=0 \\ x-4=0\rightarrow x=4 \\ x+12=0\rightarrow x=-12 \end{gathered}[/tex]We will substitute the value of (x) into equation (2) to find (y)
[tex]\begin{gathered} x=4\rightarrow y=-\frac{48}{4}=-12 \\ \\ x=-12\rightarrow y=-\frac{48}{-12}=4 \end{gathered}[/tex]so, the answer will be the numbers are: -12 and 4
The total annual sales for Nana's Nursery was $515,310 and the total accounts receivable was $27,156. What was the average collection porlod to the noarost whole day?17 days19 days21 days23 daysNone of these choices are correct.
Let's begin by listing out the given information:
Total annual sale = $515,310
Total accounts receivable = $27,156
The average collection period is obtained as shown below:
[tex]\begin{gathered} AverageCollectionPeriod=\frac{TotalAnnualSale}{TotalAccountsReceivable} \\ AverageCollectionPeriod=\frac{515,310}{27,156}=18.98\approx19 \\ AverageCollectionPeriod=19 \end{gathered}[/tex]Given the following translated function , state the translations that have occurred and write the translated equation Toolkit function :y=x^2
Solution
Step 1
Write the function:
[tex]y\text{ = x}^2[/tex]Step 2
The function is reflected over the x-axis
f(x) to −f (x) reflects the function in the x-axis (that is, upside-down).
[tex]y\text{ = -x}^2[/tex]Step 2
Rule for vertical shift
When you shift f(x) vertically upward by b units, it becomes f (x) + b shifts the function b units upward.
[tex]y\text{ = -x}^2+1[/tex]y is shift 1 unit upward.
Final step
The finally the function is shift 2 units right using the rule below
f(x) shifted b units to the right to form f (x − b) shifts the function b units to the right.
[tex]y\text{ = -\lparen x-2\rparen}^2+1[/tex]Final answer
[tex]y\text{ = -\lparen x-2\rparen}^2+1[/tex]Suppose a population consists of 63,000 people. Which of the followingnumbers of members of the population being surveyed could result in aparameter but not a sample statistic?A. 630B. 63,000C. Both 630 and 63,000D. Neither 630 nor 63,000
Explanation:
From the question,
The final answer is OPTION B
Suppose Jenny borrows $5000 at an interest rate of 16% compounded each year.Assume that no payments are made on the loan.Follow the instructions below. Do not do any rounding.
Given:
Principal amount = $5000
Interest rate = 16%
Find-:
(a) Amount owed at the end of 1 year.
(b) Amount owed at the end of 1 year.
Sol:
The compound interest rate is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where,
[tex]\begin{gathered} A=\text{ Amount after ''t'' time.} \\ \\ t=\text{ time in year.} \\ \\ r=\text{ Annual interest rate.} \\ \\ n=\text{ The number of times that interest is compounded per year.} \end{gathered}[/tex](a)
[tex]\begin{gathered} t=1 \\ \\ n=1 \\ \\ r=\frac{16}{100} \\ \\ =0.16 \\ \\ p=5000 \end{gathered}[/tex]Amount after one year.
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ =5000(1+\frac{0.16}{1})^{1\times1} \\ \\ =5000(1.16) \\ \\ =5800 \end{gathered}[/tex]The amount after one year is $5800.
(b)
[tex]\begin{gathered} P=5000 \\ \\ r=0.16 \\ \\ t=2 \\ \\ n=1 \end{gathered}[/tex]So the amount after two years is:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A=5000(1+\frac{0.16}{1})^{1\times2} \\ \\ A=5000(1.16)^2 \\ \\ A=5000\times1.3456 \\ \\ A=6728 \end{gathered}[/tex]The amount after 2 years is $6728.
is a pair of supplementary angles have degree measures in the ratio of 1:2, what's x
By definition, supplementary angles add up to 180°. Graphically,
[tex]a+b=180\text{\degree}[/tex]In this case, you have
[tex]x+2x=180\text{\degree}[/tex]Solving for x
[tex]\begin{gathered} x+2x=180\text{\degree} \\ 3x=180\text{\degree} \\ \text{ Divide both sides of the equation by 3} \\ \frac{3x}{3}=\frac{180\text{\degree}}{3} \\ x=60\text{\degree} \end{gathered}[/tex]Now the supplementary angle measure is
[tex]2x=2\cdot60\text{\degree }=120\text{\degree}[/tex]Therefore, supplementary angles whose measures of degrees in the ratio of 1: 2 are 60° and 120°.
Malcolm makes $10.53 per hour working at a restaurant, including tips. He works seven days a week. How much money does Malcolm make per week if he works 7 hours each day? A. $1,769.04 B. $73.71 C. $515.97 D. $368.55
Given:
Amount made per hour = $10.53
Number of days = 7 days
Let's find the amount he made per week if he works 7 hours each day.
To find the amount he made per week, apply the formula:
Total = Amount made per hour * Number of hours he works per day * Number of days he works a week.
Thus, we have:
[tex]\text{ Total = }10.53*7*7=515.97[/tex]Therefore, the amount of money Malcolm makes per week is $515.97
•
,• ANSWER:
C. $515.97
Question 1 Multiple Choice Worth 2 points(05.05)A boat's value over time is given as the function to and graphed below. Use A(x) = 400(b) + 0as the parent function. Which graph shows the boat's value decreasing at a rateof 40% per year?
Solving for the function for which the boat's value decreases 40% per year, we have
[tex]\begin{gathered} A(x)=400(b)^x \\ \text{Since it will decrease by 40\%, }b\text{ is equal to} \\ A(x)=400(1-0.4)^x \\ A(x)=400(0.6)^x \end{gathered}[/tex]Graphing our new function that is decreasing over time and we get
Suppose line g is the line with equation y=x. Given A(7. - 5), B(7,3), and C(-2,- 7), what are the coordinates of the vertices of A'B'C' for the reflection?RoA(Type an ordered pair.)
We want to reflect our figure over the line g, y = x.
In order to find the vertices of the new figure we just need to exchange the variables
A (x, y) → A' (y, x)
A (7, -5) → A' (-5, 7)
B (x, y) → B' (y, x)
B (7, 3) → B' (3, 7)
C (x, y) → C' (y, x)
C (-2, -7) → C' (-7, -2)
Answer: the new vertices are A' (-5, 7), B' (3, 7) and C' (-7, -2)
The table shows the outcomes of rolling two number cubes at the same time and finding the product of the two numbers. What is the theoretical probability of rolling a product greater than 10?
123456
123456
24681012
369121518
4812162024
51015202530
61218243036
A:3/4
B:10/36
C:17/36
D:19/36
In order to find the theoretical probability, we use the given table and highlight the products that are greater than 10, like this,
then, the total number of outcomes is 36, then, we divide by the total outcomes
[tex]p(x)=\frac{17}{36}[/tex]Which of the following statements is NOT true YA The slope of AB is different than the slope of BC. С. The ratios of the ris the run for the trian are equivalent. В. 2 x Х -2 A AB has the same slo as AC.
Given the line passes through the points:
A = ( -5 , -2 ) , B = ( -2 , 0 ) and C = ( 4 , 4 )
Now, we will check which statements is not true:
1) The slope of AB is different than the slope of BC
This is not true, because the three points are on the same line
So, the slope of AB = the slope of BC
2) The ratios of the rise to the run for the triangles are equivalent
This is true, the ratios rise to the run are equal to the slope
As the slope is constant the ratios will be constant
3) AB has the same slope of AC
This is true, the three points are on the same line
4) the slope of AC = 2/3
Slope = Rise/Run
Rise = 4 - (-2) = 4 + 2 = 6
Run = 4 - (-5) = 4 + 5 = 9
So, the slope = 6/9 = 2/3
So, the statement is true
So, the wrong statement is the first one which is:
The slope of AB is different than the slope of BC
An air traffic controller locates an airplane on her radar display. The plane is moving in a diagonal directionAccording to the radar, the plane moves 5 miles east and 1 mile north over the course of a minute. There are noother planes to the north of the plane on the controller display, but there is an airport to the east of t. The airtraffic controller is not concerned with the plane's northeriy velocity, but she quicy calculates the plane'seasterty velocity. What does she find the easterty velocity of the airplane to be? Please answer in miles perhour.
The plane moves 5 miles east over the course of a minute. Then, the easterly velocity is:
[tex]\begin{gathered} \text{velocity}=\frac{\text{distance}}{\text{time}} \\ \text{velocity}=\frac{\text{5 miles}}{\text{1 minute}} \\ \text{velocity}=5\frac{\text{miles}}{\text{minute}} \end{gathered}[/tex]60 minutes is equivalent to 1 hour, then
[tex]5\frac{\text{miles}}{\text{minute}}\cdot\frac{60\text{ minutes}}{hour}=300\text{ mph}[/tex]I need help with this practice problem In the picture is MY attempted answer
To determine the value of sin (θ + β), we can apply the trigonometric identity:
[tex]\sin (\theta+\beta)=\sin \theta\cos \beta+\cos \theta\sin \beta[/tex]Since we already have the value for cosθ, let's find out sin θ.
Based on trigonometric identity,
[tex]\sin \theta=\frac{y}{r};\cos \theta=\frac{x}{r}[/tex]Based on the given value of cosθ, x = -√2 while r = 3. To determine the value of y, let's apply the Pythagorean Theorem.
[tex]\begin{gathered} y=\sqrt[]{r^2-x^2} \\ y=\sqrt[]{3^2-(-\sqrt[]{2})^2} \\ y=\sqrt[]{9-2} \\ y=\sqrt[]{7} \end{gathered}[/tex]Since the given interval is between π and 3π/2 which is in Quadrant 3, y = -√7. Hence, the value of sin θ is:
[tex]\sin \theta=-\frac{\sqrt[]{7}}{3}[/tex]The next thing that we shall solve is sin β and cos β. We can use the given tangent function to determine this.
[tex]\begin{gathered} \text{tan}\beta=\frac{y}{x}=\frac{4}{3} \\ \text{Solve for r.} \\ r=\sqrt[]{x^2+y^2}=\sqrt[]{3^2+4^2}=\sqrt[]{9+16}=\sqrt[]{25}=5 \end{gathered}[/tex]Given the interval for beta, the angle is found in Quadrant 1. So, the values of sin β and cos β are:
[tex]\begin{gathered} \sin \beta=\frac{y}{r}=\frac{4}{5} \\ \cos \beta=\frac{x}{r}=\frac{3}{5} \end{gathered}[/tex]Now that we have the values for sin θ = -√7/3, cos β = 3/5, cos θ = -√2/3, and sin β = 4/5, let's plugged them into the first trigonometric identity we mentioned above.
[tex]\begin{gathered} \sin (\theta+\beta)=\sin \theta\cos \beta+\cos \theta\sin \beta \\ \sin (\theta+\beta)=(-\frac{\sqrt[]{7}}{3})(\frac{3}{5})+(-\frac{\sqrt[]{2}}{3})(\frac{4}{5}) \end{gathered}[/tex]Then, simplify.
[tex]\sin (\theta+\beta)=-\frac{\sqrt[]{7}}{5}-\frac{4\sqrt[]{2}}{15}[/tex]The final answer is shown above.
If f(x) = 3x^4 + 5, find the inverse of f.
Answer:
[tex]f\placeholder{⬚}^{-1}(x)\text{ = \lparen}\frac{x-5}{3})\placeholder{⬚}^{\frac{1}{4}}[/tex]Explanation:
Here, we want to find the inverse of the given function
We proceed as follows:
[tex]\begin{gathered} we\text{ set:} \\ y\text{ = 3x}^4+5 \\ y-5\text{ = 3x}^4 \\ x^4\text{ = }\frac{y-5}{3} \\ \\ x^\text{ = }\sqrt[4]{\frac{y-5}{3}} \\ \\ x\text{ = \lparen}\frac{y-5}{3})\placeholder{⬚}^{\frac{1}{4}} \end{gathered}[/tex]Now, we switch x and y:
[tex]f\placeholder{⬚}^{-1}(x)\text{ = \lparen}\frac{x-5}{3})\placeholder{⬚}^{\frac{1}{4}}[/tex]Consider function f, where 8 is a real number.J(=) = tan(Br)Complete the statement describing the transformations to function fas the value of B is changed.As the value of B increases, the period of the functionV, and the frequency of the functionWhen the value of B is negative, the graph of the function (reflects over the y-axis
ANSWER:
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the x-axis
STEP-BY-STEP EXPLANATION:
The period of a trigonometric function is given by the following equation:
[tex]\begin{gathered} T=\frac{\pi}{k} \\ \\ \text{ let k be the constant number that is the coefficient of the angle x} \end{gathered}[/tex]In this case, k is equal to B, if B increases then the period decreases, and since the frequency is inversely proportional to the period it would increase.
If the value of B is negative we would have the following:
[tex]f(x)=\tan(-Bx)=-\tan(Bx)[/tex]Therefore, there is a reflection on the x-axis.
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the x-axis