Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The known solutions to:
[tex]f(x)\text{ = g(x) are:}[/tex][tex]\begin{gathered} \text{when x= 1,} \\ f(1)\text{ = 14,} \\ g(1)\text{ = 14} \\ \text{and } \\ \text{when x = 9 ,} \\ f(1)\text{ = 6} \\ g(1)\text{ = 6} \end{gathered}[/tex]CONCLUSION:
The correct answers are:
[tex]\begin{gathered} \text{ x = 1 -- OPTION A} \\ \text{and } \\ \text{x = 9 }--\text{OPTION D} \end{gathered}[/tex]
Related Questions
A hospital has been vaccinating people in two different locations. At the start of the month, Location Ahas reported it has vaccinated 10 thousand people already. Since new shipments have arrived, theyclaim they can now start vaccinating 12 thousand people per week. Location B has vaccinated 40thousand people at the start of the month. They can now vaccinate 6 thousand people per week
Answers
For Location A:
People already vaccinated = 10,000
Number of people vaccinated per week after new shipments arrived = 12,000
Number of people vaccinated in location A can be modelled by the Equation
N = 10,000 + 12000x
where x is the number of weeks
When x = 0, N = 10000
When x = 1, N = 10,000 + 12,000(1) = 22,000
When x = 2, N = 10,000 + 12,000(2) = 34,000
When x = 3, N = 10,000 + 12,000(3) = 46,000
When x = 4, N = 10,000 + 12,000(4) = 58,000
When x = 5, N = 10,000 + 12,000(5) = 70,000
When x = 6, N = 10,000 + 12,000(6) = 82,000
For Location B:
People already vaccinated = 40,000
Number of people vaccinated per week after new shipments arrived = 6,000
Number of people vaccinated in location B can be modelled by the Equation
N = 40,000 + 6000x
where x is the number of weeks
When x = 0, N = 40,000
When x = 1, N = 40,000+ 6000(1) = 46000
When x = 2, N = 40,000+ 6000(2) = 52,000
When x = 3, N = 40,000+ 6000(3) = 58,000
When x = 4, N = 40,000+ 6000(4) = 64,000
When x = 5, N = 40,000+ 6000(5) = 70,000
When x = 6, N = 40,000+ 6000(6) = 76,000
The table is shown below
How does the multiplicity of a zero determine the behavior of the graph at that zero? the drop down options are: is tangent to, crosses straight through, and crosses though while hugging
Answers
Given: A seventh-degree polynomial function has zeros of -6, 0 (multiplicity of 2), 1, and 4 (multiplicity of 3).
Required: To determine the behavior of the graph at the zeros.
Explanation: The given seventh-degree polynomial can be represented as
[tex]\left(x+6\right)\left(x-0\right)^2\left(x-1\right)(x-4)^3[/tex]Now, the graph will cross straight through at x=-6 and x=1.
We have an odd multiplicity at x=4; hence the graph will cross through while hugging.
We have an even multiplicity at x=0; therefore, the graph will be tangent.
Here is the graph of the given function-
Final Answer: The graph will cross straight through at x=-6 and x=1,
the graph will cross through while hugging at x=4,
the graph will be tangent at x=0.
What is the value of the expression when y = 2?2-y+4 + y3(y + 2)yO 3212
Answers
We have the following:
[tex]\frac{2-y}{4+y}+\frac{3(y+2)}{y}[/tex]replacing, y =2:
[tex]\begin{gathered} \frac{2-2}{4+2}+\frac{3(2+2)}{2} \\ \frac{0}{6}+\frac{3\cdot4}{2} \\ 0+\frac{12}{2}=6 \end{gathered}[/tex]the answer is 6, the second option
Dirk is a physical therapist who specializes in leg injuries. His patients differ in age and type of injury. Knee pain Ankle pain 3 3 0-12 years old 13-19 years old 2 3 What is the probability that a randomly selected patient is 13-19 years old or suffers from ankle pain? Simplify any fractions.
Answers
The probability of a patient being 13-19 years old is
[tex]P=\frac{5}{11}[/tex]The probability of a patient who suffers from ankle pain is
[tex]P=\frac{6}{11}[/tex]Then, we use the following formula
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]Where,
[tex]P(A\cap B)=\frac{5}{11}\cdot\frac{6}{11}=\frac{30}{121}[/tex]Then,
[tex]P(A\cup B)=\frac{5}{11}+\frac{6}{11}-\frac{30}{121}=\frac{91}{121}\approx0.75[/tex]Hence, the probability is 91/121, or 75%.the heart of an elephant, at rest, will beat an average of 1560 beats in 60 minutes. what's the rate in beats per minute?
Answers
What is the inverse of the function f (x) = 3(x + 4)^2 – 2, such that x ≤ –4?A. f^-1(x)=-4 + square root of x/3+2B. f^-1(x)=-4 - square root of x/3+2C. f^-1(x)=-4 + square root of x+2/3D. f^-1(x)=-4 - square root of x+2/3
Answers
Given the following function:
f(x) = 3(x + 4)^2 – 2
Let's determine its inverse form.
*Change f(x) = y, swap x and y then solve for y.
[tex]\text{ f\lparen x\rparen= 3\lparen x + 4\rparen}^2\text{ - 2}[/tex][tex]\text{ y = 3\lparen x + 4\rparen}^2\text{ - 2}[/tex][tex]\text{ x = 3\lparen y + 4\rparen}^2\text{ - 2}[/tex][tex]\text{ 3\lparen y + 4\rparen}^2\text{ - 2 = x}[/tex][tex]\text{ 3\lparen y + 4\rparen}^2\text{ = x + 2}[/tex][tex]\text{ \lparen y + 4\rparen}^2\text{ = }\frac{\text{ x + 2 }}{\text{ 3}}[/tex][tex]\text{ y + 4 = }\sqrt{\frac{\text{ x + 2 }}{\text{ 3}}}[/tex][tex]\text{y = f}^{-1}(\text{x\rparen = -4 + }\sqrt{\frac{\text{ x + 2 }}{\text{ 3 }}}[/tex]Therefore, the answer is CHOICE C.
Identify the volume of a rectangular pyramid with length 7 cm, width 15 cm, and height 16 m.
Answers
To answer this question, we will use the following formula for the volume of a rectangular pyramid:
[tex]V=\frac{lwh}{3},[/tex]where l is the length, w is the width, and h is the height.
Substituting w= 15 m, l = 7 m, and h = 16 m in the above formula, we get:
[tex]V=\frac{15m\cdot16m\cdot7m}{3}\text{.}[/tex]Simplifying the above result we get:
[tex]V=560m^3.[/tex]Answer:
[tex]560m^3.[/tex]The equation y = kx represents a proportional relationship between x and y, where k is the constant of proportionality. For a moving object, the equation d = st represents a proportional relationship between distance (d) and speed (s) or between distance (d) and time (t). Explain the different ways that you can define the constant of proportionality for this equation. Then describe some other equations that represent proportional relationships in the real world and explain why they're useful. Research on the Internet, if needed.
Answers
d = st
if speed is constant, there is a proportional relation between distance (d) and time (t). The constant (s) can be defined as:
s = d/t
and you can compute it knowing the distance travelled in some time
if time is constant, there is a proportional relation between distance (d) and speed (s). The constant (t) can be defined as:
t = d/s
and you can compute it knowing the distance travelled at some speed.
Acceleration (a) is defined as:
a = s/t
this equation can be rewritten as:
s = at
where a is the constant of proportionality.
Another example is Hook's law, which states:
F = ke
where F is the force applied to a spring, k is the spring constant, and e is the extension of the spring.
Divide and round to the nearest hundredths place25.7 ÷ 0.3
Answers
85.67
Explanation:[tex]\frac{25.7}{0.3}[/tex]Using a calculator, the result is 85.6667
To the nearest hundredth: The hundredth position is at second 6. The next number after it is more than 5. So it would be rounded to 1 and added to the second 6
To the nearest hundredth, the answer is 85.67
if point c, shown on the coordinate plane below is reflected over both axes to create c what will be the coordinate of c
Answers
Explanation:
The coordinate of c in the plane looks like x= 3 while y = 2
This we assumed because there is no grid line to determine the numbers. The location shows it is within that coordinate
c (3, 2):
Reflecting acrossboth axes means reflecting across the y and reflection across the x axis
Reflection across y axis: (x, y) to (-x, y)
The coordinate of becomes: (-3, 2)
If f (p) = 3p – 1 andg(n)=n? + 2,what is (f.g)(x)?
Answers
This is a composition function, so:
[tex]\begin{gathered} f(p)=3p-1 \\ g(n)=n^2+2 \\ (f\circ g)(x)=f(g(x))=3\cdot g(x)-1 \\ (f\circ g)(x)=3(x^2+2)-1=3x^2+3\cdot2-1 \\ (f\circ g)(x)=3x^2+5 \end{gathered}[/tex]5A line passes through point (-8, 9) and has a slope of4Write an equation in Ax+By=C form for this line.Use integers for A, B, and C.
Answers
Point = (-8, 9)
slope = m = 5/4
Equation of the line
y - y1 = m(x - x1)
Substitution
y - 9 = 5/4(x + 8)
Expanding
4y - 36 = 5x + 40
General form
5x - 4y + 40 + 36 = 0
Equation of the line
5x - 4y + 76 = 0 5x - 4y = -76
A = 5 B = -4 C = 76 }}
Problem 2.
Point = (-10, -9)
slope = m = 1/2
Equation of the line
y - y1 = m(x - x1)
y + 9 = 1/2 (x + 10)
2y + 18 = x + 10
x - 2y = 18 - 10
x - 2y = 8
Mark used 0.08 of the gas in the tank. What % of the gas in the tank did Mark use?
Answers
We know that he used 0.08 of the gas in the tank where 1 represents 100%.
Let's multiply 0.08 by 100 to express it in percentage.
[tex]0.08\cdot100=8[/tex]Hence, Mark used 8% of the gas in the tank.Hello hope all is well. Can you help me with this i don't understand what I need to write
Answers
mean
Explanation:The measures of centaral tendency: mean, median and the mode
The most used one is the mean.
The mean obtained here = 86%
median = 85%
mose = 81%
Since the measures are not in a scale, the mode cannnot be used.
Also there are no missing information in the data set and there are no extreeme outliers.
Most of the data are within the range of the mean gotten.
Hence, Mario should use the mean to convince his parents that he is a maths superstar.
Evaluate.
{3 + [−5 (2−4) ÷ 2]} x 3
Answer choices:
−27
(negative 27)
−13
(negative 13)
18
(eighteen)
24
(Twenty-four)
Answers
Answer:
24
(twenty - four)
Step-by-step explanation:
Again we want to evaluate this using BPEMDAS
Which tell us in order which operations we do
Remember BPEMDAS means
Brackets
Parenthesis
Exponents
Multiplication/Division (going left to right)
Addition/Subtraction (going left to right)
{3 + [−5 (2−4) ÷ 2]} x 3
==> first we perform all operations in the innermost bracket
[3 + (−5(-2) ÷ 2)] x 3
==> we do the same thing as the first step, the operations in the inner most parenthesis. there is only multiplication and division here so we perform them going left to right
[3 + (10 ÷ 2)] x 3 ==> multiplication first because its before the division in the parenthesis
(3 + 5) x 3 ==> division next
==> next we do the final operations in the parenthesis 3+5
8 x 3
==> finally the multiplication
= 24
Using Euler's formula, how manyedges does a polyhedron with 20faces and 12 vertices have?[?] edges
Answers
Using Euler's Formula:
F + V - E = 2
Given:
F = 20, V = 12 and E = a
According to the formula:
20 + 12 - a = 2
32 - a = 2
a = 32 - 2
a = 30
ANSWER
30 edges
What is the theoretical probability that an odd number will berolled on a 6-sided die?
Answers
TIP
All possible outcome ; 1, 2 , 3, 4, 5, 6
Odd number ; 1, 3, 5
[tex]\begin{gathered} \text{Probability =}\frac{possible\text{ outcome of odd number}}{\text{Total possible outcome}} \\ \text{Probability}=\frac{3}{6}=\frac{1}{2} \\ \end{gathered}[/tex]Probability that an odd number will be
[tex]\frac{1}{2}[/tex]I need help on a problem
Answers
1.
[tex]PQ\cong RQ\to Given[/tex]2.
[tex]\begin{gathered} \angle PQS\cong\angle RQS\to Given \\ \end{gathered}[/tex]3.
[tex]QS\cong QS\to Reflexive_{\text{ }}property[/tex]4.
[tex]\Delta PQS\cong\Delta RQS\to SAS_{\text{ }}congruence[/tex]5.
[tex]\begin{gathered} \angle P\cong\angle R\to CPCTC_{} \\ \end{gathered}[/tex]please help me with mathHere’s a picture of the question
Answers
Answer:
a) Yes, triangles JNM and JLK are similar by the AA Similarity Postulate
b) JN = 4 in
c) LN = 1.5 in
JK = 3.5 in
d) Area ratio = 2.56 : 1
Explanation:
Given:
KL = 5 in
MN = 8 in
JL = 2.5 in
MK = 2.1 in
From triangle JLK and JNM, we can deduce the following;
[tex]\begin{gathered} \angle J\cong\angle J......Reflexive\text{ property of angles} \\ \angle M\cong\angle K......Corresponding\text{ angles are equal} \\ \angle N\cong\angle L.........Corresponding\text{ angles are equal} \end{gathered}[/tex]a) The AA Similarity theorem states that if two pairs of corresponding angles in two triangles are congruent, then the two triangles are similar. From the above, we can see that we have two pairs of corresponding angles that are congruent, so we can say that triangles JLK and JNM are similar.
b) Note that, in similar triangles, corresponding sides are equal in proportion.
So we can go ahead and solve for JN as seen below;
[tex]\begin{gathered} \frac{KL}{MN}=\frac{JL}{JN} \\ \frac{5}{8}=\frac{2.5}{JN} \\ 5JN=20 \\ JN=\frac{20}{5} \\ JN=4 \end{gathered}[/tex]So JN is 4 in
c)
[tex]\begin{gathered} JN=JL+LN \\ LN=JN-JL \\ LN=4-2.5 \\ LN=1.5\text{ in} \end{gathered}[/tex]So LN is 1.5 in
Let's find the length of JK;
[tex]\begin{gathered} \frac{KL}{MN}=\frac{JK}{JM} \\ \frac{KL}{MN}=\frac{JK}{JK+MK} \\ \frac{5}{8}=\frac{JK}{JK+2.1} \\ 5(JK+2.1)=8JK \\ 5JK+10.5=8JK \\ 8JK-5JK=10.5 \\ 3JK=10.5 \\ JK=\frac{10.5}{3} \\ JK=3.5\text{ in} \end{gathered}[/tex]So the length of JK is 3.5 in
d) The area ratio of two similar triangles is equal to the square of the ratio of any two corresponding sides.
So the ratio of triangle JNM to JKL is;
[tex]Area\text{ ratio}=\frac{8^2}{5^2}=\frac{64}{25}=\frac{2.56}{1}=2.56:1[/tex]What are some numbers that equal -3Here’s my equation:-5XAnd then what number could I put for the Y so it could equal -3
Answers
Equation y = -5x
-3 = -5x
Solve for x
x = -3/-5
x = 3/5 y = -3
This is my answer, could you check it please?
In 30 words of your identify which form slope intercept or point slope would be better to use why
Answers
As indicated in the question, parallel lines have the same slope.
This means the slope of the fourth parallel line is also 2. A point on that line has been identified as;
[tex](3,15)[/tex]Using the point-lope form which is;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where,} \\ x_1=3,y_1=15 \\ \text{The equation becomes;} \\ y-15=2(x-3) \end{gathered}[/tex]Further simplified, this now becomes;
[tex]\begin{gathered} y-15=2(x-3) \\ y-15=2x-6 \\ \text{Add 15 to both sides;} \\ y=2x+9 \end{gathered}[/tex]ANSWER:
It would be better to use the point-slope form to derive the equation of the 4th line because we already have the slope and one point on the equation.
What is the average mean high temperature and low temperature for the five day period? please explain
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
temperature table
average high temperature = ?
average low temperature = ?
Step 02:
We must calculate the average for the temperatures.
Average high temperature:
Average HT = (22 + 12 + 9 + 23 + 32) °F / 5
= 98 °F / 5
= 19.6 °F ===> rational number
Average low temperature:
Average LT = (0 + (-6) + (-10) + (-14) + 4) °F / 5
= (0 - 6 - 10 - 14 + 4) °F / 5
= - 26 °F / 5
= - 5.2 °F ===> rational number
The answer is:
The average high temperature is 19.6 °F
The average low temperature is - 5.2 °F
Both are rational numbers
Find the STANDARD equation for a line with slope 3 and y-intercept -2 Show work
Answers
We know that
• The slope is 3.
,• The y-intercept is -2.
We use the slope-intercept form to find an equation.
[tex]y=mx+b[/tex]Where m is the slope, and b is the y-intercept.
Replacing the given information, we have
[tex]y=3x-2[/tex]Now, we move all terms to the left side to express the linear equation in standard form.
Therefore, the standard form is[tex]-3x+y=-2[/tex]If a quadratic equation can be factored as (ax +b)(ex+d) = 0, what information do these factors provide about the graph of the equation?
Answers
Answer:
The 4th choice: The graph of the equation has roots at x = -b/a and x = -d/c
Explanation:
If we have an equation of the form
[tex](ax+b)(bx+c)=0[/tex]then it must be that either
[tex](ax+b)=0[/tex]or
[tex](bx+c)=0[/tex]The first equation gives
[tex]\begin{gathered} ax+b=0 \\ x=-\frac{b}{a} \end{gathered}[/tex]and the second equation gives
[tex]\begin{gathered} cx+d=0 \\ x=-\frac{d}{c} \end{gathered}[/tex]Hence, the roots of the equation turn out to be
[tex]x=-\frac{b}{a},x=-\frac{d}{c}[/tex]Therefore, we conclude that the equation of the form (ax + b) (cx + d) tells us about the roots of the function, and hence, choice 4 is correct.
how do I find which of the following statements are true?
Answers
Verify each statement
Option A is true because M is between A and B
Option B
Is not true
because AM=AB/2
Option C
Is true
because M is the midpoint
Option D
Is not true
because M is between A and B
Option E
we have
Is true because AB=AM+MB ------> AB-AM=MB
Option F
Is true because AB=AM+MB
Option G
Is not true
because AB=2AM
Option H
Is true
because AB=2AM
which of the following is not a line of symmetry in the figure below
Answers
From the graph the line of symmetry is the line that divides the shape into two equal halves
These lines are at
1) x = -4
2) y = 4
3) y = -x
An equation of a line that does not divides the shape into equal halves is not a line of symmetry
the table below gives the price for different numbers of books. is the price proportional to the number of books? number of books 1- price 3 3 books price-9 4 books price-12 7 books price 18
Answers
Two quantities are proportional if the ratio between those quantities is always the same.
Find the ratio of price/number of books for each row in the table:
[tex]\begin{gathered} \frac{3}{1}=3 \\ \frac{9}{3}=3 \\ \frac{12}{4}=3 \\ \frac{18}{7}=2.57\ldots \end{gathered}[/tex]We can see that the ratio price:books is 3 if the number of books is 1, 3 or 4 but it is a different ratio when the number of books is 7.
Therefore, the price is not proportional to the number of books.
Sidenote:
If the number of books on the last row was 6 instead of 7, then the ratio would still be 3 and the price would be in fact proportional. Make sure that it is not a printing error of the problem sheet.
What can you say about the 3s in 43,862 and 75,398?4 grade student Lesson Place value relationship
Answers
Remember that a place value can be defined as the value represented by a digit in a number based on its position in the number. With decimal numbers, we can have a guide from the decimal point, and with natural numbers, we have a guide from the comma.
So, if we look at the numbers on the exercise we note that
- 3s in 43,862 is placed first before the comma indicating that their place is in the thousands.
- 3s in 75,398 is placed first after the comma indicating that its place is in the hundred.
Megan scored 5 points less than twice the number scored by Darin. Together they scored a total of 42 points. How many points were scored by Megan?
Answers
If Darin scored x points, and Megan scored 5 points less than twice that score, that means Darin scored x while Megan scored 2x - 5. Together they scored a total of 42 points. Adding both scores together, we now have the equation shown;
[tex]\begin{gathered} x+(2x-5)=42 \\ x+2x-5=42 \\ 3x-5=42 \\ \text{Add 5 to both sides } \\ 3x=47 \\ \text{Divide both sides by 3} \\ \frac{3x}{3}=\frac{47}{3} \\ x=15\frac{2}{3} \\ \text{Therefore Megan scored } \\ 2x-5 \\ =2(\frac{47}{3})-5 \\ =\frac{94}{3}-5 \\ =\frac{32}{3} \\ =10\frac{2}{3} \end{gathered}[/tex]Therefore, Megan scored 10 2/3 points
a diver stands on a platform 15 ft above a lake. he doesn't dive off the platform and lands in the water below. His height (h) above the lake after X seconds is shown on the graph below. what is the maximum height the diver reached?
Answers
We are asked about the maximum height of the diver given the graph. we notice from the graph that the maximum point is h = 20 feet, therefore, the maximum height is 20 feet.