According to the synthetic division below, which of the following statements
are true?
Check all that apply.
54 -17 -15
20 15
3 0
4
A. (4x2-17x-15) - (x + 5) = (4x + 3)
B. The number 5 is a root of F(x) = 4x² - 17x - 15.
OC. (4x2-17x-15) - (x - 5) = (4x + 3)
D. (x+5) is a factor of 4x2-17x-15.
E. The number -5 is a root of F(x) = 4x²-17x-15.
OF. (x-5) is a factor of 4x2 - 17x-15.
Answers
The correct statements about the synthetic division are C, D, F.
How to illustrate the information?It should be noted that 4x² - 17x - 15 will be:
= 4x² - 20x - 3x - 15
= (x - 5)(4x + 3)
The roots of the polynomial will be:
= f(x) = 0
(x - 5) = 0
x = 5
4x + 3 = 0
x = -3/4
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Related Questions
Solve for all of the missing angles in the rhombus below, given that m∠3 = 54°. (Round to the nearest tenth as needed.)
Answers
The measure of angles 1, 2, 4, and 5 are 54 degrees, 90 degrees, 36 degrees, and angle 36 degrees.
What is a rhombus?A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.
We have shown the rhombus in the picture.
As we know the diagonals bisect at a 90-degree angle.
So angle 2 = 90 degree
angle 1 = angle 3
angle 1 = 54 degrees
angle 1 + angle 2 + angle 5 = 180
54 + 90 + angle 5 = 180
angle 5 = 36 degrees
angle 5 = angle 4 = 36 degrees
Thus, the measure of angles 1, 2, 4, and 5 are 54 degrees, 90 degrees, 36 degrees, and angle 36 degrees.
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If the probability of observing at least one car on a highway during any 20-minute time interval is 609/625, then what is the probability of observing at least one car during any 5-minute time interval
Answers
If the probability of observing at least one car on a highway during any 20-minute time interval is 609/625, then the probability of observing at least one car during any 5-minute time interval is 609/2500
Given The probability of observing at least one car on a highway during any 20 minute time interval is 609/625.
We have to find the probability of observing at least one car during any 5 minute time interval.
Probability is the likeliness of happening an event among all the events possible. It is calculated as number/ total number. Its value lies between 0 and 1.
Probability during 20 minutes interval=609/625
Probability during 1 minute interval=609/625*20
=609/12500
Probability during 5 minute interval=(609/12500)*5
=609/2500
Hence the probability of observing at least one car during any 5 minute time interval is 609/2500.
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fill in the blank 2 x 3/4 = _ + 3/4
Answers
According to multiplication you can use repeated addition to get the same product of the given equation.
Ex: 5x2= 2+2+2+2+2 ( 5 groups of 2)
Both will give you same answer (10).
Hence 2 x 3/4 = 3/4 + 3/4
Answer:
2 x 3/4 = 3/4 + 3/4
Step-by-step explanation:
Which conditional and its converse form a true biconditional?
If x = 19, then 2x – 3 = 35.
If x = 3, then x2 = 9.
If x2 = 4, then x = 2.
If x > 0, then > 0.
Answers
The conditional and its converse that form a true biconditional is; Option A; If x = 19, then 2x – 3 = 35.
How to Interpret Biconditional Statements?
A) If x = 19, then 2x – 3 = 35.
Thus, 2(19) - 3 = 35. Thus, this is a true biconditional.
B) If x = 3, then x²= 9.
This is not a true biconditional because x could also be -3.
C) If x² = 4, then x = 2
This is not a true biconditional because x could also be -2.
D) If x > 0, then |x| > 0.
This is not a true biconditional because x could also be negative which less than zero.
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Draw the image of the figure under the given rotation. Triangle PQR; 90 degrees about the the origin. Number 2 :)
Answers
The attached figure represents the image of the triangle under the rotation
How to draw the image of the triangle?The coordinates of the triangle are given as:
P = (2, 1)
Q = (4, 1)
R = (4, -3)
The rule of 90 degrees rotation about the origin is:
(x, y) = (y, -x).
So, we have:
P' = (1, -2)
Q' = (1, -4)
R' = (-3, -4)
See attachment for the figure under the rotation
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SATQuestion:
The scatterplot below shows the amount of electric energy generated, in millions of megawatt hours, by nuclear sources over a 10-year period.
\bigstar★ Scatterplot in the attachment....
Of the following equations, which best models the data in the scatterplot?
A) y = 1.674x² + 19.76x - 745.73
B) y = -1674x2 - 19.76x - 745.73
C) y = 1.674x² + 19.76x + 745.73
D) y = -16743+ 19.76x + 745.73
Please answer with proper explanation and workout. Spam, Vulgar and short answers will be deleted at the spot✓.
Answers
The equation which best models the data in the scatterplot is: D. y = -16743x² + 19.76x + 745.73.
How to interpret the scatter plot?By critically observing the scatter plot shown in the image attached below, we can logically deduce that it's data are best modelled by a quadratic equation (parabolic curve).
Mathematically, the equation of a quadratic equation (parabolic curve) is given by:
y = ax² + bx + c
Since the parabolic curve opens downward, we have:
a < 0, c > 0, x = 0 and y > 0;
y = -16743x² + 19.76x + 745.73.
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1. One group (A) contains 180 people.
One-fourth of the people in group A will be
selected to win free tickets to a concert.
There is another group (B) in a nearby town
that will receive the same number of tickets,
but there are 292 people in that group.
What will be the ratio of non-winners in
2
group A to non-winners in group B after the
selections are made?
Answers
Answer:
135:147
Step-by-step explanation:
180/4=45
180-45=135
292-45=247
135:247
Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.
f(x)=
x+a
b
g(x)=cx−d
Part 2. Show your work to prove that the inverse of f(x) is g(x).
Part 3. Show your work to evaluate g(f(x)).
Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y = x on the same graph.
Task 2
Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model:
a√x+b+c=d
Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation.
Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.
Part 3. Explain why the first equation has an extraneous solution and the second does not.
Answers
See below for the solution to the inverse function and the rational equation
The function and the inverseCreate functions f(x) and g(x)
The functions are given as:
f(x) = x + a/b
g(x) = cx − d
Let a = 4 and b = 2.
So, we have:
f(x) = x + 4/2
Rewrite as:
y = x + 2
Swap x and y
x = y + 2
Make y the subject
y = x - 2
So, we have:
g(x) = x - 2
So, the functions are:
f(x) = x + a/b ⇒ f(x) = x + 4/2
g(x) = cx − d ⇒ g(x) = x - 2
Show that the functions are inverse functions
In (a), we have:
f(x) = x + 4/2
g(x)= x - 2
If the functions are inverse functions, then:
f(g(x)) = x
We have:
f(x) = x + 4/2
This gives
f(g(x)) = g(x) + 4/2
This gives
f(g(x)) = x - 2 + 4/2
Evaluate
f(g(x)) = x
Evaluate g(f(x))
In (a), we have:
f(x) = x + 4/2
g(x)= x - 2
We have:
g(x)= x - 2
This gives
g(f(x)) = f(x) - 2
This gives
g(f(x)) = x + 4/2 - 2
Evaluate
g(f(x)) = x
Graph the functions
See attachment for the graph
The table of values is:
x f(x) g(x)
0 2 -2
1 3 -1
2 4 0
3 5 1
4 6 2
Radical equationsCreate the equations
The form of the equations is given as:
[tex]a\sqrt{x + b} + c= d[/tex]
So, we have:
[tex]\sqrt{4x + 5} + 1 = 0[/tex] --- has extraneous solution
[tex]2\sqrt{3x - 1} + 2 = 8[/tex] --- has no extraneous solution
The equation solution
Equation 1 with extraneous solution
[tex]\sqrt{4x + 5} + 1 = 0[/tex]
Subtract 1 from both sides
[tex]\sqrt{4x + 5} = -1[/tex]
Square both sides
4x + 5 = 1
Evaluate the like terms
4x = -4
Divide by 4
x = -1
Substitute x = -1 in [tex]\sqrt{4x + 5} + 1 = 0[/tex] to check
[tex]\sqrt{4(-1) + 5} + 1 = 0[/tex]
[tex]\sqrt{-4 + 5} + 1 = 0[/tex]
[tex]\sqrt{1} + 1 = 0[/tex]
Evaluate the root
[tex]1 + 1 = 0[/tex]
[tex]2= 0[/tex] --- false
Equation 2 without extraneous solution
[tex]2\sqrt{3x - 1} + 2 = 8[/tex]
Subtract 2 from both sides
[tex]2\sqrt{3x - 1} = 6[/tex]
Divide by 2
[tex]\sqrt{3x - 1} = 3[/tex]
Square both sides
3x - 1 = 9
Evaluate the like terms
3x = 10
Divide by 3
x = 10/3
Substitute x = x = 10/3 in [tex]2\sqrt{3x - 1} + 2 = 8[/tex] to check
[tex]2\sqrt{3 * \frac{10}{3} - 1} + 2 = 8[/tex]
[tex]2\sqrt{10 - 1} + 2 = 8[/tex]
[tex]2\sqrt{9} + 2 = 8[/tex]
Evaluate the root
[tex]2*3 + 2 = 8[/tex]
[tex]8 = 8[/tex] --- true
Why the equations have (or do not have) an extraneous solution
The first equation has an extraneous solution because the solution is false for the original equation and the second does not have an extraneous solution because the solution is true for the original equation
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I WILL MARK BRAINLIEST A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 20 child bikes and 6 adult bikes in a week.
Answers
Using a system of equations, it is found that since 20 child bikes and 6 adult bikes would require more testing than the allocated time, it is not possible to build this amount.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable c: number of child bikes.Variable a: number of adult bikes.Each child bike requires 4 hours to build, as do each adult bike. The company has 100 hours of testing, hence:
4c + 4a = 100.
c + a = 25.
With 20 child bikes and 6 adult bikes in a week, we have that c = 20, a = 26, hence:
c + a = 26
20 child bikes and 6 adult bikes would require more testing than the allocated time, it is not possible to build this amount.
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In the following exercises, multiply the binomials. Use any method.
258. (5x − y)(x − 4)
Answers
Answer:
Hence the expression [tex]$$(5x-y)(x-4)=5x^2-xy-20x+4y$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (5 x-y)(x-4).We have to multiply the given expression.Multiply the (5 x-y) by -4, multiply the (5 x-y) by x then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 5x & - & y \\ \times & {} & {} & {} & x & - & 4 \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}{} & {} & {} & - & 20x & + & 4y \\ 5{{x}^2} & - & xy & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}5{{x}^2} & - & xy & - & 20x & + & 4y \\ \end{matrix}$$[/tex]
You should be able to find this
without a calculator.
cos(cos-¹ 0.3) = [?]
Answers
Hello:
Let's consider this problem in steps:
Let's gather some information:
cosine and arccosine cancel each other out in this caseNow let's apply our knowledge to solve the problem:
[tex]\rm \hookrightarrow cos(cos^{-1}0.3) = 0.3[/tex]
Answer: 0.3
Hopefully that helps!
[tex]\frak{Hi!}[/tex]
[tex]\large\text{Related Concept-:}[/tex]
[tex]\boxed{\begin{minipage}{10cm} \sf{If\;you\;take\;the\;inverse\;cosine}\\ \;of\;a\;number,\;and\;then\;take\; its\;cosine,\;don't\;you\;get\;the\;number \\ you started with? \end{minipage}}[/tex]
ClarificationThe inverse cosine and the cosine are operations that undo each other.
This being said, let's solve our problem.
[tex]\bf{cos(cos^{-1}\;0.3)=0.3[/tex], based on what I said above
[tex]\cal{CALLIGRAPHY}[/tex]
Mrs. Ibarra wants to create a right triangle for a geometry test. She plans to use 15, 36, and 41 as side lengths.
Select the four true statements regarding the side lengths Mrs. Ibarra chose.
15 + 36 greater-than 41, so the side lengths will form a triangle.
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
Answers
Answer:
See below.
Step-by-step explanation:
Sides: 15, 36, 41
True: 15 + 36 greater-than 41, so the side lengths will form a triangle.
True: 15 squared + 36 squared = 1,521
True: 41 squared = 1,681
True: Since a squared + b squared not-equals c squared, it will not be a right triangle.
Answer:
A) 15 + 36 greater-than 41, so the side lengths will form a triangle.
C) 15 squared + 36 squared = 1,521
D) 41 squared = 1,681
E) Since a squared + b squared not-equals c squared, it will not be a right triangle.
Proof:
Which of the following is the difference of two squares? (Answers below)
Answers
Answer:
c and d, because they both have 2 squares
The graph of f(x) consists of 14 points. Six of the points lie in Quadrant I of the coordinate plane. If f(x) is an odd function,
what is the greatest number of points that can lie in Quadrant II?
O one
O two
O six
O eight
Answers
If f(x) is an odd function, the greatest number of points that can lie in Quadrant II is 1
How to determine the number of points?The given parameters are:
Function f(x) = Odd function
Points in quadrant IV
The number of points in the upper quadrants is:
Upper = 14/2
This gives
Upper = 7
The upper quadrants are I and II
This means that:
I + II = 7
So, we have:
6 + II = 7
Subtract 6 from both sides
II = 1
Hence, the greatest number of points that can lie in Quadrant II is 1
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The figure shown is a regular octagon. The measure of
What is the measure of
Answers
Answer:
135°
Step-by-step explanation:
X is also 135° as is S , T U , V, W and Y
Answer:
b)135°
Step-by-step explanation:
The value of an interior angle of 135° is appreciated
In a regular polygon all interior angles are equal
Angle x = 135°
Hope this helps
Suppose Z has a standard normal distribution with a mean of 0 and a standard deviation of 1. 27% of the possible Z values are smaller than __________.
Answers
Suppose Z has a standard normal distribution with a mean of 0 and a standard deviation of 1. 27% of the possible Z values are smaller than 0.613.
The standard normal distribution, also known as the z-distribution, is a special normal distribution with a mean of 0 and a standard deviation of 1. The normal distribution can be standardized by converting its value to a z-score. The Z-score indicates how many standard deviations each value has from the mean.
The standard normal distribution (z distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. Each point (x) of the normal distribution can be converted to the standard normal distribution (z) using the equation z = (x-mean) / standard deviation.
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In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS?
QS = 13
5 < QS < 8
QS > 13
3 < QS < 13
Answers
The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The length of QS can lie between 3 < QS < 13.
What is the triangle inequality theorem?The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
(a+b) > c(b+c) > a(c+a) > bAs per the given law of triangle inequality, the sum of the two sides of the triangle is greater than the third side.
x + 8 > 5
x > -3
x + 5 > 8
x > 3
8 + 5 > x
13 > x
Hence, the length of QS can lie between 3 < QS < 13.
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What is b and c in this expression?
[tex]\sqrt[4]{15^7} }[/tex]
Answers
The value of b and c is 4 and 7.
What is algebra?Algebra is the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Algebra is divided into different sub-branches such as elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.
Elementary algebra: elementary algebra, branch of mathematics that deals with the general properties of numbers and the relations between them. Algebra is fundamental not only to all further mathematics and statistics but to the natural sciences, computer science, economics, and business.
From the given question,
[tex]\sqrt[4]{15^7}[/tex] This expression can also be written in the form of [tex]a^\frac{b}{c}[/tex]
We will convert [tex]\sqrt[4]{15^7}[/tex] to the required form:
[tex](15^\frac{7c}{4b} )\left \{ {{a=15^\frac{7c}{4b} } \atop {b=b} , c = c} \right.[/tex]
Hence,
From the above equation we get the value of b and c is 4 and 7.
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Question
(01.02 MC)
For which of the following distributions is the mean most likely to be less than the median?
Answers
The distribution where the mean is most likely to be less than the median is the third histogram.
How to illustrate the information?It should be noted that when the histogram shows the day is left skewed, it means the mean is less than the median.
If it right skewed, the mean is greater than the median.
When they're equal, the data is symmetric.
In this case, based on the information, the distribution where the mean is most likely to be less than the median is the third histogram.
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what is the area of the shaded region?
Answers
To find the area of composite shapes, we can break the bigger shape down into small, simpler shapes, and find the sum of their areas.
For this triangle, we will need to know the formula to find the area of a triangle:
[tex]A=\dfrac{1}{2}bh[/tex]
Solving the QuestionThe given shape can be seen as one large triangle with a little triangle cut out of it. To find the shaded region, we can:
Find the area of the large triangleFind the area of the little triangleSubtract the area of the little triangle from the large triangleArea of the Large Triangle[tex]A=\dfrac{1}{2}bh[/tex]
⇒ Plug in the values given for the base and height:
[tex]A=\dfrac{1}{2}(5)(2+4+6)\\\\A=\dfrac{1}{2}(5)(12)\\\\A=(5)(6)\\\\A=30 mm^2[/tex]
Area of the Small Triangle[tex]A=\dfrac{1}{2}bh[/tex]
⇒ Plug in the values given for the base and height:
[tex]A=\dfrac{1}{2}(3)(4)\\\\A=(3)(2)\\\\A=6mm^2[/tex]
Subtract the Area of the Small Triangle from the Area of the Large Triangle[tex]30 mm^2-6mm^2\\=24mm^2[/tex]
AnswerThe area of the shaded region is [tex]24mm^2[/tex].
help me please please please!!!
What formula should be used to calculate an unknown side of a right angled triangle
when the hypotenuse (c) and one other side (b) are known?
a) Oa^2 = b^2-c^2
b) Oa^2 = c^2 + b^2
c) Oa^2 = c^2-b^2
d) Oc^2 = a^2 - b^2
e) Oc^2 = b^2- a^2
Answers
because it would be the hypotenuse c squared minus the side b squared
The sum of a squared plus b squared equals c squared
Answer:
c) Oa^2 = c^2-b^2
Step-by-step explanation:
the formula of finding hypotenuse (c) is
c^2 = a^2 + b^2
that means c^2 - b^2 = a^2
a^2 = c^2 - b^2.
Using a phone to drive people to Web-based survey instruments is known as a(n) online focus group. online theater system. hybrid survey. cybertracking tactic.
Answers
Answer:
Using a phone to drive people to web-based survey instruments is known as a hybrid survey.
Help please!
A vocational school admits 4 out of every
10 people who apply for admission. One
year, 640 students were admitted. How
many people applied for admission?
Answers
Answer:
319
Step-by-step explanation:
i am really not sure but i believe so i hope it is the right answer
Answer:
1600 people
Step-by-step explanation:
This is a ratio problem. We can set up the proportion by letting x be the number of people who applied for admission:
[tex]\frac{4}{10}=\frac{640}{x}[/tex]
Since we know that 4 people get in for every 10 people that apply, we can set up an equation like the one above and solve for x by cross multiplying:
[tex]6400=4x\\x=1600[/tex]
This means that 1600 people applied for admission to the vocational school.
PLS QUICK I ONLY HAVE 2 HOURS
Answers
Answer:
D
Step-by-step explanation:
As you can observe from the pattern, the numerator gets multiplied by 4 every increase in the sequence.
So , clearly, the 5th term will be = [tex]\frac{64*4}{5} =\frac{256}{5}[/tex]
and the 6th term will be = [tex]\frac{256*4}{5} =\frac{1024}{5}[/tex]
Therefore , D will be the answer.
(LOOK AT IMAGE)
EG is a tangent to the circle below at point F.
Calculate the size of angle x.
Give reasons for your answer.
Answers
[tex]\angle FHD=74^{\circ}[/tex] (alternate segment theorem)
[tex]x=77^{\circ}[/tex] (angles in a triangle add to 180 degrees)
is x/3 = 5/6, then x =
Answers
X=(5/6)/⅓
=5/2
suppose it costs $45 to attend a concert where the band plays for 1.5 hours.
a. what was the cost to attend the concert per hour?
b. what was the cost to attend to the concert per minute
make sure to show your work
Answers
Answer
$30 minutes per hour
$0.5 per minute
Step-by-step explanation:
45/1.5=30
45/90=0.5
A construction company prepares an
estimate to install a new pool for a home-
owner. The estimate includes h hours of
labor, where h>80. The company's goal
is for the estimate to be within 8 hours
of the actual number of hours of labor. If
the company meets the goal and it takes
a hours of actual labor, which inequality
represents the relationship between the
estimated number of hours of labor and
the actual number of hours of labor?
A) a+h≤8
B) a2h+8
C) ash-8
D) -8≤a-h≤8
Answers
The equation that represents the relationship between the estimated number of hours of labor and the actual number of hours of labor is D. -8≤a-h≤8.
How to illustrate the equation?From the information given, the estimate includes h hours of labor, where h>80 and the company's goal is for the estimate to be within 8 hours of the actual number of hours of labor.
Here, the equation that represents the relationship between the estimated number of hours of labor and the actual number of hours of labor is -8≤a-h≤8.
In conclusion, the correct option is D.
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find the product (2y - 2nb) (y+4nb)
Answers
Answer: 2y^2+6bny-8n^2b^2
Step-by-step explanation: I hope this helps!
I’m what quadrant does theta lie if the following statements are true? Sec(theta)<0 and (sec (theta) )(csc (theta) ) > 0
Answers
Because the cosine and sine must be negative when evaluated in theta, the angle lies on the third quadrant.
In which quadrant is the endpoint of the segment that defines the angle?We know that if:
cos(θ) > 0, then we are on the first or fourth quadrantsin(θ) > 0, then we are on first or second quadrant.Here we know that:
sec(θ) < 0
And we know that:
sec(θ) = 1/cos(θ)
Then we have cos(θ) < 0
We also have that:
sec(θ)*csc(θ) > 0
Because sec(θ) < 0, we must have that csc(θ) < 0.
Remember: csc(θ) = 1/sen(θ)
Then sen(θ) < 0.
Then we have the two conditions:
sen(θ) < 0
cos(θ) < 0
The cosine is negative on the third and second quadrants.The sine is negative on the third and fourth quadrants.The only quadrant where both are negative is the third quadrant, so that is the correct option.
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