a) The factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).
b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).
c) The function has a minimum and grows in the + y direction.
d) Marking the two x-intercepts, second, generating a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and estimate the location of the vertex and, finally, creating a parabola with a minimum and growing in the + y direction by matching the points.
How to analyze and interpret quadratic functions?
In this problem we have a quadratic function in standard form, that is, an equation of the form f(x) = a · x² + b · x + c, where a, b and c are real coefficients. a) First, we need to complete the square and find the roots to determine the factorized form:
4 · x² - 7 · x - 15 = 0
4 · [x² - (7 / 4) · x - (15 / 4)] = 0
x² - (7 / 4) · x - (15 / 4) = 0
x² - 2 · (7 / 8) · x - (15 / 4) + (289 / 64) = 289 / 64
x² - 2 · (7 / 8) · x + 49 / 64 = 289 / 64
(x - 7 / 8)² = 289 / 64
x - 7 / 8 = ± 17 / 8
x = 7 / 8 ± 17 / 8
Then, the factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).
b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).
c) The end behavior of the graph is inferred from the lead coefficient. A positive coeffcient , which is the case of the function, indicates that vertex of the polynomial is a minimum and parabola grows in the + y direction.
d) In accordance with algebra, we can generate a quadratic equation by knowing three distinct points on Cartesian plane.
First, mark the two x-intercepts, second, generate a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and, finally, generate a parabola with a minimum and growing in the + y direction.
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write the equations after translating the graph of y=|x+2| one unit to the right
write the equations after translating the graph of y=|x+2| one unit to the left
In the similar quadrilaterals below, what angle corresponds to ∠C
HURRY PLEASE!!!
∠H
∠G
∠F
∠E
Answer:
angle G
Step-by-step explanation:
the quadrilateral did not change position or ration, it only shrank, so all the angles are in the same place and angle C = angle G
Answer:
2
Step-by-step explanation:
One angle of a triangle is 30° more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.
Answer: [tex]\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}[/tex]
Step-by-step explanation:
Let the smallest angle be x.
Then, the middle angle is x+30.
The largest angle is 2x+30.
Angles in a triangle add to 180 degrees, so:
[tex]x+x+30+2x+30=180\\\\4x+60=180\\\\4x=120\\\\x=30[/tex]
So, the angles measure [tex]\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}[/tex]
The measures of all three angles are 30°,60°, and 90°.
What is meant by triangle?A triangle is a 3-sided polygon occasionally (though not frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which may be the same.
Find the measures of all three angles:
The three angles be a, b and c.
Angle “a" = x
Angle “b" = x + 30°
Angle “c" = “a" + “b"
= x + x + 30°
= 2x + 30°
Total angle in a triangle = 180°
Therefore;
“a" + “b" + “c" = 180°
Births; (x + (x + 30°) + (2x + 30°)) = 180°
So,
4x + 60° = 180°
x = (180° - 60°) ÷ 4
x = 30°
Plugging this value of x into the earlier equations for angles “a,” “b,” and “c."
“a" = x = 30°
“b" = x + 30° = 60°
“c" = 2x + 30° = 90°
The measures of all three angles are 30°,60°, and 90°.
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30% of what number is
165
Answer:
550
Step-by-step explanation:
165 x 100= 16500/30=550
The mean, median, and mode of the five numbers 5,7,8,A,B are equal. Find all possible values of A+B
If the mean, median, and mode of the five numbers 5, 7, 8, A, and B are equal, the possible values of A+B are 20, where A is 8, and B is 12.
What are the measures of central tendency?The measures of central tendency include the mode, the median, and the mean.
Statistically, a central tendency is a typical value for a probability distribution.
The mode's value appears most often in a set of data values. The median is the middle value of a dataset. The mean represents the average.
To determine the possible values of A and B, we can start by finding the median value, which is the middle value in ascending order.
Data and Calculations:Median (Middle value) = 8
Mode = 8
Total value = 40 (8 x 5)
A = 8
B = 12.
Mean = 8 (40/5)
Thus, if the mean, median, and mode of the five numbers 5, 7, 8, A, and B are equal, the possible values of A+B are 20, where A is 8, and B is 12.
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If Peter pays $84 to buy a watch after discount of 20% find the original price of the watch
Answer: 105 dollars
Step-by-step explanation:
Let's say that the original price x dollars, we can use the equation to find the original price.
80%x = 84
x = 105
Answer:
$105
Step-by-step explanation:
The multiplier is 0.8
To get the price after the discount,the original price was multiplied by 0.8(100 - 20 = 80% = 0.8
Therefore to obtain the original price from the price after the discount, we use reverse percentage:
$84 ÷ 0.8 = $105
Stillwater Junior high divides students into teams taught by a group of teachers. The table shows the number of students in each team.
The principal uses a computer to randomly select the name of a student from all the students in the school. With the computer program, it is possible to draw the name of the same student twice. If the principal selects the name of a student from the Voyagers on the first try, what is the probability she will draw the name of another student from the Voyagers on the second try?
A. 81/399
B. 41/200
C. 1/82
D. 21/100
Answer:
(A)81/399
Step-by-step explanation:
The probability that the Principal selects a voyager on the first try is
82/400
Since another student is to be selected, the total population has reduced by 1 and the number of voyagers has been reduced by 1.
Probability that another voyager is selected on the second try is
81/399
The correct answer is A.
A parallelogram has sides of length 16 units and 10 units. The shorter diagonal is 11 units. Find the measure of the longer diagonal. Round to 2 decimal places, if necessary.
The measure of the longer diagonal is 24.31 units
How to determine the longer diagonal?The side lengths are given as;
a = 16
b = 10
The shorter diagonal is represented as d1, and it is given as
d1 = 11
The longer diagonal is represented as d2, and it is calculated using
d1^2 + d2^2 = 2 * (a^2 + b^2)
Substitute the known values in the above equation
11^2 + d2^2 = 2 * (16^2 + 10^2)
Evaluate the sum
121 + d2^2 =2 * 356
Evaluate the product
121 + d2^2 = 712
Subtract 121 from both sides
d2^2 = 591
Take the square root of both sides
d2 = 24.31
Hence, the measure of the longer diagonal is 24.31 units
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veronica and marty ride their hikes 46 miles every saturday. veronica rides at an average speed of 9.2 miles per hour
Answer:
5
Step-by-step explanation:
46/9.2 = 5
Consider the statements below. Which are propositions? Mark all that apply.
2+2=7
A giant spider with hairy legs.
There are more men than women at BYU-Idaho.
2+2=4
There are more women than men at BYU-Idaho.
Ron hates spiders.
Are you tired today?
The following statements are considered to be propositions:
2 + 2 = 7There are more men than women at BYU-Idaho.2 + 2 = 4Ron hates spiders.What is deductive reasoning?Deductive reasoning can be defined as a type of logical reasoning that typically involves drawing conclusions based on a given set of rules and conditions or from one or more premises (factual statements) that are assumed to be generally (universally) true.
What is a proposition?A proposition can be defined as a type of statement (assertion) that is typically used to express an opinion or a judgement, with either a true or false answer.
This ultimately implies that, a proposition refers to a type of statement (assertion) that is either a true or false.
In this context, we can infer and logically deduce that the following statements are considered to be propositions:
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Fill in the missing amounts. July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275
July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165
This is further explained below.
What is Cumulative Balance?Generally, The term "cumulative balance" refers to the total amount of money left over at the end of a fiscal year after all surplus amounts have been subtracted from deficit amounts. If there is a negative amount in the Cumulative Balance at the conclusion of a fiscal year, then that balance will be carried forward and used as the opening balance for the next fiscal year.
The term "cumulative account" refers to the total amount of an employee's account under a defined contribution plan (for an unaggregated plan) or the total amount of an employee's account under all defined contribution plans included in an Aggregation Group (for aggregated plans), both of which are determined as of the most recent plan valuation date within the most recent 12-month period that ends on the...
In conclusion, for the following data July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165
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35. Calculate the area of ARST if b = 29.
R
S
30°
1456.65 units²
841 units²
728.33 units²
364.16 units²
b
T
None of these answers are correct.
The area based on the information illustrated will be 825 unit².
How to illustrate the information?Your information is incomplete. Therefore, an overview will be given. It should be noted that area simply means the quantity which expresses the extent of the region on a plane as well as a curved surface. Based on this information, it should be noted that the area of a rectangle is given as:
Area = Length × Width
Let's assume that the width is 25 units and the length is given as 33 units.
Then, the area will be:
= Length × Width
= 33 × 25
= 825 units²
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Express (x + 3)² as a trinomial in standard
Answer:
x² + 6x + 9
Step-by-step explanation:
(x + 3)²
= (x + 3)(x + 3)
each term in the second factor is multiplied by each term in the first factor , that is
x(x + 3) + 3(x + 3) ← distribute parenthesis
= x² + 3x + 3x + 9 ← collect like terms
= x² + 6x + 9 ← in standard form
A box has 1 red marble, 3 blue marbles, and 4 green marbles. Maya draws a blue marble randomly from the box, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles in a row? Explain
Step-by-step explanation:
there are
1 red marble
3 blue marbles
4 green marbles
in the box.
that means there are 8 marbles in the box. which gives us 8 different outcomes for pulling randomly 1 marbles.
the probability for each of these 8 outcomes is equal : 1/8.
remember, the probability is always the number of desired cases over the number of total possible cases.
so, the probability of pulling a red marble is :
1 desired case
8 total cases
->
1/8 or 0.125
the probability of pulling a blue marble is :
3 desired cases
8 total cases
->
3/8 or 0.375
the probability of pulling a green marble is :
4 desired cases
8 total cases
->
4/8 = 1/2 or 0.5
now the experiment is pulling 2 marbles in a row, but the first pulled marble is put back into the box again.
this makes this a combined event, where the first AND the second event must fulfill the desired over total cases.
if the 2 events are independent (not overlapping or influencing each other), then we can simply multiply the probabilities. which is the case here, because the first marble is put back.
why ?
because now we have 8 possible outcomes for the first ball, and again 8 possible outcomes for the second ball, and when we combine all possibilities from the first with all possibilities from the second pull, we get 8×8 = 64 possible outcomes :
red. red
red. blue1
red. blue2
red. blue3
red. green1
...
green4 green4
so, the probability to pull a blue ball first is
3/8
and the probability to pull a blue ball second is
3/8 too
the combined probability of the combined event is
3/8 × 3/8 = 9/64
we have 3×3 = 9 desired outcomes of combining 3 blue and 3 blue balls out of the total of 64 possible outcomes.
Look at the way this plane figure moved. Which set of transformations was performed? Help me please it's urgent!
A) reflect horizontally and reflect vertically
B) reflect vertically and rotate clockwise
C) translate right and rotate counter-clockwise
Using translation concepts, the set of transformations that was performed on the triangle are given as follows:
A) reflect horizontally and reflect vertically.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the orientations of the triangle changed both horizontally and vertically, with no change in the format, hence there were reflections, which means that the correct option is:
A) reflect horizontally and reflect vertically.
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ASAP help me with this question.
(6
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice cubes?
The glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y = -29.202x + 293.5.
In the question, we are informed that the equation of the line of best fit, for the, scatter plot with x representing the number of ice cubes and y representing the milliliters of juice is given as y = -29.202x + 293.5.
We are asked to tell how many milliliters of juice will be in a glass with 7 ice cubes based on the line of best fit.
To find the milliliters of juice in the glass with 7 ice cubes, we substitute x = 7, in the equation of the line of best fit, to get a value of y, representing the milliliters of juice in the glass.
Thus,
y = -29.202x + 293.5,
or, y = -29.202(7) + 293.5 {Substituting x = 7},
or, y = -204.414 + 293.5,
or, y = 89.086.
Thus, the glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y = -29.202x + 293.5.
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if u=–s^2rt then what does r equal?
The required rewritten equation in terms of variable 'r' is r = -u/s²t. By applying simple arithmetic operations, the required equation is obtained.
How to rewrite an equation in terms of another variable?Consider an equation c = ax + by. Solving for variable 'a'.
Step1: Write the required variable terms on one side
Step2: Add/Subtract like terms if any or take common if any
Step3: Divide/Multiply the coefficient of the required variable
Step4: simplify the obtained terms for the required variable
As follows:
c = ax + by
⇒ ax = by - c
⇒ ax/x = (by - c)/x
∴ a = (by - c)/x
Calculation:The given equation is u = -s²rt
dividing by 't' on both sides:
⇒ u/t = -s²rt/t
⇒ u/t = -s²r
dividing by 's²' on both sides:
⇒ u/s²t = -s²r/s²
⇒ u/s²t = -r
∴ r = -u/s²t
Thus, the required equation for variable 'r' is r = -u/s²t.
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NEED HELP QUICK
Select the correct answer.
Firewood can be sold in cords. The wood is cut into equal lengths and stacked evenly in a rack.
Which geometric shape can be used as a model to calculate the volume of the cord of wood?
A.
cylinder
B.
pyramid
C.
rectangular prism
D.
cone
The volume of the cord of wood will be similar to the volume of a rectangular prism. Then the correct option is C.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
The rectangular prism is the most typical geometric form used to approximate the volume of a cord of wood.
The wood is evenly cut into identical lengths, and when stacked, it forms a rectangular prism.
Therefore, C. rectangular prism is the right response.
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What is the center and radius of the circle?
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) = 8; = 2 P(7 ≤ x ≤ 11)
Using the normal distribution, the indicated probability is given as follows:
P(7 ≤ x ≤ 11) = 0.6247.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 8, \sigma = 2[/tex]
P(7 ≤ x ≤ 11) is the p-value of Z when X = 11 subtracted by the p-value of Z when X = 7, hence:
X = 11:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (11 - 8)/2
Z = 1.5
Z = 1.5 has a p-value of 0.9332.
X = 7:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (7- 8)/2
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
0.9332 - 0.3085 = 0.6247.
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
What is a Chord in Geometry?In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.
What is the Congruent Chords Theorem?In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.
In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.
According to the congruent chords theorem, NS = PS, thus:
8 = 2x - 6
8 + 6 = 2x
14 = 2x
Divide both sides by 2
14/2 = 2x/2
7 = x
x = 7
LP = 1/2(12)
LP = 6 units.
In summary, applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
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Evaluate each expression if a=2,b=-3,C=-1, and d=4
5+d(3b-2d)
Answer:
it's simple, put the values in the equation.
5 + d( 3b-2d) = 5 + 4( 3×-3 - 2× 4)
= 5 + 4( -9-8)
= 5+ 4 × -17
= 5-68 = -63 ans.
Below, the two-way table is given for a class
of students.
Sophomore
Freshmen
4
3
6
4
Juniors Seniors Total
2
6
Male
Female
Total
If a male student is selected at random, what is the
probability the student is a freshman.
2
3
P (Freshman | Male) = [?]%
Round to the nearest whole percent.
Enter
Answer:
2/7 = 29% (nearest percent)
Step-by-step explanation:
Calculate the totals and add them to the table:
[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} & \sf Freshman & \sf Sophmore & \sf Juniors & \sf Seniors & \sf Total \\\cline{1-6} \sf Male & 4 & 6 & 2 & 2 & 14\\\cline{1-6} \sf Female & 3 & 4 & 6 & 3 & 16\\\cline{1-6} \sf Total & 7 & 10 & 8 & 5 & 30\\\cline{1-6}\end{array}[/tex]
Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Let P(A) = probability that the student is a freshman
Let P(B) = probability that the student is male
Use the given table to calculate the probability that the student is male:
[tex]\sf \implies P(B)=\dfrac{14}{30}[/tex]
And the probability that the student is a freshman and male:
[tex]\implies \sf P(A \cap B)=\dfrac{4}{30}[/tex]
To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:
Conditional Probability Formula
The probability of A given B is:
[tex]\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}[/tex]
Substitute the found values into the formula:
[tex]\implies \sf P(Freshman|Male)=\dfrac{\dfrac{4}{30}}{\dfrac{14}{30}}=\dfrac{4}{14}=\dfrac{2}{7}=0.28571...=29\%[/tex]
Therefore, the probability that the student is a freshman given they are male is 29% (nearest percent).
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HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT
BE ZERO AND:
1) THE TELEPHONE NUMBER MUST BE A MULTIPLE OF 100?
2) ONLY ODD DIGITS CAN BE USED?
3) THE FIRST 3 DIGITS ARE 277?
Answer:
there are 8 million different phone numbers whose phone numbers whose digits aren't 0 or 1
Circle B has a radius of 24 units, Circle E has a radius of 9 units, and segment CD = 4. Find segment A.F. Round your answer to the nearest tenth.
The length of segment A.F in the circles given is: 62 units.
What is the Radius of a Circle?A radius of a circle is half the diameter of a circle, which is a point from the center to any point on the circumference of the circle. This implies that any segment that is drawn from the center of a circle to any point on the circumference of a circle is a radius. Also, all radii of a circle are always congruent to each other.
Radius of circle B = AB = BD = 24 units [all radii of a circle are congruent to each other].
Radius of circle E = CE = EF = 9 units [all radii of a circle are congruent to each other].
CD = 4
DE = x
CD + DE = CE
Plug in the values into the equation
4 + x = 9
x = 9 - 4
x = 5
DE = 5
The length of segment DE is 5 units
A.F = AB + BD + DE + EF
Plug in the values into the equation
A.F = 24 + 24 + 5 + 9
A.F = 62 units.
Therefore, the length of segment A.F in the given circle is determined as: 62 units.
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5 4 3 2 1
O (4,1)
20
Do,1 of X is:
O (4,0)
O (5,1)
3
5
4
3
2
(3.2)
y
1234 5
(4,0 X
(2,-2)
Z
The image of X after the dilation is (a) (4, 0)
How to determine the image of X?From the figure, the coordinates of X are given as:
X = (4, 0)
The dilation is given as:
Do,1
This means that we dilate X across the origin by a scale factor of 1.
So, we have:
X' = 1 * (4 - 0, 0 - 0)
Evaluate
X' = (4, 0)
Hence, the image of X after the dilation is (a) (4, 0)
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Dante is a software salesman. Let represent his total pay (in dollars). Let represent the number of copies of History is Fun he sells. Suppose that and are related by the equation 2400+120x=y
Considering the given linear function, we have that:
The change for each copy that he sells is of $120.If he sells no copies, he makes $2400.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.His payment for x copies bought is:
y = 120x + 2400.
Hence:
The change for each copy that he sells is of $120, as the slope is of $120.If he sells no copies, he makes $2400, which is the y-intercept.More can be learned about linear functions at https://brainly.com/question/24808124
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What are the next three terms in the sequence -27, -19,
-11, -3, 5, ...?
Answer:
13, 21, 29
Step-by-step explanation:
You are adding 8 to each term. -27 + 8 = -19 + 8 = -11 + 8 = -3, etc.
Find the total area of the shaded region.
The two curves intersect when [tex]y=0[/tex] and [tex]y=1[/tex]. Over the range [tex]0\le y\le1[/tex], the curve [tex]x=12y^2[/tex] lies above [tex]x=12y^3[/tex]. Hence the area of the shaded region is
[tex]\displaystyle \int_0^1 (12y^2 - 12y^3) \, dy = 4y^3 - 3y^4\bigg|_0^1 = (4-3)-(0-0) = \boxed{1}[/tex]
