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Related Questions
Given: f(x) =x^2 + 6x + 5Find the x and y value of the vertex (turning point)And what are the zeros of the parabola?
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Solution: X-value of vertex=-3
Y-value of vertex=-4
Zeros of the parabola: X=-5 and x=-1
Analysis
We can find the x-coordinate of the vertex, calculating -b/2a. First, we identify the a and b values of y=ax^2+bx+c of your quadratic equation.
b=6
a=1
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{6}{2(1)}=-3 \\ \\ After\text{ we find x-coordinate, we can find y-coordinate of the vertex replacing x-value.} \\ f(x)=x^2+6x+5\text{ = }^^(-3\text{ }^2)+6(-3)+5 \\ f(x)\text{ = 9}-18+5 \\ f(x)=-4 \end{gathered}[/tex]Now, let's find the zeros of the parabola. We factorize the quadratic equation:
[tex]\begin{gathered} f(x)=x^2+6x+5 \\ f(x)=(x+5)(x+1) \\ Let^{\prime}s\text{ equal to zero} \\ (x+5)(x+1)=0 \\ (x+5)=\text{ 0 }(x+1)=0 \\ x=-5\text{ }x=-1 \end{gathered}[/tex]any whole number is a proper subset or rational number
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Answer:
The natural numbers, whole numbers, and integers are all subsets of rational numbers
Step-by-step explanation:
hope it helps
have a good day
7x — 9y = 12—7x – 7y = -28
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In order to solve this system of equations, we can add both equations, this way we can find the value of y and then the value of x:
[tex]\begin{gathered} \begin{cases}7x-9y=12 \\ -7x-7y=-28\end{cases} \\ 7x-9y-7x-7y=12-28 \\ -16y=-16 \\ y=\frac{-16}{-16}=1 \\ \\ 7x-9=12 \\ 7x=21 \\ x=\frac{21}{7} \\ x=3 \end{gathered}[/tex]So the solution to this system is (3, 1).
100 points asap and brainliest
Answers
Answer:
68
Step-by-step explanation:
The formula S=
2S-a, n
Oan=- n
n(a₁ + an)
2
2S+ a₁n
an-- n
an-2S+a, n+n
a, 2S-a, n+n
gives the partial sum of an arithmetic sequence. What is the formula solved for a,,?
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Answer:
2S-a1n/n
Step-by-step explanation:
S = n(a1 + an)/2
2S = n(a1 + an)
2S = na1 + nan
nan = 2S - na1
an = (2S - n a1)/n
please help
Which graph represents the solution set of the system of inequalities?
{y≥12x+1y>−x−2
Responses
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.,
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.,
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The graph that represents the system of inequalities is the graph attached below.
How to Determine the Graph of a System of Inequalities?The graph that would represent the system of inequalities must be two lines that intersect each other and have the exact slope and y-intercept of each of the lines on the graph.
Determine the slope and y-intercept of each of the inequalities, and also determine their boundary lines based on which inequality sign they have.
The line that represents the inequality, y ≥ ½x + 1, will be a solid line that has a slope of ½, and a y-intercept of 1.
The second line that represents the inequality, y ≥ -x - 2, will be a dashed line that has a slope of 1, and a y-intercept of -2.
Therefore, the graph that represents the features stated above for both lines is shown in the diagram below.
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A quiz consists of two true false questions and two multiple-choice question with three choices each. How many different sets of answers are there?There aredifferent sets of answers.
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We know that
• There are two true/false questions.
,• There are two multiple-choice questions with three choices each.
In the true/false questions, there are 4 ways to answer since each question has only two choices.
In the multiple-choice questions, there are 6 ways to answer since there are 3 choices per question.
Therefore, there are 10 ways to answer in total.find the distance from line y= -3x + 4 to line y = -3x - 1
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In a math class , there are 14 girls and 16 boys. Which of the following ratios does NOT represent between girls and boys?A. 14:16B. 14/16C. 7 to 8D. 2:9its not college mathematics its middle school
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No. of girls = 14
No. of Boys =16
Therefore the ratio, from girls to boys is,
[tex]\frac{14}{16}[/tex]Which can also be written as,
[tex]\begin{gathered} 14\colon16 \\ 7\text{ to 8} \end{gathered}[/tex]Therefore, the wrong ratio is option D.
That is,
[tex]2\colon9[/tex]So, the answer is option D.
Find the length of the sloping side of the roof. Give your answer to the nearest foot. Show your work.
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Given:
The triangle having two similar angles.
This is the isosceles traingle.
Draw the altitude to the given traingle,
D divides the side BC into two equal side having length,
[tex]\begin{gathered} \frac{45}{2}=22.5 \\ BD=22.5\text{ and DC=22.5} \end{gathered}[/tex]Now, use the tan ratio for right triangle ABD,
[tex]\begin{gathered} tan15^{\circ}=\frac{AD}{BD} \\ 0.268=\frac{AD}{22.5} \\ AD=6.02=6\text{ f}eet \end{gathered}[/tex]Using the pythagorean theorem,
[tex]\begin{gathered} AB^2=AD^2+BD^2 \\ =6^2+22.5^2 \\ =542.25 \\ =23.286 \\ =23.3 \end{gathered}[/tex]The length of the sloping side of the roof is 23.3 feet.
8. Use the point-slope formula to write an equationof a line in slope-intercept form using the points(1/2,5) and (5/2,9)
Answers
We have the next two points:
- (1/2,5)
- (5/2,9)
And we must use the point-slope formula to write an equation of a line in slope-intercept
First, we need to calculate the slope of the line using the point-slope formula
[tex]\begin{gathered} y_2-y_1=m(x_2-x_1) \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Where (x1, y1) and (x2, y2) are the two points
Now, replacing the points
[tex]m=\frac{9-5}{\frac{5}{2}-\frac{1}{2}}=\frac{4}{\frac{4}{2}}=\frac{4}{2}=2[/tex]Now, we must replace the slope and one of the two points in the point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]Replacing m = 2 and (1/2, 5)
[tex]y-5=2(x-\frac{1}{2})[/tex]Finally, we must simplify to obtain the slope-intercept form
[tex]\begin{gathered} y-5=2x-1 \\ y=2x-1+5 \\ y=2x+4 \end{gathered}[/tex]ANSWER:
y = 2x + 4
I don’t understand this paper and our sub has no idea, nor the other students so if someone could help me, that would be great.
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By Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.
Given two triangles are ABC and A'B'C'.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
1) Triangle ABC is reduced to triangle A'B'C'
∠ABC=∠A'B'C'=90°
∠BAC=∠B'A'C'
So, by AA similarity
ΔABC≈ΔA'B'C'
2) Triangle ABC is enlarged to triangle A'B'C'
∠ABC=∠A'B'C'
∠BAC=∠B'A'C'
So, by AA similarity
ΔABC≈ΔA'B'C'
Therefore, by Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.
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At a party, there are 30 men, 16 of whom are without dates, and 30 women, none of of whom are without dates. Find the probability of picking someone at random and getting a person who is a woman or without a date?
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For this type of probability question, there are different ways to solve the same question but let's analyze the situation and calculate as simple as possible.
For our question, there are two parts, the first one first is the probability to pick someone who is a woman. Once there are 60 people of which 30 are women, it means this probability is 30/60. Let's keep this probability.
Now let's move on to the second part. The situation where we pick someone who is without a date. once there are 60 people and all 30 women have a date and 16 men also have a date it means 30 + 16 - 60 = 14 people does not have a date. So the probability to pick someone without a date is 14/60.
Now once we have analyzed the two parts of the question, and we have two probabilities all we need is to sum our probabilities, as follows:
But why do we sum and do not multiply? Because we use the proposition OR at "Find the probability of picking someone at random and getting a person who is a woman OR without a date" If the proposition was AND we would have multiplied both probabilities.
A coordinator will select 5 songs from a list of 8 songs to compose an event's musical entertainment lineup. How many different lineups are possible?
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The number of lineups possible is the combination of selecting 5 songs from 8 songs.
8C5 = 56.
What is combination?A combination is a mathematical way that evaluates the number of possible arrangements within a collection of items, leaving behind of the order of selection. A combination can select items in any order. Combinations can be confused with permutations Water is a combination of hydrogen and oxygen. The car interior is available in various color combinations. The formula for combinations is nC_r = n/(r!*(n - r)!), where n is the number of items and r is the number of items selected at once. Let's look at an example of how combinations are calculated. There are 10,000 possible combinations of the numbers 0-9 in a 4-digit codeTo learn more about combination from the given link:
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What is the slope and y-intercept?
y=-5x+6
Options:
Blank # 1
Blank # 2
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The y intercept (c) is 6
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
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Answer:
74.52
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]
4626ххXхA school received 46 iPads. The school library took 26 of the iPads and the rest were split equally among 4 teachers to use in theirclassrooms. Using the strip diagram and the letter x to represent the unknown quantity, which equation could be used to find thenumber of iPads each teacher received?A)4x = 46 - 26B)4x +46 +264x - 26 - 46D)4x = 26 + 46
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Given data:
The box is given.
The given expression can be written as,
[tex]\begin{gathered} 26+x+x+x+x=46 \\ 4x+26=46 \end{gathered}[/tex]Thus, the option (c) is correct.
HELP PLEASE.
Either Table A or Table B shows a proportional relationship.
Plot the points from the table that shows a proportional relationship.
( If you can, can you save the image as and edit it it will help me out a lot)
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Answer: Table A has a proportional relationship
See the diagram below
==================================================
Explanation:
Table A has a proportional relationship because all the points are on the same straight line. That line in this case is y = 2x
Whatever x is, multiply it by 2 and you'll get the y value
Example: If x = 4, then y = 2*x = 2*4 = 8 which gives the point (4,8)
Another phrase for "proportional relationship" is "direct variation".
3. Given: B is the midpoint of AC, AD = CD
Prove:
DAB = LDCB
Statements
1)
2) AB=CB
3) DB DB
4)
5) ZDAB=2DCB
A
1)
2)
3)
5)
Reasons
D
B
C
Answers
Using the congruency of the triangle we can prove all the conditions.
What do you mean by congruencey of the triangle?The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. Two triangles are said to be congruent if pairings of corresponding sides and corresponding angles are equal. They are the exact same size and form.
D is the midpoint of AC
so AB = BC
and also AD = CD
so the triangle ADB is congruent to triangle CDB
Therefore,
angle ADB = angle CDB
angle ABD = angle CBD
angle BAD = angle BCD
Using congruency of the triangle.
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The radius of a circle is 14 cm. Find its circumference in terms of pie
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Explanation.
The question wants us to determine the circumference of the circle.
Circumference of a circle simply means the perimeter of a circle, and the formula to be used is
[tex]\begin{gathered} C=2\pi r \\ where \\ r=radius=14cm \end{gathered}[/tex]A car that travels from Las Vegas to Los Angeles averages about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles. Write a function to represent the distance d remaining on the trip t hours after departure.
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The distance remaining is given by the equation d = 270 - 60t
How to solve an equation?Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let d represent the distance from Las Vegas to Los Angeles and t represent the remaining time after departure.
A car travels from Las Vegas to Los Angeles at about 60 mi/h. The distance from Las Vegas to Los Angeles is 270 miles.
Hence distance remaining is:
d = 270 - 60t
The distance remaining is d = 270 - 60t
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In the accompanying diagram of BCD m
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Given:
m∠C = 70°
m∠CDE = 130°
Question 1:
To find ∠CDB, let's use the exterior angle theorem.
The exterior angle theorem states that the sum of 2 opposite interior angles is equal to the exterior angle.
Thus,
m∠C + m∠B = 130
70 + m∠B = 130
Subtract 70 from both sides:
70 - 70 + m∠B = 130 -70
m∠B = 60°
Now, use the triangle angle sum theorem to find ∠CDB.
The triangle angle sum theorem states that the sum of interior angles in a triangle is 180°
∠CDB = 180 - 70 - 60 = 50°
∠CDB = 50°
Question 2:
∠CBA = ∠C + ∠CDB
∠CBA = 70 + 50 = 120°
∠CBA = 120°
ANSWER:
∠CDB = 50°
∠CBA = 120°
w/2 + 4 is greater than 5
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Answer:
I say w is equal to 4, because:
4 divided by 2 = 2
2 + 4 = 6
6 > 5
Step-by-step explanation:
Hope it helps! =D
Which of these shows the result of using the first equation to substitute fory in the second equation, then combining like terms? y- 3x 3x+ 2y= 18 OA. 3y 18 B. 9x= 18 OC. 6x= 18 OD. 3x= 18 m
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Find the midpoint of the line segment with endpoints (13,-14) and (-13, 10).
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Answer:
(0, -2)
Step-by-step explanation:
Add the x value and divide by 2
[tex]\frac{13-13}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
Add the y value and divide by 2
[tex]\frac{-14 + 10}{2}[/tex] = [tex]\frac{-4}{2}[/tex] = -2
A company has 40 salespeople. A board member at the company asks for a list of the top 5 salespeople, ranked in order of effectiveness. How many such rankings are possible?
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The number of rankings that are possible when the company has 40 salespeople is 78960960.
What is permutation?Based on the information given, permutations will be used. The formula is illustrated thus:
Permutations = n! / (n – r)!
N is the number of things you are choosing from,
r is the number of items.
“!” is a factorial of a number
The company has 40 salespeople and the board member at the company asks for a list of the top 5. This will be;
= 50! / (40 - 5)!
= 40! / 35!
= 40 × 39 × 38 × 37 × 36
= 78960960
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Is the answer correct if no please let me know
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Answer: 57
Given:
[tex]S_n=4n-3[/tex]We are asked to find the 15th term, meaning n = 15
[tex]S_n=4n-3[/tex][tex]S_{15}=4(15)-3[/tex][tex]S_{15}=60-3[/tex][tex]S_{15}=57[/tex]Therefore, the 15th term is 57.
I tried doing it but the whole thing is confusing
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Given the equation:
y = 828000 - 2700x
Where y is the value of the building and x is the number of months of use.
Let's find when the value of the building will be $666,000.
To find when the value will be $666,000, substitute 666000 for y in the equation and solve for x.
y = 828000 - 2700x
666000 = 828000 - 2700x
Subtract 828000 from both sides:
666000 - 828000 = 828000 - 828000 - 2700x
-162000 = -2700x
Divide both sided by -2700:
[tex]\begin{gathered} \frac{-162000}{-2700}=\frac{-2700x}{-2700} \\ \\ 60=x \\ \\ x=60 \end{gathered}[/tex]The value of the building will be $666,000 after 60 months.
Now, let's convert from months to years.
Where:
12 months = 1 year
[tex]60\text{ months = }\frac{60}{12}=5\text{ years}[/tex]Therefore, the value of the building will be $666,000 after 5 years.
ANSWER:
5 years.
If the measure of ∠ C A B = 4 x + 14 and ∠ D A E = 6 x − 18 then find the measure of ∠ C A B
CAB and DAE are suplementary
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Measure of CAB is 84.4, by using supplementary angle theory.
What is supplementary angle?
In geometry, two angles are referred to as supplementary angles if their sum is 180 degrees. For instance, if A + B = 180°, then A and B are considered supplementary angles. Complementary angles always result in a straight angle when combined (180 degrees).
Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.
We have given, CAB= 4x+14 and DAB = 6x-18
Both are supplementary angle
Therefore, CAB + DAB = 180
4x+14+6x-18=180
10x-4=180
10x=176
x=17.6
hence, CAB = 4(17.6)+14 = 84.4
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Winston is making a model of a statute using a scale where 2 inches equals 6 feet. If the actual height of
the statue is 20 feet, how tall is the model, in inches?
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Answer:
6 2/3 inches
Step-by-step explanation:
2 inches / 6 feet * 20 feet = 6 2/3 inches