The value of missing number is [tex]49[/tex].
The given equation is [tex]x^{2}+14x+c[/tex].
We have to find the missing value of [tex]c[/tex].
We can find the value of [tex]c[/tex] by perfect square trinomial.
A perfect square trinomial is a equation which we can get after the square of binomial expression.
The equation [tex]ax^{2}+bx+c[/tex] said to be a perfect square if and only if it follows the condition [tex]b^{2}=4ac[/tex].
In the equation [tex]ax^{2}+bx+c[/tex], [tex]a,b[/tex] and [tex]c[/tex] are the real numbers.
Now we compare the given equation to [tex]ax^{2}+bx+c[/tex].
After comparing we get
[tex]a=1, b=14, c=c[/tex]
To find the value of [tex]c[/tex] we put the value of [tex]a,b,c[/tex] in expression [tex]b^{2}=4ac[/tex].
[tex](14)^{2}=4\times1\times c[/tex]
[tex]196=4\times c[/tex]
Divide by [tex]4[/tex] on both sides
[tex]\frac{196}{4}=\frac{4\times c}{4}[/tex]
[tex]c=\frac{196}{4} \\c=49[/tex]
Hence, the value of missing number is [tex]49[/tex].
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The vertices of △ABC are A(2, −3), B(−3, −5), and C(4, 1). If (x,y)--> (x-2, y+3), give the vertices of △A′B′C′.
Answer:
A' = (0, 0)
B' = (-5, -2)
C' = (2, 4)
Step-by-step explanation:
Vertices of triangle ABC:
A = (2, -3)B = (-3, -5)C = (4, 1)Given mapping rule:
(x, y) → (x - 2, y + 3)
This notation tells you that the x-coordinate is translated 2 units to the left, and the y-coordinate is translated 3 units up.
Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':
⇒ A' = (2 - 2, -3 + 3) = (0, 0)
⇒ B' = (-3 - 2, -5 + 3) = (-5, -2)
⇒ C' = (4 - 2, 1 + 3) = (2, 4)
(MULTIPLE CHOICE) Write an expression that would represent the perimeter of a rectangle with a width of 10n and a length of 4.
A) 10n + 4 + 10n + 4
B) 10n + 4
C) 4(20n) (this is multiplication)
D) 10 + 4 + 20n + 4
Amy found that she could use the function P(t)=3t^2+5t+8 to model the population of a collection of fruit flies over time, where t is the time in days and P(t) is the number of flies. According to her model, how many flies will there be after 16 days?
A: 8
B: 768
C: 856
D: 2204
The total number of files after 16 days using the function P(t) = 3t² + 5t + 8 is 856.
A relationship between a group of inputs having different outputs is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output.
The function P(t) represents the population of a collection of fruit flies at a particular time in days.
P(t) is the number of flies and t is the time in days.
Now, consider the function:
P(t) = 3t² + 5t + 8
Therefore, the number of flies after 16 days will be:
When t = 16,
P(t) = 3t² + 5t + 8
P(16) = 3(16)² + 5(16) + 8
P(16) = 3 × 16 × 16 + 5 × 16 + 8
P(16) = 768 + 80 + 8
P(16) = 856
Hence, the number of flies after 16 days will be 856 flies using the function P(t).
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Mattie Evans drove 140 miles in the same amount of time that it took a turbopropeller plane to travel 540 miles. The speed of the plane was 200 mph faster than the speed of the car
Find the speed of the plane.
The speed of the plane was
(Simplify your answer.)
mph.
Since the speed of the turbopropeller plane was 200 mph faster than the speed of the car, the speed of the turbopropeller plane is equal to 70 mph.
How to determine the speed of this plane?In order to solve this word problem, we would assign variables to the distance and speed of both Mattie's car and the turbopropeller plane, and then translate the word problem into algebraic equation as follows:
Let d₁ represent the distance covered by Mattie.Let v₁ represent the speed of Mattie's car.Let d₂ represent the distance covered by the turbopropeller plane.Let v₂ represent the speed of the turbopropeller plane.Translating the word problem into an algebraic equation, we have;
v₂ = v₁ + 200
Since Mattie and the turbopropeller plane travled at the same time, we have:
Time = distance/speed
Time = d₁/v₁ = d₂/v₂
Time = 140/v₁ = 540/v₁ + 200
Cross-multiplying, we have:
140(v₁ + 200) = 540v₁
140v₁ + 28,000 = 540v₁
Next, we would rearrange the equation by collecting like terms as follows:
540v₁ - 140v₁ = 28,000
400v₁ = 28,000
Speed of plane, v₁ = 28,000/400
Speed of plane, v₁ = 70 mph.
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32+40+…+120=? Someone help PLEASE
Answer:
912
Step-by-step explanation:
the assumption is that this is an arithmetic progression
the nth term of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
use this to find which term 120 is in the sequence
with a₁ = 32 and d = a₂ - a₁ = 40 - 32 = 8 , then
32 + 8(n - 1) = 120 ( subtract 32 from both sides )
8(n - 1) = 88 ( divide both sides by 8 )
n - 1 = 11 ( add 1 to both sides )
n = 12
given the first and last terms in the sequence then sum is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first + last)
S₁₂ = [tex]\frac{12}{2}[/tex] (32 + 120) = 6 × 152 = 912
If n in an odd integer that is less than -3.25, what is the greatest possible value of n?
The greatest possible value of n is -5
How to determine the possible value of n?From the question, the given parameters are:
n = Odd integerN is less than -3.25The second highlight above can be represented as
n < -3.25
Since n is an integer, then the possible values of n are
n = -4, -5, -6, -7, -8....
Remove the even integers from the above list of numbers because n is an odd integer
So, we have
n = -5, -7, -9....
The greatest value above is n
This means that n can have the highest value of -5
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x + m = p - n + yx Solve for x
Answer:
[tex]x=\frac{-m-n+p}{-y+1}[/tex]
Step-by-step explanation:
Need help making sure I have everything correct if wrong please advise Thank you
To question 16, we see that for every change of plus 2 drinks, they pay an additional value of $2.50. It means that each drink does cost half of this value.
This way, the equation that will give the value of the total cost will be:
[tex]Y=1.25\times X[/tex]Where X stands for the number of drinks, and 1.25 is the value of a single drink.
From the solution presented above, we are able to conclude that the rate of change represents the value of a unitary drink, in the present situation.
What is x in this equation 6(x+7)=-12
Answer:
x = -9
6x + 42 = -12
6x = -54
x = -9
(01.06 MC)
Ray IL bisects angle HIJ. If mzHIL = (6x - 7)° and mzJIL = (5x + 4)°, what is mzJIL?
118°
59°
44°
11°
Option C, 59° is correct answer, The angle JIL is equal to 59 degree.
What is angle?
Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.
Given information in the question,
∠HIL = (6x-7)°
∠JIL = (5x+4)°
The ray IL bisects the ∠HIJ
Since, IL bisects angle HIJ then, angle HIL = angle JIL
So,
6x - 7 = 5x + 4
x = 11
Putting the value of x in given value of JIL to get the angle JIL
∠JIL = (6x-7)°
∠JIL = (6(11)-7)°
∠JIL = 59°
Therefore angle JIL is equal to 59 degrees.
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the altitude (i.e., height) of a triangle is increasing at a rate of 3.5 cm/minute while the area of the triangle is increasing at a rate of 4.5 square cm/minute. at what rate is the base of the triangle changing when the altitude is 7.5 centimeters and the area is 87 square centimeters?
The rate at which the base of the triangle is changing is equal to,
dB = -6.3 cm/minutes.
From the data given in the question.
The rate of increase in the area of the triangle, dA = 4.5 cm/minute
The rate of increase in the altitude of the triangle, dH = 3.5 cm/minute
The Area of the triangle, A = 87 square centimeters
The altitude of the triangle, H = 7.5 centimeters
The equation for the area of a triangle is equal to
A = 0.5×B×H
Plug in A and H to solve for B at that point:
87 = 0.5×B×7.5
B = 23.2
Differentiate the equation for the area of a triangle to find the rate of change of the area of a triangle (dA):
dA = 0.5× dB× H + 0.5×B × dH.
Plug in known variables to solve for the rate of change of the base dB
dA = 0.5 × dB × H + 0.5 × B × dH
4.5 = 0.5 × dB × 7.5 + 0.5 × 23.2 × 3.5
The rate at which the base of the triangle is changing is equal to,
dB = -6.3 cm/minutes.
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Solve for y
6x-3y=36
y = 2x - 12
Step-by-step explanation:Move all terms that don't contain y to the right side and solve.6x - 3y = 36In order to solve this linear equation, we need to group all the variable terms on one side, and all the constant terms on the other side of the equation. In our example, the term 6x will be moved to the right side. Notice that a term changes sign when it 'moves' from one side of the equation to the other.We need to get rid of expression parentheses. If there is a negative sign in front of it, each term within the expression changes sign. Otherwise, the expression remains unchanged. In our example, there are no negative expressions.Therefore, y = 2x - 12Are the following Parallel, Perpendicular, or neither: y = 2x - 5 and -x + 2y = -5
two lines are parallel if their slope is equal
equation of line is
y=mx+c
where m=slope
for y=2x-5
m=2
for -x+2y=-5
2y=-5+x
y=-5/2+x/2
m=1/2
lines are nor parallel becuase m (slope) is not equal
now we will test for perpendicularity
perpendicular lines have slopes that are reciprocal of each other
first line , m=2
second line, m=1/2
2 and 1/2 are reciprocals
therefore, the lines are perpendicular
12 nights camp accommodation costs #6720. What will be the cost of a)7 nights number b)4 nights
EXPLANATION :
The cost of a 12 nights camp accommodation is 6720.
We need to divide the cost by 12 to get the cost per day.
[tex]6720\div12=560[/tex]Now, we are asked to find the cost of 7 nights and 4 nights.
We just need to multiply the daily rate by the number of nights.
a. 7 nights :
7 x 560 = 3920
b. 4 nights :
4 x 560 = 2240
ANSWER :
a. 3920
b. 2240
The corner grocery store sells bananas for $2.91 per pound. Select the store that sells bananas at a lower unit price. Mark all that apply.Store A: $8.16 for 4 poundsStore B: $6.51 for 3 poundsStore C: $2.66 for 2 poundsStore D: $11.40 for 4 pounds
Let's find the unit price of each store
Store A : $8.16 /4 = $2.04 per pound
store B: $6.51 / 3 = $2.17 per pound
store c: $2.66 / 2 = $1.33 per pound
store D : $11.40 / 4 = $ 2.85 per pound
Therefore, store A, store B, store C and store D sells at a lower unit price than Corner grocery store.
Which of the following variable expressions represents the phrase "five more than the quotient of a number x and eight"?
The variable expression is;
[tex]5\text{ + }\frac{x}{8}[/tex]Here, we want to select an option that represents the phrase
The quotient of a number x and 8 means that we divide x by 8
That means we have a fraction, with x as the numerator and 8 as the denominator
We have this as;
[tex]\frac{x}{8}[/tex]5 more than this quotient means that we are to add 5 to the result
We have this as;
[tex]5\text{ + }\frac{x}{8}[/tex]Two similar pyramids have slant height of 4 and 6.1. Find the scale factor.2. If the volume of the smaller pyramid is 48 meters cubed, what is the volume of the larger pyramid?
1) Considering that the slant height of those pyramids is 4 and 6, we can find the scale factor by dividing their slant heights:
[tex]\frac{6}{4}=\frac{3}{2}\text{ or 1.5}[/tex]So we can state that the bigger pyramid is larger than the 1st pyramid by a scale factor of 1.5.
2) For the Volume of the Pyramid, we can write out the formula below:
[tex]V=\frac{1}{3}\cdot Ab\cdot h[/tex]Since the scale factor is 1.5 Then we can state that
[tex]\begin{gathered} V=\frac{48}{\frac{3}{2}} \\ V=32 \end{gathered}[/tex]the Volume of the smaller one is by similarity 1.5 or 3/2 times smaller than the larger one.
3) Hence, the answers are:
1.k=1.5
2. 32 m³
Graph line with slope 1/2 passing through the point (-1,3)
Answer:
Step-by-step explanation:
First, graph your first point at (-1,3) Then, take your slope which is 1/2 and use rise over run. So from your point of (-1,3) go up 1 in your y coordinate, and 2 in your x coordinate. So your next point should be at (1,4)
What is the value of this expression.
here's your answer hope it helps
Select the correct answer.An engineering firm designs a custom hexagonal screw for a computer board. A sketch of the top of the screw is below. To the nearest tenth,what is the area of the screw head?ymm8.€4-2-x mmO-2--4--4OA15.6 mm2.OB. 93.5 mm2OC 62.4 mm2OD.1871 mm²402
We will have the following:
We can see that the shape of the head can be subdivided in smaller shapes, that is:
Now, we calculate the 5 areas, that is:
[tex]\begin{gathered} A_1=\frac{(6)(3)}{2}\Rightarrow A_1=9 \\ \\ A_2=\frac{(6)(3)}{2}\Rightarrow A_2=9 \\ \\ A_3=(6)(12)\Rightarrow A_3=72 \\ \\ A_4=\frac{(6)(3)}{2}\Rightarrow A_4=9 \\ \\ A_5=\frac{(6)(3)}{2}\Rightarrow A_5=9 \end{gathered}[/tex]Now, the total area is:
[tex]\begin{gathered} A_T=A_1+A_2+A_3+A_4+A_5\Rightarrow A_T=9+9+72+9+9 \\ \\ \Rightarrow A_T=108 \end{gathered}[/tex]So, the total area is 108 mm^2-
James and Simon have a reading assignment to complete. James has read rrr pages, and Simon has read 757575 pages. Together they have read a total of 200200200 pages.
Given the linear function in slope-intercept, what is the slope
and y-intercept of this line?
f(x) = x +9
Select TWO answers.
Answer:
Slope is 1 and y-intercept is 9
Step-by-step explanation:
y=mx+b
The slope is the coefficient of x in this case it would be 1
The y-intercept is whatever b is and it is +9 so it is 9
a door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. suppose the true proportion is 0.07. if 492 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.03? round your answer to four decimal places.
The probability that the sample proportion will differ from the population proportion by less than 0.03 exists 0.9909.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Let the true proportion exists 0.07
number of samples exists 492 then we get
√(0.07)(1−0.07)/492 ≈ 0.01150291586
Since the true value of the population proportion exists 0.07, the value of p^ must fall between 0.04 and 0.10 in order for the error of estimation to be less than 0.03.
Therefore, the probability that the sample proportion will differ from the population proportion by less than 0.03 exists 0.9909.
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Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Which choice represents the sample space, S, for this event?
S = {PQR}
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
S = {PQ, PR, QR}
S = {PQ, QP, PR, RP, QR, RQ}
The resulting sample space of the given situation is S = {PQ, QP, PR, RP, QR, RQ}
Sample space:
Sample space refers the collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.
Given,
Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Here we need to find the sample space for the event.
Let us consider,
P represents Patty
Q represents Quinlan
R represents Rashad
And through the question we have know that, the teacher drawn two card at a time,
So we have consider that the teacher is going to draw out of the hat one first, without replacement, and then draw another one.
The first chosen one will be the president, and that could be P, Q or R, Now, the chosen second one is the Vice president, and already one has already being drawn, that could only be two fellows.
Therefore, the total of likely outcomes is PQ,QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.
So, the resulting sample space is
S = {PQ, QP, PR, RP, QR, RQ}
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Jeremiah keeps a record of how many pages he reads each day. He read 40% fewer pages today than yesterday. If he read 90 pages today, how many pages did he read yesterday?
Answer: 126
Step-by-step explanation:: 90 ÷ 10 = 9 (10%) 9 × 4 = 36 (40%) 90 + 36 = 126
(3x869)+(19x528)+428(3)(1049)=a
a=
The value of a in the equation (3x869)+(19x528)+428(3)(1049)=a is 1359555
How to evaluate the expression?From the question, the equation to evaluate is given as
(3x869)+(19x528)+428(3)(1049)=a
Rewrite the above equation to make it legible
So, we have the following equation
(3 x 869) + (19 x 528) + 428(3)(1049) = a
Evaluate the products in the expression
So, we have the following equation
2607 + (19 x 528) + 428(3)(1049) = a
Evaluate the other products in the expression
So, we have
2607 + 10032 + 428(3)(1049) = a
Remove the brackets in the equation
So, we have the following equation
2607 + 10032 + 1346916 = a
Evaluate the sum
1359555 = a
Rewrite as
a = 1359555
Hence, the solution to the equation is 1359555
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Donna bought 5 bags of dog treats for $12.50. What is the cost per bag of dog treats?
I really need help on this please guys
Answer:
2.5
Step-by-step explanation:
$12.50 ÷ 5 bags = $2.5 per bag
Answer:
2.50
Expination:
devide 12.50 by the total amount of dog food purchased (5 bags)
12.50/5 = 2.50
the price per bag is $2.50
Write the recurring decimal 0.45....... as a fraction.
Given the following question:
We are given the repeating decimal of 0.45
We will use the formula:
[tex]\begin{gathered} \frac{(d\times10^r)-n}{10^r-1} \\ \frac{0.45\times10^2)-0}{10^2-1} \\ \text{ Simplify} \\ \frac{0.45\times2\cdot10^2}{10^2-1}=\frac{45}{99} \\ \text{ Simplify once more} \\ \frac{45}{99}\div9=\frac{5}{11} \\ =\frac{5}{11} \end{gathered}[/tex]5. Let the graph of g be a translation 2 units up and 2 units right, followed by a reflection in the x-axis of the graph off(x) = -(x+3)^2 - 2. Write a rule for g.
Answer:
[tex]g(x)=-f(x-2)+2[/tex]Explanation:
Given the function f(x)
A translation of 2 units up = f(x)+2
Next, a translation of 2 units right = f(x-2)+2
When we reflect the result above in the x-axis, we have:
[tex]g(x)=-f(x-2)+2[/tex]A rule for g is therefore:
[tex]g(x)=-f(x-2)+2[/tex]Find the probability of at least 6 failuresin 7 trials of a binomial experiment inwhich the probability of success in anyone trial is 9%.p=[?1%Round to the nearest tenth of a percent.