-3x^2-24x+7=0 is written in the form (x-p)^2=q
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[tex] ({x}^{2} + 8x + 16) \\ bring \: out \: the \: x \: and \: ivide \: the \: 8 \: by \: 2[/tex]
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Raina and Leila are driving separate cars to Boston. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.
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(a) Leila's car, 2 gallons
At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas.(b) 300, Raina's car
The amount of gas remaining is when the graphs intersect.Since the graph for Leila's car is higher than the graph for Raina's car before 300 miles, Raina's car will have less gas.(a) Leila's car, 2 gallons At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas.
(b) 300, Raina's car The amount of gas remaining is when the graphs intersect.
What's the graph about?(a) At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas. This can be seen by looking at the graph of the two cars' gas levels. The graph for Leila's car is higher than the graph for Raina's car at this point, so Leila's car has more gas.
(b) The amount of gas remaining is when the graphs intersect. This happens at 300 miles. Since the graph for Leila's car is higher than the graph for Raina's car before 300 miles, Raina's car will have less gas at this point.
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What is a(b(x)) if a(x) = 3x 2 and g(x) = -3x + 1?
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The equivalent composite function is expressed as -9x + 5
Composite functionsComposite functions are also known as function of a function.
Given the following functions:
a(x) = 3x+2 and
b(x) = -3x + 1
Determine the value of a(b(x))
a(b(x)) = a(-3x+1)
a(b(x)) = 3(-3x+1) + 2
a(b(x)) = -9x + 3 + 2
a(b(x)) = -9x + 5
This gives the equivalent composite function.
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confused on this please help!!
Answers
Answer:
12.75
Step-by-step explanation:
it is the same as the other side just like the similar triangle is.
A particle moves along the x-axis so that at time t\ge 0t≥0 its velocity is given by v(t)=3t^2-18t+15.v(t)=3t2−18t+15. Determine all values of tt when the particle is at rest.
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When a particle is at rest, the velocity = 0. Therefore, we equate the v(t) term to zero (0)
[tex]undefined[/tex]the three sided lengths are 7,8,9 classify the triangle as an acute obtuse or right triangle
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Using the law of cosines to find m∠B:
[tex]\begin{gathered} b^2=a^2+c^2-2ac\cdot\cos (B) \\ 2ac\cdot\cos (B)=a^2+c^2-b^2 \\ \cos (B)=\frac{a^2+c^2-b^2}{2ac} \\ \cos (B)=\frac{8^2+7^2-9^2}{2\cdot8\cdot7} \\ \cos (B)=\frac{32}{112} \\ B=\arccos (\frac{32}{112}) \\ B=73.4\text{ \degree} \end{gathered}[/tex]Since B is the largest angle (because it's opposite to the longer side), then angles A and C are smaller. In consequence, the three angles are smaller than 90°, which means that the triangle is acute
Solve for m.m- 15 = 20
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Answer:
m=35
Explanation:
Given the equation:
[tex]m-15=20[/tex]We solve for the value of m by adding 15 to both sides.
[tex]\begin{gathered} m-15+15=20+15 \\ m+0=35 \\ m=35 \end{gathered}[/tex]The value of m is 35.
The result will be m=35
Ann and Tom want to establish a fund for their grandson's education. what lump sum must they deposit at a 7% annual interest rate compounded monthly in order to have $60,000 in the fund at the end of 10 years?
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Formula to calculate Principal with clompound interest:
[tex]\begin{gathered} P=\frac{A}{(1+\frac{r}{n})^{n\cdot t}} \\ \\ A=\text{Amount} \\ r=\text{Interest rate (decimals)} \\ n=\text{ number of times per unit t} \\ t=time \end{gathered}[/tex]For the given situation:
A= 60,000
r= 7% =7/100= 0.07
n= 12 (as it is compounded monthly and a year has 12 months)
t= 10 years
[tex]\begin{gathered} P=\frac{60,000}{(1+\frac{0.07}{12})^{12\cdot10}} \\ \\ =\frac{60,000}{(1+\frac{0.07}{12})^{120}} \\ \\ \approx29,855.78 \end{gathered}[/tex]Then, they must deposit approximately $29,855.75
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
Answers
The Simplification of the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths is "negative 43 over 24 times j plus negative 1 over 12". option D
The expression which is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is −19.5b − 6.9. option c
Simplification of fractionnegative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
= -1/8j + 2/3 - (5/3j + 9/12)
= -1/8j + 2/3 - 5/3j - 9/12
= -1/8j - 5/3j + (2/3 - 9/12)
= (-3j-40j / 24 + (8-9) / 12
= -43/24j + (-1)/12
The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)
open parenthesis= -13.5b - 6.3 - 6b - 0.6
collect like terms= -13.5b - 6b - 6.3 - 0.6
= - 19.5b - 6.9
So therefore, the equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9
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Write an equation that represents the line.
Use exact numbers.
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Answer:
y=0.75x+2
Step-by-step explanation: Slope as k and constant as b two points that showed by the graph: (0,2) (4,5)
so we can get 2=0*k+b b=2
5=4k+b
4k=5-2
4k=3
k=3/4
k=.75
First person to help gets brainliest!!
Answers
The value of x from the equation represented by the given bar diagram is 20.
The equation is represented using the bar diagram and from the bar diagram be can observe that the equation will be the following equation mentioned below:
3.5 x + 12.5 x = 320 equation 1
The bar diagram represents 3.5 x + 12.5 x = 320 equation. Now we will simplify this equation and will find the value of x from this equation. The steps that need to be followed to simplify this equation are shown below;
3.5 x + 12.5 x = 320
16 x = 320
Divide both sides of equation by 16 , we will get
x = 320/16
x = 20
The value of x from the equation 3.5 x + 12.5 x = 320 is 20.
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a. On what interval(s) of x is f(x) positive?
b. On what interval(s) of x is f(x) negative?
c. On what interval(s) of x is f(x) increasing?
d. On what interval(s) of x is f(x) decreasing?
e. On what interval(s) of x does f have positive concavity?
f. On what interval(s) of x does f have negative concavity?
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On (-∞, -2) ∪ (3,∞) f(x) is positive, On (-∞, -0.5) it is negative, On (0.5, ∞) it is increasing, in none of the intervals it is having positive concavity, On (-∞, ∞) it has negative concavity.
What X intervals are beneficial for fx?Seeing as how f (x) = 0 there. A function’s “positive regions” are those times when it is above the x-axis. Y-values that are positive are where it is (not zero).
The portions of a function that are below the x-axis are known as its negative regions.
How can I determine the time intervals where f is positive?You must first take the derivative, then make it equal to 0, and then determine which zero values the function is positive between in order to determine when a function is rising. In order to determine when the function is positive and, thus, rising, test values on all sides of these.
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|-102.06|
Find the absolute value
Answers
Answer:
102.06
Step-by-step explanation:
Absolute values are always positive
Answer:
Step-by-step explanation:
102.06
Absolute value is just the positive of any value.
Hope this helps! Have a nice day!
msMario bought 3 yeard of ribbon for 1.50 how much would 5 yards of the same ribbon cost? explain how u got your answer
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For 3 yards, it costs, 1.50.
So for one yard,
[tex]\frac{1.50}{3}=0.5[/tex]Therefore for 5 yards,
[tex]5\times0.5=2.5[/tex]I'll give brainliest!!
Answers
2. Y of the power of 4
3.Y of the power of 9
4.Y of the power of 6
Please help with this problem
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Answer:
The answer is I think 16
Step-by-step explanation:
You can look at the figure beside andfind this answer
If a1 = 7 and an3an-1 + 4 then find the value of a4.
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A1 = 7
An = 3A(n-1) + 4. According to this, A2 would be= 3*7 + 4 =25
A1 = 7, A2 = 25, then the difference is d = 18
The general formula for an aritmethic progression is An = A1 + (n -1)d
For A4 = 7 + (4-1)*18 = 61
What is the equation of the line that passes through the point (4,-8) and has a slope of −2
Answers
Answer:
See below
Step-by-step explanation:
Point (4,-8) slope form would be
( y - -8) = -2 ( x -4)
y+8 = -2x + 8 re-arrange to y = mx + b form
y = - 2x
Hey there Ms or Mr, could you please help me out with this problem? Just a head up, this my homework for today not a quiz. it's about Trapezoids.
Answers
We have to relate the angles of the trapezoid in order to find the measure of BAD.
Given:
[tex]\begin{gathered} AB\mleft\Vert DC\mright? \\ AD\cong BC \end{gathered}[/tex]Then
[tex]\begin{gathered} \angle BAD\cong\angle ABC \\ \angle ADC\cong\angle BCD \end{gathered}[/tex]The angles are congruent because if AD and BC are congruent, and the lines are parallel, they sides will form the same angles.
Also, as the segment AD is "cut" by two parallel lines, the angles BAD and ADC are consecutive interior angles and are, therefore, supplementary.
Then, we can write:
[tex]\begin{gathered} m\angle BAD+m\angle ADC=180\degree\text{ and }\angle ADC=\angle BCD \\ \Rightarrow m\angle BAD+m\angle BCD=180\degree \\ 2x+(3x-5)=180 \\ 5x-5=180 \\ 5x=180+5 \\ 5x=185 \\ x=\frac{185}{5} \\ x=37 \end{gathered}[/tex]Now, with the value of x, we can calculate the measure of BAD as:
[tex]m\angle BAD=2x=2\cdot37=74\degree[/tex]Answer: the measure of BAD is 74°.
which graph represents the systems of inequalities? there are 4 graphs for this question total please help
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Looking at the inequalities, it involves the 'less than or equal to' symbol. This means that the lines of both inequalities must be solid. In options B, C and D, one or two of the lines is broken. This is an indication that they don't represent the given inequality. We would check option A
Optiona
Write the equation of the line that is parallel to - 8x-6y = 5 that passes through thepoint (-9, 1)
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First,we will find the slope of the line
Using 8x - 6y = 5
we will have to re-arrange the equation above to be in the slope-intercept form.
That is; it should be in the form y = mx + b
8x - 6y = 5
6y = 8x -5
y = 8/6 x - 5/6
slope = 8/6 = 4/3
In a parellel equation the slope are the same, hence the slope of our new equation is 4/3
Next, we find the intercept of the new equation;
Using the point (-9, 1) and slope(m) = 4/3
we will substitute into the equation below and then solve for b, where b is the slope of our new equation
y = mx + b
1 = 4/3 (-9) + b
1 = 4(-3) + b
1 = - 12 + b
add 12 to both-side of the equation
1+ 12 = b
13 = b
b= 13
Substituting m = 4/3 and b = 13 into the formula; y = mx+ b
y = 4/3 x + 13
[tex]undefined[/tex]Which of the following is the equation that represents the graph?
Graph of a line the passes through the points negative 3 comma 0 and 0 comma negative 2.
y equals negative two thirds times x minus 3
y equals negative three halves times x minus 2
y equals negative three halves times x minus 3
y equals negative two thirds times x minus 2
Answers
y equals negative two thirds times x minus 2 is the equation of graph.
What is slope of line?The slope of the line is the ratio of the rise to the run, or rise divided by the run.
The given two points are 3 comma 0 and 0 comma negative 2.
i.e (3,0)(0,-2)1)
The formula for slope is (y₂-y₁)/(x₂-x₁)
slope = (-2 - 0) / (0 - 3)
= -2 / -3
The negative negative are multiplied we get positive
= 2/3
The standard form of a line is y = mx + b, where m is slope of line and b is y intercept.
slope(m) = 2/3
We can use either of points (0,-2)...x = 0 and y = -2
now sub and find b, then y intercept
-2 = 2/3(0) + b
-2 = b
so equation is : y = 2/3x - 2
Hence y equals negative two thirds times x minus 2 is the equation of graph.
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Nakeisha needs to order some new supplies for the restaurant where she works. The restaurant needs at least 566 forks. There are currently 188 forks. If each set on sale contains 8 forks, which inequality can be used to determine xx, the minimum number of sets of forks Nakeisha should buy?
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The inequality that can be used to determine the minimum number of set of forks Nakeisha should buy is xx ≥ (566 - 188) / 8.
What is the minimum set of forks she should buy?The first step is to determine the appropriate inequality signs that can be used.
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is ≥.
The form of the inequality is: xx ≥ (least number of forks needed - forks they current have) / number of forks in one set
xx ≥ (566 - 188) / 8
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Answer:
566 < 188 + 8x
Step-by-step explanation:
ASAP i need help rn before i finish this test
The triangles shown are congruent.
What is a correct congruence statement for the triangles shown?
Answers
Answer:
SAS= Side, Angle, Side
Step-by-step explanation:
According to the image, GB congruent to XP, and LB congruent to PF. So, it means that both triangle have the same angle since they both have two congruent side.
P = 1,000 m
X =
x m
150 m width
Answers
Answer:tiny bit confused what the question is asking
length=350
Step-by-step explanation:
perimeter =(length+width )x2
perimeter/2
1000/2=(length+width )
500=(length+width)
500-150=350length
The graphs below have the same shape. f(x) = x2What is the equation of the graph of g(x)?10g(x)f(x)X10510-10O A. g(x) = (x+3)2B. g(x) = (x - 3)2C. g(x) = x2 - 3D. g(x) = x2 + 3
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The equation of f(x) is
[tex]f(x)=x^2[/tex]The graph of g(x) is shifted 3 units to the left. This is a horizontal translation.
For horizontal translation, we follow the following rule >>>
Let parent function be f(x), then
• f(x+a) is the parent translated "a" units left
,• f(x-a) is the parent translated "a" units right
Thus, following the rule, we can clearly say that g(x) = f(x+3)
We can write >>
What is the value of x + y² when x = 1 and y = 9?
Answers
Answer:
=82
Step-by-step explanation:
the value of
x + y²
putting x=1,y=9
we get,
1+(9)^²
=1+81
=82
Select the correct answer. Jonathan has 30 chocolates. He gives some chocolates to his friend David. He then gives Sarah half the number of chocolates that he gave David and gives Lily two-thirds of what he gave David. After giving away the chocolates, Jonathan has 4 chocolates left. If the number of chocolates Jonathan gives David is x, which equation represents the situation? How many solutions does this equation have? A. x + 1 2 x + 2 3 x = 30 − 4 , which has no solution B. x + 1 2 x + 2 3 x = 30 , which has infinitely many solutions C. x + 1 3 x + 2 3 x − 4 = 30 , which has one solution D. x + 1 2 x + 2 3 x + 4 = 30 , which has one solution E. 1 2 x + 2 3 x = x − 4 , which has no solution
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The solution to equation x+ 1/2x+2/3x+4= 30 and has one solution x = 12 which is the correct answer would be an option (D).
The no. of chocolates given to Sarah = 1/2 of x = x/2
Then Lily has two-thirds of what he has given David. Following the distribution of the chocolates,
The number of chocolates provided to Lily is equal to two-thirds of the number of chocolates given to David.
The number of chocolates given to Lily Equals 2/3 of x = 2x/3
Now, the total number of chocolates delivered to David, Sarah, and Lily
= x+x/2+2x/3
Here LCM of 2 and 3 is 6
The Total no. of chocolates given to David, Sarah, and lily
= (6x + 3x+ 4x)/6
The total number of chocolates distributed to David, Sarah, and Lily is 13x/6.
Jonathan had four chocolates left after giving them out.
The number of chocolates left with Jonathan equals the total number of chocolates given to David, Sarah, and Lily.
⇒ 4 = 30 - 13x/6
⇒ 4 + 13x/6 = 30
⇒ 13x/6 = 30-4 = 26
⇒ x = 26×6/13 = 2×6
⇒ x = 12
Hence, the equation which represents the given situation is 30 - 13x/6 =4
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h(x)=−2x+2
Find h(−2).
Answers
Answer:
6
Step-by-step explanation:
when you change h[×] to h[-2] , -2x +2 change to -2[-2]+2
#8.Verify algebraically if the function is even, odd, or neither
Answers
g(x)= x^4 √(1+x)
g(-x) = (-x)^4 √1-x
g (-x) = x^4 √1-x
Since the obtained function is not the same or the opposite it is neither.
A backpack weighs 10 N. What is the mass of the backpack?
Answers
The mass of the backpack is 1.02 kilograms.
What is the mass of the backpack?On earth, the weight of an object of mass M is given by:
W = M*g
Where g is the gravitational acceleration:
g = 9.8m/s^2
In this case, the weight is 10N, then we can write:
10N = M*9.8m/s^2
Solving this for M we get:
10N/(9.8m/s^2) = M = 1.02 kg
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