Answer:
Step-by-step explanation:
The most basic quadratic function is f(x) = x2, whose graph appears below. ... us to graph an entire family of quadratic functions using transformations.
What is the slope of the line represented by the equation y- 6 = 2(x+3)?
Answer: 2
Step-by-step explanation:
remember y=mx^2+c
where m = gradient = slope
∴ expand and simplify y-5=2(x+3)
y-5=2x+6
y=2x+11
m=2 ∴ slope: 2
Three times my age in 5 years is 54. How old am i now.
a.10
b.11
c.12
d.13
e.14
Answer:
D. 13
Step-by-step explanation:
54 ÷ 3 = 18 (your age in 5 years)
18 - 5 = 13 (your age now)
What is the end behavior of the function f(x)=12x2?
dis i know functiin of fx is ♾
Answer:
4th option
Step-by-step explanation:
the end behaviour is what happens when x gets larger and positive (right- hand end )or larger and negative ( left- hand end )
f(x) = [tex]\frac{1}{2}[/tex] x² ← is of even degree (2) and has a positive leading coefficient , then
• even degree and positive leading coefficient
f(x) → +∞ as x → + ∞ and
f(x) → + ∞ as x → - ∞
Sandy jogs 19.7 miles in 4.5 hours. How many miles does she jog per hour
Answer:
4.378 MPH
Step-by-step explanation:
Distance in Miles
MPH= -------------------------
Time in Hours
19.7/4.5 = 4.378 MPH
what do I check off
Answer:
E. >
Because 65 is greater than 56.
The table can be used to determine the solution to the system of equations, 2y − x = 8, and y − 2x = −5.
A table with 6 columns and 2 rows. The first column, Original System has 2 y minus x equals 8 and y minus 2 x equals negative 5. The second column, Equivalent System, has 2 y minus x equals 8 and negative y plus 4 x equals 10. The third column, Sum of equations in Equivalent System, has 3 x equals 18. The fourth column, Solution to System, is blank. The fifth column, New System Using Sum, has2 y minus x equals 8 and 3 x equals 18. The sixth column, Solution to New System is blank.
Which solution can be used to fill in both blanks in the table?
The solution to the system and the solution that fills the blank space is (6, 1)
System of equationsThis are also known as a set of simultaneous equations, also known as a system of equations which is a finite set of equations for which common solutions
Given the following system of equations
2y − x = 8, and
y − 2x = −5.
From equation 2;
y = -5 + 2x ............. 3
Substitute equation 2 into equation 1 to have:
2(-5+2x) - x = 8
Expand to have:
-10 +4x -x = 8
-10 + 3x = 8
3x = 8 + 10
3x = 18
Divide both sides
by 3
3x/3 = 18/3
x = 6
Substitute x = 6 into equation 3
y = -5 + 2x
y = -5 + 2(3)
y = -5 + 6
y = 1
Hence the solution to the system and the solution that fills the blank space is (6, 1)
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Answer:
Its D (6,7)
Step-by-step explanation:
Solve the following systems of equations algebraically:
[tex]\left \{ {{y=\frac{1}{2}*2^x } \atop {y=5x+2}} \right.[/tex]
The value of x in the system of equation is 6
How to solve the system of equations?The system of equations is given as:
y = 1/2 * 2^x
y = 5x + 2
Substitute y = 1/2 * 2^x in y = 5x + 2
1/2 * 2^x = 5x + 2
Multiply through by 2
2^x = 10x + 4
Next, we use the trial by error.
Set x = 6
This gives
2^6 = 10 * 6 + 4
Evaluate the product and the exponent
64 = 60 + 4
Evaluate the sum
64 = 64
Hence, the value of x in the system of equation is 6
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The equation 2x2 − 12x 1 = 0 is being rewritten in vertex form. fill in the missing step. given 2x2 − 12x 1 = 0 step 1 2(x2 − 6x ___) 1 ___ = 0 step 2 2(x2 − 6x 9) 1 − 18 = 0 step 3 ✔ 2(x − 3)2 17 = 0 2(x − 3)2 − 17 = 0 2(x 3)2 − 17 = 0 2(x − 6)2 − 17 = 0
Given: [tex]2x^2 - 12x + 1 = 0[/tex]
Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]
Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]
Second answer: [tex]2(x - 3)^2 - 17 = 0[/tex]
Explanation in detail:
The quadratic equation a[tex]x^{2} + bx + c = 0[/tex]'s vertex form is
where a[tex](x - h)^{2} + k[/tex] equals zero
A is the [tex]x^{2}[/tex] coefficient, and h is the vertex's x-coordinate on the equation's graph.
The vertex of the equation's graph, k, has the y-coordinate.
The completing square can be used to determine the vertex form.
[tex]2x^{2} - 12x + 1 = 0[/tex] is the equation.
Put[tex]2x^{2} -12x[/tex] in a bracket and subtract 2 from them as a common component to utilize the completing square.
∵ [tex]2(x^{2} - 6x) + 1 = 0[/tex]
To determine the product of the first and second terms in the binomial, divide the second term by two.
∵ [tex]6x / 2 = 3x[/tex]
∵[tex]3x = 3 * x[/tex]
∴ The binomial's first and second terms are x and 3, respectively.
The phrase in the bracket's middle is (-)
∴ Middle of the binomial's sign is (-)
∴ The binary value is [tex](x - 3)^2[/tex]
Square 3 is nine.
To keep the equation from altering, you must deduct the same number from the bracket after adding 9 there.
∴ [tex]2(x^2 - 6x + 9 - 9) + 1 = 0[/tex]
- Remove the brace and multiply -9 by 2.
∵ [tex]2 *-9 = -18[/tex]
∴ [tex]2(x^2- 6x + 9) + 1 - 18 = 0[/tex]
- Construct a square binomial from [tex](x^{2} - 6x + 9)[/tex]
∵ [tex]x^2 - 6x + 9 = (x - 3)^2[/tex]
∴ [tex]2(x - 3)^2 + 1 - 18 = 0[/tex]
Include related terms.
∴[tex]2(x - 3)^2 - 17 = 0[/tex]
∴ The equation's vertex form is[tex]2(x - 3)^2 - 17 = 0.[/tex]
Given that: [tex]2x^2 - 12x + 1 = 0[/tex]
Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]
Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]
Step 3: [tex]2(x - 3)^2 - 17 = 0[/tex]
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The graphs below are both quadratic functions. The equation of the red graph
is fx) = ». Which of these is the equation of the blue graph, g(x)?
Answer:
A. y = 1/3x^2
Step-by-step explanation:
The red graph is stretched horizontally by a factor 1/3 to give the blue graph
the senior class was going on a field trip to disneyland. A total of 350 student went on the trip. they filled seven busses . how many student were on each bus
Answer:
50 ^^
Step-by-step explanation:
So first an easy way to solve this problem is by removing the zeros then you'll have 35 and
7x1=7
7x2=14
7x3=21
7x4=28
7x5=35
So 7x5 dont forget to add your zeros to 35 and 5 and boom your answer is 50
need more explaining tell me ^^
Simplify the expression below
Answer:
C
Step-by-step explanation:
4 is a perfect square. 2 x 2. You can pull the 2 out and everything else would be left under the square root symbol.
Geometry: complete this proof, ASAP!!!!!!!
The complete proof from the figure is:
AC ≅ DF; AB ≅ DE; ∠1 ≅ ∠6 -- Given∠1 ≅ ∠2; ∠5 ≅ ∠6 -- vertical angles∠2 ≅ ∠5 --- corresponding anglesΔABC ≅ ΔDEF --- SAS postulate∠3 ≅ ∠4 --- corresponding anglesBC || EF ---- provedHow to complete the proof?The given parameter is:
AC ≅ DF; AB ≅ DE; ∠1 ≅ ∠6
Angles 1 and 2, & Angles 5 and 6 are vertical angles
So, we have: ∠1 ≅ ∠2; ∠5 ≅ ∠6 by the definition of vertical angles.
From the figure, triangles ABC and DEF are congruent by the SAS postulate.
So, we have: ΔABC ≅ ΔDEF by the definition of SAS postulate
Angles 3 and 4 are corresponding angles
So, we have: ∠1 ≅ ∠2; ∠5 ≅ ∠6 by the definition of corresponding angles.
Hence, the lines BC and EF are parallel lines
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Solve the system of equations by substitution.
3 /8 x +1/3y =17/24
x + 7y = 8
By substitution, the value of x and y are 1 and 1 respectively.
How to solve system of equation?3 / 8 x + 1 /3 y = 17 / 24
x + 7y = 8
x = 8 - 7y
Let's substitute the value of x in equation(ii)
3 / 8(8 - 7y) + 1 / 3 y = 17 / 24
3 - 21 / 8 y + 1 / 3 y = 17 / 24
1 / 3 y - 21 / 8 y = 17 / 24 - 3
8y - 63y/24 = 17 - 72/ 24
-55y / 24 = -55 / 24
cross multiply
-1320y = -1320
divide both sides by -1320
y = -1320 / -1320
y = 1
Hence,
x + 7(1) = 8
x = 8 - 7
x = 1
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Austin is a human resources executive for a technology company. He is deciding between two types of plans for vacation allowance for the employees of the company: Unlimited and Traditional, Austin wants to deterrine, for workers in the tech Industry, if the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan Austin surveys a random sample of 17 workers who have the Unlimited plan and a random sample of 15 workers who have the Traditional plan. (These samples are chosen independently.) For each worker, he records the number of vacation days taken last year. For the workers with an Unlimited plan, the sample mean is 18.9 with a sample variance of 30.8. For the workers with a Traditional plan, the sample mean is 17.4 with a sample variance of 6.1 Assume that the two populations of vacation days taken are approximately normally distributed. Can Austin conclude, at the 0.10 level of significance, that the population mean of the yearly number of vacation days taken by workers with an Unlimited plan is greater than the population mean of the yearly number of vacation days taken by workers with a Traditional plan? Perform a one-talled test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, (If necessary, consult a list of formulas.) (*) State the null hypothesis and the alternate hypothesis (a) Determine the type of test statistic to use (a) state the null hypothesis H, and the alternate hypothesis (b) Determine the type of test statistic to use. (c) Find the value of the test statistic (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places) (e) At the 0.10 level of significance, can Austin conclude that the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan?
The question requires that we have to state the hypothesis:
null hypothesis;H0: u1 < u2, the alternate hypothesis;H1: u1 > u2. The one tail test is what is to be used.
A. How to state the hypothesisH0: u1 < u2
H1: u1 > u2
The one tail test statistic is what is to be used here
B. standard error[tex]\sqrt{\frac{30.8}{17} +\frac{6.1}{15} }[/tex]
= 1.49
The df = 17 + 15 - 2
= 30
test statistic = 18.9 - 17.4 / 1.49
= 1.007
We have the critical value on excel as T.INV(0.9,30)
= 1.310
E. At 0.1, we can conclude that t-value (1.007) does not lies in the rejection area. We fail to reject the null hypothesis. Hence we conclude that the mean vacation with the unlimited plan is greater.
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LK=
Help please asap thx so much
Answer:
LK = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
given point J (4, 4 )
then LJ = 4 and JK = 4
using Pythagoras' identity in right triangle LJK
LK² = LJ² + JK² = 4² + 4² = 16 + 16 = 32 ( take square root of both sides )
LK = [tex]\sqrt{32}[/tex] = [tex]\sqrt{16(2)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{2}[/tex] = 4[tex]\sqrt{2}[/tex]
what is the next word in the pattern below?
Fall, Winter, Spring, Summer, Fall, __, ...
A. Winter
B. Summer
C. Spring
D. Fall
The answer is A. Winter.
As the pattern is : F, W, Sp, Su, F... (letters used for convenience), then the next word in the pattern will be Winter, because that was shown in the previous sequence.
A parabola with a vertex at (0,0) has a focus along the negative part of the x-axis. which could be the equation of the parabola?
Answer:
y^2 = -8x for example.
Step-by-step explanation:
General form is y^2 = -4ax
The focus of this parabola will be at (-a , 0) on the x axis.
So the parabola might be:
y^2 = -4x
y^2 = -12x
y^2 = -0.9x and so on......
How would you solve this? Please give an explanation.
The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)
How to generate values from a recursive function
In this question we have a kind of recursive function known as Fibonacci's function, where a value of the series is generated from at least immediately previous elements. In this case, we need to find the first three elements from the fifth and fourth elements of the series:
[tex]a_{n-2} = a_{n-1} - a_{n} + 4[/tex]
a₄ = a₅ - a₆ + 4
a₄ = - 2 - 0 + 4
a₄ = 2
a₃ = a₄ - a₅ + 4
a₃ = 2 - (- 2) + 4
a₃ = 8
a₂ = a₃ - a₄ + 4
a₂ = 8 - 2 + 4
a₂ = 10
a₁ = a₂ - a₃ + 4
a₁ = 10 - 8 + 4
a₁ = 6
The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)
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1. 3k − 8 = 7
2. 8b + 9 = −15
3. 8 = 3x − 13
4. 6p + 22 = 4
5. 84 = 51 + 11c
Add 8 to both sides.
3k = 7 + 8Add 7 and 8 to get 15.
3k = 15Divide both sides by 3.
k = 15 / 3Divide 15 by 3 to get 5.
k=5 ===> Answer===> Exercise 28b + 9 = −15
Subtract 9 from both sides.
8b= −15 − 9Subtract 9 from −15 to get −24.
8b = −24Divide both sides by 8.
b = -24 / 3Divide −24 entre 8 para obtener −3.
b=−3 ===> Answer===> Exercise 38 = 3x − 13
Swap the sides so that all the terms of the variables are on the left side.
3x −13 = 8Add 13 to both sides.
3x = 8 + 13Add 8 and 13 to get 21.
3x = 21Divide both sides by 3.
x = 21 / 3Divide 21 by 3 to get 7.
x = 7 ===> Answer===> Exercise 46p + 22 = 4
Subtract 22 from both sides.
6p = 4 − 22Subtract 22 from 4 to get −18.
6p = −18Divide both sides by 6.
p = -18 / 6Divide −18 entre 6 para obtener −3.
p = −3 ===> Answer===> Excercise 584 = 51 + 11c
Swap the sides so that all the terms of the variables are on the left side.
51 + 11c = 84Subtract 51 from both sides.
11c = 84 − 51Subtract 51 from 84 to get 33.
11c = 33Divide both sides by 11.
c = 33 / 11Divide 33 by 11 to get 3.
c = 3 ===> AnswerSolution 1 :-
>> 3k - 8 = 7
>> 3k = 7 + 8
>> 3k = 15
>> k = 15 / 3
>> k = 5
Solution 2 :-
>> 8b + 9 = -15
>> 8b = -15 - 9
>> 8b = -24
>> b = -24 / 8
>> b = -3
Solution 3 :-
>> 8 = 3x - 13
>> 3x = 13 + 8
>> 3x = 21
>> x = 21 / 3
>> x = 7
Solution 4 :-
>> 6p + 22 = 4
>> 6p = 4 - 22
>> 6p = -18
>> p = -18 / 6
>> p = -3
Solution 5 :-
>> 84 = 51 + 11c
>> 11c = 84 - 51
>> 11c = 33
>> c = 33 / 11
>> c = 3
Find the area of the semicircle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal. 6
The area of the given semicircle is 56.574 sq. units. Half of the area of the circle is the area of the semicircle.
What is the area of the semicircle?The area of the semicircle is
A = [tex]\frac{1}{2}[/tex] πr² sq. units
Where r - radius
A semicircle is nothing but half part of the circle. So, its area is also half of the circle's area.
Calculation:It is given that,
The radius of the semicircle is
r = 6
So, its area in terms of π is
A = [tex]\frac{1}{2}[/tex] πr²
= [tex]\frac{1}{2}[/tex] × π × 6²
= 18π sq. units
On substituting π = 3.143, we get
A = 18 × 3.143 = 56.574 sq. units
Thus, the area of the given semicircle in terms of π is 18π or in terms of π =3.143 is 56.574 sq. units.
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A semi-circle window can be used above a doorway or as an accent window
in a room to allow more light in large rooms. The semi-circle window in your
home theater room lets too much light in so that the movie experience is not
optimal at any time of the day.
You research and find there are “room darkening” blinds and shades for
semi-circle windows. You can’t quite reach the semi-circle window to
measure but you are able to measure the window beneath. The height of the
rectangle window below is 85 in and the width of the window below the semi-circle is 50 in.
What is the area of the semi-circle window so that you can start your search for the correct size?
Be sure to show and explain your work.
A semicircle is a part of a circle, and it is referred to as half of a given circle. Thud the area of the semi-circle window is 982 [tex]in^{2}[/tex].
A circle is a shape that is bounded by a curved path which is referred to as the circumference. Some parts of a circle are radius, diameter, sector, arc, semi-circle, circumference, etc.
A semicircle is a part of a circle, and it is referred to as half of a given circle.
such that:
Area of a circle = [tex]\pi[/tex] [tex]r^{2}[/tex]
and
area of a semicircle = [tex]\frac{\pi r^{2} }{2}[/tex]
where: r is the radius of the circle, and [tex]\pi[/tex] is a constant with a value of [tex]\frac{22}{7}[/tex].
Thus from the given question, it can be inferred that;
r = [tex]\frac{50}{2}[/tex]
= 25
r = 25 in
Thus, the area of the semi-circle can be determined as;
area of the semi-circle = [tex]\frac{1}{2}[/tex] * [tex]\frac{22}{7}[/tex] * [tex]25^{2}[/tex]
= 982.1429
area of the semi-circle = 982.14 [tex]in^{2}[/tex]
The area of the semi-circle window is approximately 982 [tex]in^{2}[/tex].
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Select the correct answer.
Find the inverse of function f.
f(c) = 9x + 7
Answer:
B.) f⁻¹(x) = (1/9)x - 7/9
Step-by-step explanation:
Remember, f(x) is another way of writing "y". The inverse can be found by swapping the positions if the "x" and "y" variables and then solving to isolate the "y" variable.
f(x) = 9x + 7 <----- Original function
y = 9x + 7 <----- Substitute f(x) for "y"
x = 9y + 7 <----- Swap variable positions
x - 7 = 9y <----- Subtract 7 from both sides
(x - 7) / 9 = y <----- Divide both sides by 9
(1/9)x - 7/9 = y <----- Divide each term individually by 9
The inverse function is represented by the symbol f⁻¹(x).
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]\textsf{A. } y=3x^2+10x-8[/tex]
Step-by-step explanation:
We are given the information that a function has zeros at x = ⅔ and x = -4. In order to find the function that has those zeros, we can substitute the value of the zeros into each function. If the value of a function equates to zero with both values, then that is the function we are looking for.
..................................................................................................................................................
Standard Form of a Quadratic: ax² + bx + c = 0.
..................................................................................................................................................
[tex]\large \text{$y = 3x^2+10x-8 \implies 0=3x^2+10x-8$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{24}{3}-8\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2+10(-4)-8\\\\\implies 0=3(16)-40-8\\\\\implies 0=48-48\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]
..................................................................................................................................................
[tex]\large \text{$y = 2x^2-5x-12 \implies 0=2x^2-5x-12$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2-5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=2\left(\dfrac{4}{9}\right)-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}-\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=-\dfrac{22}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{130}{9}\ \textsf{X}\end {minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2-5(-4)-12\\\\\implies 0=2(16)+20-12\\\\\implies 0=32+20-12\\\\\implies 0=40\ \textsf{X}\end{minipage}}[/tex]
..................................................................................................................................................
[tex]\large \text{$y = 2x^2+5x-12 \implies 0=2x^2+5x-12$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2+5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}+\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=\dfrac{38}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{70}{9}\ \textsf{X}\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2+5(-4)-12\\\\\implies 0=2(16)-20-12\\\\\implies 0=32-32\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]
..................................................................................................................................................
[tex]\large \text{$y = 3x^2-10x-8 \implies 0=3x^2-10x-8$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2-10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)-\dfrac{20}{3}-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)-\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}-\dfrac{20}{3}-\dfrac{8\times3}{3}\\\\\implies 0=-\dfrac{16}{3}-\dfrac{24}{3}\\\\\implies 0=-\dfrac{40}{3}\ \textsf{X}\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2-10(-4)-8\\\\\implies 0=3(16)+40-8\\\\\implies 0=48+40-8\\\\\implies 0=80\ \textsf{X}\end{minipage}}[/tex]
..................................................................................................................................................
Therefore, the function whose zeros are ⅔ and -4 is [tex]y=3x^2+10x-8[/tex].
Which type of professional would help the government
determine where to set the price of oranges for U.S.
markets?
O Consumers
O Economists
O Exporters
O Importers
Answer:
Step-by-step explanation:
The answer is Economists
Answer: economists
Step-by-step explanation: got it right
A car travels the first 50 km of its journey at an average speed of 25 m/s and the next 120 km at an average speed of 80 km/h. The car completes the last part of its journey at an average speed of 90 km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.
Answer:81.85 km/hr is the average speed
Step-by-step explanation:
Answer: ≈ 84,3 km/h.
Step-by-step explanation:
[tex]\displaystyle\\V{average}=\frac{\Delta S}{\Delta t}=\frac{S_1+S_2+S_3}{t_1+t_1+t_3} .\\1.\ S_1=50\ km\\ t_1=\frac{S_1}{V_1}\\ V_1=25*\frac{3600}{1000} \\V_1=90\ \frac{km}{h} .\\t_1=\frac{50}{90}\\ t_1=\frac{5}{9} \ h.\\2.\ S_2=120\ km\ \ \ \ V_2=80\ \frac{km}{h} \\t_2=\frac{S_2}{V_2} \\t_2=\frac{120}{80} \\t_2=\frac{3}{2}\ h.\\[/tex]
[tex]3.\ V_3=90\ \frac{km}{h} \\t_3=35\ minutes\\t_3=\frac{35}{60} \\t_3=\frac{7}{12}\ h.\\ S_3=V_3*t_3\\S_3=90*\frac{7}{12} \\S_3=52,5\ km.\\Hence,\\V{average}=\frac{50+120+52,5}{\frac{5}{9}+\frac{3}{2} +\frac{7}{12} } \\V{average}=\frac{222,5}{\frac{95}{36} } \\Vaverege\approx84,3\ \frac{km}{h} .[/tex]
Which of the following expressions can be used to find the area of a square with a side length of m?
The answer is A = m².
We know the general formula for finding the area of a square is :
Area = side²
Now, we are given the side is equal to m.
Hence, the expression which can be used to find the area is :
A = m²
Which is the inequality in factored form that represents the region greater than or equal to the quadratic function with zeros –3.5 and 11.5 and includes the point (8.5, –54) on the boundary?
The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).
What is the expression of the quadratic inequality?
Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic equation by solving this system of linear equations:
(x₁, y₁) = (- 3.5, 0)
12.25 · a - 3.5 · b + c = 0 (1)
(x₂, y₂) = (11.5, 0)
132.25 · a + 11.5 · b + c = 0 (2)
(x₃, y₃) = (8.5, - 54)
72.25 · a + 8.5 · b + c = - 54 (3)
The solution of the system is a = 3.6, b = - 54, c = 144.9. Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:
y ≥ 3.6 · (x² - 15 · x + 40.25)
y ≥ 3.6 · (x - 11.5) · (x + 3.5)
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2. Five times a number is equal to the same number increased by 8.
Answer:
the number is 2
Step-by-step explanation:
5x = x + 8
5x - x = 8
4x = 8
x = 8/4
x = 2
What is the value of x to the nearest tenth? The figure is not drawn to scale
Answer:
x=10.5
Step-by-step explanation:
if the two triangles were ratios it would be like
19.3:7.2 to x:3.9
so 75.27 = 7.2x
whcih is 10.45 which is approximately 10.5
A hydrogen atom has one positively charged proton and one negatively charged electron.
Write an addition equation to represent how their charges combine to make the overall charge of the atom.
The addition equation to represent how their charges combine to make the overall charge of the atom is + 1 + - 1 = 0
How to write equation to represent charges of atom?A hydrogen atom has one positively charged proton and one negatively charged electron.
An atom of every elements has an electron(negatively charged) and positively charge(proton) part.
An atom as a whole is electrically neutral if the number of proton and electron are equal. They will cancel each other to make the atom neutral.
Therefore, the addition equation to represent how their charges combine to make the overall charge of the atom is as follows;
+ 1 + - 1 = 0
1 positively charged proton plus single negatively charged electron = zero(neutral)
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