ANSWER
Domain: All real numbers
Range:
[tex][2, \infty )[/tex]
EXPLANATION
The given function is
[tex]y = 3 {x}^{2} - 6x + 5[/tex]
To find the domain and range of the given function, we complete the square.
[tex]y = 3 ({x}^{2} - 2x )+ 5[/tex]
[tex]y = 3 ({x}^{2} - 2x + 1) + 3( - 1)+ 5[/tex]
[tex]y = 3 ({x - 1)}^{2} - 3+ 5[/tex]
[tex]y = 3 ({x - 1)}^{2} + 2[/tex]
The vertex is at (1,2).
The given function is a polynomial and all polynomial functions are defined everywhere.
The domain is all real numbers.
The parabola opens upwards and have vertex at (1,2). Hence the minimum y-value is 2.
The range is
[tex][2, \infty )[/tex]
Answer:
A.
Step-by-step explanation:
8-102.
The graph at right represents this situation: Cara jogs every
morning, and after 30 minutes, she has run 3.5 miles.
a. How is Cara's speed represented on the graph?
b. Write a rule for Cara's distance if t represents
the number of hours.
Distance (miles)
c.
If Cara continues to run at this rate, predict
how far she will run in 4 hours.
a. The speed is represented by 7 miles an hour
b. f(t)=7t
c. 28 miles
Rezolvati, in multimea numerelor intregi, inecuatiile
Exercitiul 8 va rog!
When solving integer inequalities, isolate the variable on one side just like an equation. If the inequality involves a negative number, remember to flip the sign.
Explanation:Since the exercise isn't specifically provided, I will walk you through a general process of solving integer inequalities.
First, treat the inequality similar to an equation. You'll need to isolate the variable (usually represented by 'x') on one side of the inequality.
Example 1: Let's say your inequality is x + 3 < 7. You can subtract 3 from both sides to isolate 'x', giving you x < 4.
Example 2: For an inequality like 5x > 30, you'd divide both sides by 5. This gives you x > 6. In both examples, the solution sets are all the integers less than 4 and greater than 6, respectively.
Remember that if you multiply or divide by a negative number, the inequality sign will flip.
Learn more about integer inequalities here:https://brainly.com/question/13298515
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A strong foundation in mathematics is most necessary for which career?
Education
Engineering
Graphic design
Medicine
Answer:
b
Step-by-step explanation:
Sabina makes $2,000 per month. She spends $150 on store credit and $250 on an auto loan each month. Does she have excessive debt?
A.)Yes, because her debt-to-income ratio is higher than 36 percent.
B.)No, because her debt-to-income ratio is lower than 36 percent.
C.)No, because her debt-to-income ratio lower than 42 percent.
D.)Yes, because her debt-to-income ratio is 50 percent.
Answer:
A or B
Step-by-step explanation:
Answer:
Should be B, No because her debt-to-income ratio is lower than 36 percent.
Step-by-step explanation:
if point c is between points a and b, then ac+cb=
Answer:
Step-by-step explanation:
ac + cb = ab
What actual floor number do each student live on? Show your work also.
Heathe lives halfway up: 42 / 2 = 21st floor.
Raveen = 42 x 4/7 = 168/7 = 24th floor.
Alveera = 42 x 3/14 = 126/14 = 9th floor.
Rafi = 42 x 4/6 = 168/6 = 28th floor.
Suha = 28-24 = 4 /2 = 2 = 24+2 = 26th floor.
Arabi = 42 x 2/3 = 84/3 = 28th floor
What are the solutions for x to the equation (x-3)(x+8)=0
For this case we have a factored expression, of a second degree equation:
([tex](x-3) (x + 8) = 0[/tex]
To find the solutions:
[tex]x-3 = 0[/tex]we add 3 to both sides of the equation:
[tex]x=3[/tex]
[tex]x+8=0[/tex]We subtract 8 on both sides of the equation:
[tex]x = -8[/tex]
Thus, the solutions of the equation are:
[tex]x_ {1} = 3\\x_ {2} = - 8[/tex]
Answer:
[tex]x_ {1} = 3\\x_ {2} = - 8[/tex]
I need help please. Very plz correct answer plz.
Answer:
Step-by-step explanation:
The 9 is in the tens place in 75, 293 so rounding to the tens place means we need to round to the place the 9 is in, and we can sort of disregard the number after that, which is a 3. It will eventually round to a 0, but if that number is 5 or greater, it rounds the 9 up. It's a 3, so the 9 stays a 9: 75, 290.
The 2 is in the hundreds place, so just like above, we can change everything after the 2 to a 0, after we use the 9 for rounding. 9 is greater than 5, so the 2 rounds up to a 3: 75, 300.
The 5 is in the thousands place, so everything after that will become 0's, but use the 2 for rounding first. 2 is less than 5, so the 5 stays a 5: 75, 000.
Monica runs on a treadmill at an average speed of 7.5 miles per hour for 15 minutes. If, the next day, she runs the same distance at a speed of 8 miles per hour, what is the average time taken?
Answer:
Option 2: 14.06 minutes
Step-by-step explanation:
For the first scenario, we will convert the minutes into hours first to get all the quantities in same unit
So,
15 minutes = 1/4 hours = 0.25 hours
Speed = 7.5 miles per hour
Now using the speed, distance and time formula
Speed = distance/time
[tex]Speed = \frac{distance}{time}[/tex]
[tex]7.5 = \frac{distance}{0.25}[/tex]
[tex]7.5 * 0.25 = Distance[/tex]
Distance = 1.875 miles
So the distance for 1st day is 1.875 miles.
For next day
Speed = 8 miles per hour
Distance = 1.875
So,
[tex]speed = \frac{distance}{time}[/tex]
[tex]8 = \frac{1.875}{time}[/tex]
[tex]time = \frac{1.875}{8}[/tex]
[tex]time = 0.234375 hours[/tex]
Converting the hours into minutes will give
0.234375 * 60 min = 14.0625 minutes
Rounding off to two decimals = 14.06 min
So 2nd option is correct..
Show all work to multiply (3+ V16)(6-
64).
Regroup terms
(3 + 16V)(6 - 64)
Simplify 6 - 64 to -58
(3 + 16V) * -58
Simplify
= -58(3 + 16V)
Use the vertical line test to determine if the relation is a function!! HELP NEEDED!!
Below is an image of the vertical line test.
The vertical line test is passed only when a vertical line only intersects the graph once. As you can see this graph intersects the graph twice, and therefore is not a function.
The answer you selected was correct!
Hope this helped!
Find the measures of the interior angles.how do you find the measures of the interior angles
Answer:
'm guessing you mean with parallels and a transversal. If this is the case, then find he angle that is either
a; supplementary (creating a flat angle, 180 degrees) or
b; complimentary (creating a 90 degree angle)
Step-by-step explanation:
subtract the supplementary/complimentary angle from either 180 or 90 and the difference is your answer. Hope I helped!
* * * * *
More likely the question is concerned with the interior angles of a polygon. If the polygon is irregular then there is no simple answer. An interior angle can have any value.
However, if it is a regular polygon then the question can be answered. The sum of all the exterior angles is 360 degrees - irrespective of the number of sides (or vertices). Suppose the polygon has n sides/vertices.
Then, since it is regular, each exterior angle is 360/n. Therefore, each interior angle is 180-360/n degrees.
The sum of interior angles of a polygon can be found using the formula (n-2) x 180 degrees.
To find the measures of the interior angles of a polygon, you must first consider the type of polygon you're dealing with. For a triangle, the sum of the interior angles is always 180 degrees. If you're working with another type of polygon, such as a quadrilateral, the sum of the interior angles is greater, and there's a simple formula to follow: (n-2) imes 180 degrees, where n represents the number of sides of the polygon. This means that for a quadrilateral, with four sides, the sum of the interior angles would be (4-2) * 180 degrees, which equals 360 degrees.
When it comes to alternate interior angles, these are pairs of angles found on the inside of two lines that are cut by a transversal. If the lines are parallel, the alternate interior angles are equal in measure. For example, if you have two parallel lines cut by a transversal forming angle a and angle f, then a and f would be alternate interior angles and thus, would have the same measure.
The sum of the exterior angles in any polygon is 360 degrees, regardless of the number of sides. When finding the measure of an exterior angle, knowing the measure of its corresponding interior angle can be helpful because the interior and exterior angles form a linear pair (adding up to 180 degrees). Therefore, if the interior angle is 150 degrees, the exterior angle would be 180 degrees - 150 degrees, which equals 30 degrees.
Would an experience downhill skier want the slope of the hill to be 1/10 or 9/10? Why?
Answer:
9/10
Step-by-step explanation:
step 1
Compare the slopes
[tex]1/10=0.10[/tex]
[tex]9/10=0.9[/tex]
[tex]0.9 > 0.10[/tex]
therefore
An experienced skier would like the 9/10 hill slope because it is steeper, while the 1/10 is a softer slope.
Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and a height of 13 inches?
With the height of the rectangular box, the baton can fit diagonally in the box.
The length of the baton that Kylie needs to pack = 38 inches
The width of the rectangular box = 13 inches
The length of the rectangular box = 35 inches
The height of the rectangular box = 13 inches
Comparing the dimensions:
The baton is 38 inches long and longer than the length and width of the box.
The height of the box is 13 inches, making the box greater than the length of the baton diagonally.
Thus, the baton will fit in the box diagonally.
10+13h-6-4h+9+12h simplified
Answer:
[tex]\boxed{\bold{21h+13}}[/tex]
Explanation:
Group Like Terms
= [tex]\bold{13h-4h+12h+10-6+9}[/tex]
Combine Similar Elements: [tex]\bold{13h-4h+12h=21h}[/tex]
= [tex]\bold{21h+10-6+9}[/tex]
Subtract: [tex]\bold{10-6+9=13}[/tex]
= [tex]\bold{21h+13}[/tex]
Mordancy.
how many solutions exist for the givien equation 3(x+10)+6=3(x+12)
For this case we solve the following equation:
[tex]3 (x + 10) + 6 = 3 (x + 12)[/tex]
We apply distributive property to the terms within parentheses:
[tex]3x + 30 + 6 = 3x + 36[/tex]
We add similar terms:
[tex]3x + 36 = 3x + 36\\36 = 36[/tex]
Since 36 equals 36, then the equation will always be true for any value of x.
ANswer:
Infinite solutions
Another Urgent one!! you know the drill. HEEEEEEEEEEELP
Answer:
Step-by-step explanation:
It is a right angle triangle with height and base = 3. The 4.24, for area, is not relevant.
Area = h * b / 2
Area = 3 * 3/2
Area = 9/2
Area = 4.5
Answer:
4.5 units
Step-by-step explanation:
A=1/2(b×h)
b=base
h=height
plug in what we know ...
A=1/2 (3×3)
A=1/2 (9)
A=4.5
solve the proportional equation below 6/2=(v-8)/(v-3)
½ = v; multiply the divisor to remove the variable from the denominator.
The choices for the first one is
1/4
1
5/4
Choice for the second one is
(3i square root 7)/4
(i square root 21)/2
(square root 112)/4
Answer:
[tex]\large\boxed{\dfrac{5\pm3\sqrt7}{4}}[/tex]
Step-by-step explanation:
[tex]m^2-\dfrac{5}{2}m=-\dfrac{11}{2}\qquad\text{add}\ \dfrac{11}{2}\ \text{to both sides}\\\\m^2-\dfrac{5}{2}m+\dfrac{11}{2}=0\qquad\text{multiply both sides by 2}\\\\2m^2-5m+11=0[/tex]
[tex]\text{Use the quadratic formula:}[/tex]
[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{We have}[/tex]
[tex]a=2,\ b=-5,\ c=11[/tex]
[tex]\text{substitute:}[/tex]
[tex]\sqrt{b^2-4ac}=\sqrt{(-5)^2-4(2)(11)}=\sqrt{25-88}=\sqrt{63}=\sqrt{9\cdot7}=\sqrt9\cdot\sqrt7=3\sqrt7\\\\m=\dfrac{-(-5)\pm3\sqrt7}{2(2)}=\dfrac{5\pm3\sqrt7}{4}[/tex]
Solve the equation 8-6z=26
8-6z=26
8-8-6z=26-8
-6z=18
divide by -6 for -6z and 18
-6z/-6=18/-6
z=-3
Check answer by using substitution method
8-6(-3)=26
8+18= 26
26=26
Answer is z=-3
Answer:
answer - 3
Step-by-step explanation:
8 - 6z = 26 Subtract 8 from both sides.
8-8 - 6z = 26 - 8
- 6z = 18 Divide by - 6
-6z/-6 = 18/-6 Do the division. Note: you must leave the letter with 1 in front of it.
z = - 3
Whitney needs to borrow $200 for school supplies. If she borrows the same amount from 5 friends, which equation will show now much she owes each friend? $200 ÷ 5 -$200 ÷ 5 $200 ÷ (-5) -$200 ÷ (-5)
Answer:
She'll owe each friend $40.
Step-by-step explanation:
That's a total of $200 borrowed from 5 friends, which comes to:
$200
------------- = $40/friend
5 friends
Answer: A. $200 ÷ 5
Step-by-step explanation:
Sorry about the answer above mine.. that's kinda embarrassing considering how easy this question is. Anyways, the correct answer is A because the outcome will be 40 which is what we want because if you did the math for any other answer, the outcome will be negative.
Please help answer this geometry
Answer:
a. [tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]
b. [tex]100x+225y=100x+225[/tex] Which means it is an identity
Step-by-step explanation:
The Pythagorean Theorem states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.
If in a right triangle there are legs of length a, and b, and the measure of the hypotenuse is c, then The following relationship is fulfilled:
[tex]a^{2} +b^{2}=c^{2}[/tex]
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram
From the exercise shown in the image, we can get the values of a, b, and c.
a = 8x+12y, b = 6x+9y, and c = 10x+15y
Write an equation using the Pythagorean Theorem
We obtain:
[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]
b. Transform each side of the equation to determine if it is an identity.
In mathematics, an identity is the realization that two objects that are mathematically written differently, are in fact the same object. In particular, an identity is an equality between two expressions, which is true whatever the values of the different ones are.
So, we transform each side of the equation
[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]
[tex](8x)^{2} +(12y)^{2} +(6x)^{2} +(9y)^{2}= (10x)^{2}+(15y)^{2}\\64x+144y+36x+81y=100x+225y\\(64x+36x)+(144y+81y)=100x+225y\\100x+225y=100x+225[/tex] Which means it is an identity
.
Answer:
a). (10x + 15y)² = (8x + 12y)² + (6x + 9y)²
b). It's an identity
Step-by-step explanation:
a). Pythagoras theorem says
(Hypotenuse)² = Height² + Base²
Therefore, form the given picture
(10x + 15y)² = (8x + 12y)² + (6x + 9y)² will be the equation.
b). For an identity we have to prove Right hand side of the equation(R.H.S.) = Left hand side of the equation(L.H.S.)
Now we solve the L.H.S. of the equation
(10x + 15y)²
= 100x² + 225y² + 300xy [ (a + b)² = a²+ b² + 2ab
Now we solve R.H.S. of the equation
(8x + 12y)² + (6x + 9y)²
= 64x²+ 144y² + 36x² + 81y² + 108y + 192xy + 108xy
= 100x² + 225y²+ 300xy
Therefore, L.H.S. = R.H.S.
The given equation is an identity.
Simplify 4!
A.24
B.10
C.9
D.4
Answer:
A. 24
Step-by-step explanation:
! = 2 multiplied by the maximum
So, 4! = 2 × 3 × 4 [24]
This is what is known as Factorials.
I am joyous to assist you anytime.
Answer:
[tex]\Huge\boxed{24}[/tex]
Step-by-step explanation:
Apply by the factorial rule.
[tex]\displaystyle 4!=1*2*3*4[/tex]
Then multiply to find the answer.
[tex]\displaystyle 1*2*3*4=4*3=12*2=24*1=24[/tex]
24, which is our answer.
Paul is going to have the exterior of his home painted. Painting USA charges $75.00 to come out and evaluate the house plus $25.00 per hour of labor. Upscale Home Painting does not charge to evaluate the house. However, they charge $40.00 per hour.
If it takes 25 hours to paint Paul’s house, the most cost effective company will be
Answer:
Painting USA is the most cost effective company.
Step-by-step explanation:
Painting USA company charges:
$75.00 to evaluate the house
Plus, $25.00 per hour of labor.
Total number of hours taken to paint the house is 25 hrs
Total cost here = $75.00 + $25.00(25) = $700.00
Upscale Home Painting company charges:
$0.00 to evaluate the house
$40.00 per hour of labor.
Total number of hours taken to paint the house is 25 hrs
Total cost here = $0.00 + $40.00(25) = $1000.00
So Painting USA is the most cost effective company since it charges $700.00 which is less that Upscale Home Painting company's painting charges of $1000.00.
Answer:
Painting USA
Step-by-step explanation:
They will charge 700
Find x when F(x)=10
f(x)=2x-6
just substitute 10 into the equation
10=2x-6
add 6 to both sides
16=2x
divide both sides by 2
x=8
How is the graph of y= 1/3x related to its parent function y=1/x
A)It is horizontally stretched by a factor of 3 and reflected over the x-axis.
B)It is horizontally stretched by a factor of 3 and reflected over the y-axis.
C)It is horizontally compressed by a factor of 3 and reflected over the x-axis.
D)It is horizontally compressed by a factor of 3 and reflected over the y-axis.
B it is horizontally stretched by a factor of of 3 and reflected over the y
Answer:
itś C on edge :)
Step-by-step explanation:
Which of the following is the solution to the quadratic equation -x2-5x-6=0 using the quadratic formula
Answer:
x = -2; x = -3
Step-by-step explanation:
(-x - 3)(x + 2) = 0
(-x - 3) = 0
x = -3
(x + 2) = 0
x = -2
What is the range of the function? f(x) = -2^x + 1
{y|1 > y}, (-∞, 1); you did not specifically mention what notation you needed, so I wrote both [Internal Notation and Set Notation].
Answer:
all real numbers less than or equal to 0
Step-by-step explanation:
EDGE 2020
which graph represents the piece wise- defined function f(x) =
Answer:
right-most fourth graph
Step-by-step explanation:
Given:
f(x)= -x+4 for 0≤x<3
i.e. from x=0 till x=3 the graph is linear line
then
f(x) = 5 for x≥3
i.e. at x=3 and onward graph is a straight line with y-axis point of 5 !
Answer:
The fourth graph, from left to right, is the correct answer.Step-by-step explanation:
The given piecewise function is
[tex]f(x)=\left \{ {{-x+4 \ ; \ 0\leq x<3} \atop {5 \ ; \ x\geq3 }} \right.[/tex]
Notice that the domain of the function specifies that, from zero to three, the function represents a decreasing (because the variable is negative) straight line. When the function is defined from 3 to infinite, the function is a constant of 5.
So, the right graph must shows first a decreasing line, where the initial point is solid and the final point is empty, as the fourth fraph (from left to right), then it must show a horizontal line with an initial point solid.
Therefore, the fourth graph, from left to right, is the correct answer.
Nita needs at least $85 to buy a skateboard. She already has $61 Which graph best represents all the possible dollar amounts that it can save to buy a
Skateboard?
I believe the answer would be B. Hope this helps!
Graph B. best represents all the possible dollar amounts that it can save to buy a Skateboard.
What is a number line?calculation:-
amount Nita needed to buy a skateboard=$85
amount had=$61
∴ amount Nita needed more= $85-$61
=$24
A number line is a horizontal line that has numbers in equal intervals.The numbers included on the line can be negative or positive taking zero as a reference point at the center called the origin.The horizontal straight lines in which the integers are placed in equal intervals increase as we go right.The horizontal straight lines in which the integers are placed in equal intervals decreases as we go left.Learn more about the number line here:https://brainly.com/question/24644930
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