Answer:
B) Both functions have the same domain.
C) Both functions have the same x-intercepts.
D) Both functions are decreasing on the interval (−∞, −2).
Step-by-step explanation:
step 1
Find the vertex of f(x)
we know that
The x-coordinate of the vertex is the midpoint of the roots
we have
x=-1 and x=-3
so
the midpoint is
(-1-3)/2=-2
The y-coordinate of the vertex is -4 (because the range is [−4, ∞))
therefore
The vertex of f(x) is the point (-2,-4)
Is a vertical parabola open upward
The vertex is a minimum
The domain is all real numbers
step 2
we have
[tex]g(x)=2x^2+8x+6[/tex]
Find the vertex
Factor the leading coefficient
[tex]g(x)=2(x^2+4x)+6[/tex]
Complete the square
[tex]g(x)=2(x^2+4x+4)+6-8[/tex]
[tex]g(x)=2(x^2+4x+4)-2[/tex]
Rewrite as perfect squares
[tex]g(x)=2(x+2)^2-2[/tex]
Is a vertical parabola open upward
The vertex is the point (-2,-2)
The domain is all real numbers
The range is the interval [−2, ∞)
Find the x-intercepts
For g(x)=0
[tex]0=2(x+2)^2-2[/tex]
[tex]2(x+2)^2=2[/tex]
[tex](x+2)^2=1\\x+2=\pm1\\x=-2\pm1[/tex]
so
The roots or x-intercepts are
x=-1 and x=-3
Verify each statement
A) Both functions have the same vertex
The statement is false
The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)
B) Both functions have the same domain.
The statement is true
The domain is all real numbers
C) Both functions have the same x-intercepts
The statement is true (see the explanation)
D) Both functions are decreasing on the interval (−∞, −2)
The statement is true
Because the x-coordinate of the vertex is the same in both functions, and both functions open upward
Answer:
The answer is A
Step-by-step explanation:
A pack of cinnamon-scented pencils sells for $5.00. What is the sales tax rate if the total cost of the pencils is $5.40?
Answer:
The sales tax rate is 5%
Given:
Sales price = 5.00
Total amount paid = 5.25
Sales tax value = Total amount paid - sales price
= $5.25 - $5.00
Sales tax value = $0.25
Sales tax rate = Sales tax / Sales price
= 0.25/5
Sales tax rate = 0.05 or 5%
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Thanks to taskmasters.
Step-by-step explanation:
tom and jerry have to stuff and seal 63 envelopes for a new marketing campaign. jerry can stuff and seal 15 envelopes in 2 minutes. tom can do 3 envelopes per minutes . how long would it take them if they work together ?
Answer:
5
Step-by-step explanation:
The time taken to stuff and seal 63 envelopes by both Tom and Jerry will be 6 minutes.
Given the Parameters :
Jerry's rate = 15/2 = 7.5 envelopes per minute Tom's rate = 3 envelopes per minuteCombined rate :
Jerry's rate + Tom's rate 7.5 + 3 = 10.5 envelopes per minuteTime taken if they work together :
Total number of envelopes = 63 Total time taken = total number envelopes ÷ combined rate Total time taken = (63 ÷ 10.5) = 6 minutesTherefore, the time taken of they both worked together will be 6 minutes
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What is y=x-4 and y=4x-10
Answer:
x=2, y=-2. (2, -2).
Step-by-step explanation:
y=x-4
y=4x-10
x-4=4x-10
x-4x-4=-10
-3x-4=-10
-3x=-10+4
-3x=-6
3x=6
x=6/3
x=2
y=2-4=-2
Tanya needs to earn another $100 to buy a new cell phone . She works 5 days this week. How much money will she have to earn each day in order to be able to buy the phone?
What is 1/9 (2m - 16) = 1/3 (2m +4)
Answer:
-7
Step-by-step explanation:
Hope it helped!
The perimeter of parallelogram ABCD is 30 cm. AD is 3cm more than twice AB FIND THE LENGTH OF AB
Answer:
4 cm
Step-by-step explanation:
Perimeter of a parallelogram is 2b+2h=30 where b is base and h is height.
if AD is 3cm more than twice AB, then it's 3+2x where x is length of AB.
Input this into the perimeter equation: 2(3+2x)+2(x)=30
Simplify to get 6+6x=30
x=24/6=4
Answer is 4 cm.
Final answer:
The length of AB in the parallelogram is 4 cm after solving the algebraic equation for the given perimeter.
Explanation:
The student is asking us to find the length of AB in a parallelogram ABCD where the perimeter is given as 30 cm, and side AD is 3 cm more than twice the length of AB. We can use algebra to determine the length of AB in a few steps.
Let's denote AB as 'x'. Since opposite sides of a parallelogram are equal, AD and BC will equal '2x + 3' while CD will also equal 'x'. The formula for the perimeter (P) of a parallelogram is P = 2(AB + BC), so substituting our known values and solving for 'x' will give us the length of AB.
Putting it all together:
P = 2(AB + BC)30 cm = 2(x + 2x + 3)30 cm = 2(3x + 3)30 cm = 6x + 630 cm - 6 = 6x24 cm = 6xx = 4 cmTherefore, the length of AB is 4 cm.
25. CHARITY In the first hour of a charity auction, $4800 was raised. This was at most
$1200 more than was raised in the second hour of the auction. Write an inequality that
represents the amount raised in the second hour.
Answer:
6000
Step-by-step explanation:
if you do 200+800=1000 and the if you do 4000+1000=5000+1000=6000
The inequality that represents the amount raised in the second hour of the charity auction is x ≤ 6000.
Explanation:To represent the amount raised in the second hour of the charity auction, let's use the variable x. According to the information given, the amount raised in the first hour is $4800, which is at most $1200 more than the amount raised in the second hour. This can be represented as the inequality:
x ≤ 4800 + 1200
Simplifying the inequality, we have:
x ≤ 6000
Therefore, the inequality that represents the amount raised in the second hour is x ≤ 6000.
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Helpppp pleaseeeeeeeeeeeeeee
Answer:
Find below the calculations of the two areas, each with two methods. The results are:
Upper triangle:[tex]Area=5000\sqrt{3}units^2[/tex]
Lower triangle:[tex]Area=14,530m^2[/tex]
Explanation:
A) Method 1
When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:
[tex]Area=side_1\times side_2\times sin(\alpha)[/tex]
Where, [tex]\alpha[/tex] is the measure of the included angle.
1. Upper triangle:
[tex]side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2[/tex]
2. Lower triangle:
[tex]side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2[/tex]
B) Method 2
You can find the height of the triangle using trigonometric properties, and then use the very well known formula:
[tex]Area=(1/2)\times base\times height[/tex]
Use it for both triangles.
3. Upper triangle:
The trigonometric ratio that you can use is:
[tex]sine(\alpha)=opposite\text{ }leg/hypotenuse[/tex]
Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:
[tex]sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units[/tex]
[tex]Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2[/tex]
3. Lower triangle:
[tex]sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2[/tex]
[tex]Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\ Area=14,529.96m^2\approx 14,530m^2[/tex]
a needle palm tree at the park is growing an average of 4.35 cm per day. A cabbage palm tree next to it is growing an avrege of 1.26 in per day. which? one is growing faster?
Answer:
The needle palm tree is growing faster.
Step-by-step explanation:
The rate of growth of needle palm tree = 4.35 cm / day
The rate of growth of cabbage palm tree = 1.26 cm /day
From the given data we can clearly see ,
4.35 > 1.26
So the needle palm tree is growing faster.
A school is designing two rectangular parking lots. The second parking lot is being designed so that its perimeter is 3/4 of perimeter of the first parking lot. Determine the Perimeter of the second parking lot.
The perimeter of second plot is 180 feet
Solution:
Given that,
The second parking lot is being designed so that its perimeter is 3/4 of perimeter of the first parking lot
Find the perimeter of first plot:Perimeter = 2(length + width)
From given figure in question,
length = 40 feet
width = 80 feet
Therefore,
Perimeter = 2(40 + 80)
Perimeter = 2(120) = 240
Thus, we got,
Perimeter of first parking plot = 240 feet
Also, given that,
[tex]\text{Perimeter of second plot }= \frac{3}{4} \times \text{Perimeter of first parking plot}\\\\\text{Perimeter of second plot }= \frac{3}{4} \times 240\\\\\text{Perimeter of second plot }= 180[/tex]
Thus perimeter of second plot is 180 feet
To find the perimeter of the second parking lot, you multiply the perimeter of the first parking lot by 3/4. For example, if the first parking lot has a perimeter of 100 meters, the second would be 75 meters.
Explanation:The problem revolves around the concept of perimeter, specifically of a rectangle. The perimeter of a rectangle is given by the formula 2*(length + width). Now, according to the question, the perimeter of the second parking lot is three-quarters (3/4) that of the first. So, if we denote the perimeter of the first parking lot as 'P', then the perimeter of the second parking lot would be (3/4)*P.
For instance, if the perimeter of the first parking lot is 100 meters, then the perimeter of the second parking lot would be (3/4)*100 = 75 meters. Hence, the second parking lot's perimeter is determined by the first parking lot's perimeter, reduced by a quarter.
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The length of a rectangle is six more than triple the width. If the perimeter is 156 inches, find the dimensions.
The width is
inches.
The length is
inches.
Answer:
lenght= 60 inches
width = 18 inches
Step-by-step explanation:
parameter = 2(L+B)
let lenght be x
width be y
so
x = 3y+6
let's put this in formula
156 = 2( x+y )
156 = 2( 3y+6 + y )
156 = 2 ( 4y + 6 )
156/2 = 4y + 6
78 = 4y + 6
4y = 78-6
4y = 72
y = 72/4
y = 18
so width is 18 inches
and lenght is 3*18+6 = 60 inches
The width of the rectangle is 18 inches, and the length is 54 inches.
Explanation:Let's denote the width of the rectangle as 'w'. According to the problem, the length of the rectangle can be expressed as 3w + 6. The problem also states that the perimeter of the rectangle is 156 inches. Remember that the formula for the perimeter of a rectangle is 2(length + width). Given that the length is expressed as 3w + 6 and the width as w, we can plug these values into the perimeter formula: 2(3w + 6 + w) = 156. Simplifying, we get 8w + 12 = 156. Isolating w, we have w = 18 inches. We also need to find the length, which is 3w + 6 = 54 inches. This gives us a width of 18 inches and a length of 54 inches.
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Which is greater 2.6 or 4.07
Answer:
4.07 is greater
Answer:
4.07
Step-by-step explanation:
You were looking at a map with a scale 1inch =40 miles if two towns are separated on the map by 6 inches what is the actual distance between them
Answer:
240 miles
Step-by-step explanation:
The actual distance between two towns, which are separated by 6 inches on a map with a scale of 1 inch to 40 miles, is 240 miles.
Explanation:The subject of this question is Mathematics, specifically focusing on understanding how map scales work. In this case, the map scale is 1 inch equals 40 miles. This means, for every inch on the map, it represents 40 miles in actual distance.
To find out the real distance between two towns that are separated by 6 inches on the map, you multiply the map scale distance (40 miles) by the number of inches (6).
Which is, 6 inches x 40 miles = 240 miles.
So, the actual distance between the two towns is 240 miles.
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decimal and integers are both classified as ______ numbers
Answer:whole numbers
Step-by-step explanation:
Decide whether 3(x-2)+5 and 3x+1 are equivalent expressions. explain how you know.
Answer:
Not equivalent
Step-by-step explanation:
Let,
3(x-2) + 5 = 3x + 1
By Multiplying
3x - 6 + 5 = 3x + 1
3x - 1 = 3x + 1
So, the expressions are not equal
Multiply simplest form
Answer:
4 [tex]\frac{8}{9}[/tex]
Step-by-step explanation:
2 [tex]\frac{1}{5}[/tex] × 2 [tex]\frac{2}{9}[/tex]
[tex]\frac{11}{5}[/tex] × [tex]\frac{20}{9}[/tex] = [tex]\frac{220}{45}[/tex] = 4 [tex]\frac{8}{9}[/tex]
A line passes through point (3,7)and has a slope of3/4
Answer:
look at picture shown.
Translate to an algebraic expression the sum of a and 8
Answer:
umm give me more examples
Step-by-step explanation:
Answer:
x=8+a
Step-by-step explanation:
sum of a and 8
x=a+8
when they say the sum of you add an equal sign
and when they said of a and 8 it means that whatever the sum is its equal to a+8
since the sum wasn't mentioned the sum will be known as a variable
lets put x as the variable
How do you do the last question using the quadratic formula?
Answer:
[tex]x = -1[/tex]
Step-by-step explanation:
To do the last question using the quadratic formula, you first need the equation in standard form.
ax² + bx + c = 0.
To convert 2(x - 2)(x + 1) = x² - 4x - 5 into standard form, simplify by expanding and collecting like terms. Then, have the equation equate to "0" by moving everything to one side.
2(x - 2)(x + 1) = x² - 4x - 5 Expand brackets first using FOIL
2(x² + x - 2x - 2) = x² - 4x - 5 Collect like terms in brackets (x - 2x = -x)
2(x² - x - 2) = x² - 4x - 5 Distribute, multiply bracket numbers by "2"
2x² - 2x - 4 = x² - 4x - 5 Now make the equation equal 0
2x² - 2x - 4 - x² = x² - 4x - 5 - x² Subtract x² from both sides
x² - 2x - 4 = -4x - 5 "x²" eliminated from the right side. Simplify left side.
x² - 2x - 4 + 4x = -4x - 5 + 4x Add 4x to both sides.
x² + 2x - 4 = -5 "4x" eliminated from right side. Simplify left side.
x² + 2x - 4 + 5 = -5 + 5 Add 5 to both sides to eliminate it on the right.
x² + 2x + 1 = 0 Simplified left side.
This is now in standard form. State the "a", "b" and "c" values based on the standard form variables.
a = 1; b = 2; c = 1
Substitute into the quadratic formula
[tex]x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}[/tex] (Please ignore the Â, it's a formatting error)
[tex]x = \frac{-2±\sqrt{2^{2}-4(1)(1)} }{2(1)}[/tex] Simplify the square root
[tex]x = \frac{-2±\sqrt{0} }{2}[/tex] The square root of 0 is 0.
[tex]x = \frac{-2}{2}[/tex] The numerator can only be -2. Simplify the fraction
[tex]x = -1[/tex] Only one answer for "x".
Whenever the square root equals "0", there will only be one answer for "x".
What is a of n equal to?
What is the 10tn term in the sequence?
Answer:
nth term, [tex]T_n=1(2)^n^-^1[/tex]
10th term, [tex]T_1_0=512[/tex]
Step-by-step explanation:
From the question;
We are given the first term, [tex]a_1=1[/tex]The common ratio, r = 2We are required to write the formula of getting nth term and find the 10th term of the sequence;
We need to know that for nth term in a geometric sequence, we use the formula;[tex]T_n=a_1r^n^-^1[/tex]
Therefore, in this case;
nth term will be given by;
[tex]T_n=1(2)^n^-^1[/tex], where n is the term in the sequence;
Therefore;
To get the 10th term of the sequence;
[tex]T_1_0=1(2)^1^0^-^1[/tex]
[tex]T_1_0=1(2)^9[/tex]
[tex]T_1_0=512[/tex]
Therefore, the tenth term of the sequence is 512
Solve 13 + x> 11. Enter your answer as an inequality.
HINT
Answer:
x>-2
Step-by-step explanation:
13+x>11
x>11-13
x>-2
#12 wire is 80.81 mils. What is the diameter in inches? Round your answer to five decimal places.
The diameter of the #12 wire is approximately 0.08081 inches.
Calculating the diameter involves converting the measurement in mils to inches, since an inch is 1000 mils. Once we have the diameter in inches, we can round the answer to five decimal places, as instructed.
So, after performing the necessary calculations, the diameter of the #12 wire with a measurement of 80.81 mils is approximately 0.08081 inches.
A mil is a unit equal to one thousandth of an inch (0.001 inch). To convert mils to inches, we divide the mil measurement by 1000. So, 80.81 mils is equal to
80.81 / 1000 = 0.08081 inches.
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Final answer:
The diameter of the #12 wire in inches is 0.08081 inches, after converting 80.81 mils using the mil to inch conversion factor. The resistance of a wire changes with its gauge; a wire of one gauge number lower would have about 20% less resistance compared to the next higher gauge for the same length.
Explanation:
To convert the diameter of a #12 wire from mils to inches, you need to understand that one mil is equivalent to 0.001 inches. The stated diameter of the #12 wire is 80.81 mils.
By multiplying the value in mils by the conversion factor, we can find the diameter in inches:
80.81 mils × 0.001 inches/mil = 0.08081 inches.
Therefore, the diameter of #12 wire in inches is 0.08081 inches, rounded to five decimal places.
Discussing the resistance and resistivity of copper wire, it's known that resistance is proportional to the length of the wire and inversely proportional to the cross-sectional area.
Gauge sizes have a standardized series of diameters which differ by about 20% from one gauge to the next, which means that a wire with one gauge number lower (higher in diameter) would have approximately 20% less resistance than one of the next higher gauge (smaller in diameter) for the same length of wire.
What is the diameter of a cylinder that has a volume of 237 cubic units and a height of 3 units? Show your calculations.
Answer:
The Diameter of the cylinder is 10.29 units
Step-by-step explanation:
Given:
Volume of the Cylinder = 237 cubic units
Height of the Cylinder = 3 units
To Find :
Diameter = ?
Solution:
The Volume of the cylinder = [tex]\pi r^2 h[/tex]
where
r is the radius
h is the height
On substituting the values
[tex]237 = \pi (r)^2 (3)[/tex]
[tex]\frac{237}{ 3 \pi} = r^2[/tex]
[tex]\frac{79}{\pi} = r^2[/tex]
[tex]25.146 = r^2[/tex]
r = 5.014 units
Noe the diameter is = 2r = 2( 5.014) = 10.29 units
At a gas station a car wash costs $6.50 and gas is $2.75 a gallon. Enter the greatest number or gallons of gas you can purchase in addition to a car wash and not spend more than $23.00
Answer:
6 gallons
Step-by-step explanation:
23.00-6.50=16.50
16.50/2.75=6
a teacher uses 36 centimeters of tape to hang up 9student projects. At this rate, how much tape would the teacher need to hang up 10 student projects?
Please help me asap i will mark branlist please explain
Answer:
I think it's B. (-1,3)
Step-by-step explanation:
The solution is the point the two lines intersect each other.
The answer is (-1,3)
Find the tenth term in the sequence: 12, 10, 8, ...
Answer:
-6
Step-by-step explanation:
12, 10, 8, 6, 4, 2, 0, -2, -4, -6
Subtracting two each time
Answer:
-6
Step-by-step explanation:
It subtracts 2 each time in the sequence.
The first term is 12.
You subtract 2 ten times to get to the tenth number in this sequence. 10*2 = 20. 12-20 = -6
Chas builds a circular pen for his dog. The radius
of the pen is 9 feet. How much fencing did Chas
use for the pen?
A 28.26 feet
C 63.585 feet
B 56.52 feet
D 254.34 feet
Do you need to
the circumfere
or the area of
circle?
Skye chose A as the correct answer. How did she get that answer?
Answer:
when ever they say fencing it is perimeter i will send rhe rest later
she did 2×pie (3.14 according to the question )×radius (9)
Answer:
The correct answer is 56.52 feet
Step-by-step explanation:
(I know the question is supposed to be about how skye got the answer but if you wanted to know the real answer im here for you).
PLEASE ANSWER
What is the slope of the graph?
Answer:
The slope is 5/3
Step-by-step explanation:
In order to find the slope from a graph, you have to use the method called "rise over run". You do this by looking at the point (0,-1). and going up on the y axis and counting until its on the SAME y axis for the next point which is at (3,4). If you count from -1 to 4, you'll get 5, which is the rise number. Next you have to solve the "run" number. Now that we already have our rise number start from (0,4) and count how many ticks/counts it takes to move the x axis to the point (3,4). It takes 3 counts. Since it's called rise/run. You put 5 at the top, and 3 at the bottom.
[tex]\frac{5}{3}[/tex]
Hope this helps :)
if f(x)=2x-5 and g(x)=x^2+1, what is g(f(x))
Answer:
4x² - 20x + 26
Step-by-step explanation:
To evaluate g(f(x)), substitute x = f(x) into g(x), that is
g(2x - 5 )
= (2x - 5)² + 1 ← expand factor using FOIL
= 4x² - 20x + 25 + 1
= 4x² - 20x + 26