volume of the speaker= 22 cubic inches
Step-by-step explanation:
The formula to find this question is V= 1/3 BHWHERE H =6 INCHESArea of base = 11 square inchestherefore,v= 1/3 (11) (6)volume of the speaker= 22 cubic inchesWhat is the average rate of change for ƒ(x) = −4x + 40 over the interval 1 ≤ x ≤ 3?
Answer:
The average rate of change is = - 4
Step-by-step explanation:
If y = f(x) is a function then the average rate of change for f(x) between the interval a ≤ x ≤ b is given by
[tex]\frac{f(b) - f(a)}{b - a}[/tex].
Now, in this case the function is given by f(x) = - 4x + 40 and the interval is 1 ≤ x ≤ 3.
Therefore, f(1) = - 4(1) + 40 = 36 and f(3) = - 4(3) + 40 = 28
So, the average rate of change is = [tex]\frac{28 - 36}{3 - 1} = - \frac{8}{2} = - 4[/tex] (Answer)
Answer:
−30
Step-by-step explanation:
−30 is the average rate of change for ƒ(x) = −4x + 40 over the interval 1 ≤ x ≤ 3.
ƒ(b) − ƒ(a)
b − a
= ƒ(3) − ƒ(1)
3 − 1
= −24 − 36
2
= −60
2
= −30
Which option gives f(x) = x² - 4x - 12 rewritten in vertex form as well as the function's correct axis of symmetry ?
f(x) = (x - 2)² - 16, x = - 16
f?(x) = (x + 2)(x - 6), x = 6
f(x) = (x + 2)(x - 6), x = -2
f(x) = (x - 2)² - 16, x = 2
y
=
−
(
x
−
2
)
2
+
16
is the vertex form
Explanation:
The vertex form of a quadratic function is given by
y
=
a
(
x
−
h
)
2
+
k
where (h, k) is the vertex of the parabola.
when written in vertex form
(h, k) is the vertex of the parabola and x = h is the axis of symmetry
the h represents a horizontal shift (how far left, or right the graph has shifted from x = 0)
the k represents a vertical shift (how far up, or down the graph has shifted from y = 0)
Now let convert this
y
=
−
x
2
+
4
x
+
12
into vertex form
y
=
−
x
2
+
4
x
+
12
y
−
12
=
−
x
2
+
4
x
y
−
12
=
−
(
x
2
−
4
x
)
y
−
12
=
−
(
x
2
−
4
x
+
4
−
4
)
y
−
12
=
−
(
x
2
−
4
x
+
4
)
+
4
y
−
16
=
−
(
x
2
−
4
x
+
4
)
y
−
16
=
−
(
x
−
2
)
2
y
=
−
(
x
−
2
)
2
+
16
is the vertex form
show the vertex in the figure below
graph{-x^2+4x+12 [-10.06, 15.25, 6.58, 19.25]} Hope iam right
The function f(x) = x² - 4x - 12 in vertex form is f(x) = (x - 2)² - 16, and the axis of symmetry is x = 2.
To rewrite the function f(x) = x² - 4x - 12 in vertex form and find the axis of symmetry, we need to complete the square. The general vertex form of a quadratic is f(x) = a(x - h)² + k, where (h, k) is the vertex, and the line x = h is the axis of symmetry.
The first step is to factor the coefficient of x², which is 1 in this case, so we can leave it as is. The next step is to rearrange the equation as x² - 4x and then add and subtract the square of half the coefficient of x, which is (4/2)² = 4. Adding and subtracting 4 inside the parentheses gives us:
f(x) = (x² - 4x + 4) - 4 - 12
Now we can rewrite this as:
f(x) = (x - 2)² - 16
This equation is in vertex form, with the vertex at (2, -16), and the axis of symmetry is the line x = 2.
Therefore, the correct option is f(x) = (x - 2)² - 16, with the axis of symmetry being x = 2.
RSTV is a parallelogram. Line RT and Line SV intersect at Q. RQ = 5x+1 and QT = 3x+15. Find QT
QT = 36
Step-by-step explanation:
Step 1 :
Lines RT and SV are the diagonals of the parallelogram RSTV.
Step 2 :
The diagonals of a parallelogram bisect each other . (Properties of a parallelogram)
Step 3 :
Given that the diagonals RT and SV intersect at Q, we have QT = RQ.
=> 5 x + 1 = 3 x + 15
=> 5 x - 3 x = 15 -1
=> 2 x = 14
= > x = 7
Step 4:
QT = 3 x + 15
=> QT = 3 * 7 + 15
=> QT = 21 + 15 = 36
Applying the properties of the diagonal of a parallelogram, the length of QT = 36 units.
Diagonals of a ParallelogramThe diagonals of a parallelogram are always congruent to each other.When the diagonals intersect, they bisect each other, that is, they cut each other into equal segments.Therefore,
RQ = QT
Substitute5x + 1 = 3x + 15
Add like terms5x - 3x = -1 + 15
2x = 14
x = 7
QT = 3x + 15
Plug in the value of xQT = 3(7) + 15
QT = 36
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find the exact value of the eighth term of the geometric sequence: 648,216,72,24
8th term is 0.30
Step-by-step explanation:
Step 1: nth term of a GP = a × r^n-1Step 2: Find r.⇒ r = a2/a1 = 216/648 = 1/3
Step 3: Calculate 8th term. a = 648, r = 1/3 and n = 8⇒ 8th term = 648 × (1/3)^8-1 = 648 × (1/3)^7 = 648/2187 = 0.30
Find the area of the triangle below. Show as much work as possible.
The area of the triangle is (5/12)x²
Step-by-step explanation:
Area of a triangle = 1/2 bhb is the base of the triangle.h is the height of the triangle.Substitute b=(5/6)x and h=x
Area = 1/2[tex]\times[/tex](5/6)x(x)
Area of triangle = (5/12)x²
Make Q the subject of formula.
[tex]T=\sqrt{\frac{PQ}{R} }-R^{2}Q[/tex]
Answer:
Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))
Step-by-step explanation:
Solve for Q:
T = sqrt((P Q)/R) - Q R^2
T = sqrt((P Q)/R) - Q R^2 is equivalent to sqrt((P Q)/R) - Q R^2 = T:
sqrt((P Q)/R) - Q R^2 = T
Add Q R^2 to both sides:
sqrt((P Q)/R) = Q R^2 + T
Raise both sides to the power of two:
(P Q)/R = (Q R^2 + T)^2
Expand out terms of the right hand side:
(P Q)/R = Q^2 R^4 + 2 Q R^2 T + T^2
Subtract Q^2 R^4 + 2 Q R^2 T + T^2 from both sides:
(P Q)/R - Q^2 R^4 - 2 Q R^2 T - T^2 = 0
Collect in terms of Q:
-Q^2 R^4 - T^2 + Q (P/R - 2 R^2 T) = 0
Divide both sides by -R^4:
Q^2 + T^2/R^4 - (Q (P/R - 2 R^2 T))/R^4 = 0
Subtract T^2/R^4 from both sides:
Q^2 - (Q (P/R - 2 R^2 T))/R^4 = -T^2/R^4
Add (P/R - 2 R^2 T)^2/(4 R^8) to both sides:
Q^2 - (Q (P/R - 2 R^2 T))/R^4 + (P/R - 2 R^2 T)^2/(4 R^8) = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4
Write the left hand side as a square:
(Q - (P/R - 2 R^2 T)/(2 R^4))^2 = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4
Take the square root of both sides:
Q - (P/R - 2 R^2 T)/(2 R^4) = sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
Add (P/R - 2 R^2 T)/(2 R^4) to both sides:
Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:
Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt((P^2)/(4 R^10) - (P T)/(R^7)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
Add (P/R - 2 R^2 T)/(2 R^4) to both sides:
Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4))
(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:
Answer: Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))
If the measure is 3= 122, then the m6= ?
122 degrees
58 degrees
68 degrees
28 degrees
Yo sup??
m3 and m6 for a supplementary pair therefore
m3+m6=180
122+m6=180
m6=58
Hope this helps
The required measure of the angle m∠6 is given as 58 degrees. Option B is correct.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
For the bisection of parallel line by transversal line,
Corresponding angles always have an equal measure,
So, ∠2 = ∠6
Now,
∠2 + ∠3 = 180
∠6 + 122 = 180
∠6 = 58°
Thus, the required measure of the angle m∠6 is given as 58 degrees. Option B is correct.
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simplify 3(4x+7)−4(12x−15)
The expression 3(4x+7)−4(12x−15) simplifies to -36x + 81. First distribute the constants to the terms inside the parentheses, then combine like terms.
Explanation:In mathematics, to simplify an algebraic expression like 3(4x+7)−4(12x−15), you need to perform the operations in a certain order, respecting the laws of arithmetic. This is often referred to as simplifying the expression using the distributive property.
First, distribute the 3 to both of the terms in the first set of parentheses: 3 * 4x + 3 * 7 equals 12x + 21.Next, distribute the -4 to both of the terms in the second set of parentheses: -4 * 12x -4 * -15 equals -48x + 60.Combine like terms: 12x - 48x equals -36x. Similarly, 21 + 60 equals 81.So the original expression, 3(4x+7)−4(12x−15), simplifies to -36x + 81.Learn more about Simplifying Algebraic Expressions here:
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A handyman charges $150 plus $25 per hour for painting a house. How much will the costumer have to pay if he paints the house for 13 hours in total?
A.325
B.475
C.1,950
D.1,975
Answer: B
Step-by-step explanation: you multiply 25 x 13 + 150
how to find the height of a square based pyramid when you are given the length of the base sides and the slant height?
Answer:
use the Pythagorean theorem
Step-by-step explanation:
The slant height is the hypotenuse of a right triangle whose legs are the height of the pyramid and the distance from the edge of the base to the center of the pyramid (where the height segment reaches the base).
For h = pyramid height, b = base edge length, s = slant height, the Pythagorean theorem tells you ...
h² + (b/2)² = s²
Solving for h gives ...
h = √(s² -(b/2)²) . . . . . the height of the pyramid
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Hana wants to buy a charm bracelet. Dayton Fine Jewelry charges $17 per charm, plus $62 for the bracelet. Cain Jewelers, in contrast, charges $18 per charm and $60 for the bracelet. If Hana wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. What would the total cost of the bracelet be? How many charms would that be?
Final answer:
To determine the number of charms for the bracelet to cost the same at both jewelry shops, we set up a system of equations and solved it using substitution. We found that Hana will need to add 2 charms, resulting in a total cost of $96 for the bracelet at either shop.
Explanation:
To determine the number of charms Hana can add to her bracelet such that the cost is the same at Dayton Fine Jewelry and Cain Jewelers, we need to set up a system of equations and solve using the substitution method.
System of Equations:
Let x represent the number of charms and y represent the total cost of the bracelet with charms.
Equation for Dayton Fine Jewelry: y = 17x + 62
Equation for Cain Jewelers: y = 18x + 60
Solution Using Substitution:
Set the two equations equal to each other since the cost is the same:Hana will need to add 2 charms to her bracelet, and the total cost of the bracelet will be $96 at either jewelry shop.
PLEASE HELP!
First determine the degree of each polynomial expression below. Explain how you determined this on each expression.Then organize the expressions from least to greatest based on their degree
I. 6x^2
II. 18x^3+5ab-6y
III.8a-5
IV. 4x^3y+3x^2-xy-4
Degree of polynomials:
[tex]6x^2 = 2\\\\18x^3+5ab-6y = 3\\\\4x^3y +3x^2-xy-4 = 4\\[/tex]
Least to greatest based on degree:
[tex]6x^2[/tex]
[tex]18x^3+5ab-6y[/tex]
[tex]4x^3y +3x^2-xy-4[/tex]
Solution:
The degree of the polynomial is the highest degree of any of the terms
Know that the degree of a constant is zero
Option I
[tex]6x^2[/tex]
Here the highest degree is 2 ( x power 2)
In this case, degree of polynomial is 2
Option II
[tex]18x^3+5ab-6y[/tex]
To find the degree of the polynomial, add up the exponents of each term and select the highest sum.
[tex]Degree\ of\ 18x^3 = 3[/tex]
[tex]Degree\ of\ 5ab = 5a^1b^1 = 1+1 = 2[/tex]
[tex]Degree\ of\ 6y = 6y^1 = 1[/tex]
Thus the highest degree is 3
Option III
[tex]8a^{-5}[/tex]
This is not a polynomial
A polynomial does not contain variables raised to negative
Option IV
[tex]4x^3y +3x^2-xy-4[/tex]
To find the degree of the polynomial, add up the exponents of each term and select the highest sum.
[tex]Degree\ of\ 4x^3y = 4x^3y^1=3+1 = 4\\\\Degree\ of\ 3x^2 = 2\\\\Degree\ of\ xy = x^1y^1 = 1+1 = 2\\\\Degree\ of\ 4 = 0[/tex]
Thus highest degree is 4
Then organize the expressions from least to greatest based on their degree
Least to greatest based on degree:
[tex]6x^2[/tex]
[tex]18x^3+5ab-6y[/tex]
[tex]4x^3y +3x^2-xy-4[/tex]
What is r/32=5/8=30/t
Step-by-step explanation:
[tex] \frac{r}{32} = \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: \frac{r}{32} = \frac{5}{8} \\ \\ \therefore \: r = \frac{32 \times 5}{8} \\ \\\therefore \: r = 4 \times 5\\ \\ \huge \orange{ \boxed{\therefore \: r = 20}} \\ \\ \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: t = \frac{8 \times 30}{5} \\ \\ \therefore \: t = 8 \times 6 \\ \\ \huge \purple{ \boxed{ \therefore \: t = 48}}[/tex]
at its highest setting, jeds shower head releases 6.2 gallons of water per minute. Jed took a shower lasting 5 minutes and 12 seconds. What is the maximum amount of water Jed could have used?
Answer:
32.24 gallons
Step-by-step explanation:
From the question,Jed’s shower head releases
6.2 gallons = 1 minute
x gallon = 5 mins 12 secs
First convert 12 secs to minutes and add it to 5 mins .
1 minute = 60secs
x minute = 12 secs
x = 12/60
= 0.2 mins + 5 mins
= 5.2 mins
Therefore,
6.2 gallons = 1 minute
x gallons = 5.2 mins
Cross multiply
x = 6.2 x 5.2 /1
= 32.24/1
= 32.24 gallons
What is the slope of the line passing through the points (2, 5) and (0, -4)?
9/2
2/9
-9/2
-2/9
Answer:
9/2
Step-by-step explanation:
Slope of line=rise/run=
y2-y1/x2-x1
Where
x1=2
x2=0
y1=5
y2= -4
Slope =(-4-5)/(0-2)
Slope=-9/-2
Slope=9/2
Answer:
look at the picture shown
Is 23 a compatible number?
Answer:
In mathematics, compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally...For instance, if we have to add 493 and 549, we can make the numbers compatible by rounding them up to the nearest tens or hundreds.
SO YES! :)
The average rate of hair growth is 2.5 centimeters every 2 months. At that rate, how many months will it take to grow 22.5 centimeters of hair?
Answer: 18 months or a year and a half
Step-by-step explanation:
2.5 centimeters every 2 months, so...
1.25 centimeters every month.
22.5 ÷ 1.25 = 18
So it will take 18 months to grow 22.5 centimeters of hair
4 - 2b = 2
What is the value of b
Answer:
Step-by-step explanation:
4 - 2b = 2
collect terms
4 - 2 = 2b
2 = 2b
divide both side by 2
2/2 = 2b/2
b = 1
Use the multiplier method to increase 258 by 43
Answer:
368.94
Step-by-step explanation:
New value =
258 + Percentage increase =
258 + (43% × 258) =
258 + 43% × 258 =
(1 + 43%) × 258 =
(100% + 43%) × 258 =
143% × 258 =
143 ÷ 100 × 258 =
143 × 258 ÷ 100 =
36,894 ÷ 100 =
368.94
To increase 258 by 43% using the multiplier method, multiply 258 by 1.43. The result is 369.14.
Explanation:To use the multiplier method to increase 258 by 43, you simply need to calculate 258 times the multiplier. The multiplier is 1 plus the rate of increase, which is 43% in this case. So, the multiplier is 1+0.43=1.43.
Here is the calculation:
258 * 1.43 = 369.14
So, 258 increased by 43% is approximately 369.14.
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6 yd
Area:
Circumference:
From the problem above, if
you doubled the length of the
radius, what would be the
ratio of the area of the
smaller circle to the larger
circle?
Answer:
Pie
Step-by-step explanation:
Answer:
pi
Step-by-step explanation:
475 in scientific notation
Answer:
Step-by-step explanation:
4.75 x [tex]10^{2}[/tex]
Answer:
Step-by-step explanation:
[tex]4.75 x 10^{2}[/tex]
PLEASE HURRY ILL DO ANYTHING
A group of seventh graders and a group of teachers at a local middle school were asked how many siblings they each have. The dot plots below show the results.
When comparing the shape of the two sets of data, what conclusion can someone draw?
The students tend to have fewer siblings than the teachers.
The teachers tend to have fewer siblings than the students.
Both the students and the teachers have a wide range of siblings.
Both sets of data have the same shape.
First, we need to find out how many siblings the students have in total and how many siblings the teachers have in total.
The students: (1 x 4) = 4 + (2 x 7) = 18 + (3 x 5) = 33 + (4 x 2) = 41. The students have a total of 41 siblings.
The teachers: (1 x 3) = 3 + (2 x 2) = 7 + (3 x 4) = 19 + (4 x 5) = 39 + (5 x 3) = 54 + (6 x 1) = 60 + (8 x 1) = 68. The teachers have a total of 68 siblings.
Now that we have this information, we know that the answer is option 1, the students tend to have fewer siblings than the teachers. This is because the students had a total of 41 siblings and the teachers had a total of 68 siblings, and 41 is less than 68 so the students have fewer siblings than the teachers.
I really hope I could help! I put a lot of work into this answer! :D
Janey wants to add 2 more equal sections to the garden. She tells Mika to buy11 tomato plants if she wants to use 3/4 of the garden for tomatoes. Is Janey correct?
need helpppppppppppppppppppppppppppp
Answer:
lower case p
Step-by-step explanation:
The law of sines: [tex]\frac{sinA}{a} = \frac{sinB}{b}[/tex]
Therefor look for which sides and angles are accounted for. If we are given angle P, Angle R, and Side r, then Side p is the last term that fits into the law of sines equation.
Solve and explain please
Therefore the inequality is x≤11
and maximum I can withdraw 11 bills.
Step-by-step explanation:
Given ,
Current balance $320
Minimum balance $100
I could spent =$(320-100) = $220
Let the number of bills be x.
Total amount of x bills = $20x
According to the problem,
20x≤ 220
⇔x ≤ [tex]\frac{220}{20}[/tex]
⇔x≤11
Therefore the inequality is x≤11
and maximum I can withdraw 11 bills.
Giving brainliest What is the value of x? A right angle is shown divided into two parts. The measure of one part of the right angle is 30 degrees. The measure of the other part is 2x 10 15 30 45
Answer:
30
Step-by-step explanation:
a right angle is 90 degrees so if it split into two parts and one is 30 degrees and the other is x (an unknown) you could do 90-30 to get 60 but since it is 2x but has to equal 60 it is going to be 30 because 30 times 2 is 60
Answer:
The answer is 30
Step-by-step explanation:
hope this helps!
Tina is fixing a rectangular sign. She plans to place a metal trim around the sign edges. The rectangle measures 32 inches by 9 inches. How much trim will Tina need?
Answer:288
Step-by-step explanation:32 x 9 = 288
mike rides his bike with a constant speed of 12 miles per hour how far can he travel in 3 1/2 hours?
Answer:
42 miles
Step-by-step explanation
Distance = Speed * Time
X=12mph*3.5h
X=42 miles
Distance he can travel is 42 miles.
Step-by-step explanation:
Step 1: Given speed = 12 miles/hour and time = 3 1/2 hours = 7/2 hoursStep 2: Calculate distance using the formula Distance = Speed × Time⇒ Distance = 12 × 7/2 = 42 miles
Find the value of y for the given value of x.
y=1−2x;x=9
Answer:
y = - 17
Step-by-step explanation:
[tex]y = 1 - 2x[/tex]
When x = 9
[tex]y = 1 - 2(9)[/tex]
[tex]y = 1 - 18[/tex]
[tex]y = - 17[/tex]
Therefore, given equation y = 1 - 2x; when x = 9, y = - 17
ASAP PLS !! WILL MARK BRAINLIST
Answer:
it is D. $9.50
Step-by-step explanation:
Answer: The answer is (D) $9.50/9.50 dollars