We are giving the function as;
[tex]g(x)=-16x^2+64x+80[/tex]If we factorize g(x) we have that
[tex]g(x)=-16(x+1)(x-5)[/tex]T0 find if the object has be launched and find the x value of the object
Therefore,
[tex]\begin{gathered} -16(x+1)(x_{}-5)=0 \\ \Leftrightarrow(x+1)(x_{}-5)=0 \\ \leftrightarrow x=-1\text{ or x=5} \end{gathered}[/tex]it will take the rocket 5 seconds to reach the ground.
Help me with number 4 please Identify the 17th term of a geometric sequence where a1 = 16 and a5 = 150.06 Round the common ratio and 17th term to the nearest hundredth.
Common ratio = 1.75
17th term = 123,802.31
Explanations:Given the following parameters:
[tex]\begin{gathered} a_1=16 \\ a_5=150.06 \end{gathered}[/tex]Since the sequence is geometric, the nth term of the sequence is given as;
[tex]a_n_{}=a_{}r^{n-1}[/tex]a is the first term
r is the common ratio
n is the number of terms
If the first term a1 = 16, then;
[tex]\begin{gathered} a_1=ar^{1-1}_{} \\ 16=ar^0 \\ a=16 \end{gathered}[/tex]Similarly, if the fifth term a5 = 150.06, then;
[tex]\begin{gathered} a_5=ar^{5-1} \\ a_5=ar^4 \\ 150.06=16r^4 \\ r^4=\frac{150.06}{16} \\ r^4=9.37875 \\ r=1.74999271132 \\ r\approx1.75 \end{gathered}[/tex]Hence the common ratio to the nearest hundredth is 1.75
Next is to get the 17th term as shown;
[tex]\begin{gathered} a_{17}=ar^{16} \\ a_{17}=16(1.75)^{16} \\ a_{17}=16(7,737.6446) \\ a_{17}\approx123,802.31 \end{gathered}[/tex]Hence the 17th term of the sequence to the nearest hundredth is 123,802.31
Simplify (a + 15) •2
(a + 15) •2
Multiply each term in the parentheses by 2
a*2 + 15*2
2a + 30
For the polyhedron, use eular's foemula to find the missing number
Given:
Edges of the polyhedron, E = 10
Vertices, V = 5
A polyhedron is a three-dimensional figure.
Let's find the number of faces using Euler's formula.
To find the number of faces of the polyhedron, we have the Euler's formula:
V + F - E = 2
Substitute values into the formula:
5 + F - 10 = 2
Combine like terms:
F + 5 - 10 = 2
F - 5 = 2
Add 5 to both sides:
F - 5 + 5 = 2 + 5
F = 7
Therefore, the number of faces of the polyhedron is 7
ANSWER:
7 faces
Complex numbers may be applied to electrical circuits. Electrical engineers use the fact that resistance R toelectrical flow of the electrical current I and the voltage V are related by the formula V = RI. (Voltage ismeasured in volts, resistance in ohms, and current in amperes.) Find the resistance to electrical flow in a circuitthat has a voltage V = (40+30i) volts and current I = (-5+ 3i) amps._+_i/_Note: Answer in the forma + bi/c. If b is negative make sure to put a negative sign in the answer box.
we have the formula
[tex]\begin{gathered} V=RI \\ R=\frac{V}{I} \end{gathered}[/tex]substitute given values
[tex]R=\frac{40+30i}{-5+3i}[/tex]Remember that
To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator
the conjugate of the denominator is (-5-3i)
so
[tex]\begin{gathered} R=\frac{40+30\imaginaryI}{-5+3\imaginaryI}*\frac{-5-3i}{-5-3i}=\frac{-40(5)-40(3i)-30i(5)-30i(3i)}{25-9i^2}=\frac{-200-120i-150i-90i^2}{25-9(-1)}=\frac{-110-270i}{34} \\ \\ R=\frac{-110-270\imaginaryI}{34} \\ simplify \\ R=\frac{-55-135\imaginaryI}{17} \end{gathered}[/tex]You TryWrite an equation for each of the following,then solve for the variable.20 is the same as the sum of 4 and g.
Given statement:
20 is the same as the sum of 4 and g
Let us break down the statement into parts and then write the equation
the sum of 4 and g:
[tex]\text{= 4 + g}[/tex]This sum is equal to 20:
[tex]4\text{ + g = 20}[/tex]Hence, the equation is:
[tex]4\text{ + g = 20}[/tex]Solving for the variable:
[tex]\begin{gathered} \text{Collect like terms} \\ g\text{ = 20 -4} \\ g\text{ = 16} \end{gathered}[/tex]Answer Summary
[tex]\begin{gathered} \text{equation: 4 + g = 20} \\ g\text{ = 16} \end{gathered}[/tex]if there are 7 teams and every teams plays everyone once how many games total played
This is a problem about combinations where the order doesn't matter. The solution is usually written as 7C2 (seven choose two) and has the value
[tex]\frac{7!}{(7-2)!2!}=21[/tex]Comment: 7C2 is the answer to the question "How many pairs (in our case, these pairs are seen as games played) can we form from a group of 7 things?".
Can anyone help me? I don't know the answer.
By means of the area formula for a square, the square has an area of 4 / 49 square meters (approx. 0.0816 square meters).
What is the area of the square?
Herein we find a representation of a solid square in the figure, whose side length measure (l), in meters, is known, and whose area (A), in square meters, has to be found. Dimensionally speaking, the area unit is the square of length unit.
The area formula of the square is shown below:
A = l²
If we know that the side length of the square has a measure of 2 / 7 meters (l = 2 / 7 m), then the area of the triangle is equal to:
A = (2 / 7 m)²
A = 4 / 49 m²
A ≈ 0.0816 m²
The area of the square is 4 / 49 square meters (approx. 0.0816 square meters).
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40% of the students on the field trip love the museum. If there are 20 students on the field trip, how many love the museum?
well, what's 40% of 20?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies 8[/tex]
Sketch and calculate the area enclosed by y² = 8-x and (y + 1)² = −3+x.
The area enclosed by y² = 8 - x and (y + 1)² = −3 + x is 243.
We are given y² = 8 - x and (y + 1)² = −3 + x.
To sketch and calculate the area enclosed, find the intersection points:
y² = 8 - x ⇒ x = 8 - y²
Substitute x = 8 - y² in (y + 1)² = −3 + x:
(y + 1)² = −3 + 8 - y²
y² + 2y + 1 = −3 + 8 - y²
2y² + 2y - 4 = 0
y² + y - 2 = 0
(y - 1) (y + 2) = 0
y = 1, -2
Substitute y = 1, -2 in x = 8 - y²:
When y = 1, x = 8 - (1) ⇒ x = 7
When y = -2, x = 8 - (-2)² ⇒ x = 4
Thus, the point of intersection is (4, -2) and (7, 1).
Graph of the region enclosed by y² = 8 - x and (y + 1)² = −3 + x:
The area of the enclosed region is given by:
A = [tex]\int \, \int \,dA[/tex]
[tex]=\int\limits^7_{-2} \, \int\limits^{3+ (y+1)^{2} } _{8 - y^{2} } \, dxdy[/tex]
[tex]=\int\limits^7_{-2} \, (x)^{3+ (y+1)^{2} } _{8 - y^{2} } \, dy[/tex]
[tex]=\int\limits^7_{-2} \, [{(3+ (y+1)^{2} )} -({8 - y^{2} })] \, dy[/tex]
[tex]=\int\limits^7_{-2} \, {(2 y^{2} + 2y -4) } \, dy[/tex]
[tex]=(\frac{2y^3}{3} + \frac{2y^2}{2} -4y)^7_{-2}[/tex]
[tex]=\frac{686}{3} + 49 - 28 + \frac{16}{3} - 4 - 8[/tex]
= 343
Hence, the area enclosed by y² = 8 - x and (y + 1)² = −3 + x is 243.
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Find the value of x in the triangle shown below.=2°31770
The sum of all the angles in a triangle is always 180°.
We can write the equation and solve for the missing angle:
[tex]31^o+77^o+x=180^o[/tex]Solving for x:
[tex]\begin{gathered} x=180^o-31^o-77^o \\ \\ x=72^o \end{gathered}[/tex]The measure of the unknown angle is 72 degrees.
With the points (8. 4) (-6, -6) (-10, 12) (2,-4). What are the new points if thescale factor of dilation is X?
With the points (8. 4) (-6, -6) (-10, 12) (2,-4). What are the new points if the
scale factor of dilation is X?
we know that
The rule of the dilation of a point is equal to
(x,y) -------> (ax, ay)
with a scale factor a
so
In this problem
the scale factor is x
therefore
(8. 4) --------> (8x. 4x)
The sphere is _____ cubic centimeters bigger than the cube. (Round to the nearest cubic centimeter.)
ANSWER
The sphere is 10762 cubic centimeters bigger than the cube.
EXPLANATION
We want to find the difference in the volumes of the sphere and the cube.
To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.
The volume of a sphere is given as:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r = radius
The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:
[tex]\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot15^3 \\ V\approx14137\operatorname{cm}^3 \end{gathered}[/tex]The volume of a cube is given as:
[tex]V=s^3[/tex]where s = length of the side
The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:
[tex]\begin{gathered} V=15^3 \\ V=3375\operatorname{cm}^3 \end{gathered}[/tex]Therefore, the difference in the volumes of the sphere and cube is:
[tex]\begin{gathered} V_d=V_s-V_c \\ V_d=14137-3375 \\ V_d=10762\operatorname{cm}^3 \end{gathered}[/tex]Therefore, the sphere is 10762 cubic centimeters bigger than the cube.
use your formula to determine the height of a trapezoid with an area of 24 square centimeters and base length of 9 cm and 7 cm
Answer
The height of the trapezoid = 3 cm
Explanation
The area of a trapezoid is given as
Area = ½ (a + b) h
where
a and b = base lengths of the trapezoid
a = 9 cm
b = 7 cm
h = height of the trapezoid = ?
Area = 24 cm²
Area = ½ (a + b) h
24 = ½ (9 + 7) h
24 = ½ (16) h
24 = 8h
8h = 24
Divide both sides by 8
(8h/8) = (24/8)
h = 3 cm
Hope this Helps!!!
The circle above is rotated about the axis as shown. What shape is formed?cylinderconedonutsphere
The answer is a donut.
A donut or Toroid is formed when you rotate an circle by a rotation axis displaced of the center of the circle.
Answer:
Step-by-step explanation:
donut
8 ( 11 - 2b ) = -4 ( 4b - 22 )
Problem
8 ( 11 - 2b ) = -4 ( 4b - 22 )
Solution
We can distribute the terms in the equation and we got:
88 -16b = -16b +88
If we add 16b in boh sides we got:
88 =88
Then for this case we can conclude that this equation has infinite solutions
Provide the missing reasons with proof. Given: AB/DB = CB/EBProve: ∆ABC~∆DBE
Answer:
Statement 1. AB/DB = CB/EB
Reason 1: Given
Statement 2: ∠ABC = ∠BDE
Reason 2: Vertical angles
Statement 3: ∆ABC~∆DBE
Reason 3: SAS (side - angle - side)
Explanation:
It is given that AB/DB = CB/EB. So, we can say that the ratio of side AB to DB is equal to the ratio of side CB to EB. This made these sides similar.
Additionally, ∠ABC and ∠BDE are vertical angles because they are opposite angles formed when two lines intersect. Vertical angles have the same measure so, ∠ABC = ∠BDE.
Now, we can say that the triangles ABC and DBE are similar by SAS (Side-Angle-Side). Because two sides are similar and the angle between them is congruent.
Therefore, the answer is
Statement 1. AB/DB = CB/EB
Reason 1: Given
Statement 2: ∠ABC = ∠BDE
Reason 2: Vertical angles
Statement 3: ∆ABC~∆DBE
Reason 3: SAS (side - angle - side)
use the invert-and-multiply rule to divide. Reduce your answer to lowest terms.4 divide (- 2/5)
ANSWER:
- 10
STEP-BY-STEP EXPLANATION:
We have the following expression
[tex]4\div\mleft(-\frac{2}{5}\mright)[/tex]We know that when dividing from, the nvert-and-multiply rule must be applied, as follows
[tex]\begin{gathered} 4\div\mleft(-\frac{2}{5}\mright)\rightarrow4\times\mleft(-\frac{5}{2}\mright)=\frac{4\cdot-5}{2}=\frac{-20}{2}=-10 \\ \end{gathered}[/tex]Therefore the result of the operation is -10
The triangle shown below are similar. which line segment corresponds to RS?
B) TS
1) Since these triangles are similar then we can write out the following ratios according to the Thales Theorem:
[tex]\frac{RS}{TS}=\frac{RO}{TU}[/tex]2) So these line segments must share the same ratio
3) Hence, the answer is TS
Answer:
TS
Step-by-step explanation:
According to the graph, what is the value of the constant in the equation below?A.2B.0.667C.3D.1.5
Solution
- The constant being asked for is the slope of the graph.
- The formula for finding the slope of a graph is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ where, \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the points on the line} \end{gathered}[/tex]- The points on the graph that we will use are:
[tex]\begin{gathered} (x_1,y_1)=(2,3) \\ (x_2,y_2)=(4,6) \end{gathered}[/tex]- Thus, we can find the constant as follows:
[tex]\begin{gathered} m=\frac{6-3}{4-2} \\ \\ m=\frac{3}{2}=1.5 \end{gathered}[/tex]Final Answer
The constant(slope) is 1.5 (OPTION D)
How much would $200 interest compounded monthly be worth after 30 years
Given:
Principal (P)=$200
Rate of interest (r) =4%
time (t)=30 years
Number of times compounded per year(n) = 12
Required- the amount.
Explanation:
First, we change the rate of interest in decimal by removing the "%" sign and dividing by 100 as:
[tex]\begin{gathered} r=4\% \\ \\ =\frac{4}{100} \\ \\ =0.04 \end{gathered}[/tex]Now, the formula for finding the amount is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Put the given values in the formula, we get:
[tex]A=200(1+\frac{0.04}{12})^{12\times30}[/tex]Solving further, we get:
[tex]undefined[/tex]The equation 8x+8y=16 in slope-intercept form
Create a "rollercoaster using the graphs of polynomials with real and rational coefficients.
The coaster ride must have at least 3 relative maxima and/or minima.
The coaster ride starts at 250 feet (let this be your y-intercept).
The ride dives below the ground into a tunnel (under the x-axis) at least once.
The graph must have at least one even multiplicity, two real solutions, and two imaginary solutions.
The polynomial that represents the rollercoaster, using the Factor Theorem, is given as follows:
y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).
What is stated by the Factor Theorem?The Factor Theorem states that a polynomial function with zeros [tex]x_1, x_2, \codts, x_n[/tex], also represented by factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex] is given by the rule presented as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial function with the given roots.
For this problem, the requirements are as follows:
At least 3 relative maxima and/or minima -> derivative of 3rd order -> 4 unique rootsy-intercept of 250 feet -> controlled by the leading coefficient.The roots will be given as follows:
Root at x = 1 with even multiplicity -> (x - 1)².Real solution at x = -1 -> (x + 1).Two imaginary solutions -> (x² + 0.1).Unique root at x = -5 -> (x + 5).Hence the function is:
y = a(x - 1)²(x + 1)(x² + 0.1)(x + 5).
At x = 0, the function assumes a value of 250, hence the leading coefficient is obtained as follows:
0.5a = 200.
a = 400.
Thus the function is:
y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).
Which has the desired features, as shown by the image at the end of the answer.
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Given the following probabilities, algebraically determine if Events A and B are:• mutually exclusive or non-mutually exclusive• independent or dependent.P(A) =P(B) 0.75P(A U B)'U0.15
We know that:
[tex]\begin{gathered} P(A\cup B)^{\prime}=1-P(A\cup B) \\ P(A\cup B)^{\prime}=1-P(A)+P(B)-P(A\cap B) \end{gathered}[/tex]Plugging the values given we have that:
[tex]\begin{gathered} 0.15=1-0.8+0.75-P(A\cap B) \\ P(A\cap B)=1-0.8+0.75-0.15 \\ P(A\cap B)=0.8 \end{gathered}[/tex]Now, since the probability of the intersection is not zero this means that the events are non-mutually exclusive.
select the graph represented by the exponential function y = 4(1/2)×
SOLUTION
We want to tell the graph that represents the function
[tex]y=4(\frac{1}{2})^x[/tex]The graph of this function is shown below
Comparing this to what we have in the options,
we can see that the correct answer is option D
PLEASE HELP!!!!! I really really really really really need help with this math problem can someome help me please its has to be done in 20 mins!!!!!!!! PLEASE HELP!!!
A) To do that we will draw a line inside the triangle that is perpendicular to the base as I have don above.
B) We will also do the same for B
Question 2b: NAME THE Y-INTERCEPTy = -2(x - 3)^2
The given equation corresponds to a parabola:
[tex]y=-2(x-3)^2[/tex]The y-intercept of the parabola is the point when it crosses the y-axis, at this point x=0, to determine this value you have to replace the formula with x=0 and calculate the value of y:
[tex]\begin{gathered} y=-2(0-3)^2 \\ y=-2(-3)^2 \end{gathered}[/tex]Solve the exponent first, then the multiplication
[tex]\begin{gathered} y=-2(-3)^2 \\ y=-2\cdot9 \\ y=-18 \end{gathered}[/tex]The y-intercept for the given function is (0,-18)
What is the mean before the rent ? What is the mean after the change ?
Given:
The data set of the monthly rent paid by 7 tenants
990, 879, 940, 1010, 950, 920, 1430
We will find the mean of the data:
Mean = Sum/n
n = 7
Sum = 990+879+940+1010+950+920+1430 = 7119
Mean = 7119/7 = $1017
One of the tenants change from 1430 to 1115
The mean after the change will be as follows:
Sum = 990+879+940+1010+950+920+1115 = 6804
n = 7
Mean = 6804/7 = 972
So, the answer will be:
Mean before the change = 1017
Mean after the change = 972
What is the domain of the function shown in the graph below? y 10 9 8 7 6 5. 4 3 2 -10 -9 -8 -7 -6 in -4 3 -2 1 6 2 8 9 10 -2 -3 -4 -5 -6 -8 9 10 W Type here to search Et TH-WL-57336
1) As the Domain is the set of inputs (x) for that function, as we can see in the graph.
There's one point in the graph x =8, where should be an asymptote i.e. a vertical or horizontal line that prevents both graphs do not trespass.
So we can write the Domain as
D =(-∞, 8) U (8, ∞)
Because in this function, the point x=8 is not included, and from point 8 on the function continues.
Given the equation of the circle, identify the center and radius (x + 1) ^ 2 + (y - 1) ^ 2 = 36
The form of the equation of the circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex](h, k) is the center
r is the radius
Let us compare it with the given equation to find the center and the radius
[tex](x+1)^2+(y-1)^2=36[/tex]From the comparing
h = -1
k = 1
r^2 = 36
Find the square root of 36 to get r
[tex]\begin{gathered} r=\sqrt[]{36} \\ r=6 \end{gathered}[/tex]The center is (-1, 1) and the radius is 6
a) How many hand-held color televisions can be sold at $ 400 per television?b) How many televisions will be sold when supply and demand are equal?c) Find the price at which supply and demand are equal.
a) Since we are interested in the number of TVs that can be sold at $400, we need to use the Demand model equation and set p=400; thus,
[tex]\begin{gathered} p=400 \\ \Rightarrow N=-7\cdot400+2820=20 \\ \Rightarrow N=20 \end{gathered}[/tex]The answer to part a) is 20 TVs per week.
b) Set N=N, then
[tex]\begin{gathered} N=N \\ \Rightarrow-7p+2820=2.4p \\ \Rightarrow9.4p=2820 \\ \Rightarrow p=\frac{2820}{9.4}=300 \\ \Rightarrow p=300 \end{gathered}[/tex]Therefore, using p=300 and solving for N,
[tex]\begin{gathered} \Rightarrow N=2.4\cdot300=720 \\ \Rightarrow N=720 \end{gathered}[/tex]The answer to part b) is 720 TVs per week.
c) In part b), we found that when supply and demand are equal, p=300. Thus, the answer to part c) is $300