Answer:
See below
Step-by-step explanation:
To pay the loan off more quickly.
To pay less overall interest.
Often get a lower interest rate for a shorter term loan.
Factorize the expressions 8a⁶ + 5a³ + 1.
Use a³+b³ +c³ - 3abc
Here a = 2a²
b= -a
And c = 1
Answer:
Step-by-step explanation:
A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.
A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°
The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, angle of depression from the helicopter can be found as follows:
tan x = opposite / adjacent
where
x = angle of depression
Hence,
tan x = 660 / 280
tan x = 2.35714285714
x = tan⁻¹ 2.35714285714
x = 67.1231281953
x = 67°
Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
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Answer:
D = 67
Step-by-step explanation:
Help with these two problems and show work please having trouble solving them !
Answer:
see explanation
Step-by-step explanation:
to find the zeros let f(x) = 0
1
f(x) = 0 , that is
x(x + 10) = 0
equate each factor to zero and solve for x
x = 0
x + 10 = 0 ⇒ x = - 10
2
f(x) = 0 , that is
x(x - 3) - 4(x - 3) = 0 ← factor out (x - 3) from each term on the left side
(x - 3)(x - 4) = 0
equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 4 = 0 ⇒ x = 4
Answer:
1) x₁ = 0, x₂ = -10
2) x₁ = 3, x₂ = 4
Step-by-step explanation:
Given functions:
[tex]1)\ f(x)=x(x+10)[/tex]
[tex]2)\ f(x)=x(x-3)-4(x-3)[/tex]
.................................................................................................................................................
Zero Product Property: If m • n = 0, then m = 0 or n = 0.
Distributive Property: a(b + c) = ab + ac.
Standard Form of a Quadratic: ax² + bx + c = 0.
.................................................................................................................................................
The Zero Product Property
1) f(x) = x(x + 10)
Step 1: Set the function to zero.
[tex]\implies 0=x(x+10)[/tex]
Step 2: Apply the Zero Product Property.
[tex]\boxed{x_1=0}[/tex]
[tex]x+10=0\implies \boxed{x_2=-10}[/tex]
The solutions to this quadratic are: [tex]x_1=0,\ x_2=-10[/tex].
.................................................................................................................................................
The Zero Product Property
2. f(x) = x(x - 3) - 4(x - 3)
Step 1: Set the function to zero.
[tex]\implies 0 = x(x - 3) - 4(x - 3)[/tex]
Step 2: Factor out [tex]x- 3[/tex].
[tex]\implies 0 = (x - 3)(x - 4)[/tex]
Step 3: Apply the Zero Product Property.
[tex]x-3=0\implies \boxed{x_1=3}[/tex]
[tex]x-4=0 \implies \boxed{x_2=4}[/tex]
The solutions to this quadratic are: [tex]x_1=3,\ x_2=4[/tex].
.................................................................................................................................................
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A committee of three people needs to be chosen. There are three men and five women available to serve on the committee. If the committee members are randomly chosen, what is the probability that two of the three people chosen on the committee are women
Answer:
probability of choosing two women over people in a community=⅔
A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.
Which is a possible turning point for the continuous function f(x)?
(–2, 0)
(0, –2)
(2, –1)
(4, 0)
On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).
A possible critical point of the function f(x) is given by: (0,-2)
What are the critical points of a function?The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
At these points, the function can change from decreasing to increasing, or vice-versa.
For the table described, we have that the function is decreasing until (0,-2), then it starts to increase, hence there can be a critical point at (0,-2).
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Answer this please !
Answer:
6
Step-by-step explanation:
[tex]\frac{y}{2} =x^{2} -7[/tex]
[tex]\frac{a}{2} =2^{2} -7[/tex]
[tex]\frac{a}{2} =-3[/tex]
[tex]a=-6[/tex]
[tex]\frac{b}{2} =1^{2} -7[/tex]
[tex]\frac{b}{2} =-6[/tex]
[tex]b=-12[/tex]
From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.
[tex]-6=2m+b[/tex]
[tex]-12=m+b[/tex]
[tex]-24=2m+2b[/tex]
[tex]18=-b[/tex]
[tex]b=-18[/tex]
[tex]-12=m-18[/tex]
[tex]m=6[/tex]
Therefore, the slope of line l is 6.
Answer:
slope = 6
Step-by-step explanation:
substitute the given points into the equation of the curve to find a and b
(2, a )
[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )
a = - 6
then point (2, a ) = (2, - 6 )
(1, b )
[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )
b = - 12
then point (1, b ) = (1, - 12 )
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )
m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6
The volume of a box without a lid is given by the formula v = 4x(10-x)^2, where x is a length in inches and v is the volume in cubic inches. what is the volume when x = 5
The volume of the box without the lid is 500 cubic inches.
What is volume?The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.
Another way to think of volume is as the amount of space a three-dimensional object takes up.
Calculation for the volume of the box-
The volume of a box without a lid is given by the formula v = 4x(10-x)².
Where,
'x' is a length in inches, and
'v' is the volume in cubic inches.
The volume when x = 5 inches.
Substitute the value of 'x' in the formula of volume;
v = 4×5(10-5)²
= 20×5²
v = 500
Therefore, the volume of a box without a lid is 500 cubic inches.
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Surface area=
Help me please thanks so much
The Surface Area of the sphere is 1017.16 unit^2.
what is the surface area of the sphere?
The surface area of the sphere is 4*pi*r^2.
where, r is the radius
Calculation :
given radius is 9 units
putting value in the formula of the sphere
S(area)=4*pi*r^2
=4*3.14*9^2
=4*3.14*81
=1017.16 UNIT^2
The Surface Area of the sphere is 1017.16 unit^2.
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The Surface Area of the sphere is 1017.16 unit^2.
The surface area of the sphere is 4*pi*r^2.
where, r is the radius
Calculation :
given radius is 9 units
putting value in the formula of the sphere
S(area)=4*pi*r^2
=4*3.14*9^2
=1017.16 UNIT^2
The Surface Area of the sphere is 1017.16 unit^2.
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The fatal crash rate of teenage drivers 16 years of age is nearly twice as high at night. Select one: True False
TRUE
The fatal accident rate for young drivers aged 16 to 19 is about four times higher than at night. Two or more passengers of the same age triple the risk of a fatal accident driving a teenager.
An accident in which someone dies. Synonyms: Accident. Type: Collateral damage.
Of the collisions between cars, angled collisions are the most deadly (about 8,000 in 2020). The interactive chart also shows the estimated number of fatalities, injuries, casualties, and all accidents in different types of car accidents.
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0.00000007 as a fraction
Answer:
7/100000000
Step-by-step explanation:
to find this out we can start by saying that 0.7 is 7/10
every 0 in front of 7 after that is adding another 0 to 10
so
0.07 is 7/100
0.00000007 is 7/100000000
PLEASE ANSWER QUICKLY
Answer:
Option (4)
Step-by-step explanation:
See attached image.
Systematic random sampling has become a popular method of drawing samples in research practices because _____.
it is a relatively easy way to draw a sample while ensuring randomness is the answer.
Systematic sampling is a probabilistic sampling method in which a researcher selects members of a population at regular intervals. For example, select every 15 people from the list of populations. If the population is in random order, this can mimic the benefits of a simple random sample.
These are generally preferred by researchers because they are easy to implement and understand. The important assumption that the results represent the majority of the normal population ensures that the entire population is sampled equally. The process also provides a higher level of control for systematic sampling compared to other sampling methods. systematic sampling also has a lower risk factor because the data is unlikely to be contaminated.
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What is the explicit formula for this sequence?
-9,-3,3,9,15
Answer: A
Step-by-step explanation:
Normally in choice questions, I would choose to substitute the values into the formulas but I think it is better if I explain to you.
In a sequence, if the numbers increase by d each time and the first number in the sequence is [tex]a_{1}[/tex], then the explicit formula is [tex]a_{1}[/tex] + (n - 1)d when n is the order of the number in the sequence, like n = 1 for the first number, n = 2 for the second number and so on. Using this, we get that the answer to this problem is [tex]a_{n}[/tex] = -9 + (n - 1)6 so the answer is A
A school offers three subjects: math, art and science. at least 80% of students study both math and art. at least 80% of students study both math and science. prove that at least 80% of students who study both art and science, also study math.
The proof to show that at least 80% of students who study both art and science, also study math is illustrated below.
How to illustrate the proof?From the information given, it was stated that at least 80% of students study both math and art and that at least 80% of students study both math and science.
Therefore, about (100 - 80) 20% doesn't study the combination of both subjects.
Here, those students who study both art and science, and also study math will be:
= 100% - 20%
= 80%
Therefore, at least 80% study the subjects.
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Help me please, I'm stuck
Answer:
Gradient: 5
y-intercept: (0, 15)
Step-by-step explanation:
The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.
Point Y is the circumcenter of ΔDEF.
Point Y is the circumcenter of triangle D E F. Lines are drawn from the points of the triangles to point Y. Lines are drawn from point Y to the sides of the triangle to form right angles and line segments Y L, Y M, and Y N. The line segments cut the sides of the triangles into 2 equal parts. The length of F Y is 3 x + 7 and the length of Y E is 5 x minus 3.
Find FY.
5
11
17
22
The length of FY in the triangle that has Y as its circumcenter is: D. 22 units.
What is the Circumcenter of a Triangle?The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of a triangle intersect.
Based on the definition of the circumcenter, and Y is the circumcenter, therefore:
YE = FY
Plug in the values
5x - 3 = 3x + 7
5x - 3x = 3 + 7
2x = 10
x = 5
FY = 3x + 7 = 3(5) + 7
FY = 22 units.
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Answer:
D
Step-by-step explanation:
PLEASE HELP FAST!
The question is below:
The transformation that produces same image are:
Translate 3 units right and 5 units down. Then rotate 90 degrees about the origin.Translate 2 units up and 4 units left. Translate 6 units down and 4 units rightThe transformation that produces different image are:
Rotate 90 degrees about the origin. Then Dilate using a scale factor of 1/2Dilate using a scale factor of 5. Translate 4 units left and 2 units upWhat is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation, reflection and rotation are rigid transformation which produces same image while dilation produces similar shapes.
The transformation that produces same image are:
Translate 3 units right and 5 units down. Then rotate 90 degrees about the origin.Translate 2 units up and 4 units left. Translate 6 units down and 4 units rightThe transformation that produces different image are:
Rotate 90 degrees about the origin. Then Dilate using a scale factor of 1/2Dilate using a scale factor of 5. Translate 4 units left and 2 units upFind out more on transformation at: https://brainly.com/question/4289712
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increase $32 in the ratio 2:5
decrease 54 litter in the ratio 5:1
Answer:
Step-by-step explanation:
32 = 2 : 5
32/7 = 4
2 x 4 : 4 x 5
8 : 20
PLEASE HELP!!!!
This year, the Nature Club made 3 exhibits per month for its annual fair. This year's fair has twice as many exhibits as last year's. How many exhibits were there in last year's fair?
Answer: 18
Step-by-step explanation:
There are 12 months in a year. The club made 3 exhibits each month. 3 times 12 is 36. They made twice as many as last year, so divide 36 by 2 and you get 18.
I hope this helps!
the area of a rectangle is (16x^2 - 9y^2) square units
16. If x= y² + 12, what is the value of y in terms of (A)x+12 (B) x-12 (C) √√x+12 (D) √√x-12
Answer:
D. y = √(x - 12)
Step-by-step explanation:
x = y² + 12
y² = x - 12
y = √(x - 12)
Shawn graphed the points listed below.
(0, 0) (1, -1) (3, 0) (4, 4) (4, 5) (5, 4) (6, -2)
Which pair of points could be used to show that the points Shawn graphed do not represent a function?
A. (4, 4) and (4, 5)
B. (4, 4) and (5, 4)
C. (0, 0) and (3, 0)
D. (1, -1) and (6, -2)
Answer: A. (4, 4) and (4, 5)
Step-by-step explanation:
The same x value maps onto more than one y value.
Determine the slope of the line.
The slope of the line is - 3 / 2 .
How to find slope?The slope of a line is the change in y coordinate with respect to the change in x coordinate.
Therefore, using (0, 6)(4, 0)
Hence,
m = slope = y₂ - y₁ / x₂ - x₁
slope = 0 - 6 / 4 - 0
slope = -6 / 4
slope = - 3 / 2
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Please help em fast I really need help
lf ƒ(x) = 2(x + 1)² and g(x) = 3x- 2 determine f[g(2)]
Answer:
f(g(2)) = 50
Step-by-step explanation:
evaluate g(2) then substitute the result obtained into f(x)
g(2) = 3(2) - 2 = 6 - 2 = 4 , then
f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50
Answer:
f[g(2)] = 50
Step-by-step explanation:
Given functions:
[tex]f(x)=2(x+1)^2[/tex]
[tex]g(x)=3x-2[/tex]
We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.
Step 1: Find the value of g(2) by substituting 2 for x in function g(x).
[tex]\implies g(2)=3(2)-2[/tex]
[tex]\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}[/tex]
Step 2: Substitute the found value into the composite function.
[tex]\\\implies f[g(2)]= 2(4+1)^2[/tex]
[tex]\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}[/tex]
Hence, the value of the composite function f[g(2)] is 50.
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the price of an all access take it to the fair is $42.99 before tax roland bought the all access ticket for 40% off then he pay 7% sales tax on the discounted price part a how much did roland paid in sale tax? part b what is the total amount that roland paid for the ticket ?
The total amount that roland paid for the ticket is $27.60
Given that the price of an all-access ticket to the fair is $42.99 before tax. Roland bought the all-access ticket for 40% off.
We need to calculate the total amount paid by the roland
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100
The price after 40% off -
= 42.99*60% = $25.794
Sales tax on 25.794
= 25.794*7% = $1.80558
Total amount Paid for the ticket
= 1.80558 + 25.794 = $27.59958
= $27.60
Hence the total amount paid by roland is $27.60
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not sure how to figure this out, help please
The second bus is traveling at a speed of 33.3 miles per hour.
Given that the speed of first bus is 60 miles per hour , distance between both the buses is 700 miles after 8 hour.
We are required to find the speed of second car which is heading towards south.
If first car is travelling at a speed of 60 miles per hour then the distance of first car after 8 hours is 60*8=480 miles.
We have been given that the distance between both the cars after 8 hours is 700 miles,So,
Distance of second car after 8 hours=700-480=220 miles.
We know that the speed is equal to distance divided by time.
We know that we have calculated distance after 8 hours so the speed of second car will be =20/6
=33.3 miles per hour
Hence the speed of second car which is heading towards south is 33.3 miles per hour.
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Find the midpoint of points A(-9, -3) and B(1, 7) graphically.
Plot the line segment AB
Answer: (-4,2)
Step-by-step explanation:
To find the midpoint of AB, we have to find the mean of the x coordinates for the x coordinate of the midpoint and the mean of the y coordinates for the y coordinate of the midpoint
So the midpoint is ((-9+1)/2,(-3+7)/2) = (-4,2)
To plot the line AB, just find the points A and B on the graph and draw a straight line from A to B
which facts are true for the graph of the function below check all that apply F(x)=log6x
Based on the graph of the function (F(x) = log6x), the following facts are true:
It is increasing. The x-intercept is (1, 0). What is a graph?A graph is a type of chart that is used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.
By critically observing the graph of the function (F(x) = log6x) attached in the image below, we can infer and logically deduce that its domain and range include all real numbers that are greater than 0 (x > 0).
This ultimately implies that, the following facts are true:
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Complete Question:
Which facts are true for the graph of the function below? Check all that apply. F(x) = log6 x
A. It is increasing.
B. The range is y > 0.
C. The x-intercept is (1, 0).
D. It is decreasing.
E. The y-intercept is (0, 6).
F. The domain is x > 6.
Alan will be traveling out of town for business. during his travel, he is scheduled to have 4 dinners, 5 lunches, and 3 breakfasts. his employer will pay him for these meals at the following rate: $20.20 for dinner, $10.70 for lunch, and $6.93 for dinner. what is the total amount alan will be paid for these meals?
money paid by employer to Alan is $ 155.09
word problemA word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.
money paid for dinner by employer=$20.20
money paid for lunch by employer =$10.70
money paid for breakfast by employer =$6.93
according to question,
in this problem we will simply multiply quantity of dinners with amount
to get our answer.
so as given in problem Alan scheduled 4 dinners , 5 lunches and 3 breakfast
(4×$20.20)+(5×$10.70)+(3×$6.93)
80.8+53.5+20.79
=$ 155.09
hence money paid by employer to Alan is $ 155.09
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Can the sides of a triangle have lengths 2, 4, and 7?
Answer:
No, they can't
Step-by-step explanation:
According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides.
2+4= 6<7
As you can see from this Equation NOT any two side are greater than the third making this NOT possibly be a tringle.
2+7=9>4
4+7=11>2