The profit of his investment after 2 years is $8,063.60.
What is the profit of his investment?The profit earned is the difference between the amount he earned from the deposit at the bank and the interest paid on the loan.
Total value of the loan in 2 years : 100,000 x (1.042²) = 108,576.40
Total value of the amount deposited in 2 years : 100,000 x (1.08²) = 116,640
Difference = 116,640 - 108,576.40 = $8,063.60
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Find the zeros of the function f(x)=x^2+9.9x+18. Round values to the nearest hundredth (if necessary).
A quadratic equation in the form of ax²+bx+c. The zeroes of the polynomial are -2.4 and -7.5.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c. The Root of the quadratic equation are given as,
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The zeroes of the polynomial are:
f(x)=x² + 9.9x + 18
0 = x² + 9.9x + 18
[tex]x= \dfrac{-9.9\pm \sqrt{(9.9)^2-4(1)(18)}}{2(1)}\\\\[/tex]
x = -2.4, -7.5
Hence, the zeroes of the polynomial are -2.4 and -7.5.
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At what input value will the function
f(x) = -x - 2 + 2 begin to have real
outputs?
The function will begin to have real output when the input value is 2
How to determine the input value?The function is given as:
[tex]f(x) = -\sqrt{x - 2} + 2[/tex]
Set the radical greater than or equal to 0
[tex]x - 2 \ge 0[/tex]
Add 2 to both sides
[tex]x \ge 2[/tex]
This represents the domian
Hence, the function will begin to have real output when the input value is 2
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Complete question
At what input value will the function [tex]f(x) = -\sqrt{x - 2} + 2[/tex] begin to have real outputs?
What is solve [c-5]=7
Step-by-step explanation:
c-5-(7)=0
c-12 = 0
c = 12Quadrilateral PQRS is dilated by a scale factor of 1/2 with point R as the center of dilation, resulting in the image P'Q'R'S'. Which statement is true about line segment P'S'?
The statement that is true about line segment P'S' is (c) Segment P'S' s 4 units long and lies on a different segment
How to determine the true statement?The complete question is in the attached image
From the image, we have:
PS = 8 units
This means that:
P'S' = 1/2 * PS
So, we have:
P'S' = 1/2 * 8
Evaluate
P'S' = 4
Also, the segment PS and P'S' do not lie on the same segment
Hence, the true statement is (c)
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What is the equation of the line passing through the points (–25, 50) and (25, 50) in slope-intercept form?
y = negative 50 x
y = negative 50
y = 50 x
y = 50
x
y
–6
–7
2
–3
8
0
The slope is 2.
The slope is One-half.
The y-intercept is –4.
The y-intercept is 8.
The points (–2, –5) and (8, 0) are also on the line.
The points (–5, –2) and (1, 10) are also on the line.
The equation of the line passing through the points (-25, 50) and (25, 50) in slope-intercept form is y = 50. Hence, 4th option is the right choice.
The slope-intercept form of a line is written as y = mx + b, where m is the slope of the line, and b is the y-intercept.
The slope of a line passing through the points (x₁, y₁) and (x₂, y₂) can be calculated using the formula, slope (m) = (y₂ - y₁)/(x₂ - x₁).
Therefore, slope of the line passing through the points (-25, 50) and (25, 50) can be calculated as m = (50 - 50)/(25 - (-25)) = 0/(-50) = 0.
We can find the equation of the line using the point-slope formula, according to which, a line having a slope m and passing through the point (x₁, y₁) can be written as y - y₁ = m(x - x₁).
Therefore, the equation of the given line can be written as:
y - 50 = 0(x - 25)
or, y - 50 = 0,
or, y = 50.
Therefore, the equation of the line passing through the points (-25, 50) and (25, 50) in slope-intercept form is y = 50. Hence, 4th option is the right choice.
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Select the two values of x that are roots of this equation. 2x2 + 7x + 6 = 0
Answer:
x = -3/2, -2
Step-by-step explanation:
2x^2 + 7x + 6 = 0
(2x + 3)(x + 2) = 0
(2x + 3)
2x = -3
x = -3/2
(x + 2)
x = -2
Answer:
[tex]\large {\textsf{A and C}}\ \implies x_1=-2,\ x_2=-\dfrac{3}{2}}[/tex]
Step-by-step explanation:
In this problem, we can use two methods to solve for the values of x (roots) of the given equation. Those methods are: using the quadratic formula and factoring.
Standard Form of a Quadratic Equation: ax² + bx + c = 0, where a ≠ 0
Given equation: 2x² + 7x + 6 = 0
⇒ a = 2, b = 7, c = 6
Method 1: Using the Quadratic Formula
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Step 1: Substitute the values of a, b, and c into the quadratic formula.
[tex]\implies x=\dfrac{-7\pm\sqrt{7^2-4(2)(6)}}{2(2)}\\\\[/tex]
Step 2: Simplify
[tex]\implies x=\dfrac{-7\pm\sqrt{\bold{7^2}-4(2)(6)}}{\bold{2(2)}}\\\\\implies x=\dfrac{-7\pm\sqrt{49-4\bold{(2)(6)}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{49\bold{-4(12)}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{\bold{49-48}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{\bold{1}}}{4}\\\\\implies x=\dfrac{-7\pm1}{4}[/tex]
Step 3: Separate into two possible cases and solve for the values of x.
[tex]\implies x_1=\dfrac{-7-1}{4}\implies \dfrac{-8}{4}\implies \boxed{-2}\\\\\implies x_2=\dfrac{-7+1}{4}\implies \dfrac{-6}{4}\implies\boxed{-\dfrac{3}{2}}[/tex]
Method 2: Solve by Factoring
In order to be able to solve this equation by factoring, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = 12) and give us the sum of the middle term (b = 7).
Factors that give a product of a • c: 4 • 3 = 12
Factors that give a sum of b: 4 + 3 = 7
Step 1: Rewrite the given equation with those factors.
2x² + 7x + 6 = 0
⇒ 2x² + 4x + 3x + 6 = 0
Step 2: Factor out 2x and 3.
(2x² + 4x) + (3x + 6) = 0
⇒ 2x(x + 2) + 3(x + 2) = 0 [ Factor out the the common factor. ]
⇒ (2x + 3)(x + 2) = 0
Step 3: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0).
a) 2x + 3 = 0 ⇒ 2x = -3 ⇒ x = -³⁄₂
b) x + 2 = 0 ⇒ x = -2
Therefore, the two roots of this equation are x = -³⁄₂ and x = -2.
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Express all the trigonometric ratios in terms of cot A.
Answer:
Who is the youngest in your family?
Given f(x) and g(x) = f(k x), use the graph to determine the value of k. Please explain how to get the answer
A) 5
B) 1/5
C) -1/5
D) -5
Using translation concepts, the value of k is given as follows:
B) 1/5.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this graph, we have that g(x) = f(kx), hence since g(-2) = f(-10):
-2 = -10k
k = 2/10
k = 1/5.
Hence option B is correct.
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Question 7 of 8
Which of the following are equal to 25 miles per gallon? Check all that apply.
A. 125 miles per 5 gallons
B. 525 miles per 15 gallons
C. 725 miles per 25 gallons
D. 625 miles per 25 gallons
E. 50 miles per 3 gallons
SUBMIT
Answer:A
Step-by-step explanation:125 miles divided by 5 gallons would equal 25, meaning 25 gallons per mile
If the two triangles are congruent, state how you know. If not, state "not congruent."
1.AAS
2.ASA
3.SSS
4.SAS
5.not congruent
If g stands for a whole number, find the first three possible values of g2 + 3.
3, 4, 7
1, 4, 7
3, 5, 7
0, 4, 7
So the first three possible values of g^2 + 3 are:
3, 4, 7
The first option is the correct one.
Which ones are the first three possible values?
The set of the whole numbers is {0, 1, 2, 3...}
Then the first possible value is when g = 0.
0^2 + 3 = 3
The second possible value is when g = 1
1^2 + 3 = 4
The third possible value is when g = 2.
2^2 + 3 = 7
So the first three possible values of g^2 + 3 are:
3, 4, 7
The first option is the correct one.
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Answer:
3,4,7
Step-by-step explanation:
jus took the test
I really need help can u help me please ?
Answer:
Answers all found below.
Step-by-step explanation:
1) Given from diagram, RT = RS + RT
RT = 2cm + 2.5cm = 4.5cm
2) Given from diagram, AC = AB + BC
BC = AC - AB
= [tex]6 in-2\frac{3}{4} in\\=3\frac{1}{4} or 3.25in[/tex]
3)Given from diagram, XZ = XY + YZ
XZ = [tex]3\frac{1}{2} +\frac{3}{4} \\=4\frac{1}{4} or 4.25in[/tex]
4)Given from diagram, WX = XY and WY = 6cm
WX = WY / 2
= 6 / 2
= 3cm
For Questions 5,6 and 7, refer to the attached photos, apologies for the terrible drawing.
5) From the diagram,
RS + ST = RT
5x + 3x = 48
8x = 48
x = 48 / 8
= 6
6) From the diagram,
RS + ST = RT
2x + 5x+4 = 32
7x + 4 = 32
7x = 32 - 4
7x = 28
x = 28 / 7
= 4
7) From the diagram,
RS + ST = RT
6x + 12 = 72
6x = 72 - 12
6x = 60
x = 60 / 6
= 10
Copy the figure below onto a separate sheet of paper. Find the image of the figure under reflections in line m and then line t. In the box below, describe the rotation equivalent to the composition of reflections with respect to lines m and t.
The reflection of the quadrilateral DEFG will be given in the figure.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Reflection does not change the size and shape of the geometry.
The image of the figure under reflections in line m and then line t.
The reflection of the quadrilateral DEFG will be given in the figure.
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A system of three linear equations in three variables is inconsistent. how many solutions to the system exist? none one three infinitely many
No solutions exist to this system of equations
A system of equations is said to be inconsistent if the two equations do not agree, meaning that there is no set of values that can simultaneously satisfy each equation. For example, the most basic inconsistent system of equations could be x = 4 a nd x = 5 at same time which is not possible.
A single equation in three unknowns can be interpreted geometrically in 3-dimensional space. If we look at a system of such linear equations, the solution set is the set of all points lying in all of the corresponding planes.
Systems of equations in three variables that are inconsistent could result from three parallel planes, two parallel planes and one intersecting plane, or three planes that intersect the other two but not at the same location.
Hence, No solutions exist to this system of equations
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Answer:
a
Step-by-step explanation:
Directions: Find the product and simplify
(3m+n)(3m-n)
ty <3
Answer:
9m²-n²
Step-by-step explanation:
(3m+n)(3m-n)
This is so easy algebraic expression.
Just rewrite as,
[tex](3m) {}^{2} - n {}^{2} [/tex]Simplifying,
[tex]9m {}^{2} - n {}^{2} [/tex][Alternate method is there]
In a school of 100 students School Population By Gender
Males Females Total
Freshman 8 17 25
Sophomores 15 10 25
Juniors 12 13 25
Seniors 15 10 25
Total 50 50 100
In a school of 100 students, what is the probability of randomly selecting a student that is either a
female or a senior?
The probability of randomly selecting a student that is either a female or a senior is 3/4.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Males Females Total
Freshman 8 17 25
Sophomores 15 10 25
Juniors 12 13 25
Seniors 15 10 25
Total 50 50 100
Now, the probability of randomly selecting a student that is either a
female or a senior
= 50/100 + 25/100
= 75/100
= 3/4
Hence, the probability of randomly selecting a student that is either a female or a senior is 3/4.
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A sprinkler rotates 360 degrees the total are watered is 204yds squared
what is the raduius
The radius of the area the sprinkler has watered is 8.06 yards.
What is Rotation ?Rotation is spinning around a fixed point with a fixed radius in circular motions.
It is given that a sprinkler rotates 360 degree
The area watered is 204 sq. yards
Radius = ?
A sprinkler rotates in circle
Therefore the area of the circle = π r²
204 = π r²
204 * 7 /22 = r²
r² = 64.91
r = 8.06 yards
Therefore the radius of the area the sprinkler has watered is 8.06 yards.
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isosceles triangle has a base that measures 14 units.
A triangle has a base length of 14. The other 2 sides have a length of y.
The value of y, the length of each leg, must be
equal to 7.
between 7 and 14.
greater than 7.
between 14 and 28.
The value of y, the length of each leg, must be greater than 7.
What is Isosceles triangle?
This is a type of triangle with two equal sides.
Rules for side length of trianglesThe sum of any two sides of a triangle must be greater than the third side.Let the first, second and third side = a, b and c respectively
(b - a) < c < (a + b)
For an isosceles triangle with base of 14 units, the two other sides must be equal.
c < (a + b)
c = 14
a = b = y
14 < (y + y)
14 < 2y
7 < y
Thus, the value of y, the length of each leg, must be greater than 7.
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Answer: C. greater than 7.
Step-by-step explanation: Trust Me!
Did it on Edge got the answer correct! :)
h is a trigonometric function of the form h(x)=acos(bxc)+d. Below is the graph of h(x) The function has a maximum point at (3,6) and a minimum point at (6.5,-9) find the formula for h(x). Give an exact expression.
h(x)=
*from klan academy*
Please Help URGENT
Answer:
acos(bxc)+d
h(x)=acos(bxc)+d
The function has a maximum point at (3,6) and a minimum point at (6.5,-9) so
h(x)=6-acos(3bx)+9
or
h(x)=-acos(3bx)+15
Step-by-step explanation:
Please analyze and reasure that this answer is correct.
An exact expression of h(x) is 7.5cos(51.4x - 154.3)-1.5.
What is a trigonometric function?Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions.
the difference in y values from max to min = 15. 15/2 = a
max cosine = 1, min cosine =-1
7.5 x 1 - 1.5 = 6
7.5x -1 -1.5 = -7.5-1.5= -9
h(x) = 7.5cos(bx+c) -1.5
now just get a period or frequency that matches the x coordinates 3 and 6.5 to get b and c
at (3,6) cosine = 1 to get a maximum value. cosine is at a max when cos(bx+c) = 1 and bx+c=0, 360, 720...
if x=3, then 3b +c=0 and c=-3b
for (6.5,-9) to be a minimum h value, then cos(6.5b+c) =-1 that happens when the angle = 180. +n360 for any integer n. 6.5b+c = 180
c= 180-6.5b
c=-3b
180-6.5b =-3b
add 6.5b to both sides to get
180= 3.5b
b = 180/3.5 = 51 1/7
c=-3b = -153 3/7
h(x) = 7.5cos(51.4x - 154.3)-1.5
Therefore, exact expression of h(x) is 7.5cos(51.4x - 154.3)-1.5.
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Please help!!! Very much appreciated!! Natalie has a budget of $15,000 dollars to spend on tracking devices to study bison. A radio tracker costs $650 and a GPS tracker costs $1400. Natalie wants to buy at least 9 radio trackers and more than 3 GPS trackers.
The following system of inequalities represents this situation, where x is the number of radio trackers and y is the number of GPS trackers.
x ≥ 9
y > 3
650x + 1400y ≤ 15000
Which yellow shaded region corresponds to Natalie's possible choices?
Answer:
d.)
Plot these inequalities:
x ≥ 9y > 3650x + 1400y ≤ 15000Graphed below (shaded yellow region):
where all the inequalities meet or touches each other.
What lines are skew to EF?
What plane are parallel to plane ADE?
The skew lines are CG, DH, AD, BC.
The parallel lines are BC, EH, FG.
What is skew lines?Two or more lines which have no intersections but are not parallel.
As, by the definition
The lines skew to EF is CG, DH, AD, BC
The parallel to AD is BC, EH, FG.
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Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet.
Old garden area = New garden area
x2 = (2x)(x – 16)
x2 = 2x2 – 32x
0 = x2 – 32x
What is the value of x that makes sense in this context?
What are the dimensions of the new garden?
The value of x that makes sense in this context is; 32.
The dimensions of the new garden is; 64 by 16.
How to find the real dimensions of the rectangle?The expression that represents the problem statement is;
x² = (2x)(x – 16)
Expanding the bracket gives us;
x² = 2x² – 32x
x² - 32x = 0
x(x - 32) = 0
Thus; x = 0 or x = 32
x can't be 0 and as such the value of x is 32.
Thus;
The length of the new garden is; l = 2x = 64.
The width of the new garden is; w = x - 16 = 32 - 16 = 16
The dimensions of the new garden are therefore; 64 by 16
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Which segment is a perpendicular bisector of triangle ABC?
helpp due 20 mins..
Answer:
SR and RZ
Step-by-step explanation:
A perpendicular bisector is a line segment that passes through the midpoint of a side of a triangle. In other words, If it goes through a side, it should split the segment in half perfectly. Furthermore, it must be perpendicular to the side it passes through (it should form a ninety-degree angle with the side). Given these two rules, one can say that one of the perpendicular bisectors is SR. SR forms a right angle with (and is thus perpendicular to) side AB. Furthermore, AS is congruent to (has the same length as) SB, which means SR cuts AB in half exactly. Another bisector would be RZ (for similar reasoning). Let me know if that doesn't make sense.
Solve 6(2)x = 384.
will mark brainliest !
Answer:
6(2)x = 384
12x = 384
12x/12 = 384/12
x = 32
Step-by-step explanation:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 16, negative 1, 2, negative 1, negative 4, negative 1. Analyze the table of values for the continuous function, f(x), to complete the statements. A local maximum occurs over the interval . A local minimum occurs over the interval
Using the definitions of local maximum and minimum, it is found that:
There is a local maximum in the interval [-1,0], as the function decreases in the interval.There is a local minimum in the interval [1,2], as the function increases in the interval.Where are there local maximums and minimum on a function?When a function changes from increasing to decreasing, there is a local maximum.When a function changes from decreasing to increasing, there is a local minimum.In this problem, we have that the function is as follows:
f(-3) = -16.f(-2) = -1.f(-1) = 2.f(0) = -1.f(1) = -4.f(2) = -1.Hence:
There is a local maximum in the interval [-1,0], as the function decreases in the interval.There is a local minimum in the interval [1,2], as the function increases in the interval.More can be learned about the maximum and the minimum of a function at https://brainly.com/question/13539822
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Answer:
-2,0 0,2
Step-by-step explanation:for anyone needing it in the future cause I couldn't find the answer
heeelllp mmmeeee im in an rush
Answer:
113.1 m
Step-by-step explanation:
Geometry) Find the value of x
Answers are
A. 108^o
B. 36^o
C. 136^o
D. 54^o
(The picture is below) THANK YOU!
The correct answer is 108° i.e Option A.
.
.
.
HOPE IT HELPS! :)
Pls, help me work this out!
Simplify 2(a + 3b) + 3(4a + b).
(A) 6a+6b
(B) 14a + 9b
(C) 14a + 4b
(D) 6a+ 7b
Answer: = 14a + 9b
Step-by-step explanation:
distribute:
2(a+3b) + 3(4a+b)
2a + 6b + 12a + 3b
combine like terms:
2a + 6b + 12a + 3b
14a + 6b + 3b
14a + 6b + 3b
= 14a + 9b
A quantity with an initial value of 6500 decays exponentially at a rate of 45%
every 2 minutes. what is the value of the quantity after 0.1 hours, to the
nearest hundredth?
1081.44 is the value of the quantity after 0.1 hours, to the nearest hundredth.
What Is percent in simple words?
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.Based on the given conditions, formulate = [tex]6500 * (1 - \frac{45}{100} )^{( 0.1 * 60/2)}[/tex]
Evaluate the equation/expression= 1081.4375
Round the number: 1081.44
Therefore, 1081.44 is the value of the quantity after 0.1 hours, to the nearest hundredth.
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