Answer:
x = 60, -70
Step-by-step explanation:
Let's move the constant (-130) to the right by adding it to both sides.
[tex]\sqrt{x} 4(x+5)^{2} =130[/tex]
Now, we can rewrite the equation as (since the square root and square cancel):
2 × | x + 5 | = 130
To get rid of the 2 multiplication, we can divide both sides by 2:
| x + 5 | = 65
This leaves us with 2 equations:
x + 5 = 65
x + 5 = -65
Simplify.
x1 = 60
x2 = -65
Use the Distributive Property to simplify (–5 – c)( –1).
5 + c
–5 + c
–5 – c
5 – c
Samantha travels 175 miles in 25 hours? How many miles does Samantha travel in 5 hours?
Answer:
THERES MUCH INFORMATION EXCLUDED!
Step-by-step explanation:
She travels 7 miles per 25 hours
If the total distance travelled was 500 miles and the time it took you was 5 hours, then your average speed was 500 / 5 = 100 miles per hour (mph).
BASED ON MY OWN CALCULATIONS:
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Yesterday, you entered into a futures contract to sell 62,500 at $1.50 per . Your initial performance
bond is $1,500 and your maintenance level is $500. At what settle price will you get a demand for additional
funds to be posted?
The settle price at which you will get a demand for additional funds to be posted is $1.4840 per €.
What is contract?
An agreement between parties that results in legal duties for both parties is known as a contract. Mutual consent, demonstrated by a valid offer and acceptance, sufficient consideration, capability, and legality are the fundamental components needed for the agreement to be a legally enforceable contract.
Provided data from the question;
Futures contract to buy in euros = €62,500
Future contract to buy in dollar = $93,750 ( €62,500 × $1.50)
Initial performance of bond = $1,500
Maintenance level = $500
To determine the settle price at which you get a demand for additional funds to be posted =
Future contract to buy in dollar - (initial bond performance - maintenance level) ÷ future contract to in euros
$93,750 - ($1,500 - $500)
= $93,750 - $1,000
$92,750 ÷ €62,500
= $1.484
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What is the coefficient in this expression?
3/2
xy
Ox
OY
in this equation ox is your answer.
Simplify the expression. 11z +9-7=
Answer: 11z+2
Step-by-step explanation:
One factor of the function f(x) = x3 − 7x2 + 14x − 8 is (x − 4). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer.
According to the plotted graph, the x intercepts are (1,0),(2,0) and (4,0) and the y intercept is (0, -8)
Intercepts:
In the graph theory, the x-intercept is the point where a line crosses the x-axis, similarly the y-intercept is the point where a line crosses the y-axis.
Given,
One factor of the function f(x) = x³ − 7x² + 14x − 8 is (x − 4).
Here we need to identify the x and y intercept of the function through the graph of the function.
Here we have to do the following steps on the graphing calculator, to plot the function,
1) Set the x and y axis values on the graphing calculator.
2) Enter the required function on the input box.
3) Which ever the point that placed on the x axis are the points that refers the x intercept
4) Similarly, which ever the point that placed on the y axis are the points that refers the y intercept.
Now, the graph of the function is plotted and attached below.
Therefore, the x intercept are (1,0), (2,0) and (4,0) and the y intercept is (0,-8)
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What is the factored form of this polynomial?
p(x) = x³ + 7x² + 4x − 12
Select the correct answer from each drop-down menu
Answer:
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x3+7x2
Group 2: 4x-12
Pull out from each group separately :
Group 1: (x+7) • (x2)
Group 2: (x-3) • (4)
Answer:
from the drop down menu the answers are:
x-1
x+2
x+6
Graphing and Solving Inequalities
m-1<-3
a
-4y <-20
5+b>1
-18
There is a graph underneath each one with lines and arrows.
The solution to inequalities are as follows.
What is inequality equation?
Inequalities are the mathematical expressions during which either side don't seem to be equal. In difference, in contrast to in equations, we tend to compare 2 values. The equal sign up between is replaced by but (or but or equal to), larger than (or larger than or equal to), or not capable sign.
Main body:
A) m-1 <-3
to solve this we need to take link terms to one side
= m< -3+1
= m < -2
B) -4y <-20
cancelling -ve sign on both sides,
= 4y <20
= y <5
C) 5+b>1
take link terms to one side
b > -4
Hence the graph is as given
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If f(x) = x + 4 and g(x) = x2 + 6x + 8, what is f(x) divided by g(x)?
Answer:
[tex]\frac{x+4}{8x+8}[/tex]
Answer: 1/(x+2)
Step-by-step explanation:
[tex]\frac{x+4}{x^2+6x+8}\\[/tex]
[tex]\frac{x+4}{(x+2)(x+4)}[/tex]
the x+4 cancel each other so we are left with 1/(x+2)
if the main question was how to foil the denominator x2 + 6x + 8, i can quickly explain that.
x2 + 6x + 8
a2 + bx + c
first step is to multiply the first variable with that last or a * c which in this case would give 1 * 8 = 8
the next step would be to look at the middle number which is b, in our case 6.
so then you look for two number that can multiply to to give 8 as well as add up to 6. With easy guessing one will come up with 4 and 2.
with this values you can impute them directly into the equation as
x^2 +4x +2x+ 8
split the equation then factor
(x^2 +4x) (2x+ 8)
x(x+4) 2(x+4) note that the factored equation must always be the same in the bracket. If they are not the same then you have made a mistake somewhere across the line.
with the results giving (x+2)(x+4)
Suppose there are 9 freshman, 13 sophomores, 13 juniors, and 16 seniors running for the offices of president, vice president, and secretary. If no person can hold more than one office, in how many different ways could these people be elected to these positions?
These people are elected in 47814 different ways to these positions.
Given, there are 9 freshman, 13 sophomores, 13 juniors and 16 seniors running for the offices of president, vice president, and secretary.
Now, the number of different ways in which these people can be elected for these positions be,
C(9 , 1)×C(13 , 1)×C(13 , 1)×3! + C(9 , 1)×C(13 , 1)×C(16 , 1)×3! + C(9 , 1)×C(13 , 1)×C(16 , 1)×3! + C(13 , 1)×C(13 , 1)×C(16 , 1)×3!
= 9×13×13×6 + 9×13×16×6 + 9×13×16×6 + 13×13×16×6
= 9126 + 11232 + 11232 + 16224
= 47814
So, these people can be elected in 47814 different ways.
Hence, these people are elected in 47814 different ways to these positions.
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)
The time taken for the rocket to reach its maximum height as required in the task content is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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x^2+8x+y^2+8y-112=0 center and radius
We can rewrite the equation of the circle as:
(x + 4)^2 + (y + 4)^2 = 12^2
So the center is (-4, -4) and the radius is 12 units.
How to find the center and radius of the circle?For a circle of radius R and center (a, b) the equation is:
(x - a)^2 + (y - b)^2 = R^2
Here we have the equation:
x^2 + 8x + y^2 + 8y - 112 = 0
We can complete squares to get:
(x^2 + 8x) + (y^2 + 8y) - 112 = 0
(x^2 + 2*4*x + 4^2) + (y^2 + 8y + 4^2) - 4^2 - 4^2 - 112 = 0
(x + 4)^2 + (y + 4)^2 = 112 + 16 + 16 = 144
(x + 4)^2 + (y + 4)^2 = 12^2
So we have a circle of radius of 12 units, with a center at (-4 , -4)
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The midpoint of a given line segment must lie on the given line segment.
A. Trime
OB. False
The midpoint of a given line segment must lie on the given line segment is True.
What is midpoint?
A midpoint is a location that sits in the middle of the line connecting two points and is situated between them. If a line is drawn connecting the two points, the midpoint is the place on the line that is equally distant from both points. A point B that is situated halfway between two other points, such as A and C, is said to be the midpoint. Because of this, finding the midway only requires measuring the length of the line segment and dividing it by 2.
Here the given statement is,
=> The midpoint of a given line segment must lie on the given line segment.
Here according to the given statement we know that the midpoint of the any line lies on the given line.
Hence the given statement is True.
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A rectangle has a width represented by the expression-2x+20.The length of the rectangle is 6 more than twice the width.which expression represents the area of the rectangle?
Answer:
8(x^2)+172x+920
Step-by-step explanation:
width=2x+20length=2(width)+62(2x+20)+6
=4x+46
area=lenght ×width(4x+46)×(2x+20)
=4x(2x+20)+46(2x+20)
=8(x^2)+80x+92x+920
=8(x^2)+172x+920
A small hardware store makes a profit of $20,000 during its first year. The store owner sets a goal of increasing profits by $5,000 each year for the next 4 years. Assuming that this goal in met, find the total profit during the first 5 years of business.
profit = $ ___________
What is the first term of the quotient of the following division problem?
(x³ - 1) = (x + 2)
O -0.5
O 1
O x²
Ox^4
The solution to the algebraic problem is [tex]x^{2}[/tex]
What is an Algebraic Equation?
An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.
Solution:
([tex]x^{3}[/tex] – 1) = (x+2)
On dividing ([tex]x^{3} - 1[/tex]) by (x+2)
The first term of the quotient will be x^2 by following the Long Division Method of Algebraic Division.
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3) Helen has $1.35 in her bank of nickels and dimes. There are 9 more nickels than dimes. Find the number she has of each kind.
please help me with this
Model equivalent to 16 2/3 % is Option D.
Given:
The number of students at Liam's elementary school has increased 16 2/3 % in the past two weeks.
Option D is divide into six parts with one filled which is equal to 16 2/3 %.
Total parts = 6 * 16 2/3
= 6*48+2/3
= 6 * 50/3
= 300/3
= 100%
Here total parts is equal to 100% so it is the correct option.
Therefore model equivalent to 16 2/3 % is Option D.
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8. Noah has a coin jar containing d dimes and 9 quarters worth a total of $5.00.
Select all the equations that represent this situation.
a. d+q=5
b. d+q=500
c. 0.1d +0.25q = 5
d. 10d+25q=500
e. d=50
f. q=20
Answer: A and C
d + q = 5 is one correct answer, not 500
0.1d + 0.25q = 5 as this is literally just the equation you are doing.
Write in slope intercept form.
Answer:
y=4x
Step-by-step explanation:
y2-y1/x2-x1
8-4/2-1
4/1
4 is the slope
We can find the intercept by finding when x is equal to zero by continuing the order pairs
(8,2),(4,1),(0,0)
The intercept is 0
Y=mx+b
M-slope
b- y intercept
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Evaluate the following functions.
Help
PLEASE HELP ASAP!!! Solve the problem.
Triangle KAP = triangle __ by rule __
Step-by-step explanation:
Statements Reasons
1. AK - angle bisector 1. Given
2. FP perpendicular AK 2. Given
3. <FAK congr <PAK 3. Definition angle bisector
4. Seg AK congr seg AK 4. Congr of seg's is reflexive
5. <AKF & <AKP are rt. angles 5. Def perpendicular lines
6. <AKF is congr <AKP 6. Thrm: Right angles are congr.
7. Triangle KAF congr triangle KAP 7. ASA
8. A_F = A_P 8. Corresp parts of congr tr are
congr
Michael made 22 out of 25 of his shots this basketball season. What percentage of his shots did he make?
Answer:
88%
Step-by-step explanation:
According to the Mini-Lesson, which of the following are TRUE regarding f(x) = a(b)? Check all that
apply. Assume a > 0.
00000
The Domain of the exponential functions is All Real Numbers.
The Domain of the exponential functions is a > 0.
The Horizontal Asymptote is the point (0, a).
The Horizontal Asymptote is the line y = 0.
The Range of the exponential functions is f(x) > 0.
The Range of the exponential functions is All Real Numbers.
The Horizontal Asymptote is the line =
= 0.
Answer:
The Horizontal Asymptote is the point (0, a).
The Horizontal Asymptote is the line =
= 0.
Step-by-step explanation:
The following statements are true regarding f(x) = aᵇ:
The Domain of the exponential functions is All Real Numbers.
The Horizontal Asymptote is the line y = 0.
The Range of the exponential functions is f(x) > 0.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The horizontal asymptote is the horizontal line that the graph of the function approaches as x approaches infinity or negative infinity. In this case, the horizontal asymptote is the line y = 0, which means that as x gets very large, the value of f(x) approaches 0.
The domain of the function is the set of all values of x that can be plugged into the function. For exponential functions, the domain is all real numbers because any real number can be raised to any power.
The range of the function is the set of all possible output values that the function can produce. For exponential functions, the range is f(x) > 0, which means that the function can produce any positive real number as output.
The following conclusions about f(x) = aᵇ are correct:
All Real Numbers are the domain of exponential functions.
The line y = 0 is the Horizontal Asymptote.
The exponential functions have a range of f(x) > 0.
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i need help asap with this question
Answer:
-8/9
Step-by-step explanation:
(-7/9) /( (-1 1/6) * (-3/4) ) make all fractions improper fractions
(-7/9) / (-7/6 * -3/4) solve brackets
(-7/9) / (7/8)
(-7/9) * (8/7)
-8/9
A boat is heading towards a lighthouse, where Aaden is watching from a vertical distance of 103 feet above the water. Aaden measures an angle of depression to the boat at point
A
A to be 18
∘
∘
. At some later time, Aaden takes another measurement and finds the angle of depression to the boat (now at point
B
B) to be 75
∘
∘
. Find the distance from point
A
A to point
B
B. Round your answer to the nearest tenth of a foot if necessary.
The slope concept shows that there are 335.3953 feet between points A and B.
What is a slope?The slope is calculated by dividing the vertical and horizontal changes. A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Additionally, it is the tangent to the depression angle.
The vertical change in this issue is 103 feet.
At point A, the horizontal position is represented by xA, and the angle there is 18o, so: tan 18 degree = 103/xA xA = 103/tan 18 degree xA = - 90.5653
At point B, the horizontal position is at, and the angle is at, so: tan 75degree = 103/xB xB = 103/tan 75 degree xB = - 244.83
The measurement is given by: d = xA - xB d = -90.5653 - ( - 244.83)
d = 335.3953
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Answer:
289.4
Step-by-step explanation:
Convert .51 kg to milligrams using unit fractions
The conversion of .51 kg to milligrams using unit fractions is given by 510,000 mg
How to convert from kilograms to milligrams?Units can be converted from one form to another.
Kilograms written as kg is a unit of massMilligrams written as mg is also a unit of mass.Convert kilogram to milligram:
1000g = 1 kg
1 kg = 1,000,000 mg
That is,
A kilogram is equivalent to one million milligrams.
.51 kg to milligrams
= .51 × 1,000,000
= 510,000 mg
Hence, the conversion of .51 kg to milligrams is 510,000 mg.
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A study is done on the number of bacteria cells in a petri dish. Suppose that the population site P(t) after t hours is given by the following. exponential function.
P(t)=2800(1.07)⁺
Find the initial population size
Does the function represent growth or decay?
O groats O decay
By what percent does the population size change each hour?
The initial population size is 2800
The function represents growth
The percentage through which the population size changes is given as 7%.
How to solve for the percentage growthThe formula is given as
[tex]Po = 2800 (1.07)^t[/tex]
From the formula that we have above, the initial population size is given as 2800.
We have p = P₀(1 + r)^t
where 1 + r = 1.07
We are to find the value of r
r = 1.07 - 1
r = 0.07
Given that the value of r is positive, this is the representation of a growth.
The percentage through which the change would occur = 0.07 x 100
= 7%
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How to find standard deviation using the range of the sample set?
The range of the data divided by four gives the standard deviation, which is approximately.
How do you find the sample standard deviation from the range?The range of the data divided by four gives the standard deviation, which is approximately. Simply put, that's it. To determine the range, find the highest value—the maximum—and deduct the lowest—the minimum. The range should then be divided by 4.
The range rule states that a sample's standard deviation is roughly equal to one-fourth of the data range.
In order to calculate the standard deviation, we must first determine the mean, take this mean away from each data point, square the differences, add them, divide by one less than the number of data points, and (at the very end) take the square root. The range rule, however, only needs one division and one subtraction.
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What is the distance between (4,5) and (-2, -3)?
Answer:
10 units
Step-by-step explanation:
The distance formula is as follows:
D = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(-2 - 4)^2 + (-3 - 5)^2]
= √(-6)2 + (-8)2
= √100
= 10
Answer:
10 Units
Step-by-step explanation:
Distance (d) = √(-2 - 4)2 + (-3 - 5)2
= √(-6)2 + (-8)2
= √100
= 10
Hope this helps! :)
