To found the amount of money after 8 years, we will use the formula below:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where p is the principal
r is the rate
n is the number the interest is applied
t is the time in year
From the question, P=7000 r=4.5% =0.045 n=4 t=8
substitute the values into the formula and evaluate
[tex]A=7000(1+\frac{0.045}{4})^{4\times8}[/tex][tex]A=7000(1+0.01125)^{32}[/tex][tex]=7000(1.01125)^{32}[/tex][tex]\approx10013.16[/tex]Hence, there would be $10013.16 after 8 years
6. 1 and 2 form a linear pair. Ifm/l = 5x + 9 and m/2 = 3x + 11, find the measures of bothangles.
Answer
Angle 1 = 109°
Angle 2 = 71°
Explanation
We are told that Angle 1 and 2 form a linear pair. This means that they sum up to give 180°.
Angle 1 = 5x + 9
Angle 2 = 3x + 11
(Angle 1) + (Angle 2) = 180°
5x + 9 + 3x + 11 = 180°
8x + 20° = 180°
8x = 180° - 20°
8x = 160°
Divide both sides by 8
(8x/8) = (160°/8)
x = 20°
Angle 1 = 5x + 9 = 5 (20°) + 9° = 100° + 9° = 109°
Angle 2 = 3x + 11 = 3 (20°) + 11 = 60° + 11° = 71°
Hope this Helps!!!
2.) The local museum has a scale model of a T-REX dinosaur. The scale is 1 inch for the model = 4 feet of a real T-REX. What is the height of the museum's model in inches? Fact: T-REX's were approximately 20 feet tall.
Given :
The scale of the model is : 1 inch = 4 feet
The height of the actual T-Rex = 20 feet
Let the height of the model = x
Using the ratio and the proportional
so,
[tex]\begin{gathered} x\colon20=1\colon4 \\ \\ \frac{x}{20}=\frac{1}{4} \\ \\ x=20\cdot\frac{1}{4}=5 \end{gathered}[/tex]find the value of x and the measure of Arc AD
First DB is a chord.
Line AC divide the chord DB into two equal length.
Hence
DE = EB
11x - 33 = 8x + 9
Collect like terms
11x - 8x = 9 + 33
3x = 42
x = 42/3
x = 14
Arc of AD
A circle is 360 degrees. Line AC divide circle into two semi circles. Hence, angle of a semi circle is 180 degrees.
Arc AD = 180 - 58 = 122
Write the inequality using interval notation. Graph the inequality.x > -5
Given:
an inequality is given as x ≥ -5
Find:
we have to write the inequality using interval notation and graph the given inequality.
Explanation:
The inequality x ≥ -5 in the interval notation is written as x ∈ [-5, ∞)
The graph of the given inequality can be drawn as below
The shaded area represents the graph of inequality x ≥ -5.
I want to know the every step and how to solve it I was absent that day and I didn’t understand anything that the teacher teaches us please help!
We want to write the following log equation:
[tex]\ln (4x+8)=x+5[/tex]As an exponential equation.
For this, we could elevate both sides of the equation with the base e. (Euler's number). This is:
[tex]e^{\ln (4x+8)}=e^{(x+5)}[/tex]There's something important we have to notice, and it is the fact that:
[tex]e^{ln(x)}=x[/tex]That's a logarithm property. So, if we apply it to our equation:
[tex]4x+8=e^{(x+5)}[/tex]And that's the exponential equation.
Use the numbers shown to complete the table value of m .Numbers maybe used once,more than once ,or not at all . 12,26,24,10,20m 2(3m+7) 6m+141.2.There are 2 spaces per spot on the table .Numbe1 and number 2 has 2 spaces on table I just couldn't draw them
Here, we want to fill in the table
Mathematically, we have it that the expressions are the same
This is because;
[tex]2(3m+7)\text{ = 6m+14}[/tex]So, what this mean is that we are going to fill in the same values on the table for each value of m
For m = 1;
We have;
[tex]\begin{gathered} 2(3(1))+7)=6(1)+14\text{ = 20} \\ \end{gathered}[/tex]For the second value, we will replace the value of m with 2
That would be;
[tex]6(2)\text{ + 14 = 12 + 14 = 26}[/tex]Conclusively, we have the value 20 in the first row and the value 26 in the second row
use the appropriate compound interest formula to compute the balance in the account after the stated period of time $24,000 is invested for 3 years with an APR of 3% and daily compounding.
Given: compound interest
Balance = P = $24,000
Time = t = 3 years
Rate = r = 3% = 0.03
Daily compounding, n = 365
so,
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]substitute with P, r, t, and n
[tex]\begin{gathered} A=24000\cdot(1+\frac{0.03}{365})^{365\cdot3} \\ \\ A=24000\cdot1.09417=26260 \end{gathered}[/tex]So, the answer will be the balance after 3 years = $26,260
can you define equation and give an example of two equations
The definition of the equation :
It is a mathematical statement or expression which have two equal sides , each side can contain certain variables or constants
For example :
[tex]2x+3=5[/tex]Another example :
[tex]6-3x=5x+8[/tex]if 4 tickets costs$40, how much does 17 tickets cost?
Explanation
Step 1
find the unit rate ( the cost of 1 ticket)
[tex]\begin{gathered} \text{unit cost=}\frac{40\text{ dollars}}{4\text{tickets}} \\ \text{unit cost=10 dollars per ticket} \end{gathered}[/tex]Step 2
now, multiply the unit cost by the number of tickets
[tex]\begin{gathered} \text{total cost= number of tickets}\cdot\text{ unit cost} \\ \text{total cost=17 tickets}\cdot10\text{ }\frac{dollars\text{ }}{\text{ticket}} \\ \text{total cost=170 dollars} \end{gathered}[/tex]I hope this helps you
2. The value of the 4th term is 80. The sequence is beingdoubled at each step. Write the recursive equation for thissequence.
Find the circumference and area of a circle with diameter 6 inches. Use 3.14 for π
Recall the definition of the area of a circle that is given by
[tex]A=\pi r^2[/tex]Since we have the diameter of the circle, the radius is 3in. So,
[tex]A=(3.14)3^2=(3.14)9=28.26[/tex]Now, to find the circumference
[tex]C=D(3.14)=(6in)(3.14)=18.84[/tex]Where D is the diameter. Thus, the area is 20.26 square inches and the circumference is 18.84 inches
One of the legs of a right triangle measures 12 cm and its hypotenuse measures 14Find the measure of the other leg. If necessary, round to the nearest tenth.
To obtain the measure of the other leg of the right triangle, the following steps are necessary:
Step 1: Draw a sketch of the right triangle and label it with the dimensions provided in the question, as below:
Step 2: Apply the Pythagorean theorem to obtain the measure of the other leg of the right triangle, as follows:
The Pythagorean theorem goes as follows:
[tex]\text{hypothenus}^2=\text{opposite}^2+\text{adjacent}^2[/tex]Thus:
[tex]\begin{gathered} 14^2=12^2+x^2 \\ 196=144+x^2 \\ 196-144=x^2 \\ 52=x^2 \\ x^2=52 \\ x=\sqrt[]{52}=7.21 \\ x=7.2\text{ (to the nearest tenth)} \end{gathered}[/tex]Therefore, the measure of the other leg of the right triangle is 7.2cm
HELP QUICK Proving the Parallelogram Side TheoremTry itGiven: ABCD is a parallelogram.Prove: ABCD and BC DAAngles segments Triangles Statements Reasonsdraw ACABCD is a parallelogramZBCA and ZDACare alt interior anglesZDCA and ZBACare alt. interior anglesBBСStatements✓ 1. ABCD is a parallelogramReasons1. givenАDCorrect! Assemble the nextstatement
Parallelogram ABCD
Then
Angles
Also AB ~CD , and BC~DA
Statements reason is
"2 lines are parallel,if alternate internal angles are CONGRUENT "
Then, this means lines BC ,and AD , are equal and parallel
A businesswoman buys a new computer for $3000 for each year that she uses it the value depreciates by $300. The equation y=-300+3000 gives the value y of the computer after x years. What does the x intercept mean in this situation? Find the x intercept. After how many years will the value of the computer be 1500?
Answer:
Explanation:
Given:
y= -300x+3000
To find the x-intercept, we let the value of y equal to zero. So,
[tex]\begin{gathered} y=-300x+3000 \\ 0=-300x+3000 \\ \text{Simplify and rearrange} \\ 300x=3000 \\ x=\frac{3000}{300} \\ \text{Calculate} \\ x=10 \\ x-intercept\text{ : (10,0)} \end{gathered}[/tex]The x-intercept means the number of years x when the value y of the computer is zero.
For the computer to be valued at $1500, the number of years would be:
Let:
y=1500
Then,
[tex]\begin{gathered} y=-300x+3000 \\ 1500=-300x+3000 \\ \text{Simplify and rearrange} \\ 300x=3000-1500 \\ 300x=1500 \\ x=\frac{1500}{300} \\ \text{Calculate} \\ x=5\text{ years} \\ \end{gathered}[/tex]Therefore, It would take 5 years for the computer to be valued at $1500.
Find the equation of the line. Use exact numbers. y = xt Y 07 8 7 6 5 ed must not mable textboo any page rly written in ink in epted. e condition of the bo as above ir -9-8-7-6-5-4-3-2 Good;F 3- 2 1 + 2 1 2 3 4 5 6 7 8 9 -2+ -3+ -47 -5 -6+ -77 -8+ -9
step 1
Find the slope
take the points
(0,3) and (2,0)
so
m=(0-3)/(2-0)
m=-3/2
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-3/2
b=3
substitute
y=-(3/2)x+3The function we need to use answer this is h(r)= √4-r
Given:
[tex]\begin{gathered} h(r)=\sqrt{4}-r............(1) \\ 3h(r)+2=4..............(2) \end{gathered}[/tex]To find:
The value of r.
Explanation:
Using function (1) in (2),
[tex]\begin{gathered} 3(\sqrt{4}-r)+2=4 \\ 3(2-r)=4-2 \\ 6-3r=2 \\ -3r=-4 \\ r=\frac{4}{3} \end{gathered}[/tex]Therefore, the value of r is,
[tex]\frac{4}{3}[/tex]Final answer:
The value of r is,
[tex]\frac{4}{3}[/tex]Working together, it takes two computers 5 minutes to send out a company's email. If it takes the slower computer 15 minutes to do the job on its own, how long will it take the faster computer to do the job on its own?Do not do any rounding.
Given:
Working together, it takes two computers 5 minutes to send out a company's email. If it takes the slower computer 15 minutes to do the job on its own
Let the faster computer has a rate of x emails per minute
And the slower computer has a rate of y emails per minutes
And let the total mails = z
When the two computers working together, the time taken to send the mails = 5 minutes
So,
[tex]x+y=\frac{z}{5}\rightarrow(1)[/tex]And the slower computer 15 minutes to do the job on its own
So,
[tex]y=\frac{z}{15}\rightarrow(2)[/tex]substitute equation (2) into equation (1)
[tex]\begin{gathered} x+\frac{z}{15}=\frac{z}{5} \\ x=\frac{z}{5}-\frac{z}{15}=\frac{2z}{15} \end{gathered}[/tex]So, the answer will be:
The faster computer will do the job in a time = 15/2 = 7.5 minutes
Identify a pair of segments that are marked perpendicular to each other on thediagram below. (Diagram is not to scale.)HEGFis perpendicular toSubmit Answerattempt out of 2
From the figure in the question,
At E there is an angle of 90 degrees
By definition of perpendicular lines
[tex]\text{Two lines are perpendicular if they form an agle of 90}^{\circ}[/tex]Therefore, since the angle at E is 90 degrees
thene
Line HE is oerpendicular to line EF
help me show your process anx simply by coming like terms
To simplify by combining like terms, we bring the terms with the same alphabets description together.
In this case, the ones with a come together, the ones with a^2 also come together.
Thus, we have;
[tex]\begin{gathered} 2a-8a^2+a-3a^2\text{ + 5 - 2} \\ \\ a-\text{terms ; 2a + a} \\ \\ a^2terms;-8a^2-3a^2 \\ \\ \text{And; +5 -2} \\ \\ We\text{ have;} \\ \\ 3a-11a^2\text{ + 3} \end{gathered}[/tex]Please help me with this problem:Solve the quadratic equation x^2 + 2x = 35 using two different methodsAnswer:Method 1:Method 2:
We must solve by two different methods the following equation:
[tex]x^2+2x=35.[/tex]Method 1: Completing the square1) We rewrite the equation above as:
[tex]x^2+2\cdot1\cdot x=35.[/tex]2) Now, we add 1² on both sides of the equation:
[tex](x^2+2\cdot1\cdot x+1^2)=35+1^2=36.[/tex]3) We see that the left and right sides can be written as squares:
[tex](x+1)^2=6^2.[/tex]4) Taking the square root on both sides, we get two solutions:
[tex]\begin{gathered} x+1=+6\Rightarrow x_1=6-1=5, \\ x+1=-6\Rightarrow x_2=-6-1=-7. \end{gathered}[/tex]Method 2: Using the quadratic formula1) We rewrite the equation above as:
[tex]x^2+2x-35=0.[/tex]2) We identify a quadratic equation:
[tex]a\cdot x^2+b\cdot x+c=0.[/tex]With coefficients:
• a = 1,
,• b = 2,
,• c = -35.
The roots of this equation are given by:
[tex]\begin{gathered} x_1=\frac{-b+\sqrt{b^2-4ac}}{2a}, \\ x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}. \end{gathered}[/tex]3) Replacing the coefficients of the quadratic equation in the formula above, we get:
[tex]\begin{gathered} x_1=\frac{-2+\sqrt{2^2-4\cdot1\cdot(-35)}}{2\cdot1}=\frac{-2+\sqrt{144}}{2}=\frac{-2+12}{2}=\frac{10}{2}=5, \\ x_2=\frac{-2-\sqrt{2^2-4\cdot1\cdot(-35)}}{2\cdot1}=\frac{-2-\sqrt{144}}{2}=\frac{-2-12}{2}=-\frac{14}{2}=-7. \end{gathered}[/tex]AnswerThe roots of the polynomial are:
• x₁ = 5
,• x₂ = -7
Without finding the inverse of the function, determine the range of the inverse of f(x) = sqrt (x-4)a) all positive real numbersb) all real numbers less than or equal to 4c) all real numbers greater than or equal to 4d) all negative real numbers
Given:
Given function is
[tex]f(x)=\sqrt[]{x-4}[/tex]Range of the inverse of f(x) be
all real numbers greater than or equal to 4.
Option C is the final answer.
An estimated brand value of some company is $133,146,000,000 round this amount to the nearest ten billion
One ten billion is a value with 10 zeros: 10,000,000,000
To round the given value to the nearest 10 billion you have to look at the value that is in the place of the billion:
$133,146,000,000
Use a graph to perform the reflection of y = f (x) across the x-axis. Identify the graph of the function and its reflection.
Solution
Step 1
A reflection is a mirror image.
Answer
Please label the inequality to find the solution set and the possible values of x so I know
For example, I can choose
2x > 6/12
the value of x can be
[tex]\begin{gathered} x>\frac{6}{12}\cdot\frac{1}{2} \\ x>\frac{6}{24} \\ x>\frac{1}{4} \end{gathered}[/tex]x must be greater than 1/4
Given the vectors u=8i – 3j and v=-i+6j, find u • v.u v= ]06iХ5?
We have the vectors:
u = 8i – 3j
and
v = - i + 6j
They can be written as:
u = 8i – 3j = (8, -3)
v = - i + 6j = (-1, 6)
In order to find the dot product between them, we simply multiply the first terms of both and the second terms of both and then we add the results:
Then,
u · v = (8, -3) · (-1, 6)
= 8· (-1) + (-3) · 6
= -8 - 18 = -26
Answer: u · v = -26Question 513 pointsFind the slope of the line passing through the points (2,1),(0,1).DiscussА 0B 1C 1/2D 2/1E-1
Answer
Option A is correct.
Slope = 0
Explanation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (2, 1) and (0, 1)
x₁ = 2
y₁ = 1
x₂ = 0
y₂ = 1
[tex]\text{Slope = }\frac{1-1}{1-2}=\frac{0}{-1}=0[/tex]Hope this Helps!!!
please help me ASAP
the answer is 5
since the first derivative of g(x) is 5
The volume of a rectangular prism is 12x^5 -27x^3. What are the dimensions of the prism?
Solution
How do you get the volume of a rectangular prism?
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
[tex]V=12x^5-27x^3[/tex][tex]\begin{gathered} V=\text{lwh} \\ \text{where} \\ l=\text{length}\mathrm{}w=\text{width,h}=\text{height} \\ Volume=12x^5-27x^3 \end{gathered}[/tex][tex]\begin{gathered} v=12x^5-27x^3 \\ =3x^3(4x^2-9) \\ =3x^3((2x)^2-3^2) \end{gathered}[/tex]Assume the length is the
[tex]\begin{gathered} length=3x^3 \\ (2x)^2-3^2 \\ \text{difference of two square} \\ (2x-3)(2x+3) \\ \text{width}=2x-3 \\ \text{height = 2x+3} \end{gathered}[/tex]Therefore the dimension of the prism are
[tex]\begin{gathered} l=3x^3 \\ w=2x-3 \\ h=2x+3 \end{gathered}[/tex]I need help with this geometry question I’m confused for some reason.
We are asked to determine which of the triangles is a right triangle. To do that we can apply the Pythagorean theorem, taking the larger side as the hypotenuse. If the Equality of the Pythagorean theorem holds, then the triangle is a right triangle.
Let's take triangle P. The largest side is 30, therefore, we take this as the hypotenuse. The Pythagorean theorem is as follows:
[tex]h^2=a^2+b^2[/tex]Where:
[tex]\begin{gathered} h=\text{ hypotenuse} \\ a,b=\text{ sides} \end{gathered}[/tex]Now we substitute the values:
[tex]30^2=12^2+24^2[/tex]Now we solve the squares:
[tex]900=144+576[/tex]Adding the terms:
[tex]900=720[/tex]Since the terms on the right side and the left side are not equal, this means that the given triangle is not a right triangle.
Now, let's do the same procedure for triangle Q. We have that the hypotenuse in this triangle is 41. Therefore, substituting in the Pythagorean theorem we get:
[tex]41^2=40^2+9^2[/tex]Solving the square:
[tex]1681=1600+81[/tex]Adding the terms:
[tex]1681=1681[/tex]Since we got the same result on both sides this means that the triangle Q is a right triangle.
Use two equations in two variables to solve the application.Peter invested some money at 6% annual interest, and Martha invested some at 12%. If their combined investment was $4,000 and their combined interest was $360, how much money (in dollars) did Martha invest?
Given
Peter invested some money at 6% annual interest, and Martha invested some at 12%. If their combined investment was $4,000 and their combined interest was $360, how much money (in dollars) did Martha invest?
Solution
Let Peter's investment be X
Let Martha's investment be Y
[tex]\begin{gathered} x+y=4000\ldots Equation\text{ (i)} \\ 0.06x+0.12y=360\ldots Equation\text{ (i}i) \end{gathered}[/tex]I will solve your system by substitution.
(You can also solve this system by elimination.)
Step 1
[tex]\begin{gathered} x+y=4000 \\ \text{make x the subject of the formula},\text{ therefore we substract y from both sides} \\ x+y-y=\text{ 4000-y} \\ x=4000-y \end{gathered}[/tex]Step 2
Substitute for x in Equation (ii)
[tex]\begin{gathered} 0.06(4000-y)+0.12y=360 \\ 240-0.06y+0.12y=360 \\ 240+0.06y=360 \\ \text{make y the subject of the formula} \\ 0.06y=360-240 \\ 0.06y=120 \\ \text{Divide both sides by 0.06} \\ \frac{0.06y}{0.06}=\frac{120}{0.06} \\ \\ y=2000 \end{gathered}[/tex]Step 3
[tex]\begin{gathered} \text{Substitute for y in equation (i)} \\ x+2000=4000 \\ x=4000-2000 \\ x=2000 \end{gathered}[/tex]The final answer
Martha's investment is $2000