Answer:
$13,200
Step-by-step explanation:
You need to use the simple interest formula
I = P * r * t
I = Interest accrued
P = Principal amount invested
r = Interest rate you need to divide by 100 to get it in decimal form
t = time, in years if you are given a partial year, divide the months by 12
P = $12,000
r = 7.5% = .075
t = 1
But, because we want I to equal $990 then I is
I = $990
So we ignore our P and instead solve for the P that will give us the desired result.
I = P * r * t
$990 = P * .075 * 1
$990 = P.075 Divide each side by .075
$990/.075 = P.075/.075
$990/.075 = P
$13,200 = P
So, to earn an annual interest income of $990, $13,200 will have to be invested in the 7.5% bond.
The $13,200 amount should be invested in the 7.5% bond.
It is required to what amount should be invested in the 7.5% bond.
What is simple interest ?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
Given that:
A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest.
We know that,
I = P * r * t
P = $12,000
r = 7.5% = .075
t = 1
I = $990
So to ignore our P and instead solve for the P that will give us the desired result.
I = P * r * t
$990 = P * .075 * 1
$990 = P.075
Divide each side by .075
$990/.075 = P.075/.075
$990/.075 = P
$13,200 = P
Therefore, $13,200 amount should be invested in the 7.5% bond.
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Solve for the variable. Show all work. 5|2x| - 6 = 24
Answer:
x=3
Step-by-step explanation
Multiply 5 for 2x then get 10x then -6 add for both sides 24+6= 30
10x = 30
_ _
10 10
x=3
multiply (apex)
(2x + 3)^2
A. 4x^2 - 12x+9
B. 4x^2 + 6x+9
C. 4x^2 + 9
D. 4x² + 12x+ 9
PLEASE HELP I WILL MARK YOU BRAINLIEST THERE IS A PICTURE AT THE BOTTOM.
Answer:
72 sq. inches
Step-by-step explanation:
We are trying to find the area of the shaded part, and so we start with finding the area of the entire half that is marked (the area with measurements). The length is 8 in, as seen on the bottom, and the height is 12 in, as seen on the side. 8 * 12 = 96, so the entire portion from the shaded part to the very right is 96 sq. inches. Now we have to take out the white triangle part to find the area of the shaded part. Area of a triangle = 1/2*base * height, so we multiply 1/2 * 12 * 4, which gets us 24. Now that we know the area of the triangle, we subtract it from the previous area we got, which was the area of the shaded part plus the triangle (96). 96 - 24 = 72, so the area of the shaded portion is 72 sq. inches. Hope this helps!
At a high school, 85 students are enrolled in fine arts, 51 are enrolled in history, and 23 are enrolled in both subjects. How many students are taking fine arts or history?
Fine arts= 85 students
History= 51 students
Both subjects=23 students
Only Fine arts=85-23=62 students
Only History=51-23=28 students
Hope you found it helpful.
Find the approximate perimeter of rectangle ABCD plotted below.
B(4,5)
A(-6,0)
C(8, -3)
D(-2, -8)
Answer:
The answer is 40.2
The approximate perimeter of the rectangle ABCD plotted below is 40.24 units.
The given coordinates are B(4,5), A(-6,0), C(8, -3) and D(-2, -8).
We need to find the perimeter of the rectangle ABCD by plotting the coordinates on the graph.
What is the formula to find the perimeter of the rectangle?The formula to find the perimeter of the rectangle is 2(Length+Breadth).
By using the distance formula find the length and breadth of a rectangle.
That is Distance = [tex]\sqrt{(x_{2}-x_{1} )^{2} -(y_{2}-y_{1} )^{2}}[/tex] units.
Now, AB=[tex]\sqrt{(4+6)^{2}+(5-0)^{2} } =\sqrt{125}[/tex]=11.18 units
BC=[tex]\sqrt{(8-4)^{2}+(-3-5)^{2} } =\sqrt{80}[/tex]=8.94 units
Now, Perimeter=2(11.18+8.94)=40.24 units
Therefore, the approximate perimeter of the rectangle ABCD plotted below is 40.24 units.
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Using the Law of Detachment if a polynomial is prime, then it cannot be factored. 5x+13y is prime.
Answer and Step-by-step explanation: Law of deduction is a mathematical logic that states the following:
1) If p happens, then q happens;
2) p is true;
Then, a there is a third statement that is
3) q is also true.
In this question,
If a polynomial is prime, then it cannot be factored.
Statement p is that 5x + 13y is a polynomial and is prime, i.e., p is true.
Statement q is that "it cannot be factored"
Therefore, 5x + 13y cannot be factored.
The law of detachment is used to confirm or refute a claim.
The true statement is: 5x + 13y cannot be factored
The law of detachment states that; for statements p and q
(1) If p then q
(2) p
If the above statements are true, then the following statement is true
(3) q
The statements in the question can be represented as:
(1) If 5x + 3y is a polynomial and is prime then it cannot be factored
(2) It cannot be factored
Using the above representations of p and q, as an illustration; the third statement would be:
(3) 5x + 3y is a polynomial and is prime
Since the third statement is true, then we can conclude that
5x + 13y cannot be factored
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change 14 % into ratio into simplest form
Answer:
7:50
Step-by-step explanation:
% means /100
14 % =
[tex]14 \% \\ \frac{14}{100} [/tex]
Cross cancel common factor : 2
[tex] = \frac{7}{50} [/tex]
Write in ratio form
[tex] \frac{7}{50} \: or \: 7:50[/tex]
☽------------❀-------------☾
Hi there!
~
[tex]14[/tex]% [tex]= \frac{5}{8}[/tex]
5/8 stays the same even if its in simplest form. Simplify 5/8 reduces the fraction 5/8 to the lowest form. You can change the numerator or denominator to simplify any other fraction.
❀Hope this helped you!❀
☽------------❀-------------☾
pls answer
Relating Solutions and Roots Complete the statements.
Graph: a b or c has one real root.
Graph a b or c has a negative discriminant.
Graph a b or c has an equation with coefficients
a = 1, b = 4, c = -2
Answer:
b,a,c
Step-by-step explanation:
just took it
Answer:
1:B
2:A
3:C
is correct
Step-by-step explanation:
A pair of jeans cost $30. There is a 6% sales tax determine the total cost of the jeans
Answer:
31.80 in total
Step-by-step explanation:
multiply 30 by 0.0 and get 1.8, then add that o 30! hope this helps!
Evaluate this expression:
10x^2-5x+10 When x= -3
Step-by-step explanation:
10x² - 5x + 10
x = -3
10(-3)² -5(-3) + 10
= (10×9) + 15 + 10
= 90 + 15 + 10
= 115
The quotient of twice a number and 6 is 42
Answer:
2x/6=42. x would have to be 126.
Step-by-step explanation:
I highly doubt you need this but stilp
1) Diego measured the number of cups of water in 15 bottles of various sizes. He
made this line plot to show how many of each size he has. Diego then took all
the bottles of the most common size and poured the water into one container.
How much water is in the container?
Bottle Sizes in Cups
Answer:
[tex] 8\frac{3}{4} [/tex] cups.
Step-by-step explanation:
From the line plot made by Diego which represents bottle sizes in cups, we can see that the most common size is the bottle having 1¾ cups (there are 5 of this sizes).
If he poured all 5 of this bottle sizes in 1 container, he would have the following:
[tex] 1\frac{3}{4} * 5 = \frac{7}{4}*5 = \frac{35}{4} [/tex]
[tex] = 8\frac{3}{4} [/tex] cups.
I need this for my homework!!!It is due tommorow.
Find the solution set of the following quadratic equations using the quadratic formula.
1.) x^2 - 7x + 9 = 0
2.) 3x^2 + 10x = -3
Answer:
1) [tex]x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2[/tex] 2) [tex]x_1=-\dfrac13\,,\quad x_2=-3[/tex]Step-by-step explanation:
1)[tex]x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b = -7\,,\ c=9\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot9}}{2\cdot1}=\dfrac{7\pm\sqrt{49-36}}2\\\\x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2[/tex]
2)[tex]3x^2 + 10x=-3\\\\3x^2+10x+3=0\quad\implies\quad a=3\,,\ b =10\,,\ c=3\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-10\pm\sqrt{10^2-4\cdot3\cdot3}}{2\cdot3}= \dfrac{-10\pm\sqrt{100-36}}6\\\\x_1=\dfrac{-10+\sqrt{64}}6=\dfrac{-10+8}6=-\dfrac13\,,\qquad x_2=\dfrac{-10-8}6=-3[/tex]Which two integers is 47 between
Answer:
46 and 48
Step-by-step explanation:
Please help i will mark u branly est please!!
Answer:
A is 180
B is 270
C 270
D is 90
E is 270
F is 180
G is 180
H is 90
I is 270
Step-by-step explanation:
11.) Sam has a total of 45 dimes and nickels. The number of dimes she has is 3 more than twice the number of nickels. How many of each coins does she have? How much money does she have altogether?
Answer:
Number of nickels: 14
Number of dimes: 31
Total money: $3.80
Step-by-step explanation:
Let number of nickels be x
Number of dimes is 2x+3
Total coins = 45
So add the number of nickels and dimes and it equals 45
x+2x+3=45
3x=45-3=42
x=42/3=14 nickels
Substitute the value of x=14 in 2x+3 to find number of dimes
2(14)+3=28+3=31 dimes
Total money is 14 nickels + 31 dimes
Nickels = 0.05 and dimes is 0.10
14(0.05)+31(0.10)=0.7+3.1=3.8
(-17,70) (5,10) find the slope
Answer:
17.4
Step-by-step explanation:
To find your slope you take y2-y1/x2-x1
70-(-17)/10-5
87/5=
17.4
Hope this helps
need to solve by factoring!!
49x² - 36 = 0
4 The width of a rectangular dance floor
length of the floor is 6 feet longer than
Which of the following expresses the pe
feet, of the dance floor in terms of w?
If f(x) = -2x + 5, what is f(-3x) equal to?
A) 2w+6
A) -6x - 5
B) 4w +12
C) 2+ 6
D) w*+ów
B) 6x + 5
Forms of Linear Equations
C) 6x-5
D) 6x2 – 15x
Linear equations can be expressed
*Note: The word "output" is intercha
Slope-Intercept Form
Select one:
O a. 6x + 5
y = mx + b
O b. 6x2 – 15x
m = slope or rate
• The change in output forex
1 for the input
O c.
- 6x - 5
buy-intercept
O 5
d. 6x - 5
Answer:
[tex] \boxed{\sf a. \ 6x + 5} [/tex]
Given:
f(x) = -2x + 5
To Find:
f(-3x)
Step-by-step explanation:
[tex]\sf Evaluate \ f(x) \ by \ substituting \ in \ the \\ \sf value \ of \ x = -3x \ into \ f(x): \\ \sf f( - 3x) = -2( - 3x) + 5 \\ \\ \ \ \ \ \ \ \ \ \ \ \ \ \sf = 6x + 5[/tex]
how do I undo dividing by 5
Answer:
Multiply by 5
Step-by-step explanation:
Since multiplying is the opposite of dividing you would multiply by 5.
3x+6 x 4x-1 step by step
Hey there!
ANSWER: [tex]27x-1[/tex]EXPLANATION:[tex]3x+6*4x-1[/tex]
Let's add parenthesis to 6 and 4 and remove the multiplication sign.
[tex]3x+(6)(4)x-1[/tex]
This equals:
[tex]3x+24x+-1[/tex]
Now we have to combine the like terms.
[tex]3x+24x+-1[/tex]
Separate with parenthesis.
[tex](3x+24x)+(-1)\\Equals\\27x+-1(ANSWER)[/tex]
[tex]-TestedHyperr[/tex]
write question correctly
Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function?
The graph of h(x) passes the vertical line test.
The graph of the inverse of h(x) is a vertical line.
The graph of the inverse of h(x) passes the horizontal line test.
The graph of h(x) passes the horizontal line test.
Answer:
The correct option is;
The graph of h(x) passes the horizontal line test
Step-by-step explanation:
In order to determine if a function has an inverse, and also if the inverse of the function is also a function, the function can be tested by drawing an horizontal line the graph of the function and viewing to find the following conditions;
A graph of a function that is intersected at only one point in all places (vertically) by an horizontal line indicates that the function has an inverse that is also a function, while a graph of a function that is intersected at more than one point in some places (vertically) by an horizontal line indicates that the function does not have an inverse that is also a function.
Answer:
D
Step-by-step explanation:
EDGE 2020
click on the pic,, plz help
Answer: - 2x^2 + 4x + 3
Step-by-step explanation:
( -x^2 - 4x - 5) + ( -x^2 + 8x + 8)
Take out parentheses:
- x^2 - 4x - 5 - x^2 + 8x + 8
Write in a way so that like terms are grouped together:
- x^2 - x^2 - 4x + 8x - 5 + 8
Combine 'x^2' terms:
- 2x^2 - 4x + 8x - 5 + 8
Combine 'x' terms:
- 2x^2 + 4x - 5 + 8
Combine integers:
- 2x^2 + 4x + 3
what is 27,430,000 as a scientific notation
Answer:
2.743 × 10^7
Step-by-step explanation:
The reason as to why 10 is to the 7th power is because the number that you turn into scientific notation (27430000), needs to be in ones form. Which is 7 decimal places away.
Solve 3(x + 1) + 6 = 33
Answer:
3(x + 1) + 6 = 33
3x+3+6=33
3x+9=33
3x=33-9
3x=24
x=24/3
x=8
Step-by-step explanation:
hope it help ^_^
Answer:
8 is the right answer of this question
What did the term 4x have in common (have the same) with x,120x, -3x?
Answer:
They're all like terms (x)
Answer:
they have all x
Step-by-step explanation:
F(x) = 3x3+ 8x-2
k(x) = 4x
What is the value of K(F(x))?
Answer:
[tex]k (3x^3 + 8x - 2) = 12x^3 + 32x - 8[/tex]
Step-by-step explanation:
Set up the composite result function.
k (F (x))
Evaluate k (F (x)) by substituting in the value of into.
[tex]k (3x^3 + 8x - 2) = 4 (3x^3 + 8x - 2)[/tex]
Apply the distributive property
[tex]k (3x^3 + 8x - 2) = 4 (3x^3) + 4 (8x) + 4(-2)[/tex]
Simplify
Multiply 3 by 4.
[tex]k (3x^3 + 8x - 2) = 12x^3 + 4 (8x) + 4(-2)[/tex]
Multiply 8 by 4.
[tex]k (3x^3 + 8x - 2) = 12x^3 + 32x + 4(-2)[/tex]
Multiply 4 by -2.
[tex]k (3x^3 + 8x - 2) = 12x^3 + 32x - 8[/tex]
Question 10(Multiple Choice Worth 1 points)
(01.04 LC)Solve (−3) ⋅ 2.
−6 please help
−5
5
6
Answer:
A —6
Step-by-step explanation:
Solve 3(k + 8) = 21
A. 3
B. 13
C. -1
D. 7
Answer:
C
Step-by-step explanation:
3(k+8)=21
3k+24=21
3k=-3
k=-1
Answer:
Step-by-step explanation:
3k + 24 = 21
3k = -3
k = -1
answer is C
