Answer:
[tex]a)~5(x-4)(x+1)[/tex]
Step-by-step explanation:
[tex]~~~5x^2 -15x -20\\\\=5(x^2 -3x -4)\\\\=5(x^2 -4x +x -4)\\\\=5\textbf{[}x(x-4) +(x-4)\textbf{]}\\\\=5(x-4)(x+1)[/tex]
Colin borrowed some money at 7.16%/a compounded quarterly. Three years later, he paid $5000 toward the principal and the interest. After another two
he paid another $5000. After another five years, he paid the remainder of the principal and the interest, which totalled $5000. How much money
did he originally borrow?
Based on the calculations below, the amount originally borrowed by Colin is $10,006.67.
How do we calculate the original amount using PV formula?To solve this question, the following present value (PV) formula will be used:
PVn = Pn / (1 + r)^n ........................... (1)
Where:
PVn = Present value of an amount paid in year n
P = Amount paid in year n
r = quarterly interest rate = 7.16% / Number of quarters in a year = 0.0716 / 4 = 0.0179
n = number of quarters = Number of years * Number of quarters in a year = Number of years * 4
Using equation (1), we can therefore proceed as follows:
PV3 = PV of $5,000 paid after three years = $5,000 / (1 + 0.0179)^(3 * 4) = $4,041.18
PV5 = PV of $5,000 paid after another 2 years (after 3 years + 2 years = 5) = $5,000 / (1 + 0.0179)^(5 * 4) = $3,506.45
PV10 = PV of $5,000 paid after another 5 years (after 3 years + 2 years + 5 years = 10) = $5,000 / (1 + 0.0179)^(10 * 4) = $2,459.04
Therefore, we have:
Original amount borrowed = PV3 + PV5 + PV10 = $4,041.18 + $3,506.45 + $2,459.04 = $10,006.67
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Is cos²α the same thing as cosα²?
Answer:
No, it is not the same thing.
Step-by-step explanation:
Hope this helps!
Question 3 of 10
10 Points
Write an equation in slope-intercept form of the line that passes through the point
(3,-2) with slope -2.
A.y=-2-2(x-3)
B. y = -2x + 4
Oc.y+2=-2(x-3)
OD. 2x+y-4 = 0
Reset Selection
The equation in slope-intercept form of the line that passes through the point is y = -2x+4 , Option B is the correct answer.
What is the equation of a straight Line ?The equation of a straight line is given by the equation
y= mx+c
Where m is the slope and
c is the intercept on y axis.
The given data is
line passes through the point (3,-2) with slope -2.
m = -2
y = -2x + c
-2 = - 2 * 3 +c
-2 = -6 +c
c = +4
y = -2x+4
Therefore Option B is the correct answer.
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Which situation can be represented by the expression -2-5−2−5minus, 2, minus, 5?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The temperature was 222 ^\text{o}\text{C}
o
Cstart superscript, start text, o, end text, end superscript, start text, C, end text and has decreased by 555 ^o\text{C}
o
Cstart superscript, o, end superscript, start text, C, end text.
(Choice B)
B
The temperature was -2−2minus, 2 ^\text{o}\text{C}
o
Cstart superscript, start text, o, end text, end superscript, start text, C, end text and has increased by 555 ^o\text{C}
o
Cstart superscript, o, end superscript, start text, C, end text.
(Choice C)
C
The temperature was -2−2minus, 2 ^\text{o}\text{C}
o
Cstart superscript, start text, o, end text, end superscript, start text, C, end text and has decreased by 555 ^o\text{C}
o
Cstart superscript, o, end superscript, start text, C, end text.
The situation that represents the expression 2 - 5 is (a) the temperature was 2°C and has decreased by 5°C
How to determine the situation?The expression is given as:
2 - 5
When the expression illustrates change in temperature, the interpretation can be:
An initial temperature of 2°C decreases by 5°C
Hence, the situation that represents the expression 2 - 5 is (a) the temperature was 2°C and has decreased by 5°C
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Simplify: 4^2+√9 what is the answer
[tex]~~4^2 +\sqrt 9\\\\=16 +3 \\\\=19[/tex]
Which one??? Please
Answer:
Step-by-step explanation:
its A
What are the coefficients in the polynomial 7x2 - 4x + 6?
a. -7,4
b. 7, 4, -6
c. 7. -4,6
d. 7. -4
if i could please get help thank you
Answer:
7 and -4
Step-by-step explanation:
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).
simplify -x(4x^2 − 6x + 1)
Answer:
[tex]-4x^3+6x^2-x[/tex]
Step-by-step explanation:
1. Distribute the X across the equation: [tex]-x(4x^2)=-4x^3\\[/tex]
2.[tex]-x(-6x)=6x^2[/tex]
3.[tex]-x(1)=-x[/tex]
3.[tex]-4x^3+6x^2-x[/tex]
if 3 + root8 by 3-root8 + 3-root8 by 3+root8 = a+broot2 find a and b
If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
[tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }\\ \\\frac{9+6\sqrt{8}+8+9-6\sqrt{8}+8 }{(3-\sqrt{8} )(3+\sqrt{8} )} \\\\\frac{34}{9-8} =34+0\sqrt{2}[/tex]
If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0
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What is the length of segment BC?
Answer:
is there any other info?
can someone do this for me please?! Just the answer pls
Answer:
I was able to solve questions 2 through 4 using the, "center = (h, k)" formula.
2. (3, -1)
3. (1, 2)
4. (-5, 2)
Hope it helps.
Can somebody help find the surface area if this
The total surface area of the object shown in the diagram is 164 inches.
What is the total surface area?
The total surface area of a 3-dimensional object is the sum of the areas of the faces or surfaces of a 3-dimensional object. The object shown is the net of a cuboid.
Total surface area of a cuboid = 2 (lw + wh + lh)
where:
• l = length
• w = width
• h = height
2 { (10 x 3) + (10 x 4) + (4 x 3)}
2 (30 + 40 + 12)
2 x 82 = 164 inches
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The surface area of the figure is 164 square inches
How to determine the surface area?From the net of the rectangular prism, we have the following dimensions:
Length = 4 inches
Width = 3 inches
Height = 10 inches
The surface area is calculated as:
Area = 2 * (Length * Width + Length * Height + Width * Height)
So, we have:
Area = 2 * (4 * 3 + 4 * 10 + 3 * 10)
Evaluate
Area = 164
Hence, the surface area of the figure is 164 square inches
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Can someone help me answer these
Answer:
1. 05+02=07
07+03=10
2. 05+04=09
09+01=10
3. 05+01=06
06+04=10
4. 05+03=08
08+02=10
5. 17+03=20
6. 19+01=20
Step-by-step explanation:
(Answers are in bold)
Anybody!!!!!! Select all that equals to 6(4)(6(-5))
Answer:
[tex]\frac{1}{6}[/tex]
[tex]6^{-1}[/tex]
[tex]\frac{1}{6^{1} }[/tex]
Step-by-step explanation:
Answer:
[tex]\frac{1}{6}[/tex] and [tex]6^{-1}[/tex] also [tex]}{\frac{1}{6^{1} } }[/tex] which is the same as [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
According to exponent rules
[tex]a^{n} *a^{m} =a^{n+m}[/tex]
[tex]a^{-x}= \frac{1}{a^{x} }[/tex]
Write a differential equation that models the given situation. The stated rate of change is with respect to time t. (Use k for the proportionality constant.) When an advertising campaign for a new product is introduced into a city of fixed population N, the rate of change of the number y of individuals who have heard about the product at time t is proportional to the number of individuals in the population who have not yet heard about the product.
The differential equation that models the given situation will be dy/dt = K(N - y).
How to compute the equation?Let y = number of individuals who have heard about the product.
Let N - y = this who haven't heard about the product.
From the given statement, the rate for change will be t = dy/dt. Therefore, the differential equation that models the given situation will be dy/dt = K(N - y).
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2.) x/2 = 1 Solving equations.
Answer: x=2
Step-by-step explanation:
To find the value of x, we have [tex]\frac{x}{2} =1[/tex]. To isolate x, we want to multiply both sides by 2 to get x alone.
x=2
Answer:
2
Step-by-step explanation:
[tex] \frac{x}{2} = 1 \\ cross \: multiplying \\ x = 2 \times 1 = 2 \\ x = 2[/tex]
1/3x + 1/4y = 1
2x – 3y = –30
Answer:
(-3, 8) is the solution
Step-by-step explanation:
The LCD of the first equation is (3)(4) = 12. Rewriting this equation, we get:
4x + 3y = 12
to which we add the second equation, obtaining:
4x + 3y = 12
2x - 3y = -30
-------------------
6x = -18
Dividing both sides by 6 yields x = -3
Substituting -3 for x in the first equation yields 4(-3) + 3y = 12, or
-12 + 3y = 12
Then 3y = 24 and y must be 8.
The solution to this system of linear equations is (-3, 8).
which type of statement has the form' "if A, then B"
Answer:
list statements please or I cannot help you.
Step-by-step explanation:
or do you want me to make a statement?
Answer: Conditional Statement
A conditional is of the form "if, then" which is often found in math classes and formal logic classes as well.
Drag each condition to the correct location on the table. Match each condition to the number of triangles that can be constructed to fit the condition. condition A: one side measuring 4 inches, another side measuring 8 inches, and a third side measuring 10 inches condition B: one angle measuring 60°, another angle measuring 40°, and a third angle measuring 90° condition C: one side measuring 4 inches, another side measuring 8 inches, and the angle between them measuring 70° condition D: one side measuring 5 inches, another side measuring 7 inches, and a third side measuring 12 inches condition E: one angle measuring 30°, another angle measuring 80°, and the length of the included side measuring 8 inches condition F: one angle measuring 40°, another angle measuring 80°, and a third angle measuring 60°
No triangles are possible for Options B and D. One triangle is possible for options A, C, and E. Many triangles are possible for option F.
How to interpret Triangles?For it to be a triangle, then it must have 3 vertices and 3 sides with the sum of 2 sides greater than the third side. Also, the sum of interior angles must be 180°.
A) Side lengths of the triangle are; 4 inches, 8 inches and 10 inches.
4 + 8 > 10. Thus, it is a triangle.
B) 60° + 40° + 90° = 190 ≠ 180°
Thus, no triangle is possible because the sum of the angles in triangle is 180°.
C) There are two sides are given and one angle. Thus, from SAS congruency theorem, one triangle is possible.
D) 7 + 5 = 12
There is no triangle possible because the sum of the two sides must be greater than the third side.
E) We are given two angles and one side. Thus, from the ASA Congruency Postulate, one triangle is possible.
F) 60° + 80° + 40° = 180°
There are three angles given, but no sides and so we can say that many triangles are possible.
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find the distance between the two points in simplest radical form.
(3,-8) and (8,4)
Answer:
13
Step-by-step explanation:
The way to find the distance between two points on the coordinate plane is to use the distance formula, which is basically a way of applying the Pythagorean Theorem.
The distance formula is [tex]\sqrt{(x_{1}- x_{2} )^2 + (y_{1}- y_{2})^2}[/tex]. Let's say the coordinate (3, -8) is (x1, y1) and the coordinate (8, 4) is (x2, y2). We can plug these values into the formula:
[tex]\sqrt{(3- 8 )^2 + (-8 - 4)^2}\\\sqrt{(-5)^{2} + (-12)^{2}} \\\sqrt{25+144} \\\sqrt{169} \\13[/tex]
So, the distance between the two points is 13.
V (x) = x(9-2x) (11-2x)
The expanded form of V(x) = x(9-2x) (11-2x) is V(x) = 4x^3 - 20x^2 + 99x
How to expand the expression?The missing information in the question is to express V(x) in standard form
We have:
V(x) = x(9-2x) (11-2x)
Open the brackets
V (x) = x(99 - 2x - 18x + 4x^2)
Evaluate the like terms
V (x) = x(99 - 20x + 4x^2)
Expand
V (x) = 99x - 20x^2 + 4x^3
Rewrite as:
V(x) = 4x^3 - 20x^2 + 99x
Hence, the expanded form of V(x) = x(9-2x) (11-2x) is V(x) = 4x^3 - 20x^2 + 99x
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What is the solution set for 2|3y+7|=10
Answer:
[tex]y = \frac{7}{2} [/tex]
Step-by-step explanation:
[tex]3y + 7 = 5y \\ 7 = 5y - 3y \\ 7 = 2y \\ \frac{7}{2} = y \\ y = \frac{7}{2} [/tex]
What is the length of AC in the given triangle?
Answer: the answer is 126.6
Step-by-step explanation:
Answer:
AC ≈ 126.6
Step-by-step explanation:
The law of sines can be used to find the side length of interest in this triangle. It tells you ...
a/sin(A) = b/sin(B) = c/sin(C)
__
missing angleIn order to use the law of sines, we must have a side length and its opposite angle. Here, the angle opposite the given side is unmarked, so we need to compute it using the angle sum theorem.
A +B +C = 180°
A +85° +53° = 180°
A = 42° . . . . . . . . . . . . . subtract (85°+53°)
unknown sideThen side AC can be found from ...
AC/sin(B) = BC/sin(A)
AC = BC·sin(B)/sin(A) = 85·sin(85°)/sin(42°)
AC ≈ 126.547
The closest answer choice is 126.6.
Ok 100 points to answer dis question and it very easy i do dis bc i want to give someone points 4 free
wut is 1+1=
Answer:
I’m thinking it’s 2 lol thank you so much!!!
Step-by-step explanation:
The local school board needs to choose whether to build an addition to the elementary school library or remodel the high school basketball court. Which sampling option might the board choose to survey the community?
Why is it important to avoid a smaller sample size?
Answer:
Don't know the full answer, though I searched it up on brainly and found this:
Hopefully it can help you with whatever you are doing/taking.
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Help me please I beg lol I can’t solve it (step by step in comments)
Answer:
272 m
Step-by-step explanation:
You have to devide the shape in 2.
Complete the steps to find the surface area of the right prism shown below.
Steps Example
1. Write the surface area formula. Surface Area = BA + ph
2. Identify the shape of the bases. right
3. Use the correct formula to find the area of one base.
4. Multiply that area by 2 (to get BA, area of both bases). BA = 2 • area of one base
BA = (2)() = units2
5. Find the perimeter of one base. p = 3 + 4 + 5 =
6. Multiply that perimeter by the height of the prism (to get LA, area of all lateral faces). LA = ph = ()(20) = units2
7. Add the results from steps 4 and 6. Surface Area = BA + LA = +
= units2
The surface area of the prism is 144 square units
How to determine the surface area?The attached image represents the missing figure in the question.
The image would be used to complete the steps, as follows:
Step 1: The surface area formula. Surface Area = BA + phStep 2: The shape of the bases are right trianglesStep 3: The area of one base; Area = 0.5 * 3 * 4 = 6Step 4: Multiply the area in (3) by 2: BA = 2 * 6 = 12Step 5: The perimeter of one base. p = 3 + 4 + 5 = 12Step 6: Multiply p by h; LA = 12 * 11 = 132Step 7: Add (4) and (6). Surface Area = 12 + 132 = 144Hence, the surface area of the prism is 144 square units
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Reflect the shape A in the line y
=
y
(-5, 6)
(4,3)
(-3, 1)
-8-7 -6 -5 -4 -3 -2 -1
4 5 6 7 8
-1
-2
-3
-4
-5
-6
-7
-8
What are the coordinates of the vertices
of the image?
A
00
8
7
6
LO
5
4
3
2
-
1
Đ
1
-2
3
-X.
2
(-5,6)
Step-by-step explanation:
Solve the quadratic equation 5x^2+x+1=0
Answer:
No Solution
Step-by-step explanation:
Answer:
[tex]x = \dfrac{-1\pm i\sqrt{19}}{10}[/tex]
Step-by-step explanation:
[tex]~~~~~~5x^2 +x +1 = 0\\\\\implies x = \dfrac{-1\pm\sqrt{1^2 -4 (5)(1)}}{2(5)}\\\\\implies x = \dfrac{-1 \pm \sqrt{-19}}{10}\\\\\implies x = \dfrac{-1\pm i\sqrt{19}}{10}[/tex]
How would you write 16,340 in scientific notation with 2 significant figures? 16,300 1.63 x 104 16,000 1.6 x 104
16340 can be written in scientific notation as 1.63 × 10⁴.
What is Scientific Notation?
Scientific Notation is a way of representing large numbers in decimal forms multiplied by the power(exponent) in terms of decimal places. The purpose of representing large numbers in scientific notation is to enable easier calculation.
This means that 16,340 in scientific notation can be expressed as:
= 1.634 × 10⁴
= 1.63 × 10⁴ ( to 2 significant figures)
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