Answer: ±i-4
Step-by-step explanation:
To solve this equation by completing the square, we first have to adjust the equation.
Let's rewrite it in this form:
x^2+8x+16+1=0
Then we can complete the square.
(x+4)^2+1=0
(x+4)^2 = -1
x+4 = ±i
x = ±i-4
the quantity negative 6 minus one half times p end quantity plus the quantity three fourths times p minus 9 end quantity
The simplified form of the expression is -46p - 72.
What is the simplified expression?In mathematics, we have to note that if we have an expression, then the expression can be written in the simplest way that is possible and this is called the simplified form of the expression.
We have that if we put the sentences into words;
(-6 1/2p) + (3/4p - 9)
(-13/2p) + (3p - 36/4)
8(-13/2p) + 8 (3p - 36/4)
-52p + 2(3p - 36)
-52p + 6p - 72
-46p - 72
Hence the expression can be said to have been simplified.
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22. Volume of Water in a Reservoir.
A reservoir shaped like a
hemispherical bowl of radius 8 m is filled with water to a depth
of 4 m.
(a) Find an estimate S of the water's volume by approximating the
water with eight circumscribed solid cylinders.
(b) It can be shown that the water's volume is V = (320•pi)/3 m³.
Find the error |V-S| as a percentage of V to the nearest
percent.
On solving the provided question, we can say that Volume of cylinder, V = [tex]\pi r^2 X h[/tex] => V = 3.14 * 8*8*4 = 803.84 cubic m
what is cylinder?One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.
here,
we have a cylinder
and,
radius, r = 8m
height, h = 4m
Volume, V = [tex]\pi r^2 X h[/tex]
V = 3.14 * 8*8*4 = 803.84 cubic m
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Arianna north borrowed $12,500 to purchase a new chilli and agreed to pay back $13,250 in 270 days what exact interest rate was she paying
Arianna North agreed to borrow $12,500 to buy a new chilli and agreed to pay back $13,250 in 270 days at an interest rate of 8.11%.
what is interest rate ?Divide this same principal by the lending rates, the duration of time, and other factors to result at simple interest. Simple return Equals principal + interest + hours is the marketing formula. This system makes it easiest to calculate interest. One of most typical technique to figuring out interest is as a portion of the principal sum. He will only pay his share of the 100% interest, for example, if he borrow $100 from with a friend and offers to return the loan with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an indicator of the overall of the loan total. The interest on the loan is this percentage.
given
Arianna North took out a $12,500 loan
She committed to repaying $13,250 over 270 days.
If x is the interest rate she was paying,
x= 13250 - 12500
= 750
So, x= 750/ 12500 (270/ 365)
x% = 750/ 9,246.57
x% = 0.0811
x%= 8.11%
Arianna North agreed to borrow $12,500 to buy a new chilli and agreed to pay back $13,250 in 270 days at an interest rate of 8.11%.
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1:3 = 3:9 means and extremes?
Answer: they are equivalent ratios
I don’t know the answer to this question can someone help me
Answer:
so the answer is
Step-by-step explanation:
-3/2
so how I got this is -4 1/2 would be
-9/2 so your new equation is 3+ -9/2 then you would just do keep change flip so no 3/2 - -9/2 and then you would get -3/2.
if i use a 30% coupon and after the coupon its 28$ what was mine orginal price
Answer:
$40
Step-by-step explanation:
$28 is the reduced price 30%, i.e. the product has a (100-30)% = 70% of its original value.
Divide the discounted price by the decimal of the percentage it represents with respect to the original price, The result is the original price
70% = 70/100 = 0.7
28/ 0.7 = 40
Hope this helps.
In an experiment with a bag of marbles, P(green) = five tenths. Interpret the likelihood of choosing a green marble.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
Answer:
The likelihood of choosing a green marble is (c) Equally likely and unlikely
How to determine the likelihood of choosing a green marble
From the question, we have the following parameters that can be used in our computation:
P(green) = five tenths.
Express five tenths as a mathematical expression
So, we have the following representation
P(green) = 5/10
Evaluate the quotient
This gives
P(green) = 0.50
A probability of 0.50 is halfway between 0 and 1
This means that it is likely and unlikely at the same time
Hence, the statement that represents the interpretation of the likelihood of choosing a green marble is (c) Equally likely and unlikely
Answer:
C
Step-by-step explanation: 5/10 is equal to 50% or 1/2 which is equally likely and unlikely.
PLS HELP!! Evaluate each arithmetic series described and show all work!!!
The Arithmetic series is as follows : -3423 , - 3443 , -3463 , -3483,.... when d = -20 and a20 = -3803
What is Arithmetic progression?
Arithmetic progression can be defined as the sequence of numbers in which the difference between any consecutive numbers is same.
Given ,
To evaluate arithmetic series.
Given ,
a20 = -3803
and d = -20
an = 197 - 200n
a20 = a+(20-1)d
a20 = a+ 19d
-3803 = a + 19*-20
-3803 = a-380
a = 380 - 3803
a = - 3423
so, a1 = -3423
a2 = a+d = -3423 + (-20)
a2 = -3443
a3 = a+2d
= -3423 - 2 * 20
= -3463
a4 = a+3d
= -3423 - 2*30
= - 3483
Hence, The Arithmetic series is as follows : -3423 , - 3443 , -3463 , -3483,.... when d = -20 and a20 = -3803
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5 digit mystery number
7 is in a place that is 100x greater than the place of the 5.
1 is in a place that is 10x less than the place of the 7.
8 is in a place that is 10x less than the place of the 5.
4 is in a place that is 100x greater than the 1.
Mrs Parkow's 5-digit mystery number is 73248.
What are Numbers up to 5 Digits?Ten thousand is the starting point for five-digit numbers, which go up to ninety-nine million, nine hundred and ninety-nine. Integers are present in the places of ones, tens, hundreds, thousands, and ten thousand in these numbers. Any positive number may be placed at these places, with the exception of 0 at the ten thousand places.
A general 5-digit number can be written as:
a×10000 + b×1000 + c×100 + d×10 + e where a, b, c, and d are single-digit numbers.
a is the ten thousand digit
b is the thousands digit
c is the hundreds digit
d is the tens digit
e is the unit digit.
Let 8 be at one's place that is e
Now, it is given that 8 is in a place that is 10 times less than the place of 4.
This implies 4 is at the ten's place that is d.
Next, it is given that 3 is in a place that is 100 times greater than the place of 4.
That is 100×10 = 1000 place
So, 3 is at the place of b.
The 2 is in a place that is 10 times less than the place of the 3. So, 2 is at the place of c.
The 7 is in a place that is 100 times greater than the 2. That is 100×100 = 10,000 places.
Thus, 7 is at the place of a.
Thus, we obtain
a= 7
b= 3
c= 2
d= 4
e= 8
Therefore, the 5-digit mystery number is 73248.
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The total number of fence posts Edwin installs varies directly with the number of hours worked. He installs 40 fence posts in 8 hours.
Write a direct variation equation to represent this relationship.
Direct variation equation for the relationship is y = 4x
y is number of fence posts.
x is number of hours.
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.
Given,
Edwin installs 40 fence posts in 8 hours
Let the number of fence posts installed be y, x be the hours worked
x and y are in direct proportion,
then,
y/x = 40/5
y/x = 5
y = 5x
Hence, y = 5x is the direct variation equation of relationship.
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1/2 div 5/3 ………..it’s worth 30 points
Answer:
Step-by-step explanation:
1 5
_ div _
2 3
1/2 x 3/5
1 3
x = 3/10
2 5
Last month Blake sold 40 pieces of jewelry. To get a bonus, she must sell 20% more jewelry this month. How many pieces of jewelry does she need to sell this month?
Answer:
48 pieces of jewelry (if you're writing this out be sure to add units as some teachers are sticklers for that!)
Step-by-step explanation:
20% of 40 is 8. This means she needs to sell 8 more than 40 this month. So, she must sell 48 pieces (40+8=48).
Hope this helps!
Lucy had 2/7 of a spool of yarn. She used 2/3 of her yarn for a project. What fraction of the spool was used for the project?
The fraction of the spool was used for the project is 4/21
What fraction of the spool was used for the project?From the question, we have the following parameters that can be used in our computation:
Yarm = 2/7
Fraction used 2/3 of the yarn
This means that
Fraction used = 2/3 * 2/7
Evaluate the product
Fraction used = 4/21
Hence, the fraction used is 4/21
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/the congruency of triangle MNO and Triangle XYZ can be proven using a reflection across the line bisecting segment OZ. However the congruency can be proven using geometric postulates theorems and definitions. Prove that the triangles are congruent using two-column proof and triangle congruency theorem.
The congruency of triangle MNO and triangle XYZ can be proven using the following two-column proof:
What in mathematics is a congruence?
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Given: Line segment OZ bisects line segment MN and line segment XZ, and MNO is reflected across line OZ to form XYZ.
Prove: Triangles MNO and XYZ are congruent.
Statements | Reasons
OZ bisects MN, OZ bisects XZ | Given
Angle MOZ = Angle XOZ, Angle NOZ = Angle YOZ | Definition of angle bisector
∠MOZ = ∠XOZ, ∠NOZ = ∠YOZ | Using Corresponding angles postulate
∠MON = ∠XOY, ∠NOZ = ∠YOZ | Using definition of angle bisector
m∠MON = m∠XOY, m∠NOZ = m∠YOZ | Using Angle addition postulate
MN = XZ, MO = XO, NO = YO | Using Segment addition postulate
MNO ≅ XYZ | Using SAS congruence theorem
Therefore, we can conclude that the triangles MNO and XYZ are congruent.
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Which graph represents the function
*{(x) = 4/x?
The graph of rectangular hyperbola represents the function f(x)=4/x.
Which graph represents the function *{(x) = 4/x?
Given that,
Which graph represents the function f(x) = 4⌈x⌉?
Now,
to represent the graph of Y = 4 IxI.
So,
Taking x = 1, we get
Y = 4 IxI
Y = 4 I1I
Y = 4 .
Taking x = 2, we get
Y = 4 IxI
Y = 4 I2I
Y = 8
Taking x = 3, we get
Y = 4 IxI
Y = 4 I3I
Y = 12.
Taking x = -1, we get
Y = 4 IxI
Y = 4 I-1I
Y = 4×1
Y = 4.
Taking x = -2, we get
Y = 4 IxI
Y = 4 I-2I
Y = 4×2
Y = 8.
Taking x = -3, we get
Y = 4 IxI
Y = 4 I-3I
Y = 4×3
Y = 12
Property of modulus function -
IxI = x , where x is positive or negative
I-xI = x.
Therefore, from the above data we have drawn a graph of function f(x) = 4ixI.
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Three times the sum of a number and 15 is at most 19
Let x be the number. Then, we have the inequality:
3(x + 15) ≤ 19
Expanding the left side:
3x + 45 ≤ 19
Subtracting 45 from both sides:
3x ≤ -26
Dividing both sides by 3:
x ≤ -8.67
So, the solution to the inequality is x ≤ -8.67, which means that the number x must be less than or equal to -8.67.
Translate and solve: Twelve more than p equals 6.
Answer:-6
Step-by-step explanation:
The solution to the equation "Twelve more than p equals 6" is p = -6.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The given equation is:
12 + p = 6
To solve for p, we need to isolate p on one side of the equation.
We can do this by subtracting 12 from both sides:
12 + p - 12 = 6 - 12
p = -6
Therefore,
The solution to the equation "Twelve more than p equals 6" is p = -6.
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Simplify 3x ^3 + 3 (3x^ 3 − 7b^ 5 ).
A. 12x^3 − 7b^5
B. 12x^3 − 21b^5
C. 3x^3 − 30x^3 b^5
D. 12x^6 − 21b^5
Answer:
From your selections of answers, It's B: 12 x^3 - 21 b^5, but it's not completely simplified.
Step-by-step explanation:
Simplify the following:
3 (3 x^3 - 7 b^5) + 3 x^3
3 (3 x^3 - 7 b^5) = 9 x^3 - 21 b^5:
3 x^3 + (9 x^3 - 21 b^5)
Grouping like terms, 9 x^3 + 3 x^3 - 21 b^5 = (3 x^3 + 9 x^3) - 21 b^5:
(3 x^3 + 9 x^3) - 21 b^5
3 x^3 + 9 x^3 = 12 x^3:
12 x^3 - 21 b^5
Factor 3 out of 12 x^3 - 21 b^5:
Answer: (3 (4 x^3 - 7 b^5)) = 12 x^3 - 21 b^5
A salesman sold 1500 worth of merchandise and received $75 in commssion for the sale. What percent of the sale was commision?
Answer:
5%
Step-by-step explanation:
1500 / 75 = 0.05 as a percentage its 5 %
Find the perimeter of the figure to the nearest hundredth.
The perimeter of the shape is 26.85 inches
What is perimeter ?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.
The shape consist of a rectangle joined with a semi circle.
Therefore the perimeter of the shape is calculated as:
7+7+ 5+ πd/2
where πd/2 is the circumference of the semi circle
= 7+7+5+(3.14× 5/2)
= 7+7+5+7.89
= 26.85 inches
therefore the perimeter of the shape is 26.85 inches
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Find the value of the variables that make the matrix equation true.
{8 0 0} { 7x+3 0 0 }
{ 0 8 0} = { 0 9y-4 0 }
{ 0 0 8} { 0 0 5z-5}
The value of the variables that make the matrix equation true are x = 5/7, y = 4/9 and z = 13/5.
What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.
For instance, consider a matrix with two rows and three columns.
We are given the matrix as;
{8 0 0} = { 7x+3 0 0 }
{ 0 8 0} = { 0 9y-4 0 }
{ 0 0 8} = { 0 0 5z-5}
So, we have 7x + 3 = 8
7x = 5
x = 5/7
Also, 9y-4 = 8
9y = 4
y = 4/9
5z - 5 =8
z = 13/5
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so i get the first few parts but i don’t know how to answer the last part, could anyone help please?
i) Sketch, on a single diagram showing values of x from-180° to +180°, the graphs of
y = tan x and y = 4 cos x.
The equation : tan x = 4 cos x
has two roots in the interval -180° ≤x≤ 180°. These are denoted by a and ß, where a <ß.
ii) Show a and ß on your sketch, and express ß in terms of a
iii) Show that the equation tan x = 4 cos x may be written as 4 sin^2x+ sin x−4=0.
Hence find the value of ß-a, correct to the nearest degree.
i) The graph of y = tan x will be a periodic function with period of 180 degrees, with asymptotes at x = (n+1/2)π, where n is an integer. The graph of y = 4 cos x will be a cosine function with amplitude 4 and period 360 degrees.
ii) The roots of the equation tan x = 4 cos x, denoted by a and ß, can be found by solving the equation tan x = 4 cos x for x. The two solutions will be a and ß, where a <ß.
iii) The equation tan x = 4 cos x can be written as 4 sin^2x+ sin x−4=0 by using trigonometric identities. The value of ß-a can be found by using the quadratic formula on this equation. However, it's not possible to give you an exact value without the specific value of a.
Your interest rate is compounded semiannually.
Beginning Balance: $1265.31
Annual Interest Rate: 8%
What will your ending balance be after six months?
The compound interest at the end of 6 months is $101.2248
what is compound interest?Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. The compound interest equals total amount of principal and interest in future (or future value) minus principal amount at present (or present value).
Given here: principal balance=$1265.31 and annual rate is i=8%
Thus compound interest after 6 months is = [P (1 + i)ⁿ] – P
=1265.31(1+0.080¹-1)
=101.2248
Hence, the compound interest after six months is $ 101.2248
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What is y = 4x^2 + 48x +135 in vertex form
Answer: search it up its a bit
Step-by-step explanation:
If f (x) = 2 x + 5 and three-halves are inverse functions of each other and StartFraction 41 Over 8 EndFraction, what
The required inverse of the function at when x = 8 is 3/2.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = 2x + 5
first we need to find the inverse of the function:
Let y = g(x)
y= 2x + 5
Replace y with x
x = 2y + 5
Make y the subject of the formula
2y = x - 5
y = (x - 5)/2
So, the inverse of the expression is [tex]f^{-1}[/tex](x) = (x - 5)/2
Substitute x = 8
[tex]f^{-1}[/tex]((8) = (8 - 5)/2
[tex]f^{-1}[/tex](8) = 3/2
Hence, the required inverse of the function at when x = 8 is 3/2
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What are the range and domain of the function in the table below? x y -5 0 -3 2 -1 4 1 2 3 0 Domain: __________________________________ Range: __________________________________
Domain: 4 1 2 3 0
Range: -5 0 -3 2 -1
What is range & domain?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
here, we have,
given that,
x y
-5 0 -3 2 -1 4 1 2 3 0
let, y=f(x)
which is domain of x-range.
hence, Domain: 4 1 2 3 0
Range: -5 0 -3 2 -1
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Anthony ordered two pizzas for a party. One was a small pepperoni pizza with a radius of 5 inches (5in.), and the other was a large cheese pizza with a 7in. radius. The circumference of the larger pizza is how much longer than the circumference of the smaller pizza?
The circumference of a circle is C=2πr.
Use π≈3.14 for the calculations.
Round your answer to the nearest hundredth.
The circumference of the larger pizza is 12.56 longer than the smaller pizza.
What is circumference?The length around the circle or the perimeter of the circle is called its circumference.
Given that, Anthony ordered two pizzas for a party. One was a small pepperoni pizza with a radius of 5 inches, and the other was a large cheese pizza with a 7 in. radius.
We need to find how much longer than the circumference of the smaller pizza,
We know that,
Circumference of a circle = 2πr.
Therefore,
Circumference of the larger pizza = 2 × 3.14 × 7 = 43.96 in
Circumference of the smaller pizza = 2 × 3.14 × 5 = 31.4 in
Therefore,
Subtracting the circumference of smaller pizza from larger pizza to get the difference = 43.96 - 31.4 = 12.56 in
Hence, the circumference of the larger pizza is 12.56 longer than the smaller pizza.
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Inga is solving 2x^2 + 12x -3=0. Which steps could she use to solve the quadratic equation? Select three options
To solve the quadratic equation 2x² + 12x - 3 = 0, the correct choices are option 1: 2(x² + 6x + 9) = 3 + 18 and option 3: 2(x² + 6x) = 3.
What is a quadratic equation?
Having the form ax² + bx + c = 0, quadratic equations are second-degree algebraic expressions. From the term "quad," which meaning square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way.
The given quadratic equation is 2x² + 12x - 3 = 0.
The first choice for solving the quadratic equation is -
2(x² + 6x + 9) = 3 + 18
Multiply 2 with every number of the other multiplier on the left side -
2·x² + 2·6x + 2·9 = 3 + 18
2x² + 12x + 18 = 3 + 18
Now, on simplifying it further -
2x² + 12x - 3 = 18 - 18
2x² + 12x - 3 = 0
The second choice for solving the quadratic equation is -
2(x² + 6x) = -3
Multiply 2 with every number of the other multiplier on the left side -
2·x² + 2·6x = -3
2x² + 12x = -3
2x² + 12x + 3 = 0
The third choice for solving the quadratic equation is -
2(x² + 6x) = 3
Multiply 2 with every number of the other multiplier on the left side -
2·x² + 2·6x = 3
2x² + 12x = 3
2x² + 12x - 3 = 0
The fourth choice for solving the quadratic equation is -
x + 3 = 21/2
Dividing 21 by 2 on right hand side -
x + 3 = 10.5
x + 3 - 10.5 = 0
x - 7.5 = 0
The fifth choice for solving the quadratic equation is -
2(x² + 6x + 9) = –3 + 9
Multiply 2 with every number of the other multiplier on the left side -
2·x² + 2·6x + 2·9 = -3 + 9
2x² + 12x + 18 = -3 + 9
Now, on simplifying it further -
2x² + 12x = -3 + 9 - 18
2x² + 12x = -12
2x² + 12x + 12 = 0
The sixth choice for solving the quadratic equation is -
(x + 3)² = 3/2
Apply the formula (a+b)² = a² + 2ab + b² on the left side and divide 3 by 2 on the right side -
x² + 6x + 9 = 1.5
x² + 6x + 9 - 1.5 = 0
x² + 6x + 7.5 = 0
Therefore, the correct choices are option 1 and option 3.
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Inga is solving 2x² + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Check all that apply.
2(x² + 6x + 9) = 3 + 18
2(x² + 6x) = –3
2(x² + =6x) = 3
x + 3 = 21/2
2(x² + 6x + 9) = –3 + 9
(x + 3)2 = 6/2
Question 7
Jorge earned 91, 84, 87 on his first three out of four Algebra tests. He wants to get an
average of 90 in the class. What should he make on his last test to achieve this goal?
To earn an average score of 90, the score on the fourth test needs to be 98.
What is average?The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.
Given the score of the first three tests as:
91, 84, 87.
The average is given by the following formula:
Average = Sum of scores ÷ total number of tests
Let us suppose the score of fourth test as x.
Given that A = 90:
90 = (91 + 84 + 87 + x) ÷ 4
x = 98
Hence, the score on the fourth test must be equal to 98, to get an average score of 90.
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3. Find f'(x) for f(x) = √(5 + e²x)
Answer:
Step-by-step explanation:
We may use the chain rule to find the derivative of f(x) = (5 + e2x). The chain rule asserts that if y = f(u) and u = g(x), then the derivative of y with respect to x is:
dy/dx = dy/du * du/dx
In this situation, let u = 5 + e2x, and we get:
f(u) = √u
And we know that the derivative of u with regard to u is:
df(u)/du = 1/(2*u)
We also know:
du/dx = 2e2x
So, when we plug these into the chain rule, we get:
df(x)/dx = du/dx = 1/(2*u) * 2e2x = e2x/((5 + e2x))
As a result, the derivative of f(x) = (5 + e2x) is:
f'(x) = e2x / (5 + e2x)