need help with question in pic
Answer:
x = 2 + [tex]\sqrt{3}[/tex] i
x = 2 - [tex]\sqrt{3}[/tex] i
Step-by-step explanation:
Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)
Center (−3, 4),
radius 3
Answer:
(x +3)² +(y -4)² = 9
Step-by-step explanation:
You want the equation of a circle with center (-3, 4) and radius 3.
Circle equationThe equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
ApplicationYou have a circle with center (h, k) = (-3, 4) and radius r = 3. Using these values in the above equation, we find the circle equation to be ...
(x -(-3))² +(y -4)² = 3²
(x +3)² +(y -4)² = 9
Put these in order from the smallest to largest 1 to the power of 8 ,2 to the power of 4 ,3 to the power of three and 5 to the power of two
A health food company packs almond butter in jars. some jars hold 250 kg. other jars hold 500g. on tuesday, the company packed 186.5 kg of almond butter in 511 jards. how many jars of each size did they pack
In linear equation, there was 235 jars with 0.5 kg almond and 276 jars with 0.25 kg almonds.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Let the number of 250g=0.25 kg jars be x and that of 500g=0.5 kg jams be y;
therefore:
total number of jars was
x+y=511
x=511-y..........i
total amount kg was:
0.25x+0.5y=186.5....ii
substituting i in ii
0.25(511-y)+0.5y=186.5
127.75-0.25y+0.5y=186.5
solving for y we get:
0.25y=186.5-127.75
0.25y=58.75
y=58.75/0.25
y=235 jars
and
x=511-x
=511-235
=276
hence , there was 235 jars with 0.5 kg almond and 276 jars with 0.25 kg almonds.
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A baker needs to make eight batches of cookies for a party. If each batch requires 2 2/4 cups of flour, how many cups will he need?
Answer:
20
Step-by-step explanation:
8x2=16 and 2/4 times 8 is 4 so 20
what is the degree of the polynomial 3x^6 - 4x^4 + 5x - 6
The degree of the polynomial 3x^6 - 4x^4 + 5x - 6 degree of polynomial is 6
Definition of degree of polynomial
The degree of polynomials in one variable is the highest power of the variable in the algebraic expression.
Here the algebraic expression is 3x^6 - 4x^4 + 5x - 6
variable is xhighest power of variable is 6 degree of polynomial is 6Polynomials appear in lots of regions of arithmetic and technological know-how. for instance, they're used to form polynomial equations, which encode a extensive variety of issues, from essential word issues to complex medical troubles;
they are used to outline polynomial features, which seem in settings ranging from fundamental chemistry and physics to economics and social technological know-how; they're utilized in calculus and numerical analysis to approximate other features.
In advanced mathematics, polynomials are used to assemble polynomial jewelry and algebraic sorts, which are imperative ideas in algebra and algebraic geometry.
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Principal:=$500
interest rate=5%
Time=5 years
What is the interest earned
Answer:
$125
Step-by-step explanation:
I = Prt
I = ($500)(.05)(5) = $2,500(.05) = $125
Augustus looks in the mirror and decides that he is gaining weight. He is afraid that all that candy will just make it worse, so he tells his parents that it would be ok if they just give him 1 candy on the first day, 2 on the second day, continuing to double the amount each day as he completes his homework. Mr. and Mrs. Gloop like Augustus’ plan and agree to it.
how many candies will he get on day 30?
The number of candies that Augustus will spend on the 30th day will be 536870912 candies.
How to illustrate the information?It should be noted that from the information, Augustus is afraid that all that candy will just make it worse, so he tells his parents that it would be ok if they just give him 1 candy on the first day, 2 on the second day, continuing to double the amount each day as he completes his homework.
Therefore, the amount that he will get on the 30th day will be:
= 1 × 2^29
= 1 × 536870912
= 536870912
Therefore, the number of candies that Augustus will spend on the 30th day will be 536870912 candies.
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An angle measures 8° more than the measure of its supplementary angle. What is the measure of each angle?
86° is the measure of each angle when its supplementary angle.
What does math's supplementary angle mean?
Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complimentary angles is 90 degrees.If two angles in geometry sum up to 180 degrees, they are considered to be supplementary angles. For instance, A and B are referred to as supplementary angles if A + B = 180°.Let the larger angle be x.
Smaller angle = x - 8
As both angles are supplementary,
x + (x - 8) = 180°
2x - 8 = 180°
2x = 188°
x = 94°
Therefore, larger angle = 94°
Smaller angle = 94° - 8° = 86°
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5. The function m(x) = |x - 79| represents the absolute deviation (in inches) of a
man's height x (in inches) from the average height of men on a college basketball
team. The function w(x) = |x - 72 represents the absolute deviation (in inches)
of a woman's height x (in inches) from the average height of women on a college
basketball team. Compare the absolute deviations for a man and a woman who are
both 76 inches tall.
Step-by-step explanation:
Reread the underlined sentence on page 4.
What does the figurative language in this
sentence suggest about the narrator?
He feels that people should have used better tools
to help them detect advanced life forms on other
planets.
He sympathizes with people for not apprehending
that there was advanced life on other planets.
He is unable to believe that there could be any
form of life more advanced than humans.
He blames people's exaggerated idea of their
superiority for their failure to imagine life more
advanced than themselves.
Expand each logarithm.
log s√7/t²
The value of logarithmic expression log s√7/t² is log (7/t²)^1/s.
By considering the given logarithmic expression
log s√7/t²
=log (7/t²)^1/s
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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what is the general process for solving an equation with one variable
Answer:
Typically when solving an equation with one variable, your objective is to isolate the variable on one side of the equation. This can be done adding/subtracting number to cancel them out on one side. You can also multiply/divide coefficients in order to isolate a variable.
Example:
Add -4 to both sides to isolate the variable.
Simplify.
Divide both sides by 2 to isolate the variable on one side.
Step-by-step explanation:
If b is the midpoint of ac find the coordinates of c if a(12,4) and b(9,11)
Answer:
good less to the worl then
(5/2-3/4)-1/4(1-x)=1/2
Answer:
Step-by-step explanation:
[tex](\frac{5}{2} -\frac{3}{4} )-\frac{1}{4} (1-x)=\frac{1}{2}[/tex]
[tex](\frac{10}{4} -\frac{3}{4}) -\frac{1}{4} -\frac{1}{4} x=\frac{1}{2}[/tex]
[tex]\frac{7}{4} -\frac{1}{4} -\frac{1}{4} x=\frac{1}{2}[/tex]
[tex]\frac{6}{4} -\frac{1}{4}x=\frac{1}{2}[/tex]
[tex]1=\frac{1}{4} x[/tex]
[tex]4=x[/tex]
[tex]x=4[/tex]
Hope this helped! Have a great day!
a root of the equation 3x-8=13
Answer:
x= 7
Step-by-step explanation:
3x= 13+8
3x= 21
x= 21/3
x= 7
What is the value of x+26
Answer:
There are no like terms
Step-by-step explanation:
x+26
There are no like terms
Answer: x+26 is 26
Step-by-step explanation:
A pharmacist dilutes 18 liters of an 8% solution with a 4.5%
solution to make a 6% solution. how many liters of the 4.5%
solution are added?
24.67 liters of the 4.5% solution are added.
As per the known fact, the relation between concentration and volume of solution is -
[tex] C_{1} V_{1} + C_{2} V_{2} = C_{final}V_{final}[/tex]
Let the [tex] V_{2}[/tex] be x. So, final volume will be (18 + x).
Keep the values in formula to find the value of volume of solution required for dilution -
8%×18 + 4.5%×x = 6%×(18 + x)
Rewriting the equation -
0.08×18 + 0.045×x = 0.06(18 + x)
Performing multiplication to find the value of x -
1.44 + 0.045x = 1.08 + 0.06x
Rewriting the equation -
1.44 - 1.08 = 0.06x - 0.045x
Performing subtraction on both sides of the equation -
0.37 = 0.015x
Shifting 0.015 to other side fo equation and performing division
x = 0.37 ÷ 0.015
x = 24.67 liters
Hence, 24.67 liters of 4.5% solution should be added to make a 6% solution.
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what is 5/9 + (-2/9)
Answer: 1/3
Step-by-step explanation:
Answe3/9
Step-by-step explanation: You just subtract the 2 from the 5 because the denominators are the same. You subtract because there is one subtraction sign and one addition sign.
If 8597 - x = 7429 -4358 , find x
Answer:
x=5526
Step-by-step explanation:
8597-x=7429-4358
Combine like terms
8597-x=3071
Group all constants on the right side of the equation
8597-x=3071
Subtract 8597 from both sides
(8597- x )-8597=3071-8597
Group like terms
-x+(8597-8597)=3071-8597
Simplify the arithmetic
-x=3071-8597
Simplify the arithmetic
-x=-5526
Isolate the x
-x=-5526
Multiply both sides by-1
-X x -1=-5526 x -1 the small x is for multiplication
Remove the one(s)
X=-5526 x -1
Simplify the arithmetic
x=5526
The area of a rectangle is 108.35 in² and the length is 7.8 in. Find the width.
A) 6.95 in.
B) 13.89 in.
C) 27.78 in.
D) 21.44 in.
Answer: 13.89 in ==> B
Step-by-step explanation:
A=area of rectangle, l=length, w=width
A=l*w
108.35=7.8*w
108.35/7.8=7.8w/7.8
w=108.35/7.8
w=13.891 ==> w=13.89 in==> B
order to have enough for the trip?
2. An aquarium has 29 large fish tanks. A total of 1,423 fish need to be kept in the
tanks. If the owner wants to split the fish into the tanks as evenly as possible,
what is the greatest number of fish that will be in one tank?
al Paleolith I-man division
50 would be the largest count of fishes that would be in the tanker.
This is because of divide rule.
If the owner wants to keep the equal number of fishes in the tanker, he have to divide the total number of fishes by total number of tankers.
so,
= [tex]\frac{1423}{29}[/tex]
= 49.
It implies that 27 tankers would have 49 fishes in each of them and rest 2 tankers will adjust the remaining extra 2 fishes in themselves , so they would accommodate 50 fishes in each of them.
As the name implies, division rules in mathematics allow one to determine if a number may be divided by another number without using the actual division procedure. When two numbers can be divided evenly, the quotient is always a whole number and the remainder is always zero.
In accordance with the rule of seven divisibility, if a number is divisible by seven, then "the difference between twice the unit digit of the provided number and the remaining portion of the given number should be a multiple of seven or it should be equal to zero." 798, for instance, may be divided by 7.
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Substitute each point (-3,5) and (2,-1) into the slope-intercept form of a linear equation to write a system of equations. Then use the system to find the equation of the line containing the two points. Explain your reasoning.
The slope-intercept form of the equation of the line described is y = -6x/5 + 7/5.
Given the following data:
Points on x-axis = (-3, 2).
Points on y-axis = (5, -1).
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope, m = (-1 - 5)/2 + 3)
Slope, m = -6/5
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the intercept.At point (2, -1), we have:
-1 = -6/5(2) + c
-1 = -12/5 + c
c = 12/5 - 1
c = 7/5
In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is y = -6x/5 + 7/5.
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Given the product (x+8) (x+3) do the following.
(a) Show that this product is equivalent to x² +11x + 24 by using any acceptable method.
(b) Test the equivalency by using x= 1. Show the intermediate calculations.
The product or multiplication of the polynomials is given as
x² +11x + 24.
A result or product is produced by multiplication or a statement that lists the factors to be multiplied.
The commutative law of multiplication states that the product is independent of the sequence in which real or complex numbers are multiplied.The order of the factors often determines the outcome of multiplying matrices or the constituents of other associative algebras.For instance, multiplication in general and in matrices are non-commutative operations in other algebras.Additionally, two complex numbers can be multiplied to get a complex number. When we multiply two integers, we always get back an integer.Given (x+8) (x+3)
let us find the product :
= x² + 8x + 3x + 24
= x² +11x + 24
Let us now test the equivalency .
(x+8) (x+3) = (1+8)(1+3) = (9)(4) = 36
x² +11x + 24 = (1)² + 11(1) + 24 = 36
Hence we can see that the product is same in both the cases.
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Question 2: Write each of the following in index form
(a) √√
(b) √y
(c) √
Va
(d) √ (e) x (1) c
Can you pls help me
Will mark brainliest
The early pay will always be $60 no matter the number of days, the deposit plus will be $35, $50, $65, $80, and the daily pay would be $0, $30, $60 $90, $120.
How much will you pay with the "Early pay" option?Based on the information, if you choose the option early pay, you will pay only $60 and you can swim as many days as you want, due to this, the total paid will always be $60.
How much will you pay with the "Deposit plus" option?Day 0: $20 (deposit)
Day 5: $20 (deposit) + $15 = $35
Day 10: $20 (deposit) + $30 = $50
Day 15: $20 (deposit) + $45 = $65
Day 20: $20 (deposit) + $60 =$80
How much will you pay with the "Daily pay" option?Day 0: $0
Day 5: $30 (6x5)
Day 10: $60 (6x10)
Day 15: $90 (6x15)
Day 20: $120 (6x20)
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If ashima drove the first 348 mi off her trip in 6 hr, how long will it take her, if she drives at the same rate, to drive the remaining 145mi
The time it will take to cover another distance of 145 miles is; 2.5 hours
How to solve proportion word problems?
We are given;
First distance driven = 348 miles
Time taken for first distance = 6 hours
Formula for speed is;
Speed = Distance/Time taken
Thus;
Speed for fist distance = 348/6
Speed = 58 mph
Now, at the same speed she wants to cover another distance 0f 145 miles. Thus;
Time taken = distance/speed
Time taken = 145/58
Time taken = 2.5 hours
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Chloe is making hair bows to sell at a craft show. The table shows the cost per yard of different types of ribbon.
Ribbon Cost per Yard ($)
Chiffon 5.88
Satin 1.50
Lace 3.29
Tulle 2.25
Chloe bought 5.5 yards of satin ribbon and 3.8 yards of tulle. If Chloe paid with a $20 bill, how much change will she receive?
The change received by Chloe after paying a $20 bill for ribbons is $3.2.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given is the table that represents the cost per yards of the ribbons.
From the question, we can write -
Ribbon Cost per Yard ($)
Chiffon 5.88
Satin 1.50
Lace 3.29
Tulle 2.25
Cost of one yard of satin ribbon → $1.50.
Then, the cost of 5.5 yards of satin ribbon [A1] → 5.5 x 1.50 = $8.25.
Cost of one yard of tulle ribbon → $2.25.
Then, the cost of 3.8 yards of tulle ribbon [A2] → 3.8 x 2.25 = $8.55.
Total cost of both the Ribbons → A1 + A2 = 8.25 + 8.55 = $16.8.
Money paid by Chloe → $20
Change received by Chloe → 20 - 16.8 = $3.2
Therefore, the change received by Chloe after paying a $20 bill for ribbons is $3.2.
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A line intersects the points
(8,-10) and (9, 4).
m = 14
Write an equation in point-slope form
using the point (8, -10).
Let f(x)=(x+1)²-2 . Find the x -and y -intercepts of f(x) and the inverse of f(x) . Is the inverse a function?
The x-intercept of the function are (√2-1,0) and(-√2-1,0). and the y-intercept of the function is (0,-1) and the inverse of the function is f⁻¹(x)=±√(x+2)-1.
The x and y intercepts of a function is defined as the points on the cartesian plane where the graph of the function intersects the co-ordinate axes.
The intercepts are calculated by substituting the value of x and y to zero to calculate the corresponding variable.
The inverse of a function y=g(x) is calculated by finding the value of x from the equation.
At x=0 , we get the y intercept.
f(0)=(0+1)²-2
or, f(0)=-1
So the y-intercept is at (0,-1) .
At y=0 we get the x-intercept.
f(x)=0
or,(x+1)²-2=0
or,(x+1)²=2
or, x+1= ±√2
or, x=±√2-1
Therefore the x-intercepts are (√2-1,0) and(-√2-1,0).
Now let us calculate the inverse of the function.
y=(x+1)²-2
or,y+2=(x+1)²
or, x+1=±√(y+2)
or, x=±√(y+2)-1
Hence the inverse of the function is written as
f⁻¹(x)=±√(x+2)-1
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Elliot is paid a salary of $600 per week plus 1% commission on sales OVER $7500. His sales last week totaled $16,700.
What is is commission for the week and his total pay for the week?
Answer:
692
Step-by-step explanation:
600 + (16,700 - 7,500) x 1%
600 + 16,700 - 7,500/100
600 + 9,200/100
600 + 92 = 692
I hope this helped.
Please correct me if I am wrong.