The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Step-by-step explanation:
Given equation is:
[tex]3x^2+3x+5 = 0[/tex]
We will use the quadratic formula for solving the given equation
The quadratic formula is:
[tex]x = \frac{-b+\sqrt{b^2-4ac}}{2a}\ \ \ ,\ \ \ x = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
Here,
a = 3
b = 3
c = 5
[tex]x = \frac{-3+\sqrt{(3)^2-4(3)(5)}}{2(3)}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{(3)^2-4(3)(5)}}{2(3)}\\x = \frac{-3+\sqrt{9-60}}{6}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{9-60}}{6}\\x = \frac{-3+\sqrt{-51}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{-51}}{6}[/tex]
As we know
[tex]i = \sqrt{-1}[/tex]
So,
[tex]x=\frac{-3+\sqrt{51*-1}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{51*-1}}{6}\\x=\frac{-3+(\sqrt{51}*\sqrt{-1})}{6} \ \ \ , \ \ \ \ x = \frac{-3-(\sqrt{51}*\sqrt{-1})}{6}\\x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Hence,
The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Keywords: Quadratic equation, quadratic formula
Learn more about quadratic equation at:
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answer pleaseeeeeeeeee
Answer:
The answer is 50.
Step-by-step explanation:
The answer is 50 because, the line that the Exterior angle is on is equal to 180. So you take the two interior angels and add them. Then subract that from 180 and you get 50.
Hope this helps :))
Answer:
The correct answer is 110°.
Step-by-step explanation:
The Exterior Angle Theorem states, "the exterior angle of a triangle is equal to the sum of its non-adjacent angles".
This means we would add 50 + 60 to get 110°.
Or we could look at the exterior angle and the adjacent angle to it. The two angles form a supplementary angle - this equals 180°. To find our answer this way, we subtract the known angle form 180:
180 - 70 = 110°
Hope this helps,
♥A.W.E.S.W.A.N.♥
Which expression is equivalent to (4 + 7¡)(3 + 4¡)?
Answer:
37i-16
Step-by-step explanation:
(4+7i)(3+4i)
12+21i+16i+28i^2
12+37i+28(-1)
37i+12-28
37i-16
If a sprinkler waters 1 over 20 of a lawn in 1 over 5 of an hour, how much time will it take to water the entire lawn?
3 over 20 hour
1 over 4 hour
4 hours
5 hours
Answer 5
Step-by-step explanation:
write an equation for the relationship between time and distance for each horse
Answer:
The relationship between time and distance is Velocity = Distance / Time
Step-by-step explanation:
Find the domain of the function (f - g)(x) where f(x) = 5 - X, g(x) =
x - 5
Answer:
ℝ
Step-by-step explanation:
[tex]\displaystyle 10 - 2x = [5 - x] - [x - 5][/tex]
All linear functions have a range and domain of all real numbers.
I am joyous to assist you anytime.
Which two statements are both true?
(Full question above)
Answer:
TU ⊥ MN and MN ║ PQ
Step-by-step explanation:
TU ⊥ MN
As the angle that is created where TU and MN intersect is a 90° angle, these two lines must be perpendicular to each other.
MN ║ PQ
As both MN and PQ intersect the line TU, we can use this to prove that they are parallel.
Both MN and PQ create a 90° angle where they intersect with TU. This means that MN is ⊥to TU and PQ is ⊥ to TU.
As both MN and PQ are perpendicular to TU, they must be parallel.
Consider the functions f(x) = (four-fifths) Superscript x and g(x) = (four-fifths) Superscript x + 6. What are the ranges of the two functions? f(x): {y| y > } g(x): {y| y > }
Answer:
f(x): {y| y > 0 }
g(x): {y| y > 6 }
Step-by-step explanation:
Hope this helps!
Because both of these are exponential functions with positive bases, we conclude that the range for both is:
{y| y > 0}.
How to find the ranges of the two functions?
Here we have two exponential functions:
f(x) = (4/5)^x
g(x) = (4/5)^(x + 6).
You can see that both of these are exponential functions with positive bases, then neither of these can have negative outcomes, while, as x increases, the outcome will also increase.
Then we can see both functions are exponential growths, so the range for both of these are the set of all real positive values, written in both cases as:
{y| y > 0}
If you want to learn more about exponential functions, you can read:
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!
Answer:
Step-by-step explanation:
1. [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex]
2. [tex]y=-5x+30[/tex]
Step-by-step explanation:Preliminary Material:
A line that is perpendicular to another has the opposite reciprocal slope of the other line.
Ex: [tex]-\frac{1}{3}x+3[/tex] is perpendicular to [tex]3x+2[/tex] because [tex]-\frac{1}{3}[/tex] is an opposite reciprocal to [tex]3[/tex].A line parallel to another has the same slope.
With this in mind, we can begin to answer this question.
1.
Setup for question 1:
A line perpendicular with [tex]-5x+5[/tex] that goes through the point (7, 5).
Before going over the point this perpendicular line must go through, let's make an equation with the slope of the perpendicular line.
A linear function can be represented with this formula: [tex]y=mx+b[/tex].
[tex]m[/tex] = the slope of the line.b = the y intercept.We know the slope of this function must be an opposite reciprocal to -5, and using the information I first gave in the beginning of this problem, we can have the slope of the function.
the opposite reciprocal of [tex]-5[/tex] (or [tex]-\frac{5}{1}[/tex]) is [tex]\frac{1}{5}[/tex].If we take this slope and insert it into the linear equation, we will have the function...
[tex]y=\frac{1}{5}x+b[/tex]So we now know the slope of this function, but what about the y intercept, [tex]b[/tex]? This is where the point given to us in the beginning of this problem comes into play. If we plug the point (7, -5) into our x and y coordinates in the above equation, we can solve for [tex]b[/tex].
Algebra:
[tex]-5=\frac{1}{5}(7)+b[/tex]
multiply out your terms.[tex]-5=\frac{7}{5}+b[/tex]
[tex]-5[/tex] is the same as the fraction [tex]-\frac{25}{5}[/tex].[tex]-\frac{25}{5}=\frac{7}{5}+b[/tex]
subtract [tex]\frac{7}{5}[/tex] from both sides.[tex]-\frac{32}{5}=b[/tex]
[tex]b[/tex] is equal to [tex]-\frac{32}{5}[/tex] or [tex]-6\frac{2}{5}[/tex]. Lets plug this into our original equation, and we're done.Answer:
Our final answer is: [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex].
2.
There will be no setup for 2. I'll show the algebra without explanation as well. If there's any confusion you can ask me :).
Algebra:
[tex]y=mx+b[/tex]
[tex]y=-5x+b[/tex]
[tex]-5=-5(7)+b[/tex]
[tex]-5=-35+b[/tex]
[tex]b=30[/tex]
Answer:
Our final answer is: [tex]y=-5x+30[/tex]I just need help factoring or solving this one
Answer:
v = 1/2(1 + i√23) , 1/2(1 - i√23).
Step-by-step explanation:
-2v^2 - v + 12 = -3v^2 + 6
-2v^2 + 3v^2 - v + 12 - 6 = 0
v^2 - v + 6 = 0
This will not factor so we could use the quadratic formula to solve it:
For the equation ax^2 + bx + c = 0 the roots are:
x = [ - b +/- sqrt(b^2 - 4ac) ] / 2a.
So here we have:
v = [-(-1) +/- sqrt((-1)^1 - 4*1*6)] / 2
v = [ 1 +/- sqrt (-23)] / 2
= 1/2 + i√23/2 , 1/2 - i√23/2
= 1/2(1 + i√23) , 1/2(1 - i√23).
1
Select the correct answer.
What is the area of the cross section that is parallel to side PQRS in this rectangular box?
A.
12 square units
B.
16 square units
C.
30 square units
D.
40 square units
Answer:
12 square units.
Step-by-step explanation:
I just took the test.
Round 832 to the nearest hundreds place.
Answer:
800
Step-by-step explanation:
Look at the tens if it's 0-4 keep the number the same if 5-9 go up one number
PLEASE MARK BRAINLIEST!
Answer:
832 --> ???
832 - we must round the underlined digit
832 --> ???
832 --> 800
The rounding rule is:
4 and below, stay down low! [Round down]. 5 and above, soar like a dove! [Round up].
So with that rule, 832 becomes 800.
800 is your answer.
I hope this helps!
If distinct planes R and S are both perpendicular to line L , which is always true?
1. Plane R is parallel to plane S
2. Plane R is perpendicular to plane S
3. Planes R and S and line L are all parallel
4. The intersection of planes R and S is perpendicular to line L
Answer:
Option 1 is correct.
Step-by-step explanation:
Let there is a line A which is perpendicular to line L at point O.
Now, rotating line A about point O by 360° will give the plane R.
So, plane R is perpendicular plane to line L.
Again, let there is a line B which is perpendicular to line L at point P.
Now, rotating line B about point P by 360° will give another plane S.
So, plane S is perpendicular plane to line L.
Since line A and line B are parallel (As they are perpendicular to the same line L) so, plane R containing line A and plane S containing line B will also be parallel to each other.
Hence, option 1 is correct. (Answer)
Jerome's credit card has an APR of 18%, calculated on the previous monthly
balance, and a minimum payment of 2%, starting the month after the first
purchase. His credit card record for the last 7 months is shown in the table
below.
End of
month
Previous
balance
$0.00
$2200.00
$2189.00
$2178.06
$2167 16
$2156.33
$2145.55
Now
charges
$2200.00
$0.00
50.00
S0.00
$0.00
$0.00
50.00
Payment
recolved
S000
$44.00
$43.78
$43.56
$43.34
$43.13
$42.91
chere
30.00
$33.00
532.84
$32.67
$3251
$32,34
$32.18
Principal
pald
30.00
$11.00
$10.95
$10.89
$10.84
$10.78
$10.73
balance
$2200.00
$2189.00
$2178.06
$2167.16
$2156.33
$2145.55
$2134.82
What is the total amount that Jerome has paid in interest over the 7 months?
Answer: 11,056.1
Step-by-step explanation: Because you have to add the first 7
Jerome has paid a total of [tex]\$195.54[/tex]rest over the 7 months.
To find the total amount that Jerome has paid in interest over the 7 months, we need to sum up the interest paid each month. The interest for each month is calculated as follows:
[tex]\[ \text{Interest for the month} = \text{Previous balance} \times \text{APR} / 12 \][/tex]
Let's calculate the interest for each month:
1. For the second month:
[tex]\[ \text{Interest} = \$2200.00 \times 0.18 / 12 = \$33.00 \][/tex]
2. For the third month:
[tex]\[ \text{Interest} = \$2189.00 \times 0.18 / 12 = \$32.84 \][/tex]
3. For the fourth month:
[tex]\[ \text{Interest} = \$2178.06 \times 0.18 / 12 = \$32.67 \][/tex]
4. For the fifth month:
[tex]\[ \text{Interest} = \$2167.16 \times 0.18 / 12 = \$32.51 \][/tex]
5. For the sixth month:
[tex]\[ \text{Interest} = \$2156.33 \times 0.18 / 12 = \$32.34 \][/tex]
6. For the seventh month:
[tex]\[ \text{Interest} = \$2145.55 \times 0.18 / 12 = \$32.18 \][/tex]
Now, sum up these monthly interest amounts:
[tex]\[ \$33.00 + \$32.84 + \$32.67 + \$32.51 + \$32.34 + \$32.18 = \$195.54 \][/tex]
So, Jerome has paid a total of [tex]\$195.54[/tex]rest over the 7 months.
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day.
C(x) = 4x³+7x²-14x-6
Step-by-step explanation:
Given that the amount of water used in normal days is given by the equation;
W(x) = 5x³ +9x²-14x +9 -----(i)
The amount of decrease in water used is modeled by the equation;
D(x)= x³+2x² +15--------(ii)
To get the function C(x) that models the water used by the car wash on shorter day you subtract equation (ii) from equation(i)
5x³ +9x²-14x +9
- x³+2x² +15
-------------------------
4x³+7x²-14x-6
Learn More
Subtraction in polynomials : https://brainly.com/question/2273346
Keywords : equation, modeled,
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Answer:
C(x) = 4x³ + 7x² − 14x - 6
Step-by-step explanation:
In a shorter day the water used by the car wash is computed as the difference between the original usage and the decrease, that is:
C(x) = W(x) - D(x)
Replacing with data:
C(x) = 5x³ + 9x² − 14x + 9 - (x³ + 2x² + 15)
C(x) = 5x³ + 9x² − 14x + 9 - x³ - 2x² - 15
C(x) = (5-1)x³ + (9-2)x² − 14x + (9-15)
C(x) = 4x³ + 7x² − 14x - 6
How many teaspoons are in 8 tablespoons?
Answer:
24 Teaspoons
Explanation:
1 tablespoon is equivalent to 3 teaspoons
8 · 3 = 24
Therefore 24 teaspoons is equivalent to 8 tablespoons.
A book is 15 centimeters long and 6 centimeters wide. What are the length and width of the book in inches.Round your answer to the nearest hundredth.
Length and width of book is 5.91 inches and 2.36 inches respectively
Solution:
Given that a book is 15 centimeters long and 6 centimeters wide
To find: length and width of book in inches
From given question,
Length of book = 15 cm
Width of book = 6 cm
The conversion factor used is:
1 cm = 0.393701 inches
Therefore, length of book in inches is:
[tex]15 \text{ cm} = 15 \times 0.393701 \text{ inches }= 5.905515 \text{ inches }[/tex]
Rounding off rules:
First look at the digit to immediate right of rounding off digit
If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.
If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.
On rounding to nearest hundredth, ( two decimal places )
[tex]5.905515 \text{ inches } = 5.91 \text{ inches }[/tex]
Width of book in inches:
[tex]6 \text{ cm} = 6 \times 0.393701 \text{ inches } = 2.362206 \text{ inches }[/tex]
On rounding to nearest hundredth, we get 2.36 inches
Final answer:
The book measures approximately 5.91 inches in length and 2.36 inches in width.
Explanation:
To convert the dimensions of the book from centimeters to inches, we use the conversion factor that 1 inch is equal to 2.54 centimeters.
The length of the book in inches is calculated as follows:
Length in inches = Length in centimeters ÷ 2.54Length in inches = 15 cm ÷ 2.54Length in inches ≈ 5.91 inches (rounded to the nearest hundredth)Similarly, the width of the book in inches is:
Width in inches = Width in centimeters ÷ 2.54Width in inches = 6 cm ÷ 2.54Width in inches ≈ 2.36 inches (rounded to the nearest hundredth)Therefore, the book measures approximately 5.91 inches in length and 2.36 inches in width.
Sue lives 6 miles from Gill. She also lives 1 mile closer to Taco Town restaurant than Gill does. Write an equation that shows this statement: the distance from Sue's to Taco Town plus the distance from Taco Town to Gill's equals the distance from Sue's house to Gill's house.
Answer:
The equation representing the statement is [tex](x-1)+x=6[/tex].
Step-by-step explanation:
Given:
Distance from Sue house to Gill house = 6 miles.
Let the distance from Gill to Taco Town restaurant be 'x'.
Also Given:
Sue lives 1 mile closer to Taco Town restaurant than Gill does.
Hence Distance from Sue to Taco Town restaurant will be = [tex]x-1[/tex]
We need to write the equation for the below statement.
the distance from Sue's to Taco Town plus the distance from Taco Town to Gill's equals the distance from Sue's house to Gill's house.
Framing in equation form we get;
[tex](x-1)+x=6[/tex]
Hence the equation is [tex](x-1)+x=6[/tex].
You have a 32-foot fence around a square garden. There are 4 equal sections. You paint 13 of one section of the fence.
What fraction of the fence did you paint?
Question:
You have a 32-foot fence around a square garden. There are 4 equal sections. You paint 1/3 of one section of the fence. What fraction of the fence did you paint?
Answer:
The fraction of the fence painted is [tex]\frac{1}{12}[/tex]
Solution:
Given that:
You have a 32-foot fence around a square garden. There are 4 equal sections
Find the length of each section:
4 sections = 32 foot
[tex]\text{ 1 section } = 32 \div 4 = 8 foot[/tex]
Find the length that is painted:
[tex]\text{ Fence painted }= \frac{1}{3} \text{ of one section }\\\\\text{ Fence painted }= \frac{1}{3} \times 8 = \frac{8}{3} \text{ foot }[/tex]
Therefore [tex]\frac{8}{3}[/tex] foot of fence is painted
Find the fraction that that is painted:
Total length of fence = 32
[tex]\text{ Fraction of the fence painted } = \frac{8}{3} \div 32 = \frac{8}{3} \times \frac{1}{32}\\\\\text{ Fraction of the fence painted } = \frac{1}{12}[/tex]
Therefore [tex]\frac{1}{12}[/tex] fraction of the fence is painted
20 POINTS BRAINLIEST
Answer:
D
Step-by-step explanation:
Using the rule of logarithms
log x - log y = log([tex]\frac{x}{y}[/tex])
Given
[tex]log_{7}[/tex]([tex]\frac{n}{2}[/tex])
= [tex]log_{7}[/tex] n - [tex]log_{7}[/tex] 2 → D
Answer:
yoink im eating them points nomnomnom
Step-by-step explanation:
1. Which of the following could be
the measurements of two
complementary angles?
A. 7º and 830
B. 83° and 830
C. 97º and 83°
D. 117° and 83°
Step-by-step explanation:
I don't know if this helps, but none of the above.
first of all, complementary angles mean that the 2 (or more) angles add up to 90 degrees. so, if you were to combine the angles, you'll get an angle that's way larger than 90 degrees. (a and b won't work cause 830 isn't an angle)
P.S. but 83 degrees and 7 degrees would be complementary...
hope you at least know why i say none of the above
3.6x - 12.2=-1.5x + 8.2
Answer:
x = 4Step-by-step explanation:
[tex]3.6x-12.2=-1.5x+8.2\qquad\text{multiply both sides by 10}\\\\36x-122=-15x+82\qquad\text{add 122 to both sides}\\\\36x-122+122=-15x+82+122\\\\36x=-15x+204\qquad\text{add}\ 15x\ \text{to both sides}\\\\36x+15x=-15x+15x+204\\\\51x=204\qquad\text{divide both sides by 51}\\\\\dfrac{51x}{51}=\dfrac{204}{51}\\\\x=4[/tex]
A shrub in Pam's back yard is about 1 3\8 feet tall. A small tree in her back yard is about 7 times as the shurd. About how tall is the tree
The height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]
Solution:
Given that shrub in Pam's backyard is about [tex]1\frac{3}{8}[/tex] feet tall
A small tree in her back yard is about 7 times as the shurd
To find: height of tree
From given information,
Height of shrub = [tex]1\frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8} \text{ feet}[/tex]
Given that small tree in her back yard is about 7 times as the shurb
So we get,
height of tree = 7 times the height of shrub
[tex]\text{ height of tree } = 7 \times \text{ height of shrub}\\\\\text{ height of tree } = 7 \times \frac{11}{8}[/tex]
Therefore on solving we get,
[tex]\text{ height of tree } = \frac{77}{8} = 9\frac{5}{8} \text{ feet}[/tex]
Thus the height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]
Olive's solar powered scooter travels at a rate of 30 miles per hour. What equation can she use to calculate her distance with relation to the time she is traveling?
m = miles
h = hours
A: h = 30m
B: h = m + 30
C: m = h + 30
D: m = 30h
Answer:
The equation to represent the distance traveled by Olive in here solar powered scooter can be given as:
D: [tex]m=30h[/tex]
Step-by-step explanation:
Given:
Speed of Olive's solar powered scooter = 30 miles/hour
[tex]m\rightarrow[/tex] miles traveled
[tex]h\rightarrow[/tex] hours of travel
To find the distance traveled by Olive.
Solution:
Distance traveled = [tex]Speed\ \times \ Time[/tex]
Thus, the equation to represent the distance traveled by Olive in here solar powered scooter can be given as:
[tex]m=30\times h[/tex]
∴ [tex]m=30h[/tex]
The dimensions of a rectangle are given in
ectangle are given in terms of s as shown below.
-s+ / -
[not drawn to scale)
Select all expressions that represent the perimeter of the rectangle.
+
4s + 1
* 2s + 1
© 4s + 2
© 2/5 + 1)
© 2s +
® 22s +
Option A and Option F
The expressions that represent the perimeter of rectangle are 4s + 1 and [tex]2(2s + \frac{1}{2})[/tex]
Solution:
From figure,
Length = s
Width = [tex]s + \frac{1}{2}[/tex]
The perimeter of rectangle is given as:
perimeter = 2(length + width)
Substituting the values we get,
[tex]perimeter = 2(s + s + \frac{1}{2})\\\\perimeter = 2(2s + \frac{1}{2})[/tex]
Thus option F is correct
On further simplification,
[tex]perimeter = 2(2s + \frac{1}{2})\\\\perimeter = 4s + 2(\frac{1}{2})\\\\perimeter = 4s + 1[/tex]
Thus Option A is correct
If f (x)= 5x -7, then what is the solution to f (x) = 4?
Answer:
11/5
Step-by-step explanation:
5x-7=4
5x=4+7
5x=11
x=11/5
The required solution of the function at x = 4 is f(4) = 13.
Given that,
A function is given f(x) = 5x - 7, the value of the function at x = 4 is to be determined.
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Given function,
f(x) = 5x - 7
put the value x = 4 in the above equation,
f(4) = 5 * 4 - 7
f(4) = 20 -7
f(4) = 13
Thus, the required solution of the function at x = 4 is f(4) = 13.
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Explain how linear equations can be used in temperature conversion.
Answer:
It is important to know that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C)
Step-by-step explanation:
It is important to know that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C).
Lets take an example, if we have 81°F and want to convert in (°C). So, here is the procedure:
C = (5/9) (81 - 32)
= (5/9) (49)
= 27.22 °C
So, it is clear that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C).
Keywords: linear equation, converter, C = (5/9)(F-32)
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Simplify: -3152 – 10(4.32 + 5 = 5)]
Answer:-523/52
Step-by-step explanation:
The simplified form of the expression is [tex]\(-3245.2\).[/tex]
To simplify the given expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). The expression given is:
[tex]\[ -3152 - 10(4.32 + 5 = 5) \[/tex]
First, we address the equality within the parentheses. The expression \[tex](4.32 + 5\) equals \(9.32\),[/tex] but the equality [tex]\(4.32 + 5 = 5\)[/tex] is not true. However, in the context of this expression, the equality sign does not affect the numerical computation; it seems to be a typographical error or a misplacement. We will treat the expression within the parentheses as [tex]\(4.32 + 5\)[/tex]and ignore the equality for the calculation.
Now, let's simplify the expression step by step:
1. Calculate the expression inside the parentheses:
[tex]\[ 4.32 + 5 = 9.32 \][/tex]
2. Multiply the result by -10 (note that the multiplication comes before addition/subtraction in the order of operations):
[tex]\[ -10 \times 9.32 = -93.2 \][/tex]
3. Finally, subtract the result from -3152:
[tex]\[ -3152 - 93.2 = -3245.2 \][/tex]
So, the simplified form of the expression is [tex]\(-3245.2\).[/tex]
You sell bracelets for $2 each and necklaces for $3 each at a local flea market. You collect$96, selling a total of 36 jewelry items. how many of each type did you sell?
Answer:
I sell 12 bracelets and 24 necklaces.
Step-by-step explanation:
The selling price of each bracelet is $2 and that of each necklace is $3.
I collect $96, selling a total of 36 jewelry items.
Let us assume that I sell x bracelets and y necklaces.
So, x + y = 36 ........ (1) and
2x + 3y = 96 .......... (2)
Now, solving equations (1) and (2) we get, 3y - 2y = 96 - 72
⇒ y = 24
Hence, from equation (1) we get x = 36 - y = 36 - 24 = 12
Therefore, I sell 12 bracelets and 24 necklaces. (Answer)
Find the midpoint of RS
Answer:
The midpoints of the given graph are ( - 1, 3 ).
Step-by-step explanation:
By the graph we have to given that the endpoints are R ( -5, 4) and S (3, 2)-
As we know that-
If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex]) and ( [tex]x_{2}, y_{2}[/tex] ) then the mid points C are-
C = ( [tex]\frac{x_{1} + x_{2} }{2}[/tex], [tex]\frac{y_{1} + y_{2} }{2}[/tex] )
Here,
R ( - 5, 4 ) and S ( 3, 2 )
then the midpoints C are-
C = ( [tex]\frac{ - 5 + 3}{2}[/tex] , [tex]\frac{4 + 2}{2}[/tex]
C= ( - 2/2 , 6/2 )
C = ( -1, 3 )
Hence the midpoints are ( - 1, 3 ).
A surveyor wants to find the distance from points A and B to an inaccessible point C. These three points form a triangle. Because point C can be sighted from both A and B, he knows that the measure of < A= 53 degrees and the measure of < B = 61 degrees. In addition, the distance from A to B is 142 meters. Find AC and BC. Draw a diagram.
Answer:
Part a) [tex]AC=135.95\ m[/tex]
Part b) [tex]BC=124.14\ m[/tex]
The diagram in the attached figure
Step-by-step explanation:
step 1
Find the measure of angle C
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]m\angle A+m\angle B+m\angle C=180^o[/tex]
substitute the given values
[tex]53^o+61^o+m\angle C=180^o[/tex]
[tex]114^o+m\angle C=180^o[/tex]
[tex]m\angle C=180^o-114^o[/tex]
[tex]m\angle C=66^o[/tex]
step 2
Find the distance AC
Applying the law of sines
[tex]\frac{AB}{sin(C)}=\frac{AC}{sin(B)}[/tex]
see the attached figure to better understand the problem
substitute the given values
[tex]\frac{142}{sin(66^o)}=\frac{AC}{sin(61^o)}[/tex]
[tex]AC=\frac{142}{sin(66^o)}(sin(61^o))[/tex]
[tex]AC=135.95\ m[/tex] ---> rounded to the nearest hundredth
step 3
Find the distance BC
Applying the law of sines
[tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}[/tex]
substitute the given values
[tex]\frac{142}{sin(66^o)}=\frac{BC}{sin(53^o)}[/tex]
[tex]BC=\frac{142}{sin(66^o)}(sin(53^o))[/tex]
[tex]BC=124.14\ m[/tex] ---> rounded to the nearest hundredth