Answer: [tex]\quad x=1+\sqrt{3}i,\:x=1-\sqrt{3}i[/tex]
Step-by-step explanation: [tex]x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:6\cdot \:24}}{2\cdot \:6}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-12\right)\pm \:12\sqrt{3}i}{2\cdot \:6}[/tex][tex]x_1=\frac{-\left(-12\right)+12\sqrt{3}i}{2\cdot \:6},\:x_2=\frac{-\left(-12\right)-12\sqrt{3}i}{2\cdot \:6}[/tex][tex]x=1+\sqrt{3}i,\:x=1-\sqrt{3}i[/tex]Fernando is trying to incorporate more exercise into his busy schedule. He has several short exercise routines he can complete at home. Last week, he worked out for a total of 88 minutes by doing 2 arm routines and 3 abdominal routines. This week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 66 minutes exercising. How long does each routine last?
Answer: Arm routine = 11 minutes
Abdominal routine = 22 minutes
Step-by-step explanation:
Let the minutes used for an arm routine be represented by x.
Let the minutes used for an abdominal routine be represented by y.
Last week, he worked out for a total of 88 minutes by doing 2 arm routines and 3 abdominal routines. This can be expressed as:
2x + 3y = 88
This week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 66 minutes exercising. This can be expressed as:
4x + y = 66
2x + 3y = 88 ...... i
4x + y = 66 ...... ii
Multiply equation I by 4
Multiply equation ii by 2
8x + 12y = 352 ...... iii
8x + 2y = 132 ...... iv
Subtract iv from iii
10y = 220
y = 220 / 10
y = 22
An abdominal routine last for 22 minutes
From equation I
2x + 3y = 88
2x + 3(22) = 88
2x + 66 = 88
2x = 88 - 66
2x = 22
x = 22/2
x = 11 minutes
An arm routine last for 11 minutes
Please, I need help.
Which expression is equivalent to (m^2-3m+7)(m-5)^-1
Answer:
a
Step-by-step explanation:
What is the area of rectangle ABCD?
Answer:
8 squares
Step-by-step explanation:
i think 8 squres iscorrect answer
Answer:
8 square units
Step-by-step explanation:
count the number of squares the rectangle is taking
or length times width
2x4
I need help !! this is geometry hw
Answer:
angle a=64, longest side AV : shortest side: TV
angle c=55 longest side: BW shortest side: CB
angle z =24 longest side: XZ shortest side: XP
Step-by-step explanation:
Find the sale price of the item. Round to two decimal places when
necessary. *
Original Price: $40.00; Markdown: 15%
$46
$34
$42
$32
First, determine what 15% of $40 is.
Convert 15% to a decimal: 0.15
Then multiply this decimal by $40: 0.15 x 40 = 6
So the discount is $6.
We subtract the discount from original price to get sale price.
40-6= 34
So the item will cost $34.
A fundraiser is being held to support a local nonprofit organization. Admission costs $10, and each raffle ticket costs $3. There are no other possible costs. If an event-goer pays the admission fee and buys x number of tickets, what type of function should be used to model the total amount spent by the event-goer at the event?
Answer:
y= 10+ 3x
10 is the admission fee
3x is the cost for each ticket
y is the total
The function for the total cost (y) spent by the event-goer at the event is
y = 3x+10
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Given that, Admission costs $10, and each raffle ticket costs $3. There are no other possible costs.
Let the total cost be y,
Therefore, establishing the function, for x number of tickets.
y = 3x+10
Hence, the required function is y = 3x+10
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Help Plz 10pts will be given
Answer:
Is the first one 3 over 7
Step-by-step explanation:
2(2.8s + 2.5) =
Please use the distributive property and answer the expression.
Answer: 5.6s+5
Step-by-step explanation: hope this helps
btw can i have brainliest?
In an electric circuit, the current varies inversely as the resistance. The current is 40 amps when the resistance is 12 ohms. Find the current when the resistance is 20 ohms.
Answer:
24 amps
Step-by-step explanation:
Current = k /resistance
k = current × resistance
= 40 × 12
= 480
If the resistance is 20 ohms then the current can be calculated as follows
Current = 480/20
= 24 amps
Put these over a common denominator: ³/5 and 4/7
ANSWER 35
Step-by-step explanation:
7 and 5 - 35
Now just simplify the 3 and 4 :)
In a recipe, for every 3/4 cup of flour, 1/3 cup of sugar is needed. How many cups of sugar are needed for 1 cup of flour? (Leave your answer in fraction form).
Answer:
1/9 cup of sugar for every 1/4 cup of flour
Step-by-step explanation: Turn the 1/3 into 3/9 and I'm sure you can figure it out from there.
Which type of data would be best displayed in a box plot?
Answer:c
Step-by-step explanation:i took the test
option C, The number of votes received by each of four candidate can be best displayed in a box plot.
Explanation:
We need to find which type of data can be displayed in a box plot from the given options.
The box plot can used to show the shape of a distribution, the lower value , higher value , the central value, and its variability.
The graph shows how the values of the data are spread out .It is the distribution of numerical data. Box plot can be used to compare multiple groups .
So, the answer can be option C
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Simplify the expression.
49^3/2
Answer:
i think its 58824.5
HELPP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
a warm front is happening
Answer:
hot
Step-by-step explanation:
When writing an equation in slope-intercept form, you need the values of the
Answer:
slope, m
y-intercept
Step-by-step explanation:
When writing an equation in slope-intercept form, there will be need for slope and y- intercept.
What is the slope intercept form of an equation ?When any equation is represented in the y = mx +c form, it is called the slope intercept form of the equation.
Here m is slope and c is constant.
To writing the slope intercept form of the equation,
There will be requirement of slope,
and y intercept, it will be in form of (0, a), here a will be value of y coordinate.
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I WILL MARK BRAINIEST
PLEASE HELP ASAP
Answer:
2101
Step-by-step explanation:
Apply -12 to the x
-(-12)^3+3(-12)^2+5(-12)+1
Then Simplify
2101
I hope it's right
need help finding out something, refer to picture
Answer:
He made a mistake in the second line.
Step-by-step explanation:
He factored out x out of 6-2x and 5+4x, which is not possible because there is not an x in both 6 and 5.
Lukas is running a lemonade stand on a hot summer day. He spent $14 for the materials and earns $1.50 for each cup of lemonade sold. What is an equation that relates the number of cups of lemonade sold, c and the profit earned, P, and explain whether Lukas selling 19.5 cups is a viable solution.
The equation would be 1.50x - 14 = P
If lucas sells 19. cups then that means he will earn a total of 29.25$ but since he spent 14$ for the materials itself that concludes to the total being 15.25.This would be a viable solution because he is earning more money then he is loosing.
Which sequence of transformations proves that shape I is similar to shape II?
A.
a reflection across the x-axis, and then a translation 6 units right
B.
translation 6 units right, and then a 90° clockwise rotation about the origin
C.
a 180° counterclockwise rotation about the origin
D.
a reflection across the y-axis, and then a translation 4 units up
E.
a reflection across the x-axis, followed by a 180° counterclockwise
rotation about the origin, and then a translation 4 units down
Answer:
E
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Jenny earned 86 of a possible 138 points on a test. She lost 2 points for each incorrect answer. How many incorrect answers did she have?
Find the value of the trigonometric ratio.
9) sin z
Answer:
SinZ=24/40 = 12/20 = 3/5
C)
The value of the trigonometric ratio Sin Z for the given triangle XYZ will be [tex]\frac{3}{5}[/tex], i.e. option C.
What are trigonometric ratios?The trigonometric ratios are the ratios of sides of two sides of right angled triangle used in trigonometry. Trigonometric ratios are used to find the value of the acute angles in a right triangle when the sides of the triangle are given.
We have,
A right-angled triangle XYZ with the given values,
Angle Y = 90°
And,
YZ = 32, XY = 24 and XZ = 40,
Now,
Using the trigonometric ratios,
i.e.
[tex]Sin Z=\frac{Perpendicular}{Hypotenuse}[/tex]
i.e.
[tex]Sin Z=\frac{XY}{XZ}[/tex]
So,
[tex]Sin Z=\frac{24}{40}[/tex]
On simplifying,
We get,
[tex]Sin Z=\frac{3}{5}[/tex]
So,
The option C is the correct answer for the given triangle find out using trigonometric ratio,
Hence, we can say that the value of the trigonometric ratio Sin Z for the given triangle XYZ will be [tex]\frac{3}{5}[/tex], i.e. option C.
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Help meeee!will give brainliest!
Answer
(2,0) Brainliest please
Step-by-step explanation:
The salesman gave me 20% off of my new laptop regularly priced $500. How
much did I save? *
Answer:
100
Step-by-step explanation:
20% of 500 is 100
Answer:
$100
Step-by-step explanation:
20% is the same as 1/5. 1/5 of 500 is 100. Then add dollar signs, and you have your answer.
Your school is installing new turf on the football field. A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet. A) what is the length of the field. B) what is the perimeter of the field. C) Turf costs $2.69 per square foot. Your school has a $150,000 budget. Does the school have enough money to purchase new turf for the entire field? Please show the steps.
Answer:
Step-by-step explanation:
1) length of the field = 18 unit= 18*20=360 ft
2) circumference = 2(l+w)
2*(18*20+8*20)=1040
3) Area of the field = 18*8 units = 18*20*8*20ft^2 = 57600ft^2
Cost for the entire area= 57600*2.69= 170,000$
No it doesn't
A) The length of the field is 360 feet
B) The Perimeter of field is 1040 feet
C) The school does not have enough money to purchase new turf for the entire field.
what is Area of rectangle?The Area of rectangle is the product of the length to its width.
Area of rectangle= length x width
Given:
1 block= 20 feet
A) length= 18 blocks
= 18 x 20
= 360 feet
width= 8 blocks
= 8 x 20
= 160 feet
B) Perimeter of field
= 2( l+w)
=2( 360 + 160)
= 2 x 520
= 1040 feet
C) Area of field
= l x w
=360 x 160
= 57600 feet²
If cost of 1 square feet is $2.96
and, the cost of 57600 feet²
= 2.96 x 57600
= $170,496
No, the school does not have enough money to purchase new turf for the entire field.
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Write the equation in slope-intercept form for a line which points go through (-2,3), parallel to x=o
Answer:
x = -2Step-by-step explanation:
Line x = 0 is parallel to y-axis
Line parallel to given line is also parallel to y-axis. It passes through point (-2, 3), so its equation is:
x = -2It took Sharon 85 minutes to wash three cars. She spent x minutes on
each car and 10 minutes putting everything away. Solve 3x + 10 = 85 to
find how long it took to wash each car.
A)5.5
B)28.3
C)25
D)31,67
Answer:
25
Step-by-step explanation:
-14x + 18 - 11 -2x + 3
Answer:
-2(8x-5)
Step-by-step explanation:
Answer:
I think you meant -14x+18-11-2x+3=0
If that's the case then x= 5/8
Step-by-step explanation:
-16x+10=0
-16x= -10
x= -10/-16 = 5/8
In decimal form it is 0.625
The wholesale price of a bicycle is $120. If the store wants to mark up the bicycle 40%, what is the final price
What is the slope of the line through the points (5,2) and (-3, -7).
Answer:
8/9
Step-by-step explanation: