[tex]x^2+7=2x\\\\\implies x^2 -2x +7 =0\\\\\text{Apply quadratic formula,}~ x =\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{in this case,}~ a = 1, b= -2 ~\text{and}~ c = 7\\\\\\x= \dfrac{-(-2) \pm \sqrt{(-2)^2 -4\cdot 1 \cdot 7}}{2\cdot 1}\\\\\\\implies x =\dfrac{2 \pm \sqrt{-24}}{2}\\\\\\\implies x = \dfrac{2 \pm i\sqrt{24}}2\\\\\implies x =\dfrac{2 \pm i2\sqrt{6}}2\\\\\implies x = \dfrac{2\left(1 \pm i \sqrt 6\right)}2\\\\\implies x = 1 \pm i\sqrt 6\\\\[/tex]
[tex]\text{Hence,}~ x = 1-i\sqrt 6 ~\text{or}~ x = 1+i\sqrt 6[/tex]
What is the equation of the line passing through the points (Two-fifths, StartFraction 19 Over 20 EndFraction) and (one-third, StartFraction 11 Over 12 EndFraction) in slope-intercept form
Step-by-step explanation:
Slope-intercept form: y = mx + b
Step 1: Find the slope.Solve for [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]y2-y1 = \frac{11}{12} -\frac{19}{20}[/tex]
[tex]x2-x1 = \frac{1}{3} -\frac{2}{5}[/tex]
To solve for the fractions you need a common denominator.
[tex]y2-y1 = \frac{11*20}{12*20} -\frac{19*12}{20*12} = \frac{220}{240} -\frac{228}{240}=\frac{-8}{240} = \frac{-1}{30}[/tex]
[tex]x2-x1 = \frac{1*5}{3*5} -\frac{2*3}{5*3} = \frac{5}{15} -\frac{6}{15}=\frac{-1}{15}[/tex]
To divide fractions you keep (the first equation), change (the division sign to multiplication), and flip (the second fraction).
[tex]\frac{y2-y1}{x2-x1}=\frac{\frac{-1}{30} }{\frac{-1}{15} } = \frac{-1}{30}*\frac{15}{-1} =\frac{-15}{-30}=\frac{1}{2}[/tex]
Step 2: Plug slope and a point into y=mx+b to solve for b.[tex]\frac{11}{12}[/tex] = ([tex]\frac{1}{2}[/tex])*([tex]\frac{1}{3}[/tex])+b
[tex]\frac{11}{12}[/tex] = ([tex]\frac{1}{6}[/tex])+b
[tex]\frac{11}{12}-\frac{1}{6}[/tex] = b
[tex]\frac{11*6}{12*6}-\frac{1*12}{6*12}=\frac{66}{72} -\frac{12}{72} =\frac{54}{72}=.75[/tex]
b = .75
y = [tex]\frac{1}{2}+.75[/tex]
Mattie Evans drove 160 miles in the same amount of time that it took a turbo propeller plane to travel 920 miles. The speed of the plane was 190 mph faster than the speed of the car. Find the speed of the plane.
Answer:
Step-by-step explanation:
The speed of the plane was 291.13mph.
What is speed?Speed is distance travelled per unit time. It is scalar quantity
Given
The difference in distances was 600 miles; the difference in speeds was 190mph. That means the time was 600/190 = 3.16 hours.
Since the plane flew 920 miles in that time, its speed was 920/3.16 = 291.13mph.
To know more about speed refer to:
https://brainly.com/question/13943409
#SPJ2
PLEASE HELP. I NEEED THIS BY TOMORROW
Find the perimeter of ABC with vertices A(0,-4), B(4,-4), and C(0,-1).
A. 7 units
B. 14 units
C. 12 units
D. 32 units
Answer:
C .12 units I think so if wrong I am sorry
Question 7 (Essay Worth 10 points)
(03.08A MC)
The number line shows the distance, in meters, of two divers, A and B, from a shipwreck located at point X:
1.5
B
Х
-2.5
A
Hot
-3 -2
+
-1
0
1 2 3
Distance (m)
Part A: Write an expression using subtraction to find the distance between the two divers. (5 points)
Part B: Show your work and solve for the distance using additive inverses. (5 points)
Answer:
45
Step-by-step explanation:
Solve the following.
Answer:
Step-by-step explanation:
The scale factor is 5.3 repeating. So I divided 24 by 5.33333333333333333 and got 4.5. I don't know if it's accurate since it's a reapeating decimal but it's close enough. Then I multiplied 2 by 5.3333333333333333333333 and got 10.6666667.
What number is needed to complete the square?
x^2 + 3x + ?
The number needed to complete the square is 9/4
Given the expression x^2 + 3x + ?
Using the completing the square;
Step 2: Get the coefficient of x
The coefficient of x is 3
Step 3: Get the half of coefficient of x
Hale of the coefficient = 3/2
Step 4: Take the square of the result
Square of the result = ()3/2)^2 = 9/4
Hence the number needed to complete the square is 9/4
Learn more on completing the square here: https://brainly.com/question/1596209
graph 56x- 19= -8y + 5
Answer/Step-by-step explanation:
Solve
Before we begin graphing, we have to solve the equation. You cannot just graph the equation as it is now. Let us simplify it:
[tex]56x-19=-8y+5[/tex]
[tex]56x-19+19=-8y+5+19[/tex] [tex]\mathrm{Add\:}19\mathrm{\:to\:both\:sides}[/tex]
[tex]56x=-8y+24[/tex]
[tex]\frac{56x}{56}=-\frac{8y}{56}+\frac{24}{56}[/tex] [tex]\mathrm{Divide\:both\:sides\:by\:}56[/tex]
[tex]\frac{56x}{56}=-\frac{8y}{56}+\frac{24}{56}[/tex][tex]\frac{56x}{56} = x\: (\mathrm{or}\: 1)[/tex][tex]-\frac{8y}{56}+\frac{24}{56}[/tex][tex]\frac{-8y+24}{56}[/tex][tex]\mathrm{Factor\:-8y+24}\\\mathrm{Rewrite\:as}\\=-8y+8\cdot \:3\\\mathrm{Factor\:out\:the\:common\:term\:8}\\=8\left(-y+3\right)\\\\=\frac{8\left(-y+3\right)}{56}\\\mathrm{Cancel\:the\:common\:factor:}\:8\\=\frac{-y+3}{7}[/tex][tex]\bold{x=\frac{-y+3}{7}}[/tex]
Graph
Now, we can graph. Graph the line using the slope and y-intercept, or two points.
[tex]\mathrm{Slope}: -7\\y-\mathrm{intercept}: (0,3)[/tex]
[tex]x\\0\\1[/tex] [tex]y\\3\\-4[/tex]
Maddie baked 7 brownies. 4 of the brownies had nuts on top. What is the ratio of the number of brownies without nuts to the total number of brownies?
217.8 as mixed number
Answer:
27 1/8
Step-by-step explanation:
217/8= 27.125 = 27
217 - (8 x 27) = 1
We've now simplified 217/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
27 1/8
Simplifying our fraction
In this case, our fraction (1/8) can be simplified down further. In order to do that, we need to calculate the GCF (greatest common factor) of those two numbers. You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 1 and 8 is 1.
1/1 = 1
8/1 = 8
When we put that together, we can see that our complete answer is:
27 1/8
Answer:
217 4/5
Step-by-step explanation:
The lifespan of a monarch butterfly is about 9 months. Assuming a 30-day month, how many minutes old is the butterfly?
Answer:
So 9 months is 273 days and 394200 minutes so if the butterfly spends 30 days means one month so it is 43800 minutes old .
hope it gonna help you.
Step-by-step explanation:
A. A cylindrical barrel has diameter 14 m and height 9 m. Find the cost of painting the inner side of the barrel at 132 per m? (Take = 3.14.)
Answer:
Here is your Answer
Step-by-step explanation:
DIAMETER = 14 M
RADIUS = DIAMETER ×0.5
RADIUS = 14÷0.5 = 7
HEIGHT = 9M
AREA OF CYLINDER = 2pi*R* H
AREA = (2× 3.14×7×9) M^2
AREA =395.64 M^2
COST FOR AREA M^2 = ₹ 32
COST FOR AREA 395.64 =₹(395.64×32)
SO, ANSWERS= ₹ 12660.48
Plz Mark Me As Brainiest
Answer:
$ 12660.5
Step-by-step explanation:
We know that
Radius = Diameter/2
Radius = 14/2 = 7 m
Now,
CSA of cylinder = 2πrh
=> 2 × 3.14 × 7 × 9
=> 395.6 m²
Now,
Cost = 395.6 × 132
=> $ 12660.5
0 6. What is the constant of proportionality for the set of data in the table? 10 8 2 Hours 70 56 42 14 Miles 48
Answer:
k = 7
Step-by-step explanation:
The constant of proportionality k is calculated as
k = [tex]\frac{miles}{hours}[/tex]
Using the values from the table , then
k = [tex]\frac{14}{2}[/tex] = [tex]\frac{42}{6}[/tex] = [tex]\frac{56}{8}[/tex] = [tex]\frac{70}{10}[/tex] = 7
10 0breros construyen un complejo 336 días, ¿cuantos días les tomaría hacer el mismo complejo a 15 obreros?
Usando proporciones, se encuentra que 15 obreros hacerían el mismo complejo en 24 días.
Esta pregunta se resuelve por proporciones, usando una regla de tres. Cuanto mayor lo número de obreros, menor el tiempo, o sea, las medidas son inversamente proporcionales, lo que implica que la multiplicación es en línea.10 obreros toman 336 dias. ¿Cual el tiempo necessário para 15 obreros?La regla de três es:
10 obreros - 336 días
15 obreros - x días
Aplicando multiplicación en línea:
[tex]15x = 336(10)[/tex]
[tex]x = \frac{336(10)}{15}[/tex]
[tex]x = 24[/tex]
15 obreros hacerían el mismo complejo en 24 días.
Para obtener más información sobre las proporciones, puedes visitar a https://brainly.com/question/24615636
3x^4 + 9x^3 - 5x^2 - 14x - 7 divided by x + 3 using synthetic division
Answer:
[tex]3x^3 - 5x + 1 - \frac{10}{x + 3}[/tex]
or
3x^3 - 5x + 1
Remainder: -10
Step-by-step explanation:
Please see attached image for full explanation!
1.) Write the coefficient of each term.
2.) Beginning with 3, multiply by -3, or x + 3 = 0 (the divisor.)
3.) Add the product to the next coefficient and repeat until you get to the last number, -7.
4.) You should have the numbers 3, 0, -5, 1, and -10.
5.) Rewrite this quotient as an equation:
3x^3 - 5x + 1
Note that the highest power is 3, one less than that of the highest power in the original equation.
6.) Don't forget the remainder!
You can include this in the equation or not, depending on the instructions.
Therefore, the final answer is 3x^3 - 5x + 1 - 10/x+3 or 3x^3 - 5x + 1 R: -10.
The zoo expected to have 120,000 visitors last year. They
actually had 110,000 visitors. Determine the percent of
error. (Round to the nearest tenth of a percent, if necessary.)
A) 8.3%
B) 9.1%
C) 91.7%
D) 109.1%
Write an equation in slope-intercept form of the line that passed through (-3, 4) and (1. 4)
Answer:
y= 0x+4
Step-by-step explanation:
This is a horizontal line, since both coordinate pairs end in 4, so the slope is 0. The y-intercept is 4 because each point is 4.
Is x=−10 a solution to the equation 28x+17=157?
Answer:
no
Step-by-step explanation:
28x+17=157 Subtract 17 on both sides.
-17 -17
28x=140
x=5
5 does not equal -10, so -10 is not a solution to the equation 28x+17=157.
Hope this helps!! Have a great day :)
3+1=5
false or true
brailest and points
Answer:
FALSE
Step-by-step explanation:
PLZ MARK BRAINLIOEST
Can someone help me. I’ve tried doing this on paper. I don’t know what I’m doing wrong
[tex]{ \huge \mathfrak \color {pink}{ \tt{answer}}}[/tex]
[tex] \large \color{cyan}{ \tt{x = 12}}[/tex]
Step-by-step explanation:
[tex] \color {cyan}{ \tt{9 + \frac{x}{6 = 11}}} [/tex]
multiply both sides of the equation by 6[tex]{ \tt{54 + x = 66}}[/tex]
move the constant to the right hand side and change its sign[tex]{ \tt{x = 66 - 54}}[/tex]
substract the numbers[tex] \huge \color{magenta}{ \tt{ = \: \: x = 12}}[/tex]
[tex] \large \color{brown}{ \tt{hope \: \: it \: \: helps}}[/tex]
which of the equations below would have a line that passes through both (1,7) and (0,-9)
Answer:
Step-by-step explanation:
(-9-7)/(0-1)= -16/-1= 16
y - 7 = 16(x - 1)
y - 7 = 16x - 16
y = 16x - 9
What percent of the model is shaded green?
(answer quick please)
Answer:
30%
Step-by-step explanation:
3 rows out of 10 are shaded green. 3/10 is 30%
Explanation:
Ignore the horizontal lines. Think of this figure as 10 skinny rectangles line up side by side. Three of them are shaded, so we have 3/10 = 0.30 = 30% of it shaded.
If you wanted to include the horizontal lines, then we have 10*3 = 30 green little squares out of 10*10 = 100 total squares. This leads to the same answer 30/100 = 0.30 = 30%
Sara is going to home depot to buy some plants for her back yard. The price of 4 rose bushes is $12 and the price of 5 tulips is $20. Sara ends up buying $80 worth of roses and tulip plants. Which equation represents the relationship between the number of rose bushes, x, and the number of tulip plants, y, that Sara bought at home depot?
Answer:
3r + 4t = 80
Step-by-step explanation:
Roses cost $3 each, tulips cost $4 each
Porfa ayúdenme a resolver lo de la ficha, plis.
Answer:
Step-by-step explanation:
Portf?
Which expression is equivalent to 7x + 5x?
a. 12x
b.12x^2
c. 35x
d. 35x^2
Answer:
12x
Step-by-step explanation:
Molly has biweekly gross earnings of $839. 52. By claiming 1 more withholding allowance, Molly would have $16 more in her take home pay. How many withholding allowances does Molly currently claim? a. 1 b. 2 c. 3 d. 4.
Molly currently claims 2 withholding allowances which can be determined by using rules of allowance.
Given that,Molly has biweekly gross earnings of $839. 52.
By claiming 1 more withholding allowance,
Molly would have $16 more in her take-home pay.
We have to determine,How many withholding allowances does Molly currently claim?
According to the question,Molly has biweekly gross earnings of $839. 52.
By claiming 1 more withholding allowance,
Molly would have $16 more in her take-home pay.
The withholding allowance is used by a person to pay less amount of tax on his or her income to the government.
Molly has biweekly gross earnings of $839. 52.
By claiming 1 more withholding allowance,
Molly would have $16 more in her take-home pay.
Therefore,
It is given that Molly has taken 1 more withholding allowance to pay tax less by the amount of $16.
So he must have possessed at least 1 allowance previously and added 1 more.
So, the minimum number of allowance possessed by Molly = 2
Hence, Molly currently claims 2 withholding allowances.
For more details about Income Tax refer to the link given below.
https://brainly.com/question/1708567
Rewrite 1/6 book over 2/3 hour as a unit rate
HELPPP please make it quickk D:
Answer:
0.25 book/hour
Step-by-step explanation:
(1/6)/(2/3)=x/1
*Simplify the equation
1/4=x
*Rearrange the equation
x=1/4
x=0.25 book/hour
i don't understand how to do this someone help me math!!
Answer:
-8
Step-by-step explanation:
ky^2 = -5y + 7y^2 +9y - 15y^2 -4y
ky^2 = -8 y^2
k = -8
Answer:
8
Step-by-step explanation:
We believe the problem here requires that all of the coefficients in the expression on the left be zero. That is, the equation will be true for any value of y.
We can work this a couple of ways. One of them is to simplify the given expression. Let 'a' represent our unknown coefficient.
[tex]-ay^2-[-5y-y(-7y-9)]-[-y(15y+4)]=0\\\\-ay^2-[-5y+7y^2+9y]+[15y^2+4y]=0\\\\-ay^2-[7y^2+4y]+15y^2+4y=0\\\\(-a-7+15)y^2+(-4+4)y=0\\\\(-a+8)y^2=0[/tex]
In order for this to be zero for all values of y, we must have (-a+8) = 0.
a = 8
The missing coefficient is 8.
_____
Since this expression must be true for every value of y, another way to work this is to choose a value of y. This will tell us what the coefficient must be for the expression to be zero. Let y = 1.
-a·1² -[-5·1 -1(-7·1 -9)] -[-1(15·1 +4)] = 0
-a -[-5-(-16)] -[-19] = 0
-a -11 +19 = 0
-a +8 = 0
a = 8 . . . . . . same as above
_____
Additional comment
The many minus signs are intended to make sure you're comfortable with arithmetic with negative coefficients and negative numbers. The key, of course, is that -(-a) = +a. The opposite of the opposite is the original.
We have assumed that the dash at the beginning of the line (before the answer box) is intended to be a minus sign. If that is not the case, then your answer will be -8, instead of 8.
Plz help!!!! Find the equation of the linear function represented by the table below in slope intercept form
Answer:
y=-5x+2
Step-by-step explanation:
rise/run
or
y2-y1/x2-x1
-8-(-3)/2-1
-8+3/2-1
-5/1=m=slope
Slope intercept formula:y=mx+b
use point (1,-3)
-3=-5(1)+b
-3=-5+b
+5 +5
2=b
Final Answer: y=-5x+2
c(n)=-6+5(n-1) Find the 8th term in the sequence
Answer:
-7
Step-by-step explanation:
c(8)=-6+5x7
c(8)=-1x7
c(8)=-7