The solutions to the equation [tex]2x^{2} +3x=-8\\[/tex] are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex] respectively.
What is a quadratic equation?
A second-degree algebraic equation is a quadratic equation in x.
[tex]ax^{2} +bx+c=0[/tex] is the quadratic equation in standard form, where a and b are the coefficients, x is the variable, and c is the constant term.
To find the root value of x, [tex]x= \frac{-b}{2a}[/tex] ± [tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]
Given, [tex]2x^{2} +3x=-8\\[/tex]
or, [tex]2x^{2} +3x+8=0[/tex]
Comparing the equation [tex]2x^{2} +3x+8=0[/tex] with the equation [tex]ax^{2} +bx+c=0[/tex] , we get
[tex]a=2, b=3, c=8[/tex]
Then, [tex]x= \frac{-3}{2*2}[/tex] ± [tex]\frac{\sqrt{3^{2} -4*2*8} }{2*2}[/tex]
or, [tex]x= \frac{-3}{4}[/tex] ± [tex]\frac{i\sqrt{55} }{4}[/tex]
Taking '+' sign, we get [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex]
Therefore, the solutions of the given equation are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex].
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the number of cars that go through the drive-in window at a local bank each hour is an example of a continuous random variable.
The first statement is false and the second statement is true.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. There are two types of random variables.
Discrete random variablesContinuous random variablesA random variable that takes a finite number of possible values can be defined as a Discrete random variable. A random variable that takes an infinite number of possible values can be defined as a Continuous random variable. A continuous random variable consists of only continuous values.
Continuous random variables are defined at intervals of values. Continuous random variables are represented by the area under a curve.
⇒ The number of cars that go through the drive-in window at a local bank each hour.
The number of cars can be counted and can be an integer like 10, 20,100 etc.
∵ The number of cars is countable it is not an example of a continuous random variable
⇒ The high daily temperature in Anchorage.
High daily temperature can be an integer or function like 60°, 120° etc
∵ The high daily temperature is an example of a continuous random variable.
Therefore, The number of cars that go through the drive-in window at a local bank each hour is not an example of a continuous random variable and The high daily temperature in Anchorage is an example of a continuous random variable.
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The complete question is
Gabriella is going back to school shopping.each notebook she buys costs $3 and each pack of markers costs $3.she buys 4 packs of markers and n notebooks.she writes the follwing expression represent how much shr spend
Answer:
$24
Step-by-step explanation:
3(4) + 3(4) = x (the total cost)
12 + 12 = x
x = $24
help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
the shorter leg = 9mm
the longer leg = 12mm
the hypotenuse is 15mm
Step-by-step explanation:
x^2 +(x+3)^2 =(x+6)^2
x^2 + x^2 + 6x +9=x^2 + 12x +36
x^2-6x-27=0
(x+3)(3-9)=0
x=-3 (impossible) ... or x=9
To train for a triathlon, Mr Greg swims, bikes, and runs everyday. Each day he bikes 10 times the distance he swims, and run 1. 5 miles more than half the distance he bikes. If Mr. Greg covers a total of 25. 5 miles on each day of training, how many miles does he swim? Bike? Run?
He covers 15 miles on the bike, 9 miles by running and 1.5 miles while swimming which sum up to 25.5 miles which is his total training distance.
What is distance?Distance is defined as an object's entire movement without regard for direction. Distance may be defined as how much ground an item has traversed regardless of its starting or finishing place. Distance is a scalar number that indicates "how much ground an item has covered" while moving. Displacement is a vector variable that describes "how far out of place an item is"; it represents the total change in position of the object. Distance is the length along a line or line segment between two locations on the line or line segment.
Here,
He rides 15 miles, which is ten times as far as he swims.
He runs 9 miles, which is half the distance he rides (15/2=7.5). Plus the additional 1.5 miles, totaling 9.
He swims.10 of what he bikes, for a total of 15x.10 = 1.5. As a result, he swims 1.5 miles.
15 miles = bike
9 miles= run
1.5 mile =swim
Add them all together and you get 25.5 miles.
He rides his bike for 15 miles, runs for 9 miles, and swims for 1.5 miles, for a total training distance of 25.5 miles.
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A survey of the worlds nation in 2004 shows a strong positive correlation between percentage of the country using cell phones and life expectancy and years at birth
1. No This survey does not mean that cell phones are good for your health.
2. The factor that can be used as the best explanation for the strong correlation would be the general economic conditions of the people.
What is meant by a strong correlation?When one variable's value rises, the other variable's value also rises in a similar way. For instance, a student's exam score tends to be greater the more hours they study. Exam results and study time have a significant positive link.
A strong correlation, also known as a high correlation, indicates that two or more variables have a significant relationship with one another, whereas a weak or low correlation indicates that the variables are rarely associated.
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complete question
A survey of the world's nations in 2004 shows a strong positive correlation (hence, a positive association) between percentage of the country using cell phones and life expectancy in years at birth.
a. Does this mean that cell phones are good for your health? select one: ____ yes ____ no
b. What might best explain the strong correlation (as a lurking variable)?
Select one:
_____ Percent of young people
____ General economic conditions of the country
____ Percent of pop. living in cities
Reflect the figure over the line y=1/3x+1
Answer:
see the attachment
Step-by-step explanation:
You want a graph of the given figure reflected over the line y = 1/3x +1.
Line of reflectionThe given line of reflection can be written in general form as ...
y = 1/3x +1
3y = x +3 . . . . . . multiply by 3
x -3y +3 = 0 . . . . subtract 3y
This is in the general form ...
ax +by +c = 0
where a=1, b=-3, c=3.
The line of reflection is the perpendicular bisector of the segment joining a point (x, y) with its reflection (x', y').
Reflected pointUsing the formula in the second attachment, we find the reflection
(x1, y1) ⇒ (x, y)
satisfies ...
(x -x1)/a = (y -y1)/b = -2(ax1 +by1 +c)/(a² +b²)
or ...
x = -2a/(a²+b²)·(ax1 +by1 +c) +x1
y = -2b/(a²+b²)·(ax1 +by1 +c) +y1
Using the known values for a, b, c, we have ...
x = -2(1)/(1² +(-3)²)·(x1 -3y1 +3) +x1 = (1/5)(4x1 +3y1 -3)
y = -2(-3)/10·(x1 -3y1 +3) +y1 = (1/5)(3x1 -4y1 +9)
Rewriting the mapping in more conventional terms, we have ...
(x, y) ⇒ ((4x +3y -3)/5, (3x -4y +9)/5)
It is convenient to let a spreadsheet do the repetitive tedious math. The third attachment shows the application of this mapping to the coordinates of the figure's vertices (clockwise from bottom).
__
Additional comment
The figure showing the reflected polygon was created by a geometry program using its "reflect over a line" feature.
Order the following from least to greatest -0.2, 4.22,2.02,-3/10, 4 1/8
The correct order is -3/10, -0.2, 2.02, 4.22, 4 1/8 .
Firstly we will convert the fractions into decimal units i.e
-3/10 = -0.3
41/8 = 5.125
We know that the higher the number in negative number line lower will the value of it so the -0.3 < -0.2
Now we can easily arrange these numbers according to the number line i.e;
Negatives will be first to come on number line and the correct order will be as follow :
-0.3 , -0.2, 2.02, 4.22, 4 1/8
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easy trig please heeelp me
Answer:
9
Step-by-step explanation:
Pythagorean triples. 3, 4, 5. Multiply by 3 and get 9.
p(x) = (x² - 9) (x² + x - 2)
factor for zeros to plot on a graph
pls help :(
Answer:
P(x) = (x - 3)(x + 3)(x + 2)(x - 1)
Answer:
Step-by-step explanation:
Solution:To write a polynomial in standard form, simplify and then arrange the terms in descending order.Expand ( x2 − 9 )( x + 2 ) using the FOIL Method.Simplify each term.
X
Work out the mean for the data set
below:
6.8, 5.7, 0.8, 4.7, 1.3
Give your answer as a decimal.
a square matrix is nilpotent if for some positive integer . let be the vector space of all matrices with real entries. let be the set of all nilpotent matrices with real entries. is a subspace of the vector space ?
An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
What is nilpotent matrix?A nilpotent matrix in linear algebra is a square matrix N such thatfor some positive integer kk. The index of occasionally the degree of the smallest such k A nilpotent transformation, more generally speaking, It is a linear transformation of a vector space such that Lk=0 for some positive integer. Both of these ideas are specific examples of the more basic idea of nilpotence, which is applicable to rings' constituent parts.acc to our question-
When n=1, the only 1×1 nilpotent matrix is (0). Thus U={(0)} and it is a subspace of VIn this case, we prove that the set U of all 2×2 nilpotent matrices is not a subspace of V.The set U is not a subspace because it is not closed under addition as the following example shows.Hence,An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
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Which of the following would earn the same amount of interest as a $600 principal with 2.5% interest for 6 years? Question content area bottom Part 1 Select all that apply. A. $80 at 75% for 18 months B. $200 at 5% for 8 years C. $225 at 10% for 4 years D. $300 at 2% for 2 years E. $250 at 10% for 2 years
The option that would earn the same amount of interest as a $600 principal with 2.5% interest for 6 years include:
A. $80 at 75% for 18 months
C. $225 at 10% for 4 years
How to calculate the interest?It's important to note that the simple interest can be calculated thus:
= Principal × Rate × Time
Therefore, the amount of interest as a $600 principal with 2.5% interest for 6 years will be:
= PRT
= (600 × 0.025 × 6)
= $90
The interest on $80 at 75% for 18 months will be:
= $80 × 0.75 × 1.5
= $90
The interest on $225 at 10% for 4 years will be:
= $225 × 0.1 × 4
= $90
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a recipe calls for 15oz of flour every 8oz of milk, if you use 150z of milk how much flour should you use
The required weight of the flour is 28.125 ounces.
A recipe calls for 15 ounces of flour for every 8 ounces of milk. It is given that we use 15 ounces of milk. Then we need to calculate the weight of flour we need to use.
The ratios of the ingredients must remain in equal proportions. The fraction of one divided by the other is referred to as the ratio. A proportion is an equation that equates two ratios. We will use the unitary method. Let the weight of the flour required be denoted by the variable "w". A variable is a quantity that can change in a mathematical problem or experiment.
w = (15/8)*15
w = 28.125
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students deliver newspapers and magazines to houses.
one day,they have to deliver 875 newspapers and 1200 magazines.
each student can deliver 35 newspapers or 50 magazines in 1 hour.
each student can only work for 8 hours
work out the minimum number of students needed
Answer:
4 students for newspapers & 3 students for magazines are needed for the deliveries to be made in a day.
Step-by-step explanation:
According to the question,
875 newspapers & 1200 magazines are to be delivered in a day by students.In an hour each student can deliver 35 newspapers or 50 magazines & each student can only work for 8 hoursSo, In 8 hours each student can deliver:
35 × 8 = 280 newspapers
50 × 8 = 400 magazines
To find out minimum number of students needed to work we need to divide work done by each student in 8 hours by total deliveries to be made.
[tex] \therefore[/tex]
For Newspapers:
875/280 = 3.125
So, by rounding of the figure we will need 4 students to deliver newspapers as each student can work only for 8 hours.
For magazines:
1200/400 = 3
3 students are needed to deliver magazines.
An account now contains $12,680 and has been accumulating interest at a 8% annual rate, compounded continuously, for 7 years. find the initial deposit. (round your answer to the nearest cent.)
The initial amount of the deposit is $7234.23
Compound interest is calculated on a deposit's or a loan's initial principal as well as the accrued interest from earlier periods. Compound interest's impact is frequency-dependent. The most frequent compounding occurs with continuously compounded rewards. The mathematical maximum that compound interest can achieve is continuous compounding. Since most interest is compounded on a monthly, quarterly, or semiannual basis, this is an extreme example of compounding.
For compound continuous problems, we use the formula [tex]A = Pe^{rt}[/tex]
where A = final amount
P = principal amount invested
e = exponent
r = rate of interest
t = time period in years
[tex]12680 = Pe^{.08(7)} \\12680 = Pe^{0.56}\\ 12680 = P*1.7506\\[/tex]
P = $7243.23
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a simple random sample of 25 observations is dervied from a normally distributed population with a population standard deviation of 8.2. compute the margin of error with 80% confidence.
The margin of error with 80% confidence interval is 2.099
Given that,
A straightforward random sample of 25 observations is taken from a population that is normally distributed and has a standard deviation of 8.2.
To find : The margin of error with 80% confidence
Margin of Error : The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.
Here we have
n=25,σ=8.2
For 80% confidence interval, the critical value of z is 1.28. So requried margin of error is
ME=[tex]Z_{c}\cdot \frac{\sigma}{\sqrt{n}}[/tex]=1.28[tex]\cdot \frac{8.2}{\sqrt{25}}[/tex]=2.0992
Thus, with 80% confidence, the error margin is 2.099.
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average temperatures were measured at five randomly selected soups. the x-bar and r-bar were found 45.25 degree and 1.05 degree, respectively. the uclr and lclr are:
The UCLR (Upper Control Limit) and LCLR(Lower Control Limit) are 2.22 and 0 respectively.
Given that,
At five soups that were chosen at random, average temperatures were recorded. X-bar and r-bar positions were 45.25 degree and 1.05 degree, respectively.
To find : UCLR (Upper Control Limit) and LCLR (Lower Control Limit)
R-bar = 1.05 Degrees
X-bar = 45.25 Degrees
Sample Size , n=5
D3=0
D4=2.114
3 Sigma control limits of Range Chart
LCLR = D3*R-bar = 0*1.05 =0
UCLR =D4*R-bar = 2.114*1.05 = 2.22
The UCLR (Upper Control Limit) and LCLR (Lower Control Limit) are therefore 2.22 and 0, respectively.
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daysha loves the caramel macchiato at the coffee shop. the 16 oz. medium size has 260 calories. how many calories will she get if she drinks the larger 20 oz. size?
After using proportion method 325 calories will she get if she drinks the larger 20 oz. size.
What is proportion?
Ratio and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics. Numerous challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship between two or more quantities and aids in comparing them.
Here 16 oz medium size has 260 calories.
Then
=> [tex]\frac{size of coffee}{ calories}[/tex]
=>[tex]\frac{16}{260}=\frac{20}{x}[/tex]
=>x=[tex]\frac{20*260}{16}[/tex]
=> x = 325
Hence 325 calories will she get if she drinks the larger 20 oz. size.
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write a congruence statement for the pair of triangles
The concurrency statement for the given triangles is that (D) △RGB ≅ △DCS under ASA condition.
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.If two triangles satisfy one of the following conditions, they are congruent: The three corresponding side pairings are all equal. The comparable angles between two pairs of corresponding sides are equal. The corresponding sides between two pairs of corresponding angles are equal.So, the congruence statement of the given 2 triangles is as follows:
△RGB ≅ △DCS
∠G = ∠CGB = CS∠B = ∠SHence, △RGB ≅ △DCS under ASA condition.
Therefore, the concurrency statement for the given triangles is that (D) △RGB ≅ △DCS under ASA condition.
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help is needed please and thank you
The required value of h(0) = 5 in the given function is represented in the shown graph.
What is a graph?A graph can be defined as a visual representation or a diagram that represents data or values.
The function is given in the represented graph of g(x)
We have to determine the value of h(0) of the given function in the graph
According to the given graph, we can see that when the value of variable x is 0 and the value of variable y is 5, the domain of the provided function h(x) is 5. This implies that h(0) = 5.
Therefore, the required value of h(0) = 5 in the given function is represented in the shown graph.
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A line with a slope of –
5 passes through the points (7,–
2) and (8,q). What is the value of q?
The line with a slope of –5 that passes through the points (7,–2) and (8,q) has q as -7.
How to find the value of q with the slope?The equation of a line can be described as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (7, –2) and (8, q) with a slope of - 5.
Hence, let's find q.
y = - 5x + b
Let's find y-intercept
-2 = -5(7) + b
b = -2 + 35
b = 33
Therefore,
y = -5x + 33
Hence, let's find q.
y = -5(8) + 33
q = -40 + 33
q = -7
Therefore, q = - 7
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Which function represents the i shown in the graph below
A. G(x)=-x+2
B. G(x)=2^x-1
C. G(x)=(x+2)^2
D. -2x
Write the following values in ascending order (smallest to largest):
0.1, 0.09, 2%,7/10,19/100
connie has a number of gold bars, all of different weights. she gives the 2424 lightest bars, which weigh 45\e% of the total weight, to brennan. she gives the 1313 heaviest bars, which weigh 26\&% of the total weight, to maya. she gives the rest of the bars to blair. how many bars did blair receive?
Blair received 15 bars as the average weight of the bars given to Brennan (light), Blair, and Maya, as well as the average weight of the bars given to the other recipients.
What is average weight?The weighted average is calculated by adding up all the variables, multiplying by their weight, and dividing by the sum of the weights. Instead of treating each item equally, a weighted average or mean multiplies each item being averaged by a number based on its relative importance. The weights or weightings correspond to including that many comparable items of the same value in the average.
Here,
The average weight of the bars given to Brennan (light), Blair, and Maya was higher than the average weight of the bars given to the other two recipients (heavy).
Let X represent the combined weight of all the bars.
The weight of the bars Brennan was given was equal to 45% of X, or 0.45X.
Maya was given bars that weighed 26% of X, or 0.26X.
The weight of the bars Claire was given was the rest, or 29% of X, or 0.29X.
Brennan received bars with an average weight of 0.45 x/ 24.
The weight of the Maya-received bars, on average, is 0.26X/13.
Similar to the previous example, if Blair receives B bars, then their average weight is 0.29X/B.
Similarly, the average weight of the bars given to Brennan (light), Blair, and Maya, as well as the average weight of the bars given to the other recipients. So blair received 15 bars.
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P(A and B)
P(B)
Find P (Junior | Girl) Hint:
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5
7 12
Junior 2
3 5
Senior 1 4 5
12 18
[?]
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
Probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to 1/6.
As given in the question,
From the given table we have,
Total number of girls and boys in the class = 30
Total number of boys in class = 12
Total number of girls in class = 18
As per given Hint: P(A/B) = P(A and B) / P(B)
A is the Junior
B is the girl
Probability as per given condition is:
P(Junior / Girl) = P(Junior and girl) / P(girl)
= (3/30) / (18/30)
= 3/18
= 1/6 ( lowest term of fraction)
Therefore, probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to 1/6.
The complete question is:
Find P(Junior / Girl) Hint: P(A/B) = P(A and B) / P(B) .
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5 7 12
Junior 2 3 5
Senior 1 4 5
12 18
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
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The top of a 15-foot ladder is 3 feet farther up a wall than the foot of the ladder is from the bottom of the wall. How far up is the foot of the ladder from the bottom of the wall?
The answer is 9 but I don’t know how to get there.
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\implies 15^2=x^2+(x+3)^2 \\\\\\ 225=x^2+(x^2+6x+9)\implies \implies 225=2x^2+6x+9 \\\\\\ 0=2x^2+6x-216\implies 0=2(x^2+3x-108) \\\\\\ 0= x^2+3x-108\implies 0=(x-9)(x+12)\implies x= \begin{cases} 9 ~~ \checkmark\\\\ -12 \end{cases}[/tex]
let's notice that "x" does have two valid values, however for this scenario 'x" cannot be negative, so we don't use that one.
Samuel has a collection of toy cars. His favorites are the 27 red ones, which make up 60%, percent of his collection.
How many toy cars does Samuel have?
Answer:
45
Step-by-step explanation:
The 27 red cars make up 60% of the total collection, here is the equation
to be solved:
27 = 60% of C C is the total cars in the collection
27 = .60 C
27 / .60 = C
45 = C
Hope this helps! :)
nine out of ten student prefer math class over lunch. how many student do not prefer math if 200student were asked
Answer:
Step-by-step explanation:
20? lol
a banana weighs 140 g a pineapple weighs 345 g bag a contains 8 bananas and bag b contains 3 pineapples which bag weighs more and by how much show your working
Answer:
Bag a, by 85 grams!
Step-by-step explanation:
1) Work out the weight of bag a
1 banana is 140 grams so to find out 8 you have to multiply them
140 x 8 = 1120
Bag a = 1120 grams
2) Work out the weight of bag b
1 pineapple weight 345 grams so to find out 3 you have to multiply them just like above
345 x 3 = 1035
Bag b = 1035
3) Find the difference
Bag a is 1120 grams and bag b is 1035
To find out out by how much you just have to subtract them
1120 - 1035 = 85
Hope this helps, have a great day!
Método de igualación. {x-2y=11
x+5y=−17
The value of x and y is 7 and -2 respectively.
The equations to solve are -
x - 2y = 11 ....[1]x + 5y =−17 ....[2]On adding equations 1 and 2 we get ,
3y = -6
y = -2
Putting the value of y in equation 1,
⇒ x - 2(-2) = 11
⇒ x + 4 = 11
⇒ x = 7
Hence ,the value of x and y is 7 and -2 respectively.
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