Given the following Quadratic equation:
[tex]-3x=-10x^2-4[/tex]You can use the Quadratic formula to solve it:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, you need to add "3x" to both sides of the equation:
[tex]\begin{gathered} -3x+(3x)=-10x^2-4+(3x) \\ 0=-10x^2+3x-4 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} a=-10 \\ b=3 \\ c=-4 \end{gathered}[/tex]Substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2^{}-4(-10)(-4)}}{2(-10)} \\ \\ x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]Answer
Complex roots:
[tex]\begin{gathered} x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]The measures of the angles of a triangle are shown in the figure below. Solve for x.
54°
(7x+1)°
The value of x according to the complete task content as given is; 5.
Sum of interior angles in a triangle.It follows from the complete task content that a right angled triangle is given(in which case one of the angles is a right angle = 90°).
Hence, the required value of x can be determined from the; sum of interior angles of a triangle as follows;
90° + 54° + 7x + 1° = 180°
7x = 180° - 90° - 54° - 1°
Evaluate the right side of the equation;
7x = 35°
Divide both sides by; 7;
x = 35°/7
x = 5.
Ultimately, the value of x according to the task content is; 5.
Remark:
The completed task content is; The measures of the angles of a triangle are shown in the figure below. Solve for x. The figure is a right triangle with the other two interior angles 54° and (7x + 1)°.
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a random sample of 80 observations results in 50 successes. a. construct the 95% confidence interval for the population proportion of successes. b. construct the 95% confidence interval for the population proportion of failures
In 95% confidence interval for the population proportion of successes
exists CI = 0.625 +/- 1.96 × sqrt(0.625 × 0.375/80).
In 95% confidence interval for the population proportion of failures
exists CI = 0.375 +- 1.96 × sqrt(0.375 × 0.625/80).
What is meant by confidence interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).
a) Sample proportion of successes (phat) = 50/80 = 0.625
z-critical for 95% CI is 1.96
CI = 0.625 +/- 1.96 × sqrt(0.625 × 0.375/80)
b) sample proportion of failures (phat) = 30/80 = 0.375
CI = 0.375 +- 1.96 × sqrt(0.375 × 0.625/80)
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What is the y-intercept in the equation y = 45x + 65?
Answer:
The y intercept is : 65
Step-by-step explanation:
The y intercept is 65 as it is in the form of y=mx+c.
The c is the y intercept, being 65
A new pet store is offering 12% off for their grand opening! A parakeet originally costs $17. What is the sale price after the discount?
Let:
Oc = original cost = $17
Sp = Sale price
D = Discount percent = 12% = 12/100 = 0.12
The sale price will be:
[tex]\begin{gathered} Sp=Oc-0.12\cdot Oc \\ Sp=17-0.12\cdot17 \\ Sp=17-2.04 \\ Sp=14.96 \end{gathered}[/tex]The sale price is $14.96
What is the value of this expression.
this is the answer to your equation hope it helps thanks
Answer:
D. [tex]\dfrac{27}{4}\\\\[/tex]
Step-by-step explanation:
[tex]\mathrm{With\;x=\dfrac{1}{8}\;and\;y = \dfrac{3}{16}\;we\;get}\\\\[/tex]
[tex]2\left(\dfrac{1}{8}+4\right)-\left(\dfrac{3}{16}\cdot 8\right)\\\\[/tex]
[tex]\mathrm{Calculate\:within\:parentheses}\:\left(\dfrac{1}{8}+4\right) = \dfrac{1}{8}+\dfrac{32}{8}} = \dfrac{33}{8}\\\\[/tex]
[tex]2\left(\dfrac{1}{8}+4\right) = 2\cdot \dfrac{33}{8} = \dfrac{33}{4}[/tex]
[tex]y \cdot 8 = \dfrac{3}{16} \cdot 8} = \dfrac{3}{2}\\\\[/tex]
So
[tex]2(x + 4) - y\cdot 8 = \dfrac{33}{4} - \dfrac{3}{2}\\\\\\= \dfrac{33-6}{4}\\\\= \dfrac{27}{4}\\\\[/tex]
Of the ice cream cones sold yesterday at Zeke's Ice Cream Shop, 3/10 were chocolate and another 3/10 were vanilla. What fraction of the ice cream cones sold were either chocolate or vanilla?
The fraction of ice cream cones sold that are either chocolate or vanilla is 3/5.
What is the fraction?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 3/5. 3 is the numerator and 5 is the denominator.
In order to determine the fraction of ice cream cones sold that are either chocolate or vanilla, add the fraction of chocolate cones sold and vanilla cones sold together. Addition is the process of determining the sum of two or more numbers.
Fraction of ice cream cones sold that are either chocolate or vanilla = 3/10 + 3/10 = 6/10 = 3/5.
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What is the answer for this as the y- intercept of two points? (-6,-5) and (-4,-4)
The slope intercept form of the equation that passes through (-6, -5) and (-4, -4) is y = 1 / 2x - 2
How to represent equation in slope intercept form?The equation in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope of the lines using (-6, -5) and (-4, -4).
m = y₂ - y₁ / x₂ - x₁
m = -4 + 5 / -4 + 6
m = 1 / 2
Therefore, lets find the y-intercept using (-4, -4)
-4 = 1 / 2 (-4) + b
-4 = -2 + b
b = -4 + 2
b = -2
Therefore, y = 1 / 2x - 2
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The slope-intercept form of the equation that passes through (-6, -5) and (-4, -4) will be; y = 1 / 2x - 2
What is slope intercept form?The equation in slope intercept form can be represented as :
y = MX + b
where m is the slope, b is the y-intercept
Therefore, to determine the slope of the lines using (-6, -5) and (-4, -4).
m = y₂ - y₁ / x₂ - x₁
m = -4 + 5 / -4 + 6
m = 1 / 2
Therefore, the y-intercept using (-4, -4)
-4 = 1 / 2 (-4) + b
-4 = -2 + b
b = -4 + 2
b = -2
Thus, y = 1 / 2x - 2
The slope-intercept form of the equation that passes through (-6, -5) and (-4, -4) will be; y = 1 / 2x - 2
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note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. 7 women and 7 men are on the faculty in the mathematics department at a school. how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
No. of ways of selecting the 5 member committee by combination= 1981
What are the number of ways of selecting the 5 member committee ?
No. of women faculty in the mathematics department = 7
No. of men faculty in the mathematics department = 7
Total number of faculty members = 14
Condition - at least one woman must be on the committee
No. of ways of selection = C (14, 5) - C (7, 5)
We know that combination C(n , r) = [tex]\frac{n!}{(n-r)!r!}[/tex]
Consider the total combination C (14, 5),
[tex]C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002[/tex]
Consider the combination of men C (7, 5) ,
[tex]C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21[/tex]
No. of ways of selection = C (14, 5) - C (7, 5)
= 2002 - 21
=1981
No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981
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-15/2 = 3x solve for x and simplify your answer as much as possible
Answer:
x = -5/2
Step-by-step explanation:
-15/2 = 3x
multiply both sides by 2:
2(-15/2) = 2(3x)
-15 = 6x
divide both sides by 6:
-15/6 = 6x/6
x = -15/6
this can be reduced to:
x = -5/2
12 friends are sharing 8 packs of pencils. What fraction of a package will each friend receive?
Answer:
33/50
Step-by-step explanation:
8/12=.66666667
.6666667=33/50
33/50 in simplest form is 33/50
hope this helped
have a good day ^^
1/2 (7/10-3/5) + -1.9
Answer: -1 17/20
Step-by-step explanation: use order of operations to solve, parenthesis, multiplication, addition/subtraction
Two numbers have a sum of 35 and a product of 250. what is the number
need help on this, thanks
In the pair of given angles, the value of 2x and x is 52° and 26°.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees. In geometry, there are several different kinds of angles.So, the value of 2x and x:
We know that the given pair of angles is an exterior alternate angle.A pair of exterior alternate angles is always 180°.Now, solve for x and 2x as follows:
2x + 128 = 1802x = 180 - 1282x = 52°x = 52/2x = 26°Therefore, in the pair of given angles, the value of 2x and x is 52° and 26°.
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Find the equivalent ratio to the ratio 9 to 27 by simplifying the ratio. 3 to 1 , 1 to 3, 1 to 27 ,9 to 3
Given data:
The given ratio is 9:27.
The given ratio can be written as,
[tex]\begin{gathered} 9\colon27=\frac{9}{27} \\ =\frac{1}{3} \\ =1\colon3 \end{gathered}[/tex]Thus, the given ratio can be written as 1:3 so, second option is correct.
What is the equation of a line that passes through the point (5, −3) and is parallel to 6x+3y=−12?
Enter your answer in the box.
Answer: Slope= -2.000
x-intercept= -2
y-intercept= -4.000
Hope this helps !
Reuben drove 243 miles using 12 gallons of gas. At this rate, how many miles would he drive using 16 gallons of gas?
Answer:
324 miles
Step-by-step explanation:
Set up a proportion
243
12
=
x
16
Cross multiply
12
x
=
3888
x=324 miles
What is the exponential form of sq.rt (5^x)?
Answer:
Step-by-step explanation:
Comment and Answer
√5^x
The square root is really 0.5 as a decimal or 1/2 as a fraction. Both are powers.
So the square root of 23 can be written as 23^.5
For your question, you divide the power (x) by 2 so it looks like this.
5^(x/2)
A store sells 3 T-shirts for 28.14
Answer:
Step-by-step explanation:
1 T shirt = 28.14
There are 2 methods this can be done.
Method `1
Adding 3 times
28.14 + 28.14 + 28.14 = $84.42
Method 2
Multiplying 28.14 by 3
28.14 times 3 = $84.42
Therefore answer is 84.42
with grade > * 0.2 Add, subtract, multiply, and divide whole numbers: word problem
A group of tourists needs rental cars to get around the city. There are 3,376 tourists in
the group. If each rental car holds 8 people, how many cars will the group need?
Using division, we know that the number of cars needed by 3,376 tourists is 422.
What is division?The division is splitting into equal parts or groups.The division allows us to divide or 'share' numbers to find an answer.Division sign (÷) is a symbol consisting of a short horizontal line with a dot above and another dot below, used to indicate mathematical division.The division of any number by zero is undefined. In this case, the result can be written as infinity. For example, 15/0 = ∞, i.e. undefined.We can represent the division with ÷, slash (/), or a horizontal line ( _ ). We can use these symbols at our convenience when dealing with different types of computations or division questions.So, the total number of groups of tourists = 3376
One car holds 8 people.To find the number of cars needed. Hence,
The number of cars needed = 3376/8= 422Therefore, using division we know that the number of cars needed by 3,376 tourists is 422.
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Which of the following values are solutions to the inequality 9 ≤ -7+ 4x?
I. - 4
II. O
III. 4
Answer: Inequality Form: x ≥ 4
lll. 4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Your answer is x ≥ 4
Step-by-step explanation:
a) Simplify both sides of the inequality.
9 ≤ 4x − 7
b) Flip the equation.
4x − 7 ≥ 9
c) Add 7 to both sides.
4x − 7 + 7 ≥ 9 + 7
4x ≥ 16
d) Divide both sides by 4.
4x/4 ≥ 14/4
x ≥ 4
Select all of the following equation(s) that are quadratic in form.
A C E
Those are the answers
Answer:
A- x4 – 6x2 – 27 = 0D- 6(2x + 4)2 = (2x + 4) + 2E- 6x4 = -x2 + 5Step-by-step explanation:
If Santa drives at an average speed of 60 miles per hour for a distance of 1,260 miles, how long will Santa's trip take?
Step 1: Speed is defined as the rate of covering a distance, mathematically it is given by
[tex]\begin{gathered} S\text{peed}=\frac{\text{distance}}{\text{time}} \\ S=\frac{d}{t} \end{gathered}[/tex]Step 2: Make the time (t) of the subject in the above speed formula
[tex]t=\frac{d}{S}[/tex]Step 3: Given the distance covered and the average speed used during the trip as
[tex]\begin{gathered} S=60\text{miles per hour} \\ d=1260\text{ miles} \end{gathered}[/tex]Step 4: Substitute the values for distance and speed in the time formula in step 2
[tex]\begin{gathered} t=\frac{d}{S} \\ t=\frac{1260}{60} \\ t=21\text{ hours} \end{gathered}[/tex]Hence, Santa's trip will take up to 21 hours
Answer:
To find out the time required to travel the distance of 1260 miles we need to divide the total distance travelled by the distance travelled in one hour.
[tex]1260/60=21[/tex]
So, it tool 21 hours for Santa to complete the trip
A car's velocity is modeled by v(t) = 0.5t^2 -14t+ 80 for 0 less than or equal to t less than or equal 14, where the velocity is in feet per second and time is in seconds. Where does the car come to a complete stop?
The car stops after moving for 20 seconds
How to determine when the car comes to a stop?From the question, the function is given as
v(t) = 0.5t^2 - 14t + 80
When the car comes to a stop, the vehicle is 0
This is represented as
v(t) = 0
So, we have
0.5t^2 - 14t + 80 = 0
Expand the equation
0.5t^2 - 10t - 4t + 80 = 0
Factorize the equation
0.5t(t - 20) - 4(t - 20) = 0
So, we have
(0.5t - 4)(t - 20) = 0
Solve for t
t = 8 and t = 20
20 is greater than 8
Hence, the car comes to a stop at 20 seconds
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You rent an apartment that costs \$1000$1000 per month during the first year, but the rent is set to go up 8% per year. What would be the rent of the apartment during the 5th year of living in the apartment? Round to the nearest tenth (if necessary).
If you rent an apartment that cost $1000 per month during the first year, but the rent is set to go up 8% per year, the the rent amount of the apartment during the 5th year of living in the apartment is $1469.32
The initial rent amount = $1000
The percent of rent increase each year = 8%
Time period = 5 years
Here we can use the compound interest equation
A = [tex]P(1+\frac{r}{100})^t[/tex]
Substitute the values in the equation
The rent amount of the apartment during the 5th year of living in the apartment = [tex]1000(1+\frac{8}{100})^5[/tex]
= $1469.32
Hence, if you rent an apartment that cost $1000 per month during the first year, but the rent is set to go up 8% per year, the the rent amount of the apartment during the 5th year of living in the apartment is $1469.32
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NEED HELP ASAP THIS IS OVERDUE !!!
Answer:
A
Step-by-step explanation:
The slope goes up by 11 and over by 1.
Answer: D
Step-by-step explanation:
y= [tex]\frac{1}{55}[/tex]×
professor smith loves dark chocolate, and she would like to find out the proportion of the population that shares her preference. she randomly sampled 150 people, and 120 people choose dark chocolate. to construct a 95% confidence interval, she should use:
Use 1-Prop Z Int to create a 95% confidence interval.
Z test should be employed because there is only one set of samples collected and the sample size is huge.
An observed percentage is compared to a theoretical one using a one proportion z-test. The test statistic is determined as follows:
z = (p-p0) / √(p0(1-p0)/n)
where:
p = observed sample proportion
p0 = hypothesized population proportion
n = sample size
You can reject the null hypothesis if the p-value associated with the test statistic z is less than your selected level of significance (popular choices are 0.10, 0.05, and 0.01).
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Convert the rectangular equation to polar form
2x - y =3
Answer:
[tex]\dfrac{3}{2\cos\theta - r\sin\theta}[/tex]
Step-by-step explanation:
The polar coordinate system uses two parameters r and θ where r is the magnitude of the radius of the circle in polar form(also known as the radial coordinate) and θ the angle which the which the radius makes relative to the x=axis
The following equations are used to convert from cartesian coordinate to polar coordinates
[tex]r = \sqrt{x^2 + y^2}\\\\\\x = r\cos\theta\\\\y= r\sin\theta\\\\[/tex]
Substituting for x and y in terms of r and θ into the equation 2x - 3y = 3 gives
[tex]2x - y = 3\\\\2r\cos\theta - r\sin\theta = 3\\\\r(2\cos\theta - r\sin\theta = 3\\\\r = \dfrac{3}{2\cos\theta - r\sin\theta}[/tex]
aghwhelrrotiuugggdddd
Solution
We have the following info:
Grades Credits
B 2
B 5
B 5
C 2
And we know that A= 4, B= 3, C=2
So we can do this:
[tex]\operatorname{mean}=\frac{3\cdot2+3\cdot5+3\cdot5+2\cdot2}{2+5+5+2}=2.86[/tex]then the weighted average is 2.86
Please solve this quickly. Thanks!
Applying the trapezoid midsegment theorem, the diameter of the bottom layer of the cake = KS = 26 inches.
What is the Diameter of a Circular Shape?The diameter of any circular shape is the length of the line segment that divides the shape into two equal halves and runs through its center.
What is the Trapezoid Midsegment Theorem?The trapezoid midsegment theorem states that the length of the midsegment of a trapezoid that is parallel to its bases is equal to half of the sum of the bases.
Using the trapezoid midsegment theorem we have:
MQ = 1/2(NP + LR)
Substitute
MQ = 1/2(8 + 20)
MQ = 1/2(28)
MQ = 14 inches
Also, we would also have:
LR = 1/2(MQ + KS) [trapezoid midsegment theorem]
Substitute
20 = 1/2(14 + KS)
40 = 14 + KS
40 - 14 = KS
26 = KS
KS = 26
The diameter = KS = 26 inches.
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The diameter(KS) of the cake's bottom layer is calculated using the trapezoid midsegment theorem is 26 inches.
What is a Diameter?The diameter of a circle is equal to the length of the line segment running through its center and dividing it into two equal halves.
According to the trapezoid midsegment theorem the length of a trapezoid's midsegment that is parallel to its bases is equal to half of the sum of the bases.
MQ = 1/2(NP + LR)
MQ = 1/2(8 + 20)
MQ = 1/2(28)
MQ = 14 inches.
And,
LR = 1/2(MQ + KS).
20 = 1/2(14 + KS)
40 = 14 + KS
40 - 14 = KS
26 = KS
KS = 26
The diameter(KS) is 26 inches.
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arrange the numbers in increasing order a. 8.08 8.081 8.09 8.008b. 14.204. 14.200. 14.240 14.210
Given:
a)
[tex]8.08,8.081,8.09,8.008[/tex]b)
[tex]14.204,14.200,14.240,14.210[/tex]Required:
To arrange in the increasing order.
Explanation:
a)
Here, the first two places' numbers are the same.
Let us check the hundredth decimal place.
The lowest number is 8.008.
The second lowest number is 8.08.
The third lowest number is 8.081
The fourth lowest number is 8.09.
So, the numbers are in ascending order is,
[tex]8.008,8.08,8.081,8.09[/tex]b) Here, the first t places' numbers are the same.
Let us check the hundredth decimal place.
The lowest number is 14.200.
The second lowest number is 14.204.
The third lowest number is 14.210.
The fourth lowest number is 14.240.
So, the numbers ar