The solutions to this quadratic equation are x = √(73/3) + 5 or x = -√(73/3) + 5.
What is a quadratic equation?In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
3x² - 30x = -2
By dividing all through by 3, we have:
x² - 10x = -2/3
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 10x + (-10/2)² = -2/3 + (-10/2)²
x² - 10x + 25 = -2/3 + 25
x² - 10x + 25 = 73/3
By simplifying, we have;
(x - 5)² = 73/3
x = √(73/3) + 5 or x = -√(73/3) + 5
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Please see the attached
The equation in slope-intercept form for the line that has slope of -2/5 and y-intercept of -4 is written as: y = -2/5x - 4.
How to Write the equation of a Line in the Slope-intercept Form?The slope-intercept form for any given straight line or linear relationship can be expressed as y = mx + b, where:
m = slope of the line
b = the y-intercept
Given the following:
slope (m) = -2/5.
y-intercept (b) = -4
To write the equation, substitute m = -2/5 and b = -4 into y = mx + b:
y = -2/5x - 4
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You are running a fundraiser for your school, selling Reese’s and Skittles candies. You recorded you sold 34 candies and made $41, but didn’t tally how many of each candy you sold (and you don't remember the original amount of candy you had).
Below is the advertisement you used to sell the candy:
Reese's sells for $1 and skittles for $1.50
Write a system of equations to represent this situation. Then, solve it algebraically using either the substitution or elimination method.
Reese sold 20 candy and Skittles sold 14 candy for a total of $41. The equation for this is x + y = 34 and x + 1.5y = 41
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
Let x represent the number of candy that Reese sell and y represent the number of Skittles candies
Reese's sells for $1 and skittles for $1.50
34 candies was sold, hence:
x + y = 34 (1)
He made $41, hence:
x + 1.5y = 41 (2)
Solving both equations simultaneously:
x = 20; y = 14
Reese had 20 candy and Skittles had 14 candy.
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Lisa an experienced shipping clerk, can fill a certain order in 9 hours. Felipe a new clerk, needs 11 hours to do the same job. Working together, how long will it take them to fill the order?
The solution is ___Hours
It will take Lisa and Felipe approximately 4.95 hours to fill the order by working together.
To solve this problem, we can use the formula:
1/T = 1/T₁ + 1/T₂
where T is the time taken to complete the job when both Lisa and Felipe work together, T₁ is the time taken by Lisa to complete the job, and T₂ is the time taken by Felipe to complete the job.
Substituting the given values into the formula, we get:
1/T = 1/9 + 1/11
Simplifying the right-hand side of the equation, we get:
1/T = (11 + 9)/(9 x 11)
1/T = 20/99
Multiplying both sides by 99, we get:
T = 99/20
Therefore, working together, Lisa and Felipe can complete the job in 4.95 hours, or approximately 4 hours and 57 minutes.
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Enter your answer by filling in the boxes to correctly complete the statements. If necessary, round to the nearest hundredth.
The practical domain of the situation is [0, ∞].
The practical range of the situation is [0, 100].
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
How to identify the domain any graph?In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [0, ∞] or 0 ≤ x ≤ ∞.
Range = [0, 100] or 0 ≤ y ≤ 100.
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You buy tomatoes in 25 pounds cases. One portion of salad requires.75 ounces of tomatoes. How many portions can be made with one case
Answer: 5.3 repeated portions or about 5 portions
Step-by-step explanation: 25 pounds = 400 ounces
400/75 = 5.3 repeated
Answer:33
Step-by-step explanation:
Non mutually exclusive events !
The missing probability is P(A or B) = 131/200
How to calculate the probabilityIt should be noted that in order to find the probability of the union of two events A and B, i.e., P(A or B), we can use the following formula:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = P(A) + P(B) - P(A and B) = (9/20) + (1/4) - (9/200)
Simplifying the expression, we get:
P(A or B) = 45/100 + 25/100 - 9/200 = (90+50-9)/200 = 131/200
The probability is 131 / 200.
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Given the circle below with secants GHI and KJI. If JI = 4, KJ = 10 and
HI = 5, find the length of GH. Round to the nearest tenth if necessary.
Answer:
GH = 6.2
Step-by-step explanation:
A circle is represented by the equation (x + 6)2 + (y − 3)2= 121.
Which of the following statements is true?
Group of answer choices
The circle is centered at (−6, 3) and has a radius of 11.
The circle is centered at (−6, 3) and has a diameter of 11.
The circle is centered at (6, −3) and has a diameter of 11.
The circle is centered at (6, −3) and has a radius of 11.
The statement that is true about the given circle equation is:
Option A: The circle is centered at (−6, 3) and has a radius of 11.
How to find the equation of a circle?The standard form for finding the equation of a circle is given by the expression:
(x - h)² + (y - k)² = r²
where:
(h, k) represents the coordinates of the center of circle
r represents the radius of the circle
We are given the equation of the circle as:
(x - 6)² + (y - 3)² = 121
Now, 121 can also be written as 11². Thus, the equation of the circle can be rewritten as:
(x - 6)² + (y - 3)² = 11²
Comparing with the standard form of equation of a circle gives:
Coordinates of center = (-6, 3)
Radius = 11
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Solve for x. Round to the nearest tenth, if necessary.
The calculated value of x in the right triangle is 8.7
Calculating the value of x in the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The value of x in the right triangle can be calculated using the following sine ratio
sin(75) = x/9
Cross multiply the equation
So, we have
x = 9 * sin(75)
Evaluate the products
x = 8.7
Hence, the value of x in the right triangle is 8.7
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A dot plot titled seventh grade test score. There are 0 dots above 5, 6, 7, 8 and 9, 1 dot above 10, 1 dot above 11, 2 dots above 12, 1 dot above 13, 1 dot above 14, 2 dots above 15, 3 dots above 16, 3 dots above 17, 2 dots above 18, 2 dots above 19, 3 dots above 20. A dot plot titled 5th grade test score. There are 0 dots above 5, 6, and 7, 1 dot above 8, 2 dots above 9, 10, 11, 12, and 13, 1 dot above 14, 3 dots above 15, 2 dots above 16, 1 dot above 17, 2 dots above 18, 1 dot above 19, and 1 dot above 20.
Students in 7th grade took a standardized math test that they also had taken in 5th grade. The results are shown on the dot plot, with the most recent data shown first.
Find and compare the means to the nearest tenth.
7th-grade mean:
5th-grade mean:
What is the relationship between the means?
Note that 7th grade mean = 277.86
the 5th grade mean = 254.77
So th relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean .
How is this so ?To compute the means here is what we did
7 th grade mean = (1 × 10) + (1 × 11) + (2 × 12) + (1 × 13) + (1 × 14) + (2 × 15) + (3 × 16) + (3 × 17) + (2 × 18) + (2 × 19) + (3 × 20) / 21
= 277.857142857
≈ 277.86
For the 5th grade mean
5th grade mean = (1 × 8) + (2 × 9) + (2 × 10) + (2 × 11) + (2 × 12) + (1 × 13) + (3 × 15) + (2 ×16) + (1 × 17) + (2 × 18) + (1 × 19) + (1 × 20) / 26 = 12.5
= 254.769230769
≈ 254.77
This means that trully, the relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean.
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The mass of 12 packets of flour and 8 packets of salt is 19 kg. When 7 packets of flour are removed, the mass became 9.9 kg. Find the mass of each packet of salt in kilogram.
Answer:
1.235 kg
Step-by-step explanation:
Let's assume that each packet of flour and salt weighs the same.
When we remove 7 packets of flour, we are left with 5 packets of flour and 8 packets of salt. The total number of packets is 13 and their total mass is 9.9 kg.
Therefore, the average mass of each packet is 9.9 kg ÷ 13 = 0.76 kg.
Since we know that 12 packets of flour and 8 packets of salt have a total mass of 19 kg, we can subtract the mass of the 12 packets of flour (12 × 0.76 kg = 9.12 kg) from the total mass to find the mass of the 8 packets of salt:
19 kg - 9.12 kg = 9.88 kg
Finally, we can divide the mass of the 8 packets of salt by the number of packets to find the mass of each packet:
9.88 kg ÷ 8 = 1.235 kg
Therefore, each packet of salt weighs approximately 1.235 kg.
what is 2x multiplied by 7 with the exponent of 4
The simplified expression of 2x multiplied by 7 with the exponent of 4 is 4,802x.
What is the simplification of the expression?
The expression is simplified by applying the rules of multiplication and exponent rules.
the expression = 2x(7⁴)
simplify 7⁴ as follows = 7 x 7 x 7 x 7 = 2,401
Multiply the resultant solution of 2,401 as follows;
= 2,401 x (2x)
= 4,802x
Thus, the simplified expression of 2x multiplied by 7 with the exponent of 4 is determined by applying basis rules of multiplication.
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1. Bill scored the following number of points in a basketball games: 22, 18, 19, 16, 32, 24, 19, 20, 22 and 22
a. Box and Whisker plot:
b. What is the range:
c. Are there any outliers?
IQR:
b. The range is 32 - 16 = 16. and IQR 4
c. 32
how to find range?a. Here is a box and whisker plot to represent the given data:
The horizontal axis shows the range of the data, and the vertical axis represents the frequency. The box represents the middle 50% of the data, with the bottom of the box being the 25th percentile and the top of the box being the 75th percentile. The whiskers represent the lowest and highest values within 1.5 times the interquartile range (IQR) of the box, and any points outside the whiskers are considered outliers.
b. The range is the difference between the highest and lowest values in the data set. In this case, the range is 32 - 16 = 16.
c. There is one outlier in the data set, which is the value of 32. It is outside the whiskers of the box and is considered to be an outlier.
The interquartile range (IQR) is the difference between the 75th and 25th percentiles of the data set. In this case, the IQR is:
IQR = Q3 - Q1
= 22 - 18
= 4
where Q1 is the first quartile (the value below which 25% of the data falls), and Q3 is the third quartile (the value below which 75% of the data falls).
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Please help. This is geometry
∠WTA and ∠HTC are vertical angles. Thus, they are equal.
As WA || HC, that means ∠AWT and ∠THC are alternate interior angles and are equal. Additionally, ∠WAT and ∠TCH are also alternate interior angles and are equal.
∠WTA = ∠HTC, ∠AWT = ∠THC, and ∠WAT = ∠TCH
Since both triangles have the same angle measurements, they are similar.
A cone has a volume of 48 cubic feet and a height of 9 feet. find the radius.
Step-by-step explanation:
V = 1/3 x π x r² x h
48 = 1/3 x π x r² x 9
48÷3π = r²
√48÷3π =r
so, r= 2.26 (3.s.f)
mrs. gordon bought a stove which cost $850. no down payment was required. mrs. gordon has to pay $160 for the next six months. what is the average amount she pays in interest each month?
Answer:
the average amount Mrs. Gordon pays in interest each month, we need to determine the total interest paid over the six-month period and divide it by the number of months.
The total interest paid can be found by subtracting the cost of the stove from the total amount paid over six months:
Total interest paid = Total amount paid - Cost of the stove
The total amount paid over six months is calculated by adding the monthly payments:
Total amount paid = $160/month * 6 months
Let's perform the calculations:
Total amount paid = $160/month * 6 months = $960
Total interest paid = Total amount paid - Cost of the stove
= $960 - $850
= $110
Now, to find the average amount Mrs. Gordon pays in interest each month, we divide the total interest paid by the number of months:
The average amount paid in interest each month = Total interest paid / Number of months
= $110 / 6 months
≈ $18.33
Therefore, Mrs. Gordon pays an average of approximately $18.33 in interest each month.
Please help with this one as well,,,
The whisker plot with the data provided should includes a range that goes from 7 to 49, and a median of 23.
How to draw a whisker plot?A whisker plot, also known as a box plot, is a graphical representation of a data set that shows the distribution of the data along with some important statistical information, such as the median, quartiles, and outliers. It is particularly useful for comparing the distribution of different data sets or for identifying potential outliers in a data set.
To create a whisker plot, follow these steps:
Collect the data you want to represent and arrange it in order from smallest to largest.Find the median, which is the middle value of the data set. If the data set has an even number of values, the median is the average of the two middle values.Find the lower quartile (Q1), which is the median of the lower half of the data set.Find the upper quartile (Q3), which is the median of the upper half of the data set.Calculate the interquartile range (IQR), which is the difference between Q3 and Q1.Learn more about whisker plots in https://brainly.com/question/2742784
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HELP ME PLEASE!!!!!
Answer:
1. True
2.True
3.True
4.False
5.False
6.True
7.True
8.True
Step-by-step explanation:
1. The area of a rectangle is found by the formula A=bh.
2. There are 4 rectangles making up the lateral area of the prism. 2+3=5. 5*6=30, and multiply by 2 since there are two of the 2x6 and two of the 3x6 rectangles to get 60. The bases of the prism have an area of 6 square inches each.
60+12+12=84
3. 3*5=15
4. The base is not a square, so you cannot multiply by 4 to get the area of all the triangles. You can multiply by two, and also multiply 1/2(3)(4) by 2 to get the area of the other two triangles.
5. The base is a triangle. 1/2(3)(4)=6.
6. 2[1/2(3)(4)]=12. 2(8*5)=80. 3*8=24. 80+24+12=116
7. A cube has 6 identical sides, so you can find the area of one side and multiply by 6 to get the surface area of the cube.
8. 9^2=81. 81*6=486.
PLS I NEED HELP WITH THIS I WILL MARK YOU AS THE BRAINLIEST!!
Answer:
linearlinearquadraticexponentialStep-by-step explanation:
You want to classify the functions shown in the tables as linear, quadratic, or exponential.
DifferencesWe notice all of the tables have x-values that are evenly spaced. this means we can look at the differences between y-values to determine the kind of function the table represents.
The differences have the following interpretation:
differences are constant — lineardifferences have a constant difference — quadraticdifferences (and terms) have a constant ratio — exponential5, 3, 1, ...The differences of y-terms are constant at 3 -5 = -2.
The function is linear.
2, 5, 8, ...The differences of y-terms are constant at 5 -2 = 3.
The function is linear.
5, 1, 5, ...We observe that the y-values have a minimum. We don't need to take differences to know this is not linear or exponential. Of the offered choices, the only one that makes sense is "quadratic."
The differences of y-terms are ...
1 -5 = -4, 5 -1 = 4, 17 -5 = 12, 37 -17 = 20
The differences of differences are ...
4 -(-4) = 8, 12 -4 = 8, 20 -12 = 8
The second differences are constant.
The function is quadratic.
1, 3, 9, ...The first differences are ...
3 -1 = 2, 9 -3 = 6, 27 -9 = 18, 81 -27 = 54
The second differences are
6 -2 = 4, 18 -6 = 12, 54 -18 = 36
We note that the first and second differences are not constant, but the ratio of terms at every level is 3/1 = 6/2 = 12/4 = 3.
The function is exponential.
Please solve using the given picture
Answer:
61°
Step-by-step explanation:
You want the angle XCA in the figure, given that angle XBA is 70°, and ABCD is a rectangle with AB=5.6m and BC=6.4m. Angles at A are right angles.
DiagonalThe length of diagonal AC is found using the Pythagorean theorem.
AC² = AB² +BC²
AC = √(5.6² +6.4²) = 0.8√113 ≈ 8.504 . . . . meters
HeightThe length XA is found using the tangent function:
Tan = Opposite/Adjacent
tan(B) = XA/AB
XA = AB·tan(B) = 5.6·tan(70°) . . . . meters
AngleThe angle XCA is found from the tangent relation:
tan(XCA) = XA/AC
tan(XCA) = 5.6·tan(70°)/(0.8√113) = 7·tan(70°)/√113
angle XCA = arctan(7·tan(70°)/√113) ≈ 61.07°
The angle XC makes with the horizontal is about 61°.
can someone help me please
The matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]
What is a matrix row operationRow operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.
performing the row operation 4R₁ + R₂ — R₂ on M, we have;
4(1) + (-5) = -1 {row 2 column 1}
4(0) + 2 = 2 {row 2 column 2}
4(3) + (-2) = 10 {row 2 column 3}
Therefore, the matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]
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Pyramid A and Pyramid B are similar. Pyramid A has a volume of 648m° and Pyramid B has a volume of 1029m?. What is the ratio of the surface areas of Pyramid A to Pyramid B?
The ratio of the surface area of Pyramid A to Pyramid B is: 36/49
We have the information from the question is:
Pyramid A and Pyramid B are similar.
The volume of Pyramid A is 648 [tex]m^3[/tex]
The volume of Pyramid B is 1029 [tex]m^3[/tex]
To find the ratio of the surface areas of Pyramid A to Pyramid B.
Now, As we know that:
If two solids are similar, then the ratio of their volumes is equal to the cube
of the ratio of their corresponding linear measures.
[tex]\frac{Vol of A}{Vol of B} =(\frac{a}{b} )^3 =\frac{684}{1029}=\frac{216}{343}\\ \\ \frac{a}{b}=\frac{6}{7}[/tex]
If two solids are similar, then the n ratio of their surface areas is equal to the square of the ratio of their corresponding linear measures.
Surface area of A/ Surface area of B [tex]=(\frac{a}{b} )^2=\frac{36}{49}[/tex]
So, the ratio of the surface area of Pyramid A to Pyramid B is: 36/49
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Evaluate each expression using the values given in the table.
Answer:
a) f(g(1)) = f(0) = 5
b) f(g(2)) = f(-3) = 8
c) g(f(2)) = g(3) = -8
d) g(f(3)) = g(2) = -3
e) g(g(1)) = g(0) = 2
f) f(f(3)) = f(2) = 3
the principal spends 96 minutes talking to the teachers and 48 minutes talking to the students. what is the basic ratio of minutes spent talking to teachers to minutes spent talking to students
The proportion is solved and ratio of minutes spent talking to teachers to minutes spent talking to students is given by 2 : 1
Given data ,
The principal spends 96 minutes talking to the teachers
And , the principal spends 48 minutes talking to students
Now , the basic ratio of minutes spent talking to teachers to minutes spent talking to students, we need to simplify the ratio by dividing both values by their greatest common factor
So , A : B = 96 : 48
On simplifying the proportion , we get
A : B = 2 : 1
Hence , the proportion is 2 : 1
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(PLEASE ANSWER BOTH)
1. What is the value of Angle X?
2. How do you know (What type of angle pairs are they)?
Answer:
angle x is 160
Step-by-step explanation:
180 - 20
50 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
A. The 51st note on a piano keyboard corresponds to a pitch of 440 cycles per second.
B. The pitch that is 73 notes higher on the keyboard has a frequency of about 1760 cycles per second.
How to determine frequency?A. Use the formula to find how many notes up the piano keyboard the pitch of 440 cycles per second corresponds to:
440 = 27.5 × 2⁽ⁿ⁻¹⁾/12
Dividing both sides by 27.5 and taking the logarithm with base 2 gives:
log₂(440/27.5) = (n-1)/12
n-1 = 12 × log₂(440/27.5)
n-1 = 12 × 4.1702 ≈ 50.042
n ≈ 51.042
Therefore, the pitch of 440 cycles per second is the 51st note up the piano keyboard.
B. Use the same formula to find the frequency of the pitch that is 73 notes up the keyboard:
73 = 1 + 12 log₂(f/27.5)
72 = 12 log₂(f/27.5)
6 = log₂(f/27.5)
f/27.5 = 2⁶
f = 27.5 × 2⁶
f ≈ 1760
Therefore, the frequency of the pitch that is 73 notes up the keyboard is approximately 1760 cycles per second.
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Select the reason that best supports Statement 5 in the given proof.
Where is the given proof
Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been if she had worked the problem correctly?
Using mathematical operations, Cindy's answer would have been 15 if she had worked the problem correctly by following her teacher's instructions.
How is the correct value determined?The correct value can be determined by reversing Cindy's calculations to find the certain number as follows:
(x - 9) ÷ 3 = 43
x = 43 x 3 + 9
x = 138
With the certain number, x = 138, the correct mathematical operations can be performed as follows:
Correction Operation:(138 - 3) ÷ 9
135 ÷ 9
= 15
Thus, Cindy's correct answer would have been 15 if she had performed the correct mathematical operations, according to her teacher's instructions.
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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 169 cm and a standard deviation of 2.2 cm. For shipment, 10 steel rods are bundled together.
Answer the following rounding to three decimals where appropriate.
Find the probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm.
P(M > 168.58) = ???
The probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm is 0.7486
How to calculate the probabilityFirst, we need to calculate the z-score for the sample mean:
z = (x - μ) / (σ / √n)
z = (168.58 - 169) / (2.2 / √10)
z = -0.67
Next, we need to find the probability that a randomly selected bundle of steel rods will have a mean length greater than 168.58 cm. This is equivalent to finding the area under the standard normal distribution curve to the right of z = -0.67.
Using a standard normal distribution table or calculator, we find that the probability is 0.7486.
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Can someone help me solve this? I don’t quite understand
According to the graph, the function that best describes the graph is
[tex]f(x)=|x| = \left\{ \begin{array}{cl}x - 2 \text{ for x \lt -3 } \\8 \text{ for -3 \lt x \lt 5}\\-x + 10 \text{ for x \gt 6}\end{array} \right.[/tex]
(option d).
As we all know that the term function is defined as a rule or relationship that maps each element in one set, called the domain, to exactly one element in another set, called the range.
While we looking into the graph we have identified that there is a straight line that cross the point (0, 8) within the range of -3 to 5.
And then the next line is moves downwards from the range of x whose value is greater than 6.
Final upward slope is moves the range of -3 or less While we looking into these range value we have identified that the the function that refers the graph is (option d).
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