The equation in standard form is, [tex]y=-6x^2+48x-97[/tex].
What is quadratic form?
A polynomial with all terms of degree two is known as a quadratic form in mathematics. A quadratic form with the variables x and y is, for instance, 4x^2 + 2xy - 3y^2. It is common to refer to a quadratic form over K when the coefficients are typically members of a specified field K, such as the real or complex numbers.
Consider, the given quadratic form
[tex]y=-6(x-4)^2-1\\[/tex]
Simplifying this,
[tex]y=-6(x^2-8x+16)-1\\y=-6x^2+48x-96-1\\y=-6x^2+48x-97[/tex]
Therefore, the standard form of the given quadratic form is, .[tex]y=-6x^2+48x-97[/tex]
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wazzupp can yall solve this with solution thank uuu
- 4u + 3 + 6u =5 + 10u
Step-by-step explanation:
[tex]- 4u + 3 + 6u =5 + 10u \\ ⇒ - 4u + 6u- 10u = 5 - 3 \\ ⇒ - 8u = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⇒u = - \frac{2}{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = - \frac{1}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
gold is sold by the troy ounce (31.103 g). what is the volume (in cm3) of 2 troy ounces of pure gold?
1.62 is the volume (in cm3) of 2 troy ounces of pure gold .
What is full answer for density?
A material substance's density is defined as its mass per unit volume. Density is defined as d = M/V, where M stands for mass, and V for volume. The unit of density that is most frequently used is grams per cubic centimeter.We determine the volume, V, corresponding to the given amount of gold. We do this by dividing the given mass, m, by the density, d, such that
V = m/d
m = 31.03 g
d = 19.3 g/ml
We proceed with the solution
V = m/d
= 31.03/19.3
≈ 1.62 ml
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26.1.2 Exam: Semester Exam
Question 24 of 25
Which situation could be represented by -8?
OA. A distance of 8 meters above sea level
OB. A rise in temperature of 8 degrees
OC. A loss of 8 points
OD. A gain of
$8
SUBMIT
A loss of 8 points is the situation which is represented by integer -8.
What is Number system?A number system is defined as a system of writing to express numbers.
The situation that could be represented by -8 is option C, a loss of 8 points.
The negative sign indicates a decrease or loss in value.
A distance of 8 meters above sea level represents a positive number because the distance is above.
A rise in temperature of 8 degrees is also positive as it is increasing.
A gain of $8 is also represents the positive value.
-8 represents a loss of 8 points.
The negative sign denotes a decrease or loss in value.
Hence, a loss of 8 points is the situation which is represented by integer -8.
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The uniform rate of water flowing of a certain pipe is 75 litres per minute. Find the time taken in minute fill a tank having the capacity of 1.5m³
The time taken in minutes to fill a tank having a capacity or work of 1.5m³ is 1.2 minutes;
What are Time and Work?
According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.
The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.
W is the amount of work done.
N is the number of people.
D is the number of days or hours needed.
In the question, It is given that:
water flowing off a certain pipe is 75 liters per minute;
and;
the tank has a capacity of 1.5m³
First converting the Efficiency in liters per second,
So,
water flowing off a certain pipe is 75 liters per minute;
So, dividing it by 60 ;
Water flowing off the pipe = 1.25;
Now using the work-time relationship:
Efficiency × Time = work;
So,
1.25×Time = 1.5
⇒Time = 1.2
So, the time taken in minutes to fill a tank having a capacity of 1.5m³ is 1.2 minutes;
Hence,
the time taken in minutes to fill a tank having a capacity of 1.5m³ is 1.2 minutes;
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when data are collected using a qualitative, nominal variable, what is true about a frequency table that summarizes the data?
The number of classes is equal to the number of variables plus 2. A pie chart can be used to summarize the data. The upper and lower class limits must be calculated. correct option is (A).
A Pie Chart is a way of summarizing a set of nominal data or displaying the different values of a given variable. This of chart is a circular divided into a series of of segments. each segment represents a particular category. A pie chart uses percentage to compare information.
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The question was incomplete. Check below the complete question.
When data is collected using a qualitative, nominal variable (in other words, male or female), what is true about a frequency distribution that summarizes the data?
A) The upper and lower class limits must be calculated.
B) Class midpoints can be computed.
C) The "2 to the k rule" can be applied.
D) The number of classes corresponds to the number of a variable's values
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The required slope of the given line is 1 which is shown in the graph.
What is the slope of the line?The slope of the line is represented as the rise of the line.
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Grab two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
We take the two points (4, 10) and (9, 22)
Let
x₁ = 0, y₁ = 1
x₂ = 8, y₂ = 9
∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in the formula
m = (9 - 1) / (8 - 0)
m = (8)/(8)
m = 1
Thus, the required slope of the given line is 1 which is shown in the graph.
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Can somebody solve this for me?
Thanks
Answer:
Rule SAS; side angle side
Step-by-step explanation:
Since they give that DM and CM are equal, and BM and AM are equal, you already have two sides. And since you have already marked vertical angles (correct because of intersection), you have 2 sides and 1 angle that are equal. This is enough to prove they are equal so it is the rule SAS or side, angle, side.
5.
People Remaining
2000
1800
1600
1400
1000
600
400
200
Hurricane Evacuation
1
2
(3. 1200)
3
4
Time (h)
S
(6.800)
Answer:
Step-by-step explanation: do your work
it 5x=_2
A bakery used 25% more butter this month than last month. If the bakery used 240 kilogrames of butter last month, how much did it use this month?
Answer:
300kg
Step-by-step explanation:
125/100=x/240
30000=100x
x=300
14) WINDOWS This window is designed in the shape of a right trapezoid If the acute angle measures 52", what is the measure of the obtuse angle?
The measure of the obtuse angle is 128 degrees
How to determine the measure of the obtuse angle?From the question, we have the following statement that can be used in our computation:
Acute angle = 52 degrees
The measure of the obtuse angle is calculated as
Obtuse angle = 180 - Acute angle
Substitute the known values in the above equation So, we have the following equation
Obtuse angle = 180 - 52
Evaluate
Obtuse angle = 128
Hence, the angle is 128 degrees
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some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 150 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions be?
Any piece of luggage must have a length, width, and height combined that is less than or equal to 150 cm. A traveler requests to take a package with the maximum permitted volume. if the length and width are to be equal, then the dimensions would be 48*96*72
Any piece of luggage must have a length, breadth, and height combined that is 216 cm or less.
L+W+H=216 (because we want the max volume, we may ignore the "less than part" and set them equal) (since we want the max volume, we can ignore the "less than part" and set them equal)
L = W if the length and width are equal.
Let's construct this new equation by swapping L for W.
Arrange H to the left so that H=216-2W when 2W+H = 216
Consequently, what is volume V=L*W*H=W=W2*(216-2W) =216W2-2W3 div./dW=432W-6W?
2\s432W-6W^2=0
72w-w2=0 divided by 6 on both sides.
W = 72 L H = 72 cm
L=2W is the only item that has altered.
Given that L+W+H=216 and that V=L*W*H=2W*W*(216-3W) =432W2-6W, 3W+H=216
864W-18W2 x 3 V prime
Set V prime to 0, solve it by dividing both sides by 18, and you'll get W = 48. dimensions will be
48, 96, and 72 cm in width ,lenght and height
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Select the correct answer. Which equation has an extraneous solution? A. x 5 = - 2 B. x + 1 3 = 10 C. x = - 5 D. x − 5 4 = 3 Reset Next
An equation which has an extraneous solution is: C. √x = -5.
What is an extraneous solution?In Mathematics, an extraneous solution can be defined as a type of solution (root) to a squared equation or transformed equation that isn't a direct solution (root) of the original equation.
This ultimately implies that, extraneous solutions are numerical values that are obtained when we solve equations that aren't solutions to the original equation as shown below:
Taking the fifth root of both sides of the equation, we have:
[tex]\sqrt[5]{x} = -2\\\\(\sqrt[5]{x})^5 = -2^5\\\\[/tex]
x = -32.
Taking the cubic root of both sides of the equation, we have:
∛(x + 1) = 10
[∛(x + 1)]³ = 10³
x + 1 = 1000
x = 1000 - 1
x = 999.
Taking the fourth root of both sides of the equation, we have:
[tex]\sqrt[4]{x-5} =3\\\\(\sqrt[4]{x-5})^4 =3^4[/tex]
x - 5 = 81
x = 81 + 5
x = 86.
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The ratio of girls to boys in the school is 3 to 1. If there is a total of 400 students, how many are boys? The answer must be a whole number.
As per the given ratio, the number of boys in the school is 133.
Ratio:
Ratio refers the relationship between two things when it is expressed in numbers or amounts.
Given,
The ratio of girls to boys in the school is 3 to 1.
Here we need to find the number of boys in the school if the total number of students is 400.
Let x be the number of boys in the school.
So, the here we have the ratio from girls to boys and we have to convert it into boys into girls, then we get,
=> girls to boys ratio = 3:1
So, boys to girls ratio = 1:3
We know that the total number of students are 400
Therefore, the number of boys in the school is,
=> 1/3 x 400 = 133
So, the number of boys in the school is 133.
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Help me with this two problems pls!
Use each unit rate to find the total.
Andy drove 840 miles in 12 hours. how far could he drive in 3 hours?
Unit rate (speed):
Distance:
Pira drives 825 miles to California.The trip takes him 17 hours. He uses 38 gallons of gas on the trip, which costs him $125
Find his speed
Find his gas mileage
Find the unit price he paid for gas.
Answer: andy drove 280 miles in 3 hours
Step-by-step explanation: are you seriousseious right now?
write the ratio 81:27 in its simplest form
Answer:
3:1
Step-by-step explanation:
bc the lcm is 3
Answer:
the ratio is 3/1
How many different 8-letter permutations can be formed from 6 identical h's and two identical t's?.
The required permutations are given as 168 letters will be formed.
Given that,
How many different 8-letter permutations can be formed from 6 identical h's and two identical t's is to be determined.
In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Here,
A total number of combinations = 8!
The number of repetitions, = 5!.2!
Permutation of letters = 8!/[5!.2!]
Thus, the required permutations are given as 168 letters will be formed.
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A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 150 nails and each large box has 400 nails. The contractor bought twice as many large boxes as small boxes, which altogether had 2850 nails. Determine the number of small boxes purchased and the number of large boxes purchased.
The total number of small boxes is 2.1 and the large boxes is 6.3.
Given;
To build a house, a contractor has to purchase nails. Both small and large boxes of nails are provided. There are 150 nails in each small box and 400 in each large box. The contractor purchased 3 more tiny boxes than large boxes. Totaling 2850 nails.
To calculate the proportion of small and large boxes that were bought,
Let's assume the small boxes as 's' and the big boxes as '3s'.
∴ s(150) + 3s(400) = 2850
150s + 1200s = 2850
1350s = 2850
s = 2850/1350
s = 2.1
∴ 3s = 2.1 * 3
= 6.3
Hence, the total number of small boxes is 2.1 and the number of large boxes is 6.3.
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Answer:
The number of small boxes purchased are 3 and the number of large boxes purchased are 6.
Step-by-step explanation:
Let the small boxes bought be x
Therefore the large boxes will be 2x
Total nails bought = 2850
Nails in x small boxes = 150x
Nails in 2x large boxes = 400. 2x = 800x
2850 = 150x + 800x
2850 = 950x
x= 2850/950 = 3
2x = 2x3= 6
2 lines are perpendicular. The slope of one line is -5/7. what is the slope of the other line?
Answer:
7/5
Step-by-step explanation:
trust me
In this figure, AB∥CD and m∠3 = 114°.
What is m∠6?
Answer:
66
Step-by-step explanation:
180 - 114) These angles are supplemental. They add to 180
66
Answer:
m<6=66°
Step-by-step explanation:
Because m<2 and m<3 are both on a straight line, we know they must add to 180°:
m<2 + m<3 =180
We know m<3=114°, so:
m<2 +114 = 180
m<2 = 66
Since AB|CD, m<2 and m<6 are corresponding angels, making them equal, and so m<6=66°.
33, 25, 42, 25, 31, 37, 46, 29, 38 what is the third quartile (upper quartile) of the data?.
The third quartile (upper quartile) of the data is 38
What is the Median?
The center value or middle value of a data set is the median.
What are the Upper Quartiles?
Upper quartile (Q3) is the center or middle data point of the second half of a data set.
The given data is 33, 25, 42, 25, 31, 37, 46, 29, 38
Order the data set given as:
25, 25, 29, 31, 33, 37, 38, 42, 46
Upper Quartile = 25, 25, 29, 31, 33, 37, 38, 42, 46 = 38
Therefore, the third quartile (upper quartile) of the data is 38
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If (3+2)+(2+ bi) = 5-4i, the value of b is
A. -2 B. 2 C. -6
D. 6
Answer:
[tex]b=\frac{-4i-2}{i}[/tex]
So the answer is...
A ) -2
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
Natasha is making a bookshelf she begin with 120  inches of oak boards she use 50.75 inches for shelves she bought 36 1/4 more inches 00 boards she didn’t use 40 1/2 inches for the top is 60.5 inches for the sides how many inches of oak boards does Natasha have left 
Natasha has left with 4.5 inches of oak boards.
What is a simplification?
The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining trade processes.
Here, we have
120 inches of oak boards
50.75 inches for shelves, 36 1/4 more inches of oak boards, and she didn’t use 401/2 inches for the top and 60.5 inches for the sides.
We have to find how many inches of oak boards Natasha has left.
We use here simplification, we get
= 120 + 36 1/4 - 50.75 - 40 1/2 - 60.5
= 4.5 inches
Hence, Natasha has left with 4.5 inches of oak boards.
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Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.
2x + 7y = -35
4x + 14y = -42
Answer:
Step-by-step explanation:
354
find 4/5 -1/2
a.3/5
b.2/5
c.3/10
d.1/2
Answer:
3/10
Step-by-step explanation:
4/5 - ½
The l.c.m of the Denominator is 10
=8-5/10
=3/10
From 48 to 90
Increase or decrease?
Amout of change:
Calculate the percent change:
The percentage change from 48 to 90 is 87.5%.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, 48 to 90 represents a increase. The increase will be:
= 90 - 48
= 42
The percentage increase will be:
= Increase / Original number × 100
= 42 / 48 × 100
= 87.5%
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Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high. If the sides of the tent are supposed to make a 50° angle with the ground, how wide is the tent?
2.1 ft
10.5 ft
5.6 ft
18.4 ft
The width of the tent is twice the width of one side which is 10.5 feet.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high and the sides of the tent make a 50° angle with the ground.
Here the opposite is the height with the reference angle of 50° and we have to determine the adjacent which is the width of the tent.
∴ tan50° = Height of the pole/width.
1.19 = 6.25/width.
width = 6.25/1.19.
width = 5.25 feet.
But the total width of the tent will be twice as we have obtained only one side width.
∴ Total width is (2×5.25) = 10.5 feet.
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Solve the inequality:
-5x + 18 < -12
Step-by-step explanation:
-5x + 18 < -12
subtract 18 from both sides:
-5x + 18 - 18 < -12 - 18
-5x < -30
divide both sides by -5: [remember, when dividing by a negative number you must FLIP the sign direction]
(-5x)/-5 > (-30)/-5
x > 6
or
(6 , ∞)
If Eddy wants to have a party and invite all his friends, it is going to cost * 1 point him $150 to cater the party, plus $4 per person for drinks. If he only has $300 to spend, how many people can he invite to his party? Write and solve the equation for the above problem. What is the maximum number of people Eddy can invite?
The maximum number of people Eddy can invite is 37.
How to illustrate the equationThe equation is simply used to show the relationship between the variables given.
In this case, it is going to cost him $150 to cater the party, plus $4 per person for drinks and he only has $300 to spend.
Let the number of persons be represented by p
The equation will be:
150 + (4 × p) = 300
150 + 4p = 300
Collect like terms
4p = 300 - 150
4p = 150
Divide
p = 150 / 4
p = 37.5
The maximum number is 37.
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series with 12 terms,a1=3 and a12=25
The 12 terms of the series will be -
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25
What is the formula to calculate the nth term of an Arithmetic Sequence ?The formula to calculate the nth term of an Arithmetic Sequence is -
a(n) = a + (n - 1)d
a - first term of A.P.
d - Common difference of A.P.
n - position of term
We have -
a[1] = 3
a[12] = 25
Then, using the formula to calculate the nth term, we get -
a(n) = a + (n - 1)d
a[1] = 3
AND
a(12) = 3 + 11 x d
25 = 3 + 11d
22 = 11d
d = 2
So, the terms of the series will be -
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25
Hence, the 12 terms of the series will be -
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25
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6.6 divided by 12 6.6 on top 12 on bottom
Answer:
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 12 on the left side and the dividend 6 on the right side like this:
12 ⟌ 6
Step 2:
The divisor (12) goes into the first digit of the dividend (6), 0 time(s). Therefore, put 0 on top:
0
12 ⟌ 6
Step 3:
Multiply the divisor by the result in the previous step (12 x 0 = 0) and write that answer below the dividend.
0
1 2 ⟌ 6
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (6 - 0 = 6) and write the answer below.
0
12 ⟌ 6
- 0
6
You are done.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 6 divided by 12 calculated using Long Division is:
0
6 Remainder
