Answer:
Option A) x=4,12 is correct.
The solution of the given quadratic equation is x=4,12
Step-by-step explanation:
Given equation is in quadratic form
Given quadratic equation is
[tex]0=4x^2-64x+192[/tex]
Rewriting the above equation
[tex]4x^2-64x+192=0[/tex]
Now dividing the equation by 4 we get
[tex]\frac{1}{4}(4x^2-64x+192)=\frac{0}{4}[/tex]
[tex]x^2-16x+48=0[/tex]
For quadratic equation [tex]ax^2+bx+c=0[/tex]
solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where a and b are coefficients of [tex]x^2[/tex] and x respectively, c is a constant
Here a=1, b=-16, c=48
[tex]x=-\frac{(-16)\pm\sqrt{(-16)^2-4(1)(48)}}{2(1)}[/tex]
[tex]=\frac{16\pm\sqrt{16^2-192}}{2}[/tex]
[tex]=\frac{16\pm\sqrt{256-192}}{2}[/tex]
[tex]=\frac{16\pm\sqrt{64}}{2}[/tex]
[tex]x=\frac{16\pm 8}{2}[/tex]
Therefore
[tex]x=\frac{16+8}{2}[/tex] and [tex]x=\frac{16-8}{2}[/tex]
[tex]x=\frac{24}{2}[/tex] and [tex]x=\frac{8}{2}[/tex]
[tex]x=12[/tex] and [tex]x=4[/tex]
Therefore the solution of the given quadratic equation is x=4,12
Option A) x=4,12 is correct.
- What is the percent of increase from 5,000 to 8.000?
Answer:
increase is 37.5%
Step-by-step explanation:
3000/8000 *100= 37.5%
dolphin is 30 feet below the surface of the water. She rises 23 feet, sinks 17 feet, and finally rises another 27 feet. If there are no other changes, the dolphin is
Answer:
Dolphin is 3 feet above the surface of the water.
Step-by-step explanation:
Dolphin is 30 feet below the surface of the water, then its position on the vertical number line is -30.
She rises 23 feet - add 23, sinks 17 feet - subtract 17, and finally rises another 27 feet - add 27.Thus,
[tex]-30+23-17+27\\ \\=(-30-17)+(23+27)\\ \\=-47+50\\ \\=3[/tex]
Dolphin is 3 feet above the surface of the water.
Final answer:
After a series of movements, the calculated final position of the dolphin is 3 feet above the surface of the water, which is a reasonable result for a dolphin.
Explanation:
The question involves calculating the final position of a dolphin relative to the water surface after a series of vertical movements (rising and sinking). Initially, the dolphin is 30 feet below the surface. Then, the following movements occur:
The dolphin rises 23 feet.
The dolphin sinks 17 feet.
The dolphin rises another 27 feet.
To find out where the dolphin is relative to the surface after these movements, we can sum the changes in position:
Initial position: -30 feet (below the surface is considered negative)
+ Rise 23 feet: -30 + 23 = -7 feet
+ Sink 17 feet: -7 - 17 = -24 feet
+ Rise 27 feet: -24 + 27 = +3 feet
After calculating these movements, the dolphin is 3 feet above the surface of the water. Dolphins are known to be able to jump several times their length out of the water, and considering they measure about 2 meters long, this result of the dolphin being 3 feet above the water is reasonable.
HI. Can you help???
The table shows the total distance a spider traveled after a light was turned on.
Between which two consecutive times was the average rate of change the greatest?
Question 3 options:
A. between Second 11 and Second 15
B.between Second 19 and Second 28
C. between Second 5 and Second 11
D.between Second 15 and Second 19
Answer:
The maximum rate of change is between second 15 and second 19.
Step-by-step explanation:
See the attached table.
The table shows the total distance a spider traveled after a light was turned on.
Now, the average rate of change between two consecutive times in the table is given by
= [tex]\frac{\textrm {Total change in Distance in feet}}{\textrm {Total change in Time in seconds }}[/tex]
Therefore, between second 5 and second 11, the average rate of change = [tex]\frac{7 - 4}{11 - 5} = 0.5[/tex]
Between second 11 and second 15, the average rate of change = [tex]\frac{13 - 7}{15 - 11} = 1.5[/tex]
Between second 15 and second 19, the average rate of change = [tex]\frac{20 - 13}{19 - 15} = 1.75[/tex]
Between second 19 and second 28, the average rate of change = [tex]\frac{24 - 20}{28 - 19} = 0.44[/tex]
Therefore, the maximum rate of change is between second 15 and second 19. (Answer)
In December one artificial Christmas tree cost $159. In January the same tree cost $62. Find the percent of decrease to the nearest whole percent.
Answer:
[tex]61\%[/tex]
Step-by-step explanation:
Cost in December[tex]=\$159[/tex]
Cost in January[tex]=\$62[/tex]
Total decrease in the cost[tex]=159-62=\$97[/tex]
[tex]Percentage\ decrease=\frac{97}{159}\times100\\\\=61.006\approx 61\%[/tex]
3. Which polynomial is equal to
(-3x2 + 2x - 3) subtracted from
(x3 - x² + 3x)?
A 2x² + 2x² + x -
B-2x² + 2x² + x + 3
C x² + 2x² +
x3
Dx² + 2? + x + 3
X
Which polynomial is equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x)?
Answer:The polynomial equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x) is [tex]x^3 + 2x^2 + x + 3[/tex]
Solution:Given that two polynomials are: [tex](-3x^2 + 2x - 3)[/tex] and [tex](x^3 - x^2 + 3x)[/tex]
We have to find the result when [tex](-3x^2 + 2x - 3)[/tex] is subtracted from [tex](x^3 - x^2 + 3x)[/tex]
In basic arithmetic operations,
when "a" is subtracted from "b" , the result is b - a
Similarly,
When [tex](-3x^2 + 2x - 3)[/tex] is subtracted from [tex](x^3 - x^2 + 3x)[/tex] , the result is:
[tex]\rightarrow (x^3 - x^2 + 3x) - (-3x^2 + 2x - 3)[/tex]
Let us solve the above expression
There are two simple rules to remember:
When you multiply a negative number by a positive number then the product is always negative. When you multiply two negative numbers or two positive numbers then the product is always positive.So the above expression becomes:
[tex]\rightarrow (x^3 - x^2 + 3x) + 3x^2 -2x + 3[/tex]
Removing the brackets we get,
[tex]\rightarrow x^3 - x^2 + 3x + 3x^2 -2x + 3[/tex]
Combining the like terms,
[tex]\rightarrow x^3 -x^2 + 3x^2 + 3x - 2x + 3[/tex]
[tex]\rightarrow x^3 + 2x^2 + x + 3[/tex]
Thus the resulting polynomial is found
If x2 = 20, what is the value of x?
Answer:
[tex]x=-2\sqrt5\ and\ x=2\sqrt5[/tex]
Step-by-step explanation:
Given:
The given equation to solve is:
[tex]x^2=20[/tex]
In order to solve the above equation, we take square root on both the sides.
While taking square root on both sides, we must consider both positive and negative values. So, this gives:
[tex]\sqrt{x^2}=\pm\sqrt{20}[/tex]
From the definition of square root function, we have
[tex]\sqrt{a^2}=a[/tex]
Therefore,
[tex]x=\pm\sqrt{20}[/tex]
Now, writing 20 into the product of its prime factors, we have
[tex]20=2^2\times 5[/tex]
Therefore, [tex]x=\pm\sqrt{2^2\times 5}[/tex]
We also know, [tex]\sqrt{a\times b}=\sqrt{a}\times\sqrt{b}[/tex]
So, [tex]\sqrt{2^2\times 5}=\sqrt{2^2}\times \sqrt{5}=2\sqrt5[/tex]
Therefore, [tex]x=\pm2\sqrt5[/tex]
So, there are two values of 'x'. They are:
[tex]x=-2\sqrt5\ and\ x=2\sqrt5[/tex]
Skippy has a total of $10,000 to split between two investments. One account offers 4% simple interest, and the other account offers 8% simple interest. For tax reasons, he can only earn $500 in interest the entire year. How much money should Skippy invest in each account to earn $500 in interest for the year
Skippy should invest $ 7500 in account offering 4 % interest and $ 2500 in account offering 8 % simple interest
Solution:
Given that Skippy has a total of $10,000 to split between two investments
One account offers 4% simple interest, and the other account offers 8% simple interest
Total interest earned = 500
Number of years = 1
Let the principal with rate of interest 4 % is x
So the principal for rate of interest 8 % is 10000 - x
Total interest earned = simple interest for 4 % interest + simple interest for 8 % interest
Simple interest is given as:
[tex]S.I = \frac{pnr}{100}[/tex]
Where "p" is the principal and "r" is the rate of interest and "n" is the number of years
Therefore,
[tex]\text{ Total interest earned } = \frac{x \times 1 \times 4}{100} + \frac{10000-x \times 1 \times 8}{100}[/tex]
[tex]500 = 0.04x + (10000 - x)0.08\\\\500 = 0.04x + 800 - 0.08x\\\\-300 = -0.04x\\\\x = 7500[/tex]
Therefore skippy should invest $ 7500 in account offering 4 % interest
And skippy should invest (10000 - x) = (10000 - 7500) = $ 2500 in account offering 8 % interest
I bought 6 and 1/2 pounds of potatoes from the local supermarket for a total price of $5.20 write an equation that would give the total cost of any amount of potatoes in pounds
Answer:
x - 0.8y
Step-by-step explanation:
5.20/6.5 = $0.80 per pound
x = total cost of potatoes
y = number of potatoes
x = 0.8y
Can someone please help. It’s fine if the answer not correct at least you tried. But could anyone help because I can’t figure out the answer
WAR is given as 57 degrees.
If you draw a line from W to R, the angle WRA would also be 57 degrees.
57 + 57 = 114
The measure of AR = 180 -114 = 66 degrees.
Answer:
66.
Step-by-step explanation:
If You See W.And R., They Are The Same Angle's, So If They Are Little And Big At The Same Time, You Can Notice It Will Be 66* :)
Tell Me If You Have Any Problomes With These!!!!
Hope This Information Helps!!!
Oder from smallest to largest 652/900 0.012 7/10 32% 1/10 0.721 65%
Answer:
The given numbers from smallest to largest is
[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]
Step-by-step explanation:
Given numbers are
[tex]\frac{652}{900}, 0.012,\frac{7}{10}, 32\%,\frac{1}{10}, 0.721, 65\%[/tex]
We have to arrange the given numbers from smallest to largest
That is to write in ascending order.
Rewritting the given numbers are
[tex]\frac{652}{900}, 0.012,\frac{7}{10}, \frac{32}{100},\frac{1}{10}, 0.721, \frac{65}{100}[/tex]
[tex]\frac{652}{900}, 0.012,0.7, 0.32, 0.1, 0.721, 0.65[/tex]
[tex]0.724, 0.012, 0.7, 0.32, 0.1, 0.721, 0.65[/tex]
Now arranging the above numbers from smallest to largest
[tex]0.012, 0.1, 0.32, 0.65, 0.7, 0.721, 0.724[/tex]
ie, 0.12, [tex]\frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]
The given numbers in ascending order is
[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]
Which expressions are equivalent to 2r+(t+r)
Choose all answers that apply:
A: 2rt+4r
B: r+t
C: None of the above
Answer:
Option C -> None of the above.
Step-by-step explanation:
Given-
2 r + ( t + r )
⇒ 2 r + t + r
⇒ 2 r + r + t
⇒ 3 r + t
∵ 2 r + ( t + r ) = 3 r + t.
∴ The given expression is equivalent to Option C : None of the above.
Answer:
C. None of the above
Step-by-step explanation:
Erin purchased 100 shares through her online broker. The price per share on the day of the purchase was $15.84. Erin’s broker charged her $0.025 per share as a brokerage fee. How much did Erin pay in brokerage fees? Erin spent $ in brokerage fees.
Answer:
$2.50
Step-by-step explanation:
The total fee is the fee per share multiplied by the number of shares:
$0.025 × 100 = $2.50 . . . . Erin's brokerage fee
Answer:
2.50
Step-by-step explanation:
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 30 books and each large box can hold 40 books. There were twice as many large boxes sent as small boxes, which altogether can hold 330 books. Determine the number of small boxes sent and the number of large boxes sent.
Answer:
Step-by-step explanation:
x = small box and y = large box
30x + 40y = 330
y = 2x
30x + 40(2x) = 330
30x + 80x = 330
110x = 330
x = 330/110
x = 3 <===== 3 small boxes
y = 2x
y = 2(3)
y = 6 <=== 6 large boxes
check...
30x + 40y = 330
30(3) + 40(6) = 330
90 + 240 = 330
330 = 330 (correct)
The sum of 3 consecutive even numbers is 408. What is the largest of the numbers
Answer: 138
Step-by-step explanation:
Let the first number be x , the second number be x + 2 and the third number be x + 4 since they are consecutive even numbers.
Their sum implies:
x + x + 2 + x + 4 = 408
3x + 6 = 408
subtract 6 from both sides
3x + 6 - 6 = 408 - 6
3x = 402
divide through by 3
3x/3 = 402/3
Therefore x = 134.
The numbers are :
134 , 136 and 138 , this means that the largest number is 138
Consider a triangle ABC with AB = 2, BC = 5, and AC = 6. If the triangle is rotated around AB, what is the volume of the solid that is generated?
The volume of the solid generated by rotating triangle ABC around AB is 24π cubic units.
To find the volume of the solid generated by rotating triangle ABC around side AB, you can use the method of cylindrical shells. The volume of the solid generated by rotating a region bounded by a curve around an axis is given by the formula:
[tex]\[ V = \int_{a}^{b} 2\pi x \cdot h(x) \, dx \][/tex]
Where:
[tex]\( a \) and \( b \) are the limits of integration along the x-axis (in this case, from 0 to the length of side AB),[/tex]
[tex]\( h(x) \) is the height of the curve at the position x, and[/tex]
[tex]\( 2\pi x \) represents the circumference of the cylindrical shell with radius x and height \( h(x) \).[/tex]
In this case, triangle ABC is a right triangle, so rotating it around AB will generate a cone with height AB and base radius AC.
Given that AB = 2 and AC = 6, the radius of the base of the cone formed by rotating the triangle will be [tex]\( r = AC = 6 \)[/tex]. The height of the cone will be the same as the length of side AB, so [tex]\( h = AB = 2 \).[/tex]
Now, we can calculate the volume:
[tex]\[ V = \int_{0}^{2} 2\pi x \cdot 6 \, dx \][/tex]
[tex]\[ = 12\pi \int_{0}^{2} x \, dx \][/tex]
[tex]\[ = 12\pi \left[\frac{x^2}{2}\right]_{0}^{2} \][/tex]
[tex]\[ = 12\pi \left(\frac{2^2}{2} - \frac{0^2}{2}\right) \][/tex]
[tex]\[ = 12\pi \left(\frac{4}{2}\right) \][/tex]
[tex]\[ = 12\pi \cdot 2 \][/tex]
[tex]\[ = 24\pi \][/tex]
So, the volume of the solid generated by rotating triangle ABC around side AB is [tex]\( 24\pi \)[/tex] cubic units.
The solid formed by rotating triangle ABC around side AB is a cone. The volume of this cone is calculated using the formula V = (1/3)πr^2h where r is the radius of the base and h is the height, resulting in approximately 57.91 cubic units.
The question asks for the volume of the solid generated by rotating a triangle around one of its sides. In this case, rotating triangle ABC with AB = 2, BC = 5, and AC = 6 around side AB will generate a conical surface. Since side AB will be the axis of rotation, the other two sides will act as generating lines of the cone, where side AC becomes the slant height (l) and side BC becomes the base's radius (r).
To calculate the volume of the cone, we use the formula V = (1/3)\u03c0r^2h, where r is the radius of the base, and h is the height of the cone. Here the height (h) of the cone is not directly provided, but with the Pythagorean theorem, we can find it since we know the slant height and radius: h = \\/(l^2 - r^2) = \\/(6^2 - 5^2) = \\/(36 - 25) = \\/11. Finally, the volume can be calculated: V = (1/3)\\(3.1415)\(5)^2\\/11\approx 57.91 cubic units.
The theorem of Pappus is a useful approach to solving this problem, but it requires knowing the centroid's distance from the axis of rotation, which is not provided, so we are not using that method here.
Anwser themm!!!!!! HELP ASAP MATH
Answer:
Please see the detailed answers below:
Step-by-step explanation:
Solution 1:
Sandwich = $9.25
Salad = $4.35
Tax = 7.5%
=> ($9.25 + $4.35) x 7.5 / 100 = 13.6 x 0.075 = $1.02
The amount of Tax on Veena's meal is $1.02
Solution 2:
Book read by Christian = (1/4) / (2/3) = (1/4) x (3/2) = 3/8
Christian will read 3/8 books per week.
Solution 3:
Sale Price = (100 - Discount Rate) x Cost Price
Let Y = Sale Price
By Putting the values in above equation:
Y = (100 - 45) x $650
Y = 0.55 x $650
Y = $357.5
Hence the Sale Price of the bicycle will be $357.5
Solution 4:
Percent error = [(Experimental Value - Accepted Value) / Accepted Value] x 100
Percent error = [(15.5 - 14.5) / 14.5] x 100
Percent error = [1 / 14.5] x 100
Percent error = 2.2%
Hence the percent error in Mark's estimate is 2.2%
a company makes concrete bricks shaped like rectangular prisms. Each brick is 10 inches long, 6 inches wide, and 4inches tall. If they used 13,200 cubic inches of concrete, how many bricks did they make?
Answer:
55
Step-by-step explanation:
Volume of a rectangular prism is width time length times height.
V = WLH
The volume of each brick is:
V = (6 in) (10 in) (4 in)
V = 240 in³
The total volume is 13,200 in³, so the number of bricks is:
13,200 in³ / 240 in³ = 55
You divide two numbers and the quotient is 2.5. What might the two numbers be? Show at least 5 solutions.
Answer:
5/2
Step-by-step explanation:
Which number belongs in the whole numbers area of the diagram?
A) −15
B) 1.5
C) 12
D) 7/8
Answer:
the answer is C) 12
Step-by-step explanation:
rawr
The adjoining figure is the figure of two pillars
mounted a squared pyramid on the top. Find the
total cost of tiling the pillars at the rate of
Rs 52 per square feet.
Answer:
[tex]Rs\ 4,296[/tex]
Step-by-step explanation:
step 1
Find out the lateral area of the pillars
we know that
The lateral area of a rectangular prism is equal to
[tex]LA=PH[/tex]
where
P is the perimeter of the base
H is the height of the prism
Determine the perimeter of the base
[tex]P=4(1)=4\ ft[/tex] ----> is a square base
[tex]H=6\ ft[/tex]
The lateral area is equal to
[tex]LA=4(6)=24\ ft^2[/tex]
Remember that the number of pillars is 2
so
[tex]LA=2(24)=48\ ft^2[/tex]
step 2
Find the cost of tiling the pillars at the rate of Rs 52 per square feet
Multiply the lateral area of the two pillars by the rate
so
[tex]48(52)=Rs\ 4,296[/tex]
a chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people
Answer:
[tex]\frac{1}{4} lbs/person[/tex]
Step-by-step explanation:
Here is the complete question: Find the rate of change for the situation:
A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.
Given: 1st situation, A chef cook 9 lbs chicken for 36 people.
2nd situation, chef cook 17 lbs chicken for 68 people.
∴ 1st situation, weight of chicken per person= [tex]\frac{9\ lbs}{36\ person} = \frac{9}{36}[/tex]
Weight of chicken per person= [tex]\frac{1}{4} lbs/ person[/tex]
2nd situation, weight of chicken per person= [tex]\frac{17\ lbs}{68\ person} = \frac{17}{68}[/tex]
Weight of chicken per person= [tex]\frac{1}{4} lbs/ person[/tex]
In both the situation chef cook same amount of chicken per person, which is [tex]\frac{1}{4} lbs/ person[/tex]
∴ Rate of change is [tex]\frac{1}{4} lbs/ person[/tex]
Answer:
i guess 1/4
Step-by-step explanation:
please help and add an explanation if you can <3
The value of [tex]x_2 = 1[/tex]
Solution:
Given that a approximate solution to the equation [tex]x^2 +6x - 2=0[/tex] can be calculated using the iterative formula shown below
[tex]x_{n+1} = \frac{2-(x_n)^3}{6}[/tex]
Also given that [tex]x_1 =2[/tex]
To find: value of [tex]x_2[/tex]
To find value of [tex]x_2[/tex] , substitute n = 1 in given iterative formula
[tex]x_{1+1} = \frac{2-(x_1)^3}{6}[/tex]
Solve the above expression by substituting [tex]x_1 = 2[/tex]
[tex]x_2 = \frac{2-(2)^3}{6}[/tex]
[tex]x_2 = \frac{2-8}{6}\\\\x_2 = \frac{-6}{6}\\\\x_2 = -1[/tex]
Thus value of [tex]x_2 = 1[/tex]
Sin Qua Corporation is a company listed on the stock exchange and issues corporate bonds. Which statement is most likely true?
Answer:
B. Investors will have to pay tax on the interest income received from the bonds.
Step-by-step explanation:
Investors will have to pay tax on the interest income received from the bonds because it is a taxable income.
The interest earned from a corporate bond is subject to taxation by both the federal and state governments.
Again, the maturity of the bond is determined at the time they are issued. Creditworthiness will only affect the bond price but not its maturity period.
There are twice as many boys as girls in Mr.Brown's first period Algebra class. the class is 24 students total. How many more boys than girls are in the class?
explanation needed.
HERE'S YOUR ANSWER:
Let number of girls be- x
and number of boys be- 2x(boys are 2 times NO. of girls)
therefore
x + 2x = 24
3x = 24
x = 24/3
x = 8
hence number of girls = 8
boys are 2 times more than girls = 16
HOPE IT HELPS...
A developer was buying land. He bought 4 acres at $1,863 per acre. He then spilt the land he purchased into 9 lots. How much should he sell each lot for just to break even.
answer: 828$
Step-by-step explanation:
step 1
Find out the total cost of the land
Multiply the total area in acres by $1,863 per acre
step 2
we know that
To determine the selling price of each lot to reach break even, divide the total cost by the number of lots.
What is measure of angle D?
pls provide explanation
Selecto two ratios that are equivalent to 3:12
Answer:
1 : 4 and 6 : 24
Step-by-step explanation:
We can generate equivalent ratios by dividing or multiplying each part of the ratio by the same value
Divide both parts by 3 , then
3 : 12 = 1 : 4 ← in simplest form
Multiply both parts by 2
3 : 12 = 6 : 24
How do you solve -3x+28=10
Answer: x = 6
Step-by-step explanation: To solve for x, we must first isolate the term containing x which in this problem is -3x.
Since 28 is being added to -3x, we subtract 28 from both sides of the equation to isolate the -3x. On the left, the +28 and -28 cancel out and on the right 10 - 28 is -18 so we have -3x = -18.
Now we can finish things off by just dividing both sides of the equation by -3. On the left the -3's cancel and we have x. On the right, -18 divided by -3 is 6 so we have x = 6 which is the solution to our equation.
Hi again, This is the last time I annoy you guys with this, but I really need help with my last question.
It would have a greater slope and perhaps start higher on the y axis.
Step-by-step explanation:
I assume you can choose your own numbers as long as they are higher than the current. This means the numbers on your y axis will change but not the numbers on your x axis because that determines the time. So let's change the y axis numbers from going by 20 and make them go by 25. You could technically keep the dots in the same place as long as you change the y axis numbers because you are still earning more money.
consider this scatter plot. you which line best fits the data
Answer:
line c
Step-by-step explanation: