9514 1404 393
Answer:
3(x)(4x -3)(2x -5)
Step-by-step explanation:
First of all, recognize that all coefficients are multiples of 3, and all terms have x as a common factor. This means your first factorization is ...
(3x)(8x^2 -26x +15)
Now, you can use the "X-method" or similar to factor the quadratic. Start by looking for factors of (8)(15) = 120 that have a total of -26. Both will be negative. Here is a list of the positive factor pairs.
120 = 1·120 = 2·60 = 3·40 = 4·30 = 5·24 = 6·20 = 8·15 = 10·12
The sums of these factor pairs are ...
121, 62, 43, 34, 29, 26, 23, 22
The pair with a sum of 26 is highlighted.
Using this information, you can complete the X-method diagram, or you can use these numbers to rewrite the quadratic x-term to have 2 parts:
8x^2 -20x -6x +15
Now, the quadratic can be factored by grouping:
= (8x^2 -20x) +(-6x +15)
= 4x(2x -5) +3(-2x +5)
Recognizing the sign difference between the parentheses contents, we can factor the quadratic to be ...
= (4x -3)(2x -5) . . . . . note the sign gets attached to the 3
So, the complete factorization of the original expression is ...
24x^3-78x^2+45x = 3(x)(4x -3)(2x -5)
Kendrick is planting a circular flower garden with a low fence around the border. He has 38 feet of fence. What is the radius of the largest garden he can make?
Answer: [tex]6.04\ ft[/tex]
Step-by-step explanation:
Given
The fence has a length of 38 ft i.e. it is the circumference of the circular flower
The circumference of the circle is [tex]2\pi r[/tex]
Insert the values
[tex]\Rightarrow 2\pir=38\\\\\Rightarrow 2\times \dfrac{22}{7}\times r=38\\\\\Rightarrow r=\dfrac{38\times 7}{2\times 22}\\\\\Rightarrow r=\dfrac{266}{44}\\\\\Rightarrow r=6.04\ ft[/tex]
The largest radius of the garden is [tex]6.04\ ft[/tex]
Which equation is represented by the number line?
Answer:
Equation 1: 6 + (-10) = -4
Step-by-step explanation:
1st segment starts at 0 and goes 6 units right so: +6
Second segment starts at 6 and goes 10 units left, so: -10
Finally the second segment lands on -4, so all together:
+6 + (-10) = -4 or 6 + (-10) = -4
Hope this helps!
A tugboat traveled -1.5 miles in 0.3 hours. What was its velocity?
Answer:
it is actually -5 because -1.5/0.3=-5
Step-by-step explanation:
hi, I need mo ney for food anything helps its been such a struggle since co vid hit.
Answer:
get a job....
jonn has a total of 50 coins in her purse The are either nickles or quarters The value of the ccoins is $7.10 Which system of equations can be used to determine the number of nickles ,n and quarters ,q, that jonna has in her purse .
Answer:
n + q = 50
.05n + .25q = 7.10
Step-by-step explanation:
total of 50 coins .... are either nickles or quarters
n + q = 50
value of the coins is $7.10
The value of each coin times the quantity is the value
.05n + .25q = 7.10
How to simplify an equation?
The process of simplify the equation is explained below.
The term equation is known as a mathematical statement that defines the equality between two expressions.
Here we have to define the process of simplifying the equation.
The first and foremost step is to remove parentheses and brackets by multiplying factors.
And then we have to use the exponent rule to remove grouping if the terms contain exponents.
Then we have to combine like terms by adding or subtracting coefficients.
Finally, we have to Combine the constants.
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PLEASE HELP?
Rewrite the function in factored form (show your work)
Standard form for the function is:
p(x)=-5x^+120x-315
Answer:
-5(x-21)(x-3)
Step-by-step explanation:
-5[tex]x^{2}[/tex] + 120x - 315 = -5([tex]x^{2}[/tex] - 24x + 63)
= -5([tex]x^{2}[/tex] - 3x - 21x + 63)
= -5[x(x-3) - 21(x-3)]
= -5[(x-21)(x-3)]
Prove that:
(1 + Tan²A) Cos²A = 1
Step-by-step explanation:
=(1+ sin^2 A/cos^2 A).cos^2 A
=[(cos^2 a+sin^2 a)/cos^2 a].cos^2 A
=[1/cos^2 a] . cos^2 a
=1
What is the discriminant of the quadratic equation 2x 5x^2 1?
The discriminant of the quadratic equation 2x + 5x² = 1 is 24.
The discriminant of a quadratic equation is the value calculated from the coefficients of the quadratic equation and it gives information about the nature of the roots of the equation. The discriminant can be used to determine the number and type of solutions/roots of the equation.
-If the discriminant is greater than zero, the equation has two distinct, real solutions (or roots).
-If the discriminant is equal to zero, the equation has one real solution (or root).
-If the discriminant is less than zero, the equation has no real solutions (or roots), only complex solutions.
The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.
Plug in the values and solve for the discriminant of the quadratic equation 2x + 5x² = 1.
b² - 4ac = (2)² - 4(5)(-1) = 24
Hence, the discriminant is 24.
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10. Jim estimates the width of his wall to be 7.5 feet. The actual wall measures 8.25 feet wide. What is
Jim's percent error?
Answer:
Below
Step-by-step explanation:
Error : (8.25 - 7.5)
% error : ( 8.25-7.5) / 8.25 * 100% = 9.1 %
Jim's percent error is 9.09%.
What is the percentage error?
The percentage error is given as the difference between the actual value and the estimated value divided by the actual value, multiplied by 100%.
The percentage error is a relative value that compares the actual value and the estimated value to explain any deviations.
Estimated width of wall = 7.5 feet
The actual width of the wall = 8.25 feet
The difference in estimate = (8.25 - 7.5) = 0.75 feet
Percentage Error = (0.75/8.25 x 100) = 9.09%
Thus, we can conclude that Jim made a percentage error of 9.09% in his estimate of the width of the wall.
betsy correctly answered 19 of 25 trivia questions. What percent of the questions did she answer correctly?
1.14 is the answer just do 19%=1.14
PLEASE HURRY!!!
Lorena and Karla are creating an art project in the shape of a right triangle. They have a 92 cm-long piece of wood, which is to be used for the hypotenuse. The two legs of the triangular support are of equal length. Approximately how many more centimeters of wood do they need to complete the support?
A. 65.1 cm
B. 130.1 cm
C. 260.2
D. 125.7
Approximately [tex]130.1[/tex] cm more centimeters of wood will need to complete the support.
What is right triangle ?Right triangle is a triangle in which one angle is of [tex]90^0[/tex] .
We have,
Hypotenuse [tex]=92[/tex] cm
Let,
Perpendicular [tex]= x[/tex] cm
Base [tex]=x[/tex] cm
So,
Using the Pythagoras theorem,
[tex]H^2=P^2+B^2[/tex]
So,
[tex]92^2=x^2+x^2[/tex]
[tex]92^2=2x^2[/tex]
⇒
[tex]2x^2 = 8464[/tex]
[tex]x^2 = 4232[/tex]
⇒[tex]x=65.05[/tex]
So,
Perpendicular [tex]= 65.05[/tex] cm
Base [tex]=65.05[/tex] cm
So,
The required wood to complete support [tex]=65.05+65.05=130.1[/tex] cm
Hence, we can say that approximately [tex]130.1[/tex] cm more centimeters of wood will need to complete the support.
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The diagram shows an isosceles triangle. All the measurements are in cm, work out the perimeter of the triangle.
Write the ratio of the first measurement to the second measurement. Compare in inches.
Answer:
when the ratio of the first measurment is already there, get the pot, put it in place and chec the correct ratio, the slope should help the gaurdian. so in that case, the answer is 75inch
You earn $35 for washing 7 cars. How much do you earn for washing 4 cars?
You earn $
for washing 4 cars.
3 divided by 3/4 IN FRACTION FORM! HELP ASAP
Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. X = 5 sqrt( y) text(, ) x = 0 text(, ) y = 4 Find the volume V of this solid. V
Answer:
V = 200 π
Step-by-step explanation:
x = 5√y , x = 0 , y = 4
Determine the volume of the solid V
when x = 0 y = 0
we can calculate the volume of the solid by applying the washer method
V = π ₀⁴∫ [ 0 + ( 5√y )^2 ] dy
= π ₀⁴∫ [ 0 + ( 25(y) ) ] dy
V = π [ 0 + 25/2 ( y^2 ) ] ⁴₀
V = π [ 25/2 ( 16 ) ]
= 200 π
What is the domain of the function f/x )= log?
The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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3. Which of the following numbers is divided by 5?
a) 1234 b) 3457 c) 4750 d) 3478
Answer:
c) 4750
Step-by-step explanation:
Take a calculator and divide it or long division. You get 950.
Answer:
c) 4750
Step-by-step explanation:
c) 4750 is the answer of your question .
hope it is helpful to you
a new health drink has 150% of the recommended daily allowance. there is a certain vitamin this vitamin is 40 mg. How many milligrams of the vitamin are in a drink?
The numbers of milligrams of the vitamin that are in a drink is 60 milligrams.
What is the vitamin about?The recommended daily allowance (RDA) for the vitamin is 40 mg. A new health drink has 150% of the RDA.
To find out how many milligrams of the vitamin are in a drink, you can use the following formula:
(RDA) x (percentage/100) = milligrams in a drink
So,
(40mg) x (150/100)
= 60mg
Therefore, there are 60 milligrams of the vitamin in a drink.
Note that the RDA of vitamins can vary depending on age, gender, and other factors, so always consult a doctor or nutritionist before starting to consume any new supplement.
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Blue's Berry Farm charges Percy a total of $24.75 for entrance and 2.5 kilograms of strawberries. The entrance fee is $6, and the price for each kilogram of strawberries is constant.
Answer:
$7.50 if the question is how much in a kilogram of strawberries you did not specify.
Step-by-step explanation:
24.75-6=2.5*x
18.75=2.5*x
7.5=x
Answer:
7.5 for 1 kg of strawberries
Step-by-step explanation:
I'm not sure what to solve, but I assumed that you wanted to know the unit price.
Of the 50 members of a staff, 40 percent worked the day shift and the remaining 60 percent worked the night shift in a given week. Of the staff members, 80 percent prefer working the day shift and the remaining 20 percent prefer working the night shift. What is the minimum number of staff members who failed to receive his or her preference of shift that week
The minimal number of employees who did not get their preferred shift that week was 20.
Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.
But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.
We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.
But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.
Thus, 20 is the minimum number of staff members who failed to receive her preference of shift that week.
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65 people were asked on the activities they engage in during their free time. The results showed that 23 visit national parks, 26 engage in cycling while 22 engage in swimming. Furthermore 9 engage in swimming and visit national parks, 9 engage in swimming only while 11 visit national parks only. How many engage in a) Swimming and cycling b) Cycling only c) Neither swimming nor visiting national parks nor cycling
Answer:
a)=57
b)=26
C)= 35
Step-by-step explanation:
there is 100 people recorded when they only wanted 65 so the 35 extra answers are not recorded.
How do you solve this? 11t-t^2=30
Answer:
t = 5, 6
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{11t-t^2=30}[/tex]
First, arrange the expression in the standard quadratic form ax² + bx + c = 0
[tex]\displaystyle{t^2-11t+30=0}[/tex]
Then factor the expression, find two numbers that add up which result in -11 and multiply which result in 30 - that two numbers are -6 and -5
[tex]\displaystyle{(t-6)(t-5)=0}[/tex]
Solve like a linear equation
[tex]\displaystyle{t=5,6}[/tex]
Therefore, the solutions to the equation are t = 5, 6
Answer:
The solution set is {5, 6}.
Step-by-step explanation:
11t-t^2=30
t^2 - 11t + 30 = 0
(t - 5)(t - 6) = 0
t = 5, 6.
Write an algebraic expression that represents five less than the product of a number and six
Answer:
6n-5
Step-by-step explanation:
let 'n' equal 'a number'
the equation above means you are multiplying 6 and that number, then reducing it by 5
This dot plot is not symmetric, and the data set has three extreme values.
Which of these measures is the best measure of variability for the dot plot? A. Interquartile range (IQR) B. Mean C. Median O D. Mean absolute deviation (MAD)
Answer:interquartile range IQR
Step-by-step explanation:ApE x
Answer:
ANSWER IS IQR
Step-by-step explanation:
DID THE TEST
Find the percent of change. Round to the nearest tenth, if necessary.
During the winter, the grill was marked at $85. In June, the price was changed to $110. 50.
PLEASE THIS IS URGENT
During the winter, the grill was marked at $85. In June, the price was changed to $110. 50. So, 23.08% is the change in percentage.
What is percentage?When the denominator is 100, percentages are really just fractions. We place the percent sign (%) next to the number to indicate that the number is a percentage.
Comparing two amounts while re basing the second amount to 100 is the simplest way to use percentages. The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin term made its way into English. It was later abbreviated to %.
Given that,
the grill was marked at $85
the price was changed to $110. 50.
Now, percentage change:
= [{(110. 50 - 85)/110.50} × 100]
= (0.2308 × 100)
= 23.08%
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One of the roots of the equation x^2-5x+q=0 is 2. Find the other root and the value of the coefficient q.
The value of q in the given equation x²- 5x + q = 0 will be 4.
What is a polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.
given an equation x²- 5x + q = 0 and the question states that it has a root that is equal to 2
Since 2 is the root of this quadratic equation it will satisfy the equation
Substituting the values in the equation
4 - 5*2 + q = 0
q = 6
Equation will be
x²- 5x + 6 = 0
The root of the given equation using the fraction method
x²- 3x - 2x + 6= 0
(x -2)(x - 3) = 0
The root of the given equation are 2 and 3
Therefore, In the given equation x²- 5x + q = 0 the value of q will be 4.
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Solve the proportion below. 7/x = 19/114 x=____
A. 8
B. 4
C. 28
D. 24
write an equation in pint-slope form, slope-intercept, and standard form
Slope: -5 (-3,-7)
(-6,10), (-4,18)
(-4,9), (1,14)
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use (-6,10), (-4,18)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{18}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{18}-\stackrel{y1}{10}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{8}{-4 +6} \implies \cfrac{ 8 }{ 2 } \implies 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y -10 = 4 ( x +6) \end{array}} \\\\\\ y-10=4x+24\implies -4x+y=34\implies \stackrel{standard~form}{{\Large \begin{array}{llll} 4x-y=-34 \end{array}}}[/tex]