Jordan had $10.00 if each drawing pen costs $1.49, how many can he buy
Identify all the real roots of 4x^4+31x^3-4x^2-89x+22=0
The real roots of a function are the rational and the irrational roots of the function
The real roots are: [tex]\mathbf{x = -2}[/tex], [tex]\mathbf{x = \frac 14}[/tex], [tex]\mathbf{x = -3 - 2\sqrt{5}}[/tex] and [tex]\mathbf{x = -3 + 2\sqrt{5}}[/tex]
The equation is given as:
[tex]\mathbf{ 4x^4+31x^3-4x^2-89x+22=0}[/tex]
Factorize
[tex]\mathbf{(x + 2) (4 x - 1) (x^2 + 6 x - 11) = 0}[/tex]
Split
[tex]\mathbf{x + 2 = 0\ or\ 4 x - 1 = 0 \ or\ x^2 + 6 x - 11 = 0}[/tex]
Solve for x
[tex]\mathbf{x = -2\ or\ x = \frac 14 \ or\ x^2 + 6 x - 11 = 0}[/tex]
Solve
[tex]\mathbf{x^2 + 6 x - 11 = 0}[/tex] using the following quadratic formula:
[tex]\mathbf{x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
So, we have:
[tex]\mathbf{x = \frac{-6 \pm \sqrt{6^2 - 4 \times 1 \times -11}}{2 \times 1}}[/tex]
[tex]\mathbf{x = \frac{-6 \pm \sqrt{80}}{2}}[/tex]
[tex]\mathbf{x = \frac{-6 \pm 4\sqrt{5}}{2}}[/tex]
[tex]\mathbf{x = -3 \pm 2\sqrt{5}}[/tex]
Hence, the real roots are:
[tex]\mathbf{x = -2}[/tex], [tex]\mathbf{x = \frac 14}[/tex], [tex]\mathbf{x = -3 - 2\sqrt{5}}[/tex] and [tex]\mathbf{x = -3 + 2\sqrt{5}}[/tex]
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Brent tosses a quarter 4 times and 3 times it comes up heads. the probability of heads is:
A basketball player practices free throws by shooting 50 free throws a day. she records the number of free throws made each day. her number of free throws made is normally distributed with a mean = 34 free throws and standard deviation = 5 free throws. using appropriate rule learned in lesson 10, approximately what percent of the days does she make less than 29 free throws?
Answer: 46%
Step-by-step explanation:
What is the best measure of the center for the data set: 2,2,2,4,4,5,5,5,7,7,15,17
Please completely factor the following expression. e. 3x^2+5xy-2y^2
A 500500-gallon tank initially contains 200200 gallons of brine containing 100100 pounds of dissolved salt. brine containing 11 pounds of salt per gallon flows into the tank at the rate of 44 gallons per minute, and the well-stirred mixture flows out of the tank at the rate of 11 gallon per minute. set up a differential equation for the amount of salt a(t)a(t) in the tank at time tt. how much salt is in the tank when it is full? (round your answer to the 2 decimal places).
the slope of the line passing through (-9,-6) and (-15,y) is 2/3. what is the value of y
Sir, please show your work
A sample of cigarette smoke contains 2.09% carbon monoxide. the u.s. national ambient air quality standard for co in a 1−hr period is 35 ppm. how many times greater than this standard is the co concentration in cigarette smoke?
What is the value of z in the equation 5z − 9 = 36?
4
5
6
9
In this question, you have to solve the equation.
5z – 9 = 36
You transpose the 9 to other side so the equation would look like this:
5z = 36 + 9
5z = 45
Divide 5 in both sides to solve the value of z:
z = 9
How many pounds must a sand bag weigh to test if a safety net can absorb the proper amount of force?
To test if a safety net can absorb the proper amount of force, you would need to determine the weight of the sand bag. This can be done by using the concept of Newton's second law and calculating the mass of the sand bag using the equation F = mg, where F is the force required and g is the acceleration due to gravity.
Explanation:To test if a safety net can absorb the proper amount of force, you would need to determine the weight of the sand bag. This can be done by using the concept of Newton's second law, which states that force equals mass times acceleration. You would first need to calculate the acceleration of the sand bag using the formula F = ma, where F is the force required to be absorbed by the safety net and a is the acceleration. Once you know the required force and acceleration, you can calculate the mass of the sand bag using the equation F = mg, where g is the acceleration due to gravity (approximately 9.8 m/s²).
For example, if the required force is 500 N and the acceleration is 5 m/s², you would calculate the mass of the sand bag as follows:
F = ma
500 N = m * 5 m/s²
m = 500 N / 5 m/s²
m = 100 kg
Therefore, the sand bag must weigh 100 kilograms (or approximately 220 pounds) to test if the safety net can absorb the proper amount of force.
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(1/3+9) x ( 8-3) tell me the steps help
Read the statement, and identify the expressions that are equivalent. the product of a number minus 17 and 5
Answer:
The expressions equivalent to 'the product of a number minus 17 and 5' are (n - 17) x 5 and 5(n - 17), where n is the unknown number. These cannot be simplified further without additional information.
Step-by-step explanation:
The statement 'the product of a number minus 17 and 5' can be translated into an algebraic expression. This expression would look like (n - 17) × 5 or 5(n - 17), where n represents the unknown number. Both expressions are equivalent and represent the same mathematical operation.
When simplifying algebraic expressions, it is important to eliminate terms wherever possible to get a more straightforward expression. However, in this case, since we don't have a specific value for n, we cannot simplify the expression further without additional information.
Always remember to check your answer to ensure that the expression makes sense and is reasonable within the context of the problem.
Kieran is making a birthday card with construction paper. He wants to cut a circle out of a square piece of construction paper. The circle will have a radius of 6 inches. In square inches, what is the area of the smallest piece of construction paper Kieran could use?
Chin woo brought a home for $160,000. He put down 20%. The mortgage is at 8 1/2% for 30 years his monthly payment is.
in the following figure find a deg,2adeg and bdeg
What is the sum of (–2.1x + 3.7) and (5 + 4.9x)?
-7.0x + 8.7
-2.8x + 8.7
2.8x + 8.7
7.0x + 8.7
Answer
C.
2.8x + 8.7
Prudence has 20 pairs of gold earrings and 4 pairs of silver earrings in a drawer in her jewelry box. If she randomly pulls six pairs of earrings out of the drawer to take with her on a trip, which of the following is the best prediction of the number of pairs of earrings that will be gold?
The best prediction of the number of gold earrings Prudence will pull out is 5 pairs.
Explanation:To predict the number of pairs of gold earrings Prudence will randomly pull out of her drawer, we need to find the probability of selecting gold earrings from the total number of options.
Prudence has 20 pairs of gold earrings and 4 pairs of silver earrings, making a total of 24 pairs of earrings in her drawer.
The probability of selecting a gold earring is given by:
Number of gold earrings / Total number of earrings = 20 / 24= 5 / 6.
Therefore, the best prediction of the number of pairs of earrings that will be gold is 5 pairs.
Given the exponential function A(x)=P(1+r)^x, what value for r will make the function a decay function
Answer:
To make the function a decay function the rate of change in the function A(x) is r<0.
Step-by-step explanation:
Given : The exponential function [tex]A(x)=P(1+r)^x[/tex]
To find : What value for r will make the function a decay function?
Solution :
The exponential function is [tex]A(x)=P(1+r)^x[/tex],
where, P is the initial value
and r is the rate of change
The condition of rate of change is
1) The function is an exponential growth if their is positive rate of change i.e r>0.
2) The function is an exponential decay if their is negative rate of change i.e. r<0.
Therefore, To make the function a decay function the rate of change in the function A(x) is r<0.
how many times does 5 go in to 47
Nicholas buys 3/8 pound of cheese. He puts the same amount of cheese on 3 sandwiches. How much cheese does Nicholas put on each sandwich?
What is the mean of the data set?
10, 15, 14, 8, 18, 11, 12, 12, 10, 10, 17, 16
12.00
12.25
12.75
15.50
Answer:
the answer is 12.75
Step-by-step explanation:
btw if you need the median is 12 :>
In a sale Gameboys are reduced by two-fifths. What is the sale price if the original price was $50.00?
(PS: Please write how you got the answer)
Megan buys 3 bracelets and 3 necklaces. Each bracelet costs 5. Megan pays on 40 and gets 4 change. what is the cost of one necklace?
Find the specified vector or scalar.
u = -4i + 1j and v = 4i + 1j; Find ||u+v||
a. sqrt32
b. 2
c. 5
d. 8
solving radical equations
check for extraneous solutions
[tex] \sqrt{2x + 30} = x + 3[/tex]
Find the common ratio of the sequence
-125,-25,-5,-1.....
1/5
5
-100
100
Answer:
Step-by-step explanation:
common ratio of a Geometric series can be found by dividing the second term by first term of the series .
we are given that first term a1= -125 and second term a2 =-25
so the common ratio must be
[tex]r=\frac{a2}{a1}[/tex]
[tex]r=\frac{-25}{-125}[/tex]
[tex]r= \frac{1}{5}[/tex]
Hence the common ratio is 1/5.
Divide. 3.2 ÷ 0.8 help me e pleaseeeeeeeeeeee !!!!!!
Mr Thomas shoveled 12 1/2 yards of sand in 2 1/2 hours . At that rate how many yards did he shovel in one hour ?
Jack and Jill are 20m apart. Jack sees the top of the building at 30 degrees and Jill sees the top of the building at 40 degrees. What is the height of the building
The height of the building seen by both Jack and Jill is 37m to the nearest whole metre.
Let the distance of Jill from the base of the building be represented with x while the height of the building be y so that by observation we get two right triangles with same opposite sides to the angles formed by Jack and Jill. We can solve for x and y using tangent of the angles as follows:
tan 40 = y/x {opposite/adjacent}
y = xtan40 {cross multiplication}
tan 30 = y/(20 + x)
y = tan30(20 + x)
Thus;
xtan40 = tan30(20 + x)
xtan40 = 20tan30 + xtan30
xtan40 - xtan30 = 20tan30 {collect like terms}
x(tan40 - tan30) = 20tan30
x = 20tan30/(tan40 - tan30)
x = 44.1230m
Putting the 44.1230m for x in y = xtan40 we have;
y = 44.1230m × tan40
y = 37.0236m.
Therefore, the height of the building approximately to the nearest whole metre is 37.