Answer:
x = - [tex]\frac{7}{2}[/tex], x = - 3
Step-by-step explanation:
Given
2x² + 13x = - 21 ( add 21 to both sides )
2x² + 13x + 21 = 0 ← in standard form
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 21 = 42 and sum = + 13
The factors are + 6 and + 7
Use these factors to split the x- term
2x² + 6x + 7x + 21 = 0 ( factor the first/second and third/fourth terms )
2x(x + 3) + 7(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(2x + 7) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x + 7 = 0 ⇒ 2x = - 7 ⇒ x = - [tex]\frac{7}{2}[/tex]
what is the answer to this system of equations pls also include explanation
-2x+5y = 75
x+5y = 45
Answer:
x=-10
Step-by-step explanation:
I explained the answer to your question in the photo
Evaluate f (x) = 3x – 5 when x = -1, x = 0, and x = 3.
When x = -1, f (x) = –2 , when r = 0, f (x) = -5), and when x = 3, f (x) = 4).
f(x) = 3x − 5 when x=−1, x=0, x=3
Answer:
-8, -2, 4
Step-by-step explanation:
1. Insert -1, 0, and 3 into x
2. Solve
Replace x with -1: f(-1) = 3(-1) − 5
Multiply 3(-1): f(-1) = -3 − 5
Subtract by 5: f(-1) = -8
The answer is -8
Now do this for the rest of the problems:
f(0) = 3(0) − 5 when x=−1, x=0, and x=3
-2 is the 2nd answer
f(3) = 3(3) − 5 when x=−1, x=0, and x=3
4 is the 3rd answer
This is my first answer, so I hope I explained it well!
Mark is building two separate pig-pens. The width of pig-pen A is w. The length of pig-pen A is 4 feet longer than its width. The width of pig-pen B is 5 feet less than the width of pig-pen A. The length of pig-pen B is 2 times its own width. If the both pig-pens have the same perimeter, then find the dimensions of each pig-pen.
Answer:
The width of pen A is 7 feet,
The Length of Pen A is 11 feet,
The width of Pen B is 6 feet,
The Length of Pen B is 12 feet
Step-by-step explanation:
The width of pen A is 7 feet,
The Length of Pen A is 7 + 4 = 11 feet,
The width of Pen B is 7+4-5 = 6 feet,
The Length of Pen B is 2*(7+4-5) = 12 feet
[tex]w+w+w+w+4+4=(w+4-5)+(w+4-5) +2*(w+4-5)+2*(w+4-5)\\4w+8=6w-6\\14=2w\\w=7\\[/tex]
graph the linear function w(x) =3/5x+2
Answer:
Use Desmos.com. It is a site that can graph basically anything you want.
Step-by-step explanation:
PLEASE HELP PLEASE!!
A circular garden has a diameter of 4 m. What is the area of the garden? Use 3.14 for TT.
Two more than three times a number is 65. Find the number.
The number is
3x + 7 = 23 - 5x
I need sum help plz!!
Answer:
x=2
Hope this helps! :)
3x+5x=8x
23-7=16
16÷8
Answer:
x = 2
Step-by-step explanation:
3x + 7 = 23 - 5x
3x + 5x = 23 - 7
8x = 16
x = 2
It is known that 5% of flashlight bulbs manufactured by a certain company are defective. a. Use the normal approximation to estimate the probability that, out of a random sample of 600 lightbulbs, at least 25 are defective. (5 points) b. Use the normal approximation to estimate the probability that, out of a random sample of 600 lightbulbs, fewer than 20 are defective. (5 points)
Using the normal approximation to the binomial, the probabilities are given by:
a) 0.8485 = 84.85%.
b) 0.0244 = 2.44%.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem, we have that:
There are 600 bulbs, hence n = 600.5% are defective, hence p = 0.05.The mean and the standard deviation of the approximation are given, respectively, by:
[tex]\mu = np = 600(0.05) = 30[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{600(0.05)(0.95)} = 5.3385[/tex]
Item a:
Using continuity correction, the probability is P(X > 24.5), which is one subtracted by the p-value of Z when X = 24.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24.5 - 30}{5.3385}[/tex]
[tex]Z = -1.03[/tex]
[tex]Z = -1.03[/tex] has a p-value of 0.1515.
1 - 0.1515 = 0.8485.
0.8485 = 84.85% probability.
Item b:
This probability is P(X < 19.5), which is the p-value of Z when X = 19.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19.5 - 30}{5.3385}[/tex]
[tex]Z = -1.97[/tex]
[tex]Z = -1.97[/tex] has a p-value of 0.0244.
The probability is of 0.0244 = 2.44%.
More can be learned about the normal distribution at https://brainly.com/question/24663213
Solve the system.
y = -6x - 14
2)
5x - 3y = 19
Answer:
x=-1
Step-by-step explanation:
Answer the following question below
Answer:
11/6
Step-by-step explanation:
2x/3 = 1/2
Cross multiply, get 4x = 3, x = 3/4
3y/4 = 3/2
Cross multiply, get 6y = 12, y = 2
x + y = 3/4 + 2 = 11/4
xy = 3/4 * 2 = 3/2
(x + y)/(xy) = (11/4)/(3/2) = 11/4 * 2/3 = 22/12 = 11/6
Sam is putting money into a checking account. Let represent the total amount of money in the account (in dollars). Let represent the number of weeks Sam has been adding money. Suppose that and are related by the equation .
Answer:
-2
Step-by-step explanation:
(8) fx=x2-2x-2
8(2)-2(8)-2
16-16-2
-2
The overall pass rate for law school graduates taking the Maryland bar exam has been reported as 76%. Assume that a certain Maryland law school has had 400 of its most recent graduates take the Maryland bar exam, but only 60% passed. When asked about these results, the dean of this university’s law school claims his graduates are just as good as others who have taken the Maryland bar exam, and the low pass rate for the recent graduates was just "one of those statistical fluctuations that happen all the time." If this university’s overall pass rate were really 76%, what would be the probability of a simple random sample of 400 having a pass rate of 60% or less
Answer:
The probability is [tex]P(X \le 0.60) = 0.000 [/tex]
Step-by-step explanation:
From the question we are told that
The overall pass rate is [tex]R = 76\% = 0.76[/tex]
The sample size is n = 400
The percentage that passed is [tex]k = 60\% = 0.60[/tex]
Generally the standard error is mathematically represented as
[tex]\sigma _{\= x } = \sqrt{\frac{R (1 -R)}{n} }[/tex]
=> [tex]\sigma _{\= x } = \sqrt{\frac{0.76 (1 -0.76)}{400} }[/tex]
=> [tex]\sigma _{\= x } = 0.0214 [/tex]
Generally the probability of a simple random sample of 400 having a pass rate of 60% or less is mathematically represented as
[tex]P(X \le 0.60) = P(\frac{X - R}{ \sigma_{\= x}} \le \frac{0.60 - 0.76}{0.0214} )[/tex]
=> [tex]P(X \le 0.60) = P(Z \le -7.48 )[/tex]
Generally from the z-table
[tex]P(Z \le -7.48 ) = 0.000[/tex]
So
[tex]P(X \le 0.60) = 0.000 [/tex]
Bryan drives 70 mph down the interstate write an equation to represent the distance y if he drives x hours
70
(
mi
hr
)
=
70
(
mi
hr
)
y
=
70
(
mi
hr
)
x
hr
=
70
(
mi
hr
)
Naomi's fish is 40 millimeters long. Her guinea pig is 25 centimeters long. How much longer is he guinea pig than her fish.
Answer:
The guinea pig is 210 millimeters longer than the fish.
Step-by-step explanation:
Match each complex number with its equivalent expression.
i
-1
1
-i
i^48
i^223
i^113
i^82
Remember that i = √(-1), so that
• i ² = -1,
• i ³ = i x i ² = i x (-1) = -i
• i ⁴ = i x i ³ = i x (-i) = -i ² = -(-1) = 1
Multiplying by i again gives i ⁵ = i and the cycle starts over.
The main observation to make here is that raising i to any multiple of 4 returns 1. So,
i ⁴⁸ = (i ⁴)¹² = 1¹² = 1
i ²²³ = i ²²⁰⁺³ = i ²²⁰ x i ³ = (i ⁴)⁵⁵ x i ³ = 1⁵⁵ x (-i) = -i
i ¹¹³ = i ¹¹²⁺¹ = i ¹¹² x i = (i ⁴)²⁸ x i = 1²⁸ x i = i
i ⁸² = i ⁸⁰⁺² = i ⁸⁰ x i ² = (i ⁴)²⁰ x i ² = 1²⁰ x (-1) = -1
i^48 = 1
i^223 = -i
i^113 = i
i^82 = -1
how would you find the equation if each copy of a book costs 18$ and shipping is 9$ per order
Answer:
18x + 9
Step-by-step explanation:
A snail moved 8mm in one minute. How many centimeters did it move?
m dm cm mm
0 8
8 mm = 0,8 cm
Step-by-step explanation:
48 cm
Find the value of xxx, yyy, and zzz in the parallelogram below.
Answer:
x = 67; y = 121; z = 65
Step-by-step explanation:
x + 1 + 112 = 180
x + 113 = 180
x = 67
y - 9 = 112
y = 121
z + 3 + 112 = 180
z + 115 = 180
z = 65
Find the measure of the missing angle.
Answer:
36 degrees
Step-by-step explanation:
The whole shape is 90 degrees.
90 - 54 = 36
36 degrees
Answer:
36*
Step-by-step explanation:
a right angle is 90* and so you do
90-54=36
meaning your missing angle is 36*
I need help with this pls
Answer:
Step-by-step explanation:
1) Parallelogram ABCD, E is the midpoint of [tex]\overline{DC}[/tex], F is the midpoint of [tex]\overline{AB}[/tex] (given)
2) [tex]DE=\frac{1}{2}DC, BF=\frac{1}{2}AB[/tex] (When a segment is bisected, each part is half the length of the whole segment)
3) [tex]\overline{DC} \cong \overline{AB}[/tex] (opposite sides of a parallelogram are congruent)
4) [tex]DC=AB[/tex] (congruent segments have equal measure)
5) [tex]DE=BF[/tex] (substitution)
6) [tex]\overline{DE} \cong \overline{BF}[/tex] (segments with equal measure are congruent)
7) [tex]\angle D \cong \angle B[/tex] (opposite angles of a parallelogram are congruent)
8) [tex]\overline{AD} \cong \overline{BC}[/tex] (opposite sides of a parallelogram are congruent)
9) [tex]\triangle ADE \cong \triangle CBF[/tex] (SAS)
10) [tex]\overline{AE} \cong \overline{CF}[/tex] (CPCTC)
Can anyone help I would really appreciate it I’m failing everything and need a boost
Answer:
2,870 and 30
Step-by-step explanation:
Math homework
Feet=9yards
Answer:
27 feet
Step-by-step explanation:
We know that 3 feet = 1 yard. So, multiply 9 by 3 and you get 27 feet. Hope this helps!
Pls help: √5 multiplied by √245
I believe it is 35!
I hope this helps you, and don't forget to give this answer brainliest if it really helped!
one shirt and one pair of pants costs $50.00. three shirts and 2 pairs of pants cost $120. how much is a shirt?
one shirt is for $25 so multiple that by 3 and get $75
Given that n is a positive number, write, in a symbolic statement, ‘the square of a positive number decreased by 10 is 6’
Answer:
n² -10 = 6
Step-by-step explanation:
If n represents a positive number, then "the square of a positive number" is represented by n². When that value is decreased by 10, it becomes ...
n² -10
and if that value is 6, the math expression is ...
n² -10 = 6
__
Additional comment
Increasing the value by 10 gives ...
n² = 16
and taking the positive square root gives us the value of the number:
n = √16 = 4
in this question we have to multiply 4 with 4 then we have to minus 16 with 10 we get the answer 6
so, first we have to multiply the 4 with 4= 4 × 4 = 16
then, we have to minus 16 with 10 we get :-= 16 - 10
we get :-= 6
in this question we have get 16 because √16 is the square root of 4help fastttt!!!!! brainliest to first
Answer:
i believe it's actually the fourth option: lines e and f are parallel bc their same side exterior angles are supplementary
Step-by-step explanation:
its part of a theorem you learn, don't remember exactly (haven't taken geo in like 2 years lol)
Answer:
i believe it shud be c
Step-by-step explanation: it really doesn't proof that for a and be the corresponding angles are congruent..
Hope this is correct!!
0.45 divided by 18 please help it is due today
Answer:
answer is 0.025
Step-by-step explanation:
answer is 0.025
Solve. . m - 15 - 20 m =
After changing its format, a radio station lost 34% of its listeners. If there were an estimated 83,000 listeners originally, how many listeners does the radio station have now
Solve this equation
(3m⁴)²
Answer:
9m⁸
Step-by-step explanation:
3^2=9
(m⁴)² = m⁸
9*m⁸