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a) Factorise x² + 5x-14
b) Solve x² + 5x-14= 0
Answers
After solving the quadratic equation, the roots are (x - 2) and (x + 7).
What is a Quadratic function?To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.
The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.
As per the given equation in the question,
x² + 5x - 14 = 0
b² - 4ac
5² - 4(1)(-14)
25 + 56 = 81
Use the equation,
-b ± \(\sqrt{b^2-4ac}/2a\)
Substitute the values,
(-5 + 9)/2 = 2 and,
(-5 - 9)/2 = -7
Therefore, the root will be (x - 2) and (x + 7).
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Related Questions
Evaluate the function E(z)=(z+1)^2 for the following values of z.
a. E(a)
b. E(a + h), h not equal to 0
Use a & b to evaluate the following, for h not equal to 0
c. E(a + h) - E(a) / h =
Answers
Answer:
a. E(a) = (a+1)²
b. E(a + h) = (a+h+1)²
c. E(a + h) - E(a) / h = (a+h+1)²- (a+1)²/h
Step-by-step explanation:
E(z)=(z+1)²
E(a) = (a+1)²
E(a + h) = (a+h+1)²
E(a + h) - E(a) / h = (a+h+1)²- (a+1)²/h
What is the solution to the equation?
5(n - 1/10) = 1/2
Answers
Answer:
i have made it in picture hope it help
I really need Help if u give right answer u get brainliest
Answers
Answer:
Step-by-step explanation:
List five numbers with eight in the ones place
Answers
Answer: 18, 28, 38, 48, 58
Step-by-step explanation:
Answer:
18, 28, 38, 48, 58
Step-by-step explanation:
I think this is pretty self explanatory.
anwser it pls aaaaaaaassaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
Answer:
Step-by-step explanation:
Volume = Bh
Turn the shape so the trapezoid is on the bottom/base
h=18 for overall shape
B = area of base, trapezoid
B = 1/2 (b₁ + b₂) h
b₁ = 11
b₂ = 25
h = 24 for trapezoid
B = 1/2 (11 + 25)(24)
B = 432
V = Bh
V = (432)(18)
V= 7776 in³
Which situation could be represented by -15?
O Having 15 fewer people go to a concert
Throwing a ball 15 more times than another player
Sleeping 15 more minutes
Reading 15 more books one year than in the previous year
Answers
the area of a rectangular field is 5229 m2 if the length of the field is 83 m what’s the width
Answers
Answer:
63
Step-by-step explanation:
trigonometric identities
Answers
1/tan x = cot x
Cot x + tan x = 1/ sin x cos x
The answer is D.
Geometric sequences
*Each number is 4 less than 3 times the previous numbers*
A. Starting with the number 10, build a sequence of 5 numbers.
B. Starting with the number 1, build a sequence of 5 numbers.
C. Select a different starting number and build a sequence of 5 numbers.
Answers
Formula for the term of a geometric sequences has been defined as,
"Each number is 4 less than 3 times the previous numbers"
Therefore, recursive formula will be,
\(T_n=3(T_{n-1})-4\)
Now we will use this formula to build the sequence,
A). If \(T_1=10\),
Then \(T_2=3(10)-4=26\)
\(T_3=3(26)-4=74\)
\(T_4=3(74)-4=218\)
\(T_5=3(218)-4=650\)
Therefore, the sequence will be,
\(10,26,74,218,650\)
B). If \(T_1=1\),
Then \(T_2=3(1)-4=-1\)
\(T_3=3(-1)-4=-7\)
\(T_4=3(-7)-4=-25\)
\(T_5=3(-25)-4=-79\)
Therefore, the sequence will be,
\(1,-1,-7,-25,-79\)
C). If, \(T_1=5\),
Then, \(T_2=3(5)-4=11\)
\(T_3=3(11)-4=29\)
\(T_4=3(29)-4=83\)
\(T_5=3(83)-4=245\)
Therefore, the sequence will be,
\(5,11,29,83,245\)
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Eastern Aviation Equipment pays Donald Simmons a $1760 monthly salary plus a 12% commission on merchandise he sells each month. Assume Donald's sales were $90,800 for last month. Calculate the following amounts:
1. Amount of Commission:
2. Gross Pay:
Answers
The equation that represent the gross pay is y = 0.12x + 1760. The commission was $10896 and gross pay was $12656
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
Let y represent the gross pay for x total sales.
Donald Simmons a $1760 monthly salary plus a 12% commission on merchandise he sells each month, hence:
y = 1760 + 12% of x
y = 0.12x + 1760
Donald's sales were $90,800 for last month. Hence:
a) Commission = 0.12 * $90800 = $10896
b) Gross pay:
y = 10896 + 1760 = $12656
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What is the best estimate for 59.87 - 42.1? A. 18 B. 22 C. 25 D. 30
Answers
Answer:
do you still need help on tge questio ?
The average daily high temperature in Madrid peaks at 92°F in the summer and drops as low as 33°F in the winter. The temperature can be modeled by T (d) = 29.5 cosine (StartFraction 2 pi Over 365 EndFraction (d minus 204) ) + 62.5, where d represents the day number of the year (January 1 is 1, January 2 is 2, and so on). How many days during the year is the high temperature expected to be 75°F or above?
Answers
Answer:
C) 131
Step-by-step explanation:
It wants us to find how many days out of the year that the temperature goes above 75 degrees Fahrenheit.
To do this, I set the y value equal to 75 (it should be \(y\geq 75\), but I thought it'd be easier to see this way).
From there, you can easily visualize the days that were above and 75 degrees.
It's just simple subtraction from here:
269-138=131
Idk why I chose to help you guys when I have a bunch of work to do, but it let me get my mind off school work for a brief amount of time. I hope this still helps you guys even after two weeks. <3
Answer:
270
Step-by-step explanation:
Edge 2023, just took the test :3
The figure below shows the distance between two cities on a map. The scale of the map is 1 }8 inch to 12 miles.
Answers
The actual distance between the two cities is 432 miles.
The figure shows a map of two cities, with a distance between them measured at 4.5 inches.
The scale of the map is given as 1/8 inch to 12 miles.
This means that 1/8 inch on the map represents a distance of 12 miles in real life.
To determine the actual distance between the two cities, we can use the scale provided.
1/8 inch on the map represents 12 miles in real life.
A proportion to find the actual distance between the cities:
1/8 inch on map = 12 miles in real life
4.5 inches on map = x miles in real life
To solve for x, we can cross-multiply and simplify:
1/8 × x = 12 × 4.5
x = 12 × 4.5 × 8
x = 432 miles
Maps with scales can be useful for determining distances, sizes, and proportions of objects in real life.
It allows us to visually represent complex spatial relationships and make measurements without physically being present at the location.
Remember to use the correct scale and make sure to convert units properly in order to accurately determine real-life measurements.
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If a person makes $5.00 in 10 minutes, how much can she make in1.5 hours?
Please help due today!!!!!!!
Answers
Answer:
$45
Step-by-step explanation:
please help me
is for my daughter
Answers
Step-by-step explanation:
To find 5/6 of the area, multiply the area that was found in part A , as the question states by 5/6.
⅚ × Area found in part A.
In Winter of 2020 there were 20 total inches of snow. In Winter 2021 there were 38 total inches of snow. What was the percer
increase in inches of snow from 2020 to 2021?
Answers
To find the answer, you need to subtract the total inches of snow in 2021 by the total inches of snow in 2020.
So 38 -20= 18
Therefore, from 2020 to 2021. The snow increased by 18 inches.
Hope this helped!
5^3 – (64 : 8) + 10^2
Answers
STEP 1: Identify and Set Up
The question is a test of our understanding of the mathematical operations to employ before the others. Typically, there is an acronym that gives a hint on the order as stated below:
B - Bracket
O - Of
D/M - Division/Multiplication
A/S - Addition/Subtraction.
We have brackets in our question so we take care of it first,
Then we treat the numbers raised to powers.
Lastly, we now do the addition and subtraction.
STEP 2: Execute
\(\begin{gathered} 5^3-(64\div8)+10^2 \\ 5^3-8+10^2 \\ 125-8+100 \\ 125+100-8 \\ 225-8=217 \end{gathered}\)Answer = 217
PLEASE HELP ME
If f(x) = -3 and g(x) = 4x2 + x = 4, find (f+ g)(x).
ОА
A. 4x2 + x - 1
O B. 6x2 - 7
O 4x
C. 43+ + 2x-1
O D. 4x+3x-7
Answers
Answer:
D. 4x² + 3x/2 - 7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x/2 - 3
g(x) = 4x² + x - 4
(f + g)(x) is f(x) + g(x)
Step 2: Find
Substitute in functions: (f + g)(x) = x/2 - 3 + 4x² + x - 4Combine like terms: (f + g)(x) = 4x² + 3x/2 - 7Answer:
The answer is C.
Step-by-step explanation:
(f+g)(x)= f(x)+g(x).
So that would be x/2-3 + 4x^2+x-4.
If you combine like terms that would be:
4x^2+x/2+x-4-3=
4x^2+3/2x-7
A survey of 2,450 adults reported that 57% watch news videos. Complete parts (a) through (c) below. Question content area bottom Part 1 a. Suppose that you take a sample of 50 adults. If the population proportion of adults who watch news videos is 0.57, what is the probability that fewer than half in your sample will watch news videos? The probability is enter your response here that fewer than half of the adults in the sample will watch news videos. (Round to four decimal places as needed.) Part 2 b. Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news videos is 0.57, what is the probability that fewer than half in your sample will watch news videos? The probability is enter your response here that fewer than half of the adults in the sample will watch news videos. (Round to four decimal places as needed.) Part 3 c. Discuss the effect of sample size on the sampling distribution of the proportion in general and the effect on the probabilities in parts (a) and (b). Choose the correct answer below. A. The probabilities in parts (a) and (b) are the same. Increasing the sample size does not change the sampling distribution of the proportion. B. Increasing the sample size by a factor of 5 decreases the standard error by a factor of 5. This causes the sampling distribution of the proportion to become more concentrated around the true population proportion of 0.57 and decreases the probability in part (b). C. Increasing the sample size by a factor of 5 increases the standard error by a factor of 5. This causes the sa
Answers
Using the normal distribution and the central limit theorem, it is found that:
a) The probability is of 0.1587 = 15.87% that fewer than half of the adults in the sample will watch news videos.
b) The probability is of 0.0125 = 1.25% that fewer than half of the adults in the sample will watch news videos.
c) The standard error is inversely proportional to the square root of n, hence increasing the sample size by a factor of 5 decreases the standard error by a factor of \(\sqrt{5}\), which causes the sampling distribution of the proportion to become more concentrated around the true population proportion of 0.57 and decreases the probability in part (b).
Normal Probability DistributionIn a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1 - p)}{n}}\), as long as \(np \geq 10\) and \(n(1 - p) \geq 10\).In this problem, we have that the proportion is p = 0.57.
Item a:
Sample of n = 50, hence the mean and the standard error are given by:
\(\mu = p = 0.57\)
\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.57(0.43)}{50}} = 0.07\)
The probability that fewer than half in your sample will watch news videos is the p-value of Z when X = 0.5, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.5 - 0.57}{0.07}\)
\(Z = -1\)
\(Z = -1\) has a p-value of 0.1587.
The probability is of 0.1587 = 15.87% that fewer than half of the adults in the sample will watch news videos.
Item b:
Sample of n = 250, hence:
\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.57(0.43)}{250}} = 0.0313\)
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.5 - 0.57}{0.0313}\)
\(Z = -2.24\)
\(Z = -2.24\) has a p-value of 0.0125.
The probability is of 0.0125 = 1.25% that fewer than half of the adults in the sample will watch news videos.
Item c:
The standard error is inversely proportional to the square root of n, hence increasing the sample size by a factor of 5 decreases the standard error by a factor of \(\sqrt{5}\), which causes the sampling distribution of the proportion to become more concentrated around the true population proportion of 0.57 and decreases the probability in part (b).
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I have to solve this system of equations using substitution. I don't understand how to do this one.
Answers
Substitution
\(\begin{gathered} -3(-3y+1)-3y=-15 \\ 9y-3-3y=-15 \\ 9y-3y-3=-15 \\ 6y-3=-15 \\ 6y=-15+3 \\ 6y=-12 \\ y=-\frac{12}{6} \\ y=-2 \end{gathered}\)\(\begin{gathered} x=-3y+1 \\ x=-3(-2)+1 \\ x=6+1 \\ x=7 \end{gathered}\)The answer would be x = 7 and y = -2
An irrational number between 4 and 7.
Answers
Answer: an irrational number between 4 and 7 would be 5
Step-by-step explanation:
Fill in the boxes to add the expressions.
(5.19+4m)+(4.18+3.95m) = (4m+_)+(5.19+_)=_
Answers
Using common factor method, sum of the given expressions is 17.14m + 9.37
what is common factor ?
In mathematics, a common factor is a factor that two or more numbers have in common. For example, the numbers 12 and 18 have common factors of 1, 2, 3, and 6. The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.
In algebra, we often use the term "common factor" when referring to expressions. When two or more algebraic expressions have a factor in common, we can use the distributive property to factor out the common factor.
According to the question:
To add the expressions (5.19+4m)+(4.18+3.95m), we can first group the like terms:
(5.19 + 4.18) + (4m + 3.95m)
9.37 + 7.95m
So, the sum of the expressions is:
(5.19+4m)+(4.18+3.95m) = 9.37 + 7.95m
Now, we can use the distributive property to factor out a common factor of m from 7.95m:
9.37 + 7.95m = 4m + (5.19 + 7.95)m
We can factor out a common factor of 1 from (5.19 + 7.95)m:
4m + (5.19 + 7.95)m = (4 + 5.19 + 7.95)m
Adding the coefficients, we get:
4 + 5.19 + 7.95 = 17.14
Therefore, the sum of the expressions is:
(5.19+4m)+(4.18+3.95m) = (4m+5.19)+(3.95m+4.18)= 17.14m + 9.37.
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if I have 10 apples and I take 2 away how many will I have
Answers
Answer:
8 apples.
Step-by-step explanation:
Answer:
8 apples
Step-by-step explanation:
Have a nice day
PLS HELP! weights (in pounds) of catfish caught in the river: 4.8 3 2.7 4.4 4.8 9.9 What is the outlier? A) 3 lbs B) 4.8 lbs C) 9.9 lbs D) none
Answers
The correct answer is C) 9.9 lbs as it is above the upper boundary 6.4865, it is the outlier in this dataset.
What is an outlier?An outlier is an observation that is much higher or lower than the other observations in a dataset.
In this case, the weights of the catfish range from 2.7 to 4.8 lbs, with one observation that is much higher at 9.9 lbs.
Therefore, 9.9 lbs is the outlier in this dataset.
To find the outlier in this dataset, we can calculate the interquartile range (IQR).
This is done by first calculating the first quartile (Q1) and third quartile (Q3).
The Q1 for this dataset =3.75
and the Q3= 4.675.
IQR= Q3 - Q1
= 0.925.
We then calculate the lower boundary as Q1 - (1.5 x IQR) = 2.3625.
The upper boundary is Q3 + (1.5 x IQR)= 6.4865.
Since 9.9 lbs is above this upper boundary, it is the outlier in this dataset.
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Which of the following methods can be used to find the derivative of y = arcsin x with respect to z ?
|. Use the quotient rule to differentiate
II. Use the chain rule to differentiate sin(arcsin x) = 2.
III. Use implicit differentiation to differentiate the function y in the relation sin y = x with respect to z.
A) I only
B) Ill only
C) II and III only
D) I, II, and III
Answers
Answer:
B) Ill only
Step-by-step explanation:
This is because y = arcsin x can be re-written as sin y = x, We then differentiate sin y = x implicitly with respect to z to obtain
d(siny)/dz = dx/dz
(cosy)dy/dz = dx/dz
dy/dz = (1/cosy)dx/dz
Which expression could have the value shown by the point on this number line?
Answers
The point on the number line is greater than 12.
We need to estimate close to the best answer that’s the square root of 12
we know that
\(12=\sqrt[]{12^2}=\sqrt[]{144}\)The value should be above the square root of 144.
From the given options, we get that the point is
\(\sqrt[]{152}>\sqrt[]{144}\)The answer is
\(\text{ Hence }\sqrt[]{152}\text{ is value of the point in the given number line.}\)3. 5p - 14 = 8p + 4
Answers
= -4-14= 8p-5p
= -18= 3p
= -18/3=p
= p=-6
Thus, your answer is -6.
P = -6
identify the slope -x+3y=10
Answers
Answer:
To find the slope use the slope-intercept form y=mx+b.
m = 1/3
Answer:
-x+3y=10
the slope is1/3
m=-1/3
Please help me in confused
Answers
Answer:
20\(c^{6}\)
Step-by-step explanation:
using the rule of exponents
\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)
given
(- 4c³)(- 5c³) ← remove parenthesis
= - 4 × c³ × - 5 × c³
= - 4 × - 5 × c³ × c³
= 20 × \(c^{(3+3)}\)
= 20\(c^{6}\)
PLEASE HELP ME ASAP. i really need help
Answers
Answer:
38
Step-by-step explanation:
A => 4.05
b =>5.95
now they told in the coffee blend their ratio is 2:1 :: B:A
So if we take x amounts of A then 2x amount of B
So cost of A => x * 4.05
So cost of B => 2x * 5.95
And result is given 606.1
Hence
x * 4.05 + 2x*5.95 = 606.1
Solve and get x = 38
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