An expression is given.
2 x² + zx - 10
The expression can be written as (x+q) (q + r), where q, r, and z are integers.
What are possible integer values of q, r, and z?
In the text box, type your answer in this format:
q =
r =
z =
Answers
Expressions are mathematical statements without the equation sign
The possible integer values of q, r, and z are 1, -5 and 8
The expressions are given as:
\(2x^{2} + zx - 10\) (say eq. 1)
(x + q)(x + r)
Both expressions are equal.
So, we have:
\(2x^{2} + z x - 10 = (x+q)(x+r)\)
we know that , roots of a quadratic equation (\(ax^{2} + bx + c = 0\)) are ,
\(m = \frac{-b + \sqrt{b^{2} - 4ac } }{2a} , n = \frac{-b - \sqrt{b^{2} - 4ac } }{2a}\)
on comparing \(ax^{2} + bx + c = 0\) with eq . 1 , we get
a = 2 , b = z , c = -10
Therefore , \(m = \frac{(-z) + \sqrt{}(z^{2} - 4.2.(-10) ) }{2.2} = \frac{-z + \sqrt{}z^{2} + 80 }{4}\),
\(n = \frac{(-z) - \sqrt{}(z^{2} - 4.2.(-10) ) }{2.2} = \frac{-z - \sqrt{}z^{2} + 80 }{4}\)
Now , we can express eq. 1 as ,
(x-m)(x-n)
By comparison, we have:
q = -m
r = -n
or
\(q = \frac{-z + \sqrt{}z^{2} + 80 }{4}\\r = \frac{-z - \sqrt{}z^{2} + 80 }{4}\)
Assume that q = 1.
So, we have:
\(1 = \frac{-z + \sqrt{}z^{2} + 80 }{4}\\or\\4 = -z + \sqrt{z^{2} + 80 } \\\)
Rearranging and Squaring both sides ,
\((z+4)^{2} = (\sqrt{z^{2} + 80 }) ^{2} \\z^{2} + 16 + 8z = z^{2} + 80\\8z = 64\)
This gives , z = 8
Substitute , z= 8 in r
So, we have:
\(r = \frac{-8 - \sqrt{8^{2} + 80 } }{4} = \frac{-8 - \sqrt{144} }{4} = \frac{-8 - 12}{4} = -5\)
Hence, the possible integer values of q, r, and z are 1, -5 and 8.
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Related Questions
One year, the population of a city was 160,000. Several years later it was 140,800. Find the percent decrease.
Answers
Answer:
Percent decrease in population = 12%
Step-by-step explanation:
Given that:
Population of city = 160,000
Population of city after several years = 140,800
Difference= 160000 - 140800 = 19200
Percent decrease = \(\frac{Difference}{Population} * 100\)
Percent decrease = \(\frac{19200}{160000}*100\)
Percent decrease = 0.12 * 100
Percent decrease = 12%
Hence,
Percent decrease in population = 12%
Evaluate the expression for x = 15
x - 9
9
24
6
12
Answers
Answer:
6
Step-by-step explanation:
Given,
x = 15
To find : The value of x - 9 = ?
Solution : -
Substitute x = 15 in x - 9,
x - 9
= 15 - 9
= 6
Hence, evaluated.
???? Helppppppppppppppp
Answers
Divide. −3.52−2.2 What is the quotient
Answers
The quotient of - 3.32 / - 2.2 is 8 ÷5.
What is the quotient?Given fraction:
-3.32 / -2.2
First step is to re-write the given fraction which is - 3.52 / - 2.2
3.52 / 2.2
Second step is to convert the decimal to fraction
352 ÷ 100 / 22 ÷10
Third step is to reduce the fraction
reducing 352/100
=(2^5 × 11)/(2^2 × 5^2)
= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]
= (2^3 × 11)/5²
= 88/25
Reducing 22/10
Divide the numerator and denominator by the greatest common divisor
= 22 ÷ 2 / 10 ÷ 2
= 11 /5
Now let determine or find the quotient
88 ÷ 25 × 11 ÷ 5
= 8 ÷ 5
Therefore we can conclude that 8 ÷ 5 is the quotient.
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The number 4 is what percent of 5? A. 0.8% B. 1.25% C. 80% D. 125%
Answers
Answer:
The answer is C. 80%
Step-by-step explanation:
Hope this helped:)
The number of students at Yellowstone High School has been increasing by 4% each year. There are
currently 4,256 students. How many students will there be in 8 years?
Answers
Answer:
5,617.92
Step-by-step explanation:
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year.
Solving our equation:
A = 4256(1 + (0.04 × 8)) = 5617.92
A = $5,617.92
The total amount accrued, principal plus interest, from simple interest on a principal of $4,256.00 at a rate of 4% per year for 8 years is $5,617.92.
answer me please as soon as possible plot the graph same as shown in the question using green orange and black colors
Answers
Due to length restrictions, we kindly invite to read the explanation of this question for further details about the table and graph of the function.
How to plot the graph of a function
In this problem we must plot the graph of a function on a Cartesian plane. The procedure is summarized below:
Create a table for a series of equally spaced x-values.Calculate the y-values for corresponding values and fill the table.Mark the points on the Cartesian plane.Match the points with line segments.After following the procedure, we have the following result:
Input, x x + 4 Output, y (x, y)
- 2 - 2 + 4 2 (- 2, 2)
0 0 + 4 4 (0, 4)
2 2 + 4 6 (2, 6)
4 4 + 4 8 (4, 8)
6 6 + 4 10 (6, 10)
8 8 + 4 12 (8, 12)
Lastly, we plot the graph of the linear function.
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What is the equation of the function that is graphed as line b?
Answers
Answer:
I feel like this is a trick question
----
Suppose that the regression for predicting weight (in pounds) from Height (in inches) is given by Weight -115+3.6 (Height) Which of the following statements is correct?
I. A person who is 61 inches tall will weigh 104.6 poulds.
II. For every additional inch of height, the predicted weight will increase, on average by 3.6 pounds
III. The correlation between weight and height is negative.
A. II only
B. Iand II only
C. I only
D. II and III only
E. III only
Answers
Answer:
B. I and II only.
Step-by-step explanation:
A person who is 61 inches tall is predicted to weight 104.6 pounds according to the regression model.
\(y(61)=-115+3.6(61)=-115+219.6=104.6\)
The slope of the linear regression model indicates the rate of change of the predicted variable in function of a unit change in the independent variable. In this case, for each additional inch in height, the predicted weight will increase, on average by 3.6 pounds, as indicated by the slope of this model.
As the slope m=3.6 is positive, the correlation is positive: when the independent variable increases, the predicted variable also increases.
A] Both I and II are correct.
Weight = - 115 + 3.6 (Height)
Here, 115 is the autonomous weight at 0 level of height, it is the intercept. 3.6 is the slope, representing change in weight due to change in height. Slope implies that : For every additional inch of height, the predicted weight will increase, on average by 3.6 pounds. So, II is True
At height = 61 inches, weight = - 115 + 3.6 (61) = - 115 + 219.6 = 104.6 So, I is True
Regression shows cause effect relationship (of height on weight). Correlation shows just co-relationship in direction of variables' movement. Nevertheless, positive regression correlation increases the probability of positive correlation (instead of negative correlation) So, III is false
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Amadi is three times as old as Chima. The sum of their ages is 24
Answers
Answer:
Amadi: 20 years old
Chima : 4 years old
please help!! 100 points
Answers
Explanation:
Plug in 4 for x
H(4)=1/5(4^2-6)-8
After solving you should get -6
\(\\ \tt\bull\rightarrowtail h(x)=1/5(x^2-6)-8\)
\(\\ \tt\bull\rightarrowtail h(4)\)
\(\\ \tt\bull\rightarrowtail 1/5(4^2-6)-8\)
\(\\ \tt\bull\rightarrowtail 1/5(16-6)-8\)
\(\\ \tt\bull\rightarrowtail 10/5-8\)
\(\\ \tt\bull\rightarrowtail 2-8\)
\(\\ \tt\bull\rightarrowtail -6\)
Can anyone tell me how you make the equations for these things?
Answers
I'm sorry a can't see it that well
3 + 2x = -6x + 4
what’s x
100 points
Answers
Answer:
x = 1/8
Step-by-step explanation:
Add 6x to both sides:
3 + 2x = -6x + 4
3 + 8x = 4
Subtract 3 from both sides:
8x = 1
Divide each side by 8:
x = 1/8
So, x = 1/8
What is the value of the expression below -64 5/6
Answers
Answer:
389/6
Step-by-step explanation:
thts the answer
Each day a bobcat drinks about 3 times as much water as a Canada goose drinks. If the Canada goose drinks 0.24 liters of water each day, how much can a bobcat drink in one day? Convert the answer to mL.
Answers
Answer:
720 mlStep-by-step explanation:
Bobcat drinks 3 times as much as Canada goose drinks:
0.24 l * 3 = 0.72 l0.72 l = 0.72 * 1000 ml = 720 mlAnswer:
Bobcat can drink 720 mL of water in one day
Step-by-step explanation:
Amount of water a Canada goose drinks in a day = 0.24 L
According to the question each day a Bobcat drinks about 3 times as much water as a Canada goose drinks.
\( \therefore \) Amount of water a Bobcat drinks in a day = 3 × 0.24 L
= 0.72 L
= 0.72 × 1000 mL
= 720 mL
Help due 30 mins....
Answers
At Silver Gym, membership is $25 per month, and personal training sessions are $30 each. At Fit Factor,
membership is $45 per month, and personal training sessions are $20 each. In one month, how many
personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Answers
Answer:
2
Step-by-step explanation:
y = mx + b
y = total cost of the gym
m = cost per personal session
x = number of sessions
b = cost of one month
Silver gym:
y = 30x + 25
Fit Factor:
y = 20x + 45
Set them Equal to each other:
30x + 25 = 20x + 45 (get Xs on one side by subtracting 20x)
10x + 25 = 45 (isolate x by subtracting 25 from both sides)
10x = 20 (divide both sides by 10)
x = 2 personal training sessions to make the cost equal
1. A circular track has a diameter of 23 meters. Tothe nearest hundredth of a meter, which is closestto the area of the track?A. 372.22 mB. 344.44 mC. 386.75 mD. 415.26 m
Answers
the formula of the area of a circle is
\(A=\pi\times r^2\)Here are the cost of tickets at a cinema venue
Answers
Answer:
A=40.8 B=8
Step-by-step explanation:
A Explanation
£7.20*3=£21.6
£9.60*2=£19.2
19.2+21.6=40.8
B Explanation
£9.60*3=£28.8
86.40-28.8=57.6
57.6/7.20=8
triangle JKL is congruent with triangle \GHI Complete the congruence statement.angle J is congruent with angle _
Answers
From the picture, the congruent angles are:
∠K ≅ ∠H
∠J ≅ ∠G
∠L ≅ ∠I
Which of the scenarios below are considered seller-based discounts? options are in the picture
Answers
The scenarios that can be considered a seller-based discount are:
A. The offer by Wire and Cable
B. Carfna's Fine Foods
C. Mouser Electronics offer
E. Carchex Car Maintenance
What is a seller-based discount?A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.
The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.
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11. Use multiplication to find an equivalent
fraction for 1/3
Answers
Answer: 1/3*2*2=2/6
Step-by-step explanation:
Hope this helps
Answer:
equivalent fractions for 1/3: 2/6, 3/9
the amount of paint needed to cover a wall is proportional to its area. the wall is rectangular and has an area of 6z2 6z square meters. factor this polynomial to find possible expressions for the length and width of the wall. (assume the factors are polynomials.)
Answers
On factoring the polynomial 6z² + 6z the values for length and width are obtained as 6z and z + 1.
What is a polynomial?
Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
We can factor the polynomial 6z² + 6z by taking out the greatest common factor, which is 6z -
6z² + 6z = 6z(z + 1)
This means that the area of the wall is equal to 6z(z + 1) square meters. Since the area of a rectangle is given by the product of its length and width, we can write -
6z(z + 1) = length × width
Therefore, the possible expressions for the length and width of the wall are -
length = 6z
width = z + 1
or
length = z + 1
width = 6z
Both of these expressions give a product of 6z(z + 1), which is equal to the area of the wall.
We can switch the roles of length and width, so there are two possible expressions for the dimensions of the wall.
Therefore, the length is 6z and width is z + 1.
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Based on the information in the two-way table, what is the probability that a person
selected at random both bikes and runs?
Round your answer to the nearest tenth of a percent.
Answers
Answer:
Step-by-step explanation:
What the meaning of statement this?
Answers
The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.
Axiom of RegularityThe set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.
The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.
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Are all intersecting lines perpendicular? Draw a picture to help explain your answer
Answers
Not all intersecting lines are perpendicular.
What are perpendicular lines?Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.
Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.
As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.
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meaning of transmission
last napo
Answers
Answer:
the action or process of transmitting something, or the state of being transmitted.
Mr. and Mrs. Tournas know that their son will attend a college, in 14 years, that they estimate to cost approximately $250,000How much should they deposit now if they assume that they can earn 8.5% compounded annually?
Answers
Compound interest formula:
\(A\text{ = }P(1+i)^n\)where:
A is the final amount, here = $250,000
P is the principal amount
i is the interest rate per year (in decimal form), here = 0.085
n is the number of years invested, here = 14
Replacing into the equation and solving for P, we get:
\(250000=P(1+0.085)^{14}\)\(\frac{250000}{1.085^{14}}=P\)
P = $79,785.5
=√s2
what equals =√s2?
Answers
See whether you're understanding the subject and skills.
Answers
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