Answer:
[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]
Step-by-step explanation:
Given equation:
[tex](8x+7)(x+1)=9[/tex]
Expand the brackets:
[tex]\implies 8x^2+15x+7=9[/tex]
Subtract 9 from both sides:
[tex]\implies 8x^2+15x+7-9=9-9[/tex]
Simplify:
[tex]\implies 8x^2+15x-2=0[/tex]
To factor a quadratic equation in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]\implies ac=8 \cdot -2=-16[/tex]
[tex]\implies b=15[/tex]
Therefore, the two numbers are: 16 and -1.
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 8x^2+16x-x-2=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 8x(x+2)-1(x+2)=0[/tex]
Factor out the common term (x + 2):
[tex]\implies (8x-1)(x+2)=0[/tex]
Apply the zero-product property:
[tex]\implies 8x-1=0 \implies x=\dfrac{1}{8}[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
Therefore, the solutions to the given quadratic equation are:
[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]
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Answer:
x = 1/8 (or) x = -2
Step-by-step explanation:
Now we have to,
→ solve the following quadratic equation.
Let's solve for quadratic equation,
→ (8x+7)(x+1) = 9
→ 8x² + 7x + 8x + 7 - 9
→ 8x² + 15x - 2
→ 8x² + 16x - x - 2
→ 8x(x + 2) - 1(x + 2)
→ (8x - 1)(x + 2)
→ x = 1/8 (or) x = -2
Hence, the solution is x = 1/8, -2.
Lenny makes 55,000 per year and gets annual raises of 20,000 how many years why will it take lenny and kenny to make the same annual salary
Answer:
14,987
Step-by-step explanation:
b. For mixing a spray to kill weeds, Howard is to
use 2 1/2 tablespoons for each gallon of water.
How many tablespoons of the spray will he
need to use for 5 gallons of water.
The 12.5 tablespoons of the spray will he need to use for 5 gallons of water.
What is arithmetic?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
For mixing a spray to kill weeds, Howard is to use 2 1/2 tablespoons for each gallon of water.
We have to find How many tablespoons of the spray will he need to use for 5 gallons of water..
According to given question we have
2 1/2 =5/2 tablespoons for each gallon of water.
5/2 tablespoons =1 gallon of water.
1 gallon of water=5/2 tablespoons
5 gallons of water=5/2*5 tablespoons
5 gallons of water=25/2 tablespoons=12.5 tablespoons
Therefore, the 12.5 tablespoons of the spray will he need to use for 5 gallons of water.
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A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a.
For a continuous distribution, the uniform distribution describes equal probability over a specific range. It is crucial as a reference distribution because of this. The creation of random numbers is one of the uniform distribution's most significant uses.
A particular probability distribution is called a binomial distribution. It is used to simulate the likelihood of getting one of two results out of a certain number of trials (N) of a discrete random event.
The expected outcome is referred to as a success in a binomial distribution, whereas any other event is referred to as a failure. A successful outcome has a probability of p, while a failure has a chance of 1 - p.
In n draws without replacement from a finite population of size N that contains exactly K objects with that feature, the hypergeometric distribution, a discrete probability distribution, describes the likelihood of k successes (random draws for which the drawn object has a specified feature), where each draw is either successful or unsuccessful. The binomial distribution, on the other hand, describes the likelihood of k successes in n draws with replacement.
The normal distribution sometimes referred to as the Gaussian distribution, is a probability distribution that is symmetric about the mean and demonstrates that data that are closer to the mean are more likely to occur than data that are farther from the mean. The normal distribution is depicted graphically as a "bell curve."
The correct option is (b) binomial probability distribution.
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HELP! 25 POINTS
Factorise: √ab(x² +1) + x(a+b)
the median of 6 consecutive integers is 9. what is the largest number
If the median of 6 consecutive integers is 9, the largest number is equal to 8.5.
Given the following data:
Median, M = 9.Number of consecutive integers, n = 6.What is a median?In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
For the largest number, we have:
Since consecutive integers must follow each other sequentially with a difference of 1, so the largest number is given by:
Largest number = Median + (n - 1)/2
Substituting the given parameters into the formula, we have;
Largest number = 6 + (6 - 1)/2
Largest number = 6 + (5)/2
Largest number = 6 + 2.5
Largest number = 8.5.
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Write down the equations for the lines whose graphs are depicted below.
The equation for the lines whose graph is depicted below is y = x/2.
How to write the equations for the lines?In order to write the equations for these straight lines, we would have to determine the slope of the straight lines.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
From the graph (see attachment), we have the following data:
Points on x-axis = (0, 2).
Points on y-axis = (0, 1).
Substituting the given points into the formula, we have;
Slope, m = (1 - 0)/2 - 0)
Slope, m = 1/2.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
At point (2, 1), we have:
y - 1 = 1/2(x - 2)
y - 1 = x/2 - 1
y = x/2 - 1 + 1
y = x/2.
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a man and a woman, both with brown eyes (bb), have a child. what is the percentage chance that the child will have blue eyes?
lillian drew a scale drawing of a county park. the scale she used was 1 inch : 4 yards. the picnic area is 80 yards wide in real life. how wide is the picnic area in the drawing?
The picnic area is 20 inches wide in the drawing in her scale of 1 inch : 4 yards.
What is unitary method ?Unitary method is a technique for first solving the value of a single digit unit and from there we can find the value of any given unit.
According to the given question lillian drew a scale drawing of a county park. the scale she used was 1 inch : 4 yards.
The picnic area is 80 yards wide in real life.
∴ The width of the picnic area in here drawing in inches will be
= 80/4 inches.
= 20 inches.
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The circle graph shows the most important problems for
the 14,054,077 high school teenagers in a country..
Without using a calculator, estimate the number of high
school teenagers for whom doing well in school is the
most important problem.
Most Important Problems for High School Teenagers
Doing Wel in School, 12%
Social Pressures and Fitting in, 22%
Drugs, 22%
Others, 29%
Getting along with Parents. 2%
Geting into College, 2%
Sexual Issues, 2%
Crime and Violence in School, 9%
Doing well in school is the most important problem for approximately how many of the high school teenagers?
OA. 4,200,000
OB. 1,400,000
LOC. 2,800,000
OD. 5,600,000
According to the circle graph, doing well in school is a problem that affects B. 1,400,000 high school teenagers.
Which high school students are affected?The circle graph shows that 12% of high school students have the problem of doing well in school.
In actual numbers, this is:
= 12% x number of high school teenagers
Solving gives:
= 12% x 14,054,077
= 1,686,489 students
= 1,400,000 approximate
In conclusion, option B is correct.
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Systems of equations with graphing
The correct option is A. x = 1(1/3) and y = 2(1/3) in the mixed fractions.
What is defined as the system of equations?A system of equations is a collection of equations that all have the same variables.
If all of the equations are linear, you get a system of linear equations! To fix a system of equations, you must first determine the variable values that will solve all of the equations involved.A solution to an equation system is a set of variable values that satisfy all of the equations at the same timeNow, the given equation in the question are-
7x - y = 7 ........(equation 1)
and x + 2y = 6 ........(equation 2)
Multiplying both side of equation 1 with 2, we get
14x - 2y = 14 ........(equation 3)
Add equation 2 and 3.
x + 2y + 14x - 2y = 6 + 14
15x = 20
x = 4/3
x = 1(1/3)
Substitute the value of x in equation 1.
4/3 + 2y = 6
2y = 6 - 4/3
2y = 14/3
y = 7/3
or y = 2(1/3)
Therefore, the values for variables x and y are calculated as:
x = 1(1/3) and y = 2(1/3).
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Determine the range of f(x) = |x| + 3
The range of the function f(x) = |x|+3 is [3,∞)
Given,
The function f(x) =|x|+3
Consider
f(0)=|0|+3= 3
f(1)=|1|+3= 4
f(2)=|2|+3= 5
We know
|x|≥0
So even if we take negative value for x, the |x| will be positive
So,
f(-1)=|-1|+3=1+3=4
f(-2)=|-2|+3= 2+3=5
We know, range is the set of all possible outcomes.
The range of the function f(x)= |x|+3 = [3,∞)
Hence, the range of the function f(x) = |x|+3 is [3,∞).
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Answer:
{y | 3 ≤ y < ∞}
Step-by-step explanation:
A bird flies from the bottom of a canyon that is 51 3/10 feet below sea level to a nest that is 737 1/10 feet above sea level.
685.8 feet
Sea level is a reference to elevation of the ocean or land interface called the shoreline.
Land that is above this elevation is higher than sea level and lower is below sea level.
The bottom of the canon is at 51 3/10 below the sea level which is also written as -51 3/10 ……(1)
The nest is at 737 1/10 feet above the sea level so it is expressed as
737 1/10 ….(2)
To find the distance between the bottom of the canyon and the bird’s nest we subtract (2) from (1)
737.1 – 51.3
= 685.8 feet
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Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. if they toll together at 11:00, at what time will they toll together again?
If Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10, and 12 seconds respectively and toll together at 11:00, then they will toll together again at 11:02.
Least common multiple abbreviated as LCM is used to determine the time at which the six bells will toll together again.
The least common multiple of two or more numbers is the smallest number that is a multiple of those numbers.
The least common multiple of 2, 4, 6, 8, 10, and 12 can be found by prime factorization.
Prime factorization of :
2 = 2^1
4 = 2 x 2 = 2^2
6 = 2 x 3
8 = 2^3
10 = 2 x 5
12 = 2 x 2 x 3 = 2^2 x 3
The least common multiple can be calculated by the multiplication of the prime factors raised to their highest power.
Therefore,
LCM = (2^3) (3) (5) = 120
Hence the bells will toll together again after 120 seconds
As 120 seconds = 2 minutes
Therefore, the time at which they will toll together again is calculated to be 11:02.
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pls help 6x+15=6(x-3) pls help with answer and explaining
Answer:
-33
Step-by-step explanation:
distribute;
6x + 15 = 6x - 18
subtract;
-15
simplify;
- 33
subtract from both sides;
-6
total;
-33
Answer:Answer is 0=-33
Step-by-step explanation:What you need to do is bring x by itself on one side and the other numbers on the other side The steps are
6x+15=6x-18
6x-6x=-18-15
0=-33
Can someone help me with the radius? please and thank you
Answer:
r=7cm
Step-by-step explanation:
the diameter (distance from one side of the circle to the opposite side) is given in the picture. the radius is 1/2 the diameter, so r=7cm
*i'm assuming the 14cm given is referring to the straight line in the circle and not the circumference
Given: B is between A and C, AB = 3x -4, BC = 4x + 2, and AC = 26. What is the value of x?
A. 6
B. 4
C. 3.7
D. 5
Answer:
B
Ab + bc =ac
3x-4 + 4x+2 =26
7x=28
x=4
what is 9^256? will give brainliest
Answer:
1.93233498E244
Step-by-step explanation:
Answer:
3.14159265
Step-by-step explanation:
each 14 pound of potting soil contains 316 cups of water.how many cups of water are contained in 1 pound of potting soil?34 cups3 over 4, cups1116 cups1 and 1 over 16, cups112 cups1 and 1 half, cups113 cups
The number of cups of water contained in 1 pound of potting soil will be 3 / 4. The correct option is A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that each 14-pound of potting soil contains 3/6 cups of water. The number of the cups will be calculated by forming an expression below:-
Number of cups = (4 x 3/6)
Number of cups = 12/16
Number of cups = 3/4 of a cup
Therefore, the number of cups of water contained in 1 pound of potting soil will be 3 / 4. The correct option is A.
The correct question is given below:-
Each 14-pound of potting soil contains 316 cups of water.
How many cups of water are contained in 1 pound of potting soil?
34 cups
1116 cups
112 cups
113 cups
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the names of 0 employees are written on 0 cards. the cards are placed in a bag, and three names are picked from the bag. what sampling technique was used?
The names of 0 employees are written on 0 cards. the cards are placed in a bag, and three names are picked from the bag - here simple random sampling technique was used.
What is simple random sampling?Basic irregular testing can provide you with an extremely precise image of how your motto performs with the typical individual, yet it won't give you nitty gritty data about unambiguous gatherings. Utilizing straightforward irregular testing permits scientists to make speculations about a particular populace and leave out any inclination. This can assist with deciding how to settle on future choices. It has been expressed that "the rationale behind straightforward arbitrary examining is that it eliminates predisposition from the choice method and ought to bring about delegate tests".
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PLEASE HELP!!! An equation in slope intercept form of the line that passes through the points (-3, 5)
and (2, 15) is
Answer:
y = 2x + 11
Step-by-step explanation:
To find the slope, use the equation (y2 - y1)/ (x2 - x1). You get (15 - 5)/(2 - (-3), or 2. Then, use the slope you just found in the equation y - y1 = slope (x - x1), or y - 15 = 2 (x - 2). Simplifying down you get y = 2x -4 + 15, or y = 2x + 11, which is your final answer.
Hope this helps! Let me know if you have any confusion!
Write the expression
(−7)⋅(−7)⋅5⋅5⋅5⋅5
using exponents.
Answer:
-7²·5⁴
Step-by-step explanation:
there are two 7
and four 5
The price of a train ticket from Atlanta to Phoenix is normally $131.00. However, the train company is offering a special 70% discount to children under the age of 16. What is the sale price of a ticket from Atlanta to Phoenix for someone under the age of 16?
$91.70
$39.30
$222.70
$55.02
Answer:
$39.30
Step-by-step explanation:
First find out 70% which is $91.70
And then do 131-91.70=39.30
please give me brainiest and hope this helped let me know if you have any questions
You will get 1 thanks, 5 stars, and 15 points if you answer!
Answer:
It's C/ Option 3
Step-by-step explanation:
trust me
Given the quadrilateral with the following vertices a(-2,3) b(-2,6) c(-6,-1) and d (-6,2). is the quadrilateral a parallelogram?
The quadrilateral is a parallelogram.
Properties of parallelogram,
a>The opposite sides of the parallelogram are equal and parallel.
b>parallel lines have an equal slope.
Let now find the length of the opposite side of the parallelogram
To find the length we have ,
[tex]\sqrt{(x_{2} ^{2} -x_{1} ^{2} ) +(y_{2} ^{2}-y_{1} ^{2} )}[/tex]
(-2, 3) , (-2, 6)
Slope = 6-3/ -2+2 = infinity
Length L1 = [tex]\sqrt{(-2 + 2)^{2} + (6 - 3)^{2} }[/tex]
= 9
(-6, -1), (-6, 2)
Slope = 2+1/ -6 + 6 = infinity
Length L2 = [tex]\sqrt{(-6 + 6)^{2} + ( 2 + 1)^{2} }[/tex]
= 9
Therefore the given vertices are of a parallelogram, as the length and slope are equal.
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PLEASE SHOW WORK
----------------------------------------------
Answer:
Step-by-step explanation:
Please help me someone
Answer:
See the table below
For n, the answer is 2n+1
Step-by-step explanation:
The number of trees in each figure represents an arithmetic sequence where the difference between subsequent figures is 2 (caled the common difference)
So the sequence is
Figure(n) Number of Trees
1 3
2 5
3 7
4 9 (7+2)
5 11 (9+2)
n 2n + 1
In general, for any arithmetic sequence we can write an equation for the nth term as [tex]a_n = a_0 + d(n-1)[/tex] where [tex]a_0[/tex] is the first term and d is the common difference
So for this example, we have [tex]a_0 = 3[/tex] and d=2 giving
[tex]a_n = 3 + 2(n-1) = 3 + 2n -2 = 2n + 1[/tex]
This is
This week felicia will practice with her band for 112 hours on monday,134 hours on tuesday, and 2 hours on wednesday. next week felicia will practice with her band for the same number of hours on monday, tuesday, and wednesday. what is the total number of hours felicia will practice with her band over these 6 days?
Felicia will practice for a total of 496 hours
How to calculate the total number of hours spent ?Felicia will practice for 112 hours on Monday
She will practice for 134 hours on Tuesday
She will practice for 2 hours on Wednesday
Total number of hours spent in week 1= 112 + 134 + 2
= 248 hours
She did the same routine the following week
= 248 × 2
= 496
Hence Felicia will practice for a total of 496 hours for the 6 days
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EVALUATING EXPI
Evaluate the expression below
when g = 10
6g²
Answer:
600Step-by-step explanation:
Expression given:
6g²Find its value when g = 10:
6g² = 6(10²) = 6(100) = 600is d=2t proprtional?????
The direct variation equation is in the form d = kt, where k is some constant. It's the constant of proportionality. In this case k = 2.
simplify the following expression:
3 - x (4 + x) if x = 2
Answer:
Step-by-step explanation: We can plug 2 into the equation for x:
3 - 2(4 + 2)
Now let's distribute:
3 - 8 - 4
Now we can solve:
3 - 8 = -5
-5 - 4 = -9
Final answer: 3 - x(4 + x) = -9