Answer: a=5 b=2
Step-by-step explanation:
They both satisfy the equation as 5+2=7 and 5-2=3
Hope this helps!
Here we have been given with two equations and we have to calculate the value of a and b by solving them simultaneously.
a + b = 7 (Equation No 1)a - b = 3 (Equation No 2)★ From Equation No 2 :
>> a - b = 3
>> a = 3 + b
★ In Equation No 1 :
Substituting here the value of a which we got above as (3 + b).
>> a + b = 7
>> 3 + b + b = 7
>> 3 + 2b = 7
>> 2b = 7 - 3
>> 2b = 4
>> b = 4 / 2
>> b = 2
★ Finding out value of a :
>> a = 3 + b
>> a = 3 + 2
>> a = 5 [tex] \: [/tex]
If the equation of the line is y=-5.9x+91.9 . Which statement is false?
A. The slope of the line indicates that test score and the time spent watching tv are negatively correlated
B. The model predicts an approximate 6 - point drop in test score for one hour spent watching tv
C. The y-intercept or the line indicates that the student who spends no tv watching tv will get the highest test score possible
D.the liner model predicts an approximate test score of 92 if no time is spent watching tv
Answer:
. The slope of the line indicates that test score and the time spent watching tv are negatively correlated
Solve the following system of equations using elimination:
-x+5y=8
And
3x+7y=-2
Answer:
x=-3, y=1. (-3, 1).
Step-by-step explanation:
-x+5y=8
3x+7y=-2
----------------
3(-x+5y)=3(8)
3x+7y=-2
--------------------
-3x+15y=24
3x+7y=-2
------------------
22y=22
y=22/22
y=1
-x+5(1)=8
-x+5=8
-x=8-5
-x=3
x=-3
Mandy bought a desktop computer system to start her business from home for $4,995. It is expected to depreciate at a rate of 10% per year. After how many years will the value of her home computer system depreciates to approximately $2150
Answer:
8.43 years
Step-by-step explanation:
Given data
Cost price P= $4995
Rate r= 10%
FInal amount A= $2150
The expression for the time/duration is given as
t= ln(A/p)/r
t= ln(2150/4995)/0.1
t= ln(0.430)/0.1
t= 0.843/0.1
t= 8.43
Hence the time it will take is 8.43 years
A juice container advertises it now contains 20% more juice. Originally, it had 27.5 ounces, how
much juice does it now contain?
Answer:
33 ounces
Explanation:
20% of 27.5 ounces is 5.5 ounces.
To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces
A financial analyst wants to set up a hypothesis test to determine if the mean yearly salaries of teachers, tutors, and professors are the same. What would be the correct setup for the null and alternative hypotheses for this test
Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.
Which null and alternative hypotheses are correct?The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.
Identify the null and alternative hypotheses.
As well as the sample size, specify.
Choose a suitable statistical test.
Gather information (note that the previous steps should be done prior to collecting data)
Based on the sample data, compute the test statistic.
Examine the null hypothesis, usually indicated by H0.
Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).
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Darnel uses 8 fluid ounces of lemon juice in one batch of lemonade. How many batches can he make with 1 pint of lemon juice?
Answer:
16 ounces = 1 pint, 8 times 2 = 16
Step-by-step explanation:
Answer in explanation:
1 pint is 16 ounces so he could make 2 batches of lemonade with 1 pint of lemon juice.
(8 x 2 = 16
your answer is 2
Hope this helps!
What is the coefficient of x3y4 in 2x 3y2 5?
The coeficient of x^3+y^4 in the algebraic expression is the number 2
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
2x^3+ 2y^4
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.
2 is the coefficient of x^3+y^4
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carman has saved 80% of the money she needs to buy a new video game. if she saved$36 how much does the video game cost
Carman buy the video game in the cost of $45.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Carman has saved 80% of the money she needs to buy a new video game.
And, she saved the cost $36.
Let total cost of the video game = x
So, We can formulate;
⇒ 80% of x = $36
⇒ 80/100 × x = 36
⇒ 8x = 360
⇒ x = $45
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Given the function f(x) = x² - x - 8, determine the average rate of change of the
function over the interval –4 < x < 3.
Answer:
Average Rate = -14/7
Step-by-step explanation:
f(3) = 3^2 - 3 - 8 = -2
f(-4) = (-4)^2 - (-4) - 8 = 12
interval: [-4, 3]
Average Rate = [f(b) - f(a)]/(b - a) interval: [a, b]
= [(-2) - 12] / [3 - (-4)]
= -14/7
What is the measure of angle ADC?
angle ADC equals 74 degrees
Are 6 8 and 9 12 equivalent?
Yes, 6/8 and 9/12 are equal. After simplifying both the fractions we got that both are equal and their value is 3/4.
Let's first try to understand what is a fraction.
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.
A fraction would be 5/10, for instance.
Here, the numerator is 5 and the denominator is 10.
6/8 is a fraction.
6/8 can be simplified further.
6/8 = 3/4
9/12 is also a fraction.
9/12 can be simplified further.
9/12 = 3/4
To compare 2 fractions first we try to make the same denominator.
we have the same value. so they are equivalent.
Given question is incomplete complete the question here:
Are 6/8 and 9/12 equivalent?
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Solve the equation by completing the squares.
x^2−10x = 11
x= __ and __
Answer:
x = 11 and x = -1
Step-by-step explanation:
We have x^2−10x = 11 and want to make a perfect square out of x^2−10x.
To do this, take half of the coefficient of x, square this half, and then add and then subtract the square immediately following x^2−10x:
Half of -10 is -5, and the square of -5 is 25.
x^2−10x = 11 becomes x^2 - 10x + 25 - 25 = 11
Rewrite x^2−10x + 25 as the square of a binomial: (x - 5)^2.
Then we have (x - 5)^2 - 25 = 11. Solve this for x -5:
(x - 5)^2 = 36. Taking the square root of both sides, we get
x - 5 = ±6
Then x = 11 and x = -1
how many solutions does y = 5x - 8 and y = 9x - 8 have
The equation y = 5x - 8 and y = 9x - 8 have one solution at
(0, -8)
How to find the solution of the equationThe equation is solved simultaneously by elimination method as follows
y = 5x - 8
y = 9x - 8
subtraction the equations
0 = -4x - 0
-4x = 0
x = 0
substituting x = 0 into y = 5x - 8
y = 5x - 8
y = 5 * 0 - 8
y =0 - 8
y = -8
The solution of the equation is at the point (0, -8)
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What is the value of the polynomial 5x − 4x^2 3 at x =- 1?
The value of the polynomial "5x - 4x^2 + 3" at x =- 1 is -6.
The polynomial is 5x - 4x^2 + 3, and it is required to find its value at x = -1,
Now solve the polynomial by putting the value of x equal to -1:
5(-1) - 4(-1)^2 + 3 , x = - 1
-5 - 4 ( 1 ) + 3 , squaring -1 gives + 1
minus 5 minus 4 plus 3
( - 9 + 3)
( - 6 )
Hence, is shown that the value - 6 is obtained when the given polynomial "5x - 4x^2 + 3" is solved for x = -1.
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P(A)=.50 P(B)=.40, and P(A and B) = .15 what is P(a and B)
Answer:
0.75
Step-by-step explanation:
Answer: 0.75
Step-by-step explanation:
Its correct on AP3X! :)
I don’t know what to do for these whatsoever
A circle has a diameter of 7.6 feet. What is the circumference of the circle in feet? Round to the nearest TENTH.
Answer:
23.88 feets
Step-by-step explanation:
C=2π2
=2×3.142×3.8
=23.8792 feets
rounded to the nearest TENTH
=23.88 feets
Find the value of x in the isosceles triangle shown below. Please help asap!!
Answer:
B 12
Step-by-step explanation:
Using pythagoras theorem
Find the length of the major arc in red
I will mark you brainlest!
Kari lost 2.88 kilograms after two weeks of exercise. One kilogram is equal to approximately 2.2 pounds. Which measurement is closest to the number of pounds that Kari lost?
A. 1.31 lbs
B. 5.08 lbs
C. 6.34 lbs
D. 0.76 lbs
Answer:
C
Step-by-step explanation:
2.88*2.2=6.336, which is approximately 6.34.
classify the relationship between angles 1 and 2
Answer:
<1 and <2 are Complementary Angles
m<1 + <2 = 90 degrees
Step-by-step explanation:
<1 and <2 are Complementary Angles
m<1 + <2 = 90 degrees
Have a great day!
Since, angle 1 and 2 sums up to make 90 degrees, hence Angle 1 and 2 are complementary angles.
What is complementary angle?Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.
What is a supplementary angle?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. In the same way, complementary angles sum to 90 degrees.
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When x²+(1/x)=3 find x⁴-2x³-x²-2x+1=
(without using calculator)
so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
we can start by squaring the equation x²+(1/x)=3
so we have x⁴ + 2x² + (1/x)² = 9
x⁴ + 2x² + 1 = 9x²
x⁴ - 7x² + 1 = 0
Now we can factor it
(x²-1)(x²-1) = 0
so x² = 1
now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1
x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1
= x⁴-2x³-2x-1
= (x⁴-2x³) - (2x+1)
= x⁴-2x³-2x-1
= (x²-x)² - (2x+1)
= (x-1)² - (2x+1)
so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
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please awnser the question below
The various statements regarding the given scatter plot is checked and found to be true or false.
What is a scatter plot?
A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities.
1)The equation of the line is y = 2500x - 125.
From the graph we can take two points on the line,
( 2,2250) and ( 10,1250)
Standard equation of line is y = mx + b
where b is y - intercept and m is slope
m = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex] = [tex]\frac{1250 - 2250}{10 - 2}[/tex] = -125
From graph, b = 2500
Equation of line is
y = -125x + 2500
Therefore the given equation is false.
2) The group of hikers descends about 250 feet every minute.
From the graph it is evident that for the interval between two points on y-axis is 250 feet and interval of x-axis is 1 minute.
So the hikers descend 250 feet every minute.
Therefore the given statement is true.
3) The hikers began at the elevation of 2500 feet.
The x-intercept of the graph is 2500 feet.
So the beginning elevation is 2500 feet.
Therefore the statement is true.
4) The graph shows a negative association.
Since the line in the graph is going down and the slope is negative, the graph shows a negative association.
Therefore the statement is true.
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Erin combined 1 17/18 pounds of peanuts with 1 5/6 pounds of M&M's to create trail mix, then evenly distributed the mix in 8 bags. how many pounds of trail mix are in each bag?
There are 17/36 pounds of trail mix in each bag.
Finding out how much pounds of trail mix are in each bagTo find out how many pounds of trail mix are in each bag,you need to first add the weight of the peanuts and M&M's together.
1[tex]\frac{17}{18}[/tex] + 1 [tex]\frac{5}{6}[/tex] =([tex]\frac{35}{18}[/tex]) +([tex]\frac{11}{6}[/tex]) = [tex]\frac{35+33}{18}[/tex] =[tex]\frac{68}{18}[/tex]
which can be simplified to 3 [tex]\frac{14}{18}[/tex]
So there are 3 [tex]\frac{14}{18}[/tex]pounds of trail mix altogether.
To find out how many pounds of trail mix are in each bag, you will divide the total weight of the trail mix by the number of bags.3 [tex]\frac{14}{18}[/tex]÷ [tex]\frac{8}{1}[/tex] =
[tex]\frac{68}{18}[/tex] ÷ [tex]\frac{8}{1}[/tex]=[tex]\frac{68}{144}[/tex]
which can be simplified to [tex]\frac{17}{36}[/tex]
So there are [tex]\frac{17}{36}[/tex]pounds of trail mix in each bag.
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A rectangular cake pan is 13 inches by 9 inches by 2 inches. A round cake pan has a diameter of 8 inches and a height of 2 inches. Which will hold more batter, one rectangular pan or two round pans?
What is the least common multiple of 51, 68 and 85?
Answer:
1020
Step-by-step explanation:
What is the length of side AB as shown on the coordinate plane? On a coordinate plane, a rectangle has 4 points. Point A is (negative 2, 1), point B is (4, 1), point C is (negative 2, negative 3), and point D is (4, negative 3). 2 units 4 units 6 units 8 units please help???
Answer:
Step-by-step explanation:
Answer is 6 units
Answer:
6 units fs
Step-by-step explanation:
1. The football team at Vindale College is having a new stadium built that
will accommodate 49,697 people. According to one fan's calculations,
that is 67% more people than their old stadium could seat. How many
seats did the old stadium have? Round to the nearest whole number.
Please Help! 10 Points + Brainly!
Answer:
17,388³
Step-by-step explanation:
To find volume you need bh the formula, which is base x height. We have to find the base first, so you multiply 27 * 23
27 * 23 = 621
Now you multiply 621 by 28 because 18 is the height.
621 * 28 = 17,388
Therefore, the volume of the figure is 17,388³ (I think, I'm not 100% sure if this is correct)
Hope this helps !!
-Ketifa
What is adjacent angle Class 7?
In class 7, adjacent angles are defined as two angles that share a common vertex and a common side but do not have any common interior points. They are angles that are next to each other.
Adjacent angles are often used in geometry to describe the angles formed by intersecting lines or figures. The adjacent angles can be classified into two types, namely:
Interior adjacent angles: They are formed by two lines that intersect inside a closed figure, such as in a parallelogram.
Exterior adjacent angles: They are formed by two lines that intersect outside a closed figure, such as in a straight line.
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