The two numbers that multiply to 12 and add to negative 4 are -6 and 2.
To find the two numbers, we need to solve the system of equations:
1. xy = 12 (Equation 1)
2. x + y = -4 (Equation 2)
From Equation 2, we can express y in terms of x:
y = -4 - x (Equation 3)
Now, we substitute Equation 3 into Equation 1:
[tex]\( x(-4 - x) = 12 \)\\ \( -4x - x^2 = 12 \)\\ \( x^2 + 4x - 12 = 0 \)[/tex]
We can factor this quadratic equation:
[tex]\( (x + 6)(x - 2) = 0 \)[/tex]
Setting each factor equal to zero gives us two possible solutions for x:
[tex]\( x + 6 = 0 \) or \( x - 2 = 0 \)[/tex]
So, [tex]\( x = -6 \) or \( x = 2 \)[/tex].
Using Equation 3 to find the corresponding y values:
If ( x = -6 ), then ( y = -4 - (-6) = 2 ).
If ( x = 2 ), then ( y = -4 - 2 = -6 ).
Therefore, the two pairs of numbers that satisfy both conditions are (-6, 2) and (2, -6). Since the question asks for two numbers, and both pairs contain the same numbers, the answer is -6 and 2.
Which system is represented by the graph?
a. y > 2x
x + 2y ≤ –8
b. y ≥ 2x
x + 2y < –8
c. y < 2x
x + 2y ≥ –8
d. y ≤ 2x
x + 2y > –8
To determine the system of two inequalities which is represented by the graph, you have to do such steps:
1 step. The dashed blue line represents sign > or <. The line has the equation y=2x, then the inequality should be y>2x or y<2x. Since point (-1,1) belongs to the blue shaded region, then the inequallity y>2x is true.
2 step. The solid red line represents sign ≤ or ≥. The line has the equation x+2y=-8, then the inequality should be x+2y≤-8 or x+2y≥-8. Since the origin (0,0) doesn't belong to the red shaded region, then the inequallity x+2y≤-8 is true.
Thus, the system is
[tex]\left\{\begin{array}{l}y>2x\\x+2y\le-8.\end{array}\right.[/tex]
Answer: correct choice is A.
What number gives you the same result when multiplied by 6 as it does when 6 is added to it?
Solve for PQ 4x+19=2x+32
Select the postulate that is illustrated for the real numbers.
6 + 0 = 6
The commutative postulate for multiplication
Multiplication by one
The addition inverse postulate
Commutative postulate for addition
The distributive postulate
The additive identity postulate
The multiplication inverse
Answer:
The additive identity postulate
Step-by-step explanation:
6 + 0 = 6
Any number added with zero, we get the same number.
That is, a + 0 = a, where "a" is any real number.
Let's take a = 9, we get
9 + 0 = 9
Let's check out a few more examples:
-9 + 0 = -9
2/3 + 0 = 2/3
22 + 0 = 22
You can see any number added with 0, we get the same number.
Here 0 is additive identity, this is called additive identity postulate.
We are given 6 + 0 = 6 which illustrated by "The additive identity postulate."
Therefore, answer is "The additive identity postulate"
At one point on the trip, the miles are recorded as 15,121 when the gas tank is 75% full. Use a ratio equation to determine the miles per gallon the sedan averages. Round your answer to the nearest whole number.
The most common size of a sedan tank is 18.5 gallons. So if it is 75% full, it contains 13.875 gallons of gas. If it recorded a mileage of 15,121 miles, mileage per gallon, therefore, is 1090 rounded off to the nearest whole number.
Given: Gas full tank of a sedan – 18.5 gallons
75% full = 13.875 gallons
Mileage using 13.875 gallons of fuel = 15,121 miles
The mileage per gallon computation using the ratio equation:
Ratio is 15121:13.875 or
X/1= 15121/13.875
13.875x = 15121
X = 15121/13.875
X =1089.80 or 1090 miles per gallon (rounded off)
A scuba diver used the expression below to describe his position in relation to sea level.
2 + (–20) + 8
Which statement could describe the diver’s movements?
Starting on a platform 2 feet above sea level, dive down to a location that is 18 feet below sea level, and then rise 8 feet.
Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
Starting 2 feet below sea level, dive down 20 more feet, and then rise to a location that is 8 feet below sea level.
Starting 2 feet below sea level, dive down 18 more feet, and then rise to a location that is 8 feet below sea level.
Answer:
Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
Step-by-step explanation:
A scuba diver used the expression below to describe his position in relation to sea level.
2 + (–20) + 8
positive number is the feet above the sea level
negative number is the feet below the sea level (deep)
starting at 2 , 2 feet above sea level then down the sea 20 feet down,
finally rise 8 feet above the sea level
So, Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
For which value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers
25/8 is the value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
We need to find the value of k will the roots of the equation 2x²-5x+k=0 be real and rational numbers.
A quadratic equation has real roots when the discriminant is positive or zero (not negative).
b²-4ac≥0
b=-5, a=2, c=k
(-5)²-4((2.k)≥0
25-8k≥0
25≥8k
Divide both sides by 8
25/8≥k
k≤25/8
Hence, 25/8 is the value of k will the roots of the equation 2x^2-5x+k=0 be real and rational numbers
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What are the coordinates for the x and y intercepts of the function 4y - 2x = 24?
What three consecutive integers have a sum of 252?
252/3 = 84
84-1 = 83
84+1=85
83 +84 +85 = 252
the numbers are 83, 84, 85
What number appears 7 times in the multiplication table?
In a multiplication table, each number from 1 to 12 would appear 12 times corresponding to each multiplier. In a table specific for a single number, that number would repeat 12 times.
Explanation:The question is asking about a number that appears 7 times in a multiplication table. In a multiplication table, numbers 1 through 12 are repeated 12 times, once for each multiplier. However, in a multiplication table between 1 and 10, the number 1 appears multiple times as it is a factor for every other number. As an exception, if we have a multiplication table that is specific to a certain number, for example, the number 7, then number 7 would appear 12 times as it is the constant multiplier for each number in the table.
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What is the meaning of life? What makes this world so great? Is there something to look forward to in the future?
Find the product.
-mnp(3m - 5n + 7p)
-3m + 5n^2+ 7p^2
3mnp - 5mnp + 7mnp
-3mnp + 5mnp - 7mnp
-3m^2np + 5mn^2p - 7mnp^2
The test that gives a list of the possible rational zeros of a polynomial function is called the test.
Answer:
rational zero
Step-by-step explanation:
Find an equation for a line that passes through the point (0, –3) and parallel to another line whose slope is 1.2.
Final answer:
The equation of the line that passes through the point (0, -3) and is parallel to another line with a slope of 1.2 is y = 1.2x - 3.
Explanation:
To find an equation for a line that passes through the point (0, –3) and is parallel to another line with a slope of 1.2, we use the fact that parallel lines have the same slope. Since a line's equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept, and we already know the slope (m = 1.2) and the y-intercept (b = -3, since the line passes through (0, -3)), our equation becomes:
y = 1.2x - 3
This means that any line parallel to one with a slope of 1.2 and passing through (0, -3) will also have a slope of 1.2, but the y-intercept will be unique to the point it passes through.
Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose a point on the line, such as (2, 5). Step 2: Choose another point on the line, such as (1, 3). Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is . Step 4: Substitute those values into the point-slope form. y – y1 = m(x – x1) y – 3 = (x – 1) Which of Talia’s steps is incorrect? Step 1 is incorrect because it uses a point that is not on the line. Step 2 is incorrect because it uses a point that is not on the line. Step 3 is incorrect because it shows an incorrect ratio for the slope. Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.
Answer:
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step-by-step explanation:
Help with finding value of x?
Eighteen cement squares cover a patio with an area of 40.5m^2. What is the side length of one of the squares
The side length of each of the cement squares is 1.5m. This is calculated by dividing the total area by the number of squares to find the area of each square, and then taking the square root to find the side length.
Explanation:To solve this question, we need to first understand that the total area of the patio equals the sum of the areas of each individual cement square. There are eighteen squares, and the total area is 40.5 square meters. This means that the area of one cement square can be acquired by dividing the total area by the quantity of the squares.
So, the calculation would be 40.5m² / 18, giving us an area of 2.25m² for each square.
Now, since these are squares and all sides of a square are equal, their area is represented by the square of one side length. Therefore, to get the length of one side, we extract the square root of the area.
The calculation is √2.25, which equals 1.5. So, the side length of one of the cement squares is 1.5m.
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Each exterior angle of an equilateral triangle has which measure?
Answer:
60 degreesStep-by-step explanation:
The seventh grade math classes are going on a field trip. the field trip will cost $7 per student. write an expression to find the cost of the field trip for s students. what is the total cost if 26 students go on the trip?
7s is the expression to find the cost of the field trip for s students and 182 is the total cost if 26 students go on the trip
What is Expression?An expression is combination of variables, numbers and operators.
Given,
The seventh grade math classes are going on a field trip.
the field trip will cost $7 per student.
Given s is number of students.
7s is the expression to find the cost of the field trip for s students.
When number of students are twenty six 26, i.e s=26
Total cost=7×26
seven times of twenty six
182
Hence 7s is the expression to find the cost of the field trip for s students and 182 is the total cost if 26 students go on the trip
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Please help ;-;!!
Math Algebra
(Image)
HELP PLEASE!!!!!
Find the radius of a circle if a central angle of 3π/2 intercepts an arc of 26.4 centimeters.
0.19 cm
3.14 cm
5.6 cm
Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.
5 rad16 rad65 radFind the arc length intercepted by a central angle of 3π/4 radians in a circle whose radius is 18.4 inches.
13.8π15.2π24.5πAnswer:
Find the radius of a circle if a central angle of 3π/2 intercepts an arc of 26.4 centimeters.
Ans: 5.6 cm
Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.
Ans: 5 rad
Find the arc length intercepted by a central angle of 3π/4 radians in a circle whose radius is 18.4 inches.
Ans: 13.8π
Find two numbers whose product is 20 and whose sum is 12
The numbers are 10 and 2 if the product is 20 and whose sum is 12 after making the two equations.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The product of two numbers is 20 and whose sum is 12
Let the numbers are x and y
xy = 20
x + y = 12
y = 12 - x
x(12 - x) = 20
x² - 12x + 20 = 0
After solving the above quadratic equation, we get:
x = 10, 2
y = 2, 10
Thus, the numbers are 10 and 2 if the product is 20 and whose sum is 12 after making the two equations.
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Solve the system:
p-3q=-1
-5p+16q=5
a. (2,1)
b.(3,3)
c. (-1,0)
d.(5,2)
Answer: The correct option is
(c) (-1, 0).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]p-3q=-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-5p+16q=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (i), we have
[tex]p-3q=-1\\\\\Rightarrow p=3q-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of p from equation (iii) in equation (ii), we get
[tex]-5(3q-1)+16q=5\\\\\Rightarrow -15q+5+16q=5\\\\\Rightarrow q=5-5\\\\\Rightarrow q=0.[/tex]
From equation (i), we get
[tex]p=3\times0-1=-1.[/tex]
Thus, the required solution is (p, q) = (-1, 0).
Option (c) is CORRECT.
What transformation takes
f(x)=15x+3 to g(x)=5x+3 ?
Question 1 options:
a horizontal compression by a factor 1/3
a translation 6 units right
a horizontal stretch by a factor of 3
a translation 6 units down
30 POINTS PLEASE HELP! An investment in a savings account grows to three times the initial value after t years.
If the rate of interest is 5%, compounded continuously, t = (blank) years.
please help me
An irregular polygon is shown below:
The area of the irregular polygon is ____ square units.
Answer:
26
Step-by-step explanation:
well we see that it is at its longest is 9, and the tallest is four
we have two missing sides...
so for the top left on long, it is 5
the full length is 9, and we have a 4 on the top, so we have 5 left, the top right line is 5
the one on the left side is two, because the middle line is a 2, and the full items height is 4.
4x2=8
2x2=4
5+9=14
8+4=12
14+12=26
An aluminum recycling center pays0.08 per pound for cans how much will make receive for 21.5 pounds of cans
I don't get how to do this please help
the answer is D
the exponent is 8.869 where the 9 is 9/1000, the 6 is 6/100 and the 8 to the right od the decimal point is 8/10
Ou can draw a quadrilateral with two sets of parallel lines and no right angles.
a. True
b. False
If two angles of a triangle are complementary, then the triangle must be