Final answer:
The number that satisfies the original equation is -4.
Explanation:
A student's question involves finding a number that satisfies the equation: 'Twelve less than negative nine times a number is equal to 8 minus 4 times the number'.
To solve this, we set up the equation -9x - 12 = 8 - 4x.
Solving for 'x' involves simple algebraic steps.
First, add 9x to both sides to get the variable terms on one side:
-9x - 12 + 9x = 8 - 4x + 9x-12 = 8 + 5xNext, subtract 8 from both sides to isolate the variable term:
-12 - 8 = 5x-20 = 5xFinally, divide both sides by 5 to find 'x':
-20 / 5 = 5x / 5-4 = xThe number that satisfies the original equation is -4.
FIFTHEEN POINTS BC I NEED THIS ASAP =
Billy is making a juice that contains 3 quarts of water, 1 quart of grape juice, 1 quart of orange juice, and 2 quarts of strawberry juice. He is putting his homemade juice into a jug that can hold 2 1⁄2 gallons. How many more quarts of juice can Billy still make before filling the jug?
Given six distinct pairs of gloves, 12 distinct gloves in all, how many ways are there to distribute two gloves to each of six sisters
a) if the two gloves someone receives might both be for the left hand or right hand.
b) if each sister gets one left and one right.
Soln:
a) So i thought about dissectng the problem first into finding the number of ways in which I could make pairs of gloves:
C(12, 2)
then I asked how many ways could the sets of gloves be assigned amongst the 6 sisters:
6!6!
and taking the product of this would give me the amount of ways this could occur:
= C(12,2) * 6!
then for part b)
using this same idea except:
C(6,1) C(6,1) for the left and right glove each .
the C(6,1)*C(6,1)*6!
Right way to think them through?
The length of a rectangle is 5 yd longer than its width. if the perimeter of the rectangle is 46 yd , find its area.
The area of the rectangle is 126 square yards.
Solving the area and perimeter of a rectangle.
The area of a rectangle is the multiplication of the length and the width. The perimeter of the rectangle is calculated by using the formula perimeter = 2(length × width).
Let the Length be (L) and the width be (w).
Length = w + 5Width = wPerimeter = 2 (length + width)
Perimeter = 2 ((w+5) +w)
Perimeter = 2w + 10 + 2w
Perimeter = 4w + 10
Since Perimeter = 46 yd, then:
46 = 4w + 10
4w = 36
w = 36/4
w = 9 yards
Length = 9 + 5 = 14 yards
The area of the rectangle is:
Area = length × width
Area = 14 yd × 9 yd
Area = 126 yd²
Does tis table represent a function ?
Answer: A function is so F(X) = Y where for every X exist only one Y, in this case you can see that F(3) = 4 and F(3) = 3, so the independent variable x = 3, has two solutions y.
So the solution is A, because a function cannot have two different y values for one x value.
Given that line bd is both the median and altitude of triangle abc, congruence postulate sas is used to prove that triangle abc is what type of triangle
Answer:
Triangle ABC is an isosceles triangle.
Step-by-step explanation:
Let AD represent both the median and altitude of triangle ABC.
A median divides the side in two equal parts so BD=BC.
An altitude is a perpendicular drawn .A perpendicular makes an angle of 90°. Hence <ADB=<ADC=90°
AD is the side common to both the triangles ADB and ADC.
Hence Δ ADB≅ΔADC by SAS congruence postulate.
So AB=AC by c.p .c .t.c(congruent parts of congruent triangles are congruent)
Hence by definition of Isosceles triangle ΔABC is an isosceles triangle.
I think it is the 2nd one.
What polynomial identity should be used to prove that 117 = 125 − 8?
Difference of Cubes
Difference of Squares
Square of Binomial
Sum of Cubes
A presidential candidate plans to begin her campaign by visiting the capitals in 44 of 5050 states. what is the probability that she selects the route of fourfour specific capitals? is it practical to list all of the different possible routes in order to select the one that is best?
The probability of the presidential candidate selecting a specific route of four capitals is approximately 0.00575. It is not practical to list all the different possible routes to select the best one.
Explanation:To find the probability that the presidential candidate selects a specific route of four capitals, we need to calculate the number of possible routes and divide it by the total number of routes. Since there are 44 capitals and we need to select 4, we can use the combination formula.
The number of possible routes is given by C(44,4) which is equal to 44!/(4!(44-4)!) = 44!/(4!40!) = (44*43*42*41)/(4*3*2*1) = 91,390.
The total number of routes is 50P44, which is equal to 50!/6! = (50*49*48*47...*7*6!)/(6!) = (50*49*48*47...*7) = 15,890,700.
Therefore, the probability of selecting the specific route of four capitals is 91,390/15,890,700 = 0.00575 (rounded to 5 decimal places). This means that there is a very low probability of selecting this specific route.
It is not practical to list all of the different possible routes in order to select the best one, as there are over 15 million routes. Instead, the candidate may use other criteria such as population density, political demographics, or strategic considerations to determine the best route.
what statement describes the function f(x)=|x^4-x^3|
did u ever get the answer for this
The given function f(x) = |[tex]x^{4}[/tex] - x³| is Option A. neither even nor odd because substituting -x changes the form of the function inside the absolute value. Thus, the function does not meet the criteria for either even or odd functions.
To determine if the function f(x) = |[tex]x^{4}[/tex] - x³| is even, odd, or neither, we need to check how it behaves under the transformation x -> -x.
An even function satisfies the property f(-x) = f(x) for all x, while an odd function satisfies f(-x) = -f(x) for all x.
First, let's consider the inside of the absolute value:
If we replace x with -x, we get: f(-x) = |[tex]-x^{4}[/tex] - (-x)³| = |[tex]x^{4}[/tex] + x³|.
We see that the expression has changed, since |[tex]x^{4}[/tex] - x³| is different from |[tex]x^{4}[/tex] + x³| . Therefore, f(x) does not exhibit the properties of being either even or odd.
This means the correct answer is:
Option A. The function is neither even nor odd.
Complete question:
Which statement describes the function f(x) = the absolute value of x^4 - x^3?
A. The function is neither even nor odd.
B. The function is both even and odd.
C. The function is even.
D. The function is odd.
Please help! Need to pass a module test!
What is the equation of the line, in slope-intercept form, that contains the points (−1, 8) and (2, −1)?
y = −3x + 5
y = −x + 5
y = x + 5
y = −x + 3
which type of triangle is best
Ryan made 4 identical necklaces, each having beads and a pendant. the total cost of the beads and pendants for all 4 necklaces was $18.80 . if the beads cost a total of $9.20 , how much did each pendant cost?
Please help me with this question!!
Ava works at a florist shop. She earns $7.50 an hour plus a fixed bonus for each bouquet she arranges.Write a formula that will help Ava determine how much money she will earn in one week. a=total amount earned h=hours worked in one week n= number of bouquets arranged b=bonus amount for each bouquet
Answer:
a = $7.50h+(n×b)
Step-by-step explanation:
Ava works at a florist shop. She earns $7.50 an hour plus a fixed bonus for each bouquet she arranges.
To determine her earnings in one week the equation will be
a = $7.50h+(n×b)
where a = total amount earned
h = hours worked in one week
n = numbers of bouquets arranged
b = bonus amount for each bouquet
Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will megan and connor have saved the same amount
Connor and Megan are separated by 50-18,5=31,5 dollars. 7,75-5,5=2,25 $ is the difference between the two saves. To save the same amount, it will take them 14 weeks.
What exactly do you mean by an equation system?Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system).
The number of equations must match the number of unknowns for a system to have a singular solution.
What function does an equation system serve?When there are multiple unknowns and there is sufficient data to set up equations in those unknowns, systems of equations are utilized to solve applications.
Generally speaking, if there are n unknowns, we require n equations set up in those unknowns.
How long will it take Megan and Connor to save the same amount of money?The number of weeks, x,
To help Megan, we have:
50+5.5x
We have these for Connor:
18.5+7.75x
For both to possess an equal sum:
50+5.5x=18.5+7.75x
How to find x?
2.25x=31.5
X=31.52.25=14.
Hence we have to save the same amount, it will take them 14 weeks.
Learn more about the system of equations here:
https://brainly.com/question/25976025.
#SPJ2.
Suppose that you only have liability and comprehensive car insurance and you allow your roommate (who doesn't have car insurance) to drive your car to run an errand. What will likely happen if there is a single-car accident causing moderate damage to your car while your roommate is driving?
There are 4,315 pistachios in the bulk bin at the grocery store. Maria wants to split the pistachios into 40 packages so that each package has the same number of pistachios with none left over. Which explains whether or not it is possible?
divide total number by number of packages
4315 /40 = 107.875
it is not possible because it doesn't divide evenly
Let f(x) = 2x2 − 2x + 7 and g(x) = x2 + 9x − 6. find f(x) − g(x). (1 point) x2 − 11x + 13 x2 − 11x + 1 x2 + 7x + 1 x2 + 7x + 13
Answer:
[tex]x^2-11x + 13[/tex]
Step-by-step explanation:
Let [tex]f(x) = 2x^2 - 2x + 7[/tex] and [tex]g(x) = x^2 + 9x - 6[/tex]
We need to find f(x)- g(x)
Replace f(x) and g(x). then subtract the expressions
[tex]f(x)-g(x) =(2x^2 - 2x + 7)- (x^2 + 9x - 6)[/tex]
Remove the parenthesis and multiply negative sign inside second parenthesis
[tex]2x^2 - 2x + 7- x^2 - 9x + 6[/tex]
Combine like terms
[tex]x^2-11x + 13[/tex]
How many slices of pizza will ashley buy if the price is 1.00?
4 slices of pizza (gradpoint)
What are the coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) ? Enter your answer in the boxes.
The centroid of a triangle is the point where the medians of the triangle meets.
The coordinates of the centroid is (-1,2)
The coordinates of the triangle are given as:
[tex]X = (-4,0)[/tex]
[tex]Y = (-1,4)[/tex]
[tex]Z = (2,2)[/tex]
The coordinates of the centroid is:
[tex]C = \frac 13(x_1 + x_2 + x_3,y_1+y_2+y_3)[/tex]
So, we have:
[tex]C = \frac 13(-4-1 + 2,0+4+2)[/tex]
[tex]C = \frac 13(-3,6)[/tex]
Expand
[tex]C = (\frac 13\times -3,\frac 13\times 6)[/tex]
[tex]C = (-1,2)[/tex]
Hence, the coordinates of the centroid is (-1,2)
Read more about centroids at:
https://brainly.com/question/14317682
Write an equation in slope-point form, of the line through point j(4,1). with slope -4.
Solve showing all work, simplify completely: 6/12+1/3
a plumber needs to replace 20 feet of copper piping. When he gets to the supply store, the lengths are given in meters. How many meters of piping does he need to purchase
Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 204204 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions of the box be?
If jimmy as three balls and gives away one and if earl gives jimmy fifteen balls and jimmy loses seven. how many balls does he have?
Answer: Jimmy has 10 balls .
Step-by-step explanation:
Since we have given that
Number of balls Jimmy has = 3
Number of lost balls = 1
Remaining balls Jimmy has = 3-1=2
Number of balls Earl gives to Jimmy = 15
Now,
Total Number of balls Jimmy has = 15+2=17
Again,
Number of balls Jimmy lost = 7
So,
Remaining balls Jimmy has = 17-7=10
So, he has 10 balls at last .
The function models the cost, in dollars, of a rug with width x feet. What is the cost of a rug that is 9 feet wide?
I need help with an Exponential Growth & Decay Word Problem. This is the problem: Mr. Jacobs won $1,000,000 in the lottery. He withdraws 10% of the money every year. How much money will he have left after 20 years? [Round your answer to the nearest dollar]
Estimate how many times larger 7 x 1010 is than 13 x 108.
Answer:
Step-by-step explanation:
18 girls out of 32 students is what percent?
18 girls represent 56.25 percent of the total number of students.
To find what percent 18 girls out of 32 students represent, you can set up a proportion comparing the number of girls to the total number of students. This proportion is represented by the fraction 18/32. To convert this fraction into a percentage, multiply it by 100.
Here's the calculation step by step:
Divide 18 by 32 to get the decimal form.
Multiply the result by 100 to get the percentage.
Performing the calculation gives:
(18/32) x 100 = 56.25%
Therefore, 18 girls represent 56.25 percent of the total number of students.
Why do astronomers say that the sun rotates once every 27 to 31 days, rather than give an exact number?
Astronomers provide a range for the Sun's rotation period due to differential rotation, with varying speeds at different latitudes.
This question demands basic understanding of planetaty motion i.e rotation and revolution in general and about motion of sun in particular
Astronomers say that the Sun rotates once every 27 to 31 days because of the phenomenon known as differential rotation. This means that the speed of rotation of the Sun varies based on its latitude.
The rotation period of the Sun is about 25 days at the equator, 28 days at latitude 40°, and 36 days at latitude 80°. Due to this variable rotation speed, astronomers provide a range rather than an exact number for the Sun's rotation period.
What is the product (2x-1)(x+4)