Factor the trinomial to find a possible combination of dimentions that the rectangle could have:
[tex]x^2-3x-18[/tex]To factor the trinomial, remember that the following product of binomials is equal to:
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]Then, we need to find two numbers a and b such that their product is equal to the constant term -18 and their sum is equal to the linear coefficient -3.
Since the product is negative, one number is negative and the other is positive.
Since the sum is negative, the greatest number is negative.
Two numbers whose difference is 3 and whose product is 18 are 6 and 3.
Notice that:
[tex]\begin{gathered} -6+3=-3 \\ (-6)(3)=-18 \end{gathered}[/tex]Then:
[tex]x^2-3x-18=(x-6)(x+3)[/tex]Therefore, the dimensions of the rectangle, are:
[tex](x-6)\text{ and }(x+3)[/tex]What is the volume of a metal box if the density is 5.4 g/cm³ and a mass of 75 grams
Answer: 0.072 cm^3
Step-by-step explanation:
density=mass*volume
Volume=gensity/mass
5.4/75=0.72
solve |2x-6|<0 not urgent. But its for a test
The inequality expression given as |2x - 6 | < 0 has a solution of x > 3
How to solve the inequality?From the question, the inequality is given as
|2x-6|<0
This gives
|2x - 6 | < 0
Remove the absolute bracket
So, we have the following representation
2x - 6 > 0
Add 6 to all sides of the inequality
So, we have
2x - 6 + 6 > 0 + 6
Evaluate the like terms
So, we have
2x > 6
Divide through by 2
x > 3
Hence, the solution to the expression is x > 3
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You are 4 feet 6 inches tall and cast a shadow that is 6 feet 9 inches long. Your friend is 6
feet tall (at the same time). Find the length of your friend's shadow (show your thinking).
Answer:
Your friends shadow would be 9 foot 3 inches
pls help will mark brainliest
The correct point slope form is y - 1 = 2 ( x - 9).
What is the point slope form?
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation.
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according to a recent student poll, \frac{5}{7} of the 21 members of the finance club are interested in a career in investment banking. if two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
The probability that at least one of them is not interested in investment banking is 13/14.
What is a probability?It is a branch of mathematics. The possibility of the outcome of any random event is termed as probability. The range of the probability must be between o to 1. Here o indicates impossibility of an event and 1 indicates certainty. Probability can be expressed in proportions. Probability deals in finding the occurrence of an event.
Probability of the first person who is not interested in investment banking is 6/21
Probability of the second person who is not interested in investment banking and also first person was not interested then it is taken as 5/20.
probability that at least one is not interested in investment banking
=1- The probability that neither one of them is not interested in investment banking
=1-((6/21)×(5/20)
=13/14
Therefore, the probability that at least one of them is not interested in investment banking is 13/14.
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g(x)=(1)/(4)x+1
what is g(16) ?
g(16)=
Suppose Jessica's route from her house to school consists of two straight legs: First, she drives straight for 5 miles, and then she makes a right turn of 45 degrees and drives another 9 miles. What is the distance (as the crow fl ies) from Jessica's school to her house in miles? (Round your answer to the nearest hundredth.
The distance from Jessica's school to her house is 7.48 miles.
Consider following diagram.
In right triangle ABC, vertex B is the Jessica's house vertex A be her school.
The route from her house to school consists of two straight legs.
She drives straight for 5 miles, and then she makes a right turn of 45 degrees and drives another 9 miles.
⇒ BC = 5 miles and AC = 9 miles
We need to find the distance from Jessica's school to her house in miles.
i.e., we need to find AB
Using Pythagoras theorem,
AC² = AB² + BC²
9² = AB² + 5²
AB = √(81 - 25)
AB = 7.48
Therefore, the distance from Jessica's school to her house is 7.48 miles.
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Write the equation of a line that forms a 45 degree angle with the positive x- axis and passes through the origin?.
Answer:
y = x
Step-by-step explanation:
an equation that an equation that forms an angle of 45 ° and passes through the origin of the axes is the bisector, and its equation is y = x.
270x-3x^2-3x^3=0
solve by factoring
Find the slope of the line that passes through the following points:
(3, -4)
(-1, 0)
Considering the expression of a line, the slope of the line that passes through the pair of points (3, -4) and (-2,0) is -1.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Equation in this caseIn this case, being (x₁, y₁)= (3, -4) and (x₂, y₂)= (-1, 0), the slope m can be calculated as:
m= (0 - (-4))÷ (-1 -3)
m= (0 +4)÷ (-1 -3)
m= 4÷ (-4)
m= -1
Finally, the slope of the line is -1.
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The figure shows a triangle with one or more of its medians.
The length of BK in the triangle is 8 units
How to determine the length of BKThe given parameters are
Shape = TriangleLength KU = 4 unitsMedian point = KAs a general rule, the median of a triangle divides the triangle into the following ratio
Ratio of median = 2 : 1
This means that
Ratio of median, BK : KU = 2 : 1
Substitute 4 for KU
So, we have
BK : 4 = 2 : 1
Multiply the right ratio by 4
BK : 4 = 8 : 4
By comparison, we have
BK = 8
Hence, the value of BK is 8 units
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A data set has these values: 6, 8, 8, 10, 10, 10, 10, 12, 12, 14. The histogram of
the distribution is shown.
Frequency
5
4
3
21
0
11
Data values
5 7 9
13 15
Which statement does not describe the data set?
The statement that does not describe the data set 6, 8, 8, 10, 10, 10, 10, 12, 12, 14 is:
(C) The range of the data set is 15.
Consider the data set,
6, 8, 8, 10, 10, 10, 10, 12, 12, 14
The mean of the data set will be:
mean = ( 6 + 8 + 8 + 10 + 10 + 10 + 10 + 12 + 12 + 14 )/ 10
mean = 100/10
mean = 10
The data set in ascending order are:
6, 8, 8, 10, 10, 10, 10, 12, 12, 14
As the number of terms is even. Therefore, the median will be the sum of two middle numbers divided by 2.
So,
Median = ( 10 + 10 )/2 = 20/2 = 10
The mode of a data set is the maximum number of times a number appears in the data set.
Therefore, the mode of the data set is 10.
The range of the data set is the difference between the highest and the lowest number in the data set.
Range = 14 - 6 = 12
The data set is a symmetric distribution if the mean, median, and mode all fall at the same point.
As the mean, median, and mode are 10, 10, and 10 respectively. Hence, the data set is symmetric.
Hence, statements (A), (B), and (D) are true.
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For the equation |2-2x| = 14, find all values of x which makes the equation true
Answer:
x=-6,8
Step-by-step explanation:
First, let's observe our equation, there is an absolute value (|x|) that means 'x' will have two answers most likely positive and negative.
First we will take off the lines.
now we have
2-2x=14
next minus 2 out of both side of the equation
2 - 2 -2x = 14- 2
-2x =12
now we will divide -2 from both side of the equation
[tex] \frac{ - 2x = 12}{ - 2} [/tex]
we will cancel out - 2
[tex]\frac{x = - 6}{1} [/tex]
x= -6
We aren't done yet since this is an absolute value we have to convert the sum of the equation ( 14) to negatives now which will be in this case (-14)
your new equation will look like this
2-2x= -14
next minus 2 out of both side of the equation
2 - 2 -2x = -14- 2
-2x = - 16
now we will divide -2 from both side of the equation
[tex] \frac{ - 2x = - 16}{ - 2} [/tex]
we will cancel out - 2
[tex] \frac{x = 8}{1} [/tex]
x = 8
Check:x = -6
2 - 2x = 14
2 - 2(-6) = 14.
2 + 12 = 14✓.
x= 8
2 - 2x = -14
2 - 2 (8) = -14
2 - 16 = -14✓
hope this helped happy learning
Given the equation: a+2b=5
Which equation below is correctly solved for a?
Answer:
E. [tex] a = 5-2b [/tex]
Step-by-step explanation:
how to find the value of a, we need to subtract 2b from both side to single out the variable
a + 2b = 5
subtract 2b from both sides
a + 2b - 2b = 5 - 2b
a = 5 - 2b
Therefore, Option E is the correct answer
I’m confused can someone help me
To determine how much flour is required for 24 cups of sugar, assume that 12 cup of flour is required.
What is meant by Fraction operation?A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction can be a portion or section of any quantity out of a whole.The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.There are in total six types of fractions such as:
Proper fraction.Improper fraction.Mixed fraction.Like fractions.Unlike fractions.Equivalent fractions.How to find amount of flour ?8 cup of flour is mixed with 16 cup of sugar
So for 8 cup of flour need 16 cup of sugar
Need to find how much flour is needed for 24 cups of sugar
Assume the amount of flour needed is x.
[tex]\frac{8}{16}[/tex] = [tex]\frac{x}{24}[/tex]
cross multiply them :
[tex]\frac{8}{16}[/tex] = [tex]\frac{x}{24}[/tex]
[tex]8 * 24 =16x[/tex]
[tex]x = \frac{8 * 24}{16}[/tex]
x = 12
12 cup flour is needed for 24 cups of sugar
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a sheet of paper measures 35cm by 25cm. A strip of 5cm width is cut from it all around. find the area of the remaining sheet and also the area of the cut-out strip
answer for brainlist
Answer the ones you know pleaseeeee it’s urgent.
Step-by-step explanation:
Please draw your graph on graph paper unlike me with a proper scale to get accurate results. for parts d and e, I simply substituted the known value back into the original equation s= 20+ 5(t) for each one to either find the s or t value. But the question said to use your graph so you must extrapolate your graph (find the corresponding value for the value they gave) and put that answer. your answer should be correct even if it's a point off from the accurate answer.
draw graph and curve in pencil. you can even shade the region between t=0 and t=10.
if you have any questions feel free to ask, and I apologize if the work is a bit messy :)
In 8x - 5 what are the monomials?
Answer:
Yes
Step-by-step explanation:
We can say this because monomial is term used when an algebraic expression consisting of one term.
PLEASE HELP NEED THIS NOW PLEASE HELP!!
When 1.450 is divided by the number m. The result is a number larger than 1450. Which number could be the value of m?
A. -25 B. -2/5 C. 1/4 D. 5/3
Answer:C
Step-by-step explanation:
i believe it is C because at first i thought it was B then realized it was a negative but c is a positive and a grater number C=5.8
The graph shows Ms. Padilla's monthly cell phone cost, where x is the number of minutes she uses the phone during the month.
Graph of a line on a coordinate plane. The horizontal x axis labeled Seconds ranges from negative 50 to 300 in increments of 25. The vertical y axis labeled Meters. ranges from negative 600 to 100 in increments of 10. A line passes through the points begin ordered pair 0 comma negative 580 end ordered pair and begin ordered pair 175 comma negative 200 end ordered pair.
Which statements are true? Select each correct answer.
Question options:
The x-intercept is meaningless here.
Ms. Padilla is charged $5/min.
Ms. Padilla is charged $0.04/min.
Ms. Padilla pays $16 for months she makes 0 min of calls.
Answer: the X intercept mean this here
Ms.
Padilla is charged $0.04/min.
Ms. Padilla pays $16 for months she makes 0 min of calls
Step-by-step explanation:
At the beginning of the week, Naveen has 87 trading cards. On Monday, he gets 9 more. On Tuesday, he gives 16 away. On Wednesday, he is given 3 by a friend. On Thursday, he sells all of his cards to a collector. The collector pays him a rate of c for every card that Naveen has. If Naveen earns $124.50 from the sale, what is c, the rate that the collector pays for each card?
a. $1.08
b. $1.50
c. $41.50
d. $83.00
in its simplest terms, construction is the process of designing and constructing a building that minimizes its impact on the environment both during construction and over its useful life.
Answer:
1+1=2
Step-by-step explanation:
1111111111111111111111
9 feet=___ yards please and thank you for your help
the ratio of feet to yards is:
[tex]\frac{3feet}{1yard}[/tex]Now, the proportion to find the equivalent yards for 9 feet is:
[tex]\frac{3feet}{1yard}=\frac{9feet}{x\text{ yards}}[/tex]Let's solve for x:
[tex]\begin{gathered} x=\frac{9ft\times1yard}{3ft} \\ x=3\text{yards} \end{gathered}[/tex]Therefore, 9 feet=3 yards.
A father is now 24 years older than his son. In 8 yrs, the father will be twice as old as his son. Find their present ages. Pls give a expression answer
Answer:
Father: 24 Son: 8
Step-by-step explanation:
Adition and subtraction
The ratio of acres of barley to acres of corn at a small farm is 3 : 4. Find the equivalent ratio that uses 18 acres of barley.
Answer:
24 acres of corn, so the equivalent ratio is 18 acres of barley to 24 acres of corn.
Step-by-step explanation:
18 ÷ 3 = 6, so multiply 4 × 6 to obtain 24 acres of corn.
Alternately: Let c be the number of acres of corn. Set up and solve this proportion.
[tex] \frac{3}{4} = \frac{18}{c} [/tex]
[tex]3c = 72[/tex]
[tex]c = 24[/tex]
Sample response: I set up an equation to show that the number of bracelets multiplied by the cost of each bracelet minus the commission is equal to the total, 6(x – 1.25) = 16.50. I divided each side by 6, then added 1.25 to each side with a result of x = 4. Hyo-Jim sold each bracelet for $4.
Each bracelet price is $4 if Hyo-Jin makes bracelets and sells them on an online craft website. Last month, she sold 6 bracelets.
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.
The equation is in the word:
With the commission of $1.25 for each bracelet sold, Hyo-Jin made a total of $16.50.
Let x be the cost of each bracelet:
Total earning = 16.50 + 7.50
Total earning = 24
Each bracelet price x = 24/6 = $4
Thus, each bracelet price is $4 if Hyo-Jin makes bracelets and sells them on an online craft website. Last month, she sold 6 bracelets.
The question is incomplete.
The complete question is:
Hyo-Jin makes bracelets and sells them on an online craft website. Last month, she sold 6 bracelets. After paying the website a commission of $1.25 for each bracelet sold, Hyo-Jin made a total of $16.50. How much does each bracelet sell for on the website? Explain the steps you followed to get your answer.
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Calculate the volume of the cuboid shown
below.
Give your answer in cm³.
If your answer is a decimal, then round it
to 1 d.p.
11 cm
16 cm
21 cm
Answer: 3696cm³
Step-by-step explanation:
The formula for a Cuboid's volume is LxWxH = V
so plug the numbers in
11cm x 16cm x 21cm = V
3696cm³ = V
Résoudre
4x-1-3(1-x)=10
[tex]4x - 1 - 3(1) - 3( - x) = 10 \\ 4x - 1 - 3 + 3x = 10 \\ 4x + 3x - 1 - 3 = 10 \\ 7x - 4 = 10 \\ 7x = 10 + 4 \\ 7x = 14 \\ \frac{7x}{7} = \frac{14}{7} \\ x = 2[/tex]
ATTACHED IS THE SOLUTION
What is the equation of this line?
The equation of the given line in the diagram above is expressed as: b. y = 2/3x.
How to Find the Equation of a Line?For a line that passes through the origin (0, 0) of a graph, the equation that represents the line can be written in slope-intercept form as y = mx, where the slope of the line is represented as m.
The y-intercept of this type of line is zero, that is why we have the equation expressed as y = mx. Where the y-intercept is not equal to zero, the equation of the line would be expressed as y = mx + b, where b is the y-intercept and m is the slope of the line.
Find the slope of the line using two points on the line, (0, 0) and (3, 2):
Slope of the line (m) = (2 - 0)/(3 - 0)
Slope of the line (m) = 2/3.
To write the equation of the line, substitute m = 2/3 into y = mx:
y = 2/3x.
The equation is: B. y = 2/3x.
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On Bennett’s 5th birthday, his uncle invested $2,000 in a CD account that was locked into a 3.2% interest rate, compounded daily. How much will Bennett have in the account when he turns 18?
The amount Bennet will have when he turns 18 will be equal to $3020.
Compound interest is the type of interest charged by banks or institutions on individuals in which the amount after 1 year becomes the principle for the next year. It can be calculated daily, monthly or yearly etc. The formula for compound interest compounded daily will be
A = P(1 + r/n) ^nt, where A is the amount, P is the principle, which is equal to $2000, r is rate of interest which is 3.2% or 0.032, n is compounding frequency which is equal to 365 and t is the time which is equal to 13 years. Now, the amount will be
A = 2000(1 + 0.032/365) ^365×13
A = 2000(1.51)
A = $3020 which is the required amount.
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