Answer:
[tex]x=-3\\x=6[/tex]
Step-by-step explanation:
We begin with [tex]x^2-3x-18=0[/tex]
To factor this, we need to look for two things:
Two numbers that add together to get [tex]-3[/tex] and two numbers that multiply together to get [tex]-18[/tex].
One method to find the answer is to write out each of the solutions to the multiplication and then check the sum of each of those digits:
The numbers that multiply together to get [tex]-18[/tex] are:
1 and -18
-1 and 18
2 and -9
-2 and 9
3 and -6
-3 and 6
Now, we can add each of these pairs of digits together to find which one gives us an answer of [tex]-3[/tex]
[tex]1+(-18)=-17\\\\-1+18=17\\\\2+(-9)=-7\\\\-2+9=7\\\\3+(-6)=-3\\\\-3+6=3[/tex]
From this, we can see that 3 and -6 gave us the result of -3. This means that these are the two factors.
To get our answer from this, we need to put our answer in the form of [tex](x+a)(x+b)=0[/tex]
This gives us the factored form of [tex](x+3)(x-6)=0[/tex]
To solve this equation, we must make either parenthesis equal to zero. This means that our solutions will be
[tex]x=-3\\x=6[/tex]
By factoring, the solutions to the quadratic equation x² - 3x - 18 = 0 are x = 6 and x = -3.
How to Solve an Equation by Factorization?To solve the quadratic equation x² - 3x - 18 = 0 by factoring, we need to find two binomials that, when multiplied, result in zero. The quadratic equation generally follows the format ax² + bx + c = 0, where a, b, and c are constants.
Here's the step-by-step process for factoring the given equation:
Step 1: Begin with the equation x² - 3x - 18 = 0.
Step 2: Identify two numbers whose product is -18 (the constant term) and whose sum is -3 (the coefficient of the x-term).
We find that the two numbers are -6 and +3 because:
-6 * 3 = -18 (the product of the two numbers is -18)
-6 + 3 = -3 (the sum of the two numbers is -3)
Step 3: Rewrite the middle term (-3x) using -6x and +3x:
x² - 6x + 3x - 18 = 0.
Step 4: Group the terms and factor them by pairs:
(x² - 6x) + (3x - 18) = 0.
Step 5: Factor out the greatest common factor from each group:
x(x - 6) + 3(x - 6) = 0.
Step 6: Notice that both terms have a common factor of (x - 6). Factor it out:
(x - 6)(x + 3) = 0.
Step 7: Apply the zero-product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:
Setting each factor to zero and solving for x:
x - 6 = 0 --> x = 6
x + 3 = 0 --> x = -3
Learn more about Factorization on:
https://brainly.com/question/25829061
#SPJ6
Which statement is true?
A. -8xy and x+y are like terms.
B. -8xy and 9x are like terms.
C. -8xy and 9y are like terms.
D. -8xy and 9xy are like terms
What is equalivent to 5=4z+13
Answer:
[tex]z = - 2[/tex]
Step-by-step explanation:
[tex]5 = 4z + 13 \\ 5 - 13 = 4z \\ - 8 = 4z \\ \frac{ - 8}{4} = \frac{4z}{4} \\ z = - 2[/tex]
An isosceles triangle △ABC with the base BC is inscribed in a circle. Find the measures of angles of the triangle, if measure of arc BC is 102°.
Answer:
angle at A: 51°base angles: 64.5°Step-by-step explanation:
The measure of the inscribed angle BAC is half the measure of the intercepted arc BC, so is 102°/2 = 51°.
The base angles at B and C are the complement of half this value, or ...
90° -(51°/2) = 64.5°
The angle measures in the triangle are ...
∠A = 51°
∠B = ∠C = 64.5°
Which expression is equal to 45 x 4-734-27
45 = 4 0
Answer:
9(5x - 3) option (c)
Step-by-step explanation:
The question isn't clear as well as incomplete without the options. Since there are no options let's determine the answer of the following mathematical expression:
45x - 27
a) 9(3x - 5)
b) 3(12x + 7)
c) 9(5x - 3)
d) 5(7x + 30)
To determine which option is equivalent to 45x - 27, we would check each option by expanding the bracket. Apply BODMAS (stands for Bracket, Of, Division, Multiplication, Addition and Subtraction) after the expansion. That is multiply before you add or subtract.
a) 9(3x - 5) = 9×3x - 5×9
= 27x - 45
b) 3(12x + 7) = 3×12x + 3×7
= 36x + 21
c) 9(5x - 3) = 9×5x - 9×3
= 45x - 27
d) 5(7x + 30) = 5×7x + 30×5
= 35x + 150
From the expansion, only option C is equal to the given expression: 45x - 27
0.5x + 6 > 3
I don’t know how to solve
Answer:
x > -6
Step-by-step explanation:
Move 6 to the other side:
0.5x > -3
x > -6
All of the following statements about the standard normal probability distribution are true EXCEPT: a) the expected value is 0 b) the total area under the standard normal curve is 1 c) the standard deviation can assume any positive value d) the probability that z assumes values between -1 and 1 is 0.6826
Answer:
d) the probability that z assumes values between -1 and 1 is 0.6826.Step-by-step explanation:
In a standard normal probability distribution, the Z-value depends on the data set, the mean and the standard deviation, that means, it's a variable measure, it's not a constant, that's why the choice d is wrong.
On the other hand, the other choices are correct regarding standard normal probability distribution.
Therefore, the right answer is d.
Solve x^2 -24x = -80 by completing the square
Answer:
(20,4)
Step-by-step explanation:
Answer:
{4,20}
Step-by-step explanation:
b on edg got 100%
I need help please!!
Answer:
3/3/8
Step-by-step explanation:
2. If the width of a pool is 60 feet and the perimeter is 200 feet, how long is the pool?
Answer:
40 feet
Step-by-step explanation:
Have a nice day
What’s the correct answer for this?
The square root of 10 is a number with the following property: when you square it, you get 10.
So, if we have [tex]a<\sqrt{10}<b[/tex], where [tex]a[/tex] and [tex]b[/tex] are positive integers, if we square the whole inequality we have
[tex]a^2<10<b^2[/tex]
Let's analyse option A for example. Given everything we said so far, we would have
[tex]1<\sqrt{10}<2 \iff 1^2<10<2^2 \iff 1<10<4[/tex]
which is false.
Option B is again false, because we would have
[tex]2<\sqrt{10}<3 \iff 2^2<10<3^2 \iff 4<10<9[/tex]
which is again false. Keep trying with options C and D following those same steps, and see which one is correct
Answer:
C
Step-by-step explanation:
√10=3.16
3.16 is between 3 and 4 hence C is the answer
100 PTS PLEASE HELP PLEASEEE
Answer:
8
Step-by-step explanation:
The square root of a number is what number multiplied by itself can result in the product of this.
For example, in this question you multiply 8 by itself to get 64
8*8=64
So, the square root is 8
A lunch menu consists of 6 different sandwiches, 4 different soups, and 4 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink?
Write this number in standard notation.
4.702 x 10
Answer:
47.02
Step-by-step explanation:
Since the exponent of the scientific notation is positive, move the decimal point 1 places to the right.
47.02
Answer:
0.0004702
Step-by-step explanation:
I need help on these 4 chooses.If you are able to help me i would appreciate it because i have been stuck on this for an hour or so.
The First choose is does not/does
The Second choose is 96/216/60
The Third choose is less/more
The Fourth choose is 106.5/194.25/25/50
Answer:
1. does (yes he can)
2. 216
3. more
4. 194.25
Step-by-step explanation:
Total wood
18 x 12 = 216
Maurice suggestion
10.5 x 10.5 = 110.25
Sides
10.5 x 2 inches x 4 sides = 84
84 + 110.25 = 194.25
216 - 194.25 = 21.75 extra
What is the next step after using the distributive
property?
Answer:
If it's a simple equation such as 2 (x + y), the next step after applying the distributive property is to do the multiplication and simplify the terms.
But in solving an equation such as
2(x + 3) = 3(x + 1)
After applying the distributive property, the next step is to separate the variables to one side, like collecting like terms and then solving the now simplified equation.
Step-by-step explanation:
For a normal equation, the distributive property, also called the distributive law of division and multiplication helps to use the variable outside the bracket to multiply the sum of terms in the bracket. For example.
2 (x + y)
The distributive property enables us to say
2×x + 2×y = 2x + 2y
So, the next step after applying the distributive property is to simplify the equation.
But in solving an equation such as
2(x + 3) = 3(x + 1)
Applying the distributive property
2x + 6 = 3x + 3
We then operate variables, collect like terms on one side
6 - 3 = 3x - 2x
3 = x
x = 3
Hope this Helps!!!
Answer:
-102 + (-25.5)
Step-by-step explanation:
ashley drove to her father's house, which was 164 miles away. It took her 2 hours to get there. After seeing her father for 2 hours, she went to her cousin's house to stay overnight, which was 125 miles from her father's house. How many minutes does it take Ashley to get to her cousin's if she drives the same speed as when she went to her father's? Do not include units in your answer and round to the nearest hundredth. Example, if answer is 19.546 minutes, put 19.55.
Answer:
Time Spent = 91.46 minutes
Step-by-step explanation:
Given
To Her Father's house
Distance = 164 miles
Time Taken = 2 hours
To Her Cousin's house
Distance = 125 miles
Required
Time Taken to get to her cousins house.
First, her average speed to her father's house needs to be calculated.
Speed is calculated as thus;
[tex]Speed = \frac{Distance}{Time}[/tex]
In this case, Distance = 164 miles and Time = 2 hours
Substitute these values;
[tex]Speed = \frac{164 miles}{2 hours}[/tex]
[tex]Speed = 82miles/hour[/tex]
It's stated in the question that; she maintains the same speed when going to her cousin's residence to spend the night;
Using the same formula for speed;
[tex]Speed = \frac{Distance}{Time}[/tex]
But in this case, Speed = 82 miles/hour and Distance = 125 miles
Substitute these values
[tex]82 = \frac{125}{Time}[/tex]
Multiply both sides by Time
[tex]82 * Time = \frac{125}{Time} * Time[/tex]
[tex]82 * Time = 125[/tex]
Divide both sides by 82
[tex]\frac{82 * Time}{82} = \frac{125}{82}[/tex]
[tex]Time = \frac{125}{82} hours[/tex]
To convert this time to minutes
If 1 hour = 60 minutes
Then,
[tex]\frac{125}{82} hours[/tex] is equivalent to [tex]\frac{125}{82} * 60 minutes[/tex]
Hence,
[tex]Time = \frac{125}{82} * 60 minutes[/tex]
[tex]Time = 91.463415 minutes[/tex]
[tex]Time = 91.46 minutes[/tex] (Approximated)
Hence, she spends 91.46 minutes to get to her cousin's place from her father's house
given that sin theta= 1/4, 0 is less than theta but less than pi/2, what is the exact value of cos theta
Answer:
[tex]\cos{\theta} = \frac{\sqrt{15}}{4}[/tex]
Step-by-step explanation:
For any angle [tex]\theta[/tex], we have that:
[tex](\sin{\theta})^{2} + (\cos{\theta})^{2} = 1[/tex]
Quadrant:
[tex]0 \leq \theta \leq \frac{\pi}{2}[/tex] means that [tex]\theta[/tex] is in the first quadrant. This means that both the sine and the cosine have positive values.
Find the cosine:
[tex](\sin{\theta})^{2} + (\cos{\theta})^{2} = 1[/tex]
[tex](\frac{1}{4})^{2} + (\cos{\theta})^{2} = 1[/tex]
[tex]\frac{1}{16} + (\cos{\theta})^{2} = 1[/tex]
[tex](\cos{\theta})^{2} = 1 - \frac{1}{16}[/tex]
[tex](\cos{\theta})^{2} = \frac{16-1}{16}[/tex]
[tex](\cos{\theta})^{2} = \frac{15}{16}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{15}{16}}[/tex]
Since the angle is in the first quadrant, the cosine is positive.
[tex]\cos{\theta} = \frac{\sqrt{15}}{4}[/tex]
Answer:
b.[tex]\frac{\sqrt{15} }{4}[/tex]
Step-by-step explanation:
pls check the attachment thank you
Those in favor of using non-traditional tests (e.g., portfolios, essays, projects) to evaluate students say that their use is much fairer than using standardized tests only. This is because it means that students who are willing to work hard but who perform poorly in standardized tests will have a better chance of doing well. However, there are challenges in the use of non-traditional tests that cast doubt on their fairness. For example, it is difficult to determine if a student received any help from others in putting together his or her portfolio. In addition, there is a growing market for customized essays whereby students can pay someone else to write essays for them via the internet. At the moment, the only deterrent is a teacher's vigilance. Although teachers might be able to identify work which seems atypical for an individual student, they won't necessarily be able to conclude whether this is due to the student's hard work or due to assistance the student received from others.
Which one of the following conclusions is best supported by the passage above?
1.Use of traditional tests may not evaluate how hard a student is willing to work to get a good evaluation.
2.Challenges of the use of non-traditional tests mean that students should only be evaluated using standardized tests.
3.Use of non-traditional tests to evaluate students is not necessarily fairer than using standardized tests to evaluate students.
Answer: 1.Use of traditional tests may not evaluate how hard a student is willing to work to get a good evaluation
Step-by-step explanation:
Proponents of Traditional Tests argue that they are fairer because hard working students who may fail standadized tests may be able to pass them.
However, the text shows that that arguement has loopholes because a student could pass those Traditional testing methods by employing methods that are void of hard-work such as receiving help from other people or buying a customized essay over the internet.
Should this be the case then, Traditional tests may not be able to properly evaluate a student's hard work because one can not know if the submitted content was solely due to hard-work or if there was assistance from somewhere.
Answer:
3.Use of non-traditional tests to evaluate students is not necessarily fairer than using standardized tests to evaluate students.
Step-by-step explanation:
The Use of non-traditional tests to evaluate students is not necessarily fairer than using standardized tests to evaluate students because it is difficult to determine if a student received any help from others in putting together his or her portfolio, essay or project except if he is closely monitored by the teacher. Also a student may pay someone online to write a customized essay for him/her via the internet therefore it cannot be concluded whether it is due to the student's hard work or due to assistance the student received from others.
5/10 as a unit fraction
Answer:
its just 5/10, or 1/2 is it not
Step-by-step explanation:
Write an equation in standard form of the line that passes through (1, 3) and has a slope of –4.
Answer:
work is shown and pictured
The number of milligrams of a drug in a person’s body after t hours is given by the function f(t) = 10e-0.3t. When will the amount of the drug be approximately 0.2 milligrams?
Answer:
amount of the drug becomes approximately equal to 0.2 milligrams after 13.04 hours
Step-by-step explanation:
Given: The function [tex]f(t)=10e^{-0.3 t}[/tex] represents number of milligrams of a drug in a person’s body after t hours
To find: time after which amount of the drug becomes approximately 0.2 milligrams
Solution:
[tex]f(t)=10e^{-0.3 t}\\0.2=10e^{-0.3 t}\\\frac{0.2}{10}=e^{-0.3 t}\\\frac{2}{100}=e^{-0.3 t}\\\frac{1}{50}=e^{-0.3 t}\\[/tex]
As [tex]e^x=y\Rightarrow x=\ln y[/tex] ,
[tex]50=e^{0.3 t}\\0.3t=\ln 50\\t=\frac{\ln 50}{0.3}=13.04\,\,hours[/tex]
So, amount of the drug becomes approximately equal to 0.2 milligrams after 13.04 hours
Answer:
13 hours
Step-by-step explanation:
right on edmentum
What is a scale factor
Answer:
To find the scale factor, locate two corresponding sides, one on each figure. Write the ratio of one length to the other to find the scale factor from one figure to the other.
Step-by-step explanation:
XYUV=123=4
The scale Factor is 4!
Express this number in stand
5.401 x 10-1 = ?
Answer:
0.5401
Step-by-step explanation:
In Standard form
due to the negativity of the power, you move the decimal point to the left...and u move it once
What does the term human capital refer to?
Answer:
its a captial of humans
Step-by-step explanation:
Answer: knowledge
Step-by-step explanation:
Human capital is a loose term that refers to knowledge, experience and skills of an employee. ... It states that companies have an incentive to seek productive human capital and to add to the human capital of their existing employees.
The sum of the first 12 terms of a geometric sequence with 10 as the first term and a common ratio of 0.3 is __________.
Answer: 14.2638366937
Step-by-step explanation:
A geometric sequence is a sequence in which each term is multiplied by a number, called the common ratio, to get the next term.
So, if the first term of the geometric sequence is 10 and the common ratio is 0.3, the sequence would be 10, 0.3(10), 0.3 x 0.3 x 10... and so forth. This becomes:
10, 3, 0.9, 0.27, 0.081, 0.00243, 0.00729, 0.002187, 0.0006561, 0.00019683, 0.000059049, 0.0000177147...
You add these first 12 terms to get 14.2638366937.
[3]
(b)
Calculate the values of c for which 2x2 – 3x + c>-2 for all values of x.
Answer:
c > -7/8
Step-by-step explanation:
Add 2 for an inequality that compares to zero:
2x^2 -3x +(c+2) > 0
This will be true when the discriminant is negative. For the quadratic ...
ax^2 +bx +c
the discriminant is ...
b^ -4ac
We want this to be negative:
(-3)^2 -4(2)(c+2) < 0
9 -8(c +2) < 0
9 -8c -16 < 0
-7 < 8c
-7/8 < c
The given inequality will be true for all values of c greater than -7/8.
Factorise - x^(3)-3x^(2)-10x+24 ( plss tel method also)
Step-by-step explanation:
I think we can do it in this way
x3 - 3x2 - 10x + 24
x2(x - 3) - 2(5x + 12)
Which of these shapes is a parallelogram but not a square?
Select all that are true.
Answer: The top right and bottom right polygons are parallelograms and not squares.
Step-by-step explanation:
A parallelogram is a quadrilateral with two pairs of parallel sides opposing each other.
A square is a quadrilateral with two pairs of parallel sides opposing each other; however, all four sides must be equal and all angles must equal 90 degrees.
Any quadrilateral that is a parallelogram and not a square has angle measures that are not 90 degrees (or have unequal sides).
The top left image is neither. There are two sets of equal sides, but they are not parallel. The top right image is a parallelogram, as it has two pairs of parallel sides opposing each other. It is not a square, as the side lengths are unequal. The middle left image is neither. There are not two sets of parallel sides. The middle right image is a square and a parallelogram. All its sides are equal, and it has two sets of opposing parallel sides. The bottom left image is neither. It only has one set of parallel opposing sides, and they are not equal in length. (This is a trapezoid.)The bottom right image is a parallelogram, as it has two pairs of parallel sides opposing each other, and the side lengths are unequal.Only the top right and bottom right images are parallelograms and not squares.
The shapes that are parallelogram but not a square is the rectangle and the parallelogram. The rhombus is a square because the angles are 90°.
What is a quadrilateral?A quadrilateral is a polygon with four sides and four angles. A parallelogram is a quadrilateral with parallel and equal opposite sides.
A square is a quadrilateral in which all sides are equal, opposite sides are parallel and each angle measures 90 degrees.
The shapes that are parallelogram but not a square is the rectangle and the parallelogram. The rhombus is a square because the angles are 90°.
Find out more on quadrilateral at: https://brainly.com/question/16691874
A right triangle has one angle that measures 59º. What is the measure of the other
acute angle?
Answer: 31°
Step-by-step explanation:
We know that a right triangle is equal to 180°. Since this is a right triangle, we know that one angle is 90°. Since we are given out other angle, it is very easy to find the missing angle.
180°=59°+90°+x
180°=149°+x
x=31°