Answer:
Impossible
Explanation:
The side lengths a, b and c can form a triangle if the inequality holds:
[tex]a+b\ge c[/tex]Given the side lengths 6,7 and 14:
[tex]\begin{gathered} 6+7=13\le14\text{ (This invalidates it)} \\ 6+14=20\ge7 \\ 6+13=19\ge7 \end{gathered}[/tex]Since the inequality does not hold in all cases, it is Impossible to form sides of a triangle.
Which function has the following characteristics? • A vertical asymptote at x = 3 • A horizontal asymptote at y = 2 Domain: {** +3] 2x - 8 X - 3 y=x2-9 2 9 x² - 4 4 OB. V C. 2x2 - 18 x² - 4 4 2x2 - 8 O D. ** - 9
SOLUTION
To get this, note that the vertical asymptote can be gotten by setting the denominator to be equal to 0.
If we do this, we will notice that the vertical asymptote of option A and option D is x = 3
That is
for option A
[tex]\begin{gathered} y=\frac{2x-8}{x-3} \\ x-3=0 \\ x=3 \end{gathered}[/tex]For option D
[tex]\begin{gathered} y=\frac{2x^2-8}{x^2-9} \\ x^2-9=0 \\ x^2=9 \\ x=3 \end{gathered}[/tex]So, the answer is either option A or D.
But to get the correct answer, let us look at the graphs for both functions
Graph of A
[tex]y=\frac{2x-8}{x-3}[/tex]From the graph, you can see that the domain is defined at x = 3. Notice that the green line cut across x = 3.
Now let's check Graph of option D
[tex]y=\frac{2x^2-8}{x^2-9}[/tex]From the graph, you can see that the domain is defined at x = -3 and x = 3. Notice that the purple and green line cut across x = -3 and x = 3. So, the domain here is
[tex]x=\pm3[/tex]Hence
You have the option of borrowing money from one source that charges simple interest or from another source that charges the same APR but compounds the interest monthly. Which would you choose, and why?
I would choose the source that charges simple interest. This is because simple interest is based only on the principal (The amount borrowed), but compound interest is based on the principal and also the interest that has been generated from it.
x² + x+49
14
7
712
+ 49
Answer:
x 2^x=49. 2x=49 2 x = 49.
Step-by-step explanation:
Step 1. Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
( 14 + 2 ) 2 0 = 5 + 4 0 what type of property is this?
The question provides the relationship as shown below:
[tex](\frac{1}{4}+2)20=5+40[/tex]If we solve both sides individually, we have the left-hand side to give
[tex](\frac{1}{4}+2)20=45[/tex]and the right-hand side to give
[tex]5+40=45[/tex]Since both sides give the same result, we can attempt to manipulate the left-hand side of the equation with a common property we are familiar with: The Distributive Property.
The Distributive Property is written out as shown below:
[tex]a(b+c)=(a\cdot b)+(a\cdot c)[/tex]Applying this rule to the left-hand side, we get:
[tex]\begin{gathered} (\frac{1}{4}+2)20=\frac{1}{4}\cdot20+2\cdot20 \\ =5+40 \end{gathered}[/tex]This is the same expression present on the right-hand side of the equation.
Therefore, the property illustrated is the DISTRIBUTIVE PROPERTY.
which description is correct for the polynomial[tex]4x {}^{2} + 3x - 2[/tex]a cubic trinomial b quartic trinomial c cubic trinomial d quadratic trinomial
4x² + 3x - 2
This is a quadratic trinomial
Explanation: A quadratic equation has 2 as its highest index power
Then a polynomial involving 3 terms is a trinomial equation.
Hence the expression
4x² + 3x - 2 has its highest index power as 2 (4x raised to the power of two) and it has three separate terms, and that makes it a quadratic trinomial.
Use the pair of functions f and g to find the following values if they exist[tex] f(x) = \sqrt{x + 2} [/tex][tex]g(x) = 3x - 2[/tex]a. (f+g)(2)b.(f/g)(0)c.(f-g)(-1)
Factor by grouping c^2-8c +16 -4d^2
INFORMATION:
We have the following expression
[tex]c^2-8c+16-4d^2[/tex]And we must factor it by grouping
STEP BY STEP EXPLANATION:
To factor it by grouping, we must:
1. group the first 3 terms of the expression
[tex](c^2-8c+16)-4d^2[/tex]2. factor the expression in the parenthesis
[tex](c-4)^2-4d^2[/tex]3. rewrite 4d^2 as unique exponential expression
[tex](c-4)^2-(2d)^2[/tex]4. factor by square difference
[tex]((c-4)+2d)((c-4)-2d)[/tex]5. simplify
[tex]=(c+2d-4)(c-2d-4)[/tex]ANSWER:
the factoring for c^2-8c +16 -4d^2 by grouping is
[tex](c+2d-4)(c-2d-4)[/tex]Question 1: Identify the vertex. *A. (-2, -1)B. (-2, 1)C. (2, -1)D. (2, 1)
The standard equation of parabola with vertex (h,k) is :
(x - h)² = 4a(y - k)
The given eqation is : (x + 2)² = 4(y - 1)
On comparing the given equation with the standard equation we get
h = -2, a = 1 and k = 1
Vertex is ( h,k)
So, the vertex of the given equation of parabola is (-2, 1)
Answer : B (-2, 1)
Darnell went to the movie theater with his friends. The movie theater started at 2:35 pm and lasted 1 hour 45 minutes. What time did the movie end?
If the movie started at 2:35 and lasted 1 hour
Answer: 4:20 pm
Step-by-step explanation:
We know that the movie started at 2:35 and lasted 1 hour and 45 minutes. We can split the time that it lasted into the hour and the 45 minutes to make things easier, since 1 hour after 2:35 is simply 3:35.
From here, we can add the extra 45 minutes. We can do this by first finding out how many minutes were left in that hour. There are 60 minutes in 1 hour, and 60 - 35 = 25 minutes
45 - 25 = 20
after adding the 25 minutes to complete the hour (4:00), we have 20 minutes left
4:00 + 0:20 = 4:20
PLS HELP MATH WILL MARK BRAINLIEST
School administrators asked a group of students and teachers which of twoschool logo ideas, logo A or logo B, they prefer. This table shows the results.Which statement is true?StudentsTeachersTotalLogo A671178Logo B331447Total10025125
From the information in the table,
67 students prefer logo A while 33 students prefer logo B
11 teachers prefer logo A while 14 teachers prefer logo B
Thus, the correct statement is
Logo B is more popular with teachers but logo A is more popular with students
2 STEP PROBLEM: QUADRATIC EQUATION 18x^2 = 21x
Explanation
[tex]18x^2=-21x[/tex]Step 1
to get the form
[tex]ax^2+bx+c=0[/tex]a) add 21 x in both sides
[tex]\begin{gathered} 18x^2=-21x \\ 18x^2+21x=-21x+21x \\ 18x^2+21x=0 \\ so\text{ a=18, b=21, c=0} \end{gathered}[/tex]Step 2
now, factorize the left hand side of the equation
[tex]\begin{gathered} 18x^2+21x=0 \\ (x)(18x+21)=0 \\ so\text{, the factors are x and (18x+21)} \end{gathered}[/tex]now, to get zero from those factors
[tex]\begin{gathered} (x)(18x+21)=0 \\ x=\text{ 0} \\ or \\ 18x+21=0 \\ \text{subtract 21 in both sides} \\ 18x+21-21=0-21 \\ 18x=-21 \\ \text{divide both sides by 18} \\ \frac{18x}{18}=\frac{-21}{18} \\ x=-\frac{21}{18}=-\frac{7}{6} \\ x=-\frac{7}{6} \end{gathered}[/tex]so, the answer is
[tex]x=\text{ 0 and x=-7/6}[/tex]I hope this helps you
Bellingham, Washington, has an area of 25.4 mi2 and a population of 74,547 during one year. Bakersfield, California, has an area of 113.1 mi? and a population of 295,536 during the same year. Which city has a greater number of people per square mile?
Bellingham
[tex]\frac{74547}{25.4}=2934.9[/tex]2934.9 people per square mile
California
[tex]\frac{295536}{113.1}=2613.1[/tex]2613.1 people per square mile
answer: Bellingham has a greater number of people per square mile
In the figure, k//l, find the values of z and y.
Answer:
• z=113°
,• y=67°
Explanation:
In the diagram below, by the principles of vertical and corresponding angles:
[tex](6y-113)\degree=67\degree\text{ (Corresponding angles)}[/tex]We solve for y:
[tex]\begin{gathered} 6y=67+113 \\ 6y=180 \\ y=\frac{180}{6} \\ y=30 \end{gathered}[/tex]Next, angles z and (6y-113) are on a straight line. Therefore:
[tex]z+(6y-113)\degree=180\degree[/tex]However, recall we stated earlier that (6y-113)°=67°, therefore:
[tex]\begin{gathered} z+67\degree=180\degree \\ z=180\degree-67\degree \\ z=113\degree \end{gathered}[/tex]The values of z and y are 113° and 67° respectively.
kelly is knitting a scarf for her brother. it took her 1/3 hour to knit 3/8 foot of the scarf. How fast is Kelly's knitting speed, in feet per hour?A[tex]4 \frac{1}{2} [/tex]B[tex]3[/tex]C[tex]2\frac{1}{2} [/tex]D[tex]1 \frac{1}{8} [/tex]
We need to divide the number of foot of scarf knitted by the number of time, in hours, taken.
[tex]\frac{\frac{3}{8}\text{ ft }}{\frac{1}{3}\text{ hour}}=\frac{3}{8}\cdot3\frac{\text{ ft}}{\text{ hour}}=\frac{9}{8}\frac{\text{ ft}}{\text{ hour}}=\frac{8+1}{8}\frac{\text{ ft}}{\text{ hour}}=1\frac{1}{8}\frac{\text{ ft}}{\text{ hour}}[/tex]Part A: Clancey and Ethan are starting new books. So far, Clancey has read 1/4 of his book, which has 240 total pages and Ethan has read 2/5 of his book, which has 170 total pages. Who has read more pages so far, Clancey or Ethan?Of the combined total number of pages in both books, what fraction have clancey and ethan read combined?
In order to find who has read more pages, let's find the number of pages read by each one.
The number of pages read by Clancey is:
[tex]\frac{1}{4}\cdot240=\frac{240}{4}=60[/tex]The number of pages read by Ethan is:
[tex]\frac{2}{5}\cdot170=\frac{340}{5}=68[/tex]So Ethan read more pages.
The combined number of pages in both books is 240 + 170 = 410.
The combined number of pages read is 60 + 68 = 128
So the fraction is:
[tex]\frac{128}{410}=\frac{64}{205}[/tex]Simplify the following expressions, SHOW UR SOLUTIONS PLS
Answer:
Q1. 3² × 3² × x² = 9 × 9 × x²
= 81x²
Q2. (2x)² × (3x)² = 4x² × 9x²
= 36x⁴
Q3. [tex](-\frac{5}{6} )^{3}[/tex] [tex]=-\frac{125}{216}[/tex]
Q4. [tex](\frac{3a^{5} }{4b^{4}}) ^{3}=\frac{27a^{15} }{64b^{12} }[/tex]
Q5. [tex](\frac{8a^{2} b^{4}c^{23} }{26a^{13}b^{5}c^{2} }) ^{3} = (\frac{4c^{21} }{13a^{11}b } )^{3}[/tex]
[tex]=\frac{64c^{63} }{2197a^{33}b^{3} }[/tex]
Q6. [tex]-4^{-1}= (-\frac{4}{1} )^{-1}[/tex]
[tex]=(-\frac{1}{4} )^{1}[/tex]
[tex]=-\frac{1}{4}[/tex]
Q7. [tex](2r)^{-2}=(\frac{2r}{1} )^{-2}[/tex]
[tex]=(\frac{1}{2r} )^{2}[/tex]
[tex]=[/tex] [tex]\frac{1}{2r}[/tex] × [tex]\frac{1}{2r}[/tex]
[tex]=[/tex] [tex]\frac{1}{4r^{2} }[/tex]
Q8. [tex](\frac{xy}{ab^{3} } )^{-1} = (\frac{ab^{3} }{xy} )^{1}[/tex]
[tex]=\frac{ab^{3} }{xy}[/tex]
Q9. [tex]9x^{0} = 9(1)[/tex]
[tex]=9[/tex]
Q10. [tex](-4r^{5}s^{6} t^{-7} )^{0} = 1[/tex]
Solve for x. 70° 37° 10x + 3x=
Let's suppose, the given equation is:
37 = 10x + 3
By solving it
37 - 3 = 10x
34 = 10x
34/10 = x
x = 17/5
Hence, the value of x is 17/5.
Calculate the maturity value of simple interest a seven months loan of $6,000 if the interest rate is 7.6%
ANSWER
[tex]6266[/tex]EXPLANATION
Given;
[tex]\begin{gathered} p=6000 \\ R=7.6\% \\ T=\frac{7}{12} \end{gathered}[/tex]Now using the formula for simple interest
[tex]I=\frac{PRT}{100}[/tex]substituting the values we have;
[tex]\begin{gathered} I=\frac{6000\times7.6\times7}{100\times12} \\ =266 \end{gathered}[/tex]Now the interest after 7 months would be
[tex]266[/tex]The maturity value is
[tex]\begin{gathered} P+I \\ =6000+266 \\ =6266 \end{gathered}[/tex]f(x) = 9x² + 5x +4
g(x) = - 8x² - 3x - 4
Find (f + g)(x).
Answer:
1x^2+2x
Step-by-step explanation:
Put into Equation
(9x^2 +5x+4)+(-8x^2-3x-4)
Distribute
9x^2+5x+4-8x^2-3x-4
Combine like terms
1x^2+2x
Hope this helped!
what is 2x exponent 3 - 4x exponent 2 -3x divide 2x
Equation
[tex]\frac{2x^3-4x^2-3x}{2x}[/tex]
To operate this fraction we will separate the numerator and divide each term with the denominator.
[tex]\begin{gathered} \frac{2x^3}{2x}-\frac{4x^2}{2x}-\frac{3x}{2x} \\ x^2-2x-\frac{3}{2} \end{gathered}[/tex]The answer would be
[tex]x^2-2x-\frac{3}{2}[/tex]Which of the following are the xintercepts on the graph of the function shown below? f(x)=(x+2)(x-7)
Which of the following are the xintercepts on the graph of the function shown below? f(x)=(x+2)(x-7)
we have the function
f(x)=(x+2)(x-7)
This is a vertical parabola written in factored form
The zeros or x-intercepts of the function are
x=-2 and x=7
Remember that the x-intercepts are the values of x when the value of the function is equal to zero
therefore
the answer is
x=-2 and x=7A rectangle, with a length of (3x+7) and a width of (4x+8), has a square with a side length of (2x+5) cut out of it. Find the simplified solution form expression to represent the remaining area.
I’ll give points + brainalist
Answer: 8x^2+72x+81
Step-by-step explanation:
Hi! I'm not sure if my answer is correct, but please check! Hope it helps.
First the rectangles area is l x w = (3x+7)(4x+8) = 12x^2+52x+56
Because there is a square cut out, we need to find the area of the square and subtract that from the area of the rectangle.
Square Area: (2x+5)(2x+5)= 4x^2+20x+25
Subtract the two areas: 12x^2+52x+56 - 4x^2+20x+25
Which would simplify to 8x^2+72x+81
(03.01 LC)
Simplify (√5)(35)
Answer:5/35=1/7
Step-by-step explanation:
PLEASE HELP ME I NEED YOU TO SOLVE FOR C
Solve the equation 8 −710c = 6−15c for c.
Answer: C =0.006
Step-by-step explanation:
Each angle of the equilateral triangle in the figure has measure (2x – 9)°. Determine the value of x.Question options:A) x = 69B) x = 34.5C) x = 25.5D) x = 60
On an equilateral triangle, each angle has a measure of 60º. Then:
[tex]2x-9=60[/tex]Solve for x. To do so, add 9 to both sides of the equation:
[tex]\begin{gathered} \Rightarrow2x-9+9=60+9 \\ \Rightarrow2x=69 \end{gathered}[/tex]Divide both sides of the equation by 2:
[tex]\begin{gathered} \Rightarrow\frac{2x}{2}=\frac{69}{2} \\ \Rightarrow x=34.5 \end{gathered}[/tex]Therefore, the value of x is:
[tex]34.5[/tex]Which of these systems of equations could be used to choose a ticket plan ?
Answer:
A. y = 0.50x + 12
y = 1.25x
Explanation:
The equation that model the total cost of plan A is:
y = 12 + 0.50x
Because there is a cost of $12 that is independent of the number of rides x and there is a cost of $0.5 for each ride.
In the same way, the equation that model the total cost of plan B is:
y = 1.25x
Because there is only a cost of $1.25 for each ride.
Therefore, the system of equations that could be used to choose a ticket plan is:
A. y = 0.50x + 12
y = 1.25x
How to graph it I know others one but not this one
Answer: (0, 2)
Explanation
The coordinates are a set of values that show the exact position of a point. In graphs, it is usually a pair of points in the form (x, y), where x represents the value in the horizontal axis and y represents the value of the vertical axis.
As we can see from the image above, in our point x = 0 (marked in red) while y = 2 (marked in purple). Rearranging the coordinate we get (0, 2).
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y= -3x-6
Step-by-step explanation:
I believe this is correct
2. FR has a midpoint M. Use the given information to find the missing endpoint. F(-2,3) and M(3,0)
ANSWER:
R(8, -3)
STEP-BY-STEP EXPLANATION:
We have that the midpoint formula is the following:
[tex]M(m_1,m_2)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]In this case, we know the midpoint M, that is, m1 and m2 and the startpoint F, that is, we know, x1 andy1, we replace to calculate the values of R, the endpoint:
[tex]\begin{gathered} 3=\frac{-2+x_2}{2} \\ 6=-2+x_2 \\ x_2=6+2=8 \\ \\ 0=\frac{3+y_2}{2} \\ 0=3+y_2 \\ y_2=-3 \\ \\ \text{Therefore, the missing endpoint is: (8,-3)} \end{gathered}[/tex]