Answer:
Perpendicular
Explanation:
Given the coordinates
A(-2,-5), B(4.7) C(0, 2) and D(8,-2), we are to determine whether AB is parallel, perpendicular to CD or neither
To do this, we need to find he slope of AB and CD first. Using the formula for calculating slope as shown;
m = y2-y1/x2-x1
For AB:
slope = 7-(-5)/4-(-2)
Slope = 7+5/4+2
Slope of AB = 12/6
Slope of AB = 2
For CD
Slope of CD = -2-2/8-0
Slope of CD = -4/8
Slope of CD = -1/2
Note that for AB to be perpendicular to CD, the product of their slope must be -1.
Given
mAB = 2
mCD = -1/2
Taking their product
mAB * mCD = 2 * -1/2
mAB * mCD = -1
Since the product is -1, hence AB is PERPENDICULAR to CD
the angle t is an acute angle and sin t and cost t are given. Use identities to find tan t , csc t, sec t, and cot t. where necessary, rationalize demonstrations.sin t= 7/25, cos t= 24/25
Answer:
tan t = 7/24
csc t = 25/7
sec t = 25/24
cot t = 24/7
Explanation:
From the question, we're told that sin t = 7/25 and cos t = 24/25. Since we know the identities of sine and cosine to be as follows we can go ahead and determine tan t as shown below;
[tex]\begin{gathered} \sin t=\frac{opposite}{\text{hypotenuse}}=\frac{7}{25} \\ \cos t=\frac{adjacent}{\text{hypotenuse}}=\frac{24}{25} \\ \therefore\tan t=\frac{opposite}{\text{adjacent}}=\frac{7}{24} \end{gathered}[/tex]Let's go ahead and find cosecant t (csc t);
[tex]\csc t=\frac{1}{\sin t}=\frac{1}{\frac{7}{25}}=1\times\frac{25}{7}=\frac{25}{7}[/tex]For sec t, we'll have;
[tex]\sec t=\frac{1}{\cos t}=\frac{1}{\frac{24}{25}}=1\times\frac{25}{24}=\frac{25}{24}[/tex]For cot t;
[tex]\cot t=\frac{1}{\tan t}=\frac{1}{\frac{7}{24}}=1\times\frac{24}{7}=\frac{24}{7}[/tex]Show all work to identify the asymptotes and state the end behavior of the function f(x) = 6x/ x - 36
Vertical asymptotes are when the denominator is 0 but the numerator isn't 0.
[tex]x-36=0 \implies x=36[/tex]
Since this value of x does not make the numerator equal to 0, the vertical asymptote is [tex]x=36[/tex].
Horizontal asymptotes are the limits as [tex]x \to \pm \infty[/tex].
[tex]\lim_{x \to \infty} \frac{6x}{x-36}=\lim_{x \to \infty}=\frac{6}{1-\frac{36}{x}}=6\\\\\lim_{x \to -\infty} \frac{6x}{x-36}=\lim_{x \to -\infty}=\frac{6}{1-\frac{36}{x}}=6\\\\[/tex]
So, the horizontal asymptote is [tex]y=6[/tex].
End behavior:
As [tex]x \to \infty, f(x) \to -\infty[/tex]As [tex]x \to -\infty, f(x) \to \infty[/tex].The first three terms of a sequence are
given. Round to the nearest thousandth
(if necessary).
4, 8, 12,..
Find the 40th term
Answer:
Step-by-step explanation:
Recall the formula for an arithmetic sequence: [tex]a_{n} =a_{1} +d(n-1)[/tex]
Where d is the common difference and a_1 is the first term of the sequence.
You are given :
a_1=4
a_2=8
a_3=12
Next is to find the common difference d.
To find the common difference, take the next term and subtract it from the current term.
a_2-a_1=8-4=4
Let try the next term start at a_2
a_3-a_2=12-8 =4
Do you see the pattern?
The patter is going up by 4 each time. So the common difference is 4 i.e d=4
Now we just need to plug into the generalize formula above and get
[tex]a_{n}=4+4(n-1)[/tex]
The question asked for the 40th term. Plug 40 into the formula and you will get:
[tex]a_{40}=4+4(40-1)=160[/tex]
I hope this helps!
I need help with this practice problem I’m having trouble
Part N 1
[tex]2^{(6\log _22)}=12[/tex]Apply property of log
[tex]\log _22=1[/tex]so
[tex]\begin{gathered} 2^{(6\cdot1)}=12 \\ 2^6=12\text{ -}\longrightarrow\text{ is not true} \end{gathered}[/tex]the answer is false
Part N 2
we have
[tex]\frac{1}{4}\ln e^8=\sqrt[4]{8}[/tex]applying property of log
[tex]\frac{1}{4}\ln e^8=\frac{8}{4}\ln e=2\ln e=2[/tex]so
[tex]2=\sqrt[4]{8}\text{ ---}\longrightarrow\text{ is not true}[/tex]the answer is false
Part N 3
we have
[tex]10^{(\log 1000-2)}=10[/tex]log1000=3
so
log1000-2=3-2=1
10^1=10 -----> is true
the answer is trueLet Events A and B be described as follows:• P(A) = buying popcorn• P(B) = watching a movieThe probability that you watch a movie this weekend is 48% The probability of watching amovie this weekend and buying popcorn is 38%. If the probability of buying popcorn is 42%,are watching a movie and buying popcorn independent?
Solution:
Given that;
[tex]\begin{gathered} P(A)=42\%=0.42 \\ P(B)=48\%=0.48 \\ P(A\cap B)=38\%=0.38 \end{gathered}[/tex]To find out if watching a movie and buying a popcorn are independent, the formula is
[tex]\begin{gathered} P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.38}{0.48}=0.79166 \\ P(A|B)=0.79\text{ \lparen two decimal places\rparen} \end{gathered}[/tex]From the deductions above;
Hence, the answer is
[tex]No,\text{ because }P(A|B)=0.79\text{ and the }P(A)=0.42\text{ are not equal}[/tex]the graph of each function is shown. write the function in factored form . do not include complex numbers
We can see from the picture that the function f(x) has roots in x = -5 and x = 5. Using sintetic division with x = 5, we get:
then, we can write the function as:
[tex]f(x)=(x-5)(2x^3+11x^2+8x+15)[/tex]since we know that another root is x = -5,we can use again the sintetic division on the right factor:
therefore, the function in factored form is:
[tex]f(x)=(x-5)(x+5)(2x^2+x+3)[/tex]Choose all equivalent expression ( s). (4) ^ (3z ^ 2); (4) ^ (- 3x ^ 2); (1/4) ^ (3z ^ 2); (pi/4) ^ (3x)
Among the given options, no one is an equivalent expression.
What is an equivalent expression?
Expressions are said to be equivalent if they do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
In the given options no one satisfies the property of an equivalent expression.
Therefore, among the given options, no one is an equivalent expression.
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Graph this steph function on the coordinate grid please help I don’t understand!
Given:
[tex]f(x)=\begin{cases}{-5\text{ }if\text{ }-5Required:
We need to graph the given step function.
Explanation:
From the given data we have, -5,-1, and 2 are the respective values of y.
[tex]-5The draw annulus to denote the points do not lie on the line since there is a symbol '<'.
Final answer:
17. What is the value of x in the rhombusbelow?AC(x+ 40)B3x⁰D
ANSWER
x = 35 degrees
EXPLANATION
Given tthat
[tex]\begin{gathered} \text{ m Follow the steps below to find the value of xRecall, that the sum of m[tex]\text{ m < C + m Therefore, x is 35 degrees
What I need to know is that what is 3.5x2
Answer:
7
Step-by-step explanation:
Just add 3.5 twice which is the same as multiplying it by 2
Answer:
7
Step-by-step explanation:
hope it helps and have a nice!!! :)
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Solve the equation 20 +7k = 8(k + 2).
[tex]k=4[/tex].
Step-by-step explanation:1. Write the expression.[tex]20 +7k = 8(k + 2)[/tex]
2. Solve the parenthesis on the right hand side of the equation.[tex]20 +7k = 8k+16[/tex]
3. Subtract 20 from both sides of the equation.[tex]-20+20 +7k = 8k+16-20\\ \\7k = 8k-4[/tex]
4. Subtract 8k from both sides of the equation.[tex]7k-8k = 8k-4-8k\\ \\-k = -4[/tex]
5. Multiply both sides by "-1".[tex](-1)-k = -4(-1)\\ \\k=4[/tex]
6. Verify.[tex]20 +7(4) = 8((4) + 2)\\ \\20 +28 = 8(6)\\ \\48=48[/tex]
7. Express the result.[tex]k=4[/tex].
Answer:
k = 4
Step-by-step explanation:
a) Simplify both sides of the equation.
20 + 7k = 8(k + 2)
20 + 7k = (8)(k) + (8)(2)
20 + 7k = 8k + 16
7k + 20 = 8k + 16
b) Subtract 8k from both sides.
7k + 20 − 8k = 8k + 16 − 8k
−k + 20 = 16
c) Subtract 20 from both sides.
−k + 20 − 20 = 16 − 20
−k = −4
Divide both sides by -1.
-k/-1 = -4/-1
k = 4
The next model of a sports car will cost 11.5% less than the current model. The current model costs $59,000. How much will theprice decrease in dollars? What will be the price of the next model?
we are given that a car cost $ 59000 and the price will decrease by 11.56%, therefore, the amount it will decrease is equivalent to:
[tex]59000\times\frac{11.56}{100}=6820.4[/tex]Therefore, the price will decrease by $6820.4. The total price will be then:
[tex]59000-6820.4=52179.6[/tex]Therefore, the price will be $52179.6
Sam graduation picnic cost $13 for decoration plus an additional $5 for each attendee.at most how many attendees can there be if sam budgets a total of $33 for his graduation picnic?
Given:
The cost of graduation picnic = $13 for decoration plus an additional $5 for each attendee
Let the number of attendance = x
we need to find x when sam budgets a total of $33 for his graduation picnic
So,
[tex]13+5x=33[/tex]solve for x, subtract 13 from both sides:
[tex]\begin{gathered} 13+5x-13=33-13 \\ 5x=20 \end{gathered}[/tex]divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}=\frac{20}{5} \\ \\ x=4 \end{gathered}[/tex]So, the answer is:
The number of attendees = 4
The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 0.9 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(19,0.9)b. What is the median giraffe height? 19 ft.c. What is the Z-score for a giraffe that is 22 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 18.9 feet tall? e. What is the probability that a randomly selected giraffe will be between 19.6 and 20.1 feet tall? f. The 70th percentile for the height of giraffes is ft.
P(6,23), Q (13,28)
Distance=?
Midpoint=?
Answer:
Step-by-step explanation:
distance between the two points:
[tex]\sqrt{ (x_2-x_1)^{2} +(y_2-y_1)^2[/tex]
[tex]\sqrt[/tex](13-6)²+(28-23)²
√(7)²+(5)²
√49+25
√74
distance: 8.6cm
midpoint=
[tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]
(6+3/2,23+28/2)
(19/2,51/2)
(9.5,25.5)
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately
σ
=
50.2
. You would like to be 90% confident that your estimate is within 1.5 of the true population mean. How large of a sample size is required?
Using the sample size relation with the standard normal distribution, the required sample size is 3032 samples.
What is Normal distribution ?
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Using the sample size relation with the standard normal distribution, the required sample size is 673 samples.
n = [(Z* × σ) / ME]²
ME = margin of error
Z* = Z critical at 90% = 1.645
Substituting the values into the equation :
n = [(Z* × σ) / ME]²
n = [(1.645 × 50.2) / 1.5]²
n = (82.6/ 1.5)²
n = 55.06
n ≈ 3032
Therefore, the Number of samples required is 3032 samples.
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Given the polynomial expression 3x2 + 3bx - 6x - 6b, factor completely.
(3x-6)(x - b)
(x-2)(x + b)
3(x-2)(x + b)
3(x + 2)(x + b)
The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.
The given polynomial expression is 3x² + 3bx - 6x - 6b.
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The factors of given polynomial can be find using grouping method, that is
(3x² + 3bx) - 6x - 6b
=3x(x+b)-6(x+b)
=(x+b)(3x-6)
=3(x-2)(x+b)
The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.
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When a number is divided by $5,$ the result is $50$ less than if the number had been divided by $6$. What is the number?
Answer:
1500$
Step-by-step explanation:
Answer: -1500
Step-by-step explanation: yes it is
Lukalu is rappelling off a cliff. The parametric equations that describe her horizontal and vertical position as a function of time are x ( t ) = 8 t and y ( t ) = − 16 t 2 + 100 and . How long does it take her to reach the ground? How far away from the cliff is she when she lands? Remember to show all of the steps that you use to solve the problem.
SOLUTION
Now the ground is assumed to be 0, so we have that
[tex]y(t)=0[/tex]So, that means we have
[tex]\begin{gathered} y(t)=-16t^2+100 \\ 0=-16t^2+100 \\ 16t^2=100 \\ t^2=\frac{100}{16} \\ t=\sqrt{\frac{100}{16}} \\ t=\frac{10}{4} \\ t=2.5\text{ seconds } \end{gathered}[/tex]Now, we have found t, which is how long it takes to get to the ground, you can plug it into x(t) to find the horizontal distance travelled, we have
[tex]\begin{gathered} x(t)=8t \\ x(2.5)=8\times2.5 \\ =20\text{ feet } \end{gathered}[/tex]Hence it takes her 2.5 seconds to reach the ground
And she is 20 feet away from the cliff
Find the exact value by using ahalf-angle formula.[?] --cos 75°
Answer::
[tex]\cos 75\degree=\frac{\sqrt[]{2-\sqrt[]{3}}}{2}[/tex]Explanation:
By the half-angle formula:
[tex]\cos \mleft(\frac{\theta}{2}\mright)=\pm\sqrt[]{\frac{1+\cos\theta}{2}}[/tex]Let θ=150°, therefore:
[tex]\begin{gathered} \cos (\frac{150\degree}{2})=\sqrt[]{\frac{1+\cos150\degree}{2}} \\ \cos (150)\degree=-\cos (180\degree-150\degree)=-\cos 30\degree \\ \implies\cos (\frac{150\degree}{2})=\sqrt[]{\frac{1+\cos150\degree}{2}}=\sqrt[]{\frac{1-\cos30\degree}{2}} \end{gathered}[/tex]Now, cos 30 = √3/2, thus:
[tex]\begin{gathered} =\sqrt[]{\frac{1-\frac{\sqrt[]{3}}{2}}{2}} \\ \text{Multiply both the denominator and numerator by 2} \\ =\sqrt[]{\frac{2-\sqrt[]{3}}{4}} \\ =\frac{\sqrt{2-\sqrt[]{3}}}{\sqrt{4}} \end{gathered}[/tex]The exact value of cos 75° is:
[tex]\cos 75\degree=\frac{\sqrt[]{2-\sqrt[]{3}}}{2}[/tex]Graph each pair of lines and use their slopes to determineif they are parallel, perpendicular, or neither.EF and GH for E(-2, 3), F(6, 1), G(6,4), and H(2,5)JK and LM for J(4,3), K(5, -1), L(-2, 4), and M(3,-5)NP and QR for N(5, -3), P(0, 4), Q(-3, -2), and R(4, 3)ST and VW for S(0, 3), T(0, 7), V(2, 3), and W(5, 3)
To find the slope of a line that passes through two points, we can use the following formula:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points which the line passes} \end{gathered}[/tex]Then, we have:
First pair of linesLine EF
[tex]\begin{gathered} (x_1,y_1)=E\mleft(-2,3\mright) \\ (x_2,y_2)=F\mleft(6,1\mright) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1-3}{6-(-2)} \\ m=\frac{1-3}{6+2} \\ m=\frac{-2}{8} \\ m=\frac{2\cdot-1}{2\cdot4} \\ m=-\frac{1}{4} \end{gathered}[/tex]Line GH
[tex]\begin{gathered} (x_1,y_1)=G\mleft(6,4\mright) \\ (x_2,y_2)=H\mleft(2,5\mright) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5-4}{2-6} \\ m=\frac{1}{-4} \\ m=-\frac{1}{4} \end{gathered}[/tex]Now, when graphing the two lines, we have:
If two lines have equal slopes, then the lines are parallel. As we can see, their slopes are equal, therefore the lines EF and GH are parallel.
Second pair of lines
Line JK
[tex]\begin{gathered} (x_1,y_1)=J\mleft(4,3\mright) \\ (x_2,y_2)=K\mleft(5,-1\mright) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-3}{5-4} \\ m=-\frac{4}{1} \\ m=-4 \end{gathered}[/tex]Line LM
[tex]\begin{gathered} (x_1,y_1)=L\mleft(-2,4\mright) \\ (x_2,y_2)=M\mleft(3,-5\mright) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-5-4}{3-(-2)} \\ m=\frac{-9}{3+2} \\ m=\frac{-9}{5} \end{gathered}[/tex]Now, when graphing the two lines, we have:
As we can see, the slopes of these lines are different, so they are not parallel. Let us see if their respective slopes have the relationship shown below:
[tex]\begin{gathered} m_1=-4 \\ m_2=-\frac{9}{5} \\ m_1=-\frac{1}{m_2} \\ -4\ne-\frac{1}{-\frac{9}{5}} \\ -4\ne-\frac{\frac{1}{1}}{\frac{-9}{5}} \\ -4\ne-\frac{1\cdot5}{1\cdot-9} \\ -4\ne-\frac{5}{-9} \\ -4\ne\frac{5}{9} \end{gathered}[/tex]Since their respective slopes do not have the relationship shown below, then the lines are not perpendicular.
Third pair of linesLine NP
[tex]\begin{gathered} (x_1,y_1)=N\mleft(5,-3\mright) \\ (x_2,y_2)=P\mleft(0,4\mright) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{4-(-3)}{0-5} \\ m=\frac{4+3}{-5} \\ m=-\frac{7}{5} \end{gathered}[/tex]Line QR
[tex]\begin{gathered} (x_1,y_1)=Q\mleft(-3,-2\mright) \\ (x_2,y_2)=R\mleft(4,3\mright) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3-(-2)}{4-(-3)} \\ m=\frac{3+2}{4+3} \\ m=\frac{5}{7} \end{gathered}[/tex]Now, when graphing the two lines, we have:
Two lines are perpendicular if their slopes have the following relationship:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \text{ Where }m_1\text{ is the slope of the first line and }m_2\text{ is the slope of the second line} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} m_1=-\frac{7}{5} \\ m_2=\frac{5}{7} \\ -\frac{7}{5}_{}=-\frac{1}{\frac{5}{7}_{}} \\ -\frac{7}{5}_{}=-\frac{\frac{1}{1}}{\frac{5}{7}_{}} \\ -\frac{7}{5}_{}=-\frac{1\cdot7}{1\cdot5}_{} \\ -\frac{7}{5}_{}=-\frac{7}{5}_{} \end{gathered}[/tex]Since the slopes of the lines NP and QR satisfy the previous relationship, then this pair of lines are perpendicular.
Fourth pair of lines
Line ST
[tex]\begin{gathered} (x_1,y_1)=S\mleft(0,3\mright) \\ (x_2,y_2)=T\mleft(0,7\mright) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-3_{}}{0-0} \\ m=\frac{4}{0} \\ \text{Undefined slope} \end{gathered}[/tex]The line ST has an indefinite slope because it is not possible to divide by zero. Lines that have an indefinite slope are vertical.
Line VW
[tex]\begin{gathered} (x_1,y_1)=V\mleft(2,3\mright) \\ (x_2,y_2)=W\mleft(5,3\mright) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3-3_{}}{5-2} \\ m=\frac{0}{3} \\ m=0 \end{gathered}[/tex]Line VW has a slope of 0. Lines that have a slope of 0 are horizontal.
Now, when graphing the two lines, we have:
As we can see in the graph, the ST and VW lines are perpendicular.
Create a graph system of linear equations that model this situation.
x represents the number of packages of coffee sold
y represents the number of packages of pastry sold
We were the cost of a package of coffee is $6 and the cost of a package of pastry is $4. If the total amount made from selling x packages of coffee and y packages of pastry is $72, then the equation representing this scenario is
6x + 4y = 72
Also, we were told that she sold 2 more packages of coffee than pastries. This means that
x = y + 2
Thus, the system of linear equations is
6x + 4y = 72
x = y + 2
We would plot these equations on the graph. The graph is shown below
The red line represents x = y + 2
The bu line represents x = y + 2
In 2016, there were 35,867 burger restaurants worldwide, with 13,232 of them located in a country. Determine the percent of burger restaurants in that country in 2016Approximately what percent ?
we have that
35,867 ------> represents 100%
Applying proportion
Find out how much percentage represents 13,232
100/35,867=x/13,232
solve for x
x=(100/35,867)*13,232
x=36.89% ------> 37%
Ariel makes $35 a day. How much can she get for 1/7 of a day? Ariel will earn ____ for 1/7 of the day.
We can calculate how much she get for 1/7 of a day by multiplying the daily pay rate by 1/7:
[tex]E=\frac{1}{7}\cdot35=\frac{35}{7}=5[/tex]Answer: Ariel will earn $5 for 1/7 of the day.
Write the fraction as a percent.34/100
Answer:
34%
Explanation:
To write the fraction as a percent we need to divide 34 by 100 and then multiply by 100%, so
34/100 x 100 = 0.34 x 100% = 34%
Therefore, 34/100 as a percent is 34%
5 A salesman sold $1,500 worth of
merchandise and received $75 in
commission for the sale.What percent of the sale was commission
Answer:20%
Step-by-step explanation:
1500/75=20(%)
√54²-43.8² +2(7)
What is the height of the space Lilly needs? Round to the nearest hundredth.
18.52
24.20
45.58
235.06
√54²-43.8² +2(7)
54-1918.44+14
-1850.44
How many gallons of a 60% antifreeze solution must be mixed with 80 gallons of 20% antifreeze to get a mixture that is 50% antifreeze?
Given
gallons which have 20% antifreeze solution = 80
Final concentration = 50% antifreeze solution
Find
Number of galloons with 60% antifreeze solution
Explanation
Let the number of gallons with 60% antifreeze solution = x
According to question
0.6x+0.2(80) = 0.50(x+80)
0.6x+16=0.5x+40
0.1x=24
x=240
Final Answer
Hence 240 gallons of 60% antifreeze solution will be required
1/2+3/4+1/8+3/16+1/32+3/64
Answer:
105/64 or 1 41/64
Step-by-step explanation:
Math
Make common denominator of 64
:]
Find the domain and range of the function represented by the graph.
543
domain: -4 ≤ x ≤ 2.
O domain: -4 < x <2.
O domain: -4 ≤ x ≤ 4.
O domain: -4 <
2
range: -4 Sy≤4
range: -4
range: -4 Sy≤2
x < 4. range: -4
Answer:
c
Step-by-step explanation:
c