Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
DAC
A
Statements
Reasons
00
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answers
Answer:
See below
Step-by-step explanation:
Proof:
Statements | Reasons
AD ≅ BC | Given
AD ║ BC | Given
AC ≅ AC | Reflexive Property
∠DAC ≅ ∠ACB | If 2 || lines are cut by a trans., the | alternate interior ∠s are congruent.
ΔADC ≅ ΔBCA | S.A.S Postulate
BA ≅ DC | Corresponding sides of congruent Δs
So, quad. ABCD is a ║gm | If a quad. has its opposite sides
| congruent, the quad. is a parallelogram.
It is prove that given quadrilateral is a parallelogram.
Given that,AD ≅ BC and AD ║ BC
By reflexive property,AC ≅ AC
If two parallel lines are cut by a transversal. Then, alternate interior angles are congruent.So that, ∠DAC ≅ ∠ACB
By Side - angle - Side congruency rule,ΔADC ≅ ΔBCA
Since, the Corresponding sides of congruent triangles are congruent.So that, BA ≅ DC
Hence, opposite sides of given quadrilateral are equal. Therefore, given quadrilateral are parallelogram.
Learn more:
https://brainly.com/question/16702162
Related Questions
Use the formula m= v 2 -v 1 x 2 -x 1 to calculate the slope of the line The slope of the line is
Answers
Answer: I actually do not know but i know that the answer is A.
Step-by-step explanation:
I'm smart
1. The following are the number of hours that 10 police officers have spent being trained in how to handle encounters with people who are mentally ill:
4 17 12 9 6 10 1 5 9 3
Calculate the (a) range, (b) inter-quartile range, (c) variance, and (d) standard deviation.
(Use N)
Answers
Answer:
[tex]Range = 16[/tex]
[tex]Inter\ Quartile\ Range = 6.75[/tex]
[tex]Variance = 20.44[/tex]
[tex]Standard\ Deviation = 4.52[/tex]
Step-by-step explanation:
Given
4, 17, 12, 9, 6, 10, 1, 5, 9, 3
Calculating the range;
[tex]Range = Highest - Lowest[/tex]
From the given data;
Highest = 17 and Lowest = 1
Hence;
[tex]Range = 17 - 1[/tex]
[tex]Range = 16[/tex]
Calculating the Inter-quartile Range
Inter quartile range (IQR) is calculates as thus
[tex]IQR = Q_3 - Q_1[/tex]
Where
Q3 = Upper Quartile and Q1 = Lower Quartile
Start by arranging the data in ascending order
1, 3, 4, 5, 6, 9, 9, 10, 12, 17
N = Number of data; N = 10
---------------------------------------------------------------------------------
Calculating Q3
[tex]Q_3 = \frac{3}{4}(N+1) th\ item[/tex]
Substitute 10 for N
[tex]Q_3 = \frac{3}{4}(10+1) th\ item[/tex]
[tex]Q_3 = \frac{3}{4}(11) th\ item[/tex]
[tex]Q_3 = \frac{33}{4} th\ item[/tex]
[tex]Q_3 = 8.25 th\ item[/tex]
Express 8.25 as 8 + 0.25
[tex]Q_3 = (8 + 0.25) th\ item[/tex]
[tex]Q_3 = 8th\ item + 0.25 th\ item[/tex]
Express 0.25 as fraction
[tex]Q_3 = 8th\ item +\frac{1}{4} th\ item[/tex]
[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]
From the arranged data;
[tex]8th\ item = 10[/tex] and [tex]9th\ item = 12[/tex]
[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]
[tex]Q_3 = 10 +\frac{1}{4} (12 - 10)[/tex]
[tex]Q_3 = 10 +\frac{1}{4} (2)[/tex]
[tex]Q_3 = 10 +0.5[/tex]
[tex]Q_3 = 10.5[/tex]
Calculating Q1
[tex]Q_1 = \frac{1}{4}(N+1) th\ item[/tex]
Substitute 10 for N
[tex]Q_1 = \frac{1}{4}(10+1) th\ item[/tex]
[tex]Q_1 = \frac{1}{4}(11) th\ item[/tex]
[tex]Q_1 = \frac{11}{4} th\ item[/tex]
[tex]Q_1 = 2.75 th\ item[/tex]
Express 2.75 as 2 + 0.75
[tex]Q_1 = (2 + 0.75) th\ item[/tex]
[tex]Q_1 = 2nd\ item + 0.75 th\ item[/tex]
Express 0.75 as fraction
[tex]Q_1 = 2nd\ item +\frac{3}{4} th\ item[/tex]
[tex]Q_1 = 2nd\ item +\frac{3}{4} (3rd\ item - 2nd\ item)[/tex]
From the arranged data;
[tex]2nd\ item = 3[/tex] and [tex]3rd\ item = 4[/tex]
[tex]Q_1 = 3 +\frac{3}{4} (4 - 3)[/tex]
[tex]Q_1 = 3 +\frac{3}{4} (1)[/tex]
[tex]Q_1 = 3 +0.75[/tex]
[tex]Q_1 = 3 .75[/tex]
---------------------------------------------------------------------------------
Recall that
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR = 10.5 - 3.75[/tex]
[tex]IQR = 6.75[/tex]
Calculating Variance
Start by calculating the mean
[tex]Mean = \frac{1+3+4+5+6+9+9+10+12+17}{10}[/tex]
[tex]Mean = \frac{76}{10}[/tex]
[tex]Mean = 7.6[/tex]
Subtract the mean from each data, then square the result
[tex](1 - 7.6)^2 = (-6.6)^2 = 43.56[/tex]
[tex](3 - 7.6)^2 = (-4.6)^2 = 21.16[/tex]
[tex](4 - 7.6)^2 = (-3.6)^2 = 12.96[/tex]
[tex](5 - 7.6)^2 = (-2.6)^2 = 6.76[/tex]
[tex](6 - 7.6)^2 = (-1.6)^2 = 2.56[/tex]
[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]
[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]
[tex](10 - 7.6)^2 = (2.4)^2 = 5.76[/tex]
[tex](12 - 7.6)^2 = (4.4)^2 = 19.36[/tex]
[tex](17 - 7.6)^2 = (9.4)^2 = 88.36[/tex]
Sum the result
[tex]43.56 + 21.16 + 12.96 + 6.76 + 2.56 + 1.96 + 1.96 + 5.76 + 19.36 + 88.36 = 204.4[/tex]
Divide by number of observation;
[tex]Variance = \frac{204.4}{10}[/tex]
[tex]Variance = 20.44[/tex]
Calculating Standard Deviation (SD)
[tex]SD = \sqrt{Variance}[/tex]
[tex]SD = \sqrt{20.44}[/tex]
[tex]SD = 4.52[/tex] (Approximated)
easy khan academy math. please answer asap
Answers
Answer:
[tex]\boxed{\sf B \ and \ C}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions to solve.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(60)=\frac{5.2}{KL}[/tex]
[tex]\sf KL=\frac{5.2}{sin(60)}[/tex]
[tex]\sf sin(90-60)=\frac{3}{KL}[/tex]
[tex]\sf KL=\frac{3}{sin(90-60)}[/tex]
5(x + 3) – 12 = 43 solve
Answers
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
We can solve this equation by isolating the variable x.
First let’s apply the distributive property:
[tex]5(x+3)-12=43\\5\cdot x + 5\cdot3 - 12=43\\5x + 15 - 12 = 43[/tex]
Combine like terms:
[tex]5x + 3 = 43[/tex]
Now we can subtract 3 from both sides:
[tex]5x + 3 - 3 = 43-3\\5x = 40[/tex]
Divide both sides by 5:
[tex]5x\div5 = 40\div5\\x = 8[/tex]
So [tex]x=8[/tex].
Hope this helped!
Answer:
x = 8
Step-by-step explanation:
5(x + 3) – 12 = 43
Add 12 to each side
5(x + 3) – 12+12 = 43+12
5(x+3) =45
Divide each side by 5
5(x+3)/5 = 55/5
x+3 = 11
Subtract 3 from each side
x+3-3 = 11-3
x = 8
The lengths, in order, of four consecutive sides of an equiangular hexagon are 1, 7, 2 and 4 units, respectively. What is the sum of the lengths of the two remaining sides?
Answers
Answer:
9
Step-by-step explanation:
Extend every other side of the hexagon so that a triangle is formed. Since the hexagon is equiangular, the overall triangle is an equilateral triangle, as well as the smaller triangles in the corners.
The length of the sides of the overall triangle is 7 + 2 + 4 = 13.
Therefore, the other two sides of the hexagon are 5 and 4.
The sum is 5 + 4 = 9.
helppppppppppppppppsdss
Answers
Answer:
t = p * n
Step-by-step explanation:
* - multiplication
t is the total cost
in order to find total cost we need to multiple cost per mile on the number of miles so we will receive cost of all miles that we went
Answer:
[tex]\boxed{t=pn }[/tex]
Step-by-step explanation:
t is total cost
The formula is in terms of t (total cost).
p is price per mile
Suppose the price per mile is £60. For every mile he travelled, he has to pay £60.
n is the number of miles travelled.
For example, Carlos travelled 4 miles and the price per mile is £30.
[tex]t=30 \times 4\\t=120[/tex]
His total cost will be £120.
PLEASE HELP QUICK!!!! What is the solution to the equation Two-thirds x + 1 = one-sixth x minus 7? x = negative 16 x = negative 4 x = 4 x = 16
Answers
Answer:
-16
Step-by-step explanation:
I solved it out.
Answer:
its d 16
Step-by-step explanation:
i did the test
Suppose Grant is going to build a playlist that contains 6 songs. In how many ways can Grant arrange the 6 songs on the playlist?
Grant can arrange the 6 songs on the playlist in
different ways.
Answers
Grant can arrange the songs 720 different ways
The different ways Grant can arrange the 6 songs on the playlist is 720.
What is the different ways to arrange a certain number of objects?The different ways to arrange 'n' number of objects are n!.
The number of songs in the playlist are 6.
Therefore, the number of ways Grant can build the playlist is
[tex]= 6!\\= (6)(5)(4)(3)(2)(1)\\= 720[/tex]
Learn more to arrange a certain number of objects in different ways here: https://brainly.com/question/18076424
#SPJ3
In graphing a trigonometric function, how does one establish which are the EXTREMUM coordinates and which are the MIDLINE INTERCEPTION coordinates. I can find the x values and the y values but do not know which X goes with which Y and the graphs end up incorrect! It is EXTREMELY frustrating. How do I discern which is which!!!!! Thank You.
Answers
Answer:
If I getting the question correctly, your doubt is the order of the values you get after doing the math. I mean, you can do the calculations, but in the end, you don't form the coordinate pairs correctly, that's why I understand from your question. So, here is what you need to do.
One way to graph is by using the definitions of those kinds of functions. For example, let's say we want to find the points to draw the function: [tex]y=sin(x)[/tex]
Remember that trigonometric functions have a specific period, that means, their drawing repeats over and over again after a certain number. That period is [tex]2 \pi[/tex], that means this number represents a cycle.
So, the main thing you need to do is to pick a starting point to then, draw the curve according to the [tex]2 \pi[/tex] period.
Now, we know that sine functions intercept the origin of the coordinate system, as you can observe in the image attached, there you can see that from the origin you draw those waves making sure you intercept the x-axis at every [tex]\pi[/tex] number. In the end, you will have a sine function.
On the other hand, if you want to have a chart with all x-values and y-values. First, you need to set x-values: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Then, you need to find each y-values for each of them.
Now, you have to draw a chart value, to keep in other the coordinate pairs, that way, you'll have the correct pairs at the end.
For example, for [tex]x=-5[/tex], we get [tex]y=-0.09[/tex], that means in the chart value, you are gonna form the pair [tex](-5, -0.09)[/tex], and now you have your first point of the drawing. Then, you keep repeating the process until you complete all the chart values.
As you can imagine, you're going to get really small decimal numbers, that's why I explained to you the first method, it's faster and easier.
Sung Lee invests $10,000 at age 18. He hopes the investment will be worth $30,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
Answers
Answer:
r=17%
Step-by-step explanation:
P is the investment
A is the targeted amount
t= time (25-18=7 years)
A=P(1+r)^t
30000=10000(1+r)^7
(1+r)^7=30000/10000
r=\root(7)(3)-1
r=0.16993 ≅0.17= 17%
check: A=P(1+r)^t ⇒10000(1+0.17)^7=30012≅30000
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
Answer:
15 pt
Step-by-step explanation:
Answer:
15 pintsStep-by-step explanation:
1 quarts = 2 pints
From the question we were given 7.5 quarts to to get the desired result multiply 7.5 by 2
Which is 7.5 × 2 = 15 pints
Hope this helps you
3)
Rick says he has
two miles already.
Which form of the verb best completes the sentence?
A)
ran
B)
run
C)
running
D)
runs
Answers
Step-by-step explanation:
Because the sentence is speaking that he has done already so we will use the past verb ran
Rick says he has ran two miles already
Answer:
b. run
Step-by-step explanation:
Rick says he has run two miles already
It will be "ran" if the sentence had said, "Rick 'ran' two miles already."
BRAINLIST PLS!
The item below is based on the following scenario.
In a third world country, 100 randomly selected people were surveyed about their socioeconomic class and religious affiliation. The results and an excerpt from this fictitious study follow:
Excerpt:
"Based on a chi-square test for independence, the working class differed from the middle class in the distribution of religious identification, χ2 (4, N = 100) = 11.73, p < .05."
The phi coefficient for this study is:________.
Answers
Answer:
φ = 0.34
Step-by-step explanation:
Given:
total number of observations = N = 100
chi-square test for independence χ2 = (4, N = 100) = 11.73
To find:
phi coefficient φ
Solution:
phi coefficient φ is computed as:
φ = √( χ2 / n )
= √ (11.73 / 100 )
= √0.1173
φ = 0.3425
A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken. The correct set of hypotheses is:________. a. H0: μ ≠ 80 Ha: μ = 80b. H0: μ 80 Ha: μ > 80c. H0: μ < 80 Ha: μ > 80d. H0: μ 80 Ha: μ < 80
Answers
Answer:
u <= 80
u > 80
Step-by-step explanation:
The happiest would be
Null hypothesis: u <= 80
Alternative hypothesis: u > 80
The correct set of hypotheses for the sample in July is H0: μ ≠ 80 Ha: μ = 80.
What is the null and alternative hypothesis?The null hypothesis H0 which is also known as the default hypothesis states that there is no relationship between the population parameters. The alternative hypothesis (H1 ) states that there is a relationship between the population parameters.
To learn more about the null hypothesis, please check: brainly.com/question/4454077
6x – 3y = 3 –2x + 6y = 14 What is the solution to the system
Answers
Answer:
No solutionStep-by-step explanation:
6x – 3y = 3
–2x + 6y = 14
lets solve by substitution:
1) lets isolate y:
6x–3y=3
-3y=-6x+3
y=(-6x+3)/-3
y=2x-1
2) plug in 2x-1 for y in order to find x:
6x-3(2x-1)=3
6x-6x+3=3
3=3
since x cancels out, it means that there is no solution to this linear system of equations
Answer:
No Solution :)
Step-by-step explanation:
Which of these is the opposite reciprocal of 3/4
Answers
Answer: -4/3
Step-by-step explanation: To find the negative reciprocal of a fraction, all you have to do is flip the fraction and change the sign.
So the negative reciprocal of 3/4 is -4/3.
butter and flour are mixed in the ratio 2:3. paul has 640 grams of butter and 880 grams of flour. how much more flour does he need? Can you explain again in a simpler format.
Answers
Answer:
80 grams of butter
Step-by-step explanation:
640/2=329
3x320=960
960-880=80
[tex]20+3x-15+x=27[/tex]
Answers
Answer:
x=11/2
Step-by-step explanation:
First we can combine similar terms on the left side. 3x + x is 4x and 20-15 is 5
Now that we have combined them, we are left with 4x+5=27
Subtract 5 on both sides to cancel out the 5.
4x=22
Divide both sides by 4
x=22/4
Simplify
x=11/2
Answer:
[tex] \boxed{\sf x = \frac{11}{2}} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: x: \\ \sf \implies 20 + 3x - 15 + x = 27 \\ \\ \sf Grouping \: like \: terms, \: 20 + 3x - 15 + x = \\ \sf (3x + x) + (20 - 15) : \\ \sf \implies \boxed{ \sf (3x + x) + (20 - 15)} = 27 \\ \\ \sf 3x + x = 4x : \\ \sf \implies \boxed{ \sf 4x} + (20 - 15) = 27 \\ \\ \sf 20 - 15 = 5 : \\ \sf \implies 4x + \boxed{ \sf 5} = 27 \\ \\ \sf Subtract \: 5 \: from \: both \: sides: \\ \sf \implies 4x + (5 - \boxed{ \sf 5}) = 27 - \boxed{ \sf 5} \\ \\ \sf 5 - 5 = 0 : \\ \sf \implies 4x = 27 - 5 \\ \\ \sf 27 - 5 = 22 : \\ \sf \implies 4x = \boxed{ \sf 22} \\ \\ \sf Divide \: both \: sides \: of \: 4x = 22 \: by \: 4 : \\ \sf \implies \frac{4x}{4} = \frac{22}{4} \\ \\ \sf \frac{ \cancel{4}}{ \cancel{4}} = 1 : \\ \sf \implies x = \frac{22}{4} \\ \\ \sf \implies x = \frac{11 \times \cancel{2}}{2 \times \cancel{2}} \sf \implies x = \frac{11}{2} [/tex]
If mBC in circle Ais 60°, what is mZ BDC?
a. 60 degrees
b. 45 degrees
c. 30 degrees
d. 25 degrees
Answers
Answer:
Option (C)
Step-by-step explanation:
Measure of the arc BC of a circle A = 60°
Since, measure of an arc is equal to the measure of the central angle that intercepts the arc.
Therefore, m∠A = 60°
Since, measure of the inscribed angle is half of the central angle subtended by the same arc.
Therefore, m∠A = [tex]2\times m(\angle {BDC})[/tex]
60° = 2 × m(∠BDC)
m∠BDC = 30°
Therefore, Option (C) will be the answer.
Answer:
It’s C
Step-by-step explanation:
12+[(15-5)]+(9-3)] what is the answer
Answers
Answer:
28
Step-by-step explanation:
12+[(15-5)]+(9-3)]
PEMDAS
Parentheses first
12+[(10)]+(6)]
Then add
12+10+6
Answer: 28
Step-by-step explanation:
URGENT It is given that a regular n-sided polygon has 5 sides more than a
regular m-sided polygon. If the sum of interior angles of the regular
n-sided polygon is twice that of the latter, find the values of m and n.
Answers
Answer:
m = 7; n = 12
Step-by-step explanation:
"a regular n-sided polygon has 5 sides more than a
regular m-sided polygon"
n = m + 5
The sum of the measures of the interior angles is
180(n - 2) for the n-sided polygon and
180(m 2) for the m-sided polygon.
"If the sum of interior angles of the regular
n-sided polygon is twice that of the latter"
180(n - 2) = 2(180)(m - 2)
We have a system of equations with 2 equations.
n = m + 5
180(n - 2) = 2(180)(m - 2)
Simplify the second equation:
n - 2 = 2m - 4
n + 2 = 2m
Substitute m + 5 for n.
m + 5 + 2 = 2m
7 = m
m = 7
n = m + 5 = 7 + 5 = 12
Answer: m = 7; n = 12
A first number plus twice a second number is 14. Twice the first number plus the second totals 10. Find the numbers.
Answers
Answer:
first number(x) = 2 second number(y)= 6
Step-by-step explanation:
This is an example of a simultaneous equation.
First write this word problem as equations, where x is the "first number" that you've mentioned and y is the "second number".
x + 2y = 14 (equation 1)
2x + y = 10 (equation 2)
This is solved using the elimination method.
We need to make one of the coefficients the same - in this case we can make y the same. In order to do this we need to multiply equation 2 by 2, so that y becomes 2y.
2x + y = 10 MULTIPLY BY 2
4x + 2y = 20 (this is now our new equation 2 with the same y coefficient)
Now subtract equation 1 from equation 2.
4x - x + 2y - 2y = 20 - 14 (2y cancels out here)
3x = 6
x = 2
Now we substitute our x value into equation 1 to find the value of y.
2 + 2y = 14
2y = 12
y = 6
Hope this has answered your question.
Answer:
6 and 2
Step-by-step explanation:
Let the first number =a
Let the second number =b
A first number plus twice a second number is 14.
a+2b=14Twice the first number plus the second totals 10.
2a+b=10We solve the two equations simultaneously
[tex]a+2b=14 \implies a=14-2b\\$Substitute into the second equation$\\2(14-2b)+b=10\\28-4b+b=10\\-3b=10-28\\-3b=-18\\b=6[/tex]
Recall:
a=14-2b
=14-2(6)
=14-12
a=2
The two numbers are 6 and 2.
A pretzel company calculated that there is a mean of 75.4 broken pretzels in each production run with a standard deviation of 5.2. If the distribution is approximately normal, find the probability that there will be fewer than 66 broken pretzels in a run.
Answers
Answer:
P [ Z < 66 ] = 35,15 %
Step-by-step explanation:
Normal Distribution
Population mean μ₀ = 75,4
Standard deviation σ = 5,2
Then:
P [ Z < 66 ] = ( 66 - 75,4 ) / 5,2
P [ Z < 66 ] = - 9,4 / 5,2
P [ Z < 66 ] = - 1,81
In z-table we look for the reciprocate area for that z score and find
P [ Z < 66 ] = 0,3515
P [ Z < 66 ] = 35,15 %
Show all work! I don't understand this! Brainleist!
I attached a picture this time!
Answers
Answer:
2.94 seconds.
Step-by-step explanation:
The ball will hit the ground when the height of the ball is 0 meters.
The equation is...
h = 61 - 6t - 5t^2.
-5t^2 - 6t + 61 = 0
5t^2 + 6t - 61 = 0
We can use the quadratic formula to solve.
[please ignore the A-hat; that is a bug]
[tex]\frac{-b ± \sqrt{b^2 - 4ac} }{2a}[/tex], where a = 5, b = 6, and c = -61.
= [tex]\frac{-6 ± \sqrt{6^2 - 4 * 5 * (-61)} }{2 * 5}[/tex]
= [tex]\frac{-6 ± \sqrt{36 - 20 * (-61)} }{10}[/tex]
= [tex]\frac{-6 ± \sqrt{36 + 1,220)} }{10}[/tex]
= [tex]\frac{-6 ± \sqrt{1,256} }{10}[/tex]
= [tex]\frac{-6 ± 35.44009029}{10}[/tex]
Since time cannot be negative, we will not minus the 35.44009029.
(-6 + 35.44009029) / 10 = 29.44009029 / 10 = 2.944009029
That is approximately 2.94 seconds.
Hope this helps!
Answer:
[tex]\boxed{t = 2.94 \ seconds}[/tex]
Step-by-step explanation:
When the ball hits the ground, h = 0
Putting this in the equation:
=> [tex]0 = 61-6t-5t^2[/tex]
=> [tex]61-6t-5t^2 = 0[/tex]
Taking -1 as common
=> [tex]-1(5t^2+6t-61) = 0[/tex]
Dividing both sides by -1
=> [tex]5t^2+6t-61 = 0[/tex]
Using Quadratic Equation:
=>t = [tex]\frac{-b+ / - \sqrt{b^2-4ac} }{2a}[/tex]
=> [tex]\frac{-6 +/- \sqrt{6^2-4(5)(-61)} }{2(5)}\\\frac{-6 +/- \sqrt{36+1220} }{10}[/tex]
=> t = [tex]\frac{-6 +/- 35.44}{10}[/tex]
Either:
t = [tex]\frac{-6+35.44}{10}[/tex] OR t = [tex]\frac{-6-35.44}{10}[/tex]
t = 29.44/10 OR t = -41.44/10
t = 2.94 OR t = -4.14
Time can never be negative so t = 2.94 secs
In a multiple regression, the following sample regression equation is obtained:yˆ = 152 + 12.9x1 + 2.7x2.a. Predict y if x1 equals 20 and x2 equals 35. (Round your answer to 1 decimal place.)
Answers
Answer:
The predicted value of y is 504.5.
Step-by-step explanation:
Let be [tex]y = 152 + 12.9\cdot x_{1} + 2.7\cdot x_{2}[/tex], for all [tex]x_{1}, x_{2} \in \mathbb{R}[/tex]. If [tex]x_{1} = 20[/tex] and [tex]x_{2} = 35[/tex], the predicted value of y is:
[tex]y = 152 + 12.9\cdot (20) + 2.7\cdot (35)[/tex]
[tex]y = 504.5[/tex]
The predicted value of y is 504.5.
What are the zeros of the quadratic function f (x) = 2x^2 -10x-3?
Answers
Answer:
x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4
Step-by-step explanation:
1. Need to factor or can use the quadratic formula
2x^2-10x-3=0
a=2, b=-10, c=-3
[-b+-sqrt(b^2-4*a*c)]/(2*a)
[10+-sqrt(100-4*(-200)]/4
[10+- sqrt(300)]/4
x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4
Derek is building a deck. The sum of the interior angles is 10800 and each interior angle is 1350. How many sides does his deck have
Answers
sum of angles = 10800
measurement of a single angle= 1350
Therefore,
No. of sides = sum of angles / single angle
No of sides = 10800 / 1350
No of sides = 8
Answer:
8 sides.
Step-by-step explanation:
If the sum of the angles is 10,800 degrees, and each angle is 1,350 degrees, the deck will have the number of sides of the sum of the angle measurements divided by each angle's measurements.
10,800 / 1,350 = 1,080 / 135 = 8 sides.
Hope this helps!
Find the slope of the line passing through the points (-4, 2) and (-6,5).
Answers
Answer:
-3/2
Step-by-step explanation:
Hey there!
Well to find the slope of a line with 2 points we use the following formula,
y2 - y1 / x2 - x1
5 - 2 = 3
-6 - -4 = -2
Slope = -3/2
Hope this helps :)
Answer:
[tex]Slope = -\frac{3}{2}[/tex]
Step-by-step explanation:
[tex](-4, 2) \:(-6,5).\\\\m =\frac{y_2-y_1}{x_2-x_1} \\\\x_1 = -4\\y_1 =2\\x_2 = -6\\y_2 =5\\\\m = \frac{5 -2}{-6-(-4)}\\ m = \frac{3}{-6+4}\\ m = \frac{3}{-2}\\ \\Slope = -\frac{3}{2}[/tex]
What is the value of $\sqrt{36 \times \sqrt{16}}$?
Answers
Answer:
24
Step-by-step explanation:
If we have two square roots like [tex]\sqrt{36}\cdot\sqrt{16}[/tex], we could do this either of two ways.
1. Multiply 36 by 16 and find the square root of that
[tex]\sqrt{36\cdot16} = \sqrt{576} = 24[/tex]
2. Find the square root of both of them then multiply.
[tex]\sqrt{36} = 6, \sqrt{16} = 4, 6\cdot4 = 24[/tex]
Hope this helped!
select the decimal that is equivalent to the fraction 57 over 100
Answers
Answer:
0.57.
Step-by-step explanation:
57 / 100
We divide 57 by 100:
= 0.57