Answer:
the solution is (40, 21)
Step-by-step explanation:
Let the two numbers be x and y.
Then x + y = the sum = 61, and
x - y = the difference = 19.
Solve the system of linear equations
x + y = 61
x - y = 19
Combining these two equations:
x + y = 61
x - y = 19
---------------
2x = 80, so x must be 40.
Substituting 40 for x in the first equation, we get 40 + y = 61.
Combining the constants, we get y = 21.
Then the solution is (40, 21).
The numbers whose sum is 61 and difference 19 are 40 and 21. This is obtained by using algebraic expression for the given condition.
Find the algebraic expression for the question:Given that sum of numbers is 61 and difference is 19.
Let the larger number be x and smaller number be y.
Then we can write that, x+y=61 (sum) and x-y=19 (difference)
Calculate the numbers:By solving the algebraic equations we can find the numbers.
From second equation we can write, x = 19+y Substitute this in first equation,(19+y) + y = 61
19+2y = 61
2y = 61 - 19 = 42
y=42/2=21 ⇒ y=21 is the smaller number
x = 19+y = 19+21 =40 ⇒ x=40 is the larger number
Hence the numbers whose sum is 61 and difference 19 are 40 and 21.
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PLEASE HELP FAST!! I apologize for the pictures being sideways.
Answer:
a) 180
b) CJ= 5.83095189485
CK= 9.89949493661
CL= 8.0622577483
c) All angles formed by a point and its image, with the vertex at the center of rotation, are congruent. Each point on the original figure is the same distance from the center of rotation as its image.
Step-by-step explanation:
Drag each tile to the correct box. Consider the given functions f, g, and h.
h(x)=x²+x-6
Place the tiles in order from least to greatest according to the average rate of change of the functions over the interval [0, 3].
function H function f function g
Answer:
g, f, h
Step-by-step explanation:
By definition, the average rate of change of a function f over an interval [a,b] is given by
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
So, in your case, we want to compute the quantity
[tex]\dfrac{f(3)-f(0)}{3}[/tex]
for all the three function
Average rate of change of f:
We will simply use the table to check the values for f(3) and f(0):
[tex]\dfrac{f(3)-f(0)}{3}=\dfrac{10-1}{3} = 3[/tex]
Average rate of change of g:
We will use the graph to to check the values for g(3) and g(0):
[tex]\dfrac{g(3)-g(0)}{3}=\dfrac{8-1}{3} = \dfrac{7}{3}[/tex]
Average rate of change of h:
We can plug the values in the equation to get h(3) and h(0):
[tex]h(3)=3^2+3-6=9+3-6=6,\quad h(0)=0^2+0-6=-6[/tex]
And so the average rate of change is
[tex]\dfrac{h(3)-h(0)}{3}=\dfrac{6-(-6)}{3} = 4[/tex]
Answer:
g,f,h
I just took the test and was right
Step-by-step explanation:
Find the sum of the series. Include each term that leads to the final sum and show the expression for finding that term. ∑5k=3(−2k+5)
Answer:
[tex]\large\boxed{\sum\limits_{k=3}^5(-2k+5)=-9}[/tex]
Step-by-step explanation:
[tex]\sum\limits_{k=3}^5(-2k+5)\to a_k=-2k+5\\\\\text{Put}\ k=3,\ k=4\ \text{and}\ k=5:\\\\a_3=-2(3)+5=-6+5=-1\\a_4=-2(4)+5=-8+5=-3\\a_5=-2(5)+5=-10+5=-5\\\\\sum\limits_{k=3}^5(-2k+5)=-1+(-3)+(-5)=-9[/tex]
Find the length of segment BC. Please help ASAP
BC also has length 12 because arcs DC and CE add up to 117 degrees in measure, so that arc DE is congruent to arc BC, and the chords DE and BC that respectively intercept these arcs must also be congruent.
20. The surface areas of two similar solids are 216 m² and 1014 m². The volume of the larger one is 2197 m³. What is the volume of the smaller one?
Answer:
216 m³
Step-by-step explanation:
The ratio of linear dimensions is the square root of the ratio of area dimensions.
s = √(216/1014) = √(36/169) = 6/13
Then the ratio of volume dimensions is the cube of that. The smaller volume is ...
v = (6/13)³·2197 m³ = 216/2197·2197 m³ = 216 m³
The volume of the smaller solid is 216 m³.
70 POINTS!!!!
Find the focus, directrix, and equation of the parabola in the graph.
Answer:
Option B
Part a) The focus is [tex](1/28,0)[/tex]
Part b) The directrix is [tex]x=-1/28[/tex]
Part c) The equation is [tex]y^{2}= (1/7)x[/tex]
Step-by-step explanation:
step 1
Find the equation of the parabola
we know that
The parabola in the graph has a horizontal axis.
The standard form of the equation of the horizontal parabola is
[tex](y - k)^{2}= 4p(x - h)[/tex]
where
p≠ 0
The vertex of this parabola is at (h, k).
The focus is at (h + p, k).
The directrix is the line x= h- p.
The axis is the line y = k.
If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left
In this problem we have that the vertex is the origin
so
(h,k)=(0,0)
substitute in the equation
[tex](y - 0)^{2}= 4p(x - 0)[/tex]
[tex]y^{2}= 4p(x)[/tex]
The points (7,1) and (7,-1) lies on the parabola-----> see the graph
substitute the value of x and the value of y in the equation and solve for p
[tex](1)^{2}= 4p(7)[/tex]
[tex]1= 28p[/tex]
[tex]p=1/28[/tex]
The equation of the horizontal parabola is
[tex]y^{2}= 4(1/28)(x)[/tex]
[tex]y^{2}= (1/7)x[/tex]
step 2
Find the focus
we know that
The focus is at (h + p, k)
Remember that
[tex](h,k)=(0,0)[/tex]
[tex]p=1/28[/tex]
substitute
[tex](0+1/28,0)[/tex]
therefore
The focus is at
[tex]F (1/28,0)[/tex]
step 3
Find the directrix
The directrix is the line x = h- p
Remember that
[tex](h,k)=(0,0)[/tex]
[tex]p=1/28[/tex]
substitute
[tex]x=0-1/28[/tex]
[tex]x=-1/28[/tex]
Answer:
B
Step-by-step explanation:
Confirmed on E D G 2021
Kahn Academy Question, Please help!
[tex]g\circ f(-9)=g(f(-9))[/tex]
By definition of [tex]f[/tex],
[tex]f(-9)=3\cdot9-8=19[/tex]
and by definition of [tex]g[/tex],
[tex]g\circ f(-9)=g(f(-9))=g(19)=\sqrt{14-19}-10=\sqrt{-5}-10[/tex]
which is undefined if [tex]f,g[/tex] are supposed to be real-valued functions. If they're complex-valued, then [tex]\sqrt{-5}=i\sqrt 5[/tex] and [tex]g\circ f(-9)=-10+i\sqrt 5[/tex].
What is the ordered pair for point B?
The answer is C. (5,3)
Explanation:
(X,Y) is how ordered pairs should be set up.
Answer:
C (5,3)
Step-by-step explanation:
The first point in an ordered pair is the x coordinate.
We move 5 units to the right, so it is +5
The second coordinate is the y coordinate.
We move 3 units up, so it is +3
(5,3)
Please help me out!....
Check the picture below.
The length of a phone conversation is normally distributed with a mean of 4 minutes and a standard deviation of .6 minutes. What is the probability that a conversation lasts longer than 5 minutes? 0.04746 0.45254 0.54746 0.95254
Answer:
0.04746
Step-by-step explanation:
To answer this one needs to find the area under the standard normal curve to the left of 5 minutes when the mean is 4 minutes and the std. dev. is 0.6 minutes. Either use a table of z-scores or a calculator with probability distribution functions.
In this case I will use my old Texas Instruments TI-83 calculator. I select the normalcdf( function and type in the following arguments: :
normalcdf(-100, 5, 4, 0.6). The result is 0.952. This is the area under the curve to the left of x = 5. But we are interested in finding the probability that a conversation lasts longer than 5 minutes. To find this, subtract 0.952 from 1.000: 0.048. This is the area under the curve to the RIGHT of x = 5.
This 0.048 is closest to the first answer choice: 0.04746.
Kylie and Ethan have each saved some money. I’m their savings, each coin is worth leas then 50 cents and each bill is less then $10. Kylie has saved more money than Ethan, but he has more bills and coins than Kylie. She has one bill and seven coins. What is the amount of money each person could have?
Answer:
Kylie could have a $5 bill and seven quarters while Ethan could have two $1 bills and forty pennies.
Step-by-step explanation:
Since Kylie has seven quarters, that is seven multiplied by the value of the quarter, a quarter is 25 cents. So 7 x 25 = 125 OR $1 and 25 cents. Leaving Kylie with a total of $7 and 25 cents with the addition of the $5 bill.
Ethan has two $1 bills and forty pennies, forty multiplied by the value of the penny, a penny is 1 cent. So 40 x 1 = 40 OR 40 cents. Leaving Ethan with $2 and 40 cents with the addition of the two $1 bills from earlier.
Ethan has more bills and coins than Kylie and yet still has less money than Kylie.
A survey of 225 students showed the mean number of hours spent studying per week was 20.6 and the standard deviations was 2.7
Answer:
The margin of error is approximately 0.3
Step-by-step explanation:
The following information has been provided;
The sample size, n =225 students
The sample mean number of hours spent studying per week = 20.6
The standard deviation = 2.7
The question requires us to determine the margin of error that would be associated with a 90% confidence level. In constructing confidence intervals of the population mean, the margin of error is defined as;
The product of the associated z-score and the standard error of the sample mean. The standard error of the sample mean is calculated as;
[tex]\frac{sigma}{\sqrt{n} }[/tex]
where sigma is the standard deviation and n the sample size. The z-score associated with a 90% confidence level, from the given table, is 1.645.
The margin of error is thus;
[tex]1.645*\frac{2.7}{\sqrt{225}}=0.2961[/tex]
Therefore, the margin of error is approximately 0.3
Answer:
.3 is the answer.
Step-by-step explanation:
A 12 pack of cola costs $5.46. How much does one can of cola cost?
Answer:
46¢
Step-by-step explanation:
Note that there are 12 cola's in all. The total cost is $5.46. Divide the total cost with the amount of cola's there is:
5.46/12 = 0.455
Round: 0.455 rounded to the nearest hundredths is $0.46 (You round to the nearest hundredths, for the smallest amount for US currency is a penny, which is 1/100 of a dollar bill).
Each cola costs $0.46
~
Factor –8x3 – 2x2 – 12x – 3 by grouping. What is the resulting expression?
The answer is (-4x-1)(2x^2+3) when factoring this expression by grouping
Answer:
The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]-8x^3-2x^2-12x-3[/tex]
The above expression can be written as:
[tex](-8x^3-2x^2)+(-12x-3)[/tex]
Take out the greatest common factor from each group.
[tex]-2x^2(4x+1)-3(4x+1)[/tex]
Further solve the above expression.
[tex](4x+1)(-2x^2-3)[/tex]
Hence, the required expression is
[tex](4x+1)(-2x^2-3)[/tex]
The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]
2 fair dice are rolled. what is the probability that the sum is even given that the first die is rolled is a 2?
Wouldnt you add 6+6=12 then divide that with the probability of getting a 2?
===================================================
Explanation:
"given that the first die rolled is a 2" means we know 100% that the first die shows a 2. Either we can see the die or a friend is telling us the status. Since we know the first die is a 2, this means we can effectively ignore it. Everything will hinge on the second die. If the second die shows an odd number, something like 1, then 2+1 = 3 is the result which is also odd.
The general rule is odd+even = odd and even+even = even.
Therefore, the two dice must together be even for the sum to be even.
Of the six possible ways to roll a die {1,2,3,4,5,6}, there are 3 even values {2,4,6} so the chances of rolling an even number on the second die is 3/6 = 1/2. Again we dont need to consider the first die at all since everything practically hinges on this second die.
Answer:
50%
Step-by-step explanation:
For the total to be even, when the first number is even, the second number also has to be even.
2, 4, and 6 are even, out of 6 numbers. That is 3 numbers out of 6, which gives us that the probability is 1 out of 2, or 50%.
Which statement is correct about y = cos^–1 x?
Answer:
A) If the domain of y=cos(x) is restricted to [0, π], y=cos^-1(x) is a function.
Step-by-step explanation:
In order for the inverse function to be a function, the original must pass the horizontal line test: a horizontal line must intersect the function in only one place.
As you can see from the attached graph, restricting the cosine function to the domain [0, π] allows it to pass the horizontal line test, so its inverse will be a function.
__
Restricting the domain to [-π/2, π/2] does not limit cos(x) to something that will pass the horizontal line test.
The inequality -x^2 -6 <0 has how many critical points
Answer:
See below.
Step-by-step explanation:
This inequality is < 0 for all real values of x. We see this by solving -x^2 - 6 = 0 for x:
-x^2 - 6 = 0
-x^2 = 6
x^2 = -6 for which there are no real solutions of x. So the graph does not pass through the x axis.
At x = 0. f(x) < -6 so that is the one critical value - all values of f(x) are below this value.
Answer:
0 critical points
Step-by-step explanation:
Just did it and got it right
If g=26.4 and F=35° find h. Round to the nearest tenth (picture provided)
For this case we have to, by definition:
[tex]cos (F) = \frac {h} {26.4}[/tex]
This means that, the cosine of the angle F, will be equal to the leg adjacent to the angle on the hypotenuse of the triangle.
So, by clearing h we have:
[tex]h = 26.4 * cos (35)\\h = 26.4 * 0.81915204\\h = 21.6256[/tex]
Rounding out the value of h we have:
[tex]h = 21.6[/tex]
Answer:
Option B
Answer:
The correct answer is option b. 21.6
Step-by-step explanation:
Points to remember:-
Trigonometric ratio
Cos θ = adjacent side/Hypotenuse
From the figure we can see a right triangle triangle FGH.
To find the value of h
It is given that, g=26.4 and F= 35°
Cos F = adjacent side/Hypotenuse
Cos 35 = adjacent side/Hypotenuse
= FG/FH = h/g
h = g * Cos F = 26.4 * Cos 54 = 26.4 * 0.8191 = 21.62 ≈ 21.6
Therefore the correct answer is option b. 21.6
Can somebody please help me.
Answer:
72
Step-by-step explanation:
The two acute angles add up to 90 degrees. That's because the given triangle is a right triangle.
So x + 4x + 90 = 180 All triangles = 180°. Combine left side terms.
5x + 90 = 180 Subtract 90°
5x + 90 - 90 = 180 - 90 Combine
5x = 90 Divide by 5
5x/5 = 90/5 Combine
x = 18
The larger angle is 4x so
The larger angle = 4*18 = 72
Please HELP!
Pedro needs a 2 on the roll of die in order to win a game. What is his probability of failure?
A-1
B-1/6
C-0
D-5/6
The answer is D, he has to hit 1/6 sides so the chances are 5/6 hit hits 1,3,4,5, or 6
Answer:
D
Step-by-step explanation:
there are six sides on a die and only one side with a 2 so you have 1 side witha two 6-1=5 =5/6
Which theorem(s) can be used to prove that the given triangles are congruent to each other with only the information shown? Select all that apply.
A. ASA similarity
B. AA similarity
C. SAS similarity
D. SSS similarity
Ian's parents asked him to creat a budget for his $ 1,000 monthly income . He determines that he would like to save the remaining amount. What percent of his budget will go towards saving. Expense : Amount ($) Car payment $ 350 Car insurance $ 100 Fuel $ 120 Cell phone $ 80
35%
First, we need to find the amount of money that is being spent. Add all of the amounts together.
$350 + $100 + $120 + $80
$450 + $120 + 80
$570 + $80
$650
So, Ian spends $650 of his budget each month. How much does that leave for savings? Just subtract $650 from $1,000 to find that he saves $350 each month.
Now, you just need to find the percentage. The percentage is the same as the numerator in a fraction with a denominator of 100, so x% = x/100. For example, 1% = 1/100. $350 / $1000 = x / 100
How do we turn 1,000 into 100? Divide it by 10. And if you do something to the denominator of a fraction, you have to do it to the numerator as well. So, divide $350 by 10 and divide $1000 by 10, leaving you with $35 / $100 = x / 100
Multiply both sides by 100 to get x by itself. This leaves you with 35 = x, so 35% of Ian’s budget with go towards saving.
Please please help me
Answer:
18 in^2.
Step-by-step explanation:
The ratio of their areas = the ratio of the squares of corresponding sides. So:
9^2 / 12^2 = x / 32
81/144 = x / 32
x = (81 * 32) / 144
= 18 in^2.
Write the equation of the ellipse in standard form
Answer:
h=1 K =2 a =6 b=2
Step-by-step explanation:
look this solution :
Answer:
h = 1, k = 2, a = 6 and b = 2.
Step-by-step explanation:
Start by grouping the terms in x and y together:
4x^2 - 8x + 36y^2 - 144y = -4
Factor out the coefficient:
4(x^2 - 2x) + 36(y^2 - 4y) = -4
Complete the squares:
4 [(x - 1)^2 - 1] + 36 [y - 2)2 - 4] = -4
4(x - 1)^2 - 4 + 36(y - 2)^2 - 144 = -4
4(x - 1)^2 + 36(y - 2)^2 = 144
Divide through by 144:
(x - 1)^2 / 36 + (y - 2)^2/ 4 = 1
(x - 1)^2 / 6^2 + (y - 2)^2 / 2^2 = 1 (answer).
Correlation Coefficients. Image attached for the problem.
A. 11
B. 9
C. 3
D. 5
Answer:
A
Step-by-step explanation:
y bar basically means the average of the y-values.
To get the average, we add up all the y-values in the table and divide by the total number of values (here we have 5 values). Hence,
y bar = [tex]\frac{5+7+10+15+18}{5}=11[/tex]
correct answer is A
Spencer opened a savings account and deposited $10. The account pays 3.5% interest and compounds the interest monthly. How much money will Spencer have after 10 years? **n=12 because it is compounded monthly.
Answer:
[tex]\$14.18[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$10\\ r=0.035\\n=12[/tex]
substitute in the formula above
[tex]A=P(1+\frac{0.035}{12})^{12*10}=\$14.18[/tex]
5
∑ (2n-1)
n-1
Find the sum of the series. Show your work. Thanks for the help
Answer:
225
Step-by-step explanation:
15(1+15/2) *2= 240-15=225
The sum of the arithmetic series given by the terms (2n - 1) for n=1 to 5 is 25, computed using the formula for the sum of an arithmetic series.
The series in question is an arithmetic series with a difference of 2 and the sum of the first n terms can be represented by the formula for the sum of an arithmetic series, Sn = n/2[2a + (n-1)d], where 'a' is the first term and 'd' is the common difference between the terms.
In the provided series, each term is of the form (2n - 1) starting with n=1 and going till n=5. So the first term, a = 2(1) - 1 = 1, and the common difference, d = 2 since each subsequent term increases by 2.
We can compute this sum directly by evaluating S5, using the formula for an arithmetic series: S5 = 5/2[2(1) + (5-1)(2)] = 5/2[2 + 8] = 5/2[10] = 25. So, the sum of the series is 25.
Which number line represents the solution set for the inequality –x ≥ 4?
Answer:
It is the second choice.
Step-by-step explanation:
-1/2 x ≥ 4
x ≤ 4 * -2
x ≤ -8.
The number line with solid circle at -8 and shaded region extending to the left, serves as the appropriate number line representation for the inequality -1/2x ≥ 4. It clearly conveys that all values of x less than or equal to -8 are part of the solution set.
The correct answer is option B.
To represent the solution set of an inequality, we employ a number line with various markings to indicate the values that satisfy the inequality's criteria. In this case, we're dealing with the inequality -1/2x ≥ 4.
The inequality symbol ≥ signifies that the value on the left-hand side is greater than or equal to the value on the right-hand side. When we rewrite the inequality as x ≤ -8, we're essentially saying that any value of x less than or equal to -8 satisfies the inequality.
Option B accurately represents this solution set through a solid circle at -8, indicating that -8 is a direct solution to the inequality. The shaded region extending to the left of -8 further emphasizes that all values of x less than -8 also satisfy the inequality.
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SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Remember to be mindful of signs when adding and subtracting. 2c^2+5c+4
P(A) =0.20 P(B) = 0.25 P(A and B) = 0.10. What is P(B/A)?
A. 0.25
B. 0.40
C. 0.50
D. 0.05
Answer:
Final answer is [tex]P(B/A)=0.5[/tex]
Step-by-step explanation:
Given that P(A) =0.20
P(B) = 0.25
P(A and B) = 0.10.
Now we need to find about what is the value of P(B/A).
P(A and B) = P(A) * P(B/A)
Plug the given values into above formula:
[tex]0.10=0.20\cdot P(B/A)[/tex]
[tex]\frac{0.10}{0.20}=P(B/A)[/tex]
[tex]0.5=P(B/A)[/tex]
[tex]P(B/A)=0.5[/tex]
Hence final answer is [tex]P(B/A)=0.5[/tex]
Answer:
c is the answer
Step-by-step explanation: