Answers
m<B = 60
so
m<ACB = 180 - m<ACD
m<ACB = 180 - 100
m<ACB = 80
m<A = 180 - (60 + 80)
m<A = 180 - 140
m<A = 40
Answer:
The measure of ∠BAC is 40° .
Step-by-step explanation:
As given the figure in the question be as follow .
∠ACD = 100° , ∠B = 60°
Noe by using the the exterior angle is equal to the sum of the interior angle .
Thus
∠ACD = ∠CBA + ∠BAC
Put all the values in the above
100° = 60° + ∠BAC
∠BAC = 100° - 60°
= 40°
Therefore the measure of ∠BAC is 40° .
Related Questions
can someone help answer and explain to me how to solve this? log (lowercase 6) 1/36
Answers
-------------------------------------------
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Explanation:
We will use the log rule that log(x^y) = y*log(x). Call this log rule 1. This log rule basically allows us to pull the exponent down.
Another log rule that we will use is [tex]\log_x\left(x\right) = 1[/tex] where x is any positive real number but x = 1 is NOT allowed. Call this log rule 2.
Because 36 = 6^2, this means that 1/36 = 6^(-2)
-------------
So,
[tex]\log_6\left(\frac{1}{36}\right)=\log_6\left(\frac{1}{6^2}\right)[/tex]
[tex]\log_6\left(\frac{1}{36}\right)=\log_6\left(6^{-2}\right)[/tex]
[tex]\log_6\left(\frac{1}{36}\right)=-2*\log_6\left(6\right)[/tex] Use log rule 1 (see above)
[tex]\log_6\left(\frac{1}{36}\right)=-2*1[/tex] Use log rule 2 (see above)
[tex]\log_6\left(\frac{1}{36}\right)=-2[/tex]
This means that the given expression simplifies to -2
You can use a calculator to type in "log(1/36)/log(6)" without quotes and you should get -2 as the answer
so 6² = 36
therefore, 6⁻² = [tex] \frac{1}{36} [/tex]
so your answer will be -2
the power is the answer
Please help with these questions thank you very much!
Answers
2. 60 and 80
3. 60
4.37
The equation of line m is 5x−3y=2. What is the slope of a line that is perpendicular to line m? Enter your answer in the box.
Answers
y=-5/-3x+2/-3
y=5/3x-2/3
compare y=mx+c || m =5/3
for perpendicularity
m=-1/M
m=-1/5/3
m= -3/5
Step 1
Find the slope of the line M
we have
[tex]5x-3y=2[/tex]
isolate the variable y
[tex]3y=5x-2 \\ \\y=\frac{5}{3}x-\frac{2}{3}[/tex]
the slope of the line is [tex]\frac{5}{3}[/tex]
Step 2
Find the slope of the line perpendicular to line M
we know that
if two lines are perpendicular , then the product of their slopes are equal to minus one
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=\frac{5}{3}[/tex]
Find m2
[tex]m2=-1/m1[/tex]
[tex]m2=-1/(5/3)[/tex]
[tex]m2=-\frac{3}{5}[/tex]
therefore
the answer is
[tex]-\frac{3}{5}[/tex]
Can someone pleasee match these for me ASAP?? I need them rn and u get 27 pts! The first second and fourth on the ones with operations are multiplication. The fifth is subtraction. If u could do the questions as a thru f and g and the answers as 1 thru 6 and 7 and tell me the order that'd be great, thanks!
Answers
______________________________________
Question a): ANSWER: 1 ; √(28a⁴b³c) = 2a²b √(7bc) ;
_______________________________________________________
Question b): ANSWER: 6 ; √(98a⁴b³c) = 7a²b √(2bc) ;
_______________________________________________________
Question c): ANSWER: 3 ; √(56a³b⁴c²) = 2ab²c √(14a) ;
_______________________________________________________
Question d): ANSWER: 5 ; √(48a⁵b⁶c³) = 4a²b³c √(3ac) ;
_____________________________________________________
Question e): ANSWER: 2 ; √(24a⁵b⁴c²) = 2a²b²c √(6a) ;_____________________________________________________
Question f): ANSWER: 4 ; √(54a⁶b⁵c²) = 3a³b²c √(6b) .
_____________________________________________________
What is the answer?
Answers
This come from x = -5
Move over -5 into the other side to make the equation equal to zero
x + 5 = 0
Answer: x + 5
What is the answer to: jason has 4 tiles. each tile has a number printed oon it. the numbers are 2,3,6, and 8, a decimal number is formed using the titles and the clues. be a math detective and find the number.?
Answers
I believe this problem has the following clue:
digit in the tens place is the largest number. digit in tenths place is less than the digit located in the hundredths place. the digit in the ones place is greater than the digit in the hundredths place
From this clue, we can say that the number is:
86.23
The function f(x)=3(2.5)x is shown on the coordinate plane.
Select from the drop-down menus to correctly describe the end behavior of f(x) .
As x decreases without bound, the graph of f(x) .
As x increases without bound, the graph of f(x) .
An exponential curve on a coordinate plane with horizontal x axis ranging from negative 4 to 4 in increments of 1. The vertical y-axis ranges from negative 1 to 7 in increments of 1. The curve begins infinitely close to the x axis in the second quadrant. The curve increases through begin ordered pair 0 comma 3 end ordered pair. DO NOT DELETE THIS PLZ HOEFULLY SOMEONE CAN TRY TO ANSWER IT
Answers
As x increases without bound, the graph of f(x) approaches y=0 increases without bound .
We have function [tex]f(x)=3(2.5)^x[/tex]
From the graph we can see that as x decreases without bound the graph of f(x) approaches y=0.
Also the exponential function in the graph is approaching y=0 as x decreases on the left side of the curve.
Here as the exponential function here the power is x variable and the exponential function cannot be negative for any value of x.
Therefore as x increases without bound, the graph of f(x) approaches y=0 increases without bound .
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Step-by-step explanation:
i took the test :)
50 POINTS + BRAINLIEST
Answers
2y = -x + 6
y = -1/2 x + 3 so slope = -1/2
parallel lines has same slope = -1/2
perpendicular lines slope is opposite and reciprocal so slope = 2
if slope not equal either -1/2 or 2 then neither.
y = -1/2 x - 5 ....m= - 1/2.... parallel
-2x + y = -4
y = 2x - 4...m = 2 ....perpendicular
-x + 2y = 2
2y = x + 2
y = 1/2 x + 1 ...m = 1/2 ...neither
x + 2y = -2
2y = -x - 2
y = -1/2 x - 1 ...m = -1/2 .....parallel
hope it helps
Answer:x + 2y = 6
2y = -x + 6
y = -1/2 x + 3 so slope = -1/2
parallel lines has same slope = -1/2
perpendicular lines slope is opposite and reciprocal so slope = 2
if slope not equal either -1/2 or 2 then neither.
y = -1/2 x - 5 ....m= - 1/2.... parallel
-2x + y = -4
y = 2x - 4...m = 2 ....perpendicular
-x + 2y = 2
2y = x + 2
y = 1/2 x + 1 ...m = 1/2 ...neither
x + 2y = -2
2y = -x - 2
y = -1/2 x - 1 ...m = -1/2 .....parallel
Claire has received scores of 85,82, and 75 on her algebra tests. what score must she receive on the fourth test to have an overall test score average of at least 82
Answers
85 + 82 + 75 + 86 = 328
328 divide by 4 (as there are four tests) = 82
A bag contains purple and orange marbles. Sam randomly takes out one marble and then returns it to the bag. He does this 18 times, and 12 of those times an orange marble is pulled out. What is P(green)?
Answers
holly and melanie were playing a video game. the ratio of holly's score to melanie's score was 8:3. after melanie scored 34 points, the ratio of their scores became 2:5. what were their scores at the end?
Answers
Since we don't know the actual numbers, let's say their scores were originally 8x for Holly and 3x for Melanie.
Then Melanie scored 34 points, so her score became 3x + 34.
Holly's score remained the same at 8x.
The new ratio is 2:5, so
8x/(3x + 34) = 2/5
Now we solve the equation for x.
40x = 6x + 68
34x = 68
x = 2
With x, we can find the scores.
Holly ended up with 8x = 8 * 2 = 16
Melanie ended up with 3x + 34 = 3(2) + 34 = 40
The product of two numbers is 40. if one of the numbers is 5/11, what is the other number?
Answers
Final answer:
To find the other number when the product of two numbers is 40 and one of the numbers is 5/11, we divide 40 by 5/11 to solve for the unknown number. The other number is found to be 88.
Explanation:
The question asks to find the other number when the product of two numbers is 40 and one of the numbers is given as 5/11. To do this, we can set up an equation where the product of 5/11 and the unknown number (which we can call 'x') is equal to 40.
The equation would be: (5/11) × x = 40. To solve for x, we need to do some algebraic rearrangement by dividing both sides of the equation by 5/11. This brings x into the numerator on the left side and shifts the 5/11 to the denominator on the right side. Therefore, we get x = 40 × (11/5).
Next, we multiply 40 by 11/5. This calculation results in x = 88. Thus, the other number is 88.
Alexandra bought a $90000 life insurance policy at $10.98 for a 20 year term. She will pay ___ over 20 years for the premium
Answers
The expression on the left side of an equation is shown below.
-5(x+2) +3x =___
If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?
A. -5(x-3) +2x
B. -5x-10
C. x-2x +2 +3x
D. -2(x +5)
Answers
-5(x + 2) + 3x =
-5x - 10 + 3x =
-2x - 10 =
-2(x + 5) ....so ur original equation can be broken down to this...
so -5(x + 2) + 3x = -2(x + 5) would produce infinite solutions because it is basically the same expression <=
After solving the equation, the equivalent equation obtained which has an infinite solution will be equal to -2(x + 5). Hence, option D is correct.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
-5(x + 2) + 3x
Now, solve the equation,
-5x - 10 + 3x
= -5x + 3x - 10
= - 2x - 10
So, the equivalent equation will be,
-2(x + 5), it has an infinite solution because it is the same equation.
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Randy solved the following problem: 7/8 + 9/15. He said, "I can add 7 and 9 to get 16 and add 8 and 15 to get 23. The answer is 16/23. " Is Randy correct? Explain your answer.
Answers
To add two fractions, you must first have he same denominator in both.
Then you add the numerators and write the same denominator. You do not add the denominators.
Jill has 8.75. Jack has three times as much as Jill, but he spent 5.00 to buy a book. How much money does jack have ?
Answers
Answer = 21.25
True or false: the regression sum of squares (ssr) can never be greater than the total sum of squares (sst).
Answers
What is the remainder of the following division problem? in the pic?
A. x
B.1
C. 0
D.–1
Answers
hope this helps
0 + 1 = 1
so your answer is 1 1/x
Answer : Option B is correct.
Explanation :
Since we have given that
f(x) = x+1
and
g(x) =x
and when we divide f(x) with g(x) i.e.
[tex]\frac{f(x)}{g(x)}[/tex]
And we know the division algorithm , i.e.
[tex]f(x)=g(x).q(x) +r(x)[/tex],
Where q(x) represents quotient and r(s) denotes remainder
So, we write it in this manner ,
[tex]x+1=x.1+1\\\\\text{Remainder becomes 1}[/tex]
Hence, Remainder = 1
So, Option B is correct.
Which unit fraction should be used to convert 15 inches to centimeters?
Answers
To convert from inches to centimeters, the unit fraction used is 2.54 cm/1 in. Therefore, 15 inches is equal to 38.1 centimeters.
Explanation:To convert a measurement from inches to centimeters, we utilize a unit conversion factor. In this instance, the unit conversion factor we're interested in relates inches to centimeters. One inch is equivalent to 2.54 centimeters. Hence, the unit fraction used for such conversion is 2.54 cm/1 in.
To determine the equivalent value in centimeters for 15 inches, we multiply the number of inches (15) by our unit conversion factor (2.54 cm/1 in). This gives us the following
15 inches * 2.54 cm/1 in = 38.1 cm.
So, 15 inches is equivalent to 38.1 centimeters when converted.
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If AB = 18 and AC = 3x +6 then x=
Answers
set AB=AC
18=3x+6
minus 6 on both sides
12=3x
divide both sides by 3
x=4
What’s the rule for the translation (x,y) (x+3,y+7)
Answers
For the y value, if you are adding a number to the y coordinate, you are moving it up, whereas when you subtract a number, you are moving it down that amount.
M(8, 5) is the midpoint of JK. The coordinates of point J are (5, −6) . What are the coordinates of point K?
Answers
The midpoint is the exact middle of a line segment which divides the line into two equal lengths. Hence, the coordinate of K is (11, 16)
We can obtain the distance between the coordinates of JM thus :
Distance = y2 - y1 ; x2 - x1
Distance = (8 - 5) ; (5 - (-6) = (3, 11)
Hence, the change in the coordinates is (3, 11)
Therefore, the coordinates of K can be obtained thus :
(8 + 3) ;(5 + 11) = (11, 16)
Hence, the coordinate of K is (11, 16)
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The temperature rose 4 f every 90 minutes before noon and rose 2 f for every 45 minutes after noon are these rates equivalent
Answers
You have already saved $55 you earn $9 per hour babysitting you ate saving for a camera that costs $199
Answers
There are 18 players on the baseball team. Of these players 1/3 are girls. How many girls play on the baseball team?
Answers
divide 18 by 3
18 / 3 = 6
there are 6 girls on the team
Find the midpoint of the segment with the given endpoints. m(–2, 1) and n(–3, 2)
Answers
Solve for x.
x2(^) + 9x = 0
Answers
x(x+9)=0
x=0, -9
Divide.
(5 1/4)÷(−2 1/2)
Enter your answer as a mixed number, in simplified form, in the box. Please Explain your answer.
Answers
To divide (5 1/4)÷(−2 1/2), convert the mixed numbers into improper fractions and then multiply by the reciprocal of the divisor. Simplify the result to get the quotient as -2 1/10.
Explanation:To divide the given mixed numbers, (5 1/4)÷(−2 1/2), we first convert them into improper fractions.
5 1/4 can be written as (4*5 + 1)/4 = 21/4.
(−2 1/2) can be written as (-2*2 + 1)/2 = -5/2.
Now, we can divide the fractions by multiplying the reciprocal of the divisor: (21/4) * (-2/5) = (-21/4) * (2/5) = -21/10.
Finally, we simplify the result by dividing both the numerator and the denominator by their greatest common factor, which is 1. The simplified result is -21/10, which can be written as -2 1/10 as a mixed number.
The baggage limit for an airplane is set at 100 pounds per passenger. thus, for an airplane with 200 passenger seats there would be a limit of 20,000 pounds. the weight of the baggage of an individual passenger is a random variable with a mean of 95 pounds and a standard deviation of 35 pounds. if all 200 seats are sold for a particular flight, what is the probability that the total weight of the passengers' baggage will exceed the 20,000-pound limit?
Answers
At a mean of 95 pounds per passenger and standard deviation of 35 pounds, multiplying this with the total number of passengers = 200, results in:
absolute mean = 95 * 200 = 19,000
absolute std dev = 35 * 200 = 7,000
Calculating for the z score:
z = (x – u) / s
where x is sample value = more than 20,000; u is the sample mean = 19,000; s is std dev = 7,000
z = (20,000 – 19,000) / 7,000
z = 0.143
From the distribution tables,
P (z = 0.14) = 0.5557
Therefore a 55.57% chance that it will be more than 20,000 pound limit
Final answer:
Using the Central Limit Theorem, we calculate the probability that the total weight of passengers' baggage exceeds 20,000 pounds for an airplane with 200 passengers to be approximately 0.0217.
Explanation:
To solve this problem, we use the Central Limit Theorem which states that if we have a large enough sample size, the distribution of the sample means will be approximately normally distributed regardless of the original distribution's shape. Given that the mean weight of an individual passenger's baggage is 95 pounds with a standard deviation of 35 pounds, and that there are 200 passengers, we can calculate the mean and standard deviation of the total baggage weight.
The mean total weight, μtotal, is calculated as the product of the mean individual weight and the number of passengers, so μtotal = 95 pounds × 200 = 19,000 pounds. The standard deviation of the total weight, σtotal, is calculated as the standard deviation of the individual weight multiplied by the square root of the number of passengers, so σtotal = 35 pounds × √200 ≈ 494.97 pounds.
Using the standard normal distribution, we find the z-score for the probability that the total weight exceeds 20,000 pounds by subtracting the mean from the limit and dividing by the standard deviation: z = (20,000 - 19,000) / 494.97 ≈ 2.02.
Looking up this z-score in a standard normal table or using a calculator, we find that the probability of the total baggage weight exceeding 20,000 pounds is approximately 0.0217.
The sum of two numbers is 39 . the larger number is 17 more than the smaller number. what are the numbers?
Answers
Larger Number = S + 17
Smaller Number = S
S + 17 + S = 39
2S + 17 = 39
2S = 39 - 17
2S = 22
S = 22/2
S = 11
Larger Number is S + 17
Larger Number is 11 + 17
Larger Number is 28
Smaller Number is 11
The smaller number is 11 and the larger number is 28.
Explanation:Let's assume the smaller number is 'x'.
The larger number is 17 more than the smaller number, so the larger number can be represented as 'x + 17'.
The sum of the two numbers is 39, so we can set up the equation: x + (x + 17) = 39.
By simplifying the equation, we get 2x + 17 = 39.
Subtracting 17 from both sides gives us 2x = 22.
Dividing both sides by 2 gives us x = 11.
So, the smaller number is 11 and the larger number is 11 + 17 = 28.
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