The measure of base angle is [tex]$$\boxed{{{70}^ \circ }} if the vertex angle is {40^ \circ }$$[/tex] .
Further explanation:
Given:
Vertex angle of the isosceles triangle is [tex]{40^ \circ }[/tex] .
Explanation:
The triangle three sided close Figure.
There are three type of triangles.
1. Equilateral triangle
2. Isosceles triangle
3. Scalene triangle
Equilateral triangle has all sides equal and all the angles are equal.
Isosceles triangle has 2 sides equal to each other and the two base angles are equal to each other.
Scalene triangle has all sides unequal and the angles are also not equal to each other.
The sum of all the angles of the triangle is [tex]{180^ \circ }[/tex].
Consider the base angle as y.
The value of y can be obtained as follows,
[tex]\begin{aligned}y+y+40&=180\\2y+40&=180\\2y&=180-40\\2y&=140\\y&=\frac{{140}}{2}\\y&={70^ \circ }\\\end{aligned}[/tex]
The measure of base angle is [tex]$$\boxed{{{70}^ \circ}} if the vertex angle is {40^ \circ}$$[/tex].
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: vertex angle, isosceles triangle, base angle, perpendicular, altitudes, point, triangle, circumcenter, bisectors, perpendicular bisectors, angles, angle bisectors, median, intersection, incenter, right angle triangle, equilateral triangle, obtuse, acute.
A student solved the problem below by first dividing 20 by 10. What mistake did the student make? A baseball team has won 20 games and lost 10 games. What percent of the games did the team win?
Answer:
Step-by-step explanation: The student divided the number of wins by the number of losses.
The student should have divided the number of wins by the total number of games.
The student should have first added 20 and 10 to find that there were a total of 30 games.
Answer:
SAMPLE RESPONSE: The student divided the number of wins by the number of losses, instead of dividing the number of wins by the total number of games. The student should have divided 20 by 30.
Step-by-step explanation:
other answer: The student divided the number of wins by the number of losses.
The student should have divided the number of wins by the total number of games.
The student should have first added 20 and 10 to find that there were a total of 30 games.
Maricella plots two ordered pairs on the grid below.
Answer:
B. [tex](0,-10)[/tex]
Step-by-step explanation:
We have been given an image of a line segment on coordinate plane. We are asked to find the y-intercept of line, is the line segment is extended to cross both the axes.
We will find the equation of line in slope-intercept form: [tex]y=mx+b[/tex], where,
m = Slope of line,
b = The y-intercept.
We will find slope of our given line using the coordinates of our given points (6,2) and (8,6).
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{6-2}{8-6}[/tex]
[tex]m=\frac{4}{2}[/tex]
[tex]m=2[/tex]
Now, we will substitute [tex]m=2[/tex] and coordinates of point (8,6) in slope-intercept form of equation.
[tex]6=2*8+b[/tex]
[tex]6=16+b[/tex]
[tex]6-16=16-16+b[/tex]
[tex]-10=b[/tex]
Since y-intercept of our given line is [tex]-10[/tex], which is at [tex]x=0[/tex], therefore, option B is the correct choice.
Maricella plots two ordered pairs on the grid below.
Answer: (0,-10)
Step-by-step explanation:
The equation of a line (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
From the given graph , the line is passing through (6,2) and (8,6) is given by :_
[tex](y-6)=\dfrac{6-2}{8-6}(x-8)\\\\\Rightarrow\ y-6=\dfrca{4}{2}(x-8)\\\\\Rightarrow\ y-6=2(x-8)\\\\\Rightarrow\ y=2(x-8)+6[/tex]
To find the y intercept put x =0 , we get
[tex]y=2(0-8)+6=-16+6=-10[/tex]
Hence, the y-intercept of the graph : (0,-10)
Write the decimal 2.06 as a mixed number.
In how many ways can the letters BEACH be rearranged
I really need explanation for this Mean Value Theorem. Thanks
A line passes through the point (-8,5) and has a slope of 3/2
Write an equation in slope-intercept form for this line.
To write the equation for this line in slope-intercept form, substitute the given values into the formula and solve for the y-intercept.
Explanation:To write an equation in slope-intercept form, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept.
Given that the line passes through the point (-8,5) and has a slope of 3/2, we can substitute these values into the equation.
So, the equation of the line in slope-intercept form is y = (3/2)x + b. To find the y-intercept, we substitute the coordinates of the point (-8,5) into the equation and solve for b.
5 = (3/2)(-8) + b
5 = -12 + b
b = 17
Therefore, the equation in slope-intercept form is y = (3/2)x + 17.
Convert the following temperatures from K to °C.
100 K = °C
273 K = °C
6 K = °C
143°C = K
573°C = K
we know that
The formula to convert K to C is equal to
[tex]\° C =\°K - 273.15\°[/tex] --------> equation [tex]1[/tex]
and
The formula to convert C to K is equal to
[tex]\° K =\°C +273.15\°[/tex] --------> equation [tex]2[/tex]
case a) [tex]100\° K[/tex]
convert to C
substitute in the equation [tex]1[/tex]
[tex]\° C =100\°- 273.15\°=-173.15\°[/tex]
therefore
the answer Part a) is
[tex]\° C =-173.15\°[/tex]
case b) [tex]273\° K[/tex]
convert to C
substitute in the equation [tex]1[/tex]
[tex]\° C =273\°- 273.15\°=-0.15\°[/tex]
therefore
the answer Part b) is
[tex]\° C =-0.15\°[/tex]
case c) [tex]6\° K[/tex]
convert to C
substitute in the equation [tex]1[/tex]
[tex]\° C =6\°- 273.15\°=-267.15\°[/tex]
therefore
the answer Part c) is
[tex]\° C =-267.15\°[/tex]
case d) [tex]143\° C[/tex]
convert to K
substitute in the equation [tex]2[/tex]
[tex]\° K =143\°+ 273.15\°=416.15\°[/tex]
therefore
the answer Part d) is
[tex]\° K =416.15\°[/tex]
case e) [tex]573\° C[/tex]
convert to K
substitute in the equation [tex]2[/tex]
[tex]\° K =573\°+ 273.15\°=846.15\°[/tex]
therefore
the answer Part e) is
[tex]\° K =846.15\°[/tex]
how do you find all possible combinations to pay for 65 cent lemonade. you have 3 quarters, 5 dimes, and 5 nickels
153 inches to 19 feet
The Soup Shack usually makes tomato soup with 9 tomatoes for every 12 cups of soup. Today, they made 8 cups of soup with 6 tomatoes. How does today's soup compare to the usual recipe?
Answer: We compare today's soup to the usual recipe by using "Unitary Method".
Step-by-step explanation:
Since we have given that
The Soup Shack makes tomato soup with 9 tomatoes for every 12 cups of soup.
For every 12 cups of soup , 9 tomatoes is needed
For every 1 cup of soup , the number of tomato is needed is given by
[tex]\frac{9}{12}=\frac{3}{4}[/tex]
Today, they made 8 cups of soup with 6 tomatoes ,
For 8 cups, 6 tomatoes are used .
For 1 cup, number of tomato is used is given by
[tex]\frac{6}{8}=\frac{3}{4}[/tex]
So, we can see that both the soup has same quantity .
∴ We compare today's soup to the usual recipe by using "Unitary Method".
As part of a traffic safety campaign a speed detector was used to record speed in the entrance driveway to the Jefferson High School parking lot. The box and whisker plot shows the results.
HELP ME PLEASE ASAP
If a flower is 6.5 cm wide, its width expressed in millimeters is x mm, where x is
A unit of measure is the actual unit in which the associated values are measured. If a flower is 6.5 cm wide, its width expressed in millimeters is 65 mm,
What is Unit of Measurement?A Unit of measure is the actual unit in which the associated values are measured.
Unit of Measurement is used as a standard for measurement of the same kind of quantity. The weight is measured in kilograms, grams. The kilogram is unit of mass. litres is the unit of measuring liquids and length is measured in different units, feet, inches, meters, kilometers, centimeters.
We know that 1 centimeter = 10 milli meters.
So if a flower is 6.5 cm wide, its width expressed in millimeters is x mm
We need to find the value of x.
6.5 cm = 6.5×10
=65
So 6.5 cm in millimeters is 65 mm.
Hence if a flower is 6.5 cm wide, its width expressed in millimeters is 65mm.
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A chicken soup recipe calls for 15 cups of chicken stock. How much is this in quarts?
Joaquin has $1,300 in the bank and has investments worth $4,000. He also has $7,000 worth of credit card debt. What is Joaquin's net worth? Select the best answer from the choices provided. $1,300 -$7,000 $5,300 -$1,700
Action movies make up 85% of Devon’s movie collection. If he has 20 movies, how many action movies are in Devon’s collection ? Explain your reasoning to classmate
You make $0.75 for every newspaper you sell. How many newspapers do you have to sell to buy soccer cleats? (soccer cleats are $36.00)
Write an equation then solve
Alex wants to start an IRA that will have $1,250,675 in it when he retires in 30 years. How much should he invest semiannually in his IRA to do this if the interest is 4.5% compounded semiannually? Assume an Annuity Due. Round to the nearest cent.
Answer:
$9828.44
Step-by-step explanation:
The semi annual payment is such that the future value of the annuity due is equal to the desired amount when he retires.
The formula to calculate future value of an annuity due periodic payment of M for time period T for given periodic return r,
A=[tex]\frac{M(1+r)^{T+1}-(1+r)}{r}[/tex]
in this question there are 30*2= 60 payments and the semi annual rate= 4.5/2= 2.25%
putting values we get
1250675= [tex]\frac{M(1+2.25%)^{60+1}-(1+2.25%)}{2.25%}[/tex]
on solving we get M= $9828.44
Alex needs to invest $9828.44 semiannually in his IRA
The school is 3.65 miles from Tonya’s house and 1.28 miles from Jamall‘s house. How much farther from school is Tonyas house than Jamall‘s house? Explain how you can use a quick picture to solve the problem.
The answer is 2.37 miles. The possible explanation for this is I can illustrate 3.65 using 3 squares for ones, 6 lines for tenths, and 5 circles for hundredths. I would now then reform 1 tenth as 10 hundredths. Then, I would subtract 8 hundredths from 15 hundredths. Then, I would take away 2 tenths from 5 tenths. Last, I would deduct 1 from 3.
Which of the following best describes the square root property of equality
if they have two quantities that are equal to the same things, then they would be equal to each others.
Marianna martinez sells copy paper to local schools. SHE EARNS A 13 PERCENT STRAIGHT COMMISSION ON ALL SALES. IN NOVEMBER HER SALES TOTALED $28,540. WHAT WAS HER COMMISSION?
What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?
y = x + 4
y = x +
y = –5x + 4
y = –5x +
we know that
If two lines are parallel, then their slopes are the same
Step 1
Find the slope of the given line
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
in this problem we have
[tex](x1,y1)=(-5,-4)\\(x2,y2)=(0,-3)[/tex]
substitute in the formula
[tex]m=\frac{(-3+4)}{(0+5)}[/tex]
[tex]m=\frac{(1)}{(5)}[/tex]
[tex]m=\frac{1}{5}[/tex]
Step 2
Find the equation of the line
we know that
the equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{1}{5}[/tex]
[tex](x1,y1)=(-2,2)[/tex]
substitute
[tex]y-2=\frac{1}{5}(x+2)[/tex]
[tex]y=\frac{1}{5}x+\frac{2}{5}+2[/tex]
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
therefore
the answer is
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
A rectangular box with a volume of 784 ft3 is to be constructed with a square base and top. the cost per square foot for the bottom is 15¢, for the top is 10¢, and for the sides is 1.5¢. what dimensions will minimize the cost
Find the probability of getting exactly 6 girls in 8 births.
The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].
Further explanation:
Concept used:
The probability of an event [tex]E[/tex] is calculated as follows:
[tex]\boxed{P(E)=\dfrac{n(E)}{n(S)}}[/tex]
Here, [tex]n(E)[/tex] is the number of favorable outcomes in an event [tex]E[/tex] and [tex]n(S)[/tex] is the number of element in sample space [tex]S[/tex].
The probability of exactly [tex]r[/tex] success in [tex]n[/tex] trial is expressed as follows:
[tex]\boxed{P(F)=^{n}C_{r}p^{r}q^{n-r}}[/tex]
Here, [tex]r[/tex] is the probability of success in an event and [tex]q[/tex] is the probability of failure.
Calculation:
Consider [tex]A[/tex] as an event of having a girl in first birth and [tex]P(A)[/tex] as the probability of event [tex]A[/tex].
The probability of having a girl is [tex]P(A)=\frac{1}{2}[/tex].
Assume that [tex]A'[/tex] is the complement event of an event [tex]A[/tex] and [tex]P(A')[/tex] is the probability of complementary event [tex]A'[/tex].
The event is the event of not having a girl in the first birth.
The probability of event [tex]A'[/tex] is calculated as follows:
[tex]\boxed{P(A')=1-P(A)}[/tex] …… (1)
Substitute [tex]P(A)=\frac{1}{2}[/tex] in the equation (1) to obtain the probability of event [tex]A'[/tex].
[tex]\begin{aligned}P(A')&=1-\dfrac{1}{2}\\&=\dfrac{1}{2}\end{aligned}[/tex]
The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is calculated as follows:
[tex]\begin{aligned}P(F&)=^{8}C_{6}\left(\dfrac{1}{2}\right)^{6}\left(\dfrac{1}{2}\right)^{8-6}\\&=\dfrac{8!}{6!\cdot 2!}\cdot (0.5)^{6}\cdot (0.5)^{2}\\&=28(0.5)^{8}\\&=0.10937\end{aligned}[/tex]
Thus, the probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].
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Answer details:
Grade: Senior school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, exact event, sample space, number of element, complement event, success, failure, favorable, trial, P(E)=n(E)/n(S), P(A')=1-P(A).
Final answer:
To find the probability of getting exactly 6 girls in 8 births, we use the binomial probability formula. In this case, the probability is approximately 0.01.
Explanation:
To find the probability of getting exactly 6 girls in 8 births, we can use the binomial probability formula:
P(x = 6) = C(n, x) * pˣ * (1-p)(n-x)
Where:
C(n, x) is the binomial coefficient, which represents the number of ways to choose x objects from a set of n objects.p is the probability of success (in this case, the probability of having a girl) in a single trial. n is the number of trials (in this case, the number of births).x is the desired number of successes (in this case, the desired number of girls).In this particular case, P(x = 6) = C(8, 6) * (0.5)⁶ * (0.5)(8-6) = 28 * 0.015625 * 0.015625 = 0.009765625, or approximately 0.01.
Solve the exponential equation. 2x = 1/2
Options: -1
-1/2
1
The exponential equation, 2ˣ = 1/2, has a value of -1.
What is an exponential equation?Exponential equations are equations in which variables occur as exponents.
Given is an exponential equation, 2ˣ = 1/2, we need to solve it,
2ˣ = 1/2
Taking ㏒ both the side,
㏒ 2ˣ = ㏒ 1/2
x ㏒ 2 = ㏒ 0.5
x = -0.301029996 / 0.301029996
x = -1
Hence, the exponential equation, 2ˣ = 1/2, has a value of -1.
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Find the exact circumference of a circle with an area equal to 36 sq. in.
1) 12
2) 18
3) 324
Answer:
The answer would be option 1) 12
Answer:
The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].
Step-by-step explanation:
The area of a circle when we know the circumference is
[tex]A=\frac{C^2}{4\pi }[/tex]
We know the area [tex]A=36 \:{in^2}[/tex], we plug this value into the above equation and we solve for C the circumference.
[tex]36=\frac{C^2}{4\pi }\\\frac{C^2}{4\pi }=36\\\frac{C^2\cdot \:4\pi }{4\pi }=36\cdot \:4\pi \\\\C^2=144\pi \\C=\sqrt{144\pi }\\C=12\sqrt{\pi }[/tex]
The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].
What is the percent increase from 250 to 900?
1. Write the percent change formula for an increase.
Percent Increase =
Amount of Increase
Original Amount
2. Substitute the known quantities for the amount of the increase and the original amount.
Percent Increase =
900 − 250
250
3. Subtract.
Percent Increase =
650
250
4. Express the ratio as a percent:
%
Answer:
260 %
Step-by-step explanation:
1) Since, the percentage formula is,
[tex]\text{Percent Increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}[/tex]
2) Given,
Original amount = 250,
New amount = 900
So, the amount of increase = New amount - Original amount = 900 - 250 = 650
By substituting the values,
[tex]\text{Percentage increase}=\frac{650}{250}[/tex]
3) Now, for expressing the ratio into percentage we need to multiply by 100,
[tex]\frac{650}{250}\times 100=\frac{65000}{250}= 260\%[/tex]
A pail holds
4 1/4
gallons of water. How much is this in cups?
When more than one function has the same name they are called ________ functions?
If ying zyiyu covered the first 200 miles of a trip going at 50 mph and the last hundred miles going at 40 mph, what was his average speed for the entire trip? Teacher told me it is not 45
The average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex]
Average speed is the ratio of the total distance traveled by a body to the total time taken by the body to cover the total distance.
Here, ying zyiyu covered the first [tex]200\;\rm miles[/tex] of the trip at [tex]50\;\rm mph[/tex] so,
Total time taken by ying zyiyu to cover [tex]200\;\rm miles[/tex] is calculated as-
[tex]t_1=\dfrac{200}{50}\\t_1=4\;\rm hour[/tex]
Similarly, ying zyiyu covered the first [tex]100\;\rm miles[/tex] of the trip at [tex]40\;\rm mph[/tex] so,
Total time taken by ying zyiyu to cover [tex]100\;\rm miles[/tex] is calculated as-
[tex]t_2=\dfrac{100}{40}\\t_2=2.5\;\rm hour[/tex]
So, the total time taken by ying zyiyu to travel [tex]300\;\rm miles[/tex] is [tex]4+2.5=6.5\;\rm hours[/tex]
Now, the average spped is calculated as-
[tex]\rm{Average\;Speed}=\dfrac{Total\;Distance}{Total\;Time}\\\rm{Average\;Speed}=\dfrac{300}{6.5}\\\rm{Average\;Speed}=46.15\;\rm mph[/tex]
Hence, the average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex].
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