Given: ABCD is a trapezoid, AB=CD, MN is a midsegment, MN=30, BC=17, AB=26 Find: m∠A, m∠B, m∠C, and m∠D
Answers
Answer:
m∠A=m∠D=60°, m∠B=m∠C=120°
Step-by-step explanation:
Consider isosceles trapezoid ABCD with midsegment MN. Draw two trapezoid heights BF and CE. Then quadrilateral FBCE is rectangle and EF=BC=17 units.
By the trapezoid midsegment theorem,
[tex]MN=\dfrac{AD+BC}{2},\\ \\30=\dfrac{AD+17}{2},\\ \\60=AD+17,\\ \\AD=60-17=43\ units.[/tex]
Segments FA and ED are equal to [tex]\dfrac{43-17}{2}=13\ units.[/tex]
In right triangle ABF, the hypotenuse AB is twice greater than the leg FA, then m∠FBA=30°.
m∠B=m∠FBA+m∠CBF=30°+90°=120°.
In isosceles trapezoid
m∠B=m∠C=120°,
m∠A=m∠D and m∠A=180°-m∠B=180°-120°=60°=m∠D.
In a trapezoid with equal bases and a midsegment, the angle measures of the trapezoid can be determined using the properties of the figure. In this case, the angle measures are 90 degrees for each angle.
Explanation:In a trapezoid ABCD, the midsegment MN is parallel to the bases AB and CD, and its length is equal to the average of the lengths of the bases. Given that AB = 26, CD = 26, and MN = 30, we can set up the equation: MN = (AB + CD) / 2. Substituting the given values, we get 30 = (26 + 26) / 2. Solving for the angle measures, we can use the fact that the opposite angles in a trapezoid are congruent. So, m∠A = m∠C and m∠B = m∠D. Since the sum of the interior angles of a trapezoid is always 360 degrees, we can use the equation: m∠A + m∠B + m∠C + m∠D = 360. Substituting the angle measures we found, we get 2(m∠A) + 2(m∠B) = 360. Solving for the angle measures, we get m∠A = m∠C = 90 degrees and m∠B = m∠D = 90 degrees.
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Related Questions
DONT KEEP SCROLLING PLEASE
Please I don’t understand 50 POINTS BRAINLIEST
Answers
Answer:why didn’t you want me to scroll down ? Can you answer my question
Step-by-step explanation:
1)Not necessarily a parallelogram
2)parallelogram
3)parallelogram
4)parallelogram
How determine if a quadrilateral is a parallelogramTo classify a shape as a parallelogram, the following four conditions must be satisfied
1. Opposite sides are equal in length.
2. Opposite angles are equal.
3. Consecutive angles are supplementary
4. Diagonals bisect each other.
Each of these conditions contributes to the definition of a parallelogram, and all of them must be satisfied for a shape to be considered a parallelogram.
From the figures
1) Not necessarily a parallelogram
The opposite sides are not equal.
GH is congruent to Gl and HJ is congruent to IJ. These are adjacent sides instead of opposite sides equality.
2) Given
RS is parallel to TU
SU is parallel to R(Converse of the Opposite Sides Are Congruent (OSAC) Theorem)
Since the both pairs of opposite sides of the quadrilateral are congruent, then the quadrilateral is a parallelogram.
3) Given PQRS
PQ||RS(given)
PR||QS(Converse of the Opposite Sides Are Congruent (OSAC) Theorem)
Since the both pairs of opposite sides of the quadrilateral are congruent, then the quadrilateral is a parallelogram.
4) <ABC ≅ DCB(alternate angles, AB||CD BC is transversal)
<ACB ≅ DBC(alternate angles,AC||BD,BC is transversal)
Therefore
Opposite angles are equal.
Pairs of opposite sides are parallel.
Adjacent angles are supplementary.
so, the quadrilateral is a parallelogram.
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Someone help me with this question ASAP and show work please and thank you
Answers
Answer:
g(f(x)) = x
Step-by-step explanation:
You are given f(x) = -4x - 1 and g(x) = [tex]\frac{x+1}{-4}[/tex]. Keep in mind that f(x) or g(x) is the same as a y = equation, but two separate equations.
You are trying to find g(f(x)), which means that you will use f(x) and substitute this value into the x value in the equation of g(x).
It will look like: g(-4x - 1) = [tex]\frac{x+1}{-4}[/tex]
[tex]\frac{(-4x-1)+1}{-4}[/tex]
Now evaluate the expression to solve the problem. Start by combining like terms.
[tex]\frac{(-4x)}{-4}[/tex]
You are left with -4x/-4. We can simplify this even further by dividing both sides of the fraction by -4/-4. The -4's cancel out and become 1's, so you are left with:
[tex]x[/tex]
Answer:
Step-by-step explanation:
g(f(x)) means that wherever you see an x in g(x) you put f(x) in it's place. Read that sentence a couple of times until it makes sense.
g(x) = (x + 1)/-4
g(f(x)) = (f(x) + 1) / - 4 Now wherever you see f(x), put in -4x - 1
g(f(x)) = [(-4x - 1) + 1] / - 4 Remove ( )
g(f(x)) = [-4x - 1 + 1 ] / - 4
g(f(x)) = [-4x] / - 4 Do the division
g(f(x)) = x
Neat problem. thanks for posting.
3. The population of Detroit, MI was 673,104 in 2018. The population of the United States was about 325.7 million in 2017 (a) Write each population in scientific notation. (2 points) (b) About how many times larger was the population of the United States than the population of Detroit, MI? Show your work
Answers
Answer:
a) 6.73104 x 10⁵
b) about 480 times larger
Step-by-step explanation:
a) 673,104 people in scientific notation is 6.73104 x 10⁵
b)325.7 million is the same as 325700000 = 3.257 x 10⁸
so (3.257 x 10⁸) divided by (6.73104 x 10⁵) ≈ 0.48 x 10³
480 times larger
You invest 23,400 annual interest rate of 4% compounded annually for seven years what is the balance of the account at the end of that time
Answers
Answer: 30792.80
=====================================
Work Shown:
We deposit P = 23400 dollars for t = 7 years, which is compounded n = 1 times per year at an interest rate of r = 4% = 0.04 (we'll use the decimal form of the interest rate)
So this means...
A = P*(1+r/n)^(n*t)
A = 23400*(1+0.04/1)^(1*7)
A = 23400*(1+0.04)^(7)
A = 23400*(1.04)^(7)
A = 23400*1.31593177923584
A = 30792.8036341187
A = 30792.80
What is the center of the circle given by the equation by the equation (x-3)2 + (y-9)2=16
Answers
Answer:
centre = (3, 9 )
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 3)² + (y - 9)² = 16 is in this form
with centre = (3, 9) and r = [tex]\sqrt{16}[/tex] = 4
Answer:
(3,9) -apex!!!!!!
Step-by-step explanation:
Write the equation of a line with the slope of 2, which contains the point (4,-8).
Answers
Answer:
y = 2x-16
Step-by-step explanation:
To find a line when we know the slope and a point, we can use the point slope formula for a line
y-y1 = m(x-x1)
where the point is (x1,y1) and the slope is m. Substituting the known information in.
y--8 = 2 (x-4)
y+8 = 2(x-4)
We can manipulate this into slope intercept form by distributing the 2
y+8 = 2x-8
and subtracting 8 from each side
y+8-8 = 2x-8-8
y = 2x-16
If the number 38,469 is rounded to the nearest thousand, how many zeros does the rounded number have?
Answers
This rounded number has three zeros. The number 38,469 rounded to the nearest thousand is 38,000.
To find the number of zeros in 38,469 when rounded to the nearest thousand, we first need to round the number appropriately. We look at the hundreds place (the third digit from the right), which is '4'. Since 4 is less than 5, we do not round up.
Identify the digit in the hundreds place of 38,469 (which is '4').Since 4 is less than 5, do not round up.Change all the digits after the thousands place to zero.The rounded number is 38,000, which contains three zeros.There are 1600 kilocalories in 5 cups of dog food that mike gives his adult dog. Mike gives his puppy 2 cups of the same dog food. How many kilocalories are there in this 2-cup serving?
Answers
Answer:
640 kilocalories are there in this 2-cup serving.
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
As per the given statement: There are 1600 kilocalories in 5 cups of dog food that mike gives his adult dog. Mike gives his puppy 2 cups of the same dog food.
Let x kilocalories are there in 2-cup serving.
then, by definition of proportion;
[tex]\frac{1600}{5} =\frac{x}{2}[/tex]
Multiply both sides by 2 we get;
[tex]x = \frac{1600}{5} \times 2[/tex]
Simplify:
[tex]x = 320 \times 2 = 640 kilocalories[/tex]
Therefore, 640 kilocalories are there in this 2-cup serving.
A special paint requires a mixture of paints: A, B and C. The ratio is: 60% A, 25% B, and 15% C. If you want 20 gallons of the special color, how many gallons of paint A will you need?
Answers
[tex]20 \times .6 = 12[/tex]
12 gallons
You would need 12 gallons of paint A. You can find this answer by finding what 60% of 20 is, and do that by multiplying 20 • (0.6). This is what gives you 12. Following that, you’ll need 3 gallons of C, and 5 gallons of B.
What is the slope for (-3,14)(5,10)
Answers
Answer:
slope = -1/2
Step-by-step explanation:
The formula for slope is (y2-y1)/ (x2-x1)
m = (10-14)/(5--3)
= (-4)/(5+3)
= -4/8
= -1/2
find the exact value of x
Answers
ΔABC and ΔCBD are similar. Therefore we have the proportion:
[tex]\dfrac{AB}{BC}=\dfrac{BC}{BD}\\\\AB=6;\ BC=x;\ BD=2[/tex]
Substitute:
[tex]\dfrac{6}{x}=\dfrac{x}{2}[/tex] cross multiply
[tex](x)(x)=(6)(2)\\\\x^2=12\to x=\sqrt{12}\\\\x=\sqrt{4\cdot3}\\\\x=\sqrt4\cdot\sqrt3\\\\\boxed{x=2\sqrt3}[/tex]
In the first week students at RSM solved 25 percent of their monthly quota of problems. In the second week, they solved 110 percent of the number of problems solved in the first week. In the third week they solved 60 percent of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. How many problems did students solve in the four-week month?
Answers
Answer:
The number of problems solved = 2000
Step-by-step explanation:
Let us assume the monthly quota of problems be x
number of problem solved in first week = 25 % of x =[tex]0.25x[/tex]
number of problems solved in 2nd week = 110% of (problems solved in 1st week)
= [tex]1.10 (0.25x)[/tex]
=[tex]0.275x[/tex]
number of problem solved 3rd week= 60% of ( problems solved in 1st and 2nd week)
= [tex]0.60(0.25x+0.275x)[/tex]
=[tex]0.60(0.525x)[/tex]
=[tex]0.315x[/tex]
number of problem solved in 4th week = [tex]320[/tex]
now we have
number of problems solved in ll 4 weeks = x
[tex]0.25x +0.275x+0.315x+320=x[/tex]
[tex]0.84x+320=x[/tex]
[tex]320=x-0.84x[/tex]
[tex]320=0.16 x[/tex]
[tex]x=\frac{320}{0.16}[/tex]
[tex]x=2000[/tex]
Hence the number of problems solved = 2000
Final answer:
In the third week they solved 60% of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. The total number of problems solved in the four-week month is 492.
Explanation:
To solve this problem, we need to find the number of problems solved in each week and then add them together to get the total number of problems solved in the four-week month.
In the first week, the students solved 25% of their monthly quota of problems. Let's say their monthly quota is 'x'. So, they solved 0.25x problems in the first week.
In the second week, they solved 110% of the number of problems solved in the first week. That means they solved 1.1 * 0.25x = 0.275x problems in the second week.
In the third week, they solved 60% of the number of problems they had solved in the first two weeks. So, they solved 0.6 * (0.25x + 0.275x) = 0.345x problems in the third week.
In the fourth week, they solved the remaining 320 problems. This means the total number of problems solved in the first three weeks is 0.345x, and we can set up the following equation to find x: 0.345x + 320 = x.
Solving this equation, we get x = 491.429. Since we can't have a fractional number of problems, we can round x up to 492. Therefore, the students solved a total of 492 problems in the four-week month.
please help me with these im stuck
Answers
Answer:
Is it 15?
Step-by-step explanation:
Since it is asking for the sites, aren't you just supposed to count the dots...?
Answer:
15
Step-by-step explanation:
The question is asking how many sites are shown in this data set. So, on the side of the rectangle, it says "Number of Sites" & the dots represent the number of sites. So, there are 15.
Sorry if I'm incorrect...
write 423% as a decimal
Answers
[tex]p\%=\dfrac{p}{100}\\\\423\%=\dfrac{423}{100}=4\dfrac{23}{100}=4.23\\\\\boxed{423\%=4.23}[/tex]
Answer:
4.23
Step-by-step explanation:
423%
Percent means out of 100
423/100
Pt the decimal 2 places to the left of the 3
4.23
F(x)=x^3+4x^2+x-6
What are the real zeros
Answers
To find the real zeros of the given function, set it equal to zero and solve the resulting equation.
Explanation:The real zeros of the function F(x) = x^3 + 4x^2 + x - 6 are the values of x that make the function equal to zero.
Step 1: Set the function equal to zero: x^3 + 4x^2 + x - 6 = 0.Step 2: Solve the equation by factoring, synthetic division, or using the Rational Root Theorem.Step 3: The real zeros of the function F(x) = x^3 + 4x^2 + x - 6 are the solutions obtained from Step 2.A petri dish has 246 bacteria. It grows at a rate of 7% per month. How many bacteria will there be in 5 months? Round your answer to the nearest whole number. Question 20 options:
A.253
B.345
C. 171
D.281
Answers
Answer:
B 345
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
What is $4.99 x 0.5lb + $6.99 x 0.25lb?
Answers
Answer:
$3.77
Step-by-step explanation:
$4.99 x 0.5lb + $6.99 x 0.25lb?
First we multiply
2.495+1.725
Then we add
3.77
We will spend $3.77
What is the slope of the line that passes through (5,4) and (7,10)?
Answers
(10-4)/(7-5)=6/2=3.
The slope of the line that passes through those two points is 3.
The slope of the line that passes through (5,4) and (7,10) is 3.
Given that,
It passes through (5,4) and (7,10).We need to find out the slope of the line.Based on the above information, the slope of the line is:
[tex]= \frac{y_2 - y_1}{x_2 - x_1} \\\\= \frac{10-7}{5-4} \\\\= \frac{3}{1}\\[/tex]
= 3
Therefore we can conclude that the slope of the line that passes through (5,4) and (7,10) is 3.
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(02.06) The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 42 hours. 1 day 24 hours 12 hours 12 hours (3 points) 1 and 1 over 4. days 1 and 1 over 2. days 1 and 3 over 4. days 2 days
Answers
Answer:
1 and 3/4 days are equal to 42 hours
Step-by-step explanation:
42 hours = (42 hours) (1 day / 24 hours)
42 hours = 42/24 days
Simplyfing the fraction: Dividing the numerator and denominator by 6:
42 hours = (42/6) / (24/6) days
42 hours = 7/4 days
42 hours = (4+3)/4 days
42 hours = (4/4+3/4) days
42 hours = 1 3/4 days
To determine how many days are equal to 42 hours, you divide 42 by 24 which results in 1.75. Therefore, 42 hours is equivalent to 1 and 3/4 days.
Explanation:In this mathematics problem, we are asked to convert 42 hours into a measurement of days. To begin with, we know that 1 day equals 24 hours. Therefore, to convert 42 hours into days we will divide 42 by 24.
The result of this division is 1.75. In terms of a day fraction, this value represents 1 and 3/4 days. As such, we can say that 42 hours is equivalent to 1 and 3/4 days.
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during a hoagie sale fundraiser a ski club sold 42 Italian hoagies and 53 roasted beef Hoagies what is the ratio of Italian hoagie sold to the total number of Hoagies sold
Answers
Answer:
42:53 would be the answer
Step-by-step explanation:
In a ski club fundraiser, the ratio of Italian hoagies sold to the total number of hoagies sold, when the numbers of Italian and roast beef hoagies are 42 and 53 respectively, is 42:95.
Explanation:The student is asking for the ratio of Italian hoagies sold to the total number of hoagies sold at a ski club fundraiser. To calculate this ratio, one must add the number of Italian hoagies to the number of roast beef hoagies to determine the total hoagies sold. In this case, 42 Italian hoagies were sold, and 53 roast beef hoagies were sold, yielding a total of 95 hoagies sold. Thus, the ratio of Italian hoagies sold to total hoagies sold is 42:95. In ratio terms, this expresses that for every 42 Italian hoagies sold, there were 95 total hoagies sold.
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What is the value of 3b when b = 18?
Answers
Answer:
54
Step-by-step explanation:
to evaluate substitute b = 18 into 3b
3b = 3 × 18 = 54
[ Answer ]
54
[ Explanation ]
B = 18
Substitue B for 18
3 * 18
= 54
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Oceanside bike rental shop charge 15 dollars plus 8 dollars an hours for renting a bike. Jason paid 79 dollars to rent a bike. How many hours did pay to have the bike checked checked out?
Answers
Answer:
8 hours
Step-by-step explanation:
Firstly, the cost for renting the bike needs to be subtracted from the total amount:
79 - 15 = 64
Now this can be divided by 8 to find the hours:
64 ÷ 8 = 8
So he paid for 8 hours.
Hope this helps!
The number p and −1.2 are additive inverses. Drag and drop −1.2 and p to their correct positions on the number line. Drag and drop the label “Sum” to the sum of −1.2 and p
Answers
Answer:
p=1.2
Step-by-step explanation:
Additive inverse of any number means a number which can be added to the original number to get
Two numbers are said to be additive inverse of each other if sum of both numbers is 0. For example if 5 is the given number then -5 will be it's additive inverse. So to find additive inverse, we basically change the sign of number.
Given number p is additive inverse off -1.2 so p must be 1.2.
Sum will obviously be 0.
So to graph them on number line, we make a point at -1.2, 1.2 and at 0 for their sum.
Answer:P=1.2
Step-by-step explanation:
problem 1: two numbers add together equals 47. their difference is 13. write and solve a system to find the two numbers
problem 2: the sum of two numbers is 54 and their difference is 12. write and solve a system to find the two numbers
Answers
Answer:
34+13= 47
Step-by-step explanation:
47-34=13
In a certain year, brand A of heart-rate watch cost $39.99 and brand B cost $59.99. A nonprofit community health organization purchased 34 heart-rate watches for use at a wellness center. If the organization spent $1619.66 for the watches, how many of each type did they purchase?
Answers
Answer:
Brand A = 21 heart-rate watches.
Brand B = 13 heart-rate watches.
Step-by-step explanation:
Let A be the number of Brand A heart watches and B be the number of Brand B heart watches.
We have been given that a nonprofit community health organization purchased 34 heart-rate watches for use at a wellness center.
We can represent this information in an equation as:
[tex]A+B=34...(1)[/tex]
We have been given that in a certain year, brand A of heart-rate watch cost $39.99 and brand B cost $59.99 and the organization spent $1619.66 for the watches.
We can represent this information in an equation as:
[tex]39.99*A+59.99*B=1619.66...(2)[/tex]
We will use substitution method to solve our system of equations.
From equation (1) we will get,
[tex]A=34-B[/tex]
Substituting [tex]A=34-B[/tex] in equation(2) we will get,
[tex]39.99*(34-B)+59.99*B=1619.66[/tex]
[tex]1359.66-39.99*B+59.99*B=1619.66[/tex]
[tex]-39.99*B+59.99*B=1619.66-1359.66[/tex]
[tex]20*B=260[/tex]
[tex]B=\frac{260}{20}[/tex]
[tex]B=13[/tex]
Therefore, the organisation purchased 13 heart-rate watches of brand B.
Now let us substitute B=13 in equation (1).
[tex]A+13=34[/tex]
[tex]A+13-13=34-13[/tex]
[tex]A=21[/tex]
Therefore, the organisation purchased 21 heart-rate watches of brand A.
What is the slope of this line
Answers
help please. its math. please explain your answer
Answers
Answer:
Step-by-step explanation: 20 percent
:)
What are the zeros of the polynomial function f(x)=x^3+2x^2-24x?
Answers
Immediately, we can factor an x out of each term to simplify the polynomial.
x(x^2 + 2x - 24)
In doing this, we know the first zero will be x = 0.
Using the AC method, we can find the next two zeros.
x(x - 4)(x + 6)
The zeros, or x-intercepts of the polynomial, are 0, 4, and -6.The zeros of the polynomial function f(x) = x^3 + 2x^2 -24x are x = -6, 0, and 4.
Explanation:The question requires finding the zeros of the polynomial function f(x) = x^3 + 2x^2 -24x. The zeros of this function can be found by setting the function equal to zero and solving for x. So, we have 0 = x^3 + 2x^2 - 24x. All terms have an 'x', so we can factor out 'x' to give: 0 = x (x^2 + 2x - 24). The quadratic formula (which is used for expressions of the form ax^2 + bx + c = 0) to solve x^2 + 2x - 24 = 0, we get x = -6 and x = 4. Therefore, the zeros of the function are x = -6, 0, and 4.
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In math, how do you solve 2h<200?
Answers
Answer:
h < 100
Step-by-step explanation:
isolate h by dividing both sides by 2
h < 100
If (6 to the 0 power ) to x power = 1, what are the possible values of x? Explain answer
Answers
The value of x can be any real number because raising 1 to any exponent will always result in 1.
The question needs us to solve for x in the equation [tex](6 to the 0 power)^x[/tex]= 1. We know that any non-zero number raised to the 0 power is 1 (e.g.,[tex]10^0[/tex] = 1). Thus, 6 to the 0 power is 1 regardless of the value of 6. From this, we have[tex]1^x[/tex], which is still 1 for any value of x because 1 raised to any power is always 1. Hence, the equation remains true for any real number value of x.