In the diagram of ABCD shown below, BA is drawn from vertex B to point A on DC, such that BC & BA.DAСa.In AABD, mZD = 30° and mZDAB = 120°. Find the measure of all angles.b.What kind of triangle is AABD? Explain.hat kind of triangle is ADBC? Explain.
Answers
We have that BC = BA and m
We will have that the angle DAB and BAC are supplementary, therefore:
DAB + BAC = 180°
And replecing the value of DAB, we will get:
120 + BAC = 180 => BAC = 60.
By theorem the angles that oppose equal sides are equal, therefore: ACB = 60.
From this, we will also get that ABC = 60.
And B = 90.
Triangle ABD will be a scalene triangle.
Triangle DBC will be a rectangle triangle.
Related Questions
A school assembly had 40 students in attendance, and 80% of them were first-graders. How many first-
graders were at the assembly?
Answers
Answer: 32 first graders were at the assembly
Step-by-step explanation:
80% of 40 can be written as 80% × 40
= 80/100 × 40
= 32
Thus, 80% of 40 is 32.
A local produce stand has eight pumpkins on display the diameters of the pumpkin in inches are given in the table
Answers
SOLUTION
We will be pairing the pumpkins as follows
AB, CD, EF and GH
For AB, we have
[tex]\begin{gathered} 16\frac{1}{2}\div5\frac{1}{2} \\ \frac{33}{2}\div\frac{11}{2} \\ \frac{33}{2}\times\frac{2}{11} \\ =\frac{33}{11} \\ =3 \end{gathered}[/tex]Hence B is 3 times larger than A
For C and D, we have
[tex]\begin{gathered} 41\frac{1}{4}\div8\frac{1}{4} \\ \frac{165}{4}\div\frac{33}{4} \\ \frac{165}{4}\times\frac{4}{33} \\ =\frac{165}{33} \\ =5 \end{gathered}[/tex]Hence D is 5 times larger than C
E and F, we have
[tex]\begin{gathered} 13\frac{3}{4}\div3 \\ \frac{55}{4}\div\frac{3}{1} \\ \frac{55}{4}\times\frac{1}{3} \\ =\frac{55}{12} \\ =4.5833333333 \\ =4.583 \end{gathered}[/tex]Hence E is 4.583 times larger than F
And the last G and H, we have
[tex]\begin{gathered} 22\frac{3}{4}\div10\frac{1}{2} \\ \frac{91}{4}\div\frac{21}{2} \\ \frac{91}{4}\times\frac{2}{21} \\ =\frac{91}{21\times2} \\ =\frac{91}{42} \\ =2.167 \end{gathered}[/tex]Hence G is 2.167 times larger than H
Which set of ordered pairs does not represent a function?
O {(6, 7), (-4,-5), (-1, 7), (-9, -7)}
O{(-6, 1), (-9, -6), (6, 7), (1, -8)}
O {(5,9), (7,2), (1,6), (-6,9)}
O {(-1, 1), (4, -6), (-3,0), (-3, 8)}
Answers
Answer:
it's 4
Step-by-step explanation:
#4 because we can see how x repeats its self 2 times such as (-3,0) and (-3,8)
Express the distance,d, from a point on the graph x+y=2 to the point (6,8) as a function of x
Answers
Answer:
[tex]d=\sqrt[]{2(x^2+36^{})}[/tex]Explanation:
Given the equation of the line as;
[tex]x+y=2[/tex]We can express y in terms of x by subtracting x from both sides of the equation;
[tex]y=-x+2[/tex]Let the point on the line be P(x, y)
We'll use the below distance formula to determine the distance between point P(x, y) to the given point (6, 8) as seen below;
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(6-x)^2+(8-y)^2} \\ d=\sqrt[]{(36-12x+x^2)+\lbrack8-(-x+2)\rbrack^2} \\ d=\sqrt[]{(36-12x+x^2)+(6+x)^2} \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{(36-12x+x^2)+(36+12x+x^2)} \\ d=\sqrt[]{72+2x^2} \\ d=\sqrt[]{2(x^2+36^{})} \end{gathered}[/tex]is the expression 15y a coefficient or a constant
ASAP
Answers
Answer: The expression is not a coefficient, so it is a constant.
Step-by-step explanation:
Answer:
Constants are the terms in an expression that includes only numbers, the value of which does not change. Coefficient of a variable is the number written along with the variable in the term. So the expression 15y is a coefficient.
what is one important difference between a normal distribution and a t distribution? group of answer choices the t distribution has heavier tails than a normal distribution. the normal distribution has heavier tails than a t distribution. the two distributions have similar tails, it's just that the t distribution can be skewed, while the normal distribution may not be skewed.
Answers
The t distribution has heavier tails than a normal distribution. the normal distribution has heavier tails than a t distribution. the two distributions have similar tails, it's just that the t distribution can be skewed, while the normal distribution may not be skewed.
There are a few important differences between a normal distribution and a t distribution. First, the t distribution has heavier tails than the normal distribution. This means that there is a greater chance of observing extreme values in the t distribution. Second, the t distribution can be skewed, while the normal distribution may not be. This means that the t distribution is more likely to have values that are not evenly distributed around the mean. Finally, the t distribution is more variable than the normal distribution. This means that the t distribution is more likely to have values that are far from the mean.
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What is the vertex of the graph of p(x) = x2 +6 ?
Answers
The graph p(x) = x² + 6 is a parabola. The equation can also be written as y = x² + 6.
A parabola follows the standard equation y = a (x - h)² + k where the vertex is (h,k).
From our equation y = x² + 6, we can convert this into a standard form which is y = 1 (x - 0)² + 6. Please take note that this standard form is just equal to the given equation.
From this converted standard form y = 1 (x - 0)² + 6, we can see that our h = 0, and our k = 6, therefore, our vertex is found at point (0,6).
Over the course of 5 hours, the temperature dropped 10°C.
The temperature dropped the same number of degrees each hour.
What operation represents
the change in temperature
each hour?
Answers
Using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operations which represent this is 10/5 = 2°C.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."
The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
So, the operation that represents the change in temperature:
Time taken is 5 hours.
The temperature drop is 10°C.
The same amount of temperature in each hour.
Then, the operation will be:
10/5 = 2°C
Therefore, using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operation which represents this is 10/5 = 2°C.
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9. Use the figure shown to identify each.
a. Vertical angles
b. Adjacent angles
c. Linear pairs
d. Supplementary angles
e. Complementary angles
Answers
Answer:
Step-by-step explanation:
For some of the questions there are multiple answers that could be correct. Here’s some of the possible answers. Hope that helps!
a. 3 & 5
b. 3 & 4
c. 4 & 5
d. 4 & 5
e. 1 & 2
Maya is asked to solve the equation 2(3x + 6) - 3(x - 10). The table shows her steps.Step 1: 6x + 12 = 3(x - 10)Step 2: 6x + 12 = 3x + 30Step 3: 3x + 12 = 30Step 4:3x = 18Step 5: x= 6Where did Maya make a mistake in solving the equation, and why?A. Maya made a mistake between the Given and Step 1 because she did not correctly distribute 2 to (3x + 6).B. Maya made a mistake between Step 1 and Step 2 because she did not correctly distribute 3 to (x10).C. Maya made a mistake between Step 2 and Step 3 because she did not correctly subtract 3x from 6x.D. Maya made a mistake between Step 3 and Step 4 because she did not correctly subtract 12 from 30.
Answers
Let's solve the following equation to see where Maya made a mistake:
2 (3x + 6) = 3 (x - 10)
Step 1: Solving parenthesis
6x + 12 = 3x - 30
Step 2: Like terms
6x - 3x = -30 - 12
Step 3: Complete the subtractions at both sides
3x = -42
Step 4: Dividing by 3 at both sides
3x/3 = -42/3
x = -14
Maya didn't multiply correctly 3 * - 10
Yes, Javionery, option B is the correct one.
Simplify this expression:
4(1 − 2b) + 76 – 10.
Type the correct answer in the box.
Answers
Answer:
-8b + 70
Step-by-step explanation:
4(1 − 2b) + 76 – 10.
4 - 8b + 76 - 10
-8b + 70
I hope this helps!
To change a fraction into a decimal do you, divide the denominator by the numerator.
Answers
To change a fraction into a decimal do you, divide the denominator by the numerator. FALSE. You should divide the numerator by the denominator (the top by the bottom).
Answer:
No.
You divide the numerator by the denominator.
Step-by-step explanation:
No.
You divide the numerator by the denominator.
For example, 8/2 = 8 divided by 2 = 4
1/5 = 1 divided by 5 = 0.2
18. Maddie has no more than $40 to spend at the store on new paint and paintbrushes for her art project. Paintbrushes cost $3 each and paint colors are sold for $6 each. If Maddie buys 4 paintbrushes, how many new paint colors can she afford?
Answers
Explanation:
Let 'x' be the number of paint colors Maddie can buy.
She buys 4 paintbrushes that cost $3 each. This means that she already spent 4x3=$12 in paintbrushes. This amount plus the amount of money she'll spend in the paint colors must be at most $40:
[tex]12+6x\le40[/tex]Solving for x:
[tex]\begin{gathered} 12-12+6x\le40-12 \\ 6x\le28 \\ x\le\frac{28}{6} \\ x\le4.\bar{6} \end{gathered}[/tex]Since x must be a whole number (is the amount of paint colors) and it has to be less than 4.666... then Maddie can afford 4 paint colors
Answer:
Maddie can afford 4 paint colors
The scale on the map shows that 4 cm = 52 miles. How many miles apart are two towns if the measurement is 22 cm?
Answers
The distane between two towns can be determined as,
[tex]\begin{gathered} 4\text{ cm=52 miles} \\ 1\text{ cm=}\frac{52\text{ miles}}{4} \\ =13\text{ miles} \\ 22\text{ cm=22}\times13\text{ miles} \\ =286\text{ miles} \end{gathered}[/tex]Thus, the required distance is 286 miles.
A four-digit number is to be made using the digits 1, 3, 5, and 8. How many numbers can be made if repeated digits are allowed?
Answers
We want to make a four digit number using numbers 1, 3, 5 and 8 and allowing repetition.
Therefore, there is four possibilities each for the units, tens houndreds and thousands.
Then, the total number of possibilities is:
[tex]4\cdot4\cdot4\cdot4=4^4=256[/tex]The total cost to develop camera pictures is proportional to the number of pictures being made. Maria paid 5.50 for 50 pics made. What number represents the constant in this proportional relationship.
Answers
Answer: 0.11
Step-by-step explanation:
Suppose y represents the cost, x represents the number of pictures, then y=kx {positive proportional function}
when x=50, y=5.5
5.5=50k
k=5.5/50
k=55/500
k=0.11
X =
(3x - 18)°
(7x-54)°
Answers
Answer:
[tex]x=\frac{289\pm \sqrt{1873}}{42}[/tex]
Solve for x. x+15.09=−2.57x =
Answers
To solve the presented question for X, every change we make in one of the sides of the equality, we must do the same to the other. This way, the equality remains. In the present case, we will subtract 15.09 in both sides, as it follows:
[tex]\begin{gathered} x+15.09=-2.57 \\ x+15.09-15.09=-2.57-15.09 \\ x=-17.66 \end{gathered}[/tex]The mean of the data set shown in the table is 57. What is the mean absolute deviation?699.512
Answers
To find the mean absolute deviation of the data set, first, you have to calculate the absolute value of the difference between each value of the data set and the mean.
The data set is
[tex]\mleft\lbrace6,9,9.5,12\mright\rbrace[/tex]The mean of the data set is 57
The function B(t) 17,550(0.88) models the value of a boat. t years after it was purchased. Which statement is true about the value of the boat? A The value of the boat is increasing by 12% each year. B. The value of the boat is increasing by 88% each year. C. The value of the boat is decreasing by 12% each yearD. The value of the boat is decreasing by 88% each year.
Answers
Answer:
Explanation:
The function that models the value of the boat is given as:
[tex]B\mleft(t\mright)=17,550\mleft(0.88\mright)^t[/tex]We can rewrite this as:
[tex]B(t)=17,550(1-0.12)^t[/tex]This is in the form of an exponential decay
Danielle is trying to solve the equation 25^x+3=176 Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answers
Given:
Equation is:
[tex]\begin{gathered} 25^x+3=176 \\ \end{gathered}[/tex]Find-:
Solve the equation
Explanation-:
Simplify the equation then,
[tex]\begin{gathered} 25^x+3=176 \\ \\ 25^x=176-3 \\ \\ 25^x=173 \\ \\ 5^{2x}=173 \end{gathered}[/tex]Taking ln both sides then,
[tex]\ln5^{2x}=\ln173[/tex]Use logarithmic property
[tex]\ln a^b=b\ln a[/tex]Then the value is:
[tex]\begin{gathered} \ln5^{2x}=\ln173 \\ \\ 2x\ln5=\ln173 \\ \\ 2x=\frac{\ln173}{\ln5} \\ \\ x=\frac{\ln173}{2\ln5} \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} x=\frac{\ln173}{2\ln5} \\ \\ x=\frac{5.1533}{2\times1.6094} \\ \\ x=\frac{5.1533}{3.2189} \\ \\ x=1.601 \end{gathered}[/tex]So, the value of "x" is 1.601
You are now on your way to college and need to make some money decisions. Your parents are going to help pay for some of your necessities but they want to know what you need. You are budgeting your money for textbooks and trying to decide how many hardback and paperback textbooks you can afford. Hardback books cost $45 and paperback books cost $20. You have $440 dollars to spend on textbooks. You know you need to buy 12 textbooks for the school year. Your task is to find out how many hardback and paperback textbooks you can buy.
Answers
You can buy 8 hardbacks and 4 paperback textbooks.
What is a Simultaneous Equation?This refers to two or more algebraic equations that have common variables and are resolved at the same time.
From the question:
Hardback books cost, H =$45
paperback books cost, P = $20.
The total amount to spend on textbooks = $440.
The total amount of textbooks needed for the school year is Hardback books+ paperback books= 12.
Solving Simultaneously we have:
H + P = 12 ..............(i)
45H + 20P = 440...........(ii)
Equation (i) * -20
-20H - 20P = -240............(iii)
Add Equation (iii) and Equation (ii)
45H + 20P = 440...........(ii)
+ -20H - 20P = -240............(iii)
We have:
25H = 200
H =200/25
H = 8
Substitute H = 8 into Equation (ii)
45(8) + 20P = 440...........(ii)
360 + 20P = 440
collecting like terms:
20P =440 - 360
20P = 80
Divide both sides by the coefficient of P
20P/20 =80/20
P= 4
Hence, You can buy 8 hardbacks and 4 paperback textbooks.
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Factor completely, then place the factors in the proper location on the grid.
b2 - 7b + 12
Answers
Answer:
(b - 4)(b - 3)
Step-by-step explanation:
b² - 7b + 12
consider the factors of the constant term (+ 12) which sum to give the coefficient of the b- term (- 7)
the factors are - 4 and - 3 , since
- 4 × - 3 = + 12 and - 4 - 3 = - 7 , then
b² - 7b + 12 = (b - 4)(b - 3)
You have 26 video games in your collection.Some are for the X-Box system and someare for PlayStation. You have 4 fewerPlaystation games than X-Box games.Write a variable expression to model thesituation. How many of each type of gamedo you have?
Answers
Total number of videogames = 26
PLaystation games = y
x box games = x
x+y=26
You have 4 fewer (-4) PlayStation games than X-Box games.
y = x-4
The system is:
x+y=26 (a)
y = x-4 (b)
Puy (b) into (a)
x+ (x-4) =26
x+x-4 =26
Solve for x:
2x= 26+4
2x=30
x=30/2
x=15 (c)
(c) into (b)
y=15-4
y=11
X box games = 15
Playstation games = 11
I need the answer! I snap a pic to try n get it but no answer lol someone help!!! I’m on the clock
Answers
The given equation is
x^2 + 7x = 8
By subtracting 8 from both sides, it becomes
x^2 + 7x - 8 = 0
We would find two terms such that their sum or difference is 7x and the product is - 8x^2. The terms are - x and 8x. Replacing 7x with - x and 8x, we have
x^2 - x + 8x - 8 = 0
By factorising, we have
x(x - 1) + 8(x - 1) = 0
Since x - 1 is common, it becomes
(x + 8)(x - 1) = 0
x + 8 = 0 or x - 1 = 0
x = - 8 or x = 1
Option C is correct
A line has a slope of 2 and passes through the point (-2,8). What is the equation of theline?
Answers
The general equation of line passes through the point (x_1,y_1) and has slope m is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line passing through point (-2,8) and has slope of 2.
[tex]\begin{gathered} y-8=2(x-(-2)) \\ y=2\cdot x+2\cdot2+8 \\ y=2x+12 \end{gathered}[/tex]So answer is y = 2x + 12.
Shane bought 36 gallons of gas this week this amount is 6 gallons more than twice the amount of gas he bought last week how many gallons of gas in Shane by last week
Answers
so, she bought 15 gallons of gas last week
Explanation
Step 1
Let
36 gallons this week
x= number of gallons of gas Shane bought las week
this amount is 6 gallons more than twice the amount of gas he bought last week , then
[tex]36=2x+6[/tex]Step 2
solve for x
[tex]\begin{gathered} 36=2x+6 \\ \text{subtract 6 in both sides} \\ 36-6=2x+6-6 \\ 30=2x \\ \text{divide each side by 2} \\ \frac{30}{2}=\frac{2x}{2} \\ x=15 \end{gathered}[/tex]so, she bought 15 gallons of gas last week
What is the solution to the system of equations graphed below?
Answers
Answer:
(0,-4)
Step-by-step explanation:
write the coordinates of the point where the two lines intercept themselves
Answer:
A. (0,-4)
x is 0 and y is -4
Choose all the sets containing the number pi
natural numbers
whole numbers
integers
rational numbers
irrational numbers
real numbers
Answers
Answer:
π is an irrational number, so it is also a real number.
which angle is congruent to
Answers
The angle congruent to ∠CGD is the angle ∠AGF as they are vertical angles.