Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
so in first picture
1 is exterior angle of the triangle
it means that
1=2+3
so is evident that m 1 > m 2
in the second picture
1 is the exterior angle of the triangle
so
1=3+4
but 3=2 as alternate interior angles
definition:The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
so is evident that m 1 > m 2
Answer:
see explanation
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
(1)
∠ 1 is an exterior angle of the triangle, then
∠ 1 = ∠ 2 + ∠ 3
Thus ∠ 1 must be > ∠ 2
(2)
∠ 3 = ∠ 2 ( alternate angles )
∠ 1 is an exterior angle of the triangle, then
∠ 1 = ∠ 3 + ∠ 4 = ∠ 2 + ∠ 4
Thus ∠ 1 > ∠ 2
Question in image. :)
Answer:
All real numbers greater than or equal to 0.
General Formulas and Concepts:
Algebra I
Domain is the set of x-values that can be inputted into function f(x)Step-by-step explanation:
According to the graph, we see that our x-values span from 0 to infinity. Since 0 is a closed dot, it is inclusive in the domain:
[0, ∞) or x ≥ 0 or All Real Numbers greater than or equal to 0.
vector a~ is 2.54 units long and points in the positive y direction. vector b~ has a negative x component 2.32 units long, a positive y component 2.88 units long, and no ~z component. find a~ · b~ .
Therefore [tex]\overrightarrow{\mathrm{a.b}}=3.00 \hat{i}+6.00 \hat{j}[/tex]
Ax=-2.54 Ay=2.32
The sum of two or more vectors is called the Resultant.
The Resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together. If displacement vectors A, B, and C are added together, the result will be vector R.
[tex]$$\mathrm{A}_{\mathrm{x}}=-3.00, \mathrm{~A}_{\mathrm{y}}=2.00$$(a) $\overrightarrow{\mathrm{A}}=\mathrm{A}_{\mathrm{x}} \hat{\mathrm{i}}+\mathrm{A}_{\mathrm{y}} \hat{\mathrm{j}}=-3.00 \hat{\mathrm{i}}+2.00 \hat{\mathrm{j}}$(b) $|\overrightarrow{\mathrm{A}}|=\sqrt{\mathrm{A}_{\mathrm{z}}^2+\mathrm{A}_{\mathrm{y}}^2}=\sqrt{(-3.00)^2+(2.00)^2}=3.61$$$\theta=\tan ^{-1}\left(\frac{\mathrm{A}_{\mathrm{Y}}}{\mathrm{A}_{\mathrm{K}}}\right)=\tan ^{-1}\left(\frac{2.00}{-3.00}\right)=-33.7^0$$[/tex]
[tex]$\theta=180^{\circ}+\left(-33.7^{\circ}\right)=146^{\circ}$[/tex]
[tex]$\mathrm{R}_{\mathrm{x}}=0, \mathrm{R}_{\mathrm{y}}=-4.00$ and $\overrightarrow{\mathrm{R}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$, thus $\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{R}}-\overrightarrow{\mathrm{A}}$ and$$\mathrm{B}_{\mathrm{x}}=\mathrm{R}_{\mathrm{x}}-\mathrm{A}_{\mathrm{x}}=0-(-3.00)=3.00, \mathrm{~B}_{\mathrm{y}}=\mathrm{R}_{\mathrm{y}}-\mathrm{A}_{\mathrm{y}}=-4.00-2.00=-6.00$$[/tex]
[tex]\text { Therefore, } \overrightarrow{\mathrm{a,b}}=3.00 \hat{i}+6.00 \hat{j}[/tex]
[tex]\text { Therefore, } \overrightarrow{\mathrm{a.b}}=3.00 \hat{i}+6.00 \hat{j}[/tex]
learn more about Vector sum: brainly.com/question/10435343
#SPJ4
I'll give brainliesst! just help me please...
Answer:
The second table shows a linear function
Step-by-step explanation:
The linear function intersect at -2
Rita ran for class president. She received 90 votes in the election. These votes represent 60% of the total number of students in her class. How many students are in her class?
Answer:
54 students
Step-by-step explanation:
90× 60% = 54
9/12 divided by 1/4 in a model
Answer:
9/3 or 3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
9/12 divided by 1/4 is 9/12 x 4/1=36/12=3
Find the missing angle in the triangle below
Answer:
120
Step-by-step explanation:
Exterior angle theorem
50 + 70 = 120
Answer:
120
Step-by-step explanation:
the insides of a triangle add up to 180 degrees. You're given 70 and 50 degrees which add to 120 and that means the other angle is 60 degrees. Since you're trying to find an outside angle, you need to do subtract the 60 degrees we just found from 180 (because its a supplementary angle). 180-60 is 120 and thats the answer
Find the selling price of a karaoke machine with a 60.5% markup.
Answer:
$99.91
Step-by-step explanation:
If the markup is 60.5%, then the selling price would be 160.5% of the original price.
160.5%=1.605
$62.25*1.605=$99.91125
Since you can't have 0.00125 dollars, lets round to the nearest hundredth.
The selling price is $99.91
OPTIONS
Pack of 24 for $1.68
UNIT PRICE
$
per
Pack of 12 for $1.08
$
per
Please help! State which property of equality justifies the statement:
If VR+TY=EN+TY, then VR=EN.
The property of equality that justifies the statement where the statement is given as "If VR + TY = EN + TY, then VR = EN" is the subtraction property of equality
How to determine the property of equality that justifies the statement?The statement is given as
If VR + TY = EN + TY, then VR=EN
In the above statement, we have the following equation
VR + TY = EN + TY
By applying the subtraction property of equality, we have the following equation
So, we have
VR + TY - TY = EN + TY - TY
Evaluate the difference in the above equation
So, we have
VR = EN
Hence, the property of equality that justifies the statement where the statement is given as "If VR + TY = EN + TY, then VR = EN" is the subtraction property of equality
Read more about subtraction property at
https://brainly.com/question/1601404
#SPJ1
A concession stand sells bags of popcorn for $3 and cotton candy for $2. A customer purchased
bags of popcorn as well as cotton candy and spent $12.
Help easy math question!!!
Answer:
The length of the third side of the triangle is 30.
Step-by-step explanation:
Here is the formula for the Pythagorean Theorem:
[tex]a^{2} + b^{2} = c^{2}[/tex]
The hypotenuse, based on the problem, is 50. Anyways, let's get back to calculating!
We need to multiply 40 times 40 and 50 times 50.
40 times 40, or 40 squared, equals to 1600.
50 times 50, or 50 squared, equals to 2500.
[tex]c^{2} - b^{2} = a^{2}[/tex]
Now, let's subtract. 2500 - 1600 = 900. We need to find the square root of 900--which is 30, because 30 times 30, or 30 squared, equals to 900.
Answer:
30
Step-by-step explanation:
c=√a^2+b^2
a=√c^2-b^2 = √50^2-40^2 = 30
What is the value of x + y + 5 if x = 6 and y = 15?
Answer:
26
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
x + y + 5
x = 6
y = 15
Step 2: Evaluate
Substitute: 6 + 15 + 5Add: 21 + 5Add: 26find all values of c in the open interval (a, b) such that f'(c)=(f(b)-f(a))/(b-a)
f(x)=4sin(x), [0,π]
There is only one value of c that satisfies the requirements.
=======================================================
Work Shown:
Let's compute the function value at the given endpoints of the interval.
[tex]f(x) = 4\sin(x)\\\\f(\pi) = 4\sin(\pi) = 0\\\\f(0) = 4\sin(0) = 0\\\\[/tex]
Which means,
[tex]f'(c) = \frac{f(b)-f(a)}{b-a}\\\\f'(c) = \frac{f(\pi)-f(0)}{\pi-0}\\\\f'(c) = \frac{0-0}{\pi}\\\\f'(c) = \frac{0}{\pi}\\\\f'(c) = 0\\\\[/tex]
We want to find all values of c such that the derivative is 0.
This can be rephrased into wanting to solve [tex]4\cos(x) = 0\\\\[/tex] since the derivative of sine is cosine
In other words, [tex]f(x) = 4\sin(x)\\\\[/tex] turns into [tex]f'(x) = 4\cos(x)\\\\[/tex]
Solving that equation leads to:
[tex]4\cos(x) = 0\\\\\cos(x) = 0\\\\x = \frac{\pi}{2}\\\\[/tex]
Use a reference table or the unit circle to determine this.
This is the value of c that satisfies f ' (c) = 0, such that [tex]0 < c < \pi[/tex]. No other value of c works.
If you graphed f(x) = 4sin(x), and only focused on the interval [0,pi], then you'll find that there's a horizontal tangent at the point (pi/2, 4). Note how the endpoints have the same y value so that's why the average rate of change over [0,pi] is 0.
Side note: this is an application of Rolle's Theorem
if y=2
Evaluate the following expression
4(2y-3)
Answer:
4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
4(2y - 3)
y = 2
Step 2: Evaluate
Substitute in y: 4(2(2) - 3)Multiply: 4(4 - 3)Subtract: 4(1)Multiply: 4Answer:
4
Step-by-step explanation:
Substitute y for 2
4((2×2)-3)
Simplify
4(4-3)
Simplify further
4×1
4×1=4
what is 1 plus -1
I lsdkfjaofh;khr;fjhdkjafh;fdokja;
Answer:
0
Step-by-step explanation:
ndjejdge Hell wkdbs hru osdhdvgd
Answer: i have no clue
Step-by-step explanation:
14/54=21/m what is the number for m?
Answer:
m=81
Step-by-step explanation:
14 x 1.5 = 21
54 x 1.5 = 81
Answer:
m = 81
Step-by-step explanation:
divide by 54/14 from both sides.
you'll remain with 81/m
then divide with m/1 on both sides giving you m= 81
A friend gives you two baseball cards for your birthday. Afterward, you begin collecting them. You buy the same number of cards once each week. The equation y = 4x + 2 describes the number of cards, y, you have after x weeks.
Discuss which points on the line do not make sense in this situation. Then plot three more points on the line that do make sense.
Answer:You have 2 cards upfront, so the constant term in this linear equation is 2. The slope represents how many more cards you buy or acquire per day, week or month (depending upon how eager you are to fatten your collection). ;)
y = 2 + (rate of acquisition of cards)(time)
y = 2 + rt
I need some help with this plz
Dasher was super hungry after his big night so he ordered 4 candy cane pies. He ate 3/5 of the pies on the way home. How much pie did he have left when he got home?
Answer:
He had 3 2/5 pies left when he got home.
Step-by-step explanation:
Hope this helped have an amazing day!
The fraction of candy cane pies that Dasher left is 8/5.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.
As per the given,
Number of candy cane pies that Dasher order = 4
Fraction he ate = 3/5
Left = 4 - ate
Left = 4 - (3/5)4
Left = 4(1 - 3/5)
Left = 4(2/5)
Left = 8/5
Hence "The fraction of candy cane pies that Dasher left is 8/5".
For more about fractions,
https://brainly.com/question/10354322
#SPJ2
Complete the statement to describe the expression (a+b+c)(d+e+f)
The expression consists of _ factors, and each factor contains _ terms.
Fill in the blanks.
Answer:
Please check the explanation.
Step-by-step explanation:
We know that if we multiply 3 and 4, we get 12.
In other words, 3 × 4 = 12
Thus, 3 and 4 are factors of 12.
now
Given the expression
[tex](a+b+c)(d+e+f)[/tex]
The given expression consists of two factors which are:
(a+b+c)(d+e+f)We also know that an expression can consist of terms, a term may be a constant or a variable. It can be both as well.
For example, in the expression, 4b + 2, 4b and 2 are terms.
so,
The factor (a+b+c) consists of 3 terms. These terms are a, b and c.Similarly, the factor (d+e+f) consists of 3 terms. These terms are d, e, and f.given a piece wise
function f(x)={2x,x<1 5, x=1
Idk what to choose!
Answer:
AAS
Step-by-step explanation:
im bad at this stuff you can take your risk or look at other answers
Help pleaseeeeeeeeeee
Given that,
The cone and the sphere have the same volume.
___________________________________________
Volume of the cone
[tex] = \frac{1}{3}\pi {r}^{2} h[/tex]
[tex] = \frac{1}{3} \times \frac{22}{7} \times 2.4 \times 2.4 \times 8.3[/tex]
[tex] = 1 \times \frac{22}{7} \times 0.8 \times 2.4 \times 8.3[/tex]
[tex] = \frac{22}{7} \times 1.92 \times 8.3[/tex]
[tex] = \frac{22}{7} \times 15.93[/tex]
[tex] = 22 \times 2.27[/tex]
[tex] = 49.94[/tex]
[tex] = 50 {cm}^{3} (rounded)[/tex]
Also,
Volume of the sphere
= 50cm³
[tex] = \frac{4}{3} \pi {r}^{2} = 50[/tex]
[tex] \pi {r}^{2} = 50 \times \frac{3}{4} [/tex]
[tex]\pi {r}^{2} = 37.5[/tex]
PLEASEEE HELPPPP!!!!!
Answer:
the answer is 9.85
Step-by-step explanation:
the answer is 9.85 because the area is 19.7 so all you have to do is divide it by 2
The owner where your work explains that you’re paid $8/hour and receives a $25 bonus each month for being the manager. If the owner hands you a check for $250, How many hours did you work this month? Write an equation and solve.
Answer:
28.125 hours
Step-by-step explanation:
250- the 25 dollar bonus=225
225/8 dollars an hour= 28.125 hours
Answer:
6.25
Step-by-step explanation:
250/8= 31.25
then take away the added bonus
31.25-25= 6.25
Anybody know the answer to these
what is the length of segment AB?
Mary read six books in January, four books in February, and eight books in March.What
was the average number of books read each month?
Please help me the picture is posted above
Answer: C, D, E
Step-by-step explanation: sub in -3 for x and 6 for y in all equations. Only c and d are true. In the graphs, E is the only one that has the point (-3,6)
Answer:
c, d, and e
Step-by-step explanation:
A car travels 195 miles in 3 hours assuming that the distance the car travels write an equation that represent this relationship in the form of d=kt
Answer:
195 = 3 mph
Step-by-step explanation:
This is probly wrong but I tried