Please help! I’m this figure, which angles are congruent? Find the measure of all the angles if m< 2= 76 degrees
Answers
Problem 1.
Yes it is true that vertical angles are congruent, but that's not what your teacher is asking. Instead, your teacher is asking basically how the term "congruent" is defined.
Two segments are congruent if they are the same length. Two angles are congruent if they are the same measure. Two triangles are congruent if they have the same angles and sides.
So in short, "congruent" just means "same". You can think of having mirror copies.
==========================================
Problem 2.
Angles 2 and 4 are one pair of vertical angles. They are opposite one another in this X shape formed by the two lines. The other pair of vertical angles are angle 1 and angle 3.
Angle 2 is given to be 76 degrees, so this means angle 4 is this measure as well.
Angle 1 = 180 - (angle 2) = 180 - 76 = 104, which is also the measure of angle 3 as well. I'm using the idea that the adjacent angles form a straight angle. This is known as a linear pair (ie the angles form a straight line).
==========================================
Problem 3.
If all three angles are the same (all 60 degrees), then we have an equilateral triangle. We could say it's equiangular, but it's also equilateral as well meaning all 3 sides are the same length. "equi" means "equal", "angular" means what you'd expect, and "lateral" means "side".
If only two angles are equal with the third one different, then we have an isosceles triangle. An isosceles triangle is one where only two sides are the same length.
If none of the angles are the same, then we have a scalene triangle. As you probably expect, none of the sides are the same length with a scalene triangle.
----
If all three angles are less than 90 degrees, then the triangle is acute
If one angle is 90 degrees, then we have a right triangle
If one angle is over 90 degrees (but less than 180), then the triangle is obtuse
---
Often you'll see the terms of the previous two sections combined. For instance, we could have an isosceles right triangle. Or we might have an obtuse scalene triangle. Any equilateral triangle is acute (as all three angles are less than 90).
To solve this problem we have to understand what congruent angles are and then find the angles that are congruent to one other in this given question.
What are Congruent Angles?Congruent angles are angles that are equal to one another and in the given question, we were given m<2 = 76 degrees.
Data;
m<2 = 76 degreesIf we look critically at the angles, we can use opposite angle theorem here to predict angles that are congruent to another here.
angles 2 and angle 4 are congruent to one another while angle 1 and angle 3 are congruent to one another.
This implies that
m<2 = 76°m<4 = 76°Let's solve for other angles.
But the some of angles at a point is equal to 360°
Applying that theorem here,
[tex]m > 1=x\\m > 2 = 72^0\\m > 3 = x\\m > 4 = 72^0[/tex]
Let's substitute the values and solve.
[tex]x+ x + 72+72 = 360\\2x + 144 = 360\\2x = 360 - 144\\2x = 216\\x = \frac{216}{2} \\x = 108^0[/tex]
This can be further summarized as
m<1 = 108°m<2 = 72°m<3 = 108°m<4 = 72°Learn more on corresponding angles here;
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Related Questions
37. What is the slope of the equation ?
-3
y = x + 2
HELP! answer if you can!
Answers
Answer:
Slope =1Step-by-step explanation:
Method 1 : Standard form method
[tex]y = x + 2\\\mathrm{Convert\:to\:standard\:form}:\quad x-y=-2\\\\\mathrm{Slope}\:\mathbf{m}\:\mathrm{of\:a\:line\:of\:the\:form}\:\\\mathbf{Ax+By=C}\:\mathrm{equals}\:\mathbf{-\frac{A}{B}}\\\\\mathbf{A}=1,\:\mathbf{B}=-1\\m=-\frac{1}{-1}\\m=1[/tex]
Method 2 : Slope -intercept Form
[tex]\mathrm{Slope\:of\:}y=x+2:\\\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:} :\\\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}\\\\m=1[/tex]
A circle is centered at C(-1,-3) and has a radius of 6. Where’d does the point P(-6,-6) lie?
Answers
The sides of two cubes are in ratio of 1:3. What is the ratio of the areas of these cubes ? What is the ratio of their volume ?
Answers
Answer:
The ratio of their surface areas would 1:9 and the ratio of their volumes would be 1:27
Step-by-step explanation:
Given Info: The sides of two cubes are in ratio of 1:3. We can assign one square x and the other square 3x.
We know that the area of a square is its side squared, and that a cube has 6 sides. So thus if we assign one side of the cube x we can assume that surface area is 6x^2:
Surface Area of Cube #1= 6x^2
Surface Area of Cube #2= 6((3x)^2) = 6(9x^2) = 54x^2
Ratio of Surface Area: 6x^2 : 54x^2 = 6:54 = 1:9
Now for the volume we know that it is equivalent to one side cubed. So after assigning x to one cube, we can assume that volume would be x^3.
Volume of Cube #1= x^3
Volume of Cube #2= (3x)^3 = 27x^3
Ratio of Volume: x^3: 27x^3 = 1:27
Hope this helps!
Please answer this question now
Answers
Answer:
320 sq in
Step-by-step explanation:
4(1/2*8*16) + (8*8)
= 4(64) + (64)
= 5(64)
= 320
s the value of the expression 6x − y when x = 3 and y = 1? (5 points) 3 8 12 17
Answers
Answer:
(6)(3)−1
=17
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
6x − y
Let x =3 and y=1
6*3 -1
18-1
17
Which is a complete list of factors of each term in the expression 15 + 20 x? 15: 1, 3, 5, 15 20x: 1, 2, 4, 5, 10, 20, x 15: 1, 3, 5, 15 20x: 1, 2, 4, 5, 10, 20 15: 3, 5 20x: 4, 5, x 15: 1, 3, 5 20x: 1, 2, 4, 5, 10, x
Answers
Answer:
15: 1 3 5 15
20: 1 2 4 5 10 20
Step-by-step explanation:
This assumes you are only factoring the coefficients of the expression. Using this assumption, we simply create a list of factors of the coefficients.
15 -> 1 * 15, 3 * 5 --> 1 3 5 15
20 -> 1 * 20, 2 * 10, 4 * 5 --> 1 2 4 5 10 20
If you don't assume factoring of just the coefficients, then 20x factors
20x: 1 2 4 5 10 20 x
Cheers.
Answer:
b
Step-by-step explanation:
Given that v = u + 10t, find y when
u= 6 and t = 9.
Answers
Answer:
hey here is the answer
Step-by-step explanation:
Subject of the formula:
It is a variable which is expressed in terms of other variables involved in the formula.
Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.
For example:
In the formula v = u + at, v is the subject.
To find v in the example, we substitute the values u, a and t in the R.H.S. of the equation.
Changing the subject of the formula:
To change the subject of a formula, begin with the variable to become the new subject, and apply inverse operation as for solving equations in the opposite order to the order conventions.
1. To make ‘u’ the subject of the formula in v = u + at,
[subtract at from both sides]
v - at = u
or, u = v - at
2. To make ‘t’ the subject of the formula, v = u + at,
[subtract u from both sides]
v - u = at
or, (v - u )/a = t
or, t = (v - u)/a
Change the Subject of a Formula
The value of the equation is v = 96 when u = 6 and t = 9
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
v = u + 10t be equation (1)
when u = 6 and t = 9
Substitute the value of u and t in the equation , we get
v = 6 + 10 ( 9 )
On simplifying the equation , we get
v = 6 + 90
v = 96
Therefore , the value of v is 96
Hence , the equation is v = 96
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PLEASE HELP ASAP!!!! A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows: First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3, 0 Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2 Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3 Which is the best measure of center for second period, and why? Mean, because there are no outliers that affect the center Median, because there is one outlier that affects the center Interquartile range, because there is one outlier that affects the center Standard deviation, because there are no outliers that affect the center
Answers
Answer:
Answer: D : Median, because there is 1 outlier that affects the center
Step-by-step explanation:
Mean and median terms are use to measure the central tendency in a data set.
Mean is the best measure of center if there is no outlier present in the data otherwise median is the best measure of center if there is outlier present because outliers effects the means value of a data but not the median value.
In the third period, there is an outlier present as 8 that affects the center, then the best measure of center for third period must be Median.
20 points! Thank you :)
Answers
Answer:
[tex]\Large \boxed{x=-2 \ \mathrm{and} \ x=3}[/tex]
Step-by-step explanation:
The quadratic expression is given.
[tex]2x^2-2x-12=0[/tex]
Factor the left side of the equation.
[tex]2(x+2)(x-3)=0[/tex]
Set the factors equal to 0.
[tex]x+2=0[/tex]
[tex]x=-2[/tex]
[tex]x-3=0[/tex]
[tex]x=3[/tex]
The two solutions work in the original equation. The solutions make the equation true.
The quadratic expression:
[tex]2 {x}^{2} - 2x - 12[/tex]
★ By split middle term,we get
[tex]2 {x}^{2} - 6x + 4x - 12[/tex]
[tex]2x(x - 3) + 4( x - 3)[/tex]
[tex](2x + 4) (x - 3)[/tex]
[tex]2x + 4 = 0 \: \: and \: \: x - 3 = 0[/tex]
[tex]2 x = - 4 \: \: and \: \: x = 3[/tex]
[tex]x = - 2 \: \: and \: \: x = 3[/tex]
Therefore , the two solution of given quadratic equations is -2 and 3.
What is 12x-10y=-19 in slope intercept form?
Answers
Answer:
-10y=-12x-19
-y= -12x-19
10
y= 12x + 19
10
Step-by-step explanation:
form slope intercept its y=mx+b
so you find y what equal .
For which system of inequalities is (3,-7) a solution? A. x + y < -4 3x + 2y < -5 B. x + y ≤ -4 3x + 2y < -5 C. x + y < -4 3x + 2y ≤ -5 D. x + y ≤ -4 3x + 2y ≤ -5
Answers
Answer:
The correct option is;
D x + y ≤ -4, 3·x + 2·y ≤-5
Step-by-step explanation:
A. For the system of inequality, x + y < -4, 3·x + 2·y <-5
We have;
y < -4 - x, When x = 3, y < -7
y < -2.5 - 1.5·x, When x = 3, y = -7
B. For the system of inequality, x + y ≤ -4, 3·x + 2·y <-5
We have;
y ≤ -4 - x, When x = 3, y ≤ -7
y < -2.5 - 1.5·x, When x = 3, y < -7
C. For the system of inequality, x + y < -4, 3·x + 2·y ≤-5
We have;
y < -4 - x, When x = 3, y < -7
y ≤ -2.5 - 1.5·x, When x = 3, y ≤ -7
D. For the system of inequality, x + y ≤ -4, 3·x + 2·y ≤-5
We have;
y ≤ -4 - x, When x = 3, y ≤ -7
y ≤ -2.5 - 1.5·x, When x = 3, y ≤ -7
Therefore, the system of inequality for which (3, -7) is a solution is D, x + y ≤ -4, 3·x + 2·y ≤-5.
Bob and Carol want to hire Able Refinishing to sand and refinish the dining room floor to match the floor in the living room. Able charges $2.41 per square foot to sand and refinish a hardwood floor. The dining room is rectangular and measures 17 feet 10 inches by 11 feet 9 inches. Find the area of the dining room floor and the cost of the work.
Answers
Answer:
Area = 209.5 ft² (nearest tenth)
Cost = $505 (approximated)
Step-by-step explanation:
Step 1: convert the inches to be in feet by dividing length in inches by 12.
17 feet 10 inches => [tex] 17 + \frac{10}{12} = 17.83 ft [/tex]
11 feet 9 inches => [tex]11 + \frac{9}{12} = 11.75 ft[/tex]
Step 2: Find the area of the floor of the dinning room
Area = 17.83*11.75 = 209.5 ft² (nearest tenth)
Step 3: Find the cost of the work.
Cost = 209.5 ft² × $2.41 = $505 (approximated)
-36 + x < 8 Solve for x
Answers
Answer:
[tex]x < 44[/tex]
Step-by-step explanation:
We can simplify this inequality by isolating x on one side.
[tex]-36 + x < 8[/tex].
Let's add 36 to both sides.
[tex]-36 + 36 + x < 8 +36\\\\x < 44[/tex]
Hope this helped!
Answer:
x<44
Step-by-step explanation:
Add 36 to both sides:
-36 + x < 8
+36 +36
x < 44
Find four rational number between 1/4 and 2/3.
Answers
Answer:
4/12, 5/12, 6/12, 7/12
Step-by-step explanation:
1/4 x 3/3 = 3/12
2/3 x 4/4 = 8/12
between 3/12 and 8/12
4/12, 5/12, 6/12, 7/12
you can simplify these if you wish
Hope that helped!!! k
HELP ME ASAP I DONT UNDERSTAND
Answers
Answer
False
Step-by-step explanation:
3 is an element of A but {3} is not so it is false.
Malia measures the longer side of a dollar bill using a ruler at school. Which of the following is most likely the quantity she measured?
Answers
Answer:
Step-by-step explanation:
The most likely quantity is centimetres.
The second option can be inches.
Hope this helps
plz mark it as brainliest!!!!!!!!!
Find a101 of the sequence 5,8,11,
Answers
Answer:
305
Step-by-step explanation:
This sequence es the sum of 3
5+3 =8
8+3 = 11
then
101 = 100 + 1
the fisrt date is 5
the another 100:
100*3 = 300
300 + 5 = 305
solve for x 3x - 4 = 3x - 10
Answers
Answer:
no solution
Step-by-step explanation:
3x - 4 = 3x - 10
Subtract 3x from each side
3x-3x - 4 = 3x-3x - 10
-4 = -10
This is never true so there is no solution
Answer:
Step-by-step explanation:
I think you might have copied down the problem incorrectly.
If you try and solve this problem by moving the variables onto one side and the constants onto the other, you get:
3x-4=3x-10
+10 +10
3x+6=3x
-3x -3x
6=0 (which is FALSE)
Hope this helps!
P.S. Please give me brainliest. Thanks :)
Please help me this question
Answers
Answer:
∠ BNM = 150°
Step-by-step explanation:
Project MN to meet AB at point P, then
Δ ANP is a right triangle with sum of angles = 180°, thus
x = 180° - (90 + 30)° = 180° - 120° = 60°
∠ BNM = x + 90 = 60 + 90 = 150°
solve the equation below[tex]\sqrt[5]{27(x-2)}=3[/tex]
Answers
Answer:
x = 11
Step-by-step explanation:
Raising both sides to the fifth power, we get:
27(x - 2) = 3⁵
x - 2 = 3⁵ / 27
x - 2 = 3⁵ / 3³
x - 2 = 3⁽⁵⁻³⁾ = 3² = 9
x = 11
Tan x is ........ Cos x is ........ Sin x is ..........
Answers
Answer:
Tan x= 3/4 Cos x= 4/5 Sin x=3/5
Step-by-step explanation:
"soh-cah-toa"
Just an easy way to remember how Sine, Cosine and Tangent work:
Soh...
Sine = Opposite / Hypotenuse
...cah...
Cosine = Adjacent / Hypotenuse
...toa
Tangent = Opposite / Adjacent
Answer:
tan(x)=0.75 sin(x)=0.6 Cos(x)=0.8
Step-by-step explanation:
[tex]tan(x)=\frac{opposite}{adjacent}=\frac{3}{4}=0.75[/tex]
[tex]cos(x)=\frac{adjacent}{hypotenuse}= \frac{4}{5} =0.8[/tex]
[tex]sin(x)=\frac{opposite}{hypotenuse}=\frac{3}{5}=0.6[/tex]
opposite=3
adjacent=4
hypotenuse=5
try remembering it as SOH CAH TOA
(−2a+5−b)⋅(−5) <- does this equal to 10a−25+5b?
Answers
Answer:
Yes!
Step-by-step explanation:
Solving Inequalities and graphing them.
Answers
Answer:
I used to know this not anymore sry g
WILL MARK BRAINLIEST!!!!20 POINTS!!!!URGENT!!!
Answers
Answer:
the firsts third and last one
Step-by-step explanation:
hope this helped
What is the multiplicity of each of the roots of the graph of
f(x) = 2x4 + 12x} + 16x2 – 12x – 18?
A.-3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1
B.-3, multiplicity 2; 1, multiplicity 2
C.-3, multiplicity 1; -1, multiplicity 1; 1, multiplicity 1
D.-3, multiplicity 2; -1, multiplicity 3; 1, multiplicity 1
Answers
Answer:
The correct option is;
C. -3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1
Please find attached the required function graph
Step-by-step explanation:
To solve the equation f(x) = 2·x⁴ + 12·x³ + 16·x² -12·x - 18, by graphing the function, we have;
x [tex]{}[/tex] F(x)
-4[tex]{}[/tex] 30
-3[tex]{}[/tex] 0
-2[tex]{}[/tex] 6
-1[tex]{}[/tex] 0
0 [tex]{}[/tex] -18
1[tex]{}[/tex] 0
2[tex]{}[/tex] 150
The shape of a graph with multiplicity of 2
Given that the graph bounces of the horizontal axis at the y-intercept at point x = -3, the factor (x - 3) must be a quadratic of the form (x - 3)², thereby having a multiplicity of 2 in the solution which are;
x = 1, -1, and, giving
(x - 1)·(x + 1)·(x - 3)² = 0
Therefore, the correct option is -3, multiplicity 2; -1, multiplicity 1; 1 multiplicity 1.
Answer:
C
Step-by-step explanation:
Aisha saves 2 Dhs on first week of the month of June, 4Dhs on second week of the month, 8 Dhs on third week of the month and so on. What will be her saving at the end of second week of July? What value is being shown by Aisha? Is saving is a good habit? How often do you save money? What are the different ways of saving money?
Answers
Answer:
she is saving in an exponential way, that is an amazing habit that will multiply her savings over time. At the end of the second week of July she will have 126 if she kept multiplying the amount every week from June into July but she will have 38 if she starts over with saving 2 on the 1st week of the second month. I save money often, my way of saving is only spending the money i have on things I need rather than want. I also save in a linear way buy saving five dollars every month which is slower than aishas way in the long run but it is easy for me. There are so many different ways of saving money but some are slower than others and some are faster.
Step-by-step explanation:
Hope this helps, please give brainliest, i never got it before
find the Perimeter Of a circle whose radius is 14cm
Answers
Answer:
Step-by-step explanation:
Firstly, we will use the formula π × d
Which will be 22\7 × 28 (this is the radius multiplied by 2)
After multiplying you will get 88 cm as your perimeter
=88 cm
What is the final concentration if a saline solution consisting of 20% NaCl is diluted using a 1/4 solution?
Answers
Answer: C.V=C1.V1 +C2.V2
Step-by-step explanation: C=(C1V1 + C2V2)/V -> C=(20%.V+25%V)/2V-> C=22,5%
23458+98432 find the sum
Answers
Answer:
121,890
Step-by-step explanation:
23458+98432
=121,890
please help will give you a 5 star rating
Answers
Answer:
3
Step-by-step explanation:
To find the average rate of change
f(0) - f(-2)
-----------------
0 - -2
Taking the values for f(0) = 6 and f(-2) =0
6 - 0
---------
0+2
6/2
3
Answer:
Slope I think its says, so: 3
Step-by-step explanation:
Take
6 = y2 , 0 = y1 , 0 = x2 , -2 = x1
y2 - y1 over x2 - x1
6-0
0+2 (because 2 is negative)
=
6/2
which reduced makes 3!
Hope this helps, and have a good day.
And for the 0 + 2:
its
0 - ( - 2 )
- ( - makes a big plus so add :)
