[tex]a(n) = 6 + 3(n - 1)[/tex]
[tex]a(1) = 6 + 3(1 - 1)[/tex]
[tex]a(1) = 6 + 3 \times 0[/tex]
[tex]a(1) = 6 + 0[/tex]
[tex]a(1) = 6[/tex]
_________________________________
[tex]a(2) = 6 + 3(2 - 1)[/tex]
[tex]a(2) = 6 + 3 \times 1[/tex]
[tex]a(2) = 6 + 3 [/tex]
[tex]a(2) = 9[/tex]
_________________________________
[tex]a(3) = 6 + 3(3 - 1)[/tex]
[tex]a(3) = 6 + 3 \times 2[/tex]
[tex]a(3) = 6 + 6[/tex]
[tex]a(3) = 12[/tex]
_________________________________
[tex]a(4) = 6 + 3(4 - 1)[/tex]
[tex]a(4) = 6 + 3 \times 3[/tex]
[tex]a(4) = 6 + 9[/tex]
[tex]a(4) = 15[/tex]
Please Help!
1.
Given: ΔABC is a right triangle
∠A is a right angle
m∠B = 45˚
Prove: ∠B ≅ ∠C
STATEMENT: REASON:
2.
Given: m∠X = 4a + 2
m∠Y = 21a + 3
∠X and ∠Y are a linear pair
Prove: ∠Y is an obtuse angle
STATEMENT: REASON:
3.
Given: ∠A and ∠B are complementary angles
∠B and ∠C are complementary angles
Prove: ∠A ≅ ∠C
STATEMENT: REASON:
4.
Given: ΔMNP is a right triangle
∠M is a right angle
Prove: ∠N and ∠P are complementary angles
STATEMENT: REASON:
Answer:
1. ∠C ≅ ∠B by definition of congruency
2. m∠Y by definition of obtuse angle
3. ∠C ≅ ∠A by definition of congruency
4. ∠N and ∠P are complementary angles by definition of complementary angles
Step-by-step explanation:
1. The given parameters are;
Statement [tex]{}[/tex] Reason
ΔABC is a right triangle [tex]{}[/tex] Given
∠A is a right angle [tex]{}[/tex] Given
m∠B = 45° [tex]{}[/tex] Given
m∠A + m∠B + m∠C = 180° [tex]{}[/tex] Sum of interior angles of a triangle
m∠C = 180° - (m∠A + m∠B) [tex]{}[/tex]
m∠C = 180° - (90° + 45°) = 45° [tex]{}[/tex] Substitution property
m∠C = 45° = m∠B [tex]{}[/tex] Substitution property
∠C ≅ ∠B [tex]{}[/tex] Definition of congruency
2. Statement [tex]{}[/tex] Reason
m∠X = 4·a + 2 [tex]{}[/tex] Given
m∠Y = 21·a + 3 [tex]{}[/tex] Given
∠X and ∠Y are linear pair [tex]{}[/tex] Given
m∠X + m∠Y = 180° [tex]{}[/tex] Sum of angles of linear pair
4·a + 2 + 21·a + 3 = 180° [tex]{}[/tex] Substitution property
25·a + 5 = 180° [tex]{}[/tex]
a = (180 - 5)/25 = 7
m∠Y = 21 × 7 + 3 = 150° [tex]{}[/tex] Substitution property
m∠Y = 150° > 90
m∠Y is an obtuse angle [tex]{}[/tex] Definition of obtuse angle
3. Statement [tex]{}[/tex] Reason
∠A and ∠B are complementary angles [tex]{}[/tex] Given
∠A + ∠B = 180° [tex]{}[/tex] Definition of complementary angles
∠B and ∠C are complementary angles [tex]{}[/tex] Given
∠B + ∠C = 180° [tex]{}[/tex] Definition of complementary angles
∠B + ∠C = ∠A + ∠B [tex]{}[/tex] Transitive property
∠C = ∠A [tex]{}[/tex] Reverse of addition property of equality
∠C ≅ ∠A [tex]{}[/tex] Definition of congruency
4. Statement [tex]{}[/tex] Reason
ΔMNP is a right triangle [tex]{}[/tex] Given
∠M is a right angle [tex]{}[/tex] Given
∠M + ∠N + ∠P = 180° [tex]{}[/tex] Sum of interior angles of a triangle
∠N + ∠P = 180° - ∠M [tex]{}[/tex] Subtraction property of equality
∠N + ∠P = 180° - 90° = 90° [tex]{}[/tex] Substitution property of equality
∠N + ∠P = 90° [tex]{}[/tex] Substitution property of equality
∠N and ∠P are complementary angles [tex]{}[/tex] Definition of complementary angles.
Given: mZ1= 74
Find the measures of 4, 3, 2, 8, 5, 7, and 6
It would help a lot :D
Write the equation of the line fully simplified slope intercept form.
Answer:
Y=5/2x -4
Step-by-step explanation:
Mary and her family ordered a large pizza for dinner. Half of the pizza is plain and half of the pizza has pepperoni. Mary loves pepperoni so she ate 1/5 of the full pizza (all of which had pepperoni). How much of the remaining full pizza has pepperoni?
Answer:
3/10 of the renaming full pizza has pepperoni
Step-by-step explanation:
Here, we want to calculate how much of the remaining pizza had pepperoni.
From the question, 1/2 has pepperoni and 1/2 is plain without pepperoni
she eats 1/5 of the pizza having pepperoni, this means that she is actually left with some parts is the half having pepperoni
The actual of the half remaining with pepperoni will be 1/2 - 1/5 = 3/10
This means that 3/10 of the remaining full pizza has pepperoni
URGENT: The measure of 8 is 85°
What is the measure, in degrees, of 5?
Answer:
95
Step-by-step explanation:
help so i can finis this already
Answer:
its microwave
Step-by-step explanation:
Answer:
ok so I cant make promises but I think the answer is -11/12
Step-by-step explanation:
I hope its right and I'm sorry if its not
What is the equation in point slope form of the line that passes through the point (3, 1) and has a slope of –2?
Drag and drop the appropriate number, symbol, or variable to each box.
Answer:
y = -2x + 7
Step-by-step explanation:
you can use y–y1=m(x–x1) but I just plug straight into y=mx+b and solve from their (much simpler)so plugging the numbers in y=mx+b it will become 1 = -2(3) + bsimplify so 1 = -6 +b or b – 6 = 1add six to both sides to get b=7slope or m is -2 and b or y-intercept is 7y= -2x+7Integrated math 2 NEED HELP ASAP
Answer:
56
Step-by-step explanation:
Since the 2 triangles are congruent, the ratio of their sides are also equal. Therefore, we can set up an equation:
[tex]\frac{10}{16}=\frac{3x+2}{5x+1}\\\frac{5}{8}=\frac{3x+2}{5x+1}\\5(5x+1)=8(3x+2)\\25x+5=24x+16\\x=11[/tex]
Now that we know x, we can plug in x as 11 into the expression of DE to solve for DE:
5*11+1
=56
what is the lenght of the diagonal of the rectangle
Answer:
P = 2l + 2w
Step-by-step explanation:
The density of gold is 19.3 grams per cubic centimeter. Rachel determines that the density of a coin is 18.7 grams per cubic centimeter. Based on this evidence, she concludes that the coin is not gold or at least not entirely gold. Is this an example of inductive or deductive reasoning?
Answer:
The reasoning is a deductive.
The reason is because the pattern of thought is logical, here, scientific methods ( i.e mathematically obtaining and comparing the density of the coin and the gold ) are used to support the conclusion.
Step-by-step explanation:
Gnerally the reasoning is a deductive.
The reason is because the pattern of thought is logical and scientific methods (eg mathematical equation (formula for density)) are applied to arrive at the conclusion.
The sum of 3 consecutive numbers is 72. What is the largest of these numbers?
23
25
26
28
Answer:
25
Step-by-step explanation:
23+24+25=72
hope i helped!! :)
( if it is right, pls mark brainliest!!)
Answer:
25
Step-by-step explanation:
let x represent the first consecutive number.
let x+1 represent the second consecutive number.
let x+2 represent the third consecutive number.
x + x+1 + x+2 = 72
3x + 3 = 72
3x = 72 - 3
3x = 69
3x/3 = 69/3
x= 23
first number= x = 23
second number = x+1
= 23+1
=24
third number= x+2
=23+2
=25
the largest of these numbers is 25
Help plz okays thanks
Please help!!!
I will give brilliance!!
Answer:
15
Step-by-step explanation:
sqrt 230 = 15.165...
54 equals 9 more than a number $t$ .
Answer:54 = t + 9
Step-by-step explanation:
The area of a square is equal to (n2-14n +49) square units. Find the binomial
that represents the length of the sides of the square?
Marie and Jorge are both trying to lose weight. After 3 months they compared their weight loss. Marie’s weight went from 175 to 150. Jorge’s weight went from 190 to 180. Which statements are true regarding their weight loss? Select three options.
Answer:1,2,3
Step-by-step explanation:
Answer:
1. Jorge’s weight change was approximately 5%.
2.Marie’s weight change was approximately 14%.
3.Marie had the greater percent change.
Step-by-step explanation:
edge 2021
6x + 1 = 6x - 8 what is the value of x
Answer:
No solution
Step-by-step explanation:
6x + 1 = 6x - 8
-6x -6x
1 ≠ -8
PLEASE PLEASE PLEASE HELP
Answer:
its the last choice
Step-by-step explanation:
Answer:
it is the second from the top
Which expression is equivalent to 3^-4*3^6
Answer:
3^2
Step-by-step explanation:
3^-4*3^6
3^-4+6
3^2
Lucia has 18 muffins she splits them evenly among b boxes write an expression that shows how many muffins that are in each box
Your expression would be 18÷b=
please help this is very urgent!!! :((((
Answer:
7
Step-by-step explanation:
x = 2
3x/2+4
3(2)/2 + 4
3+4
7
what are the solutions to this quadratic equation?
x^2+10=0
Answer:
Correct choice: C. [tex]x=\pm\sqrt{10}\mathbf{i}[/tex]
Step-by-step explanation:
The quadratic equation to solve is:
[tex]x^2+10=0[/tex]
Since this equation is incomplete, we can solve it without using the quadratic solver formula.
Subtracting 10:
[tex]x^2=-10[/tex]
Taking square root:
[tex]x=\pm\sqrt{-10}[/tex]
Recall the square root of a negative number leads to imaginary solutions where the Unit Imaginary Number (i) is used, where:
[tex]\mathbf{i}=\sqrt{-1}[/tex]
The solutions to the equation are:
[tex]x=\pm\sqrt{10}\mathbf{i}[/tex]
Correct choice: C. [tex]x=\pm\sqrt{10}\mathbf{i}[/tex]
Answer:
Look at the step by step explanation
Step-by-step explanation:
What is the best estimate of the product 3780 times 2
Answer:
7560
Step-by-step explanation:
I used google calculator
Here are the correct answers for these questions below
A = 028
B = 210
Umm...... Okay then..?
What is 5 x 10^8/4 x 10^5?
Answer:
12500000000000
Step-by-step explanation:
Answer:
5
4
x100100000
Step-by-step explanation:
5x108
4
x105
Simplifies to:
5
4
x100100000
=
5
4
x100100000
what is the slope of the line that goes through the points (2,-1) and (6,1)
Answer: The slope is [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
1. You set up your Slope Formula [tex]M=\frac{y2-y1}{x2-x1}[/tex].
2. Substitue your points into the formula.[tex]M=\frac{1--1}{6-2}[/tex].
3. Once you substitute, you will solve the equation[tex]M=\frac{2}{4}[/tex].
4. Simplify the equation if you have to [tex]M=\frac{1}{2\\}[/tex].
Perform the indicated operation.
5(-3)
Answer:
-15
Step-by-step explanation:
positive x positive = positive
positive x negative = negative
negative x negative = positive
(same goes with division)
Solve C=85x+60 for x
Answer:
it is 85x and I'm only in middle school
Question 2c: Which dog sitting service is better if you need 5 hours of service? Explain your answer PLEASE!
Triangle FUN, with vertices F(−2, 4), U(0, −5), and N(−3, −8) was dilated to form triangle PET with vertices P(−1.6, 3.2), E(0, −4), and T(−2.4, −6.4).Which scale factor was used? A. 1.25
B. −1
C. 2/3
D. 0.8
Suppose these statements about two triangles are
true:∠G=∠S,∠R=∠,and ∠M=∠N. Which statement is correct? Select all that apply.
A.The sides are congruent.
B.The sides are proportional.
C. ΔGRM is similar to ΔNST
D. ΔMGR is similar to ΔNST
Answer:
For first question answer is D.0.8
For second question answer is D.ΔMGR is similar to ΔNST.
Step-by-step explanation:
Here triangle FUN is dilated to get triangle PET
So, let's take F and P.
F(-2,4) and P(-1.6, 3.2)
Let's find the scale factor by dividing the coordinates.
Scale factor =[tex]\frac{-1.6}{-2} =0.8[/tex]
Using y coordinates of the same points
Scale factor =[tex]\frac{3.2}{4} =0.8[/tex]
So, scale factor is 0.8
Now, for the second problem
<G= <S
<R= <T
<M=<N
So, the corresponding angles are congruent when two triangles similar.
So, we can say ΔMGR is similar to ΔNST.
