Given:
AC = BC
∠3 = ∠4
Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove that triangle ACM is congruent to triangle BCM. If it is not possible to prove the triangles are congruent, choose "not possible".
Choices:
SSS
SAS
ASA
not possible
Answer:
SAS Postulate
Step-by-step explanation:
Find three consecutive odd integers whose sum is negative 465
465 / 3 = 155
so -153 + -155 + -157 = -465
Two integers with the sum of -17 and the product of 52?
Emily has 32 grams of a 25% sugar syrup, but this is just too sweet for her! How much pure water should she add to have a 10% syrup?
Find the 31st term of the following sequence.
9, 15, 21, ...
Notice that the above sequence is arithmetic because the common difference: d is constant.
d = second term - first term.
= 15 - 9
= 6
The general term of an arithmetic sequence is,
a_{n} =a_{1} +(n-1)d
Where , nth term = [tex] a_{n} [/tex]
[tex] a_{1} [/tex] = First term
and d = common difference.
The given sequence is: 9, 15, 21, ...
Here a_{1} = 9,
d = 6
We need to find the 31st term. So, n = 31.
Next step is to plug in these values in the above formula. Therefore,
[tex] a_{31} =9 +(31-1)*6 [/tex]
= 9 + 30* 6
= 9 + 180
= 189
So, 31st term of this sequence is 189.
Hope this helps you.
Answer:
189
Step-by-step explanation:
The length of a rectangular plot of land is 10 yards more than its width. If the area of the land 600 square yards , find the dimensions
Final answer:
The dimensions of the rectangular plot of land, where the length is 10 yards more than its width and the area is 600 square yards, are 20 yards by 30 yards. We arrived at this by setting up a quadratic equation and solving for the width.
Explanation:
To find the dimensions of a rectangular plot of land where the length is 10 yards more than its width and the area is 600 square yards, we can set up an equation. Let w be the width of the plot. Then the length is w + 10 yards. The area of a rectangle is given by the formula length × width, which in our case is (w + 10) × w = 600.
Setting up the equation, we get:
w(w + 10) = 600
w^2 + 10w - 600 = 0
To solve the quadratic equation, we can factor it, use the quadratic formula, or complete the square. Factoring the equation, we find that:
(w - 20)(w + 30) = 0
Thus, the width w can be either 20 yards or -30 yards. Since a width cannot be negative, we take w = 20 yards. Then, the length is:
w + 10 = 20 + 10 = 30 yards
The dimensions of the rectangular plot of land are 20 yards by 30 yards.
Find the 20th term in arithmetic sequence -4, 1, 6, 11, 16,
The point MegaMarket sold 450 organic pears last season. this season they only sold 360 What was the percent decrease in sales
MATH PLEASE HELP 50 POINTS 1 QUESTION
Complete the reasons in the proof below.
Given: ∠1 and ∠5 are supplementary.
Prove: a ∥ b
Statements
1. ∠1 and ∠5 are supplementary
2. ∠1 ≅ ∠2
3. ∠2 and ∠5 are supplementary
4. a ∥ b
i need someones help please?
Merry and pippin were working on a project in carpentry class. they needed to cut 4 lengths of 1 5/8 feet from a board. how long must the board be to allow this?
Answer:
Hence, the length of board is:
6.5 feet
Step-by-step explanation:
Merry and pippin were working on a project in carpentry class.
They needed to cut 4 lengths of 1 5/8 feet from a board.
That means each of the piece is of length 1 5/8 feet which could be written in fraction as:
[tex]1\frac{5}{8}=\dfrac{13}{8} feet[/tex]
Hence, the otal length of the board is addition of length of each board.
i.e.
[tex]\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}=4\times \dfrac{13}{8}=\dfrac{13}{2}feet=6.5feet[/tex]
Hence, the length of board is:
6.5 feet
PLZ HELP ILL GIVE A BRAINLIEST SHOW ALL WORK!!!!
Given that a line has a slope of -3 and a point on the line is (2,-4),
1.what is the equation of the line in point-slope form?
2.how do we create slope-intercept form?
*please show all work, step by step.
PLEASE HELP!!!! WILL MARK THE BRAINLIST!!!! PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE
a) The shoe store manager borrowed $17,000.00 from the bank to purchase 1000 pairs of shoes. The bank charges a simple interest rate of 5% per year on a loan to a business. If it takes 3 years to pay back the loan and interest, what is the total amount of interest that the shoe store will pay? (2 points)
b) What is the total amount, including interest, that the shoe store must pay on the loan? (2 points)
c) How could you use estimation to determine if your answer is reasonable? Explain. (2 points)
A) 17000*(1+(0.05*3) = 19550
19550-1700 = $2,550 total interest
B) $19,550 total amount
C) multiply 5 by 3 = 15 than multiply by 17 = 17 * 15 = 255 , then make it a thousands amount by adding a zero at the end
Answer:
A)
p = 17000
r = 5% or 0.05
t = 3
Simple interest formula = p x r x t
Interest paid in 3 years = [tex]17000\times0.05\times3=2550[/tex] dollars
B)
Total amount to be paid = [tex]17000+2550=19550[/tex] dollars
C)
You can first multiply the years and rate that is 5 and 3 to make 15. Then you can multiply by 17. Then put proper decimals as per the values.
Jesse ate 100 donughts i 5 days each day she ate 6 more then the day before how many did she eat each day
Which postulate or theorem proves that △JHG and △EFG are congruent?
SAS Congruence Postulate
ASA Congruence Postulate
HL Congruence Theorem
AAS Congruence Theorem
The postulate that proves that △JHG and △EFG are congruent is;
Option B; ASA Congruence Postulate
From the given image, we can see two triangles namely;
△JHG and △EFG
Now, we can see that;
FG = GH
That is given because we see that G has divided FH into 2 equal parts.
Also, we see the right angle sign at ∠F and ∠H of both triangles.
Thus, since they are both right angles, then we can say that;
∠EFG = ∠JHG
Also, at point G, we have two vertically opposite angles which are;
∠EGF and ∠JGH
Now, from vertically opposite angle theorem, vertically opposite angles are always equal;
Thus; ∠EGF = ∠JGH
So far, we have;
FG = GH
∠EFG = ∠JHG
∠EGF = ∠JGH
This is 2 corresponding equal angles and 1 corresponding equal side. The side is included between the two angles and as such the proof that △JHG and △EFG are congruent is the ASA Congruence Postulate.
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Which postulate or theorem proves that these two triangles are congruent?
Answer:
option B
Step-by-step explanation:
Given in the question are ∠x ≅ ∠y and ∠zwx ≅ ∠ ywz and wz is common in both.
These angles are adjacent angles of triangles.
We know theorem for congruence is Angle - Angle - Side
Therefore, for the congruence of these two triangles option B, AAS congruence theorem is the answer.
Find the value of x so that the line passing through (10, 5) and (x, 9) has a slope of -2.
You were assigned to read 5⁄8 of your book. how many sixteenths is that? fraction
Each of ten tickets is marked with a different number from 1 to 10 and put in a box. if you draw a ticket from the box, what is the probability that you will draw 2, 8, or 4?
Answer: [tex]\dfrac{3}{10}[/tex]
Step-by-step explanation:
Given : Each of ten tickets is marked with a different number from 1 to 10 and put in a box.
i.e. The total number of outcomes : 10
Favorable outcomes : 2, 8, or 4
i.e. Number of favorable outcomes = 3
Now, the probability that you will draw 2, 8, or 4 is given by :-
[tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}\dfrac{3}{10}[/tex]
What is the value of N?
-10= N over -0.2
An automobile manufacturing organization noted a drop in sales after an incident occurred due to the lack of a safety feature in their cars. Many customers began considering other brands of cars after this incident. How can the organization avoid losing customers
Answer:
introducing customer retention strategies
Step-by-step explanation:
given a line whose slope is, m, is -6/5, and passes through point (-5,3), the graph will?
If f(x)=5x^0+4x^-3 then f(a)=?
To find f(a) for the given function, substitute a for x in the function and simplify the expression.
Explanation:Given the function f(x) = 5x0 + 4x-3, we need to find f(a). To find f(a), we substitute a for x in the function. Plugging in a, we get f(a) = 5a0 + 4a-3. Since any number raised to the power of 0 is equal to 1, we have f(a) = 5(1) + 4a-3. Simplifying further, we get f(a) = 5 + 4/a3.
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Which expression is a perfect cube?
A. -8x21y8
B. -64x64y64
C. -125x9y20
D. -216x9y18
does anyone know how to do this?
Please help with these questions thank you.
Solve x ym = y x3 for m.
The inequality x2 + 12x + 35 ≥ 0 has two critical points and three possible intervals for solutions. Choose each set of possible test points for the three intervals.
–8, –6, –4
–10, –6, 0
–6, 0, 6
–6, 0, 10
-8,-6,-4
-10,-6,0
these are the possible test points for your three intervals
The given inequality is, x² + 12 x+35≥0
→ x²+7 x +5 x+5×7≥0
→ x (x+7) +5(x+7)≥0
→ (x+5)(x+7)≥0
→ x+5=0 ∧ x+7=0 gives x= -7 ∧ x= -5
Now drawing the number line and marking point ,-5 and -7 on it.
Now the three intervals are (-∞ , -7], [-7,-5] and [-5,∞).
The solution set of inequality (x+5)(x+7)≥0 is (-∞ , -7] and [-5,∞).
The set of possible test points for
⇒ (-∞ , -7] → -8, -10
⇒ [-7,-5] → -6
⇒ [-5,∞) → -4, 0
Option (1) -8,-6,-4 and Option (2) -10,-6,0 satisfies the given condition.
Which ordered pair comes from the table ? HELPPP!