Answers
This means that:
measure angle MNJ is equal to measure angle LNK as they are opposite angles.
So,
5x+2 = 3(x+14)
5x+2 = 3x + 42
5x-3x = 42-2
2x = 40
x = 20
Therefore:
measure angle MNJ = 5(20)+2 = 102 degrees
measure angle LNK = 3(20+14) = 102 degrees
You will notice that they are both equal as stated in the beginning.
Related Questions
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
Answers
For 2, due to that 1 and 2 are vertical angles (angles that are opposite to each other when two lines cross according to Math is Fun)
For 3, since ∠1=∠2, ∠1 can be substituted by ∠2 in ∠1+∠5=180 to get ∠2+∠5=180. Therefore, they are supplementary.
For 4, due to that we have Consecutive Interior Angles (they are angles that are on one side of a transversal, which is the line that cuts through a and b,but inside the two lines according to Math is Fun) adding up to 180 degrees, a || b
Feel free to ask if you have any questions!
Two integers with the sum of -17 and the product of 52?
Answers
you have x+y=-17 ---------(1)
xy=52 ---------(2)
from eqn (1) x=-17-y --------(3)
, so subsitute eqn (3) in to eqn(2)
(-17-y)y=52
-17y-y²=52
:
-y²-17y-52=0 same as y²+17y+52=0
y²+13y+4y+52=0
y(y+13)+4(y+13)=0
(y+4)(y+13)=0
therefore y=-4 or -13
now substitute y=-4 or -13 in eqn (3)
x=-17-(-4) or -17-(-13)
x= -13 or -4
so when x=-13 ,y=-4 and when x=-4 ,y=-13
so the integers are -13 and -4
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)
Answers
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.
Which postulate or theorem proves that these two triangles are congruent?
Answers
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 three consecutive odd integers whose sum is negative 465
Answers
465 / 3 = 155
so -153 + -155 + -157 = -465
does anyone know how to do this?
Answers
such that pq=12 and p+q=b
Assuming we're looking for simple values, you can start by factorizing 12:
12 = 3*4 = 2*6 = 12*1 = -3*-4 = -2*-6 = -12*-1
For 3 and 4, b would be 7
2 and 6 => b=8
12 and 1 => b=13
and for the negatives
b can be -7, -8 or -13
So the total set is -13, -8, -7, 7, 8, 13
There are many ways to do this.
X^2+bx+12=0
[tex](-b +- \sqrt{ b^{2} -4*12 } )/2 [/tex]
This equation gives a good answer if
[tex]b ^{2} \geq 48[/tex]
Find the 20th term in arithmetic sequence -4, 1, 6, 11, 16,
Answers
PLZ HELP ILL GIVE A BRAINLIEST SHOW ALL WORK!!!!
Answers
(√3 + 2√3) + √7
Step 2. Simplify
3√3 + √7
That's all.
What is the volume if something measures 6.2 cm x 13.7 cm x 26.9 cm?
Answers
The calculated volume is 2284.886 cubic centimeters.
The volume of a rectangular prism (or box) is calculated using the formula:
Volume = length x width x height
For the given measurements:
Length (l) = 6.2 cmWidth (w) = 13.7 cmHeight (h) = 26.9 cmPlug the values into the formula:
Volume = 6.2 cm x 13.7 cm x 26.9 cm
First, calculate the product of the length and width:
6.2 cm x 13.7 cm = 84.94 cm²
Next, multiply this result by the height:
84.94 cm² x 26.9 cm = 2284.886 cm³
Therefore, the volume of the object is 2284.886 cubic centimeters.
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
Answers
Answer:
SAS Postulate
Step-by-step explanation:
Jesse ate 100 donughts i 5 days each day she ate 6 more then the day before how many did she eat each day
Answers
hoped it helped! :D
You were assigned to read 5⁄8 of your book. how many sixteenths is that? fraction
Answers
You just multiply the numerator and the denominator by 2
Hope I helped :)
Please help with these questions thank you.
Answers
2. B
3.A
these should be correct
Find the value of x so that the line passing through (10, 5) and (x, 9) has a slope of -2.
Answers
(y2 - y1)/(x2-x1)
y2 = 9
y1 = 5
x2 = x
x1 = 10
So:
(9-5)/(x-10) = -2
Now, we just solve for x,
9-5 = -2(x-10)
4 = -2x+20
2x = 16
x = 8
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?
Answers
original water content= 32*75/100=24 grams
original sugar content= 32*25/100= 8grams
total mass at 10% syrup:
8grams/total mass=10%=0.1
total mass=8/0.1=80grams
total mass of water=80grams- 8grams of sugar content= 72 grams
total mass of water added=72grams- 24grams original water content= 48grams.
answer: 48grams
25%+0%=10%
32g xg (32+x)g
Now, we create an equation:
(0.25^32)+(0^x)=0.1^(32+x)
8+0=3.2+0.1x
8=3.2+0.1x
4.8=0.1x
48=x
Answer: 48 gram.
Solve x ym = y x3 for m.
Answers
xym (1-1x2) = 0
xym (1 (un cuadrado)-1x2)=0
xym(1+x)(1-x)=0
1+x=0
1-x=0
m= 0
x=-1
x=1
Is true
m=0;x= -1;1
The point MegaMarket sold 450 organic pears last season. this season they only sold 360 What was the percent decrease in sales
Answers
450 - 360 = 90
Next, you would need to create an equation to determine what percentage 90 is of 450. Let x represent the unknown sales decrease percentage.
[tex] \frac{90}{450} [/tex] = [tex] \frac{x}{100} [/tex]
Cross multiply.
450x = 9,000
Now, all you would need to do is isolate the x. To do this, you would divide both sides of the equal sign by 450.
x = 20
x = 20%
The percent decrease was 20%.
I hope this helps!
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?
Answers
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
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
Answers
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.
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
Answers
Recalling the effected car and fixing the issue
Answer:
introducing customer retention strategies
Step-by-step explanation:
Which of the sets of ordered pairs represents a function? (4 points)
A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}
you can do both or neither as well THX
Answers
If f(x)=5x^0+4x^-3 then f(a)=?
Answers
f(a)=5(a^0)+4a^-3 a^0=1
=5(1)+4/a^3
=5+4/(a^3)
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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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.
Answers
y + 4 = -3(x - 2)
We can convert this to Slope-Intercept Form by isolating y.
y + 4 = -3(x - 2)
y + 4 = -3x + 6
Subbtract 4 from both sides.
y = -3x + 2
The equation in Slope-Intercept Form is y = -3x + 2.
Which ordered pair comes from the table ? HELPPP!
Answers
What is the value of N?
-10= N over -0.2
Answers
Find the 31st term of the following sequence.
9, 15, 21, ...
Answers
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:
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?
Answers
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]
given a line whose slope is, m, is -6/5, and passes through point (-5,3), the graph will?
Answers
y₁ = 3; x₁ = -5; m = [tex]- \frac{6}{5} [/tex]
⇒ y - 3 = [tex]- \frac{6}{5} [/tex] ( x - (-5))
⇒ y - 3 = [tex]- \frac{6}{5} [/tex] (x + 5)
Now, you can approach here in two ways: put it in the y-intercept form or the general form.
In the y-intercept form;
y - 3 = [tex]- \frac{6}{5} [/tex]x + ([tex]- \frac{6}{5} [/tex] (5))
y - 3 = [tex]- \frac{6}{5} [/tex]x - 6
y = [tex]- \frac{6}{5} [/tex]x - 3
In the general form;
y - 3 = [tex]- \frac{6}{5} [/tex] (x + 5)
by multiplying through by 5
⇒ 5 ( y - 3 ) = -6 ( x + 5)
⇒ 5y - 15 = -6x - 30
⇒ 5y + 6x = -15
∴ the line that passes through (-5, 3), with gradient [tex]- \frac{6}{5} [/tex] is
y = [tex]- \frac{6}{5} [/tex]x - 3 (y-intercept form) OR 5y + 6x = -15 (general form).
i need someones help please?
Answers
m = slope
plug in 1 and -7 to it's respective places
y (-7) = -2/3(x + 1)
D is your answer
hope this helps
The answer would be y+7= -2/3(x-1)
Hope this helps!
Which postulate or theorem proves that △JHG and △EFG are congruent?
SAS Congruence Postulate
ASA Congruence Postulate
HL Congruence Theorem
AAS Congruence Theorem
Answers
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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