Answer:
[tex]x=7\text{ and } m\angle KLM = 34^\circ[/tex]
Step-by-step explanation:
We are given ethat KM and JN are parallel.
And we want to find the value of x.
Notice that ∠JKM and ∠LKM form a linear pair. Linear pairs total 180°. Therefore:
[tex]m\angle JKM + m\angle LKM = 180[/tex]
We know that ∠JKM measures (14x + 8). Substitute:
[tex](14x+8)+m\angle LKM =180[/tex]
Solve for ∠LKM:
[tex]m\angle LKM = 172-14x[/tex]
Next, since KM and JN are parallel, by the Corresponding Angles Theorem:
[tex]\angle JNM \cong \angle KML[/tex]
Since we know that ∠JNM measure (10x + 2), we can conclude that:
[tex]m\angle KML = 10x+2[/tex]
Next, recall that the three interior angles of a triangle must total 180°. Therefore:
[tex]m\angle KLM + m\angle LKM + m\angle KML = 180[/tex]
Substitute:
[tex](5x-1)+(172-14x)+(10x+2)=180[/tex]
Solve for x. Rewrite:
[tex](5x-14x+10x)+(-1+172+2)=180[/tex]
Combine like terms:
[tex](1x)+(173)=180[/tex]
Therefore:
[tex]x=7[/tex]
To find ∠KLM, substitute in 7 for x and evaluate. So:
[tex]m\angle KLM = 5(7) - 1 =34^\circ[/tex]
What is the value of the expression below
(-64)^2/3
Answer:
16
Step-by-step explanation:
[tex](-64)^2/3[/tex]
64 = [tex]2^{6}[/tex]
[tex]2^{6} ^{\frac{1}{3} } ^{2}[/tex]
[tex]2^{ 2^{2} }[/tex]
[tex]2^{4}[/tex]
16
Using the number line below, draw a box and whisker plot for the following data: 12,18,18,20,22,22,25,26,30,30,32,32,35,35,38,49,42
Answer:
Step-by-step explanation:
Population size: 17
Median: 30
Minimum: 12
Maximum: 49
First quartile: 21
Third quartile: 35
Interquartile Range: 14
Outliers: none
In the graph increasing, decreasing, or constant?
Answer:
Step-by-step explanation:
slope>0 so graph is increasing.
Using the formula for the area of a triangle, , write an expression for the area of ΔABC. Base your answer on the work you did in parts G through I. Show your work.
Answer:
[tex]Area = \frac{1}{2} * AC * D[/tex]
Step-by-step explanation:
From the complete question, we have:
Length D to be perpendicular to side AC
So, the area of the triangle is:
[tex]Area = \frac{1}{2} * Base * Height[/tex]
Since:
Length D is perpendicular to side AC
Then:
[tex]Base = AC[/tex]
[tex]Heigjt =D[/tex]
So:
[tex]Area = \frac{1}{2} * AC * D[/tex]
translate the sentence into an equation
three more than the quotient of a number and 2 is 9
Answer:
Well the correct answer is 9=2+(x/3) or
(3/x)+2=9
Hi i need help please
Find the volume of this sphere.
Use 3 for TT.
V
11 in
V ~ [?]in3
V= inr3
Answer:
So the volume of a sphere is calculated using the formula: [tex]\frac{4}{3} \pi r^{3}[/tex]
r = the radius = 11 inchesπ = 3.14Substitute in the value of r and solve:
[tex]\frac{4}{3} \pi 11^{3}\\\\=\frac{4}{3} \pi *1331\\\\=\frac{4*3.14*1331}{3}\\\\=5,575.28[/tex]
Jacob went blueberry picking along a 3-mile walking path. He picked blueberries steadily along the walk. When he was finished, he had collected 50 ounces of blueberries.
How many ounces of blueberries did Jacob pick each mile?
Write your answer as a proper fraction or mixed number.
Answer:
16 2/3 ounces per mile
Step-by-step explanation:
50 ounces of blueberries/3 miles = 16.666 repeated
16.666 repeated = 16 2/3 ounces/mile
Helpppp someone please
Given:
The graph of system of inequalities.
To find:
The system of inequalities.
Solution:
From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be [tex]\leq[/tex].
[tex]y\leq 10[/tex].
The shaded region lies on the right side of the y-axis. So, [tex]x\geq 0[/tex].
Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-1=\dfrac{2-1}{1-0}(x-0)[/tex]
[tex]y=1(x)+1[/tex]
[tex]y=x+1[/tex]
The boundary line [tex]y=x+1[/tex] is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be [tex]>[/tex].
[tex]y> x+1[/tex]
So, the required system of inequalities is:
[tex]y> x+1[/tex]
[tex]y\leq 10[/tex]
[tex]x\geq 0[/tex]
Therefore, the correct option is B.
I need help ASAP !!!!
Which number line represents the solution set for the inequality -4(x + 3) 3-2-2x? -7 -6 -5 -4 -3 -2 -1 0 1 G 4 4 4 6 OT 7 -7 -6 -5 -4 -3 -2 -1 3 4 091 6 7 tuum ແຕ່ແຕ່nານານແນານານານານາສາສນາພແ[ -7 -6 -5 -4 -3 -2 -1 0 1 B 5 5 6 T -7 -6 -5 -4 -3 -2 -1 0 1 3 4 A
HURRY!!!!
Answer:
Option (1)
Step-by-step explanation:
Given inequality is,
-4(x + 3) ≤ -2 - 2x
Further solve this inequality,
-4x - 12 ≤ -2 - 2x
-4x + 2x - 12 ≤ -2 - 2x + 2x
-2x - 12 ≤ -2
-2x - 12 + 12 ≤ -2 + 12
-2x ≤ 10
-x ≤ 5
x ≥ -5
Therefore, on a number line draw an arrow starting with a solid circle (because of equal to sign) and moving towards the numbers greater than -5.
Option (1) is the answer.
please help asap
Find the volume of this cone.
Use 3 for TT.
5in
V =
Answer:
V=πr2h /3
V=πr2h /3=π·2.52·8 /3≈52.35988
so the volume is 52.36 inches
Shirley buys fiction books for $20 each, and then marks up by 25% to
resell. What is the markup in dollars?
Answer:
$5
Step-by-step explanation:
Find the markup by finding 25% of 20:
20(0.25)
= 5
So, the markup is $5
Determine the length of AC.
32 units
35.2 units
38.5 units
10.3 units
Answer:
38.5
Step-by-step explanation:
b^2= 29^2+20^2-2×20×29× Cos 102
b^2=841+400-1160 (-0.2079)
=1241- 241.164
b^2=1482.164
b= square root of 1482.164
AC = 38.5
Determine whether each sequence is arithmetic or geometric. Sequence 1: –10, 20, –40, 80, ... Sequence 2: 15, –5, –25, –45, ...
A. Sequence 1 is arithmetic and Sequence 2 is geometric.
B. Both sequences are geometric.
C. Sequence 2 is arithmetic and Sequence 1 is geometric.
D. Both sequences are arithmetic.
sequence 2 may be arithmetic because -20 but I can't find out what sequence 1 is
Answer:
Step-by-step explanation:
C-10,20,-40,80,...[tex] u_{n+1}=(-2)*u_{n}[/tex]. is geometric1
i'm kinda confused in this question, please help me.
Answer:
there you go
Step-by-step explanation:
angle DOB is 60 degree.
Answer:
see explanation
Step-by-step explanation:
Given ∠ DOC = 90° then
∠ DOB = 90 - p and
Since AOB is a straight angle , then
4p + 90 - p = 180
3p + 90 = 180 ( subtract 90 from both sides )
3p = 90 ( divide both sides by 3 )
p = 30
4p = 4 × 30 = 120
Then
∠ DOB = 180° - 4p = 180° - 120° = 60°
An angle in standard position measures 5п 8 radians. In which quadrant does the terminal side of this angle lie? O Quadrant I II Quadrant Quadrant IIT Quadrant IV
Answer:
I've attached a picture of a unit circle with the quadrant labeled.
Calculate the degree of 5п 8 radians:
[tex]\frac{5\pi }{8} =\frac{5*180}{8} =\frac{900}{8} =112.5[/tex]
Locate the general location of 112.5° on the unit circle:
It's between 120°([tex]\frac{2\pi }{3}[/tex]) and 90°([tex]\frac{\pi }{2}[/tex]).
Find the quadrant it lies in:
Quadrant II
find missing side of triangle, help!
Answer:
2√10 km
Step-by-step explanation:
By Pythagoras theorem,
x^2 + 9^2 = 11^2
x^2 + 81 = 121
x^2 = 121 - 81
x^2 = 40
= 4 x 10
x^2 = 2^2 x 10
x = 2√10 km
P(x) is a polynomial. here are a few values of p(x).
P(-5) = - 2
P(-3) = 6
P(3) = 7
P(5) = -1
What is the remainder when P(x) is divided by (x+5)?
What is the remainder when P(x) is divided by (x-3)?
Given:
Values of a polynomial P(x).
[tex]P(-5)=-2[/tex]
[tex]P(-3)=6[/tex]
[tex]P(3)=7[/tex]
[tex]P(5)=-1[/tex]
To find:
The remainder when P(x) is divided by (x+5).
The remainder when P(x) is divided by (x-3).
Solution:
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder is P(-5).
[tex]P(-5)=-2[/tex]
Therefore, the remainder is -2 when P(x) is divided by (x+5).
If the polynomial P(x) is divided by (x-3), then the remainder is P(3).
[tex]P(3)=7[/tex]
Therefore, the remainder is 7 when P(x) is divided by (x-3).
Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate integrating factor. y(6x y 6) dx (6x 2y) dy
Answer:
[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor
Step-by-step explanation:
The correct format for the equation given is:
[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]
By the application of the general differential equation:
⇒ Mdx + Ndy = 0
where:
M = 6xy+y²+6y
[tex]\dfrac{\partial M}{\partial y}= 6x+2y+6[/tex]
and
N = 6x +2y
[tex]\dfrac{\partial N}{\partial x}= 6[/tex]
∴
[tex]f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)[/tex]
[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)[/tex]
[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y)[/tex]
f(x) = 1
Now, the integrating factor can be computed as:
[tex]\implies e^{\int fxdx}[/tex]
[tex]\implies e^{\int (1)dx}[/tex]
the integrating factor = [tex]e^x[/tex]
From the given equation:
[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]
Let us multiply the above given equation by the integrating factor:
i.e.
[tex](6xy+y^2 +6y)dx +(6x +2y)dy=0[/tex]
[tex](6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0[/tex]
[tex]6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0[/tex]
By rearrangement:
[tex]6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0[/tex]
Let assume that:
[tex]6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)[/tex]
and:
[tex]y^2e^xdx +e^x2ydy=d(y^2e^x)[/tex]
Then:
[tex]d(6xe^xy)+d(y^2e^x) = 0[/tex]
[tex]6d (xe^xy) + d(y^2e^x) = 0[/tex]
By integration:
[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor
The graph of g(x) = |x - h1 + k is shown on the
coordinate grid. What must be true about the signs of h
and k?
Answer:
Step-by-step explanation:
D.The sign of h must be negative and the signal of k must be positive *it’s for sure the answer.
Answer:
D.The sign of h must be negative and the signal of k must be positive EDGE 2021
Help
Find the volume of this cone.
Use 3 for TT.
Answer:
[tex]180ft^{3}[/tex]
Step-by-step explanation:
Volume of a cone:
[tex]V=\pi r^{2} \frac{h}{3}[/tex]
Take [tex]\pi[/tex] as 3, as mentioned in the question
'r' is 'radius' ⇒ {diameter is given so divide by 2: 12/2 = 6}
'h' is 'height'
[tex]V=(3)(6)^{2} (\frac{5}{3} )[/tex]
[tex]V=(3)(36)(\frac{5}{3} )[/tex]
[tex]V=108(\frac{5}{3} )[/tex]
{multiply 108 with 5 and then divide the answer by 3}
[tex]V=108[/tex] × [tex]5[/tex]
[tex]V=540[/tex]
[tex]V=540/3[/tex]
[tex]V=180ft^{3}[/tex]
Find the total number of outcomes in each experiment. Write your answers on a sheet of paper.
1. tossing a coin
2. tossing 3 coins
3. rolling a die 10 times
4. rolling two dices
5. pressing a number key on a calculator
6. picking a card from a regular deck of cards
7. choosing a letter from the English alphabet
8. choosing a letter from the word OUTCOME
9. choosing a letter from the word PREDICTION
10. picking a crayon from a box with 36 crayons of different colors
Answer:
Step-by-step explanation:
In each option you need to find the number of outcomes of a single event and then multiply that by the number of times that event takes place.
1. 2 outcomes (heads and tails)
2. 6 outcomes (2 outcomes * 3 tosses)
3. 60 outcomes (6 outcomes per die * 10 rolls)
4. 12 outcomes (6 outcomes per die * 2 rolls)
5. 10 outcomes (10 numbers on the pad)
6. 52 outcomes (52 cards in a regular deck)
7. 32 outcomes (32 letters in the alphabet)
8. 7 outcomes (7 letters to choose from)
9. 10 outcomes (10 letters to choose from)
10. 36 outcomes (36 crayons to choose from)
Expand the following using the Binomial Theorem and Pascal’s triangle (2x − 3y)^4
Answer:
Step-by-step explanation:
Binomial Expansion:
[tex](2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4[/tex]
Pascal's Triangle:
Zero row 1
First row 1 1
Second row 1 2 1
Third row 1 3 3 1
Fourth row 1 4 6 4 1
Determine the area of the triangle.
90.6 square units
50.1 square units
94.2 square units
106.0 square units
Answer:
94.2 square units.
I got 94.09 but that seems to be the closer answer.
a. 32
b. 44
c. 22
d. 8
Answer:
sorry I don't know
Step-by-step explanation:
.........
Proportional relationships between x and y help anyone
Answer:
The table on the right, the green table, is the one that shows a proportional relationship
Step-by-step explanation:
What is the quotient of 23 and 56?
Answer:
0.410714
Step-by-step explanation:
Dividend ÷ Divisor = Quotient
I really need some help with this question also.
A) 2/5
B) 3/5
C) 11/25
D) 14/25
Region A has a total of 81,218,576 acres. Estimate the number of acres owned by the government in Region A. Choose the correct estimate below.
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]Region\ A = 81218576[/tex]
Required
The acres owned by the government
The question is incomplete as the proportion (p) owned by the government is not given.
However, the formula to use is as follows:
[tex]Govt = p * Region\ A[/tex]
Assume the proportion is 28%, the equation becomes
[tex]Govt = 28\% * 81218576[/tex]
[tex]Govt = 22741201.28[/tex]
The acres owned by the government will be 22741201.28
common factors of 8xy⁴,6x²y,10x²y²
Answer:
[tex]2^{3}[/tex]×5×3×[tex]x^{2}[/tex]×[tex]y^{4}[/tex]
Step-by-step explanation:
[tex]8xy^{4}[/tex]= [tex]2^{3}[/tex]×[tex]x[/tex]×[tex]y^{4}[/tex]
6[tex]x^{2} y[/tex]= 2×3×[tex]x^{2}[/tex]×[tex]y^{}[/tex]
10[tex]x^{2} y^{2}[/tex] = 2×5×[tex]x^{2}[/tex]×[tex]y^{2}[/tex]
[tex]2^{3}[/tex]×5×3×[tex]x^{2}[/tex]×[tex]y^{4}[/tex]