I need the steps to this, please. It says solve for x. Each figure is a parallelogram. Show your work.
Answers
FH is one diagonal that is split into two equal pieces by the other diagonal EG.
The two parts of FH (KH and KF) are congruent to each other, so KH = KF. They combine back to FH
By the segment addition postulate
KH + KF = FH
KH + KH = FH .... KF has been replaced with KH (works because KF = KH)
2*KH = FH
Now use substitution
2*KH = FH
2*15 = FH .... replace KH with 15 (since KH = 15)
2*15 = 4x-2 ... replace FH with 4x-2 (since FH = 4x-2)
and solve for x
2*15 = 4x-2
30 = 4x-2
30+2 = 4x-2+2 ... add 2 to both sides
32 = 4x
4x = 32
4x/4 = 32/4 ... divide both sides by 4
x = 8
----------------------------------------
----------------------------------------
Answer: x = 8
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Two lines that do not intersect are parallel.alwayssometimesnever
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How to solve more complex problems involving angles the backwards Method
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Simplify 2y^2-7y-15/3y^2-8y-2 9y^2-1/4y^2-9 / y^2+3y-10/2y^2-9y+9
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Please help me with 18 and 19
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What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?
Enter your answer in the box. Do not round any side lengths.
Answers
AB=4-1=3
BC=√((7-4)²+(2-(-2))²)=√(9+16)=√25=5
CD=BC=5
DE=4-1=3
AE=6-(-2)=8
Perimeter=3+5+5+3+8=24.
Using the distance formula, the perimeter of the polygon that has the given vertices is calculated as: 24 units.
What is the Perimeter of a Polygon?
Perimeter = sum of all sides of the polygon.
Name the vertices as follows:
A(−2, 1)B(−2, 4)C(2, 7)D(6, 4) E(6, 1)Perimeter of the polygon = AB + BC + CD + DE + EA
Use the distance formula, [tex]d = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find the length of each segment:
AB = |1 - 4| = 3 units
BC = √[(2−(−2))² + (7−4)²]
BC = 5 units
CD = √[(2−6)² + (7−4)²
CD = 5 units
DE = |4 - 1| = 3 units
EA = |6 - (-2)| = 8 units
Perimeter of the polygon = 3 + 5 + 5 + 3 + 8
Perimeter of the polygon = 24 units
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If 15% of x is 42, what is x?
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[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 42&15 \end{array}\implies \cfrac{x}{42}=\cfrac{100}{15}\implies x=\cfrac{42\cdot 100}{15}[/tex]
3/20x=42
x= 42* 20/3 (reciprocal)
x=14*20
x=406
MARTIN CHARGES $10 FOR EVERY 5 BAGES OF LEAVES HE RAKES. LAST WEEKEND, HE RAKED 24 BAGES OF LEAVES. HOW MUH MONEY DID HE AERN
Answers
The game of clue involves 6 suspects, 6 weapons, and 9 rooms. one of each is randomly chosen and the object of the game is to guess the chosen three. (a) how many solutions are possible? in one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards. let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. also, let x denote the number of solutions that are possible after that player observes his or her three cards. (b) express x in terms of s, w, and r. (c) find e[x].
Answers
Given that the game of clue involves 6 suspects, 6 weapons, and 9 rooms.
The number of ways that one of each is randomly chosen is given by:
[tex] ^6C_1\times{ ^6C_1}\times{ ^9C_1}=6\times6\times9=324[/tex]
Therefore, the number of solutions possible is 324.
Part B:
Given that a players is randomly given three of the remaining cards, let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player.
The number of suspects, weapons, and rooms remaining respectively after the player observes his or her three cards are: 6 - s, 6 - w, and 9 - r.
Let x denote the number of solutions that are possible after that player observes his or her three cards, then:
[tex]x={ ^{6-s}C_1}\times{ ^{6-w}C_1}\times{ ^{9-r}C_1}=(6-s)(6-w)(9-r)[/tex]
Therefore, x in terms of s, w, and r is given by x = (6 - s)(6 - w)(9 - r).
Part C:
The expected value E(x) of a data set [tex]x_i[/tex] with probabilities [tex]p(x_i)[/tex] is given by [tex]E(x)=\Sigma xp(x)[/tex]
There are [tex] ^{3+3-1}C_{3-1}={ ^5C_2}=10[/tex] possible combinations s, w and r. They are (3, 0, 0), (0, 3, 0), (0, 0, 3), (2, 1, 0), (0, 2, 1), (1, 0, 2), (2, 0, 1), (1, 2, 0), (0, 1, 2), (1, 1, 1)
Thus the expected value is given by
[tex]E(x)=3\cdot6\cdot9p(3, 0, 0)+6\cdot3\cdot9p(0, 3, 0)+6\cdot6\cdot6p(0, 0, 3) \\ 4\cdot5\cdot9p(2, 1, 0)+6\cdot4\cdot8p(0, 2, 1)+5\cdot6\cdot7p(1, 0, 2)+4\cdot6\cdot8p(2, 0, 1) \\ +5\cdot4\cdot9p(1, 2, 0)+6\cdot5\cdot7p(0, 1, 2)+5\cdot5\cdot8(1, 1, 1) \\ \\ = \frac{1}{ ^{21}C_3} (162\cdot{ ^6C_3}\cdot{ ^6C_0}\cdot{ ^9C_0}+162\cdot{ ^6C_0}\cdot{ ^6C_3}\cdot{ ^9C_0}+216\cdot{ ^6C_0}\cdot{ ^6C_0}\cdot{ ^9C_3} \\ \\ +180\cdot{ ^6C_2}\cdot{ ^6C_1}\cdot{ ^9C_0}+192\cdot{ ^6C_0}\cdot{ ^6C_2}\cdot{ ^9C_1}[/tex]
[tex]+210\cdot{ ^6C_1}\cdot{ ^6C_0}\cdot{ ^9C_2}+192\cdot{ ^6C_2}\cdot{ ^6C_0}\cdot{ ^9C_1}+180\cdot{ ^6C_1}\cdot{ ^6C_2}\cdot{ ^9C_0} \\ \\ +210\cdot{ ^6C_0}\cdot{ ^6C_1}\cdot{ ^9C_2}+200\cdot{ ^6C_1}\cdot{ ^6C_1}\cdot{ ^9C_1} \\ \\ =\frac{1}{1,330}(324\cdot20+216\cdot84+360\cdot90+384\cdot135+420\cdot216+200\cdot324) \\ \\ =\frac{1}{1,330}(6,480+18,144+32,400+51,840+90,720+64,800) \\ \\ =\frac{1}{1,330}(264,384) \\ \\ =\bold{198.78}[/tex]
Answer:
(a) 324 solutions are possible
(b) (6 - s)(6 - w)(9 - r)
(c) 198/78
Step-by-step explanation:
Just a pure guess and also give brainliest to the other person
Bill weighs 120 lbs and is gaining ten lbs each month. Phil weighs 150 lbs and is gaining four lbs each month. How many months will it take for bill to wiegh the same as phil?
Answers
Bill: 120 + 10x
Phil: 150 + 4x
If we set them equal to each other, then solve for x, that will be the number of months where their weights equal each other:
120+10x = 150 + 4x [starting equation]
-120 -4x -120 -4x [ subtract 120 from both sides, and 4x from both sides, to isolate the term with the variable]
6x = 30 [divide both sides by 5]
5 5
x=6. They will weigh the same in six months.
Algebraic equations are equations that contain variables that are unknown. These unknown variables are represented by any letters of the Alphabet.
it will take 5 months for Bill to weigh the same as Phil.
Let's represent the number of months they gain extra weight as: m
Step 1
Bill weighs 120 lbs and is gaining ten lbs each month. The algebraic equation for the above statement is :
120 ib + 10 ib x m
120 + 10m ........Equation 1
Phil weighs 150 lbs and is gaining four lbs each month. The algebraic equation for the above statement is :
150 ib + 4 ib x m
150 + 4m ........Equation 2
Step 2
We equate equations 1 and 2 to each other
Equation 1 = Equation 2
120 + 10m = 150 + 4m
Collect like terms
10m - 4m = 150 - 120
6m = 30
Divide both sides by 6
6m/6 = 30/6
m = 5
Therefore, it will take 5 months for Bill to weigh the same as Phil
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Help
simply. this math problem
Answers
- 4 1/5 = -21/5 = -42/10
-13 1/10 = -131/10
-42/10 - -131/10=
-42/10 + 131/10 = 89/10 = 8 9/10
answer is A
Deshawn has several dimes and quarters that total $2.05. he has 3 fewer quarters than dimes. how many of each doe he have
Answers
x = the number of dimes
y = the number of quarters
The total sum is $2.05, therefore
0.10x + 0.25y = 2.05
Divide through by 0.05 to obtain
2x + 5y = 41 (1)
There are 3 fewer quarters than dimes, therefore
y = x - 3 (2)
Substitute (2) into (1).
2x + 5(x - 3) = 41
2x + 5x - 15 = 41
7x = 56
x = 8
y = x - 3 = 5
Answer: 8 dimes, 5 quarters
Round 256 and 321 ( need to when rounding in the hundreds place do we not change the entire number?
Answers
If they are whole numbers, rounded to the hundreds place would be 300 for both. Rounded to two digits would be 260 and 320, respectively.
Please clarify what you mean.
Carl is boarding a plane. He has 2 checked bags of equal weight and a backpack that weighs 4 kg. The total weight of Carl's baggage is 35kg. Write an equation to determine the weight, w ww, of each of Carl's checked bags. Find the weight of each of his checked bags.
Answers
2+4b=35
35-2=33
33/4=8.25kgs
Answer:
15.5 kg (each)
Step-by-step explanation:
Let [tex]w[/tex] be the weight of each checked bag (there are 2). Thus, we can write, from the information given:
[tex]w+w+4=35\\2w+4=35[/tex]
Now we solve this equation for [tex]w[/tex] to find weight of each checked bag:
[tex]2w+4=35\\2w=35-4\\2w=31\\w=\frac{31}{2}\\w=15.5[/tex]
So, the weight of each of his checked bags is 15.5 kg.
If an employer spends $30,000 for weight-lifting equipment for the company gym. The company charges $100 a year to each employee who wants to buy a gym pass. The pass is for an unlimited amount of uses. There are 50 employees that work for this company. How many years will it take to pay off the weight-lifting equipment if half of the employees buy the gym pass each year?
Answers
half of 50 is 25
25 *100 = 2500 a year
30,000 / 2500 = 12
it will take 12 years
Determine the axis of symmetry the vertex and the x-and y intercepts f(x)=x2+2x-3
Answers
The x- and y intercepts is: x- intercept: (1,0),(-3,0)
y intercept: (0,-3)
Hope this helps!:)
The x- and y intercepts is: x- intercept: (1,0),(-3,0)
y intercept: (0,-3)
If I put $1500 into my savings account in earned $180 of an interest at 4% simple interest how long was my money in the bank
Answers
It took Leo 3.5 hours to complete a route walking at a rate of 4.2 mph. How long would it take Leo to complete the same route walking at a rate of 2.8 mph?
plz give exact answer
Answers
3.5 hrs * 4.2 mph = 14.7 mi
t = S/V
14.7 mi/ 2.8 mph = 5.25 hrs
What is a security deposit
Answers
Write the following statement as a conditional. All flowers are beautiful.
Answers
A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 minutes. after treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 minutes and a standard deviation of 42.3 minutes (based on data from cognitive behavioral therapy vs zopiclone for treatment of chronic primary insomnia in older adults," by silverstein et al., journal of the american medical association, vol. 295, no. 24). assume that the 16 sample values appear to be from a a normally distributed population and construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments. what does the result suggest about the mean wake time of 102.8 minutes before the treatment
Answers
To construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments, use the formula: Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size).
Explanation:To construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments, we can use the formula:
Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size)
Given that the sample mean after treatment with zopiclone is 98.9 minutes, the standard deviation is 42.3 minutes, and the sample size is 16, we need to find the critical value for a 98% confidence level. The critical value can be found using a t-distribution table or calculator.
Once the critical value is obtained, we can plug in the values into the formula to calculate the confidence interval estimate.
Solve 4(c + 2) < 4c + 10.
Answers
4c + 8 < 4c + 10
4c - 4c < 10 - 8
0 < 2...no variables
this inequality has no solution
[tex]4c+8\ \textless \ 4c+10 [/tex]
[tex]8\ \textless \ 10 [/tex] [tex]\text{Cancel 4c on both sides}[/tex]
[tex]\text{Since}[/tex] [tex]8\ \textless \ 10 [/tex] [tex]\text{is always true, there are infinitely many solutions}[/tex]
In triangle JKL, if line JK is equal to line JL, angle J equals 23x-4, angle K equals 4x-1, and angle L equals 9x-31, find x and the measure of each angle.
Answers
Equation: 4x - 1 = 9x - 31
Solved: x = 6
Angle measures: ∡J = 23(6) - 4 = 138 - 4= 134
∡K = ∡L = 23
m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° is the answer.
From the figure attached,
JK and JL are equal sides of the triangle.m(∠J) = 23x - 4m(∠K) = 4x - 1m(∠L) = 9x - 31Since, two sides JK and JL of ΔJKL are equal in measure,
Therefore, ΔJKL is an isosceles triangle.
By the property of an isosceles triangle, opposite angles of the equal sides are equal.
Therefore, m(∠K) = m(∠L)
4x - 1 = 9x - 31
9x - 4x = 31 - 1
5x = 30
x = 6
By substituting the value of 'x' in the measures of each angle,
m(∠J) = 23x - 4
= 23(6) - 4
= 138 - 4
= 134°
m(∠K) = 4x - 1
= 4(6) - 1
= 24 - 1
= 23°
m(∠L) = 9x - 31
= 9(6) - 31
= 23°
Therefore, m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° will be the answer.
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What is the value for ƒ(x) = 4²ˣ - 100 when x = 2 ?
Answers
__________________________________________
Given: f(x) = 4^(2x) - 100 ;
__________________________________________
When "x = 2" ;
f(2) =4^(2*2) - 100 = [4^(4) ] - 100 ;
= (4* 4 * 4 * 4) - 100 ;
= (16 * 4 * 4) - 100 ;
= (64 * 4) - 100 ;
= (256) - 100 ;
= 156 .
____________________________________
Answer:
f(x)=156
Step-by-step explanation:
Choose the abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent.
Given:
∠C, ∠F are rt.∠'s; AC = DF; BC = EF
Answers
The two legs, ie the sides adjacent to the right angle, for the two triangles are also given to be congruent to one another
leg AC = leg DF
leg BC = leg EF
Because we have two pairs of legs congruent for these two triangle triangles, we use the Leg Leg Theorem which abbreviates to the LL Theorem, or simply LL.
This is why the answer is choice B) LL
Answer:
LA
Step-by-step explanation:
Odyssey
Write an additional word problem in which the estimated sum is 14,000
Answers
7,000 + 7,000 = 14,000
The problem is about estimating the total sales sum of 7 TVs sold in a day, each priced at approximately $2,000, which gives us a total estimate of $14,000.
Explanation:The mathematics problem could be something along the lines of this: In a local electronics store, 7 high-definition smart TVs were sold in one day. If each TV is approximately priced at $2,000, what is the estimated total sales sum for that day?
First, analyze the problem. We want to find the estimated total sales sum for the smart TVs.Then, we use estimation to solve it. We know each TV costs around $2,000 and that 7 TVs were sold.Just multiply $2,000 by 7. Thus, $2,000 * 7 = $14,000So, the estimated sum is $14,000This estimation gives us a total sum of $14,000, which is close to the actual total if each TV is priced at $2,000.
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does velocity or mass impact momentum more and why
Answers
Both mass and velocity equally affect momentum in classical physics. However, at relativistic speeds, velocity has a more significant effect on momentum due to relativistic mass increase.
Explanation:The impact of mass and velocity on momentum depends on the context of the object's motion. In classical physics, momentum is defined as the product of an object's mass and velocity, thus both mass and velocity equally influence momentum. However, for objects moving at relativistic speeds—approaching the speed of light—the effect of velocity on momentum is more pronounced due to the relativistic mass increase. To illustrate, a football player with greater mass has a larger impact due to having more momentum when moving at the same velocity as a player with less mass. In contrast, at relativistic speeds, an increase in velocity would result in an exponentially greater momentum, surpassing the effect of just increasing mass.
The profits of a company are found by subtracting the company's costs from its revenue. If a company's cost can be modeled by 14x + 120,000 and its revenue can be modeled by 40x - 0.0002x^2, what is an expression for the profit?
Answers
The profit function is given by [tex]\( P(x) = -0.0002x^2 + 26x - 120,000 \).[/tex]
To find the expression for the profit, we need to subtract the cost function from the revenue function.
Given:
Cost function: [tex]\( C(x) = 14x + 120,000 \)[/tex]
Revenue function: [tex]\( R(x) = 40x - 0.0002x^2 \)[/tex]
The profit function, ( P(x) ), is given by:
[tex]\[ P(x) = R(x) - C(x) \][/tex]
Substitute the given functions into the profit function:
[tex]\[ P(x) = (40x - 0.0002x^2) - (14x + 120,000) \][/tex]
Now, let's simplify:
[tex]\[ P(x) = 40x - 0.0002x^2 - 14x - 120,000 \][/tex]
[tex]\[ P(x) = 26x - 0.0002x^2 - 120,000 \][/tex]
This is the expression for the profit:
[tex]\[ {P(x) = -0.0002x^2 + 26x - 120,000} \][/tex]
So, the profit function is given by [tex]\( P(x) = -0.0002x^2 + 26x - 120,000 \).[/tex]
Graph each line y -7 = x + 4
Answers
We should rewrite the equation in "slope-intercept form" ; that is:
" y = mx + b " ;
______________________
in which: "y" remains an isolated variable on the "left-hand side" of the equation (with "no coefficients"—except the "implied coefficient of "1"
{since "1" , multiplied by any value, results in that same value} ;
"m" refers to the "slope" of the line;
and "m" is the coefficient of "x" ;
"b" refers to the "y-intercept" of the graphed (linear) equation; or more precisely, the value of "y" of the coordinate of the [ point on the graphed line of the equation—where the line crossed the "y-axis" ] ; that is; the "y-coordinate of the "y-intercept" ; that is, the value of "y" when "x = 0" ;
______________________________________________________
{Note that: "m" (the slope) may be a negative value; & that: "y" may be a negative value; as regard to the "slope-intercept form" equation:
that is:
"y = mx + b" . }.
______________________________________________________
So; given the equation:
______________________________________________________
" y − 7 = x + 4 " ;
______________________________________________________
Add "7" to each side of the equation;
to isolate "y" on one side of the equation;
→ {specifically, the "left-hand-side" of the equation} ;
and to rewrite the equation in "slope-intercept form" ; that is;
→ to rewrite the equation in the format:
" y = mx + b " ;
_______________________________________________________
As such: "y − 7 = x + 4 " ;
_______________________________________________________
→ Add "7" to each side of the equation:
_______________________________________________________
→ y − 7 + 7 = x + 4 + 7 ;
to get:
_______________________________________________________
→ y = x + 11 ;
_______________________________________________________
Now, let us graph the equation:
_______________________________________________________
Let us make a table:
_______________________________________________________
x ║ (x + 11) ║ y ║
_______________________________________________________
-20 ║ (-20 + 11) ║ -9 ║
-19 ║ (-19 + 11) ║ -8 ║
-18 ║ (-18 + 11) ║ -7 ║
-17 ║ (-17 + 11) ║ -6 ║
-16 ║ (-16 + 11) ║ -5 ║
-15 ║ (-15 + 11) ║ -4 ║
-14 ║ (-14 + 11) ║ -3 ║
-13 ║ (-13 + 11) ║ -2 ║
-12 ║ (-12 + 11) ║ -1 ║
-11 ║ (-11 + 11) ║ 0 ║
-10 ║ (-10+ 11) ║ 1 ║
-9 ║ (-9 + 11) ║ 2 ║
-8 ║ (-8 + 11) ║ 3 ║
-7 ║ (-7 + 11) ║ 4 ║
-6 ║ (-6 + 11) ║ 5 ║
-5 ║ (-5 + 11) ║ 6 ║
-4 ║ (-4 + 11) ║ 7 ║
-3 ║ (-3 + 11) ║ 8 ║
-2 ║ (-2 + 11) ║ 9 ║
-1 ║ (-1 + 11) ║ 10 ║
0 ║ (0 + 11) ║ 11 ║
1 ║ (1 + 11) ║ 12 ║
2 ║ (2 + 11) ║ 13 ║
3 ║ (3 + 11) ║ 14 ║
4 ║ (4 + 11) ║ 15 ║
5 ║ (5 + 11) ║ 16 ║
_________________________________________________
Now, we plot these points on a graph, and draw a line through these points; the slope is "1" ; since the equation is:
" y = x + 11 " ; Note: The slope, "m", is "1", since there is an "implied coefficient of "1" ; i.e. " y = 1x + 11 " .
___________________________________
Graph of: "y = x + 11 " ;
_____________________________________
To graph y - 7 = x + 4, rewrite the equation in slope-intercept form as y = x + 11. Plot the y-intercept at (0, 11), choose another value for x to find a second point, like (1, 12), and draw the line through these points to visualize the dependence of y on x.
Explanation:To graph the line given by the equation y - 7 = x + 4, we first need to write it in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. So, we add 7 to both sides of the equation to get y = x + 11. This tells us the slope of the line is 1 (since for every increase by 1 in x, y increases by 1) and the y-intercept is 11 (this is where the line crosses the y-axis).
We can then plot the y-intercept on the graph by putting a point at (0, 11). To find another point, we can choose any value for x and solve for y. For example, if we choose x = 1, then y = 1 + 11 = 12, so another point on the line is (1, 12). By plotting these two points and drawing a line through them, we create the graph of the equation.
For more accurate results, plotting more points using various x values and connecting them would be ideal. This graphical representation illustrates the dependence of y on x.
How many gallons is 15 percent of 55 gallons?
Answers
Divide. 42/−8 Enter your answer as a mixed number, in simplified form, in the box.