Answers
The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
An equilateral triangle is a shape with three sides that have an equal measure of side length.
The 3 sides of triangle JKL are equal to each other, therefore we can equate any of the two sides together to find the unknown variable called x.
So, JK = KL
JK = 13x + 5
KL + 17x - 19
13x + 5 = 17x - 19
Collect like terms;
17x - 13x = 19 + 5
4x = 24
x = 24/4
x = 6
We can now proceed to find the sides;
JK = 13x + 5
13 x 6 + 5
= 78 + 5
= 83
JK = 83
KL = 17x - 19
= 17 x 6 - 19
= 102 - 19
= 83
KL = 83
JL= 8x + 35
= 8 x 6 + 35
= 48 + 35
= 83
JL = 83
Hence, The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.
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Related Questions
two debt payments, the first for $800 due today and the second for $600 due in nine months with interest at 10.5% compound monthly, are to be settled by a payment of $800 six months from now and a final payment in 24 months. Determine the size of the final payment if money is now worth 9.5% compounded quarterly.
Answers
Given:
First payment = $800 due today
Second payment = $600 in 9 months
Interest rate = 10.5% compounded monthly
The interest is to be settled in a payment of $800 in 6 months and a final payment in 24 months.
Let's determine the final payment if the money is now worth 9.5% compounded quarterly.
Apply the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Let x represent the initial amount of debt.
Thus, we have the equation:
[tex]\begin{gathered} (x-800)(1+\frac{0.105}{12})^{12\ast\frac{9}{12}}=600 \\ \\ (x-800)(1.00875)^9=600 \\ \\ (x-800)(1.08156)=600 \\ \\ x-800=\frac{600}{1.08156} \\ \\ x=1340.44 \end{gathered}[/tex]For the amount due in six months, we have:
[tex]\begin{gathered} A=1340.44(1+\frac{0.095}{4})^{4\ast\frac{6}{12}}_{} \\ \\ A=1340.44(1.02375)^2 \\ \\ A=1404.87 \end{gathered}[/tex]Hence, the amount which is due after 6 months will be:
$1404.87 - $800 = $604.87
Now, let's find the payment due in 24 months.
Number of months remaining = 24 - 6 = 18 months.
Hence, we have:
[tex]\begin{gathered} A=604.87(1+\frac{0.095}{4})^{4\ast\frac{18}{12}} \\ \\ A=604.87(1.02375)^6 \\ \\ A=696.35 \end{gathered}[/tex]Therefore, the final payment if the money is now worth 9.5% compounded quarterly is $696.35
ANSWER:
$696.35
Is z(x) = 1 + 6x^2 + 4x a quadratic function? I don't believe it's linear or constant, just wanted to make sure.
Answers
Given function is
[tex]z(x)=1+6x^2+4x[/tex]In the given function, the maximum power of x is 2 and it is of the form
[tex]ax^2+bx+c[/tex]Therefore, it is a quadratic function.
A toy costs 35 000 lndonesian rupiah (Rp).
The conversion rate is Rp 1000 = 5$0.145 598.
Without using a calculator, estimate the price of
the toy in S$.
Answers
here is your answer I hope this helps
Move numbers to the blanks to rewrite each square root. [tex] \sqrt{ - 4} = [/tex][tex] \sqrt{ - 5 = } [/tex]answers:[tex]2i[/tex][tex] - 2[/tex][tex]4i[/tex][tex] \sqrt{5i} [/tex][tex] - \sqrt{5} [/tex][tex]i \sqrt{5} [/tex]
Answers
We have 2 expressions:
[tex]\begin{gathered} a)\text{ }\sqrt[]{-4} \\ b)\sqrt[]{-5} \end{gathered}[/tex]Case a.
We can rewrite our square root as
[tex]\sqrt[]{-4}=\sqrt[]{-1\times4}=\sqrt[]{-1}\times\sqrt[]{4}[/tex]but by definition
[tex]\sqrt[]{-1}=i[/tex]which is the imaginary number. So, our square root is equal to
[tex]\sqrt[]{-4}=\sqrt[]{4}i[/tex]which corresponds to option 3.
Case b.
Similarly,
[tex]\sqrt[]{-5}=\sqrt[]{-1}\times\sqrt[]{5}[/tex]and the answer is
[tex]\sqrt[]{-5}=i\sqrt[]{5}[/tex]which corresponds to option 6
For each expression, combine like terms and write an equivalent expression with fewer terms.a. 4x+3xb. 3x+5x-1c. 5+2x+7+4xd. 4-2x+5xe. 10x-5+3x-2
Answers
To simplify the expressions you have to combine the like terms.
This means that you'll solve the operations between the terms that have the same variables, for example x + 2x=3x
Or the terms that have no variables and are only numbers, for example 4+5=9
a. The expression is
[tex]4x+3x[/tex]Both terms have the same variable "x", so you can add them together. To do so, add the coefficients, i.e. the numbers that are being multiplied by x
[tex]4x+3x=(4+3)x=7x[/tex]And you get that the simplified expression is 7x
b. The expression is
[tex]3x+5x-1[/tex]In this expression you have two types of terms, the x-related terms and one constant. In this case you have to solve the operation for the x-related terms together and leave the constant as it is
[tex](3x+5x)-1=(3+5)x-1=8x-1[/tex]The simplified expression is 8x-1
the quotient of two numbers is -1 their difference is 8 what are the numbers
Answers
Let the two numbers be represented with x and y.
Quotient of two numbers = -1:
[tex]\frac{x}{y}=-1\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}.(1)[/tex]Difference of two numbers = 8:
[tex]x\text{ - y = 8}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(2)[/tex]From the first equation, make x the the subject.
Thus, we have:
x = -y
Substitute -y for x in equation 2:
-y - y = 8
-2y = 8
Divide both sides by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{8}{-2} \\ \\ y\text{ = -4} \end{gathered}[/tex]Now, substitute -4 for y in equation 2:
x - y = 8
x - (-4) = 8
x + 4 = 8
Subtract 4 from both sides:
x + 4 - 4 = 8 - 4
x = 4
Therefore,
x = 4 and y = -4
Thus, the numbers are 4 and -4
ANSWER:
4 and -4
Are these lines parallel or not: L1: (1,2), (3,1), and L2: (0,-1), (2,0)
Answers
First find the slope of the first line
L1
m = ( y2-y1)/(x2-x1)
m = ( 1-2)/(3-1)
= -1/2
Now find the slope of the second line
L2
m= ( y2-y1)/(x2-x1)
= ( 0 - -1)/(2 -0)
= (0+1)/(2-0)
= 1/2
Parallel lines have the same slope
These lines do not have the same slope, they are different by a negative sign.
These lines are not parallel.
1260/27 as a mixed number
Answers
A laptop computer is purchased for $2100. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth$300 or less?
Answers
SOLUTION:
After the first year, the price of the laptop computer is;
[tex]P_1=0.75\times2100=1575[/tex]After the second year, the price of the laptop computer is;
[tex]P_2=0.75\times1575=1181.25[/tex]After the third year, the price of the laptop computer is;
[tex]P_3=0.75\times1181.25=885.94[/tex]After the fourth year, the price of the laptop computer is;
[tex]P_4=0.75\times885.94=664.45[/tex]After the fifth year, the price of the laptop computer is;
[tex]P_5=0.75\times664.45=498.34[/tex]After the sixth year, the price of the laptop computer is;
[tex]P_6=0.75\times498.34=373.75[/tex]After the seventh year, the price of the laptop computer is;
[tex]P_7=0.75\times373.75=280.32[/tex]CORRECT ANSWER: 7 years
A grocer wants to mix two kinds of nuts. One kind sells for $2.00 per pound, and the other sells for $2.90 per pound. He wants to mix atotal of 16 pounds and sell it for $2.50 per pound. How many pounds of each kind should he use in the new mix? (Round off the answersto the nearest hundredth.)
Answers
Let
x -----> pounds of one kind of nuts ($2.00 per pound)
y ----> pounds of other kind of nuts ($2.90 per pound)
we have that
2x+2.90y=2.50(16) ------> equation 1
x+y=16-----> x=16-y -----> equation 2
solve the system of equations
substitute equation 2 in equation 1
2(16-y)+2.90y=40
solve for y
32-2y+2.90y=40
2.90y-2y=40-32
0.90y=8
y=8.89
Find out the value of x
x=16-8.89
x=7.11
therefore
the answer is
7.11 pounds of one kind of nuts ($2.00 per pound)8.89 pounds of other kind of nuts ($2.90 per pound)Deborah bought a yard of ribbon for $14.76. How much did Deborah pay per inch? (1 yard = 3 feet.)
$0.41
$0.49
$1.23
$4.92
Answers
Answer:
$0.41 per inch
Step-by-step explanation:
Deborah bought a yard of ribbon for $14.76. How much did Deborah pay per inch? (1 yard = 3 feet.)
$0.41
$0.49
$1.23
$4.92
paid $14.76 for 1 yard or 3 feet. Solve for per foot:
$14.76 / 3 = $4.92 per foot
There are 12 inches per feet. Solve per inch:
$4.92 / 12 = $0.41 per inch
A firefighter has an annual income of $46,870. The income tax the firefighter has to pay is 16%. What is the amount of income tax in dollars and cents that the firefighter has to pay? (TEKS 7.13A-S)
Answers
amount of income tax:
[tex]Tax=46,870\times0.16=7499.2[/tex]Answer:
$7499.2
Which equation represents a line that is perpendicular to the line represented by
y=2/3x+1?
1) 3x+2y=12
2) 3x-2y=12
3) y=3/2x+2
4) y= -2/3x+4
Answers
Answer: (1)
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals. So, since the slope of the given line is 2/3, the slope of the line we want to find is -3/2.
Rearranging equations 1 and 2 into slope intercept form,
[tex]3x+2y=12 \implies 2y=-3x+12 \implies y=-\frac{3}{2}x+6\\\\3x-2y=12 \implies 2y-3x=-12 \implies 2y=3x-12 \implies y=\frac{3}{2}x-6[/tex]
From this, we see that equation 1 is the answer.
A single fair die is tossed. Find the probability of rolling a number greater than 5
Answers
Using the probability concept, the odds of rolling a number greater than 5 is 1 :5
What is probability ?
probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true . the probability of an event is a number between 0 and 1 , where ,roughly speaking ,0 indicates impossibility of the event and 1 indicates certainty.
The odd of a particular experiment is defined thus :
Number of possible outcomes greater than 5 : number of possible below or equal to 5
Sample space = {1, 2, 3, 4, 5, 6}
Outcomes greater than 5 = {6} = 1
Outcomes below or equal to 5 = {1, 2, 3, 4, 5} = 5
The odds equals to 1 : 5
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Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
8)
Answers
He make $84475 for the month including his base salary and commission.
Define commission.The percentage or fixed payment attached to a specific volume of sales is known as the commission rate. For illustration, a fee can be $30 for each sale or 6% of sales. The payment that is either a fixed amount or a percentage of a sale is the commission rate. When they make a sale, people in commission-based professions like insurance brokers, real estate agents, and automobile salespeople get compensated. A business pays its employees according to the revenue they bring in through a commission structure. An employee receives a commission when they conduct business or provide a service, according to the definition of commission.
Given,
Salary = $1500
Commission = 3%
Sales = $82975
= 1500 + 82975 + [tex]\frac{3}{100}[/tex]
= 84475.03
84475(approximately)
He make $84475 for the month including his base salary and commission.
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find the perimeter of ABC with vertices A(-4,4), B(5,-6) and C(7,-9)
Answers
Answer:
The answer is maybe about around 26
Step-by-step explanation:
Please correct me if I am wrong, but I hope this helped.
A quarterback completed 19 out of 30 attempts to pass the football.What was his percent of completion
Answers
The percentage of completion is 63.34%.
ATTACHMENTS OBJECTIVES A banana is 7 inches long. How many slices of banana can be cut from the 7-inch piece if each piece is 1/2 long? inch sation to solve and check your solution. Submission VIEW GRADE DETAILS M 9
Answers
As the banana is 7 inches long and each piece is 1/2 inches you divide 7 into 1/2 to find how many slices of banana can be cut:
Division of fractions:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]Yo have: 7/1 divided into 1/2:
[tex]\frac{\frac{7}{1}}{\frac{1}{2}}=\frac{7\cdot2}{1\cdot1}=14[/tex]Then, in a banana of 7inches you can cut 14 slices of 1/2inchIf f(x) is an exponential function where f(4) = 7 and f(5.5) = 53, then find thevalue of f(5), to the nearest hundredth.
Answers
Given:
f(x) is an exponential function.
f(4) = 7.
f(5.5) = 53.
Since f(x) is an exponential function, f(x) can be expressed as,
[tex]f(x)=ab^x[/tex]Here, a and b are constants.
Hence, we can write
[tex]\begin{gathered} f(4)=ab^4----(1) \\ f(5.5)=ab^{5.5}\text{ ------(2)} \end{gathered}[/tex]Divide equation (2) by (1).
[tex]\frac{f(5.5)}{f(4)}=\frac{ab^{5.5}}{ab^4}[/tex]Substitute f(4) = 7 and f(5.5) = 53 in the above equation.
[tex]\begin{gathered} \frac{53}{7}=\frac{b^{5.5}^{}}{b^4} \\ \frac{53}{7}=b^{5.5-4} \\ \frac{53}{7}=b^{1.5} \\ \frac{53}{7}=b^{\frac{3}{2}} \\ b=(\frac{53}{7})^{\frac{2}{3}} \\ b=3.855 \end{gathered}[/tex]Now, the value of a can be obtained as,
[tex]\begin{gathered} f(4)=ab^4 \\ 7=a(\frac{53}{7})^{\frac{2}{3}} \\ a=\frac{7}{(\frac{53}{7})^{\frac{2}{3}}} \\ =1.815 \end{gathered}[/tex]Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the
rectangle: A(-8,-6), B(-3,-6), C(-3,-4), and D(-8,-4).
Given these coordinates, what is the length of side AB of this rectangle?
Answers
The length of side AB of this rectangle is = 5 units
what is rectangle ?
A shape with four straight sides and four angles of 90 degrees ( right angle ) . two of the sides are longer than the other two . a rectangle with four sides of equal length is square .
we could use distance formula to find the length
A (-8,-6) ; B (3 , -6 )
distance =(( X2 - X1 )^2 +( Y2 - Y1 ) ^2 ) ^1/2
AB = (( -3+8)^2+(-6-[-6]^2)^1/2
AB= 5^2
AB = 5 units .
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To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of ___, a second point by going up 3 and over ___, and then draw a line through the points.
Answers
To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of y = 7, a second point by going up 3 and over y = 10, and then draw a line through the points.
How to know if a point lies in the graph of a function?
All the points (and only those points) which lie on the graph of the function satisfy its equation. Thus, if a point lies on the graph of a function, then it must also satisfy the function.
Given that:
y = 3/4x + 7
At x = 0
y = 7.
Going over by 3 then,
7 + 3 = 10.
So, now y = 10
10 = 3/4x +7
3/4x = 10-7
3/4x = 3
x = 4.
Now,
To draw a graph of 3/4x + 7, a person can draw c point x of 0 and y of 7, a second point by going over 3 and up 4.
Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of 7, a second point by going over 3 and up 10 and then draw a line through the points.
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3. Which of the following equations would be a parabola with vertex (2,-3) that opendownwards? Select ALL.a.h.y = -2(x - 2)2 – 3i.y = (-x + 2)2 + 3C.y = -(x - 2)2 – 3b. y = -(x + 2)2 – 3y = -(x - 2)2 + 3d. y=-(x + 2)2 +3y = -(x - 2)3 +3f. y = -(x - 2)3 – 3y=-{(x - 2)2 - 3j. y = (-x - 2)2 – 3k. y = (-x + 2)2 – 3: نه1. y = (-x - 2)2 – 3m. y =} (x - 2)2 – 3g.n.y = 2(x - 2)2 - 3
Answers
Solution:
Given:
[tex]\text{Parabola with vertex (2,-3) that open downwards}[/tex]The equation of a parabola in vertex form is given by;
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ \text{where;} \\ (h,k)\text{ is the vertex} \\ \\ \text{Hence,} \\ h=2 \\ k=-3 \end{gathered}[/tex]Hence, the equation of the parabola is;
[tex]\begin{gathered} y=a(x-2)^2-3 \\ \\ \text{For the parabola to open downwards, then;} \\ a<0 \\ a\text{ must be negative} \end{gathered}[/tex]Hence, from the options, the equations that have a as negative and in the form gotten above will be selected.
Therefore, the equations of a parabola with vertex (2,-3) that open downwards are;
[tex]\begin{gathered} y=-2(x-2)^2-3 \\ \\ y=-(x-2)^2-3 \end{gathered}[/tex]Write rules for the composition of translations.
Answers
Answer: gurl you think i know
Step-by-step explanation:
The width of a Rectangle is 3.6 inches and the perimeter is 72 inches. What is the length of the rectangle?
Answers
We know that
• The width of the rectangle is 3.6 inches.
,• The perimeter is 72 inches.
The perimeter formula for a rectangle is
[tex]P=2(w+l)[/tex]Where P = 72, w = 3.6, and we have to solve for l.
[tex]\begin{gathered} 72=2(3.6+l) \\ \frac{72}{2}=3.6+l \\ 36=3.6+l \\ l=36-3.6 \\ l=32.4 \end{gathered}[/tex]Therefore, the length of the rectangle is 32.4 inches.what is 338.8882 rounded to the nearest thousandth
Answers
Answer:
338.8882 rounded to the nearest thousandth is 338.888
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Solve form. 2m - p = 11f
Answers
ANSWER
[tex]m=\frac{11f+p}{2}[/tex]EXPLANATION
We want to solve for m in the equation:
[tex]2m-p=11f[/tex]This means that we want to make m the subject of formula.
That is:
[tex]\begin{gathered} \text{Add p to both sides of the equation:} \\ 2m-p+p=11f+p \\ 2m=11f+p \\ \text{Divide both sides by 2:} \\ \frac{2m}{2}=\frac{11f+p}{2} \\ m=\frac{11f+p}{2} \end{gathered}[/tex]That is the answer.
PLEASE HELP
What is the value of x?
Answers
Answer: x = 50
Step-by-step explanation:
The two angles are opposite each other, meaning that they are equivalent.
So, we can set them equal to each other and then solve for x.
2(x + 10) = 3x - 30
2x + 20 = 3x -30
x = 50
Answer:
x = 50
Step-by-step explanation:
Since the two angles are opposite each other, you know that they are equal.
Set both equations equal to each other to isolate x:
2(x + 10) = 3x - 30
Distribute 2 on the left side
2x + 20 = 3x - 30
Subtract 2x from both sides
20 = x - 30
Add 30 to both sides
50 = x
On a piece of paper, graph yz 2x - 3. Then determine which answer choicematches the graph you drew.ABсD(2, 1)(2, 1)(2, 1)((2, 1)(0-3)0,-3)(0-3)(0-3)A. Graph DOB. Graph BO C. Graph AD. Graph
Answers
The graph says
[tex]y\ge x-1[/tex]The upper section of the graph will be shaded since y is greater than or equals to x - 1.
The answer is A . Graph A
In the following figure PR is perpendicular to QS. PR= 14cm, QR=15 cm and QS =12 cm. What is the perimeter of PQR?
Answers
If the figure looks like what I drew in this image, it should work as an answer. If not, remember that perimeter means adding all of the side lengths together. Ex. For a rectangle, P = 2l + 2w. And for a triangle, P = a + b + c, where the variables represent each of the sides.
6) Paul bought and sold a computer
He wrote his business activity as
follows:
cost price of computer = $1064
5 marked price of computer = $1399
Anscount on marked price
(if paid in cash)
Calculate.
5%
The selling price, if paid
Cash.
"1) The profit or loss as a percent.
of the cost price
Answers
The profit percentage of the computer sold by Paul is 31.5%
What is profit?It should be noted that profit simply means the gain that's derivd from selling a particular product.
In this case, the cost price of computer is $1064 and the marked price of computer is $1399.
The profit percentage will be:
= Profit / Cost price × 100
= (1399 - 1064) / 1064 × 100
= 335/1064 × 100
= 31.5%
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