parallelogram pqrs has diagonals PR and SQ that intersect at T find the value of X and Y
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If a parallelogram PQRS has diagonals PR and SQ that intersects at T, then, T is the midpoint of PR and T is the midpoint of SQ
Given
[tex]\begin{gathered} PT=y \\ TR=3x+1 \end{gathered}[/tex][tex]y=3x+1[/tex]Also
[tex]\begin{gathered} QT=3y \\ TS=4x+13 \end{gathered}[/tex][tex]3y=4x+13[/tex]Now we are going to solve the system of equations with two unknowns
[tex]\begin{gathered} y=3x+1 \\ 3y=4x+13 \end{gathered}[/tex]Substitute equation 1 into 2
[tex]\begin{gathered} 3(3x+1)=4x+13 \\ 9x+3=4x+13 \\ 9x-4x=13-3 \\ 5x=10 \\ x=\frac{10}{5} \\ x=2 \\ \end{gathered}[/tex]x = 2
Substitute x = 2 into equation 1
[tex]\begin{gathered} y=3x+1 \\ y=3(2)+1 \\ y=6+1 \\ y=7 \end{gathered}[/tex]y = 7
The answer would be x = 2, y = 7
Related Questions
Perform the indicated operation numbers be sure to express your answer in reduced form
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We need to calculate the following sum:
[tex]\frac{8}{15}+\frac{7}{25}[/tex]The first step is to calculate the least common multiplier between the two denominators. This is done below:
[tex]\begin{gathered} 15=3\cdot5 \\ 25=5\cdot5 \end{gathered}[/tex]We broke down the two denominators into their factors, now we need to multiply the factors that are unique. This is done below:
[tex]\text{LCM}=3\cdot5\cdot5=75[/tex]Now we have to replace the denominators by 75 and calculate new numerators. The new numerators must be calculated as follows:
1 - Divide the LCM by the old denominator
2 - Multiply the result of 1 by the old numerator.
This is done below:
[tex]\begin{gathered} \frac{5\cdot8}{75}+\frac{3\cdot7}{75} \\ \frac{40}{75}+\frac{21}{75} \end{gathered}[/tex]Since both fractions have their denominators with the same value, we can just directly add them.
[tex]\frac{40+21}{75}=\frac{61}{75}[/tex]The fraction is already in its most reductable form, therefore the answer is 61/75.
What is the length of the hypotenuse of the right triangle with coordinates:(-2, -1), (-6,5), and (4, 3)?
Answers
ANSWER:
10.2 units
STEP-BY-STEP EXPLANATION:
The first thing is to make a sketch of the triangle formed in the Cartesian plane, like this:
The hypotenuse is the side opposite the right angle, therefore, it would be the side from the point (-6, 5) to the point (4, 3).
We calculate the distance between these two points using the following formula:
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]We replace and calculate the length of the hypotenuse:
[tex]\begin{gathered} d=\sqrt{\left(4-\left(-6\right)\right)^2+\left(3-5\right)^2} \\ d=\sqrt[]{(4+6)^2+(3-5)^2} \\ d=\sqrt[]{(10)^2+(-2)^2} \\ d=\sqrt[]{100+4} \\ d=\sqrt[]{104} \\ d\cong10.2 \end{gathered}[/tex]The length of the hypotenuse is 10.2 units.
please solve this for me
Answers
The equation of the line in slope intercept form is y = -x + 6
How to write equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptThe slope of the line can be found as follows:
using (6, 0) and (5, 1)
m = slope = 1 - 0 / 5 - 6
slope = 1 / -1
slope = -1
Therefore, let's find the y-intercept of the line using (0, 6).
y = -x + b
6 = -(0) + b
b = 6
Therefore, the equation of the line is y = -x + 6
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891 to which closer to hundred
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891 is closer to 900.
Consider the following:
800, 820, 840, 860, 880, 900
891 is found between 880 and 900
Thus, the hundred 891 is closer to is 900
Find the amount of interest and the monthly payment for the loan described.
Purchase of a living room set for $2,700 at 12% add-on interest for 3 years
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The amount of interest is $972 and monthly payment is $102.
What is Simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
Given that, a loan described as purchase of a living room set for $2,700 at 12% add-on interest for 3 years
SI = P*R*T/100
SI = 2700*12*3/100 = $972
Amount to be paid = $972+$2,700 = $3672
Amount to be paid monthly = $3672/3*12 = $102
Hence, The amount of interest is $972 and monthly payment is $102.
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A polynomial has one root that equals 2 + i. Name one other root of thispolynomial.
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In a polynomial, if it has an imaginary root, then it also has the conjugate of that root. In this case, since 2 + i, is a root then 2 - i, is also a root.
3x=4 1/2 I need help to solve for x
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We need to solve the equation:
[tex]3x=4\frac{1}{2}[/tex]First, notice that the mixed number 4 1/2 can be written as:
[tex]4\frac{1}{2}=4+\frac{1}{2}[/tex]Now, we can solve the equation for x by dividing both sides of the equation by 3. We obtain:
[tex]\begin{gathered} \frac{3x}{3}=\frac{\mleft(4+\frac{1}{2}\mright)}{3} \\ \\ x=\mleft(4+\frac{1}{2}\mright)\cdot\frac{1}{3} \\ \\ x=4\cdot\frac{1}{3}+\frac{1}{2}\cdot\frac{1}{3} \\ \\ x=\frac{4}{3}+\frac{1}{6} \\ \\ x=\frac{8}{6}+\frac{1}{6} \\ \\ x=\frac{9}{6} \\ \\ x=\frac{3}{2} \\ \\ x=1\frac{1}{2} \end{gathered}[/tex]Therefore, the solution is:
[tex]\mathbf{x=1\frac{1}{2}}[/tex]Answer:
Exact form:
x = 3/2
decimal form:
x = 1.5
mixed number form:
x = 1
1/2
Step-by-step explanation:
Joni took out a loan for $21,912. To pay it back, she will make 42 monthly paymentsof $931. How much will he pay in interest? Round answer to a whole number.
Answers
Given:
Loan of $21,912
42 monthly payments of $931.
Find amount of interest.
First, find the total amount that Joni will pay.
[tex]42\times\$931=\$39,102[/tex]Next, subtract the result by the amount of loan
[tex]\$39,102-$\$21,912=$\$17,190[/tex]Therefore, Joni will pay $17,190 in interest.
Cindy has a jacket with the first letter of her school's name on it. determine the area of the letter on Cindy's jacket.
Answers
To find the area of the letter, use the area of a rectangle formula below:
Area = Length x Width
Find the
Total area = ( 10 x 2) + (6 x 2) + (6 x 2)
= 20 + 12 + 12
= 44 in²
Therefore, the area of the letter on Cindy's jacket is 44 in²
ANSWER:
44 in²
Question 2 (5 points) (04.01 LC) Simplify +5x+6 X+2
A x²+1
B x²-1
C X +3
D X-3
Answers
[tex]\bf{\dfrac{x^{2} +5x+6 }{x+2} }[/tex]
Rewrite the term.
x² + 2x + 3x + 6
Group the terms into two fractional parts.
(x² + 2x + (3x + 6)
Factor the expression
x(x + 2) + 3 (x + 2)
[tex]\boldsymbol{\sf{\dfrac{(\not{x+2)(x+3)}}{\not{x+2}}=x+3 \to Option \ C }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{\cfrac{x {}^{2} + 5 x + 6 }{x + 2} }[/tex]
Answer :
Note: To solve a problem like this, we must first determine which of the two numbers add 5 and multiply 6, we know that they are 2 and 3 and then we must Rewrite the expression using the above.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{(x+2)(x+3)}[/tex]
Now, we must put a fraction since we can more easily solve the problem posed.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \cfrac{(x + 2)(x + 3)}{x + 2} }[/tex]
Now the last thing we have to do is Cancel [tex]\bold{x+2}[/tex] to have a final result that is the following:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x+3}[/tex]
What is 5,421 rounded to the nearest hundred?A.4,000B.5,000C.5,4000D.5,200
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We have the following number:
[tex]5,421[/tex]By rounding down this number to the nearest hundred, we get
[tex]5,400[/tex]which corespond to option C
find the length of each chord. horizontal chord and vertical
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Consider the circle
we have the intersecting chords theorem, which states that
[tex]a\cdot b=c\cdot d[/tex]In our case we have a=x, b=12, c=6 and d=x+4. So we have
[tex]12\cdot x=6\cdot(x+4)[/tex]distributing on the right side we get
[tex]12\cdot x=6x+6\cdot4=6x+24[/tex]Subtracting 6x on both sides, we get
[tex]24=12x\text{ -6x=6x}[/tex]Dividing boht sides by 6, we get
[tex]x=\frac{24}{6}=4[/tex]So, the value of x is 4. Now we replace this value to find the length of each chord, so we have
x---->4
12---->12
x+4----->4+4=8
6----->6
The diameter of a circle is 12 meters. What is the area of a sector bounded by a 102° arc?Give the exact answer in simplest form.
Answers
Answer:
The area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]Explanation:
The Area of a sector can be calculated using the formula;
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]Where:
A = area of the sector
Angle theta = the angle bounding the sector
r = radius
Given:
[tex]\begin{gathered} \theta=102^0 \\ r=\frac{\text{diameter}}{\text{2}}=\frac{12m}{2}=6m \\ r=6m \end{gathered}[/tex]substituting the given values, we have;
[tex]\begin{gathered} A=\frac{102}{360}\times\pi(6^2) \\ A=10.2\pi m^2 \\ A=32.04m^2 \end{gathered}[/tex]Therefore, the area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]
Jeff receive six dollars for each hour he babysits how much money will just make after six hours eight hours 10 hours in 12 hours right the function and then find each answer to the correct function table that matches this situation
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Jeff receive six dollars for each hour he babysits
Function:
f(x) = 6x
Where x is the number of hours
for 6 hours:
F(6) = 6(6) = 36
For 8 hours:
F(8)= 6(8) = 48
For 10 hours:
F(10)= 6(10)= 60
For 12 hours:
F(12)=6(12)=72
For each row of the table, choose the equivalent expression
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Ok, so:
Let's make all operations and then choose the equivalent expression for each one.
Let's start in order:
a. 4/12 + 4/12 = 8/12
b. 1/12 + (3/12 + 3/12) = 7/12
c. 4/12 + 5/12 = 9/12
d. 2/12 + 2/12 + 2/12 = 6/12.
Notice that the last operations are the columns of the table.
So, let's do it the same with the upper rows:
e. 5/12 + 4/12 = 9/12
f. (1/12 + 3/12) + 3/12 = 7/12
g. 1/12 + 2/12 + 3/12 = 6/12
h. 15/12 - 7/12 = 8/12.
Now, let me draw the table to make this problem more understandable.
This is the order you have to put the answer:
can you please help me
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We have two types of crust, each of them with a different type of sauce and choice of toppings. The answer would be 54 single topping pizzas because we have two types of crust for 3 types of sauce 2*3 = 6
and 9 choices of toppings for each of them 6*9 = 54
The baghrams make regular monthly deposits in a savings account. The graph shows the relationship between the numbers x of months and the amount y in dollars in the account.what is the equation for the deposit?A- y/x = $40/monthB- y/x = $25/monthC- y/x = $50/monthD- y/x = $75/month
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The two point throught which line passes are (2,100) and (4,200).
Determine the equation of line passes through the points.
[tex]\begin{gathered} y-100=\frac{200-100}{4-2}(x-2) \\ y-100=50(x-2) \\ y=50x-100+100 \\ y=50x \\ \frac{y}{x}=50 \end{gathered}[/tex]T
help me Plss Im begging you
Answers
Answer:
2:1
Step-by-step explanation:
No of hydrogen atoms = 4
No of carbon atoms = 2
Ratio of hydrogen atoms to carbon atoms mean that the no of hydrogen atoms need to be divided by the no of Carbon atoms
that is 4/2 = 2/1 = 2 : 1
what property do we use to check that our factored form is equivalent to the standard form
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Lets solve an example:
[tex]\begin{gathered} y=x^2+6x+8 \\ \end{gathered}[/tex]this quadratic polynomial is in standard form. We can write the same polynomial in factored form as
[tex]y=(x+4)(x+2)[/tex]In the case of quadratic polynomials, a fast check is
that is, 4 plus 2 must be equal to 6 in the term 6x and
4 times 2 must be 8 in the constant term, which is 8.
write a linear equation that has m=4 and has an x intercept of (5,0)
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the equation is of the form y = mx + b, then
for b:
[tex]\begin{gathered} 0=4(5)+b \\ 0=20+b \\ 0-20=20+b-20 \\ b=-20 \end{gathered}[/tex]the equation is:
[tex]y=4x-20[/tex]In the diagram, GH bisects ∠FGI.Solve for x and find m∠FGH.a. X=b. Find m∠HGI.C. Find m∠FGI.(Simplify your answer.)
Answers
Answer:
(a)19 degrees
(b)29 degrees
(c)58 degrees
Explanation:
If GH bisects ∠FGI, it means it divides it into two equal parts ∠FGH and ∠HGI.
[tex]\begin{gathered} m\angle FGH=m\angle\text{HGI} \\ (2x-9)^0=(3x-28)^0 \end{gathered}[/tex](a)We solve the equation above for x.
[tex]\begin{gathered} 3x-2x=-9+28 \\ x=19 \end{gathered}[/tex](b)
[tex]\begin{gathered} m\angle HGI=3x-28 \\ =3(19)-28 \\ =57-28 \\ =29^0 \end{gathered}[/tex](c)
[tex]\begin{gathered} m\angle FGI=2\times m\angle HGI \\ =2\times29^0 \\ =58^0 \end{gathered}[/tex]A figure has an area of 100 units `2 what will the new area be after dilation with a scale factor of 2\5
Answers
16 u²
1) If a figure has an area and it's been dilated of k= 2/5
2) Then we can sketch that situation, concerning to areas:
So, we can state this dilated figure is going to have an area of 16 u².
Hence, the answer is 16 u²
Decide whether the relation defines y as a function of x. Give the domain. x+2y=——— 5A) Does the equation describe y as a function of x?1. Yes2. NoB) Give the domainThe domain is _____
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Answer:
A) 1.yes
B) The domain is All real numbers.
Explanation:
The problem gives us a relationship:
[tex]y=\frac{x+2}{5}[/tex]For this relationship to be a function, for each value of x, we should get a single value of y. We can see that this is true, given a value of x, we get a unique value of y. Thus, A is true.
Now, we need to find the domain. The domain is the set of all values of x for which the function is defined. In this case, the function is a line:
[tex]\begin{gathered} y=\frac{x+2}{5} \\ . \\ y=\frac{x}{5}+\frac{2}{5} \\ . \\ y=\frac{1}{5}x+\frac{2}{5} \end{gathered}[/tex]The equation is a line with slope 1/5 and y-intercept 2/5. We know that any line is defined for all real numbers.
Thus, the domain is all real numbers.
An archer hits a bullseye 64% of the time. What is the probability the archer hitsthe bullseye exactly 4 times during 10 total attempts?a. 242b. .365C..077d. 168
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If the probability of hitting the bullseye is 64% (P(H) = 0.64), then the probability of not hitting the bullseye (P(H_bar)) is:
[tex]P(\bar{H})=1-P(H)=1-0.64=0.36[/tex]Now, if we have 10 attempts, and the archer hits 4 times, then he misses 6 times.
So we have 4 cases of hitting (P(H)) and 6 cases of not hitting(P(H_bar)), and the probability is the product of the probabilities of each case:
[tex]P=P(H)^4\cdot P(\bar{H})^6=(0.64)^4\cdot(0.36)^6=0.16777\cdot0,0021767=0\text{.}0003652[/tex]We also need to multiply this probability by a combination of 10 choose 4, because the 4 hits among the 10 attempts can be any of the 10, in any order:
[tex]C(10,4)=\frac{10!}{4!(10-4)!}=\frac{10!}{4!6!}=\frac{10\cdot9\cdot8\cdot7}{4\cdot3\cdot2}=210[/tex]So the final probability is:
[tex]P^{\prime}=P\cdot C(10,4)=0.0003652\cdot210=0.077[/tex]So the answer is C.
Select the recursive and explicit formula for the Arnold family 2 answer
Answers
ANSWER:
[tex]\begin{gathered} A\left(n\right)=a_{n-1}\times 2 \\ A\left(n\right)=0.05\cdot\left(2\right)^{n-1} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the Arnolds family are going to save a nickel on the first day of the month and then double the amount each day.
One nickel is equal to $0.05, therefore, we can make an recursive formula, it is a geometric sequence where the initial value is 0.05 and the ratio is equal to 2, because it doubles every day, therefore:
[tex]A(n)=0.05\cdot(2)^{n-1}[/tex]Now, from the above we can deduce the explicit formula, since the next value will be double the previous value, therefore, the explicit formula would be:
[tex]A(n)=a_{n-1}\times2[/tex]Therefore, the correct answers are the 1st and 4th options.
11. Reflect quadrilateral CONE with C(5,1), 0(1,6),N(-7,0) and E(-2,-4) in the line y = -2.
Answers
Step 1
y = -2 is the mirror line.
Step 2
The graph below shows the result after reflection about y = -2.
Bea crió algunas vacas y algunos pavos. Crió un total de 28 vacas y pavo. habia 96 patas en total cuantas vacas y cuantos pavos crió bea?
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1) Coletando los datos:
Vacas: v
Pavos: p
p+v =28
2p+4v=96 Como las vacas tienen 4 patas e los pavos tienen 2 patas
2) Multiplicando por - 2, la primera ecuación
-2p -2v =-56
2p +4v =96
-------------------
2v = 40
v= 20
3) Substituindo en la primera ecuación
p +20 =28
p =28 -20
p=8
Entonces, había 20 vacas y 8 perus
Hi i have uploaded the question in the image. Equation no. 2 (ii).
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Let's determine if g(x) is a factor of f(x).
[tex]\text{ f(x) }=\text{ }x^3\text{ }-3x^2+4x-4[/tex][tex]\text{ g(x) = }x\text{ - 2}[/tex]Given that g(x) = x - 2, at x = 2, let's check the value of f(x) at x = 2, If f(x) = 0, then g(x) is a factor, otherwise, g(x) is not a factor of f(x).
We get,
At x = 2,
[tex]\begin{gathered} \text{ f(x) }=\text{ }x^3\text{ }-3x^2+4x-4 \\ \text{ f(2) = (2)}^3-3(2)^2\text{ + 4(2) - }4 \\ \text{ f(2) = 8 - 12 + 8 - }4 \\ \text{ f(2) = 16 - 1}6 \\ \text{ f(2) = 0} \end{gathered}[/tex]Therefore, g(x) is a factor of f(x).
what is the area of triangle Givenchy height 137 and base 203
Answers
the area is calculated according to:
[tex]area=\frac{1}{2}\times203\times137=13,905.5[/tex]
Ezra is finding the perimeter of different-sized regular pentagons. There is a proportional relationship between the side length of the regular pentagon in inches, x, and the perimeter of the regular pentagon in inches, y. The equation that models this relationship is y=5x. What is the perimeter of a regular pentagon with a side length of 2 inches? Write your answer as a whole number or decimal.
Answers
The perimeter of the regular pentagon Ezra is finding is 10m inches
How to find the perimeter of a regular pentagon with a side length of 2 inchesPerimeter refers to the total outside length of an object,
The equation given in the problem is
y = 5x
where
the side length of the regular pentagon in inches, x,
the perimeter of the regular pentagon in inches, y
if the side length is 5, we plug in 2 into the equation above
y = 5x
y = 5 * 2
y = 10 inches
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