The answer is 15 cause you start at 15 and go from there
15 is the correct answer to the fill-in-the-blanks in this problem.
Extended Response
6. The coordinates of the vertices of parallelogram RSTU are R(0, 0), S(2, 3), T(6, 3), and U(4, 0). What are the coordinates of the vertices of Ry=x(RSTU)?
Answer:
The Coordinate of the vertices of Parallelogram RSTU are R(0,0), S(2,3),T(6,3) and U (4,0).
we have to find the vertices of a point which cuts the side of parallelogram ST .It is given that line y = x passes through R.
Suppose that it cuts the side ST at M (p,q).
Equation of line passing through T(6,3)and S (2,3) is
[tex]\frac{y-3}{x-2}= \frac{3-3}{6-3}\\\frac{y-3}{x-2} = 0\\y- 3=0[/tex]
it passes through (p,q)∴
∴ q -3 =0 ...........(1)
Line y=x passes through (p,q).
p -q=0
p=q
Equation (1) becomes
p= q=3
So the line y =x cuts TU at M (3,3).
A researcher determined the amount of ducks that were in a pond over a four-year time span. The results are shown in the table below.
Year Ducks
1 64
2 78
3 92
4 106
Select an equation that best models the amount of ducks (d) that will be in the pond during the nth year.
Every year there are 14 more ducks. The starting point would be 50 and the equation is:
d = 14*year+50
What is 8 times 8 plus for and add 1,600
Answer:
1668
Step-by-step explanation:
8(8)= 64
64+4=68
1,600+68= 1,668
Solve 3kx + 24 = 9kx for x.
24 = 6kx
4 = kx
4/k = x
Let's solve for x.
3kx+24=9kx
Step 1: Add -9kx to both sides.
3kx+24+−9kx=9kx+−9kx
−6kx+24=0
Step 2: Add -24 to both sides.
−6kx+24+−24=0+−24
−6kx=−24
Step 3: Divide both sides by -6x.
[tex]\frac{-6kx}{-6x}[/tex] = [tex]\frac{-24}{-6k}[/tex]
[tex]x=\frac{4}{k}[/tex]
Answer is: 4/k
1. Simplify by collecting like terms. Show your work when more than one step is required.
A and B for #1 are done I just need C
c. ?
2. Evaluate each expression for the given value of the variable. Show your work.
I need both A and B
a. ?
b. ?
3. The freshman class will be selling carnations as a class project. What is the class's income after it pays the florist a flat fee of $200 and sells c carnations for $2 each? Write an algebraic expression that models the situation.
I need this one as well
Hello,
Please, see the attached files.
Thanks.
Using the slope formula, find the slope of the line through the given points. (4,9) and (6,1)
The slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (4, 9) and (6, 1).
Substitute
[tex]m=\dfrac{1-9}{6-4}=\dfrac{-8}{2}=-4[/tex]
HELP ASAP PLSSSSSSS
Select the correct answer.
What is the rhyme scheme in this excerpt from Robert Frost’s "The Road Not Taken"?
Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;
A.
abacb
B.
abaab
C.
ababa
D.
babab
Answer:
B because eaxh section either repeats itself or is close to repeating its previous part
Step-by-step explanation:
A cube shaped packing box can hold 729 cubic inches of packing material. Solve 729= s ^3 to find the length of one side of the box
729 = s^3
9^3 = s^3
s = 9 in.
$.87 per day is equal to how many dollars per year
solve the quadratic equation y^2-2y-35=0
Hello,
To solve we need to factor y^2-2y-35:
(y-7)(y+5)=0
Now solve for :
(When will (y-7)(y+5)equal zero?)
When y-7=0 or y+5=0
Solve for the 2 equations above and;
y= 7,-5
Hope this helps, have a great day!
Based on the quadratic model, what was the approximate number of workers that were hired during the seventh year?
To determine the approximate number of workers hired during the seventh year based on the quadratic model, we need more information about the model and the values of a, b, and c.
Explanation:To approximate the number of workers hired during the seventh year based on the quadratic model, we need more information about the model. Quadratic models are typically of the form y = ax^2 + bx + c, where x represents the time and y represents the number of workers hired. Without knowing the values of a, b, and c, we cannot determine the exact number of workers hired in the seventh year. However, if we have the values of a, b, and c, we can substitute x = 7 into the equation to find the approximate number of workers hired during the seventh year.
Jason spent half of his allowance going to the movies. he washed the family car and earned 8 dollars. What is his weekly allowance if he ended up with 11 dollars.
$6 dollars because 11-8 = 3, 3x2 =6
He starts with $6.00
It says he spends 1/2 of his allowance on the movies. 6/2=3
He has $3. Then it says He gained $8.00 for washing the "family" car.
$6.00+$8.00
=$11
Answer=$6.00
If you have $10 and bananas cost 80 cents per pound and apples are $1.40 per pound will you have enough money
Which steps transform the graph of y = x2 to y = –2(x – 2)2 + 2? (1 point)
A. translate 2 units to the left, translate down 2 units, stretch by the factor 2
B. translate 2 units to the right, translate up 2 units, stretch by the factor 2
C. reflect across the x-axis, translate 2 units to the left, translate down 2 units, stretch by the factor 2
D. reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2
y = x^2 to Green
y = –2(x – 2)^2 + 2 Blue
The correct answer is D.
Answer:
The correct option is D.
Step-by-step explanation:
The parent function is
[tex]y=x^2[/tex]
The transformed function is
[tex]y=-2(x-2)^2+2[/tex] .... (1)
The translation is defined as
[tex]f(x)=k(x+a)^2+b[/tex] .... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (1) and (2) it is clear that
[tex]a=-2,b=2,k=-2[/tex]
It means,
a=-2<0 the graph shifts 2 units right.
b=2>0 the graph shifts 2 units up.
k=-2, the graph reflect across the x-axis and stretch by the factor 2.
The graph reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2. Therefore the correct option is D.
Carol has only 20p and 10p coins in her purse she has three times as many 20p coins and 10p coins if Carol has ?4.20 altogether, how many 20p coins does she have
Suppose that Carol has x 10p coins in her purse. Since she has three times as many 20p coins as 10p coins, then she has 3x 20p coins in her purse.
x coins of 10p value $0.10x and 3x coins of 20p value $0.60x.
In total this amount of money is $(0.10x+0.60x)=$0.70x that is exactly $4.20. Thus, you get the equation
0.70x=4.20.
Solve it:
[tex]x=\dfrac{4.20}{0.70}=6.[/tex]
Carol has 6 coins of 10p and 3·6=18 coins of 20p.
Answer:
I'm not sure how euros work but I'm almost certain there are 18 20p coins
Step-by-step explanation:
Which package has the lowest ratio of cost to number of lessons? $90 for 10 lessons $160 for 20 lessons $80 for 10 lessons $120 for 20 lessons
$90/10 = 9
$160/20 = 8
$80/10 = 10
$120/20 = 6
The package that has the lowest ratio cost to number of lessons is $120 for 20 lessons.
Hope this Helps!!
The package with the lowest ratio of cost to number of lessons is the $120 for 20 lessons option, calculating to a cost of $6 per lesson, which is the most cost-effective option.
To find this, we calculate the cost per lesson for each package by dividing the total cost by the number of lessons.
For $90 for 10 lessons: $90 / 10 = $9 per lessonFor $160 for 20 lessons: $160 / 20 = $8 per lessonFor $80 for 10 lessons: $80 / 10 = $8 per lessonFor $120 for 20 lessons: $120 / 20 = $6 per lessonTherefore, the package with the lowest ratio of cost to number of lessons is $120 for 20 lessons, with a cost of $6 per lesson.
Match the reasons with the statements in the proof.
Given: m1 = m3
m2 = m3
Prove: / | | m
1. m∠1 = m∠3 and m∠2 = m∠3 Substitution
2. m∠1 = m∠2 Definition of alternate interior angles
3. ∠1 and ∠2 are alternate interior angles If alternate interior angles are equal,
4. l||m then the lines are parallel.
Given
Answer:
Given: [tex]m\angle 1 = m\angle 3[/tex] and [tex]m\angle 2 = m\angle 3[/tex]
To prove that:
[tex]l || m[/tex]
1. [tex]m\angle 1 = m\angle 3[/tex] [Given]
[tex]m\angle 2 = m\angle 3[/tex]
Substitution property of equality says that:
If x = y, then x can be substituted in y, or y can be substituted in x.
2 [tex]m\angle 1 = m\angle 2[/tex] [ By Substitution Property]
Alternate interior angles states that when two lines are crossed by transversal , a pair of angles on the inner sides of each of these two lines on the opposite sides of the transversal line.
3. [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are alternate interior angles [By definition Alternate interior angle].
Alternating interior angles theorem states that if two parallel lines are intersected by third lines, then the angles in the inner sides of the parallel lines on the opposite sides of the transversal are equal.
4. [tex]l || m[/tex] ; then the lines are parallel [By Alternate interior angles theorem]
Correct match is as follows:
1. [tex]m\angle 1 = m\angle 3[/tex] [Given]
[tex]m\angle 2 = m\angle 3[/tex]
2. [tex]m\angle 1 = m\angle 2[/tex] [Substitution]
3. [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are alternate interior angle [By definition of alternate interior angles ]
4. [tex]l || m[/tex] the lines are parallel [If alternate interior angles are equal]
The question involves a geometrical proof where measurements of angles are given and a conclusion regarding parallel lines need to be derived. The steps of proof are matched with relevant geometric concepts. The matching involves principles like substitution, definition of alternate interior angles, and a theorem about alternate interior angles and parallel lines.
Explanation:In the context of the given problem, the matching would be as follows:
m∠1 = m∠3 and m∠2 = m∠3 would be matched with Substitution. This is because the measure of angle 1 is set to equal the measure of angle 3, and similarly, the measure of angle 2 is set to equal the measure of angle 3. This is a direct application of the substitution postulate in geometry. m∠1 = m∠2 would be matched with Definition of alternate interior angles. We know that alternate interior angles are equal in measure when two lines are cut by a transversal. So, when m∠1 = m∠2, these angles are defined as alternate interior angles.∠1 and ∠2 are alternate interior angles would be matched with If alternate interior angles are equal, then the lines are parallel. This phrase essentially summarizes the transversal line theorem, which states that if the pairs of alternate interior angles are equal, then the two lines that are cut by the transversal are parallel.l∥m would be matched with Given. This is provided as a part of the problem statement.Learn more about Geometry here:https://brainly.com/question/31408211
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What is the probability the person is a clown, given they are a boy? (30 pts)
Answer: Answer would be 23
Step-by-step explanation:
URGENT MATH HELP NEEDED PLEASE!!! WILL MARK BRAINLIEST!!!!
1. A bag contains the letters of the word “PROBABILITY”.
A. If a single tile is chosen at random, what is the probability the letter “B” is chosen? (Show your work).
B. If a single tile is chosen at random, what is the probability a vowel OR a “T”? (show your work).
C. If two tiles are chosen (with replacement) what is the probability of choosing an “O” and a “B”? (Show your work).
probability has 11 letters
2/11 chances that you could get a B
5/9 for a T or vowel
3/11 for an O or B
you just look at the letters and the number of them
Which basic geometric figure is labeled as CD? A. Plane B. Segment C. Line D. Angle
Answer:
B
Step-by-step explanation:
In mathematics, we usually label a segment using two letters, one at the beginning of the segment and the second one at the end. On the other hand, in mathematics, angles are labeled using 3 letters (∠ABC).Lines are labeled using just one capital letter (where the line starts)And finally a plane is generally labeled using 3 letters (Plane ABC)Therefore a geometric figure labeled CD would be a segment and the correct answer is B)
Graph the image of the given triangle after the transformation that has the rule (x, y)→(−x, −y) .
Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides.
Please answer fast, need the help : ))
Answer:
It is given that Graph the image of the given triangle after the transformation that has the rule (x, y)→(−x, −y) .
From the given figure it is noticed that the vertices of the triangle are (6,7), (7,4), (-2,5).
From the given rule (x, y)→(−x, −y) the vertices of the image are (-6,-7), (-7,-4) and (2,-5).
Plot these points on the coordinate plane.
In the below graph, the image of the given triangle is represented by green lines.
What is the best estimate of the square root of 96 to the nearest tenth
I believe the answer is 9.8
Hope this helps :)
Samuel has 20$ in his savings account before he makes a deposit of $160. After 2 weeks, he withdraws $160. How did samuels savings account balance change?
There was no change in Samuel's savings account balance. He made a deposit of $160 but after two weeks, he withdrew the same sum. He still had $20 in his account as a result.
Explanation:This math query relates to fundamental financial operations. Samuel has $20 in his savings account at the start of the story. His total now stands at $180 after his subsequent $160 deposit. He withdraws $160, though, after two weeks. He now has $20 in his account after that. Finally, there was no change in Samuel's savings account balance. His account was $20 from beginning to end.
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During 4 days, the price of the stock of PEV Corporation went up 1/4 of a point, down 1/3 of a point, down 3/4 of a point, and up 7/10 of a point. What was the net charge?
The price of the stock of PEV Corporation varies as shown. we have to determine the net charge. Net change is just how much it changed overall, so we will look for all the ups minus all the downs.
Here, "went up" goes with a + sign, and "went down" goes with a - sign.
So, Net charge = [tex]\frac{1}{4} - \frac{1}{3}-\frac{3}{4} + \frac{7}{10}[/tex]
= [tex]\frac{1}{4}-\frac{3}{4}- \frac{1}{3} + \frac{7}{10}[/tex]
= [tex]-\frac{2}{4}- \frac{1}{3} + \frac{7}{10}[/tex]
= [tex]-\frac{1}{2}- \frac{1}{3} + \frac{7}{10}[/tex]
LCM of 2,3 and 10 is 30
= [tex]\frac{-15-10+21}{30}[/tex]
= [tex]\frac{-4}{30}[/tex]
= [tex]\frac{-2}{15}[/tex]
So, the net charge is [tex]\frac{-2}{15}[/tex]
Determine the number of real solutions each quadratic equation has.
y = 12x2 - 9x + 4 _____real solution(s)
10x + y = -x2 + 2 _____real solution(s)
4y - 7 = 5x2 - x + 2 + 3y ______ real solution(s)
y = (-x + 4)2 ______real solution(s)
Answer:
1) a=12 , b=-9 , c=4
2) a=-1 , b=-10 , c=2
3) a=5 , b=-1 , c=9
4) a=1 , b=-8 , c=16
Step-by-step explanation:
(1) y = 12x² - 9x + 4 no real solutions.
(2) 10x + y = -x² + 2, two real solutions.
(3) 4y - 7 = 5x² - x + 2 + 3y, no real solution.
(4) y = (-x + 4)², one real solution.
How to calculate the solutions of the quadratic equations?The number of real solutions for each quadratic equation is determined using discriminant.
The discriminant, denoted as Δ, is used to determine the nature of the roots of a quadratic equation of the form ax² + bx + c = 0.
Δ = b² - 4ac
From the given equations;
y = 12x² - 9x + 4
a = 12, b = -9, c = 4
Δ = (-9)² - 4(12)(4)
Δ = 81 - 192
Δ = -111
Since the discriminant Δ is negative (-111), this quadratic equation has no real solutions.
10x + y = -x² + 2
y = -x² - 10x + 2
a = -1, b = -10, c = 2
Δ = (-10)² - 4(-1)(2)
Δ = 100 + 8
Δ = 108
Since the Δ is positive and greater than zero, the equation has two real solutions.
4y - 7 = 5x² - x + 2 + 3y
4y - 3y = 5x² - x + 2 + 7
y = 5x² - x + 9
a = 5, b = -1, c = 9
Δ = (-1)² - 4(5)(9)
Δ = 1 - 20(9)
Δ = 1 - 180 = -179
No real solution.
y = (-x + 4)²
when y = 0
0 = -x + 4 or
0 = -x + 4
x = 4
The equation has one real solution.
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Solve for d. Show each step: d(e-f)=g
Hey there!!
Given equation :
d(e-f) = g
Solve for d :
Dividing by ( e - f ) on both sides :
d = g / e - f which is [tex]d=\frac{g}{e-f}[/tex]
Hope my answer helps!
Factor the expression completely over the complex numbers.
x^4−625
Factor the expression completely over the complex numbers.
x^4+10x^2+25
[tex]x^4-625=(x^2-25)(x^2+25)=(x-5)(x+5)(x-5i)(x+5i)\\\\x^4+10x^2+25=(x^2+5)^2=((x-\sqrt5i)(x+\sqrt5i))^2=(x-\sqrt5i)^2(x+\sqrt5i)^2[/tex]
Answer:
1) [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]
2) [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]
Step-by-step explanation:
1) Given : Expression [tex]x^4-625[/tex]
To find : Factor the expression completely over the complex numbers ?
Solution :
We can re-write the expression as,
[tex]x^4-625=(x^2)^2-(25)^2[/tex]
Applying identity, [tex]a^2-b^2 = (a+b)(a-b)[/tex]
[tex]x^4-625=(x^2+25)(x^2-25)[/tex]
[tex]x^4-625=(x^2+25)(x^2-5^2)[/tex]
Again apply same identity,
[tex]x^4-625=(x^2+25)(x+5)(x-5) [/tex]
The factor of [tex]x^2+25=(x+5i)(x-5i)[/tex]
Factor form is [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]
2) Given : Expression [tex]x^4+10x^2+25[/tex]
To find : Factor the expression completely over the complex numbers ?
Solution :
Expression [tex]x^4+10x^2+25[/tex]
Let [tex]x^2=y[/tex]
[tex]y^2+10y+25[/tex]
To factor we equate it to zero.
[tex]y^2+10y+25=0[/tex]
Apply middle term split,
[tex]y^2+5y+5y+25=0[/tex]
[tex]y(y+5)+5(y+5)=0[/tex]
[tex](y+5)(y+5)=0[/tex]
Substitute back,
[tex](x^2+5)(x^2+5)=0[/tex]
[tex](x^2+5)^2=0[/tex]
[tex]x^2+5=0[/tex]
[tex]x^2=-5[/tex]
Taking root both side,
[tex]x=\sqrt{-5}[/tex]
[tex]x=\pm \sqrt{5}i[/tex]
So, The factors are [tex](x+\sqrt{5}i)(x-\sqrt5 i)[/tex]
Factor form is [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]
What’s the answer?? (SOMEONE PLEASE HELP ME)
x = 6 or x = - 1
rearrange the equation into standard form and factorise
subtract ( - 2x - 4 ) from both sides
x² - 5x - 6 = 0 ← in standard form
the factors of - 6 which sum to - 5 are - 6 and + 1
(x - 6)(x + 1) = 0
equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 1 = 0 ⇒ x = - 1
Antonio's father bought tickets for the planetairium.He bought 6 tickets each ticket cost 16 what is the total cost of the 6 tickets?
Answer:
$96
Step-by-step explanation:
Multiply The Number Of Tickets By Amount Of People Going
16 * 6
Hi can you help?
Find the missing x- and y-values and Pythagorean triples using the identity given
[tex](x^{2}-y^{2})^{2}+(2xy)^{2}+(x^{2}+y^{2})^{2}[/tex]
X Value: 4
Y Value: 3
Pythagorean Triples: ?
X Value: 5
Y Value: ?
Pythagorean Triples: (9,40,41)
X Value: ?
Y Value: 3
Pythagorean Triples: (27,36,45)
X Value: 7
Y Value: 5
Pythagorean Triples: ?
(x²-y²)² + (2xy)² = (x²+y²)²
Find the missing x- and y-values and Pythagorean triples using the identity given
A Pythagorean triple consists of three positive integers a, b, and c, that satisfy the equation from the Pythagorean theorem, thus, a² + b² = c², such triple is commonly written (a,b,c).
We are given the equation : (x²-y²)² + (2xy)² = (x²+y²)² since this, we have :
a = (x²-y²)
b = (2xy)
c = (x²+y²)
Question 1)
X Value = 4
Y Value = 3
Pythagorean triples: ?
We can replace the values of x and y, to determine a, b and c.
a = (x²-y²) = (4²-3²) = 16-9 = 7
b = (2xy) = (2*4*3) = 24
c = (x²+y²) = (4²+3²) = 16+9 = 25
Answer 1 : Pythagorean triples : (7,24,25)
Question 2)
X Value = 5
Y Value = ?
Pythagorean Triples: (9,40,41)
Now we have a, b, and c, to determine Y
b = (2xy) = 40
Y = 40/2x = 40/2*5 = 40/10 = 4
Answer 2 : Y = 4
Question 3)
X Value = ?
Y Value = 3
Pythagorean Triples: (27,36,45)
Now we have a, b, and c, to determine X
b = (2xy) = 36
X = 36/2y = 36/2*3 = 36/6 = 6
Answer 3 : X = 6
Question 4)
X Value = 7
Y Value = 5
Pythagorean Triples: ?
We can replace the values of x and y, to determine a, b and c.
a = (x²-y²) = (7²-5²) = 49-25 = 24
b = (2xy) = (2*7*5) = 70
c = (x²+y²) = (7²+5²) = 49+25 = 74
Answer 4 : Pythagorean triples : (24,70,74)
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
By using the given identity and substituting known values of x and y, we can find missing x or y values and compute the Pythagorean triples. For instance, when x=4 and y=3, the Pythagorean triple is (7,24,25). Similarly, we can find missing triples or variables for other sets.
Explanation:This question pertains to the topic of Pythagorean triples and their relationship with a given identity. A Pythagorean triple consists of three positive integers (a, b, c), such that a2 + b2 = c2. Inserting known values of x and y into the identity provided can help us find the Pythagorean triples.
For x=4 and y=3: (42 - 32)2 = 72, (2*4*3)2 = 242, (42 + 32)2 = 252. Therefore Pythagorean triple is (7,24,25).For x=5, the Pythagorean triple is (9,40,41), therefore by reversing the process we find y=4.For y=3, the Pythagorean triple is (27,36,45), therefore by inserting values and solving the equation we find x=6.Finally, for x=7 and y=5, the process yields the Pythagorean triple (12,35,37).Learn more about Pythagorean triples here:https://brainly.com/question/31900595
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