Answer: 36
Step-by-step explanation:
The legs are given to be :
3x - 1 and -x + 27
The base = 5x + 1
One of the properties of an isosceles triangle is that two sides are equal , that is the two legs are equal. This means that
3x - 1 = - x + 27
3x + x = 27 + 1
4x = 28
x = 7
To calculate the length of the base, substitute x = 7 into the length of the base given , that is
Length of the base = 5(7) + 1
L = 35 + 1
L = 36
identical vacation houses, equally spaced along a street, are number consecutively beginning with 10. maria lives in house #17. joshua lives 4 houses away from maria. what are possible numbers for joshua's house?
Answer:
Possible numbers for Joshua's house are #13 and #21.
Step-by-step explanation:
Given:
Vacation houses are equally spaced along a street.
The first house is marked with #10 and so on.
Maria lives in house marked as #17.
Joshua lives 4 houses away from Maria.
So, the difference between Joshua's house number and Maria's house number is 4.
Let 'x' be the house number of Joshua's house.
Case 1: If Joshua's house is after Maria's house. So, [tex]x> 17[/tex]
[tex]x-17=4\\x=17+4=21[/tex]
Case 2: If Joshua's house is before Maria's house. So, [tex]x<17[/tex]
[tex]17-x=4\\17-4=x\\13=x\ or\\x=13[/tex]
Therefore, the possible numbers for Joshua's house are #13 and #21.
Solve (factorise ).
Answer: (1) x²y (2) 7pqr (3) a (4) 6a² (5) y³z²
Step-by-step explanation:
(1) x^4y³ and x²y
x^4y³ = x²y(x²y²)
x²y = x²y
Therefore the Highest Common factor
x²y which is the common factor.
(2) 14p²qr^4 = 2 x 7 x p² x q x r^4
49p²q²r = 7 x 7 x p² x q² x r
35pqr = 5 x 7 x p x q x r
Therefore HCF = 7 x p x q x r
= 7pqr
(3) -a^5 = -( a x a x a x a x a )
= -(a^5)
ab³ = a x b x b x b
Therefore HCF = a
(4) 6a² = 2 x 3 x a x a
-18a6 = -( 2 x3 x 3 x a x a x a x a x a x a)
-12a² = -( 2 x 2 x 3 x a x a )
Therefore HCF = 2 x 3 x a²
= 6a²
(5) 3y³z² = 3 x y x y x y x z x z , 3 x y³ x z²
15y^4z² = 3 x 5 x y x y x y x y x y x z x z, 3 x 5 x y^4 x z²
y^6z³ = y^6 x z³
Therfore HCF = y³ x z²
= y³z²
if oak plywood costs $56.00/sheet sq ft. how much is 17 sq ft.
Answer:
$952
Step-by-step explanation:
I don't know why sheet is after 56, but I think they just want you to multiply 57 and 17.
A landscaper installed a circular sprinkler system using 50.25 feet of copper tubing to create the circle. To the nearest whole foot, what is the diameter of the circular sprinkler
Answer:
4 foot
Step-by-step explanation:
√50.25 / 3.1416 = 4
The diameter of the circular sprinkler is 16 feet.
Explanation:To find the diameter of the circular sprinkler, we can use the formula for the circumference of a circle: C = πd, where C is the circumference and d is the diameter. In this case, we are given the length of the copper tubing used, which is equal to the circumference. So we can rearrange the formula to solve for the diameter: d = C/π. Plugging in the given values, we have d = 50.25/π. Using the value of π as approximately 3.14, we can calculate the diameter to the nearest whole foot.
d ≈ 50.25/3.14 ≈ 16.01 feet
Therefore, the diameter of the circular sprinkler to the nearest whole foot is 16 feet.
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Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 2-√6 , 2+ √6 , and 7-i
Answer:
[tex]x^{4} -18x^{3}+104x^{2} -172x-100[/tex]
Step-by-step explanation:
The 3 roots are given out of which 2 are real and 1 is imaginary. For a polynomial of least degree having real coefficients, it must have a complex conjugate root as the 4th root. Therefore, based on 4 roots, the least degree of polynomial will be 4. Finding the polynomial having leading coefficient=1 and solving it based on multiplication of 2 quadratic polynomials, we get:
[tex]\\\\x_{1} = 2-\sqrt{6} \\x_{2} = 2+\sqrt{6} \\x_{3}=7-i \\x_{4}=7+i \\\\P(x)=1(x-x_{1})(x-x_{2} )(x-x_{3} )(x-x_{4} ) \\\\=(x-(2-\sqrt{6}))( x-(2+\sqrt{6} )) (x-(7-i))( x-(7+i))\\=((x-2)+\sqrt{6})( ( x-2)-\sqrt{6} ) ((x-7)+i)( (x-7)-i)\\=((x-2)^{2} -(\sqrt{6} )^{2} )((x-7)^{2}-(i)^{2})\\=(x^{2} -4x-2)(x^{2} -14x+50)\\=x^{4} -18x^{3}+104x^{2} -172x-100\\[/tex]
Answer:
X^4-16x^3+73x^2-30x-250
Step-by-step explanation:
What is the value of the expression? (8/9)/(-2/3)x(-4 1/2)
Answer:
Step-by-step explanation:
1. Find the value of each expression. Show your work.
(a) 1.22
(b) 23 +17 - 3.4
(c) 9 +33
Answer:
ASAP PLS 15 points
Answer: A) 1.44 B) 13 C) 3
Step-by-step explanation:
A) 1.2 * 1.2 =1.44
B) (8) +17 - (12)= (8+17) -12= (25)- (12)= 13
C) (9*9) / (3*3*3)= (81) / (27)= 3
A square pyramid has a base area of 36 ft2. The pyramid’s total surface area is 144 ft2.
Answer:
The area of each triangle face is 27 square feet .
Step-by-step explanation:
Given as :
The base area of square pyramid = A = 36 square feet
The total surface area of square pyramid = TSA = 144 square feet
Let The area of each triangle face = x square feet
Now, According to question
Total surface Area of square pyramid = Base area of square pyramid + Area of four triangle faces
Or, TSA = A + 4 × x
Or, 144 ft² = 36 ft² + 4 × x ft²
Or, 4 × x = 144 ft² - 36 ft²
Or 4 × x = 108 ft²
∴ x = [tex]\dfrac{108}{4}[/tex]
i.e x = 27 ft²
So, The area of each triangle face = x = 27 square feet
Hence, The area of each triangle face is 27 square feet . Answer
Which statements are true about the ordered pair
-1, 5) and the system of equations?
ſ+y=4
1
-Y= -6
Select each correct answer.
The ordered pair (-1, 5) is a solution to the first equation because it makes the first
equation true
The ordered pair (-1, 5) is a solution to the second equation because it makes the
second equation true.
The ordered pair (-1, 5) is not a solution to the system because it makes at least one
of the equations false.
The ordered pair (-1, 5) is a solution to the system because it makes both equations true
Answer:
-The ordered pair (-1, 5) is a solution to the first equation because it makes the first equation true.
-The ordered pair (-1, 5) is a solution to the second equation because it makes the second equation true.
-The ordered pair (-1, 5) is a solution to the system because it makes both equations true
Step-by-step explanation:
The correct question is
Which statements are true about the ordered pair (−1, 5) and the system of equations?
x+y=4
x−y=−6
we know that
If a ordered pair is a solution of a equation, then the ordered pair, must satisfy the equation (makes the equation true)
If a ordered pair is a solution of the system of equations, then the ordered pair, must satisfy the equations of the system (makes both equations true)
we have
[tex]x+y=4[/tex] ----> first equation
[tex]x-y=-6[/tex] ----> second equation
step 1
Verify if the ordered pair satisfy the first equation
Substitute the values of x and y of the ordered pair in the first equation
For x=-1, y=5
[tex]-1+5=4[/tex]
[tex]4=4[/tex] ---> is true
The ordered pair satisfy the first equation
so
The ordered pair is a solution to the first equation because it makes the first equation true
step 2
Verify if the ordered pair satisfy the second equation
Substitute the values of x and y of the ordered pair in the second equation
For x=-1, y=5
[tex]-1-5=-6[/tex]
[tex]-6=-6[/tex] ---> is true
The ordered pair satisfy the second equation
so
The ordered pair is a solution to the second equation because it makes the second equation true
therefore
The ordered pair (-1, 5) is a solution to the system because it makes both equations true
Quadrilateral ABCD is dilated by a scale factor of 1 over 3 centered around (1, 2). Which statement is true about the dilation?
segment B prime D prime will run through (1, 2) and will be shorter than segment BD.
segment B prime D prime will run through (1, 2) and will be longer than segment BD.
segment B prime D prime will be parallel to segment BD and will be shorter than segment BD.
segment B prime D prime will be parallel to segment BD and will be longer than segment BD.
Note: Since you missed to add the figure. So, after a little research I am kind of able to find the figure and hence, assuming it as a reference. Hence, I am attaching the figure and solution of that figure is also visible in the same figure. Please check the attached figure (a)
Answer:
Segment B'D' will be parallel to segment BD and will be shorter than segment BD. Please see the attached figure (a) for better understanding.
Step-by-step explanation:
As we know that there are certain rules when a quadrilateral is dilated by a certain scale centered around a certain point.
So,
Let suppose P(a, b) is the point.
The dilation rule by a scale factor of 1 over 3 or (1/3) centered around (1, 2) is
P(a, b) → [tex]P(\frac{x+2}{3}, \frac{y+4}{3})[/tex]
Hence,
A(1, 2) → A'(1, 2)
B(2, 3) → B'(4/3, 7/3)
C(4, 2) → C'(2, 2)
D(2, 1) → D'(4/3, 5/3)
The attached figure show that if we draw the all these points in the coordinate plan i.e. A(1, 2), B(2, 3), C(4, 2), D(2, 1) and A'(1, 2), B'(4/3, 7/3), C'(2, 2), D'(4/3, 5/3), we can determine that Segment B'D' will be parallel to segment BD and will be shorter than segment BD.
Keywords: dilation, quadrilateral, segment
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Answer: C) segment B prime D prime will be parallel to segment BD and will be shorter than segment BD.
if x-1 is a factor of P(x)=x^3- 5x^2 + 7x-3 which of the following represents the complete factorization for P(x)?
Answer:
P(x) = (x-1)² (x-3)
Step-by-step explanation:
P(x)=x³- 5x² + 7x-3 = x² (x-1) - 4x(x-1) + 3(x-1) = (x²-4x+3)(x-1)
P(x) = (x-1)(x-3)(x-1) = (x-1)² (x-3)
Help please i need help lollolol
Answer:
Oh it is C
Step-by-step explanation:
Answer:
40 miles per hour
Step-by-step explanation:
1 hour=3600 seconds
(1/4)/22.5=x/3600
cross product
22.5*x=(1/4)(3600)
22.5x=3600/4
22.5x=900
x=900/22.5
x=40
Students were asked to write 6x^5 + 8x-3x^3+7x^7 in standard form
Answer:
The standard form is [tex]7x^7 +6x^5-3x^3 + 8x[/tex]
Step-by-step explanation:
Given:
[tex]6x^5 + 8x-3x^3+7x^7[/tex]
To Find :
standard form of [tex]6x^5 + 8x-3x^3+7x^7[/tex]
Solution:
A polynomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc.
In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to write.
Now lets check the degree of each term in the polynomial
The degree of 6x is 5
The degree of 8x is 1
The degree of 3x is 3
The degree of 7x is 7
Now rewrite the polynomial in the order of the degree, from highest to lowest
[tex]7x^7 +6x^5-3x^3 + 8x[/tex]
Luis ans Carrie purchased two types of tea .the herbal tea variety cost $1.50 per box and the regular variety cost $1.00 per box they bought A total of 10 boxes and spent $11.50 how many boxes of each type did they buy
Answer:
I'm not Certain but I'm thinking that it would be 4 boxes of the regular tea and 5 of the herbal tea.
Step-by-step explanation:
herbal- $1.50
regular- $1
$1*4 =$4
$1.50*5 = $7.50
$4.00+ $7.50=11.50
Answer:
Herbal tea box = 3
Regular tea box = 7
Step-by-step explanation:
Le x be the number of herbal tea box and y be the number of regular tea box.
The herbal tea variety cost $1.50 per box and the regular variety cost $1.00 per box they bought A total of 10 boxes and spent $11.50.
[tex]x+y=10\Rightarrow y=10-x[/tex] .... (1)
[tex]1.50x+1.00y=11.50[/tex] ... (2)
From (1) and (2) we get
[tex]1.50x+1.00(10-x)=11.50[/tex]
[tex]1.50x+10-1.00x=11.50[/tex]
[tex]0.50x=11.50-10[/tex]
[tex]0.50x=1.50[/tex]
[tex]x=\dfrac{1.50}{0.50}=3[/tex]
Substitute x=3 in equation (1).
[tex]y=10-x=10-3=7[/tex]
Therefore, the number of herbal tea boxes is 3 and the number of regular tea boxes is 7.
A spinner with the colors orange, yellow, purple, and green is spun. What is the theoretical probability, as a decimal, of stopping on the color purple? Round the decimal to the nearest hundredth.
Answer:
Step-by-step explanation:
a spinner with the colors orange, yellow, purple, and green.....so this spinner only has 4 spaces....and 1 of those spaces is purple...so the ratio of stopping on purple is 1/4 or 0.25
The spinner has 4 colors, and purple is one of these. To find the theoretical probability of it stopping at purple, we divide 1 by 4, resulting in 0.25. Therefore, the theoretical probability of the spinner stopping on purple rounded to nearest hundredth is 0.25.
Explanation:The probability of the spinner stopping on the color purple can be calculated by dividing the number of ways this can happen (which is 1, as there's only one purple on the spinner) by the total number of outcomes in the sample space (which is 4, as there are 4 colors on the spinner).
So, the probability would be 1 ÷ 4 = 0.25.
To get the value as a rounded decimal to the nearest hundredth, it stays 0.25 as it is already to the nearest hundredth.
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Emma has two 10$ bills three 5$ bills and two 1$ bill how much more money does she need to buy a game that costs 45$ ?explain.
Answer:
She needs $8 more to buy a game that cost $45
Step-by-step explanation:
10 * 2 = 20
5 * 3 = 15
1 * 2 = 2
20+15+2 = 37
45-37 = $8
She needs $8 more to buy a game that cost $45
In the 2006 Winter Olympics, Sweden won 3 medals more than China. Germany
secured one more than twice the number of medals bagged by sweden. It 54
medals were won in all, how many medals did Germany secure?
Final answer:
To find out how many medals Germany secured in the 2006 Winter Olympics, we denote the number of medals Sweden won as S and create an equation based on the problem's description. Solving for S, we find that Sweden won 14 medals, so Germany, with one more than twice the number of Sweden's medals, secured 29 medals in total.
Explanation:
The question requires us to solve a problem that involves understanding and creating equations based on the given information.
Let's denote the number of medals Sweden won as S. According to the problem, China won S - 3 medals, and Germany won 2S + 1 medals. The total number of medals won by all three countries is 54, so the equation to represent this information is:
S + (S - 3) + (2S + 1) = 54
By combining like terms, we get:
4S - 2 = 54
Now, we will solve for S:
4S = 56 ⇒ S = 14
Now that we know Sweden won 14 medals, we can determine the number of medals Germany secured, which is 2S + 1:
2(14) + 1 = 29
Therefore, Germany secured 29 medals in the 2006 Winter Olympics.
Introduction to the triangle midsegment theorem‼️ can someone help me find BC,DE, and CE please ❓
Answer:
Part 1) [tex]BC=68\ units[/tex]
Part 2) [tex]DE=36\ units[/tex]
Part 3) [tex]CE=34\ units[/tex]
Step-by-step explanation:
we know that
The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side
so
Part 1) Find the length of BC
Applying the Midpoint Theorem
[tex]DF=\frac{1}{2}BC[/tex]
we have
[tex]DF=34\ units[/tex]
substitute the given value
[tex]34=\frac{1}{2}BC[/tex]
solve for BC
[tex]BC=34(2)=68\ units[/tex]
Part 2) Find the length of DE
Applying the Midpoint Theorem
[tex]DE=\frac{1}{2}AC[/tex]
we have
[tex]AC=72\ units[/tex]
substitute the given value
[tex]DE=\frac{1}{2}(72)[/tex]
[tex]DE=36\ units[/tex]
Part 3) Find the length of CE
we know that
[tex]BC=CE+BE[/tex] ----> by addition segment postulate
The point E is the midpoint segment BC
That means
[tex]CE=BE[/tex]
so
[tex]BC=2CE[/tex]
we have
[tex]BC=68\ units[/tex]
substitute
[tex]68=2CE[/tex]
solve for CE
[tex]CE=68/2[/tex]
[tex]CE=34\ units[/tex]
I need help finding what x is
Answer:
Therefore the value of x is 4.
Step-by-step explanation:
Given:
AO = 5x - 8
BO = 3x
AM ≅ BM
To Find :
x = ?
Solution:
In Δ AMO and Δ BMO
AM ≅ BM ……….{Given}
∠ AMO ≅ ∠ BMO …………..{measure of each angle is 90° given}
MO ≅ MO ……….{Reflexive property}
ΔAMO ≅ Δ BMO ….{ By Side-Angle-Side test}
∴ AO ≅ BO ...{corresponding sides of Congruent triangles or CPCT}
on substituting the values we get
[tex]5x-8=3x\\\\5x-3x=8\\\\2x=8\\\\x=\frac{8}{2}=4[/tex]
Therefore the value of x is 4.
Given: ∆AFD, m ∠F = 90°
AD = 14, m ∠D = 30°
Find: Area of ∆AFD
Answer:
[tex]\frac{49\sqrt3}{2}[/tex]
Step-by-step explanation:
30 60 90 Right Trianlge.
what is the solution to y=x+2 and x=-3
Answer:
x=-3, y=-1. (-3, -1).
Step-by-step explanation:
y=x+2
y=-3+2=-1
After completing the fraction division 8 divided by 1/6, Patel used the multiplication below to check his work. 1/48 x 6 = 1/48 x 6/1 = 6/48 = 1/8 which is the most accurate description of patels work? A. Patel found the correct quotient and checked his work using multiplication correctly. B. Patel found the correct quotient but checked his work using multiplication incorrectly. C. Patel found an incorrect quotient but checked his work using multiplication correctly. D. Patel found an incorrect quotient and checked his work using multiplication incorrectly.
Answer:
D. Patel found the incorrect quotient and checked his work using multiplication incorrectly.
Step-by-step explanation:
The dividend is [tex]8,[/tex] the divisor is [tex]\dfrac{1}{6}.[/tex] Divide the dividend by the divisor (division by fraction means multiplication by its reciprocal):
[tex]8\div \dfrac{1}{6}=8\times \dfrac{6}{1}=8\times 6=48,[/tex]
so the quotient is 48, not [tex]\dfrac{1}{48}.[/tex]
To check the answer, Patel has to multiply the quotient by the divisor to get the dividend. Check answer:
[tex]48\times \dfrac{1}{6}=\dfrac{48}{6}=8[/tex]
Hence, Patel found the incorrect quotient and checked his work using multiplication incorrectly.
The most accurate description of Patel's work is option D. Patel found an incorrect quotient and checked his work using multiplication incorrectly. therefore, option D. Patel found an incorrect quotient and checked his work using multiplication incorrectly.
Patel initially calculated 8 divided by 1/6 as 1/48, which is incorrect.
The correct quotient is 48.
When Patel multiplied 1/48 by 6, he got 1/8, which is also incorrect.
The correct result should be 48, not 1/8.
So, Patel's division was incorrect, and his check using multiplication was also incorrect.
In summary, Patel made an error in the initial division and didn't accurately check his work using multiplication, leading to an incorrect final result in both cases.
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A baseball team played 32 games and lost 8 Katy was the catcher in 5/8 of the winning games and 1/4 of the losing games
Answer:
a. Fraction of games won by team is [tex]\frac{3}{4}[/tex].
b. Total games played by Katy as catcher is 17.
Step-by-step explanation:
Here is the complete question: A baseball team played 32 games and lost 8 Katy was the catcher in 5/8 of the winning games and 1/4 of the losing games.
a. What fraction of the games did the team win?
b. In how many games did Katy play catcher?
Given: Total number of games= 32
Total games lost= 8.
Katy was the catcher in 5/8 of the winning games.
Katy was the catcher in 1/4 of the losing games.
Now, finding total number games that team won.
Winning total= [tex]32-8= 24[/tex]
∴ Total number of games that team won is 24.
Next finding fraction of the games did the team win.
Fraction of games won by team is [tex]\frac{Games\ won}{Total\ number\ of\ games}[/tex]
∴ Fraction of games won by team = [tex]\frac{24}{32} = \frac{3}{4}[/tex]
Fraction of games won by team is [tex]\frac{3}{4}[/tex]
Lets find out numbers of games Katy play chatcher.
We know, Katy was the catcher in 5/8 of the winning games.
∴ Katy was catcher= [tex]\frac{5}{8} \times 24= 5\times 3[/tex]
Katy was catcher in 15 of the wining games.
We also know, Katy was the catcher in 1/4 of the losing games.
∴ Katy was catcher= [tex]\frac{1}{4} \times 8= 1\times 2[/tex]
Katy was the catcher in 2 of the losing games.
Total games played by Katy as catcher= Catcher in wining games+ catcher in losing games.
∴ Total games played by Katy as catcher= [tex]15+2= 17 games.[/tex]
Hence, total games played by Katy as catcher is 17.
Aaron is going to a carnival that has games and rides. Each game costs $2.75 and each ride costs $4.75. Aaron spent $20.50 altogether at the carnival and the number of games he played is twice the number of rides he went on. Determine the number of games Aaron played and the number of rides Aaron went on.
Answer:
Step-by-step explanation:
2.75g + 4.75r = 20.50
g = 2r
2.75(2r) + 4.75r = 20.50
5.50r + 4.75r = 20.50
10.25r = 20.50
r = 20.50 / 10.25
r = 2 <==== Aaron went on 2 rides
g = 2r
g = 2(2)
g = 4 <==== Aaron played 4 games
check...
2.75g + 4.75r = 20.50
2.75(4) + 4.75(2) = 20.50
11 + 9.5 = 20.50
20.50 = 20.50 (correct)
Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options
Answer:
SAS , ASA, SSS
Step-by-step explanation:
SAS , side A= side A . Angle B= Angle C, side R= side R
ASA, Angle A= Angle A . Side B= side C, Angle R= Angle R
SSS
side A= side A . Side B= side c, side R= side R
An insurance company pays its agents 40% commission on the first year’s premium and 5% on the second year’s premium for life insurance policies. If the premiums are 500$ per year, what is the total commission that will be paid during the two years?
The total commission that will be paid during the two years is $ 225
Solution:
Given that insurance company pays its agents 40% commission on the first year’s premium and 5% on the second year’s premium for life insurance policies
The premiums are 500$ per year
Commission on first year:
40% commission on the first year’s premium
Thus 40 % commission on $ 500
[tex]\rightarrow 40 \% \text{ of } 500\\\\\rightarrow 40 \% \times 500\\\\\rightarrow \frac{40}{100} \times 500\\\\\rightarrow 200[/tex]
Thus commission paid for first year is $ 200
Commission on second year:
5 % commission on the second year’s premium
Thus 5 % commission on 500
[tex]\rightarrow 5 \% \text{ of } 500\\\\\rightarrow 5 \% \times 500\\\\\rightarrow \frac{5}{100} \times 500 = 25[/tex]
Thus commission paid for second year is $ 25
Total commission paid = $ 200 + $ 25 = 225
Thus Total commission paid is $ 225
Graph the linear equation find three points that solves the equation 2y=5x+11
Answer:
AttachmentStep-by-step explanation:
Convert to the slope-intercept form (y = mx + b):
[tex]2y=5x+11[/tex] divide both sides by 2
[tex]\dfrac{2y}{2}=\dfrac{5x}{2}+\dfrac{11}{2}\\\\y=\dfrac{5}{2}x+\dfrac{11}{2}[/tex]
We choose any three x values and calculate the y value:
for x = -1
[tex]y=\dfrac{5}{2}(-1)+\dfrac{11}{2}=-\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{6}{2}=3\to A(-1,\ 3)[/tex]
for x = 1
[tex]y=\dfrac{5}{2}(1)+\dfrac{11}{2}=\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{16}{2}=8\to B(1,\ 8)[/tex]
for x = -3
[tex]y=\dfrac{5}{2}(-3)+\dfrac{11}{2}=-\dfrac{15}{2}+\dfrac{11}{2}=-\dfrac{4}{2}=-2\to C(-3,\ -2)[/tex]
Mark the points on the coordinate plane and draw a line through the given points.
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-7, -5), B(-7, 6 C(-4, 6) and D(-4, -5) Given these coordinates, what is the length of side CD of this rectangle?
(-8,1) should be the correct answer! Good Luck and Happy Holidays!!
You want to put $2500 in a simple interest account. it has 4% Annual interest rate how long will it take you to earn $200 in interest?
Answer:
2 years
4% of 2500 is 100
So 100x2 years would be 200
Answer:
Step-by-step explanation:
SI = PRT/100
$200 = 2500 * 4*T/100
200 *100 / 2500 *4 = T
T = 200 * 100 /2500*4 = 2
T = 2 years
Please help!! Which table shows a proportional relationship between x and y?
Answer: The second table
Step-by-step explanation:
For the table to show proportional relationship between x and y , then they must have a common ratio. that is x/y must be the same throughout
Table 1
[tex]x_{1}[/tex] = 1 [tex]y_{1}[/tex] = 2
[tex]x_{2}[/tex] = 3 [tex]y_{2}[/tex] = 5
[tex]x_{3}[/tex] = 4 [tex]y_{3}[/tex] = 8
[tex]x_{4}[/tex] = 7 [tex]y_{4}[/tex] = 14
[tex]\frac{x_{1}}{y_{1}}[/tex] = 1/2
[tex]\frac{x_{2}}{y_{2}}[/tex] = 3/5
[tex]\frac{x_{3}}{y_{3}}[/tex] = 4/8 = 1/2
[tex]\frac{x_{4}}{y_{4}}[/tex]= 7/14 = 1/2
Since the ratio is not the same throughout , then x and y are not proportional
Table 2
[tex]x_{1}[/tex] = 7 [tex]y_{1}[/tex] = 1
[tex]x_{2}[/tex] = 14 [tex]y_{2}[/tex] = 2
[tex]x_{3}[/tex] = 28 [tex]y_{3}[/tex] = 4
[tex]x_{4}[/tex] = 35 [tex]y_{4}[/tex] = 5
[tex]\frac{x_{1}}{y_{1}}[/tex] = 7/1 = 7
[tex]\frac{x_{2}}{y_{2}}[/tex] = 14/2 = 7
[tex]\frac{x_{3}}{y_{3}}[/tex] = 28/4 = 7
[tex]\frac{x_{4}}{y_{4}}[/tex]= 35/5 = 7
Since the ratio is the same throughout , it means that x and y are proportional.
Doing the same for table 3 and 4 , x and y are not proportional