A rectangle has a fixed area of 24 cm². Complete these sentence: The length and width of the rectangle are ________ proportional and can be written in symbols as ________
Answers
Answer:
Step-by-step explanation:
The rectangle's are is 24cm²
Let x be the lenght and y be the width x*y = 24 ⇒ x=24/y so the width and lenght of a triangle are inversly proprtional and can be written in symbols as x∝ 1/y
Related Questions
marcus receives an inheritance of $13,000. he decides to invest this money in a 10-year certificate of deposit (CD) that pays 3.0% interest compounded monthly. how much money will marcus receive when he redeems the CD at the end of 10 years?
Answers
Answer:
Marcus will receive a total of $17,542.2 when he redeems the certificate of deposit (CD) at the end of 10 years
Step-by-step explanation:
Principal(p)=$13,000
Rate(r)=3.0%
Period(n)=12 months
Time(t)=10 years
A=p(1+r/n)^nt
=13,000(1+0.03/12)^12*10
=13,000(1+0.0025)^120
=13,000(1.0025)^120
=13,000(1.3494)
=17,542.2
A=$17,542.2
Marcus will receive a total of $17,542.2 when he redeems the certificate of deposit (CD) at the end of 10 years
Which theorem can you use to prove that GHJ and GKJ are congruent?
A. ASA
B. SAS
C. SSS
D. HL
Answers
Answer:
D) HL
Step-by-step explanation:
ΔGHJ ≅ ΔGKJ by HL Congruence rule.
What is Congruence?According to the hypotenuse-leg (HL) theorem, a right triangle is congruent if each of its hypotenuse and legs are congruent with their corresponding hypotenuse and legs in another right triangle.
Given:
In ΔGHJ and ΔGKJ
<H = <K= 90 degree
GJ= GJ {common}
GH= GK= 8 units.
Thus, ΔGHJ ≅ ΔGKJ by HL Congruence rule.
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Monique is factoring the expression 4 x + 16 x y. Her work is shown below. Factors of 4x: 1, 2, 4, x Factors of 16xy: 1, 2, 4, 8, 16, x, y GCF: 4x Factored expression: 4 x (0 + 4 y) Which best describes the accuracy of Monique's solution? Monique's solution is accurate. Monique made an error when listing the factors, which affected the GCF and the factored expression. Monique made an error when determining the GCF from her list of factors. Monique made an error when writing the factored expression.
Answers
Answer:
Monique made an error when writing the factored expression.
Step-by-step explanation:
The factorisation of the expression 4x+16xy is 4x(1+4y).
The given expression is 4x+16xy.
What is factorisation?In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
Now, 4x=2×2×x and 16xy=2×2×2×2×x×y
so, the GCF of terms 4x.
Now, 4x(4x/4x+16xy/4x)=4x(1+4y)
Therefore, the factorisation of the expression 4x+16xy is 4x(1+4y).
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Write the slope-intercept form of the equation of the line that has the same y-intercept as the black line shown and passes through the point (4, 4) on the blue line. Explain how you determined your answer.
Answers
Answer:
y = 0.5x + 2
Step-by-step explanation:
the y-intercept is 2, as shown in the graph
the slope is 0.5. this is because while the x-value goes up by 2, the y-value goes up by one (from 0, 2 to 2, 3).
using the slope formula of rise / run, you get 1/2, which is equal to 0.5
Kite E F G H is inscribed within a rectangle. Points F and H are midpoints of the sides of the rectangle. Points E and G are parallel to the side of the rectangle.
Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle.
Which statement describes how the location of segment EG affects the area of EFGH?
The area of EFGH is One-fourth of the area of the rectangle if E and G are not midpoints.
The area of EFGH is One-half of the area of the rectangle only if E and G are midpoints.
The area of EFGH is always One-half of the area of the rectangle.
The area of EFGH is always One-fourth of the area of the rectangle.
Answers
Answer:
The area of EFGH is always One-half of the area of the rectangle.Step-by-step explanation:
If F and H are midpoints of sides of rectangle then FH is parallel to the other side of rectangle so FH is perpendicular to the EG. That means the lenght of FH is equal to lenght of rectangle, and the lenght of EG is equal to width of rectangle.
So the area of the rectangle: [tex]A_{rectangle}=EG\cdot FH[/tex]
FH ⊥ EG so the area of quadrangle EFGH:
[tex]A_{_{EFGH}}=\frac12EG\cdot FH=\frac12A_{rectangle}[/tex]
no matter the location of segment EG
The area of EFGH is always One-half of the area of the rectangle.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have given that;
the kite EFGH is inscribed in a triangle and F and H are midpoints and EG is parallel to the side of rectangle.
The kite consists of 2 triangle that are EFG and EHG.
Now,
In a triangle EFG is,
= 1/2 x EG x h......(1)
where h is the height from F to EG
Also the area of EHG:
= 1/2 x EG x h₁
where is the height from H to EG
We also know that h₁ + h is the width of the rectangle and EG is the length of the rectangles.
Area of Kite = = 1/2 x EG x h + 1/2 x EG x h₁
Also, The area of a rectangle is rectangle length × rectangle width.
Thus, The Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle.
Hence, The statement describes how the location of segment EG affects the area of EFGH is the area of EFGH is always One-half of the area of the rectangle.
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The equations x minus y = 2, x minus 2 y = negative 2, x + y = 2, and x + 2 y = negative 2 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, 2) and (2, 0). Orange line goes through (2, 0) and (0, negative 2). Pink line goes through (2, negative 2), and (0, negative 2). Blue line goes through (0, negative 2) and (2, 2). Which system of equations has a solution of approximately (0.7, –1.4)? x minus y = 2 and x + 2 y = negative 2 x minus 2 y = negative 2 and x + y = 2 x minus y = 2 and x minus 2 y = negative 2 x + y = 2 and x + 2 y = negative 2
Answers
Answer:
x - y = 2 and x + 2y = -2
Step-by-step explanation:
Since you have the graph, you can easily see that the point of interest is nearest the intersection of the orange and pink lines.
__
Recognizing that the intercepts of a line in standard form are ...
ax +by =c
x-intercept: c/a
y-intercept: c/b
You can easily determine the corresponding intercepts for the given lines. We can tell from the graph that we only need to know what the y-intercept is in order to match the equation to the line. Here are the y-intercepts:
x -y = 2 ⇒ (0, -2) — orangex -2y = -2 ⇒ (0, 1) — bluex +y = 2 ⇒ (0, 2) — greenx +2y = -2 ⇒ (0, -1) — pinkThe system of equations with the desired solution is ...
x -y = 2 and x +2y = -2
Answer:
A: x-y= 2 and x+2y= -2
Step-by-step explanation:
I got it right on Edge 2020
Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = –9(x + 1)2 – 7 g(x) = 4(x – 3)2 + 1 g(x) = –3(x – 4)2 – 6 g(x) = 8(x – 3)2 – 5
Answers
Answer:
[tex]g(x) = 8\cdot (x-3)^{2}-5[/tex]
Step-by-step explanation:
Given that parent function represents a parabola, the standard form with a vertex at (h,k) is now described:
[tex]y-k = C\cdot (x-h)^{2}[/tex]
[tex]y = C \cdot (x-h)^{2} + k[/tex]
Where:
[tex]x[/tex], [tex]y[/tex] - Independent and dependent variables, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical component of the vertex, dimensionless.
[tex]C[/tex] - Vertex factor, dimensionless. (If C > 0, then vertex is an absolute minimum, but if C < 0, there is an absolute maximum).
After reading the statement of the problem, the following conclusion are found:
1) New function must have an absolute minimum: [tex]C > 0[/tex]
2) Transformation to the right: [tex]h > 0[/tex].
3) Transformation downwards: [tex]k < 0[/tex]
Hence, the right choice must be [tex]g(x) = 8\cdot (x-3)^{2}-5[/tex].
Answer:
Choice D
Step-by-step explanation:
Took the test
help quick plz must get this correct I will make u a brainllest
Answers
Answer:
CPCTC
Step-by-step explanation:
You already proved that triangle BAD is congruent to CAD, this means that all of the corresponding angles and sides with be congruent (CPCTC). That means BD is congruent to CD. Hope this helps!
Help me please as fast as fast as you can 20 points!!
Answers
Answer:
see below
Step-by-step explanation:
4! = 4*3*2*1 = 24
10 C3 = 10 CHOOSE 3 =10! /(3! (10 - 3)!) = 10! / 3! * 7! = 10*9*8 / 3*2*1 = 120
7P3 = permutation = 7! / (7-3)! = 7! /4! = 7*6*5 = 210
Which of the following r-values represents the strongest correlation?
Answers
Answer:
A. -0.91
Step-by-step explanation:
Correlation coefficient is represented by values from -1 to 1. The closer the value is to -1 or 1, the stronger the correlation coefficient, which indicates that the data points being plotted on a scatter plot are clustered more closely along the best line of fit.
Correlation could be positive or negative.
If negative, it means, as one variable increases, the other variable decreases also. But, if positive, it means as one variable increases, the other variable increases also, or as one variable decreases, the other decreases also. Both change in the same direction.
A correlation coefficient that has a value closer to -1 shows a strong negative correlation. Meaning, the data points are clustered closely along the line slope on the scatter plot.
Therefore, r-value that is the strongest among the given options in the question is -0.91.
The answer is A. -0.91.
A magician asks two volunteers to each draw a card from a standard deck of cards. What is the probability that the first card is a heart and the second card is a dimand?
Answers
Answer:
The probability of choosing a heart, P(Heart) = 13/52 = 0.25
Step-by-step explanation:
Please help ASAP ‼️‼️‼️‼️‼️‼️
Answers
Answer:
B. [tex]\bold{g(x)=(\frac12x)^2}[/tex]Step-by-step explanation:
vertex of g(x) is (0, 0), so:
[tex]g(x)=a(x-0)^2+0\\\\g(x)=ax^2 \qquad and\qquad (2,\,1)\in g(x)\\\\1=a\cdot2^2\\1=4a\\a=\frac14\\\\g(x)=\frac14x^2=(\frac12x)^2[/tex]
When using a debit card: Question options: A:There are always fees. b:Identification is always required. c:You still need to record transactions in your checkbook. d:You are not personally liable for more than $50 if it is stolen.
Answers
Answer:
D.
Step-by-step explanation:
Since this isn't a credit card, there are no interests or fees on a debit card, so A is incorrect. B is also incorrect. You only need identification when you are withdrawing or depositing at a bank, but purchases made in stores or online do not need your identification. You also don't need to record transactions in your checkbook (but it is recommend to keep track of purchases). Modern day technology already records transaction history and all you need to do is access it online.
D is correct because if someone steals your PIN for your debit card, they could go to stores and use that money. You can dispute charges and report to the bank if that happens.
The Lewis family and the Perry family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was per hour. The water output rate for the Perry family's sprinkler was per hour. The families used their sprinklers for a combined total of hours, resulting in a total water output of . How long was each sprinkler used
Answers
The Lewis family and the Perry family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 15 L per hour. The water output rate for the Perry family's sprinkler was 40 L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850 L . How long was each sprinkler used
Answer:
Hours of use of sprinkler by Lewis family is 30 hours.
Hours of use of sprinkler by Perry family is 35 hours.
Step-by-step explanation:
Let W = hours of use by Lewis family
65 - W = hours of use by Perry family
Then;
15W + 40*(65 - W) = 1850
15W + 2600 - 40W = 1850
(15 - 40)W = 1850 - 2600
-25W = −750
W = 750/25 = 30
Therefore;
W = 30
65 - W = 65 - 30 = 35
Hence,
Hours of use by Lewis family is 30 hours.
Hours of use by Perry family is 35 hours.
Lunch Combinations
Soup + Salad = $4.25
Soup + Sandwich = $4.75
Salad + Sandwich = $5.50
Ehat is the individual price of soup
Answers
Answer: Soup is $1.75
Step-by-step explanation:
Salad is $2.50
Sandwich is $3
Soup is $1.75
Answer:
Step-by-step explanation:
Answer: Soup is $1.75
Step-by-step explanation:
Salad is $2.50
Sandwich is $3
Soup is $1.75
prime factor of 841
Answers
Answer:
the prime factor of 841 is 29
Step-by-step explanation:
841 divided by 29 gives back 29 without any remainder
NEED ANSWER ASAP What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?
Answers
Answer:
(A) 1
Step-by-step explanation:
We know that the formula is x = (m/m+n) (x2-x1) + x1.
But the trick to the question which is why everyone is getting it wrong is because it asks for F to D not D to F.
The reason everyone else was getting 4 was because they were using this.
They solved the equation x = (8/8+5) (9-[-4]) -4 where it was D to F. This equation does turn out to be 4 but it is incorrect.
However, the correct equation (because it is supposed to be F to D) is
x = (8/8+5) (-4 -9) +9 which is in fact equal to 1.
I also just took the quiz and got 100%.
PRESS THAT THANKS BUTTON!!!
Which expression is equivalent to -36 - 8−36, 36, minus, 8? Choose 1 answer: Choose 1 answer: (Choice A) A -36+(-8)−36+(−8)minus, 36, plus, left parenthesis, minus, 8, right parenthesis (Choice B) B -8+36−8+36minus, 8, plus, 36 (Choice C) C 8-368−368, minus, 36 (Choice D) D 36+836+8
Answers
Answer:
Choice A: -36 + (-8)
Step-by-step explanation:
We want to find the equivalent expression to -36 - 8
The correct option is Choice A.
Choice A is -36 + (-8)
The reason is that the product of the signs + and - is -, i.e.
+ * - = -
Hence, + (-8) is the same thing as -8 and Choice A becomes -36 - 8
what is the greatest common factor of the polynomial below? 8x^2-4x
Answers
Answer:
4x
Step-by-step explanation:
8x^2 = 2*2*2 *x*x
4x = 2*2 *x
The greatest common factor is 2*2*x = 4x
Answer:
A
Step-by-step explanation:
8x² - 4x
Factor out the greatest common factor.
4x(2x) - 4x(1)
4x(2x - 1)
The greatest common factor of the polynomial is 4x.
Carlos' hourly wage increased by 30% this year. If his previous salary was $20 an hour, what is his new hourly wage?
Answers
Answer:
$26.
Step-by-step explanation:
His original salary was $20. It increased by 20%. In other words, the total salary he earns is now:
[tex]20+20(.3)=20(1.3)=26[/tex]
His new salary is $26.
Note: For the second step, I used the distributive property.
[tex]20(1)+20(.3)=20(1+.3)=20(1.3)[/tex]
Select the correct answer.
A particular strain of a common bacteria replicates itself every 14 minutes. Which of the following does this situation represent
Answers
Answer:
c
Step-by-step explanation:
Answer:
Both a relation and a function
Step-by-step explanation:
Replicates itself every 14 minutes, which is exponential function
Evaluate the following expression using the values given: Find 2r2 + 3s3 − r2 + 4t2 − r2 if r = −2, s = −3, and t = 5.
Answers
Answer:
The evaluated answer to this equation is 19.
Step-by-step explanation:
2r² + 3s³ - r² + 4t² - r²
In the problem, we are given values for the variables in the equation.
r = -2
s = -3
t = 5
Let's plug these numbers into the equation.
2(-2)² + 3(-3)³ - (-2)² + 4(5)² - (-2)²
First, simplify the exponents.
2(4) + 3(-27) - (4) + 4(25) - (4)
Next, multiply the numbers starting from left to right.
8 + (-81) - 4 + 100 - 4
Add 8 and -81 together.
-73 - 4 + 100 - 4
Subtract 4 from -73.
-77 + 100 - 4
Add -77 to 100.
23 - 4
Subtract 4 from 23.
19
So, your final simplified answer to this equation is 19.
State if a triangle is acute ,obtuse, or right
Answers
Answer:
It is an acute angle due to the angle formed at the vertex being less than 90 degrees
Answer:
acute triangle
Step-by-step explanation: sorry no step by step explanation i am in a rush anyway have a great day bye!!! :D please give brainliest
Please show your work! *grade 9 work*
Answers
Answer:
c = 6√2 cm
Step-by-step explanation:
a² + b² = c²
6² + 6² = c²
36 + 36 = c²
108 = c²
c = ± √108 = ± 6√2
Since the side length of a triangle can't be negative, c = -6√2 is an extraneous solution; therefore the answer is c = 6√2.
Answer:
72 cm or 6 square root of 2
Step-by-step explanation:
a^2+b^2=c^2
6^2+6^2=c^2
36+36=72
c= 72 cm. or 6 square root of 2
hope this helps.
The whole number which is not a natural number is
Answers
Answer:
All negative numbers
Step-by-step explanation:
They are not whole numbers
Answer:
0
Step-by-step explanation:
Since negative numbers are not considered whole numbers, they are not included here. All natural numbers are whole numbers but not all whole numbers are natural numbers. 0 is a whole number but it doesn't count as a natural number which makes the answer 0
Please answer if in two minutes
Answers
Answer:
y = 7
z = 1
Step-by-step explanation:
If the triangles are congruent
AB = QR
y+ 34 = 41
Subtract 34 from each side
y = 41-34
y = 7
and QP = BC
38 = z+37
Subtract 37 from each side
38-37 = z
1 =z
Answer:
y = 7
z = 1
Step-by-step explanation:
The triangles are congruent, the length of the sides are equal.
y + 34 = 41
y = 41 - 34
y = 7
z + 37 = 38
z = 38 - 37
z = 1
(2*6)^3/2 in simplest form
Answers
Answer:
[tex]\sqrt{1728}[/tex]
Step-by-step explanation:
=> [tex](2*6)^{3/2}[/tex]
=> [tex](12)^{3/2}[/tex]
=> [tex]1728 ^{1/2}[/tex]
=> [tex]\sqrt{1728}[/tex]
Can someone help me solve this?
What is side b? Thank you
Answers
Answer:
The answer is
b = 39.32 feetStep-by-step explanation:
To find side b we use cosine
cos ∅ = adjacent / hypotenuse
From the question
side c is the hypotenuse
side c = 48 feet
side b is the adjacent
∅ = 35°
We have
cos 35 = b/c
cos 35 = b / 48
b = 48 cos 35
b = 39.319
b = 39.32 feet to 2 decimal places
Hope this helps you
Answer:
b ≈ 39.32 ft
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{b}{c}[/tex] = [tex]\frac{b}{48}[/tex] ( multiply both sides by 48 )
48 × cos35° = b, thus
b ≈ 39.32 ft ( to 2 dec. places )
Find the solution set. 8x^2-2x-3=0 separate the two values with with a comma.
Answers
Answer:
x = -1/2, 3/4
Step-by-step explanation:
Step 1: Factor
(2x + 1)(4x - 3) = 0
Step 2: Find roots
2x + 1 = 0
2x = -1
x = -1/2
4x - 3 = 0
4x = 3
x = 3/4
Tanesha can make 3 scrapbook albums in 2 hours. How long will it take her for to make 105 albums?
Answers
Answer: 70 hours
Step-by-step explanation:
First do 105/3(35) Then multiply 35*2(70)
Explanation 3_____2
105_______x
Then2*105=210
3x=210
X=70