Susan has a rectangle and a right triangle.
• The length of the rectangle is 4 more than its width, w.
.
• The length of the shorter leg of the triangle is equal to the rectangle's
width.
• The length of the longer leg of the triangle is twice the length of the
rectangle.
Answers
Answer:
A. 2w² + 8w
Step-by-step explanation:
rectangle: A = w(w+4) = w² + 4w
triangle: A = 1/2(2(w+4)(w)) = 1/2(2w+8)(w) = 1/2(2w²+8w) = w² + 4w
Total Area = w² + 4w + w² + 4w = 2w² + 8w
Related Questions
Choose the pair of complementary angles
Answers
Answer:
B is the answer
Step-by-step explanation:
When you add AOB and NOM its 90 degrees. AOB is 29 + NOM that is 61. 61 + 29 = 90 degrees. Since complementry angles are 90 degrees, it is correct! Pls tell me if its correct or not!
Answer:
B is the answer
Step-by-step explanation:
ADD-
AOB and NOM
=90 degrees
AOB =29
add "NOM"
NOM= 32
=61.
61 + 29 = 90 degrees.
Complementary angles are 90 degrees
Please hurry I’m being timed!!
The line about which a three-dimensional figure is rotated to obtain an object identical to the original is aan)
A. horizontal plane.
B. plane of symmetry.
C. reflectional axis.
D. axis of symmetry.
Answers
gogle said:
The line about which a three-dimensional figure is rotated to obtain an object identical to the original is a(n) horizontal plane.
The line about which a three-dimensional figure is rotated to obtain an object identical to the original is a horizontal line.
The correct option is A.
What is rotation?Each point in a figure is transformed into a rotation by rotating it a certain amount of degrees around another point.
From the given choices:
The horizontal line is an appropriate line to obtain an object identical to the original.
The line about which a three-dimensional figure is rotated to obtain an object identical to the original is a horizontal line.
Therefore, the required line is a horizontal line.
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Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years find out how much he owes and interest and how much he needs to pay back
Answers
Answer:
P=3000$
T=2 years
R=1.6% per annum
Now,
interest=(3000×2×1.6)/100=96$
Amount=P+interest=3096$
Hence,Conan needs to pay back 3096$ and the interest is 96$
I need the answer to this question please!
Answers
5 * root(x ^ 2, 3) is the equivalent expression.
Why do roots grow in numbers?Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.
Only if the numbers under the radical sign are equal can you add or subtract square roots themselves. The original number will still be in the radical sign after adding or subtracting the coefficients (numbers in front of the radical sign). Implement the suggested action.
5 * root(x ^ 2, 3) is the equivalent expression.
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What is the 36th term of 12,17 and 22
Answers
a=12,d=17-12=5
nth term =a+(n-1)d
36th term=12+(36-1)5
=12+(35×5)
12+175
36th term=187
Answer: 187
Step-by-step explanation: 17 - 12 = 5 and 22 - 17 = 5
aₙ = a₁ + (n - 1) d
where a₁ = 12, n = 36, d = 5
a₃₆ = 12 + (36 - 1) 5
a₃₆ = 12 + 35 × 5
a₃₆ = 12 + 175
a₃₆ = 187
187 is the 36th term
Mason bought 16 tickets to a baseball game. The group rate saved him $5.75 per ticket. He paid a total of $296.00 for the tickets. What was the regular price of a ticket to the game
Answers
The regular price of a ticket to the game was $204.00.
We can use algebra to solve the problem. Let x be the regular price of a ticket to the game.
We know that the group rate saved Mason $5.75 per ticket, so the regular price of a ticket is x + $5.75.
We know that Mason bought 16 tickets and paid a total of $296.00, so we can set up the following equation:
x + $5.75 = (x + $5.75) * 16 = 16x + $92
So the regular price of a ticket is x = $296.00 - $92 = $204.00
Therefore, the regular price of a ticket to the game was $204.00.
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1. Two equivalent cubes are shown. The edge length of each dice are 3 centimeters,
What is the combined volume of the both dice in cubic centimeters?
A 54 cm
B 18 cm
C 9 cm
D 27 cm
Answers
Answer:
Step-by-step explanation:
Four years ago, Spencer borrowed money from his cousin who charged him simple interest. If Spencer paid his cousin back $62, what was the interest rate? Could you have figured this out if the interest rate was compounded instead?
Answers
Answer: Municipal Bank will charge him 8% simple interest
Step-by-step explanation:
You invest $20,000 in two accounts paying 12% and 11% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $2,255.00.
Answers
Answer: [tex]\$5500, \$14,500[/tex]
Step-by-step explanation:
Given
[tex]\$20,000[/tex] is invested in two accounts with a 12% and 11% rate of interest.
Total interest after a year is [tex]\$2255[/tex]
Suppose x amount is invested in first, so the remaining amount is invested in other
Simple interest and Compound interest is the same for a year
[tex]\therefore \text{Interest}=\dfrac{P\times R\times T}{100}[/tex]
For first investment
[tex]I=\dfrac{x\times 12\times 1}{100}\\\\I=0.12x[/tex]
For second investment
[tex]II=\dfrac{\left(20,000-x\right)\times 11\times 1}{100}\\\\II=0.11\left(20,000-x\right)[/tex]
The sum of the two must be [tex]\$2255[/tex]
[tex]\Rightarrow 0.12x+0.11\left (20,000-x\right)=2255\\\Rightarrow 0.01x=2255-2200\\\\\Rightarrow x=\dfrac{55}{0.01}\\\\\Rightarrow x=\$5500[/tex]
Remaining amount is
[tex]\Rightarrow 20,000-5500\\\Rightarrow \$14,500[/tex]
which two angles named below are supplementary in the figure? ill give brainliest
Answers
Answer:
D. Angles 4 and 7
Step-by-step explanation:
Answer 1 and 4 are supplementary angles.
Step-by-step explanation:
Supplementary angles are angles adding up to 180, the only angles listed that are supplementary angles is 1 and 4.
Have a good day!
Find the magnitude and direction of the vector <3,9>. Round angles to the nearest degree and other values to the nearest tenth.
Answers
Answer:
Magnitude: 3√10
Direction angle: 71.56°
Step-by-step explanation:
The magnitude ||v|| of a vector <a,b>, would be:
[tex]||v||=\sqrt{a^{2}+b^{2}[/tex]
[tex]||v||=\sqrt{3^{2}+9^{2}[/tex]
[tex]||v||=\sqrt{9+81}[/tex]
[tex]||v||=\sqrt{90}[/tex]
[tex]||v||=3\sqrt{10}[/tex]
The vector's reference angle would be:
[tex]tan\alpha =|\frac{b}{a}|[/tex]
[tex]tan\alpha =|\frac{9}{3}|[/tex]
[tex]tan\alpha =|3|[/tex]
[tex]tan\alpha =3[/tex]
[tex]\alpha = 71.56[/tex]
If [tex]\alpha[/tex] is your reference angle, then your direction angle ∅ depends on what quadrant the vector is located in. Since <3,9> is located in Quadrant I, then ∅= [tex]\alpha[/tex], which means your direction angle is also 71.56°
Answer:
9.5; 72°
Step-by-step explanation:
HELP PLEASE LAST QUESTION AND I CAN SUBMIT!!! AND NO LINKS OR I WILL REPORT....
c) The height of each cylinder in a set of food-storage containers is 30 cm.
The radius of the largest container is 10 cm.
The volume of the smallest container is one-third the volume of the largest container.
The volume of the middle-sized container is two-thirds the volume of the largest
container. What is the volume of each container?
Answers
Answer:
137 cm. are the volume each con... because of 2 serinemital factors...
Step-by-step explanation:
HOPE IT HELPS!!
How do you find the value of 3 7?
Answers
Step-by-step explanation:7/3 and if it goes in a inf loop it's a repeating
Graph the solution to this inequality on the number line.
-4x> 8.4
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
Answers
The Graph solution to this inequality on the number line is lies between -4 > 8.4 and their numbers are -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3.
How do you graph an inequality's solution on a number line?Draw a circle around the number to indicate an inequality, such as x>3, on a number line (e.g., 3). In case the sign also states equal to, complete the circle (or ). If the sign doesn't include equal to (> or), leave the circle empty.
How would one graph an inequality?When plotting an inequality, use the,, >, or sign as a = sign. If the inequality is either or, graph the equation as a dotted line. If the inequality is either or, graph the equation as a solid line.
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Is 4x² 3x 7 a polynomial in one variable?
Answers
'x' is the only variable in the provided polynomial. As a result, the polynomial 4x² - 3x + 7 has one variable.
what is polynomial ?A polynomial is an expression in mathematics made up of variables (sometimes referred to as indeterminates) and coefficients that only employs the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that combines variables, constants, and exponents utilizing addition, subtraction, multiplication, and division of numbers (No division operation by a variable).
given
'x' is the only variable in the provided polynomial. As a result, the polynomial 4x² - 3x + 7 has one variable.
The following list includes a few examples of polynomials with one variable: x+2. x2+3x+2.
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what is the sqaure of
3
4
and
5
Answers
The square of the given numbers 3, 4, and 5 are 9, 16, and 25 respectively.
What is the square of a number?The square of a number is the product of the number with itself. Therefore, if there is a number x then its square will be the product of x and x. It is denoted by 2 in superscript form over the number whose square is needed to be calculated.
The squares of the given numbers are,
3² = 3 × 3 = 9
4² = 4 × 4 = 16
5² = 5 × 5 = 25
Hence, the square of the given numbers 3, 4, and 5 are 9, 16, and 25 respectively.
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What is the value of x in log2 x 3?
Answers
value of x = 8 as per logarithm laws.
What is logarithm?In mathematics, logarithm is an exponent or power for which a particular number is raised to achieve a required number. In other words, logarithm is a mathematical expression that states about how many times a number can be multiplied by the same number to get some required numbers.
The method of expressing any exponential relationship in the inverse form is called log notation.
What is the value of x in the question?In this question, we are given a log base 2 or binary logarithm.
given, ㏒₂ x = 3
as per the logarithm laws ㏒a y = m
y = a∧m
we write. ㏒₂ x = 3
x = 2³
hence, x = 8
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WILL MAKE BRAINLIEST!!Match the radical to its simplified form.
1. 9i
2. 5i√2
3. 12√6
4.6i√7
A. √-81
B. 4√54
C. √-50
D. √-252
Answers
After simplification the correct matching is
1) 9i - A)[tex]\sqrt{-81}[/tex]
2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]
3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]
4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]
What is simplification?
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
Here to convert radical to simplified form we need to simplify them then
A)=> [tex]\sqrt{-81}[/tex] = [tex](\sqrt{i*9*9} })[/tex] = 9i
B) => [tex]4\sqrt{54} = 4\sqrt{9*6}= 4\sqrt{3^2*6}= 4*3\sqrt{6} = 12\sqrt{6}[/tex]
C) => [tex]\sqrt{-50} = \sqrt{i^2*25*2}=\sqrt{i^2*5^2*2}=5i\sqrt{2}[/tex]
D) => [tex]\sqrt{-252} = \sqrt{i^2*36*7}=6i\sqrt{7}[/tex]
Hence the correct matching is
1) 9i - A)[tex]\sqrt{-81}[/tex]
2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]
3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]
4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]
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To simplify a square root, simply factor the number and extract the roots of any perfect squares found from the radical sign.
What is meant by simplification?To simplify means to make something easier. Simplifying an equation, fraction, or problem in mathematics means taking it and making it simpler. Calculations and problem-solving techniques help to simplify the situation.Simplify a radical expression that use the Product Property.
Find the radicand's largest factor that is a perfect power of the index. Using that factor, rewrite the radicand as a product of two factors.Rewrite the radical as the product of two radicals using the product rule.Simplify the perfect power's root.To convert radicals to simplified forms, we must first simplify them.
A) = [tex]\sqrt{-81}[/tex]
= ([tex]\sqrt{i*9*9}[/tex] )
= 9i
B) = 4[tex]\sqrt{54}[/tex]
= 4[tex]\sqrt{9*6}[/tex]
= 4[tex]\sqrt{3^{2}*6 }[/tex]
= 4*3√6
= 12√6
C) = [tex]\sqrt{-50}[/tex]
= [tex]\sqrt{i^{2}*25*2 }[/tex]
= [tex]\sqrt{i^{2}*5^{2}*2 }[/tex]
= 5i√2
D) = [tex]\sqrt{-252}[/tex]
= [tex]\sqrt{i^{2}*36*7 }[/tex]
= 6i√7
As a result, the correct match is
1) 9i - A) [tex]\sqrt{-81}[/tex]
2) 5i - C) [tex]\sqrt{-50}[/tex]
3) 12 - B) 4[tex]\sqrt{54}[/tex]
4) 6i - D)[tex]\sqrt{-252}[/tex]
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What is the equation of this line of best fit in slope-intercept form?
y = negative one halfx + 8
y = −2x + 8
y = −8x + one half
y = −8x + 2
Answers
Therefore , the solution of the given problem of slope comes out to be
y = (-1/2)x + 8.
Define slope.The slope-intercept formulation of an equation is used to represent each time the formula of a line is stated as y = mx + b. The line's slope is represented by the m. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in the formula y = 3x - 7.
Here,
Locate the slope first.
These two positions (0, 8) and are in the line, therefore we know that (6,5)
Slope: (y2-y1)/(x2 - x1)
Slope = 8-5 / 0-6
Slope = 3/-6 => Slope = -1/2
The gradient is -1/2. When x = 0, you can find the y-intercept. We also know that the line passes through the point (0,8), and since x = 0, the y-intercept is equal to 8.
using the slope-intercept form, which is
Using the equation y = mx + b, where m denotes the slope and b the y-intercept, we get:
y = (-1/2)x + 8
Therefore , the solution of the given problem of slope comes out to be
y = (-1/2)x + 8.
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A figure made by two intersecting lines or two rays extending from the same point.
Answers
A figure made by two intersecting lines or two rays extending from the same point is called an angle.
What is an angle?
Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.
A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.
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How do I complete this equation
Answers
Answer:
130°
Step-by-step explanation:
All the interior angles should add up to 540 degrees because it's a pentagon
∠T ≅∠S, so ∠T is also 115°
∠P and ∠R are both 90°
Add everything up and solve for ∠Q:
115 + 115 + 90 + 90 + m∠Q = 540
410 + m∠Q = 540
m∠Q = 130°
What is the reflection point of (- 3/4 across the line y 2?
Answers
According to the following graph, the reflection point of (-3,4) across the line y = 2 is (-3,0).
The term reflection point in math is defined as
Here we need to find the reflection point of (-3, 4) across the line y = 2.
Here first we have t plot the point on the graph, and then we have to plot the line equation y = 2 on the graph,
Here in order to find the reflection of a point along the x-axis, then we have to keep the abscissa constant and see the reflection of ordinate along the x-axis.
Based on these rule, the resulting graph is obtained as follows.
Through the graph we have identified that the resulting reflection point is (-3,0).
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Answer the statistical measures and create a box and whiskers plot for the following set of data.
2, 4, 4, 6, 6, 6, 7, 9, 10, 13, 13, 13, 15
Answers
Answer:
Step-by-step explanation:
Answer:Min:2
Q1:5
Med:7
Q3:13
Max:15
gary has two ladders for a project one reaches 16 3/7 while the other reaches 12 /5/7 how much higher can the longer ladder reach
Answers
The longer ladder can reach 3 8/7 feet higher than the shorter one.
The Proportionality Theory.The longer ladder can reach 4 2/7 feet higher than the shorter ladder. To calculate this, we need to subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet).We can represent this calculation with a fraction equation, as follows:[tex]\frac{16 \frac{3}{7}}{12 \frac{5}{7}} - 12 \frac{5}{7} = \frac{4 \frac{2}{7}}{1}[/tex]To solve this equation, we first need to convert the fractions into equivalent fractions with a common denominator. In this case, the denominator is 7. This means that the first fraction becomes 16 3/7, the second fraction becomes 12 5/7, and the third fraction becomes 4 2/7.Once we have the fractions in the same denominator, we can now subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet). This gives us a result of 4 2/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To put this into perspective, if we were to use the ladders to reach a height of 16 3/7 feet, the shorter ladder would only reach 12 5/7 feet, while the longer ladder would reach 16 3/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To learn more about The Proportionality Theory refer to:
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[tex]\sqrt{12}+\sqrt{75}[/tex]
Answers
7-/3
7 sq rt. 3
5x - 7 = 5 - x
Using balancing method in algebra
Answers
Answer:
5x-7-5+X=5-x-5+X
or,6x-12=0
or,6x=12
or,X=12/6
:.X=2
Or
X=12/6 and there is more ways but those are two ways
what can 25 and 3 both be divided by
Answers
Answer:1
Step-by-step explanation:
because 1 devided by 3 is 3 and 1 devided by 25 is 5
What is the equation of a line written in slope-intercept form with a slope of 4 that passes through the point (-3, -3)?
Answers
Matthew scored a total of 168 points in his basketball season. He scored 147 of those points in the regular season and the rest were scored in his playoff game. What percent of his total points did he score in the playoff game?
Answers
Answer:
168 - 147 = 21
21/168 = 12.5
The regular polygon below is to be rotated about its center. Which angle of rotation
would carry the figure onto itself?
Answer choices:
324°
150°
225°
300°
Answers
The shape of a decagon will remain the same when it is rotated through
its angle of rotational symmetry.
How to find the rotation?
The rotation about the center will carry a regular decagon back to itself is 36°.
Note the following
The angle of rotational symmetry of a decagon is the smallest angle that a decagon can be rotated by such that the image formed by the rotation coincide with the preimage;
A decagon has 10 sides, the interior angle of a regular decagon is given as follows;
Each interior angle = (n-2)*180/10 = 144⁰
A decagon has a reflective symmetry, therefore, the lines of symmetry joining opposite vertices are straight lines.
The number of diagonals in a decagon = 5
Rotating through the vertex and opposite vertex of the diagonals gives the number of image of the rotation that is similar to the preimage of a decagon as ten.
Therefore, a rotation of (360/10) = 36⁰, about the center will carry a regular decagon back to itself.
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