The length of a rectangle is 4 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the dimensions of the rectangle.
Answers
Answer:
The dimensions are 10 inches and 24 inches.
Step-by-step explanation:
Since the quadrilateral is a rectangle, the diagonal divides the rectangle into two right triangles. That means we can use the Pythagorean Theorem, which applies only to right triangles.
On the bottom left triangle, the sides forming the right angle are the legs. They measure x and 2x + 4. The are a and b in the Pythagorean Theorem equation. The side of the triangle measuring 2x + 6 is the hypotenuse of the right triangle, the side opposite the right angle and the longest side in a right triangle. The hypotenuse is c in the Pythagorean Theorem equation.
Start with the equation of the Pythagorean theorem.
[tex] a^2 + b^2 = c^2 [/tex]
Now substitute the values we have for a, b, and c.
[tex] (x)^2 + (2x + 4)^2 = (2x + 6)^2 [/tex]
Square the two binomials. You an use the pattern:
[tex] (a + b)^2 = a^2 + 2ab + b^2 [/tex]
which I will use, or you can use FOIL and collect like terms.
[tex] x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36 [/tex]
Collect like terms, and move all terms to the left side equaling zero.
[tex] 5x^2 + 16x + 16 = 4x^2 + 24x + 36 [/tex]
[tex] x^2 - 8x - 20 = 0 [/tex]
Try to factor the left side. We need two numbers whose product is -20 and whose sum is -8. -10 and 2 work.
[tex] (x - 10)(x + 2) = 0 [/tex]
Set each factor equal to zero, and solve for x.
x - 10 = 0 or x + 2 = 0
x = 10 or x = -2
Since one side of the rectangle measures x, x = -2 cannot be a solution since you cannot have a negative side length.
x = 10 is acceptable.
2x + 4 = 2(10) + 4 = 24
Answer: The dimensions are 10 inches and 24 inches.
Related Questions
Fill in the tables and create a recursive and explicit equation for all three questions.
Answers
Answer:okay
Step-by-step explanation:hm
PLSS HELP :((
will mark brianlist if its the correct answer ty
Answers
The step 2 is incorrect angle o and angle p form supplementary angles not alternate interior angle that is :
∠o + ∠p = 180°
What are alternate interior angle ?
An alternate interior angle is one formed on the inside side of two parallel lines and opposite on the outer side of the transversal when those two parallel lines are intersected by a transversal and they are equal.
Alternate angles between a transverse and parallel lines are equal .
Here, the step 1 is correct :
as the sum of angles of a triangle is 180 degree therefore,
∠m +∠n + ∠o = 180°.............(1)
the step 2 is incorrect :
as angle o and angle p form supplementary angles not alternate interior angle therefore it will be :
∠o + ∠p = 180°........(2)
after that step 3 and 4 is correct to get the final result as :
step 3 : ∠m +∠n + ∠o = ∠o + ∠p
step 4 : ∠m +∠n = ∠p
Therefore, the step 2 is incorrect angle o and angle p form supplementary angles not alternate interior angle.
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How do you solve this?? It says solve for X.
Answers
Answer:
x = 7
Step-by-step explanation:
Ok, so these angle are equal, because they are opposite angle
So we could write as x+16 = 4x - 5
Now we solve the equation:
x+16 = 4x - 5
16+5 = 4x -x
21 = 3x
7 = x
- The flag of Equatorial Guinea contains an isosceles triangle.
(Recall that an isosceles triangle contains two angles with the
same measure.) If the measure of the third angle of the trian-
gle is 30° more than twice the measure of either of the other
two angles, find the measure of each angle of the triangle.
(Hint: Recall that the sum of the measures of the angles of a
triangle is 180°.)
Please show me step by step how you got the answer, Thanks
Answers
The measure of each angle of the triangle is 40°, 40° and 100°.
What is the triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.Given:
In an isosceles triangle two of the three angles measure the same.
Let the two angles be equal to x.
The third angle is 20 more than twice the measure of either angle, which means 2x+20.
The angles of a triangle add up to 180 degrees.
(x)+(x)+(2x+20)=180
4x+20=180
4x=160
x=40 degrees
So, the two angles measure 40° each and the third angle would be,
2x+20
=2*40+20
=100°
Therefore, the measure of each angle of the triangle is 40°, 40° and 100°.
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In the figure below, AD and AB are tangent to the circle centered at O. The segment DB passes through the center of the circle. Given that AD=10.6 and DB=5.6, find DC.
Answers
The length of DC found using Pythagorean theorem given AD = 10.6 and DB = 5.6 and AD and AB are tangent of circle O, is DC = 1.6
How can Pythagorean theorem be used to find DC?The given parameters are;
The tangents of circle O = AD and AB
The segment passing through O = DB
AD = 10.6
DB = 5.6
Required; The length of DC
Solution;
According to Pythagorean theorem, we have;
AB = √(10.6² - 5.6²) = 9
AB = AC = 9
AD = DC + AC
Which gives;
10.6 = DC + 9
DC = 10.6 - 9 = 1.6
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how do i right it please help
Answers
The contrapositive statement is:
If x ≠ 2, then x^2 ≠ 4
And it is false.
How to write the contrapositive statement?
First, we have two propositions:
p = "x^2 = 4"
q = "x = 2"
The contrapositive statement is:
¬q → ¬p
The negation of the propositions are:
¬q = "x ≠ 2"
¬p = "x^2 ≠ 4"
Then the contrapositive statement with the given propositions is:
If x ≠ 2, then x^2 ≠ 4
Now, is this statement true?
No, because we can have:
x = -2 (which is different than 2, so the hypothesis is true)
and x^2 = (-2)^2 = 4
Then the conclusion is false, so the statement is false.
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In 11 years, John's age will be 5 less than 5 times his current age. How old is he?
If xrepresents John's current age, which of the following equations could be used to solve this problem?
Answers
Answer:
x=4
Step-by-step explanation:
I really dont know how to do this please help!
Answers
Angles ECD and ACB are congruent, since they form a pair of vertical angles. Let their measure by [tex]y[/tex].
The sum of the interior angles of any triangle is 180°. This means
• in ∆CDE, we have
[tex]x + 100^\circ + y = 180^\circ[/tex]
• in ∆ABC, we have
[tex]4x + 49^\circ + y = 180^\circ[/tex]
Solve for [tex]x[/tex] by eliminating [tex]y[/tex].
[tex](x + 100^\circ + y) - (4x + 49^\circ + y) = 180^\circ - 180^\circ[/tex]
[tex]-3x + 51^\circ = 0[/tex]
[tex]3x = 51^\circ[/tex]
[tex]\boxed{x = 17^\circ}[/tex]
Which number sentence represents 8 times as many as 9
Answers
Answer:
72
Step-by-step explanation:
this number sentence will be represented as,
72 is 8 times as many as 9
MATHEMATICS: The 5 and 11 terms of an Arithmes Progression (AP) are 13 and 31 respectively. Find the sum of its first term and common difference!
Answers
Answer:
[tex]a_1 = 1\\d = 3[/tex]
Step-by-step explanation:
The nth term of an arithmetic progression is [tex]a_n = a_1 + (n - 1)d[/tex].
You are given that [tex]a_5 = 13[/tex] and [tex]a_{11} = 31[/tex].
Therefore, we can solve the following system of equations to get the first term, as well as the difference.
[tex]-\begin{cases}a_1 + 4d = 13\\a_1 + 10d = 31\end{cases}\\\\\to 6d = 18\\\to d = 3\\\\\text{Substitute d = 3 into one of the equations to find }a_1\text{:}\\a_1 + 4 \times 3 = 13\\a_1 + 12 = 13\\\to a_1 = 1[/tex]
PLEASE HELP!!! I NEED HELP ASAP IF YOU CAN HELP IT WILL BE VERY NICE!!!!!!!!! (PLEASE HELP ME WITH THE QUESTIONS BELOW)
Answers
The solution to question 8, in scientific notation is 9.563 x 10¹¹.
The solution to question 9, in scientific notation is 9.83 x 10⁸.
The solution to question 10, in scientific notation is 1.35759 x 10⁹.
The solution to question 11, in scientific notation is 8.70366 x 10⁴.
What is scientific notation?
Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.
Solution to question 8, in scientific notation(9.5 x 10¹¹) + (6.3 x 10⁹)
= (950 x 10⁹) + (6.3 x 10⁹)
= (950 + 6.3) x 10⁹
= 956.3 x 10⁹
= 9.563 x 10¹¹
Solution to question 9, in scientific notation(1.03 x 10⁹) - (4.7 x 10⁷)
= (103 - 4.7) x 10⁷
= 98.3 x 10⁷
= 9.83 x 10⁸
Solution to question 10, in scientific notation(1.357 x 10⁹) + 590,000
= (1.357 x 10⁹) + (5.9 x 10⁵)
= (13570 x 10⁵) + (5.9 x 10⁵)
= (13570 + 5.9) x 10⁵
= 13,575.9 x 10⁵
= 1.35759 x 10⁹
Solution to question 11, in scientific notation87,100 - (6.34 x 10¹)
= 87,100 - 63.4
= 87,036.6
= 8.70366 x 10⁴
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y=8 and x= -1 are equations parallel, perpendicular or neither
Answers
Answer:
Parallel
Step-by-step explanation:
The endpoints of YZ are Y(1, -6) and Z(-2, 8). Find the coordinates of the midpoint M.
Midpoint M
Find YZ. Round your answer to the nearest tenth if necessary.
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Y(\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad Z(\stackrel{x_2}{-2}~,~\stackrel{y_2}{8}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -2 +1}{2}~~~ ,~~~ \cfrac{ 8 -6}{2} \right) \implies \left(\cfrac{ -1 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies \stackrel{\textit{\LARGE M}}{(-0.5~~,~~1)}[/tex]
The coordinates of the midpoint M are (-1/2, 1), and the length of YZ is approximately 14.32 units.
We have,
To find the coordinates of the midpoint M of the line segment YZ, we can use the midpoint formula:
Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints Y and Z, respectively.
Given:
Y(1, -6) and Z(-2, 8)
Now, apply the midpoint formula:
Midpoint M = ((1 + (-2)) / 2, (-6 + 8) / 2)
Midpoint M = (-1 / 2, 2 / 2)
Simplify:
Midpoint M = (-1/2, 1)
To find the length of YZ, we can use the distance formula:
Length of YZ = √[(x₂ - x₁)² + (y₂ - y₁)²]
Given:
Y(1, -6) and Z(-2, 8)
Now, apply the distance formula:
Length of YZ = √[(-2 - 1)² + (8 - (-6))²]
Length of YZ = √[(-3)² + (8 + 6)²]
Length of YZ = √[9 + 196]
Length of YZ = √205
Length of YZ ≈ 14.32 (rounded to the nearest tenth)
Thus,
The coordinates of the midpoint M are (-1/2, 1), and the length of YZ is approximately 14.32 units.
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Ruth's new lunch box is only 5 centimeters in height, so it fits in her backpack along with all her books. The lunch box has 3 sections for different types of food. The length and width of the lunch box are 22 centimeters and 14 centimeters. What is the volume of Ruth's new lunch box?
Answers
The volume of Ruth's new lunch box is 1,540 cm³.
What is the volume?The volume is a measure of an object occupied in a three-dimensional space.
Volume is a three-dimensional quantity that measures the capacity of a shape or the amount of three-dimensional space a closed figure can occupy.
The formula for computing a volume is height x length x width.
Data and Calculations:Height = 5 cm
Length = 22 cm
Width = 14 cm
Volume = 1,540 cm³ (5 x 22 x 14)
Thus, the volume of Ruth's new lunch box, showing the three-dimensional space within, is 1,540 cm³.
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What volume in milliliters, of a 60% hydrochloric acid solution must be added to 100ml of a 30% hydrochloric acid solution to make a 36% hydrochloric acid solution?
Answers
Answer:
Since 30% of 100 ml = .3*100 = 30 ml
60 % of X ml = .6x which we are trying to solve
add
(X+100).36 = 30+.6x
.36x+36 = 30+.6x
so
6 = .24x
x = 25 ml
Step-by-step explanation:
I hope this helps you
After three quarters of the season has past, the Tigers basketball tean has won 48 out of 72 games. How many of the remaining games must they win in order to win more than 70% of all their games this season?
Answers
Answer: at least 3 more games
Step-by-step explanation:
70% of 72 is 50.4
50.4 - 48 = 2.4
Because one can't win only a fourth of a game, you need to round up. Bringing us to at least 3 more games to win
Solve the following radical equations.
∛x-1=√x-1
Answers
The solution of the radical equation of x is 1.
A linear equation in one variable is an equation which can be represented in the form of ax+b where x is the variable and 'a' is the coefficient and 'b' is the two constants.
A radical equation is defined as an equation where the variable is under a radical or root.
We know that n-th root of a variable x can be written as x to the power of (1/n). Mathematically : [tex]\sqrt[n]{x} =x^{\frac{1}{n} }[/tex]
In the given equation:
∛x-1=√x-1
adding 1 to both sides we get:
or, ∛x=√x
Cross multiplying we get:
or, ∛x/√x =1
We know that (aˣ/aⁿ)=a⁽ˣ⁻ⁿ⁾
therefore :
or, [tex]x^{\frac{1}{3}-\frac{1}{2} }=1[/tex]
or, [tex]x^{-\frac{1}{6} }=1[/tex]
or, x=1
Hence the value of x in the radical equation is 1
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The number line shows the distance in meters of two birds, A and B, from a worm located at point X:
Answers
A. Using subtraction, the distance between the two birds = |-2.5 - 2.5| = |-5| = 5 meters.
B. Using additive inverses, the distance = 2.5 + 2.5 = 5 meters
How to Find the Distance on a Number Line?The distance between any two points on a number line is the absolute difference of the coordinates of the two points.
What is an Additive Inverse of a Number?The additive inverse of a number is the number that is added to the number to make it zero. For example, the additive inverse of a is -a.
Part A:
Using subtraction, the distance between the two birds = |-2.5 - 2.5| = |-5| = 5 meters.
Part B:
The additive inverse of -2.5 is 2.5.
Using additive inverses, the distance = 2.5 + 2.5
Using additive inverses, the distance = 5 meters
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find the constant of proportionality on this graph
PLEASE HELP GIVING BRAINLIEST :))
Answers
Answer:
I think the constraint of proportionality is 25 because each dot it increases buy 25.
I also believe that at 10 the total should be at 225.
The difference of two numbers is 29. The largest number is 3 more than twice the smallest number. What are the two numbers?
Answers
Answer:
x + y = 29 equation 1
Five more than means add 5+5 three times the smaller number:
3x equals the larger number: = y 3x + 5 = y equation 2
From equation 1x + y = 29subtract x from both sidesy = 29 - x
We now have two things that are both equal tothe larger number y.
They must be equal to each other.
3x + 5 = 29 - x
Add x to both sides 3x + x + 5 = 29 - x + x4x + 5 = 29
subtract 5 from both sides 4x + 5 - 5 = 29 - 54x = 24
divide both sides by 44x/4 = 24/4x = 6
We now know x = 6
We also know y=29-x y = 29 - 6y = 23
Your numbers are 6 and 23
Step-by-step explanation:
1. Elena wants to put together some of her favorite songs on her computer. She wants to store 60 minutes
worth of music. Elena wonders how many songs she will be able to include. She looks online and finds a
source that says the average song length is 3 minutes. If this is true, about how many songs will Elena be
able to store? Show your work
Answers
Answer:
20 Songs
Step-by-step explanation:
60 minutes / 3minutes per song =20 songs
The atoms of a certain element each contain 11 protons and 1 valence electron. Which statement correctly identifies this element and describes its chemical reactivity?
Answers
The correct option is D). The element is sodium, and it is highly reactive.
What type of atom has 11 protons?The atomic number of the element sodium (Na) is 11. It means that the sodium has 11 protons in total and because it is neutral it has 11 number of electrons.
Valence electrons (VE) refers to the electrons that usually presents in the outer shell of an atom. Thus, the sodium has only 1 valence electron.
Basically, the mass number of an element tells about the number of protons and neutrons in an atom and sodium is the atom that has 11 atomic number.
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Complete question:- The atoms of a certain element each contain 11 protons and 1 valence electron. Which statement correctly identifies this element and describes its chemical reactivity?
A The element is sodium, and it is highly reactive.
B The element is fluorine, and it is not very reactive.
C The element is sodium, and it is not very reactive.
D The element is fluorine, and it is highly reactive.
Solve one step equalities using multiplication & division
X/2 = 17/1
Answers
Answer:
[tex] \sf \: x=34[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
x/2 = 17/1
Step 1: Cross-multiply.
x/2 = 17/1
x*(1)=(17)*(2)
x=34
Any expression divided by remains the same
X/2= 17
Multiply both sides of the equation by 2
X=34
a chessplayer won 32 of the games he played if the ratio of wins to lossses was 8:3 how many games did he play total
Answers
Answer:
Step-by-step explanation:
i don't know if this is right but here is how i would do it.
Wins: Losses = 8:3 = 32: 12 = 32 wins + 12 losses = 44 games played.
Write an expression to represent:
2 times the sum of 5 and x.
Answers
5x + 8
2(5x+8)
2(5x+8) is the express of twice the sum of 5 times a number and 8
answer: 2 (5x+8) = 12
simplify -2(-3 - x) + 6x
Answers
Simplify and u get 6+8x
Answer:
0.75
Step-by-step explanation:
1. distribute the 2 into the perenthesis
2. combine like terms
3. simplify on both sides
Which angle is the included angle for sides ABand BC?
A
C
O Angle B
Angle C
O Angle A
B
Answers
For the given sides AB and BC the angle included would always be Angle B
When we form a triangle we name the vertex as A, B and C. So, the sides AB and BC will always have an Angle B regardless of the naming convention we use.
A triangle is a polygon with three vertices and three edges that has three sides. It is a basic geometric shape. The term "abc" refers to a triangle containing the vertices a, b, and c. Any three non-collinear points in Euclidean geometry combine to create a singular triangle and a singular plane.
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A sorter at a recycling center separates pieces of glass
into large bins. The table shows the number of pieces
of each color of glass. If each bin can hold 150 pieces of
glass, how many bins will the pieces completely fill? table:
Answers
The number of large bins that the pieces will completely fill is 3.
How many bins will the pieces completely fill?Each large bin can contain only one type of colour. In order to determine the number of large bins that would be used for each color, divide the color for each piece.
Number of large bins that would be used for Brown color = 283 / 150 = 1.89.
1 large bins would be completely filled with brown glass color
Number of large bins that would be used for Green color = 116 /1 50 = 0.7
No large bin would be completely filled with the green glass color
Number of large bins that would be used for Clear color = 315 / 150 = 2.1
2 large bins would be completely filled with the clear glass color
The total number of large bins that would be completely filled = 1 + 2 = 3
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Four more than the quotient of a number and three is at least nine.
Answers
Answer:
umber is greater than or equal to 15.
Step-by-step explanation:
Let number be x
Quotient of number and 3 =
4 more than = 4+
4+ is at least 9
4+≥9
Simplifying it ,we get
≥9-4
≥5
x ≥ 5(3)
x≥15
Number needs to be greater than or equal to 15
Equation
(x ÷ 3) + 4 ≥ 9
___________
Solution
x ≥ 15
Step-by-step explanation:
Solve the inequality
[tex]\left(x\div3\right)+4\ge \:9\\x\div 3+4-4\ge \:9-4\\x\div 3\ge \:5\\3x\div 3\ge \:5\cdot \:3\\x\ge \:15[/tex]
Thus, the inequality solution is x ≥ 15
Mike drove a nail 2.5 in. long through a board 0.75 in. thick into a post. How far did the nail go into the post?
Answers
Answer:
1.75 inches deep into the post
Step-by-step explanation:
First, you do 2.5 - 0.75 which is 1.75 in
The answer is 1.75 in
Hope this helps!