the area of the compound shape below is 30mm^2.
Calculate the value of x.
If your answer is a decimal, give it to 1 d.p
Answers
Answer:
x = 2.5 mm-------------------------------------
Set equation for area of given shape:
x*4 + x*(2x + 3) = 30Simplify and solve for x:
4x + 2x² + 3x = 302x²+ 7x = 302x² + 7x - 30 = 0x = [-7 ± √(7² - 4*2*(-30))] /4x = (-7 ± √289)/4x = (-7 ± 17)/4x = (10/4) and x = (- 24)/4 (discarded as negative number for the segment length)x = 2.5 mmAnswer:
x = 2.5 mm
Step-by-step explanation:
A compound shape is made up of two or more basic shapes.
From inspection of the given compound shape, we can see that it is made up of two rectangles.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a rectangle}\\\\$A=w \cdot l$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]
Dimensions of the smaller rectangle:
w = xl = 4 mmDimensions of the larger rectangle:
w = xl = (2x + 3) mmTherefore, the equation for the area of the compound shape is:
[tex]\begin{aligned}\implies \textsf{Area}&=x \cdot 4 + x \cdot (2x+3)\\&=4x+x(2x+3)\\&=4x+2x^2+3x\\&=2x^2+7x\end{aligned}[/tex]
Given the area of the compound shape is 30 mm², substitute this value into the found equation for area and solve for x:
[tex]\begin{aligned}\implies 2x^2+7x &=30\\2x^2+7x-30&=0\\2x^2+12x-5x-30&=0\\2x(x+6)-5(x+6)&=0\\(2x-5)(x+6)&=0\\\\2x-5&=0 \implies x=2.5\\x+6&=0 \implies x=-6\end{aligned}[/tex]
As length is positive, x = 2.5 mm only.
Related Questions
HELPP!!!
angles of a triangle
Math
help please! Thank u.
Answers
Answer:Try 81
Step-by-step explanation:
Duncan begins to hike a trail that is at an elevation of 1000 feet. As he hikes, his elevation increases 2000 feet each hour that he hikes. Determine the y-intercept.
Answers
The y-intercept in Duncan's hike situation as described in the task content is; 1000 feet.
What is the y-intercept in Duncan's hike scenario as described?It follows from the task content that the y-intercept of Duncan's hike scenario is to be determined.
In context, the y-intercept is otherwise termed; the starting value.
According to the task content; Duncan begins to hike a trail that is at an elevation of 1000 feet.
On this note, Duncan's starting elevation is; 1000 feet and consequently, the y-intercept in this scenario is; 1000 feet.
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help me find the slope please
answer needs to be correct or i will report and ban you.
thank you
-lazyuser30
Answers
Can you tell me the
Measure of
Answers
Answer:
please tell us what you need help with
Step-by-step explanation:
you did not include a number
Answer: what
Step-by-step explanation:
The expression 10x – x2
can be written in the form p – (x – q)2
for all values of x.
a) Find the values of p and q.
b) The expression 10x – x2
has a maximum value.
(i) Find the maximum value of 10x – x2
.
(ii) State the value of x for which this maximum value occurs.
Answers
The values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
Expression 10x – x²
The expression can be written as
10x – x² = p – (x – q)²
10x – x² = p - x² - q² + 2xq
10x – x² = - x² + 2xq + p - q²
Compare the quantities on both sides,
10x = 2xq and 0 = p - q², p = q²
q = 10x / 2x = 5
p = 5² = 25
Therefore, the values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.
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if kenneth has 11 dimes and nickels in his pocket, and they have a combined value of 80 cents, how many of each coin does he have?
Answers
Answer: let d=# of dimes
let n= # of nickels
n+d=11
5n+10d=80
5d+25
5 dimes and 6 nickels
Use synthetic division to find the result when 2x^3-14x^2+15x-18 is divided by x-6.
Answers
The Answer:
2x^2−2x+3
The result of the expression (2x³ - 14x² + 15x - 18) ÷ (x - 6) on dividing will be (2x² - 2x + 3).
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ (2x³ - 14x² + 15x - 18) ÷ (x - 6)
The factor of the expression (2x³ - 14x² + 15x - 18) is given as,
⇒ (2x³ - 14x² + 15x - 18)
⇒ 2x³ - 12x² - 2x² + 12x + 3x - 18
⇒ 2x²(x - 6) - 2x (x - 6) + 3(x - 6)
⇒ (x - 6)(2x² - 2x + 3)
Then the expression is written as,
⇒ (2x³ - 14x² + 15x - 18) ÷ (x - 6)
⇒ [(x - 6)(2x² - 2x + 3)] / (x - 6)
⇒ (2x² - 2x + 3)
The final solution of the expression (2x³ - 14x² + 15x - 18) ÷ (x - 6) on dividing will be (2x² - 2x + 3).
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ssdfmsfamong treatments1743 435.751.27error total5503.4615step 6 of 8: what is the variation of the individual measurements about their respective means? please round your answer to two decimal places.
Answers
The variation of the individual measurements about their respective means is 2295.04.
Given that,
The table of the treatments and total amount is
SS DF MS F
Among Treatments 4974.88 621.86 2.98
Error ?
Total 7269.92 19
We have to find how do the various measurements differ from their respective means.
We know that,
We know the formula
SSE= SSTotal -SST
= 7269.92-4974.88
=2295.04
The variation of the individual measurements about their respective means is SSE that is 2295.04
Therefore, The variation of the individual measurements about their respective means is 2295.04.
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Selena and Luis are building a model bridge out of balsa wood. To make a strong bridge, they create each post by laying out two long wooden poles horizontally, as shown in the diagram, and connecting them with smaller strips of balsa wood laid diagonally in a triangle pattern. The triangle pattern is continued down the entire length of the wooden poles.
The poles are 12 centimeters apart, and each small strip of balsa wood is 13 centimeters long.
If the two poles are each 100 centimeters long, how many small strips of balsa wood will they need to connect them?
Answers
If the two poles are each 100 centimeters long, The number of small strips of balsa wood they will need to connect them is: C. 20.
How to find the number of small strips?Using Pythagorean theorem formula to find triangle side a.
a=√b²+c²
a = √ 13² - 12²
a = √ 169 - 144
a = √ 25
a = 5
Hence, the number of small strips of balsa wood they need to connect them is:
100 / (2a)× 2
100 / ( 2×5) ×2
100/ 10 ×2
10 × 2
=20
Therefore the correct option is C.
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In 2014, 100 trees were planted by the people in Cherry Hill. The table below shows the number of trees planted of each type.
Trees Planted
Tree Number of Trees
Oak 45
Maple 17
Palm 28
Pine 10
Which circle graph correctly shows the information from the table?
Answers
Answer:
where is your circle graph
Step-by-step explanation:
i need the graph in order to solve this
Write the sum using summation notation. There may be multiple representations. Use i as the index of
summation.
1/3 - 1/9 + 1/27 - 1/81 + 1/243 - 1/729
Answers
The summation notation of the sum is given as follows:
[tex]\sum_{i = 1}^{6} \frac{(-1)^{i-1}}{3^i}[/tex]
How to write the summation notation?The summation notation of the sum is written considering the patterns of the terms that compose the terms.
First we look at the fact that the sum has six terms, and the first term is considered as having index 1, hence:
[tex]\sum_{i = 1}^{6}[/tex]
Then we consider that the signal is alternating, with the terms with odd indices being positive and those with even indices being negative, hence the numerator is of:
[tex](-1)^{i - 1}[/tex]
(any of -1 or +1 would work here).
Then we considering that the denominator is composed by the powers of 3, hence it is given by:
[tex]3^i[/tex]
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If m<1=55, then find the value of m<3
Answers
The measure of angle 3 is given as follows:
m < 3 = 55º.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
The vertical angles in this problem are listed as follows:
1 and 3.2 and 4.The measure of angle 1 is given as follows:
m < 1 = 55º.
Angle 1 and angle 3 are vertical angles, hence the measure of angle 3 is obtained as follows:
m < 3 = 55º.
As angle 3 is congruent to angle 1.
Angles 2 and 4 are also supplementary to angles 1 and 3, meaning that the sum of their measures is of 180º, hence m<2 = m<4 = 125º.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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#35
On the real number line, what is the midpoint of
-3 and 11?
A. -5
B. 0
C. 4
D. 7
E. 14
Answers
Answer:
C. 4
Step-by-step explanation:
You want the midpoint between -3 and 11 on the number line.
MidpointThe midpoint is the average of the end point coordinates:
(-3 +11)/2 = 8/2 = 4
The midpoint is 4.
Question included in file
please help I need an answer quick
Answers
The midpoint of the line AN is (3(1/2) , -1).
What is midpoint?
The midpoint is located halfway between the two end points. Its x and y values are in the middle of the two x and y values.Add both "x" coordinates, divide by 2, and add both "y" coordinates, divide by 2 to calculate it.Midpoint of the line(x , y) = (x₁ + x₂ / 2) , (y₁ + y₂ / 2)
x₁ = 2, x₂ = 5
y₁ = -3, y₂ = 1
So,
Midpoint of the line(x , y) = (2+5/2) , ((-3)+1 / 2)
= (7/2 , -2/2)
= (7/2, -1)
We can write 7/2 as 3(1/2)
Hence, the midpoint of the line AN is (3(1/2) , -1)
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Points A, B, and C are collinear. Point B is between A and C. Find the value of x.
AC = 24
AB = 2x + 1
BC = 3x − 2
Responses
A 55
B 33
C 99
D 7
Answers
Therefore, the value of the given equation of x comes out to be x =5.
What kinds of equations are there?Equations can be classified as either identities or conditioned equations. For each amount of the variables, an identity is true. Only specific values of the variables make a conditional equation legitimate. The equality sign ("="), which separate the two expressions, is a symbol for an equation.
Here,
Given data: A, B, and C are parallel, B is located between A and C, AC equals 24, AB equals 2x+1, and BC equals 3x-2.
In the event where A, B, and C are collinear and B is positioned between A and C, we obtain
Replace the given equation with AC = 24, AB = 2x+1, and BC = 3x-2.
AB plus BC equals AC
=> AC= AB + BC
On combining like terms we get
=> 2x+1 + 3x-2 = 24
=> 5x -1 =24
=>5x =25
=>x =5
Therefore, the value of x comes out to be x =5.
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i need help, i don’t understand
Answers
Answer:
x = 2; y = 10
Step-by-step explanation:
y = 5x
2x + 3y = 34
You have a system of equations. Since the first equation is already solved for y, we can easily use the substitution method. Substitute 5x for y in the second equation.
2x + 3y = 34
2x + 3(5x) = 34
2x + 15x = 34
17x = 34
x = 2
Now substitute 2 for x in the first equation.
y = 5x
y = 5(2)
y = 10
Solution: x = 2; y = 10
The trinomial x² - 14x + 49 can be expressed as
(1) (x-7)²
(2) (x + 7)²
(3) (x-7)(x + 7)
(4)) (x-7)(x + 2)
Answers
Answer:
(1)
Step-by-step explanation:
This is because (x-7)²=(x-7)(x-7), which when expanded using the FOIL method, is equal to x²-7x-7x+49=x²-14x+49.
LOT OF POINTS!!
PLEASE NEED ANSWERS QUICKLY!!
Answers
By using the properties of angle,
The proof of ∠1 ≅ ∠3 has been given below
What is angle?
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle
1. ∠2 ≅ ∠4 [Given]
2. m∠2= m∠4 [Angle Congruence Postulate]
3. ∠2 and ∠3 are supplementary [Given]
4. m∠2+m∠3 = 180° [Definition of Supplementary angles]
5. ∠1 and ∠4 are supplementary [Angle on a straight line]
6. m∠1+m∠4 = 180° [Definition of supplementary angles]
7. m∠1+m∠4 = m∠2+ m∠3 [ Substitution from 4 and 6]
8. m∠1+m∠4 = m∠4+m∠3 [Substitution from 2]
9. m∠1=m∠3 [Cancellation property]
10. ∠1 ≅ ∠3 [Converse of angle congruence theorem]
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Find the absolute value. |4 - 5i|
Answers
The absolute value for |4 - 5i| =[tex]\sqrt{41}[/tex].
Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0. A negative number has a positive absolute value, too. If x 0, then |x| = -x gives the absolute value of the supplied number.
For illustration, |-2| = 2. No matter what the numerical value's sign, the absolute value is always positive.
Here complex number form =|a+ib|
= |4-5i| Here a=4, b=(-5).
[tex]|a+ib| = \sqrt{a^{2}+b^{2} } \\\\\sqrt{4^{2}+5^{2} } \\\\\sqrt{16+25} \\\\\sqrt{41} \\[/tex]
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Determine if you have enough information to find the missing lengths. If so, find them. If not, explain why.
DE is parallel to AC . Find the lengths of AC and AD.
Answers
The lengths of AC and AD using the concept of similar triangles are; AC = 12.5 and AD = 3
How to solve similar triangles?We are given that;
∆BDE is a similar triangle to ∆BAC.
This means that their sides are proportional. Thus, we can say that;
BD/BA = BE/BC
Thus;
2/BA = 4/(6 + 4)
BA = 2 × 10/4
BA = 5
Similarly;
BE/BC = DE/AC
4/10 = 5/AC
AC = 5 × 10/4
AC = 25/2
Finally,
AC = 25/2 = 12.5.
Thus;
AD = BA - BD = 5 - 2 = 3.
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Jerry bulit a table with a square top. the perimeter of the tabletop is 18 feet. He knows that the side lentgh of the table is 3, 3 1/4 4 or 4 1/2 use the equation 18 = 4s where s is the side length of the table to determine the side length explain how you found your answer
Answers
Answer:
4 1/2 ft
Step-by-step explanation:
18 = 4s
Divide both sides by 4.
18/4 = 4s/4
9/2 = s
4 1/2 = s
The side of the table is 4 1/2 ft.
There are 3 fewer yellow beads than red beads. There are twice as many green beads as yellow beads. Write expressions for the number of red, green, and yellow beads.
Answers
Answer:
yellow = red - 3 and green = yellow x 2 and red = yellow + 3
or
green= (red-3) x 2
Step-by-step explanation:
Three fewer yellow than read is the same as saying red -3
twice as many green as yellow is the same as yellow x 2
if green is yellow x 2 you can substitute yellow for the equation to find yellow
you can flip the equation for yellow around by doing inverse operations. To have the equation equal red you need to move the three by doing its inverse. The opposite of subtraction is addition so you'd add 3 to each side, getting rid of the -3 and isolating the red to make the equation red=yellow+3
Xander was in the lead for 75% of the laps during PE. If the race lasted 12 laps, how many laps did Xander lead?
Answers
Answer:
9 laps
Step-by-step explanation:
75% of something is the same as three-fourths, or multiplying by 0.75
12 x 0.75 = 9
or you can divide by 4 and then multiply by three if you know what to separate the original number into
12/4 = 3 3 x 3 = 9
• Solve for x.
• Show all of your work to earn full credit.
•
Use the "mountain" icon to upload a piucture of your handwritten work.
→
-1 + 14x
12x + 17
If you do this for me you have to show me your work ;)
Answers
The value of 'x' for the given (alternate exterior angles) is found as 9.
Explain the term alternate exterior angles?The pair of angles the outside of the two parallel lines but on the opposing side of the transversal are known as alternate exterior angles.A transversal that crosses two parallel lines produces alternate exterior angles. They form two pairs (total four angles) of alternate outside angles since they are situated "outside" the pair of parallel lines but on different sides of the transversal.For the stated question.
-1 + 14x = 12x + 17 (alternate exterior angles)
Simplifying,
14x - 12x = 17 + 1
2x = 18
x = 9
Thus, the value of 'x' for the given (alternate exterior angles) is found as 9.
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an inequality shows the Relationship between numbers
Answers
The answer to this Question is YES. Inequalities do show the relation between Numbers.
What are Inequalities?
Inequalities are the operators the we want to compare the data when equality is not valid
Solution:
The Inequalities shows nice relation between numbers like when we say for example 2 and 4 we know that 2 is not equal to 4 but we know that
2 is less than 4 in this case inequalities help us to develop relations between numbers that are not equal
Inequalities are also used in inequations where they represents large set of data .
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Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour. How many pages can Shawn type in one hour? A. B. C. D.
Answers
Answer:
5 1/7 pages in one hour. And what does "A.B.C.D." Mean?
Step-by-step explanation:
Use the first five terms of the trigonometric series to approximate the value of sin 4pi/5 to four decimal places. Then
compare the approximation to the actual value.
Answers
The first five terms of the given trigonometric series are (C) 0.5884, 0.5878.
What is a trigonometric series?
A mathematical series where the sines and cosines of integral multiples of a variable angle are used to connect the components.
Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent are the six trigonometric functions.
Below is a graph of the first five terms in the trigonometric series of sin:
sinx = x - x³/3! + x⁵/5! - x⁷/7! + x⁹/9! .......
Insert x = 4π/5
sin4π/5 = 4π/5 - (4π/5)³/3! + (4π/5)⁵/5! - (4π/5)⁷/7! + (4π/5)⁹/9! .......
Upon resolution, we determine an approximate value of:
sin4π/5 = 0.5884
Find the true value now:
sin4π/5 = 0.5878
Therefore, the first five terms of the given trigonometric series are (C) 0.5884, 0.5878.
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Complete question:
Use the first five terms of the trigonometric series to approximate the value of sin to four decimal places. Then compare
the approximation to the actual value.
a. -0.9568, -0.9659
b. -0.9649, -0.9659
C. 0.5884, 0.5878
d. -0.9609, -0.9659
Someone please answer this my question is in the picture I will give you brainliest and your getting 50 points no fraud answers.
Answers
Step-by-step explanation:
I will help you sir.
Given
Opposite Sides are Congruent
Reflexive
SSS
CPCTC
How to turn 33.3 into a decimal and a fraction
Answers
Turn 33.3 into a fraction:
Write down 33.3 like this:
[tex]\dfrac{33.3}{1}[/tex]
Multiply the numerator and denominator by 10(since there is 1 digit after the decimal):
[tex]\dfrac{33.3\times10}{1\times10} \rightarrow\dfrac{333}{10}[/tex]
[tex]\dfrac{333}{10}[/tex] would be the fraction form of [tex]33.3[/tex].
To turn [tex]\dfrac{333}{10}[/tex] into a decimal, divide the numerator by the denominator:
[tex]333\div10=33.3[/tex]
Hope this helps!
In his free time, Gary spends 9 hours per week on the Internet and 12 hours per week playing video games. If Gary has five hours of free time per day, what percent of his free time is spent on the Internet and playing video games
Answers
Answer: 11.64%
Step-by-step explanation:
