help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
The length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.
By Pythagorean theorem,
[tex]( Hypotenuse)^{2} = (Base)^{2}+ (Perpendicular)^{2}[/tex]
Let base = x+5
perpendicular = x
Hypotenuse = x+6
[tex](x+6)^{2} = x^{2} +(x+5)^{2}[/tex]
[tex]x^{2} +12x+36 = x^{2} +x^{2}+10x+25[/tex][tex]2x^{2} +10x+25-x^{2} -12x-36=0[/tex]
[tex]x^{2} -2x-11=0[/tex]
[tex]x = \frac{-(-2) + \sqrt{4 - 4(1)(-11)} }{2*1}[/tex] or [tex]\frac{-(-2) - \sqrt{4 - 4(1)(-11)} }{2*1}[/tex]
[tex]x=\frac{2 + \sqrt{4 +44} }{2}[/tex] or [tex]\frac{2 - \sqrt{4 +44} }{2}[/tex]
[tex]x = \frac{2 + \sqrt{48} }{2}[/tex] or [tex]\frac{2 - \sqrt{48} }{2}[/tex]
[tex]x = \frac{2+2\sqrt{12} }{2}[/tex] or [tex]\frac{2-2\sqrt{12} }{2}[/tex]
[tex]x = 1+\sqrt{12}[/tex] or [tex]1-\sqrt{12}[/tex]
[tex]x = 1+3.5[/tex] or [tex]1-3.5[/tex]
[tex]x = 4.5[/tex] or [tex]-2.5[/tex]
As, length can't be negative, we will take x = 4.5
Therefore, x = 4.5
x + 5 = 4.5 + 5
= 9.5
x + 6 = 4.5 + 6
= 10.5
Hence, the length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.
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laws exponents multiplication band power to a power simplifymake it small steps please the smallest you can like the minimum steps
Answer:
-64x^12
Explanation:
Given the expression
m = -4x^4
You are to look for m^3 as shown;
[tex]\begin{gathered} m=-4x^4 \\ m^3\text{ = (-4x}^4\text{)}^3 \\ m^3=(-4)^3\times(x^4)^3 \end{gathered}[/tex]Open the bracket:
[tex]\begin{gathered} (-4)^3\text{ }\times(x^4)^3\text{ = (-4}\times-4\times-4\text{)}\times x^{^{12}} \\ (-4)^3\text{ }\times(x^4)^3\text{ = (16}\times-4\text{)}\times x^{^{12}} \\ (-4)^3\text{ }\times(x^4)^3=-64x^{12} \end{gathered}[/tex]THe correct answer is -64x^12
Lina picks a 4 digit number.
The number is more than 5000.
The number is odd.
The second digit is a prime number.
How many different possible numbers could Lina pick?
Answer:
1000
Step-by-step explanation:
The easiest way to go about this is by turning our number into ABCD.
A will be in the 1000th spot, B 100th, C 10th, and D 1st.
A has to be ≥ 5. So 5, 6, 7, 8, 9.
B has to be a prime number. 2, 3, 5, 7.
C is able to be any number it wants, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Since the number is odd, D has to be 1, 3, 5, 7, 9.
A has 5 different possibilities. B has 4, C has 10, and D has 5.
You'll then multiply all of these numbers for your answer.
5 * 4 * 10 * 5 = 1000
find 3 consecutive odd integers when the sum of the first and third integer is 26
Let's call the first odd number x.
The next odd number will be x + 2, and the last one will be x + 4.
If the sum of the first number and the last one is 26, we have that:
[tex]\begin{gathered} x+x+4=26 \\ 2x+4=26 \\ 2x=22 \\ x=\frac{22}{2}=11 \end{gathered}[/tex]So the numbers are:
[tex]\begin{gathered} x\to11 \\ x+2\to13 \\ x+4\to15 \end{gathered}[/tex]11, 13 and 15.
Question 3 of 30
sin 0=/941 and cos 0 =-40/41. Find tan 0.
O A. 40/9
OB. 9/40
C. -40/9
D. - 9/40
Answer:
answer Is -9/40
Step-by-step explanation:
the formula Is
tan0= sin0/cos0
tan0= (9/41)/(-40/41)
tan0=(9/41)*(-41/40)
tan0= -9/40
while shopping for clothes, Daniel spent $26 less than 2 times what curtis spent. Daniel spent $10. write and solve an equation to find how much curtis spent. let x represent how much curtis spent
while shopping for clothes, Daniel spent $26 less than 2 times what curtis spent. Daniel spent $10. write and solve an equation to find how much curtis spent. let x represent how much curtis spent
Let
x ------> amount that Curtis spent
we have that
10=2x-26 ------> equation that represent this situation
solve for x
2x=10+26
2x=36
x=$18
therefore
Curtis spent $186. Find the are of the Rectangle
776
in
13
in
Answer:
about 3.09
Step-by-step explanation:
A = l x w
A = 13/7 x 7/6
A = 1.857 x 1.666
A = 3.09
Hope it helps!
the product of 5 - 2i and i is
Answer:
5i + 2
Step-by-step explanation:
(5-2i)(i)
5i - 2i^2
i^2= -1
5i -2(-1)
= 5i + 2
Someone please Help!! 30 Points
There are currently 1,250 pine trees on Judy's plot of land. The number of pine trees on her land is currently decreasing at a rate of 14% per year.
Which of the following graphs shows the number of pine trees, Np, on Judy's land x years from now?
Answer: we would need to see the graphs to address this question fully, but you should look for the graph that starts at x = 0, 1250 and decreases by 14% compared to the previous year
so for example, x = 1, the y value should be 1250 - (0.14)(1250)
Step-by-step explanation:
ſ x - 5y = -9( 4x + 4y = - 12Step 1 of 2: Determine if the point (-4,1) lies on both of the lines in the system of equations by substituting theordered pair into both equations.
Given:
[tex]\begin{gathered} x-5y=-9\ldots\ldots(1) \\ 4x+4y=-12\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]The given point is (-4,1)
Let's check the ordered pair (-4,1) in the first equation
[tex]\begin{gathered} x-5y=-9 \\ (-4)-5(1)=-9 \\ -4-5=-9 \\ -9=-9 \end{gathered}[/tex]Hence, (-4,1) is a solution of the first equation x-5y=-9.
Now, let's check (-4,1) in the second equation.
[tex]\begin{gathered} 4x+4y=-12 \\ 4(-4)+4(1)=-12 \\ -16+4=-12 \\ -12=-12 \end{gathered}[/tex]So, (-4,1) is a solution of the second equation 4x+4y=-12.
Hence, (-4,1) is a solution of both equation in the system, then it is a solution to the overall system.
Charlotte states that (43)3
can be rewritten as 218
. Which of the following explains how she is correct? Select all that apply.
The statement that explains why Charlotte's submission is correct is that (4³)³ simplifies to (4⁹) and (4⁹) simplifies to 2¹⁸
How to determine why Charlotte's submission is correct?From the question, the expression is given as
(43)3
Rewrite the expression properly
So, we have the following representation
(4³)³
Apply the law of indices to rewrite the exponents in the expression properly
So, we have
(4³)³ = 4³*³
Next, we evaluate the products
So, we have the following notation
(4³)³ = 4⁹
Solving further, we need to express 4 as the square of 2
So, we have
(4³)³ = (2²)⁹
Apply the law of indices to rewrite the exponents in the expression properly
So, we have
(4³)³ = 2²*⁹
Next, we evaluate the products
So, we have the following notation
(4³)³ = 2¹⁸
Hence, Charlotte's expression is correct
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Possible question
Charlotte states that (4³)³ can be rewritten as 2¹⁸. Which of the following explains how she is correct? Select all that apply.
There are 27 students in Mrs. Mello's class. fin the total number of pages they read by the end of November.
The total number of pages they read by the end of November is 2916 pages.
As the question, Chapter 1 has 35 pages, Chapter 2 has 38 pages and Chapter 3 has 35 pages. All these pages are read by all 27 students by the end of November.
⇒ Total number of pages in Three chapters [tex]=35+38+35[/tex]
[tex]=108[/tex]
⇒ Total number of pages in all three chapters read by one student = 108
⇒ Total number of pages read by 27 students
[tex]= total number of pages in three chapters * 27[/tex]
[tex]=108*27[/tex]
[tex]=2916[/tex]
Therefore, The total number of pages 27 students read by the end of November = 2916.
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The full question is
There are 27 students in Mrs. Mello's class. fin the total number of pages they read by the end of November.
Use the elimination method to solve the system of equations.3x + 4y = 8x - y = 12
Answer:
We have to use to elimination method to solve the provided system of equations, this method essentially involves eliminating one of the variables in the first equation by adding or subtracting a multiple of the second equation:
[tex]\begin{gathered} 3x+4y=8\rightarrow(1) \\ \\ x-y=12\rightarrow(2) \end{gathered}[/tex]The elimination of the variable y in equation (1) is achieved by adding the 4 times the equation 2 into the equation (1), the steps of the process are as follows:
[tex]\begin{gathered} 3x+4y=8 \\ \\ + \\ \\ 4\times(x-y)=4\times12 \\ \\ ------------------------------- \\ \\ 3x+4x=8+48 \\ \\ \\ 7x=56 \\ \\ \\ x=8 \end{gathered}[/tex]We have found the x value, the last step is to plug in the variable x value in any of the (1) or (2) equations, and solve for the y variable, the steps are as follows:
[tex]\begin{gathered} x-y=12 \\ \\ x=8 \\ \\ \therefore\Rightarrow \\ \\ 8-y=12\rightarrow y=8-12=-4 \\ \\ y=-4 \end{gathered}[/tex]The final answer is as follows:
[tex](8,-4)\Rightarrow\text{ Option \lparen B\rparen}[/tex]Therefore the answer is Option(B).
A driver accelerates her car from rest to a velocity of 35.9 mi/hr in 8.2 seconds. What is the acceleration of the car?
The acceleration of the car will be 0.002 m / s².
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The velocity of the car = 35.9 m/hr
The time take by car = 8.2 seconds
Now,
Since, We know that;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
Since, The driver accelerates her car from rest to a velocity of 35.9 mi/hr.
So, Initial velocity = 0
And, Final velocity = 35.9 m / hr
= (35.9 / 3600) m/s
= 0.01 m / s
So, We get;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
⇒ Acceleration = (0.01 - 0) / 8.2
⇒ Acceleration = 0.01 / 8.2
⇒ Acceleration = 0.002 m / s²
Thus, The acceleration of the car will be 0.002 m / s².
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point(10) On Myra's family vacation, her mom drove on the highway at aconstant speed of 60 miles per hour. Based on this rate, which of thefollowing times and miles driven are correct? Select all that apply. GRP.30190 miles driven in 3 hours150 miles driven in 2.5 hours30 miles driven in 30 minutes
help me out with this question..this is a k11..remember this is a practice question not a graded one
Each flight has a probability of 60% or 0.6 of being on time. This means that its complement, or the probability that the flight isn't on time is:
[tex]\text{\textasciitilde{}P(on time)}=1-0.6=0.4[/tex]It is 40% or 0.4. "~P(on time)" stands for the probability of the flight not being on time.
1. The probability that at least 2 flights are on time is:
To find the probability that 2 or more flights are on time we can fight the probability that "0" or "1" are not on time.
[tex]P(0\text{ on time)}=0.4^9=0.000262144[/tex][tex]\begin{gathered} P(1\text{ on time})=\frac{9!}{1!\cdot(9-1)!}\cdot0.6\cdot(0.4)^8 \\ P(1\text{ on time)}=9\cdot0.6\cdot(0.4)^8=0.003538944 \end{gathered}[/tex][tex]\begin{gathered} P(1\text{ or less on time)}=P(0\text{ on time)}+P(1\text{ on time)} \\ P(1\text{ or less on time)}=0.000262144+0.003538944=0.003801088 \end{gathered}[/tex]The probability of 2 or more flights are on time is:
[tex]P(2\text{ or more on time)}\cdot=1-0.003801088=0.996198912[/tex]The probability of 2 flights or more are on time is 0.996198912
2.
We need to calculate the probabilities of 7,8 and 9 flights are on time and then subtract by 1.
[tex]\begin{gathered} P(7)=\frac{9!}{7!\cdot(9-7)!}\cdot0.6^7\cdot0.4^2 \\ P(7)=36\cdot0.6^7\cdot0.4^2=0.161243136 \end{gathered}[/tex][tex]\begin{gathered} P(8)=\frac{9!}{8!\cdot(9-8)!}\cdot0.6^8\cdot0.4 \\ P(8)=9\cdot0.6^8\cdot0.4=0.060466176 \end{gathered}[/tex][tex]P(9)=0.6^9=0.010077696[/tex]The probability of at most 6 flights are on time is:
[tex]\begin{gathered} P(6\text{ or less on time) = 1 - (}P(7)+P(8)+P(9)) \\ P(6\text{ or less on time) = 1-(0.161243136+0.060466176+0.010077696)=}0.768212992 \end{gathered}[/tex]The probability of 6 or less are on time is 0.768212992.
3.
The probability of exactly 5 flights are on time is:
[tex]\begin{gathered} P(5)=\frac{9!}{5!(9-5)!}0.6^5\cdot0.4^4 \\ P(5)=126\cdot0.6^5\cdot0.4^4=0.250822656 \end{gathered}[/tex]The probability of exactly 5 flights are on time is 0.250822656.
Solve for z in -3 < z-1 < 3.Give the result in the interval notation and graph on a number line
Answer:
(-2,4)
Explanation:
Given the inequality:
[tex]-3First, we add 1 to all parts of the inequality.[tex]\begin{gathered} -3+1We can represent this in interval notation as:[tex](-2,4)[/tex]The solution set is graphed on the number line below:
Help
In 1846 the depth of the river was 5 feet deep.
In 1847 it dropped to 3.8 feet.
This year, 1848, it rose to 6.4 feet.
Find the percent change in river depth & complete the table.
The percent change in river depth is 52%
How to calculate the percentage?From the information, the depth of the river was 5 feet deep, it dropped to 3.8 feet and in 1848, it rose to 6.4 feet. The new feet will be:
= -5 - 3.8 + 6.4
= 2.4
Therefore, the percentage change will be:
= New feet / Initial feet × 100
= (5 - 2.4) / 5 × 100
= 2.6 / 5 × 100
= 52%
Note that there was no table given.
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Complete the similarity statement relating the three triangles in the diagram. Show work.
Answer:
[tex]\Delta JKM\approx\Delta MKL\approx\Delta JML[/tex]Explanation:
There are three right angled triangles are in the diagram of three different sizes.
Identify the right angles.
In the first triangle, the right angle is angle M. In the second one, the right angle is angle K and in the third triangle, it is angle K.
Now, identify the shortest sides of each.
The shortest side in the first triangle is MJ, in the second triangle, it is JK and in the third triangle, it is MK.
In the given triangle JKM, notice that JK is the shortest side and angle K is the right angle. Write the other two tringles also in the similar form with the first two letters gives the short side and middle letter represents the right angle.
So, the similarity statement is
[tex]\Delta JKM\approx\Delta MKL\approx\Delta JML[/tex]Manuel took a total of 20 quizzes over the course of 2 weeks. How many weeks of school will Manuel have to attend this quarter before he will have taken a total of 90 quizzes? Assume the relationship is directly proportional.
Manuel will attend the quarter in 9 weeks.
Given,
In the question:
Total taken quizzes is 90
Manuel took a total of 20 quizzes over the course of 2 weeks.
To find the how many weeks of school will Manuel have to attend this quarter ?
Now, According to the question:
Based on the given conditions :
Formulate:
Let the no. of weeks be x
Total quizzes = 90
Here, The relationship is directly proportional.
20/2 = 90/x
If the fraction is defined, the denominator cannot be equal 0.
Solve the equation:
10 = 90/x
10x = 90
x = 9
Hence, Manuel will attend the quarter in 9 weeks.
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If ABCD is dilated by a factor of 2, thecoordinate of B' would be:543С2B1-8 -7-6-5-4-3-2-1 012.34567891011-1A-2D-3B' = ([?], [ ]=4Cotor
We have a figure ABCD that is dilated by a factor of 2.
We have to find the coordinate of the image point B'.
If the center of dilation is the origin (0,0) and the factor is k = 2, we can write the rule:
[tex](x,y)\longrightarrow(2x,2y)[/tex]Then, for B(-1,1), we will get:
[tex]B=(-1,1)\longrightarrow B^{\prime}=(2\cdot(-1),2\cdot1)=(-2,2)[/tex]Answer: B' = (-2,2)
solveeeeeeeeeeeee for x
Answer:
7.5/3
Step-by-step explanation:
set AC and BD equal to eachother because they are equal and solve
Type the correct answer in each box. Use numerals instead of words. This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form? Graph shows upward parabola plotted on a coordinate plane. The parabola has vertex at (2, minus 8) with the left slope at (0, 0) and the right slope at (4, 0).
The function’s equation written in factored form and in vertex form are respectively;
f(x) = 2x(x - 4)
f(x) = 2(x - 2)² - 8
How to Interpret Quadratic Graphs?The factored form of a quadratic function is;
f(x) = a(x - p)(x - q)
where:
p and q are the x-intercepts
a is a constant
Now, we are given x-intercepts as; (0, 0) and (4, 0)
Thus;
f(x) = a(x - 0)(x - 4)
f(x) = ax(x - 4)
To find a, substitute the given vertex (2, -8) into the equation and solve for a:
2a(2 - 4) = -8
-4a = -8
a = 2
Thus;
f(x) = 2x(x - 4)
The vertex form of a quadratic equation is;
f(x) = a(x - h)² + k
where:
(h, k) is the vertex
a is constant
Since vertex is (2, -8), then we have;
f(x) = a(x - 2)² - 8
Put the coordinate (0, 0) to find a;
0 = a(0 - 2)² - 8
4a = 8
a = 2
Thus;
f(x) = 2(x - 2)² - 8
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Madeline earns $17,500 annually. What is the gross amount of hersemimonthly paycheck?a. $2,916.67b. $1,458.33c. $729.17d. $673.08
Given:
Annual earnings = $17,500
Asked: What is the gross amount of her semimonthly paycheck?
Solution:
To find the answer, we need to divide first the annual earnings by 12 to get the monthly paycheck. After that, we will divide it by 2 because we are looking for the semimonthly paycheck.
[tex]\begin{gathered} \frac{17,500}{12}=1,458.33 \\ \frac{1,458.33}{2}=729..17 \end{gathered}[/tex]ANSWER: C. $729.17
BD bisects ABC, m/ABD = 2(3x), and m/ABC = 42°.
What is the value of x?
In the given triangle ABC where BD bisects ABC and according to the values of the given angles, the value of x is found out to be 3.5.
It is given to us that -
BD bisects ABC.
m/ABD = 2(3x) ----- (1)
and, m/ABC = 42 ------- (2)
We need to find out the value of x.
Since BD bisects triangle ABC,
The angles created with respect to the bisector are equal.
=> m/ABD = m/CBD ----- (3)
Also, it is also known that -
m/ABD + m/CBD = m/ABC ----- (4)
Substituting equation (3) in equation (4),
m/ABD + m/CBD = m/ABC
=> m/ABD + m/ABD = m/ABC
=> 2 m/ABD = m/ABC ----- (5)
Substituting the values of m/ABD and m/ABC from equation (1) and (2) in equation (5), we get
2 m/ABD = m/ABC
=> 2*2(3x) = 42
=> 12x = 42
=> x = 3.5
Thus, according to the values of the angles of the triangle, the value of x is 3.5.
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an arithmetic sequence has these properties: a1=2an = an-1 + 5 what are the first four terms of the sequence?
we have that the arithmetic sequence have:
[tex]\begin{gathered} a_1=2 \\ a_n=a_{n-1}+5 \end{gathered}[/tex]so we can replace for n=2,3,and 4 to find the first four terms so:
for n=2
[tex]\begin{gathered} a_2=a_{2-1}+5 \\ a_2=a_1+5 \\ a_2=2+5 \\ a_2=7 \end{gathered}[/tex]for n=3
[tex]\begin{gathered} a_3=a_{3-1}+5 \\ a_3=a_2+5 \\ a_3=7+5 \\ a_3=12 \end{gathered}[/tex]and for n=4
[tex]\begin{gathered} a_4=a_{4-1}+5 \\ a_4=a_3+5 \\ a_4=12+5 \\ a_4=17 \end{gathered}[/tex]So the first four numbers are
[tex]2,7,12,17[/tex]What number is in the hundreds place after
simplifying?
(21 × 10¹)+(3×
X
10²) + (9 × 10²)
a) 4
b) 1
c) 3
d) 7
The digit in the hundreds place is 4
From the question, we have
(21 × 10¹)+(3×10²) + (9 × 10²)
=210+300+900
=1410
The digit in the hundreds place is 4 and the value is 400.
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Brian had p pencils. Then he bought 4 more.
How many does he have now? due tm pleaseeeeeeeeeeeeee help
Answer: The number of pencils Brian has is p+4
Step-by-step explanation:
Because p is the original number of the pencil ( we don't know how many are there so we keep it p). Then he bought 4 more which mean +4, so the answer is p+4
Pls do this for me asap
a) The area of the rectangle has the following inequality: 12 ≤ 6 · x ≤ 36.
b) The value of the variable x has the following inequality: 2 ≤ x ≤ 6.
How to build and interpret an inequality associated to the area of an rectangle
The area of a rectangle (A) is described by the following formula:
A = b · h
Where:
b - Base of the rectangleh - Height of the rectanglea) If we know that b = 2 · x and h = 3, then the area of the rectangle is:
A = (2 · x) · 3
A = 6 · x
And the inequality is:
12 ≤ 6 · x ≤ 36
b) And the solutions for the values of x are represented by the following inequality:
2 ≤ x ≤ 6
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The area of circular pound is 21.5 m2. Work out the diameter of the circle. Give your answer correct to the nearest centimetre.
The diameter of the circle is 5.2m.
The area of circular pond is 21.5 m2
area of a circle is given by the formula
area = πr²
21.5 = 3.14 r²
r² = 6.84
r = ±2.6
r is a length and it cannot be negative
So, r = 2.6
Diameter is twice of radius
d = 2r
d = 2(2.6)
d = 5.2
Therefore, the diameter of the circle is 5.2m.
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