The value of n in the right triangle is 12 cm.
How to find the side of a right triangle?The shortest side of a right angle triangle is 6cm shorter than the hypotenuse.
The difference in length of the other two sides is 3cm.
The hypotenuse side is the longest side of a right triangle.
Hence,
hypotenuse side = n - 3 + 6
hypotenuse side = n + 3
Shortest side of the right triangle = n - 3
Other side = n
Therefore, using Pythagoras theorem,
(n + 3)² = (n - 3)² + n²
(n + 3)(n + 3) = (n - 3)(n - 3) + n²
n² + 3n + 3n + 9 = n² -3n -3n + 9 + n²
n² + 6n + 9 = 2n² - 6n + 9
Therefore,
2n² - n² + 9 - 9 = 6n + 6n
n² = 12n
n² - 12n = 0
n(n - 12) = 0
n = 0 and n = 12
Therefore,
n = 12
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A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds
and each large box of paper weighs 75 pound's. A total of 24 boxes of paper were
shipped weighing 1410 pounds altogether. Write a system of equations that could be
used to determine the number of small boxes shipped and the number of large boxes
shipped. Define the variables that you use to write the system.
A total of 24 boxes of paper were shipped weighing 1410 pounds altogether, the system of equations are X + Y = 24, and 45X + 75Y = 1410 and the variables that you use to write the system X = 13 and Y = 11.
What is pound?The primary unit of sterling is the pound (sign: £), while the term "pound" is also frequently used to refer to the British pound or pound sterling in foreign settings.
The oldest currency that is still in the circulation and has been used continuously since its origin is sterling. After US dollar, euro, and Japanese yen, it is currently fourth most traded currency on the foreign exchange market. It makes up basket of currencies used to determine the value of IMF special drawing rights along with the other three currencies and the renminbi. Sterling is also fourth-most-held reserve currency in the world's reserves as of mid-2021.
Let X equal number of small boxes
Let Y equal number of big boxes
The first equation is: X + Y = 24 ( this shows that total number of boxes = 24)
The second equation is: 45X + 75Y = 1410 ( this is because small box weighs 24 pounds and big box weighs 75 pounds. The total weight of small boxes is 45 times weight of each individual box. And the total weight of second boxes is equal to 75Y.
When you solve system, X = 13 and Y = 11
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Suppose 54 gallons of water came out of a pipe in 9 minutes. What was the rate in gallons per minute?
Answer:
6 gallons per minute
Step-by-step explanation:
54 gallons came out in 9 minutes
54/9 = 6
the rate is 6 gallons per minute
?:12 =7:14 what is the answer
two coins are tossed. the probability of at least getting one head is ?
Answer:1/2
Step-by-step explanation:
2 heads
2 tails
2 + 2 = 4
heads - 2/4 - total
1/2
Un barco navega 300 km al oeste, después 100 km al sur, al final de su viaje, que tan lejos está de su posición inicial? Elabora en tu libreta el dibujo y resuelve.
Answer: 400 KL you have to add 300 KL + 100 KL = 400 KL
2x-5y = 2
3x - 7y=1
solve the system by elimination
Answer:
x= -9, y= -4
Step-by-step explanation:
Solving a linear equation can be done by two main methods, namely elimination and substitution. Elimination works by making the numerical value of one of the variable's coefficient the same, such that we can subsequently eliminate (or remove) the variable by subtracting or adding the two equations together.
Start by labelling the 2 given equations:
2x -5y= 2-----(1)
3x -7y= 1-----(2)
I will be working to eliminate the x term here, since we would be dealing with smaller numbers in this case. Eliminating the y term would also work.
The lowest common multiple of 2 and 3 is 6, thus multiply equation (1) by 3 and (2) by 2 so that the coefficient of x in both equations is 6. Then label the equations.
(1) ×3:
6x -15y= 6 -----(3)
(2) ×2:
6x -14y= 2 -----(4)
Since the coefficient of x in both equations is positive 6, we can subtract one equation from the other to eliminate the x term. If both coefficients have different signs (e.g. +6 and -6), the addition of the two equations would eliminate the term.
(3) -(4):
6x -15y -(6x -14y)= 6 -2
Expand:
6x -15y -6x +14y= 4
-y= 4
Divide both sides by -1:
y= -4
Then use substitution to find the value of y. Note that at this point, you could work to eliminate the y term from equations (1) and (2) to solve for x but it is commonly understood that when a question states solve by elimination, it is only for the first variable.
Substitute y= -4 into (1):
2x -5(-4)= 2
2x +20= 2
Subtract 20 from both sides:
2x= 2-20
2x= -18
Divide both sides by 2:
x= -9
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what does x have to measure to make the lines parallel?
PLEASE HELP ASAP
Answer:
23) 30°
24) 12°
Step-by-step explanation:
23) Lines will be parallel if the co interior angles are supplementary.
∠3 + ∠5 = 180°
3x+ 25 + 4x - 55 = 180
3x + 4x + 25 -55 = 180
Combine like terms,
7x - 30 = 180
Add 30 to both sides,
7x = 180 + 30
7x = 210
Divide both sides by 7,
x = 210 ÷ 7
x = 30
24) If the lines are parallel, then the alternate interior angles are congruent.
∠7 = ∠2
11x - 36 = 8x
Add 36 to both sides,
11x = 8x + 36
Subtract 8x from both sides,
11x - 8x = 36
3x = 36
x = 36 ÷ 3
x = 12°
You invested a total of $30,000 at 3% and 4 1 2 % simple interest. During one year, the two accounts earned $1200. How much did you invest in each account?
Answer:
$20,000 at 4.5% simple interest
$10,000 at 3% simple interest
Step-by-step explanation:
[tex].045x + .03(30000 - x) = 1200[/tex]
[tex].045x + 900 - .03x = 1200[/tex]
[tex].015x + 900 = 1200[/tex]
[tex].015x = 300[/tex]
[tex]x = 20000[/tex]
$20,000 at 4.5% simple interest
$30,000-$20,000=$10,000 at 3% simple interest
Which of the following is a solution to the equation
2x² + 4x = 3 + 3x² ?
A) -1
B)
0
C) 3
D) 6
===========================================================
Reason:
Let's check to see if choice A is the answer. We'll replace each x with -1
2x^2 + 4x = 3 + 3x^2
2(-1)^2 + 4(-1) = 3 + 3(-1)^2
2(1) + 4(-1) = 3 + 3(1)
2 - 4 = 3 + 3
-2 = 6
We don't end up with the same thing on both sides, so x = -1 is not a solution to the equation.
--------------
Now try x = 0
2x^2 + 4x = 3 + 3x^2
2(0)^2 + 4(0) = 3 + 3(0)^2
2(0) + 4(0) = 3 + 3(0)
0 = 3
That's false as well, which allows us to rule out choice B.
--------------
Next up plug x = 3 into the equation
2x^2 + 4x = 3 + 3x^2
2(3)^2 + 4(3) = 3 + 3(3)^2
2(9) + 4(3) = 3 + 3(9)
18 + 12 = 3 + 27
30 = 30
We get the same thing on both sides so we have confirmed x = 3 is a solution.
--------------
There may be other solutions. If we tried x = 6, then it leads to 96 on the left hand side and 111 on the right hand side. That rules out x = 6 as a solution.
An urn has 10 balls that are identical except that 6 are white and 4 are red. a sample of 7 is selected randomly without replacement. what is the probability that exactly 5 are white and 2 are red? what is the probability that at least 5 of the balls are white?
The question tests on probability and combinations.
To obtain the probability for selecting exactly two red and 5 white urns is:
If Wi and Ri are events for selecting the ith ball, apply the multiplicative rule to obtain:
=P(W1∩W2∩W3∩W4∩W5∩R1∩R2)
= P(W1)P(W2|W1)P(W3|W1∩W2)P(W4|W1∩W2∩W3)P(W5|W1∩W2∩W3∩ W4)P(R1|W1∩W2∩W3∩W4∩W5)P(R2|W1∩W2∩W3∩W4∩W5∩R1)
=6/10×5/9×4/8×3/7×2/6×4/5×3/4
= 1/10
The probability is 1/10.
Alternatively, use the Bayes theorem. This uses combinations. To get the probability for exactly 5 white and 2 red, obtain the chance for selecting 5 white balls and 2 red balls; 6C5 and 4C2.
(6C5×4C2)/10C7 = 6×6/120 = 1/10
The probability for at least 5 balls is obtained by the probability of either selecting 5 or 6 balls.
Using combination;
(6C6 X6C5)/10C7 = (1x6)/120 = 6/120 = 1/20.
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PLEASE HELP!!!!!!!!!!!
(1 point)
Suppose U={1,2,3,4,5,6,7,8,9,10} is the universal set, and P={2,4,6,8,10}. What is P?
When compared to the universal setU={1,2,3,4,5,6,7,8,9,10}, the set P=2,4,6,8,10 has a prime that is equal to P'=1,3,5,7,9 as its element.
This is further explained below.
What is a set prime?Generally, Assigned the letter A (A prime), The components that are included in the Universal set but are absent from Set A are denoted by the letter A.
U={1,2,3,4,5,6,7,8,9,10}
P={2,4,6,8,10}
Therefore, the prime of the set P={2,4,6,8,10} in relation to the universal set U={1,2,3,4,5,6,7,8,9,10} is
P'={1,3,5,7,9}
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Suppose U={1,2,3,4,5,6,7,8,9,10} is the universal set, and P={2,4,6,8,10}. What is P'?
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The solution of the inequality will be;
⇒ A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The expression for the inequality will be;
⇒ 3(8 – 4x) < 6(x – 5)
Now, Solve the inequality as;
The expression for the inequality will be;
= 3(8 – 4x) < 6(x – 5)
Divide by 3 both side,
= 8 - 4x < 2 (x - 5)
= 8 - 4x < 2x - 10
Add 4x both side;
= 8 - 4x + 4x < 2x - 10 + 4x
= 8 < 6x - 10
Add 10 both side;
= 18 < 6x
Divide 6 both side;
= 3 < x
So, The solution of the inequality will be;
⇒ A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
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rereciporical of 1/2
Answer: 2 or 2/1
Step-by-step explanation: the reciprocal of 1/2 is 2/1. in decimal form, 2 is the reciprocal of 0.5.
PLSSS I NEED HELP ASAP
Answer:
19. x=20 y=7 20. x=10 y=25 21. x=12 y=31
Step-by-step explanation:
worksapce thingy
3x+17=5x-7
2x=24 x=12
53
no idea if im right .-.
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds
and each large box of paper weighs 80 pounds. There were 4 more large boxes
shipped than small boxes and the total weight of all boxes was 1750 pounds. Write a
system of equations that could be used to determine the number of small boxes
shipped and the number of large boxes shipped. Define the variables that you use to
write the system.
The system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped are:
50x+80y=1750
y = x+4 ,
where x represent the number of small boxes of paper and y represent the number of large boxes of paper.
We have:
Weight of small box of paper = 50 pounds
Weight of large box of paper = 80 pounds
Total weight of boxes = 1750 pounds
Let us consider that the number of small boxes of papers be x.
The number of large boxes of papers be y.
Then, according to question
50x+80y=1750
y = x+4
Therefore, the equations 50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped.
where, x represent the number of small boxes of paper and y represent the number of large boxes of paper.
Henry is buying school supplies for the start of the school year for every 3 pencils he buys 2 pens if Henry buys 21 pencils how many total pencils and pens did Henry buy
Total number of pencils and pens bought by Henry = 35.
What is the unitary method of problem solving?
The unitary technique, in its most basic form, is used to calculate the value of a single unit from a specified multiple. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.
Given, for every 3 pencils, number of pens bought = 2
Therefore, every 1 pencil, number of pens bought = 2/3
Thus, for 21 pencils, number of pens bought = (2/3)*21 = 14
Therefore, total number of pencils and pens bought by Henry = 21 + 14 = 35.
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It's Joey's 8th birthday! Joey's favorite present is the 8 baseball cards that he got from his dad. Joey has never owned a baseball card before this gift, and he decides that he wants to start collecting baseball cards.
He plans to collect 3 baseball cards each month until he has a total of 50 cards.
Let x represent the number of months Joey collects the baseball cards.
Which equation can Joey use to determine how many months it will take to reach his goal?
The equation that Joey can use to determine how many months it will take to reach his goal will be 8 + 3x = 50 and the number of months is 14.
How to illustrate the information?From the information, Joey's favorite present is the 8 baseball cards that he got from his dad and he has never owned a baseball card before this gift and he plans to collect 3 baseball cards each month until he has a total of 50 cards.
This will be illustrated as:
8 + 3x = 50
Collect like terms
3x = 50 - 8
3x = 42
Divide through 3
3x / 3 = 42 / 3
x = 14
The number of months is 14.
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Solve the equation. If there is no solution, write no
solution (still show work).
| + 2| = 4
Answer: no solution
Step-by-step explanation:
What is the distance between (3,-4) and (5,6)
Answer:
Step-by-step explanation:
eedrfgrtrf3re3
ANSWER:
(3,-4)= -2 (5,6)= -10 and if you need to divide it would be 0.2
Step-by-step explanation:
What I did was get the y- axis number with each other and minus them so that would be (3, - 5) = -2 and then I did (-4 - 6)= -10 and then you can divided -2/-10= 0.2. Hope this helped!
1/3 of a number is added to 5. The result is one and a half times the original number
Answer:
let the number be x...therefore 1/3 of x equals to 1/3x
1/3x+5=6/5x....collect like terms
1/3x-6/5x=-5
0.3x - 1.2x = -5
-0.9x = -5
Divide both sides by coefficient of x....
X = -5/-0.9
=5.55
=5.6
Find the solution to the following system on the calculator. Round
your answer to two decimal places.
{y= 3x - 6 y = -5x + 14
Answer:
y=3x=16/3
Step-by-step explanation:
Write the equation of a line that has a slope of 1/2 and a y-intercept of (0,-4) in standard form.
Write the equation that contains the point (-5,2) and in which the slope equals 1/2 in standard form.
Write the equation of the line in which the x-intercept is 2 and the y-intercept is 8 in slope-intercept form.
Considering the definition of a line, you get:
the equation of a line that has a slope of 1/2 and a y-intercept of (0,-4) is y= 1/2x -4.the equation that contains the point (-5,2) and in which the slope equals 1/2 is is y= 1/2x +9/2.the equation of the line in which the x-intercept is 2 and the y-intercept is 8 is y=-4x +8.Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Equation of a line that has a slope of 1/2 and a y-intercept of (0,-4)In this case, you know:
The line has a slope of 1/2.The line passes through the point (0, -4).Substituting the value of the slope m and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained:
-4= 1/2×0 + b
-4= 0 + b
-4 = b
Finally, the equation of the line is y= 1/2x -4.
Equation that contains the point (-5,2) and in which the slope equals 1/2In this case, you know:
The line has a slope of 1/2.The line passes through the point (-5, 2).Substituting the value of the slope m and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained:
2= 1/2×(-5) + b
2= -5/2 + b
2 + 5/2= b
9/2 = b
Finally, the equation of the line is y= 1/2x +9/2.
Equation of the line in which the x-intercept is 2 and the y-intercept is 8Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Being (x₁, y₁)= (2,0) [x-intercept] and (x₂, y₂)= (0,8) [y-intercept] , the slope m can be calculated as:
m= (y₂ - y₁)÷ (x₂ - x₁)
m= (8- 0)÷ (0 -2)
m= 8÷ (-2)
m= -4
Considering point 2 and the slope m, you obtain:
8= -4×0 + b
8= 0 +b
8=b
Finally, the equation of the line y=-4x + 8.
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any number raised to the 2nd power is said to be
Answer: squared
Step-by-step explanation:
3. Triangle JKL is shown below. Which of the following is not a true statement about the angles in the triangle? A. The sum of 2J + 2K+ ZL = 180°. B. The measure of ZJ is 65°. C. The measure of ZK is 89°. D. The measure of ZL is 43°. 7x+2 J K 8x 7x + 2 4x + 7 L
The statement that is not true about the angles in the triangle is OPTION C. The measure of ∠K is 89°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
From the diagram:
∠J + ∠K + ∠L = 180° (angles in a triangle)
Substituting:
(7x + 2) + (8x) + (4x + 7) = 180
19x + 9 = 180
x = 9
∠J = 7x + 2 = 7(9) + 2 = 65°
∠K = 8x = 8(9) = 72°
∠L = 4x + 7 = 4(9) + 7 = 43°
∠k ≠ 89°
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Which describes two similar triangles?
Two triangles for which a set of rigid motions can be used to show that all corresponding pairs of angles are equal and all corresponding pairs of sides are equal.
Two triangles for which a set of rigid motions can be used to show that all corresponding pairs of angles are equal and all corresponding pairs of sides are proportional.
Two triangles for which a set of rigid motions and dilations can be used to show that all corresponding pairs of angles are equal and all corresponding pairs of sides are equal.
Two triangles for which a set of rigid motions and dilations can be used to show that all corresponding pairs of angles are equal and all corresponding pairs of sides are proportional.
Answer:
Definition. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
FIRST PERSON TO ANSWER GETS BRAINLIEST
2. Melanie’s bank account balance is. She needs to pay $55 to her cell phone carrier and $80 to the landscaper. She also expects $250 from her sister to be added to her account.
(a) Write an expression Melanie can use to determine her bank account balance after paying these bills and receiving money from her sister.
(b) What is Melanie’s bank account balance after paying her bills and receiving money? Show any necessary work. Answer in a complete sentence
Answer:
Describe how anthropology challenges more commonly held notions of progress
Step-by-step explanation:
Hello! Can you check these for me please :)
Triangles ADT and EDT are congruent by SSS rule and triangles BLG and PFX are congruent by SAS rule.
In triangle ADT and EDT, we get that:
AD = DE (given)
AT = ET (given)
DT = DT (common)
So, ΔADT ≅ Δ EDT (SSS congruency rule)
In triangle BLG and PFX, we get that:
BL = PF (given)
BG = PX (given)
∠ B = ∠ P (given)
So, ΔBLG ≅ Δ PFX (SAS congruency rule)
Therefore, we get that, triangles ADT and EDT are congruent by SSS rule and triangles BLG and PFX are congruent by SAS rule.
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emma says the gcf of 16 and 12 is 48.Her friend grace says the answer is 4. Who is right? Explain
Answer:
Grace
Step-by-step explanation:
48 is the LCM, 4 is the GCF
Need help asap!!!!!!!!
If two numbers are multiplied, they are written as "a multiplied by b."
The answer is 9 3/7.
How to multiply?Multiplication is the product of 2 or more numbers/things.
Multiplying in math is equivalent to adding like groups.
The quantity of items in the group expands as we multiply.
A multiplication question has two factors, a product, and two factors. The factors and the product in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, respectively.
4 2/7 * 2 1/5 = 30/7 * 11/5
On simplifying,
= 6/7*11
= 66/7
=9 3/7
The answer is 9 3/7.
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The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is greater than 2". Find P(not A). Outcome Probability 1 0.22 2 0.08 3 0.13 4 0.33 5 0.24
Remember that
[tex]P(\text{not A)}=1-P(A)[/tex]We know that:
[tex]\begin{gathered} P(A)=0.13+\text{0}.33+0.24 \\ \rightarrow P(A)=0.7 \end{gathered}[/tex]This way,
[tex]\begin{gathered} P(\text{not A)}=1-0.7 \\ \rightarrow P(\text{not A)}=0.3 \end{gathered}[/tex]