ANSWER:
x = 4
STEP BY STEP EXPLANATION:
See attachment for complete question
From the attachment, the parallelogram has two diagonals. And the diagonals of a parallelogram bisect one another.
Because 2x - 1 and 7 are opposite sides of a diagonal; We can say that:
2x - 1= 72x−1=7
Add 1 to both sides
2x - 1 + 1 = 7 + 12x−1+1=7+1
2x = 82x=8
Divide through by 2
x =4
Points A, B, C, D, E, F and G are on a number line such that B, C, D, E and F divide segment AG into 6 equal pieces. If A is at 13 and G is at 59, what is the sum of the numbers at B, C, D, E and F
The sum of numbers at B, C, D, E and F is 110.5
Since B, C, D, E, and F divide the segment AG into 6 equal pieces, each piece has a length of (59-13)/6 = 6.5.
Therefore, the numbers at B, C, D, E, and F are located at 13 + 6.5, 13 + 6.52, 13 + 6.53, 13 + 6.54, and 13 + 6.55 respectively.
The sum of the numbers at B, C, D, E and F is (13 + 6.5) + (13 + 6.52) + (13 + 6.53) + (13 + 6.54) + (13 + 6.55)
= 13 + 6.5*(1+2+3+4+5) = 13 + 6.5*15 = 13 + 97.5
= 110.5
In Maths, number lines are the horizontal straight lines in which the integers are placed in equal intervals. All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.
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bags of clementines have 12 each. for a party, sal, trisha, and joe each brought bags of clementines. altogether, there were 180 clementines. sal brought 4 bags and joe brought 6. write the equation to determine how many bags trisha brought, t.(2 points)
The equation to determine how many bags Trisha brought is: T = 180 - (4 + 6)
We know that the total number of clementines is 180, Sal brought 4 bags and Joe brought 6. To determine how many bags Trisha brought, we need to determine the total number of bags that Sal and Joe brought together. We can do this by combining the two numbers together (4 + 6). This will give us a total of 10 bags. To determine how many bags Trisha brought, we need to subtract the total number of bags that Sal and Joe brought (10) from the total number of clementines (180). This gives us an answer of 170. This means that Trisha brought 170 clementines, or 7 bags. Therefore, the equation to determine how many bags Trisha brought is: T = 180 - (4 + 6).
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a rectangular pool is 30 feet wide and 40 feet long. it is surrounded on all four sides by a wooden deck that is x feet wide. the total area enclosed within the perimeter of the deck is 2576 square feet. what is the width of the deck?
On solving the provided question, we can say that length of the rectangle pool is is = 17.58
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
[tex](30+2x)(40+2x)-1200=3696\\1200+60x+80x+4x^2 -1200=3696\\4x^2 +140x-3696=0\\x=17.58 or -52.58\\[/tex]
length is = 17.58
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What is 1/6 (12x - 30) + 4x simplified
Answer: 6x - 5
Step-by-step explanation:
Given:
1/6 (12x - 30) + 4x
Distribute:
2x - 5 + 4x
Combine like terms with addition:
6x - 5
Answer:
6x - 5
Step-by-step explanation:
Given expression,
→ (1/6)(12x - 30) + 4x
Let's simplify the expression,
→ (1/6)(12x - 30) + 4x
→ ((12x - 30)/6) + 4x
→ 2x - 5 + 4x
→ (2x + 4x) - 5
→ 6x - 5
Hence, the answer is 6x - 5.
the area of a square is increasing at a rate of 28 square centimeters per minute. at the time when the side length of the square is 6, what is the rate of change of the perimeter of the square? round your answer to three decimal places (if necessary).
The rate of change of the perimeter of the square is 11.2 cm/min when the side length is 6 cm.
Step 1: The area of a square is A = s2, where s is the side length.
Step 2: The rate of change of the area of the square is 28 cm2/min.
Step 3: The perimeter of the square is
P = 4s.
Step 4: Substitute s = 6 into the equation for P to get
P = 24 cm.
Step 5: Differentiate P with respect to time to get the rate of change of
the perimeter:
dP/dt = 4ds/dt.
Step 6: Substitute the rate of change of the area (dA/dt = 28 cm2/min) into the equation for dP/dt to get dP/dt = 4(28 cm2/min)/dt.
Step 7: Simplify the equation to get
dP/dt = 112 cm/min.
Conclusion: The rate of change of the perimeter of the square is 112 cm/min when the side length is 6 cm
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suppose that you draw a card from a standard deck of cards. what is the probability that the card is a face card (i.e., a jack, queen, or king) or a heart?
The probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13
In the given question, suppose that you draw a card from a standard deck of cards.
We have to find the probability that the card is a face card (i.e., a jack, queen, or king) or a heart.
As we know that in a deck of cards have total 52 cards.
In which 26 cards are in heart shape.
Every different type of card have 3 face cards and have total four different type of cards. That means there are total 12 face cards.
In 26 cards of heart have total 6 face cards.
So, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart
P = (Total face cards + total heart shape card - 6 face cards)/Total cards in a deck
P = (12 + 26 - 6)/52
P = (38 - 6)/52
P = 32/52
P = 8/13
Hence, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13.
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Sally makes a fruit drink by mixing pineapple juice and mango juice in the ratio 2:3
She buys pineapple juice in 1.5 litre cartons that cost 1.30 each.
She buys mango juice in 1 litre cartons.
The cartons are only sold in packs of 4 which cost 3.20.
Sally makes 60 litres of her fruit drink for a party.
At the party she fills 190 cups and sells all of them for 50p per cup.
Work out how much profit she makes.
6
Step-by-step explanation:
um7
I need help with this
Answer:
12
Step-by-step explanation:
Draw a horizontal line that splits the hexagon in half
x = 180 - measure of a angle in the pentagon - half of the angle in the hexagon
x = 180 - 540/5 - 1/2*(720/6)
x = 180 - 108 - 60 = 180 - 168 = 12
Hope this helps :)
Have a great day
Consider the following sample of observations on coating thickness for low-viscosity paint:
.83 .88 .88 1.04 1.09 1.12 1.29 1.31 1.48 1.49 1.59 1.62 1.65 1.71 1.76 1.83
Assume that the distribution of coating thickness is normal (a normal probability plot strongly supports this assumption).
a. Calculate a point estimate of the mean value of coating thickness, and state which estimator you used.
b. Calculate a point estimate of the median of the coating thickness distribution, and state which estimator you used. c. Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90%, and state which estimator you used. [Hint: Express what you are trying to estimate in terms of m and s.]
d. Estimate P(X < 1.5), i.e., the proportion of all thickness values less than 1.5. [Hint: If you knew the values of m and s, you could calculate this probability. These values are not available, but they can be estimated.]
e. What is the estimated standard error of the estimator that you used in part (b)?
The coating thickness distribution is normal and has a mean value of 1.245.
What is mean?In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode.
To calculate the data's coating thickness, sample mean is employed.
The following formula is used to determine the mean value's point estimate:
[tex]\bar x = \frac{1}{n} \sum x_i[/tex]
The typical probability plot shown there has a rather straight pattern. Assume right now that the coating thickness distribution is normal and has a mean value:
[tex]\bar x = \frac{19.92}{16}\\\\\bar x = 1.245[/tex]
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Determine the value of x using a trigonometric ratio. Question 9 options: A) 4.98 B) 4.18 C) 10.11 D) 8.49
Using the trigonometric ratios the correct option is option a) 4.98.
We have a known hypotenuse, but an unknown opposite side. Use the sine ratio to tie the two together to be able to solve for x.
Trigonometric ratios are a set of ratios that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.
These ratios can be used to find missing side lengths or angle measures in a right triangle, and they have many applications in mathematics, physics, engineering, and other fields.
sin(angle) = opposite/hypotenuse
sin(50) = x/6.5
6.5*sin(50) = x
x = 6.5*sin(50)
x = 4.97928888027336, make sure your calculator is in degree mode
x = 4.98
Therefore, Using the trigonometric ratios the correct option is option a) 4.98.
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A photographer prints an 8x10 team photo. The team would like to get it blown up by 200% in order to display it in the trophy case. What will be the new dimensions of the photo?
Answer:
16x20
Step-by-step explanation:
I think, 200% likely means x2. Just an idea, try it if you'd like!
Suppose linda's mom invests $10,000, part at 3% and the rest at 2.5%, in interest bearing accounts. the total yearly income (interest) is $283. how much did lindsay's mom invest at each rate?
She reportedly invested $6600 at 3% and $3400 at 2.5%, according to the statement.
Why do individuals invest?Investing is a smart way to put your money to work and could make you richer. If you make smart investing choices, your money may increase in value as outpace inflation. The major factors contributing to investment's increased growth potential are the possibility of compounding and the trade-off amongst risk and return.
Simple interest is calculated as follows: deposit amount multiplied by time and interest rate.
Let "a" represent the money placed in the account earning 3% interest.
Let's use the symbol to represent the amount deposited into the account earning 2.5% interest (10,000 - a)
a * 0.03 plus (10,000 - a) * 0.025 = 283
0.03a + 250 - 0,025a = 283
Collect like terms
0.03a - 0.025a = 283 - 250
0.005a = 33
a = $ 6600
What was put into the 2.5% account = 1000 - 6600 = $ 3400
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Helllllp please thank you
Step-by-step explanation:
A no
n + 7 = 16
n + 7 - 7 = 16 - 7
n = 9
that is not n = 15
B yes
(2/3)v = 8
3×(2/3)v = 3×8
2v = 24
2v/2 = 24/2
v = 12
C no
6z = 84
6z/6 = 84/6
z = 14
that is not z = 8
3x − (2x² +1 − 8x) − (3x − 2x² + 7)
Answer: The answer is 5x
Answer: x=1
Step-by-step explanation:
=3x-[tex]2x^{2}[/tex]-1+8x-3x+[tex]2x^{2}[/tex]-7
= -1+8x-7
= -8=-8x
X=1
Cuál es la raíz cuadrada de 169
El número natural 169 tiene como raíz cuadrada igual a 13.
¿Cómo encontrar la raíz cuadrada de un número entero?Los números naturales comprenden a un conjunto discreto conformado por los números {1, 2, 3, 4, 5, ..., n, ...}, n ∈ N, donde N es el conjunto de los números naturales.
Los números naturales pueden ser números primos o números compuestos, los números compuestos pueden ser definidos como un producto de números primos. El número natural 169 es equivalente al siguiente producto de números primos:
169 = 13 × 13 = 13²
En consecuecia, la raíz cuadrada del número natural 169 es la siguiente: (nótese que la potencia al cuadrado es el opuesto a la raíz cuadrada)
x = √169
x = √(13²)
x = (13²)^(1 / 2)
x = 13
La raíz cuadrada del número natural 169 es igual a 13.
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What is the measure of angle x?
Answer:
46
Step-by-step explanation:
The type of angle below is called an alternate angle where the opposite angle is the equal size.
As the angle given is 46 the alternating angle would be 46!
Have a lovely day :)
Answer:
46 because 46 is alternative angle
22/3 times x = 1.6 divided by 6/11
PLS HELP
[tex]\cfrac{22}{3}x=\cfrac{1.6}{~~ \frac{6 }{11 } ~~}\implies \cfrac{22x}{3}=\cfrac{\frac{16}{10}}{~~ \frac{6 }{11 } ~~}\implies \cfrac{22x}{3}=\cfrac{16}{10}\cdot \cfrac{11}{6}\implies \cfrac{22x}{3}=\cfrac{8}{5}\cdot \cfrac{11}{6}[/tex]
[tex]\cfrac{22x}{3}=\cfrac{8}{6}\cdot \cfrac{11}{5}\implies \cfrac{22x}{3}=\cfrac{4}{3}\cdot \cfrac{11}{5}\implies \cfrac{22x}{3}=\cfrac{44}{15} \\\\\\ \stackrel{\textit{multiplying boths sides by }\stackrel{LCD}{15}}{15\left( \cfrac{22x}{3} \right)=15\left( \cfrac{44}{15} \right)}\implies 110x=44\implies x=\cfrac{44}{110}\implies \boxed{x=\cfrac{2}{5}}[/tex]
5x+6=7x-6
Please help
Answer:
x = 6
Step-by-step explanation:
5x+6=7x-6
-6 -6
--------------------
5x = 7x - 12
-7x -7x
--------------------
-2x = -12
------------
-2 -2
--------------------
x = 6
Answer:
6
Step-by-step explanation:
first we combine like terms
6+6=7x-5x
then we simplify
12=2x
lastly we divide both sides by 2
2x ÷2=12÷2
an we simplify again
x=6
then the value of x is 6
check
5(6)+6=7(6)-6
30+6=42-6
36=36
6 × x × у im a bit stuck help xx
Answer:
6x^2y
Solution
6x2 y
Step-by-step explanation:
hopefully this helped.bye:)
PLEASE HELP!!!!!! NEED ONLY RIGHT ANSWER!!!!!
Answer: because the mean is 48
Step-by-step explanation:
the average (mean) is 48 so therefore its reasonable that half scored under half scored higher
The table shows the rate at which water is being pumped into a swimming pool
The unit rate of the relationship between the amount of water pumped and time is the amount of water pumped in one minute for 14 hours.
How is the unit price calculated?To calculate unit price, you need to divide the first term (quantity) by the second term (unit). The resulting value is the unit price.
For example, if you want to calculate the unit price for a bag of 4 $3 apples, divide the total cost ($3) by the number of apples (4).
$3 / 4 apples = $0.75 / apple
In this example, the unit price is $0.75 per apple. So the price per apple is $0.75.
Given by the equation:
The unit rate of water pumped versus time is the amount of water pumped in one minute, so:
28/2=14
That means 14 gallons of water is being pumped every minute.
Now you can calculate the water pumped in 3/2 minutes like this
14*3/2=21
So in total, water pumped in 12 minutes plus 3/2 minutes gives water pumped in 15/2 minutes.
14*15/2=105
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restaurants often slip takeout menus under zach's apartment door. so far, zach has collected 18 menus, including 4 for japanese food. what is the probability that one of zach's takeout menus, selected at random, will be from a japanese restaurant? write your answer as a fraction or whole number. p(japanese) =
So, the probability of selecting a menu from a Japanese restaurant is 4/18, which can also be simplified as 2/9.
The probability of selecting a Japanese restaurant menu from Zach's collection of 18 menus is found by taking the number of Japanese restaurant menus (4) and dividing it by the total number of menus in the collection (18). This can be written mathematically as:
p(japanese) = 4/18
So the probability of selecting a menu from a Japanese restaurant is 4/18, which can also be simplified as 2/9.
In other words, if Zach selects a menu at random from his collection, there is a 2/9 chance that it will be from a Japanese restaurant.
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How do I solve this?
The evaluation of the piecewise function gives:
when x = -3, f(x) = -4; when x = 2, f(x) = 0; and when x = 4, f(x) = 2.
when x = -3, w(x) = 2; when x = 2, f(x) = 5; and when x = 4, f(x) = 5
How to evaluate a piecewise function?A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.
We want to evaluate the piecewise function when x = -3, x =2 and x = 4:
{ -4, x < 2
f(x) = { x-2, -2 ≤ x≤ 4
{0 x > 4
when x = -3:
f(x) = -4 because x < 2 (i.e. -3 < 2)
when x = 2:
f(x) = x-2
f(2) = 2-2 = 0
when x = 4:
f(x) = x-2
f(2) = 4-2 = 2
{ -x - 1, x ≤ -3
w(x) = { 2x + 2, -3 < x < 2
{5, x ≥ 2
when x = -3:
w(x) = -x - 1
w(-3) = -(-3) - 1 = 2
when x = 2:
f(x) = 5
when x = 4:
f(x) = 5
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a gym class has $12$ students, $6$ girls and $6$ boys. the teacher has $4$ jerseys in each of $3$ colors to mark $3$ teams for a soccer tournament. if the teacher wants at least one girl and at least one boy on each team, how many ways can he give out the jerseys? (jerseys of the same color are indistinguishable.)
So, the teacher can give out the jerseys in 840 ways.
The teacher wants to divide the 12 students into 3 teams, each with at least one girl and one boy.
One possible way to count the number of ways to divide the students is to use the stars and bars method.
For the first team, we have 5 stars and 2 bars, so the number of ways to pick 6 students is:
(5+2)!/(5!2!) = 7
For the second team, we have 4 stars and 1 bar, so the number of ways to pick 6 students is:
(4+1)!/(4!1!) = 5
For the third team, we have 3 stars, so the number of ways to pick 6 students is:
(3+0)!/(3!0!) = 4
Then we can multiply the number of ways to pick students for each team together to find the total number of ways to divide the students:
7 * 5 * 4 = 140
Then, as the jerseys are indistinguishable, we just have to multiply the number of ways to divide the students by the number of ways to distribute jerseys:
140 * 3! = 840
Therefore, the teacher can give out the jerseys in 840 ways.
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Write down the equations corresponding to the augmented matrix in Exercise 12 and verify your answer to Exercise 12 is correct by substituting the solutions you obtained back into the original equations.
Both equations are satisfied, so the solutions to the equations are correct.
What is matrix?Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.
The augmented matrix in Exercise 12 is:
\begin{bmatrix}
1 & 4 & 5 & -10 \\
2 & 8 & 6 & -20
\end{bmatrix}
The corresponding equations are:
1x + 4y = -10
2x + 8y = -20
To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:
1(5) + 4(-2) = -10
2(5) + 8(-2) = -20
Both equations are satisfied, so the solutions to the equations are correct.
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Both equations are satisfied, so the solutions to the equations are correct. This can be solved using the concept of matrix.
What is matrix?Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.
The augmented matrix in Exercise 12 is:
[tex]\left[\begin{array}{cccc}1&4&5&-10\\2&8&6&-20\end{array}\right][/tex]
The corresponding equations are:
1x + 4y = -10
2x + 8y = -20
To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:
1(5) + 4(-2) = -10
2(5) + 8(-2) = -20
Both equations are satisfied, so the solutions to the equations are correct.
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How do I find the area of this hexagon
The area of this hexagon is 374.4 in².
What is the area of the hexagon?
The area of the hexagon is calculated by applying the following formula.
total area of the regular hexagon = 6 x area of one face
Area of one face = ¹/₂bh
where;
b is the base of the triangleh is the height of the triangleArea of one face = ¹/₂ x ( 12 in ) x ( 10.4 in )
Area of one face = 62.4 in²
Total area of the hexagon = ( 6 ) x ( 62.4 in² ) = 374.4 in²
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Ice-Cream Palace has received an order for 3 1⁄2 gallons of ice-cream. The shop packages its ice-cream in 1-quart containers. How many containers will the shop need for this order?
Answer:
There are 4 quarts in a gallon, so 3 1/2 gallons is equal to 3.5 x 4 = 14 quarts.
Since the shop packages its ice-cream in 1-quart containers, the shop will need 14 containers to fulfill the order.
Step-by-step explanation:
ASSUME THAT 13% OF PEOPLE ARE LEFTHANDED, IF WE RANDOMLY SELECT 12 PEOPLE FROM THIS POPULATION, WHAT IS THE PROBABILITY THAT THEY ARE NOT ALL RIGHT HANDED
It is simpler to compute the likelihood of the complement event when calculating probabilities since you can then just subtract it from 1 to determine the probability.
What do probability and example mean?the variety of strategies for success. all events that could possibly occur.
Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.
P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).
where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.
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P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. It is simpler to compute the likelihood of the complement event when calculating probabilities.
What do probability and example mean?the variety of strategies for success. all events that could possibly occur.
Since 13% of people are lefties and 87% are righties, we'll assume that everyone is either a righty or a lefty, thus the decimal percentage of 0.87 divided by the total number of participants, 12, is the mean.
P(Right handed) = 1 - 0.13 = 0.87 where P(Left handed) = 0.13 and P(Right handed) = 0.13 12 people make up the nth number. The binomial probability distribution will be used in this case, and it can be computed using the formula P(X = n|N,p) = NCn*(pn)*(1-p) (N-n).
where p is the chance of success and n is the sample size, or 12, in this case. Additionally, q represents the 0.13 failure chance.
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√2x+5=5 then the value of x
Answer:
x = 0Step-by-step explanation:
√2x + 5 = 5
-5 - 5
√2x = 0
√2x^2=0^2
2x=0
2x/2 = 0/2
x = 0[tex]\huge\red{ANSWER}[/tex]
[tex]\sf \sqrt{2} x+5=5[/tex]
[tex]\sf \sqrt{2} x=5-5[/tex]
[tex]\sf \sqrt{2} x = 0[/tex]
[tex]\sf \frac{\sqrt{2} x }{2}=0[/tex]
[tex]\sf x=0[/tex]
________......
[tex]\pmb{ \orange{LearningLifeII}}[/tex]
List five vectors in Span {v1,v2}. Do not make a sketch.v1=6 4 −8v2=−6 2 0
The five vectors in span {v1,v2} are we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together.
1. v3 = (3v1 + 2v2) = (18 8 −16)
2. v4 = (2v1 + 3v2) = (−12 6 0)
3. v5 = (4v1 + v2) = (0 6 −32)
4. v6 = (−2v1 + 5v2) = (36 10 0)
5. v7 = (−v1 + 4v2) = (−36 8 0)
To calculate the vectors, we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together. For example, for v3 we multiplied v1 by 3 and v2 by 2 and then added the components together to get the vector (18 8 −16). We performed similar calculations for the other vectors.
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