The number of the system equations are: 8 and 27.
System of Equations
A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
First, you should convert the text of the question in the math expression. Then,
x+y= 35 (1)
x+4y=116 (2)
After that, you should multiply equation(2) by -1. Thus,
x+y= 35 (1)
-x-4y= - 116 (2)
Now, when you sum equations 1 and 2, you eliminate x . Thus, from this sum, you will have:
-3y=-81
3y=81
y=81/3
y=27
From equation (1), you can find x.
x+y=35
x+27=35
x=35-27
x=8
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What is the area of this composition shape enter your answer in the box 7 inches and 3 inches in 5 inches in 12 inches blank inches square
The area of the composite shape that is given in the image below = 40 in.².
How to Find the Area of a Composite Shape?In the diagram given below, the shape can be decomposed into a triangle and a rectangle, since it is composed of both shapes.
Thus:
The area of the composite shape = area of rectangle + area of triangle.
Area of the triangle = 1/2(b)(h)
base = 12 - 7 = 5 in.
height = 5 - 3 = 2 in.
Area of the given triangle = 1/2(5)(2)
Area = 5 in.²
Area of the given rectangle = (l)(w)
length = 7 in.
width = 5 in.
Area of the given rectangle = (7)(5) = 35 in.²
The area of the composite shape given = 35 + 5 = 40 in.².
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Maria bought 5 tickets for $20 each. Each ticket had a $2 fee. Write an expression that shows how much Maria paid for the tickets. plssss help will give 10 points :)
The expression to illustrate the information when Maria bought the tickets is C = (5 × $20) + ($2 × 5) and the total amount paid is $110.
How to illustrate the information?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. A mathematical expression shows the value of something by combining numbers, variables, and operators. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.
From the information, Maria bought 5 tickets for $20 each. Each ticket had a $2 fee.
The expression that can be used to illustrate this will be:
C = (5 × $20) + ($2 × 5)
where C = Total cost
C = $100 + $10
C = $110
Therefore the expression to illustrate the information when Maria bought the tickets is C = (5 × $20) + ($2 × 5) and the total amount paid is $110.
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Question 6 of 25
The table below shows the cost of sending packages of various weights.
What is the cost of mailing a 6-ounce package?
Weight
(ounces)
1
2
3
4
50
6
7
Cost
(dollars)
.32
.64
.96
1.28
1.60
1.92
2.24
Answer here
dollars
PLEASE HELP FAST
Answer:
$1.92
Step-by-step explanation:
The corresponding row to 6 ounces is this
A machine costing $214,200 with a four-year life and an estimated $19,000 salvage value is installed in Luther Company’s factory on January 1. The factory manager estimates the machine will produce 488,000 units of product during its life. It actually produces the following units: 123,200 in Year 1, 123,600 in Year 2, 120,900 in Year 3, 130,300 in Year 4. The total number of units produced by the end of Year 4 exceeds the original estimate—this difference was not predicted. (The machine cannot be depreciated below its estimated salvage value.)
The appropriate journal entries for year 4 depreciation is:
Dr. depreciation $52,210
Cr. Accumulated depreciation $52,210
What is depreciation?
Depreciation is the gradual systematic allocation of the cost of asset over its useful years, the fact that the machine in this case would be used for 4 years means that its initial cost needs to be allocated over the 4 years.
Depreciation(straight-line method)=(cost-salvage value)/useful life
Depreciation(straight-line method)=( $214,200-$19,000)/4=$48,800 per year
Depreciation rate per unit=($214,200-$19,000)/488000
Depreciation rate per unit=$0.40
Depreciation in year 4=130,300*$0.40
Depreciation in year 4=$52,210
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Additional information provided by the student in the comment section:
How do I record the 4th year?
make rates equivalent.
16 points scored in 4 games.
48 points scored in 8 games.
The rates aren't equivalent based on the information given regarding the games.
How to illustrate the information?It should be noted that 16 points were scored in 4 games. Therefore, the points per game will be:
= 16 / 4
= 4 points.
Also, 48 points scored in 8 games. Therefore, the points per game will be:
= 48 / 8
= 6 points.
Therefore, the rates aren't equivalent.
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16 points scored in 4 games.
48 points scored in 8 games.
Are the rates equivalent?
Which equations have the same solution as the equation 4y - 3 = -2y + 1?
Choose all that apply.
A. 2y-3=1
B. 4y = -2y + 4
C. -3=-6y +1
D8y-3=-4y + 1
E. 8y-6=-4y+2
Answer:
B and C
Step-by-step explanation:
B = 4y - 3 + 3 = -2y + 1 + 3
= 4y = -2y + 4
C = 4y - 3 -4y = -2y + 1 -4y
= 3 = -6y +1
The average ocean depth is 3.7*10^(3)m, and the area of the oceans is 3.6*10^(14)m^(2). What is the total volume of the ocean in liters? (One cubic meter contains 1000 liters.)
The total volume of the ocean in litres is [tex]1.332\times10^{21}[/tex] litres.
Given that, the depth of an ocean =[tex]3.7\times 10^{3}[/tex] m and the area of the ocean = [tex]3.6\times10^{14}[/tex] m².
We need to find the total volume of the ocean in litres.
What is volume?Volume is defined as a capacity occupied by a three-dimensional solid shape. Any shape is hard to visualize but can be compared between shapes. The volume of any object is the product of the area of a base and the height of the object.
Now, the volume of the ocean=[tex]3.6\times10^{14}[/tex]×[tex]3.7\times 10^{3}[/tex]
=[tex]13.32\times10^{17}[/tex] m³
=[tex]13.32\times10^{17}\times1000[/tex]
=[tex]1.332\times10^{21}[/tex] litres
Therefore, the total volume of the ocean in litres is [tex]1.332\times10^{21}[/tex] litres.
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When Rahul moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 32 inches tall and Tree B was 20 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the number of years after the trees were planted when both trees have an equal height.
A= B=
Answer:
The equation to represent the growth of the trees is given by
AA=32+6t and BB=20+9t and both the trees will be of equal height after 3 years.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Equation is defined as the quality of being equal and is frequently represented by a mathematical statement with equal values on either side or by a problem requiring consideration of a number of factors.
Given that tree A is 32 inches tall and tree B is 20 inches tall.
Tree A grows 6 inches per year.
Length of the tree A after t years = 32 + 6t
Tree B grows 9 inches per year
Length of the tree B after t years = 20 + 9t
Now let us consider that both trees grows equal after a certain period of time.
If we equate both the expressions then we can form an equation to calculate the value of t.
∴ 32+6t = 20+9t
or, 6t - 9t = 20 - 32
or, -3t = -12
or, t = 4 years
The trees will be of equal length after 4 years.
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For distinct complex numbers [tex] \rm z_1,z_2, \cdots, z_{673},[/tex] the polynomial
[tex] \rm(x - z_1 {)}^3(x - z_2 {)}^3 \dots(x - z_{673} {)}^3[/tex]
can be expressed as
[tex] \rm {x}^{2019} + 20 {x}^{2018} + {19}x^{2017} + g(x),[/tex]
where g(x) is a polynomial with complex coefficients and with degree at most 2016.
[tex] \rm The \: value \: of \left | \sum \limits_{1 \leq j < k \leq673 }z_{j} z_k\right| [/tex]
can be expressed in the form m/n, where m and n are relatively prime positive integers. Find m+n.
Let
[tex]S = \displaystyle \sum_{1\le j<k\le673} z_jz_k[/tex]
and
[tex]p_{\mu,\nu}(x) = (x-z_1)^\mu (x-z_2)^\mu \cdots (x-z_\nu)^\mu[/tex]
The [tex]z_jz_k[/tex] terms occur in the coefficient of the [tex]x^{\mu\nu-2}[/tex] term, given by
[tex]\displaystyle \left[x^{\mu\nu-2}\right] p_{\mu,\nu} = \binom\mu2 \sum_{r=j}^\nu z_j^2 + \mu^2 \sum_{1 \le j < k \le \nu} z_jz_k[/tex]
(essentially due to Vieta's formulas)
With [tex]\mu=3[/tex] and [tex]\nu=673[/tex], we have
[tex]\displaystyle \left[x^{2017}\right] p_{3,673} = \binom32 \sum_{j=1}^{673} z_j^2 + 3^2 S \\\\ ~~~~ \implies S = \frac{19}9 - \frac13 \sum_{j=1}^{673} z_j^2 \\\\ ~~~~ \implies S = \frac{19}9 - \frac13 \left(\left(\sum_{j=1}^{673} z_j\right)^2 - 2 S\right) \\\\ ~~~~ \implies S = \frac{19}3 - \left(\sum_{j=1}^{673} z_j\right)^2[/tex]
The remaining sum on the right is the sum of the roots of [tex]\sqrt[3]{p_{3,673}(x)} = p_{1,673}(x)[/tex].
Recall that the sum of the roots of a polynomial
[tex]P_n(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_0[/tex]
is [tex]-\frac{a_{n-1}}{a_n}[/tex]. Then the sum of the roots of [tex]p_{3,673}(x)[/tex] is -20, which is 3 times the sum of the roots (counting multiplicity) of [tex]p_{1,673}[/tex], so
[tex]\displaystyle \sum_{j=1}^{673} z_j = -\dfrac{20}3 \\\\ ~~~~ \implies S = \frac{19}3 - \left(-\frac{20}3\right)^2 = -\frac{343}9 \\\\ ~~~~ \implies |S| = \frac{343}9, m=343, n=9 \implies m+n = \boxed{352}[/tex]
Seven subtracted from seven times a number is 147. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is
B) Solve your equation in part [A] for
The translation of the statement is 7x - 7 = 147 and the numerical value of x is 22.
What is the numerical value of x?Given the statement in the question?
"Seven subtracted from seven times a number is 147"
Translate the statement into an equation;
Let x represent the unknown number.
Seven times a number ⇒ 7 × x = 7xSeven subtracted from ⇒ -7Is 147 ⇒ = 147Now, combine
7x - 7 = 147
Therefore the translation of the statement is 7x - 7 = 147.
Next, we solve for x
7x - 7 = 147
Add 7 to both sides
7x - 7 + 7 = 147 + 7
7x = 154
x = 154/7
x = 22
Therefore, the translation of the statement is 7x - 7 = 147 and the numerical value of x is 22.
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At the lakeside aquarium there are 7 freshwater fish on display for every 5 salt water fish
Based on the number of freshwater fish per s-a-l-t-water fish, the ratio for s-a-l-t-water fish to freshwater fish is 5 : 7.
What is the ratio?The ratio between the s-a-l-t-water fish and the freshwater fish putting both figures against each other as a ratio.
The ratio would be:
Number of s-a-l-t-water fish : Number of freshwater fish
Putting in the quantities gives:
5 s-a-l-t-water fish fish : 7 freshwater fish
5 : 7
In conclusion, the ratio is 5 : 7.
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The perimeter of the parallelogram below is 32.2. What equation would you set up to solve for x? What is the value of x?
The value of x from the given figure is 8/3
Perimeter of a parallelogramThe sum of all the ides of the parallelogram is perimeter. According to the given figure;
2(3x-8)+2(16) = 32.2
Expand to have:
6x-16 + 32 = 32.2
6x + 16 = 32.2
Subtract 16 from both sides
6x = 16
x = 16/6
x = 8/3
Hence the value of x from the given figure is 8/3
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Answer:
Step-by-step explanation:
The circumference of a circle is 9.36cm.
Find the length of the diameter.
Give your answer rounded to 2 DP.
Answer:
The circumference of a circle with diameter 9.36 is 29.41
Step-by-step explanation:
the circumference of a circle is
2×pi×r
with r being the radius and therefore, 2×r being the diameter.
2×pi×r = 9.36 cm
2r = diameter = 9.36/pi = 2.979380535... ≈ 2.98 cm
Someone HELP ME PKS PLS PLS PLS S I BEG U PLS JUST HELP ME
Answer:
How about this: A bag of 8 oranges is $6.50 and you want to know the price per orange? Or how about this: You have a soda vending machine and each soda is $2.00. A case of soda (24 cans) costs you $15.00. You need to know how much the case costs per can to see if you will make a profit.
Step-by-step explanation:
A unit rate is a type of ratio that compares one unit of some quantity to a different number of units of a quantity.
What is 31 lb to g (Convert from on to kg, then kg to g).
Answer:
The answer would be 14061.364 grams.
Which of the following explains the relationship between angles C and D?
Lines JK and JM intersect at point J creating four angles identified as angle B, angle D, angle C, and angle A clockwise from the top right.
Adjacent angles
Corresponding angles
Complementary angles
Vertical angles
The term that explains the relationship between angles C and D is: A. Adjacent angles.
What are Adjacent Angles?When two angles share a common vertex and a common side, the two angles are referred to as adjacent angles.
In the diagram given, lines JK and JM intersect at point J to form 4 angles of which angles C and D share a common side and a common vertex (point J).
Therefore, the term that explains the relationship between angles C and D is: A. Adjacent angles.
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Answer:
A
i took the test and got it right
PLEASE HELP! DUE IN LESS THAN 2 HOURS! IM STUCK! I THINK THEY ARE ALL TRUE! WHAT ONE IS FALSE AND WHY! PLEASE HELP ME! YOU WILL GET 50 POINTS! THANKS QUESTION DOWN BELOW!!!
=====================================================
Reason:
Let's go through the four answer choices to see which are true and which are false. We'll rule out the ones that are true.
A) This is true. We can use inductive reasoning to form a conjecture. A conjecture is basically a generalized guess. For example, a guess would be something like "the sum of the first n odd numbers is n^2". So 1+3 = 4, 1+3+5 = 9, 1+3+5+7 = 16, 1+3+5+7+9 = 25, and so on. Does the pattern go on forever? Or does it stop at some point? That's why a proof is needed.B) This is true. See choice A.C) This is true. Some conjectures have been proven (such as the example I mentioned in choice A) while others have not. A famous unproven conjecture is Goldbach's Conjecture. D) This is false. Inductive reasoning helps form a conjecture, but it does not lead to definitive proof. We would need deductive reasoning.Parts of algebraic expressi
Consider the expression x² + x + 7.
- 22
Complete 2 descriptions of the parts of the expression.
1. The entire expression is a sum with
2. The coefficients are
The terms in the expression x² + x + 7 + 22 are x², x, 7 and 22.
What is an expression?
The value of anything is represented by a group of numbers, symbols, and operators called an expression.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. In a mathematical expression, this proposition is denoted by the equation x/2 + 6.
The terms in the given expression are x², x, 7 and 22.
The coefficient of x² is 1 and coefficient of x is also 1.
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An item is regularly priced at $55. It is on sale for 45% off the regular price.
An item is $55 before sale, and bought for 45 percent off the regular price. therefore the sale price of item is $30.25.
What is Markup and Markdown?Markup is the amount that will be increased in the original price of the considered thing.
Markdown is the amount that will be decreased from the original price of the considered thing.
Think of "up" and "down" as increasing and decreasing prices respectively.
Given that item is $55 before sale, and bought for 45 percent off the regular price.
WE have to do that as; 45% off $55 implies subtract 45% from $55
= 45/100 × 55 = $24.75
therefore the item bought at $55 - $24.75= $30.25.
Hence, the sale price of item is $30.25.
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The complete question is
An item is regularly priced at $55. It is on sale for 45% off the regular price. What is the sale price?
⦁ Sally and Mary are best friends. Their families both went to the beach on June 1st to celebrate the start of summer vacation. After that day Sally’s family continues to go to the beach every 4 days. Mary’s family only goes to the beach every 14 days.
⦁
⦁ Would you use Greatest Common Factor or Least Common Multiple to help solve this problem?
Based on the fact that Mary's family goes every 14 days and Sally's family goes every 4 days, the method of solving this problem is the Least Common Multiple.
When to use Least Common Multiple?The Least Common Multiple is used to find out when two or more events will occur at the same time if those events occur at fixed intervals that are different from each other.
Sally's family goes to the beach every 4 days and Mary's family goes every 14 days.
You can therefore solve for the day that they will next meet on the beach using their Least Common Multiple which is 28. They will next be at the beach on the same day after 28 days.
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The last of my points. Given the unit circle, what is the value of y? This my last question.
Answer:
y = - [tex]\frac{\sqrt{111} }{20}[/tex]
Step-by-step explanation:
using Pythagoras' identity in the right triangle formed by the radius 1 and the given point, then
y² + (- [tex]\frac{17}{20}[/tex] )² = 1²
y² + [tex]\frac{289}{400}[/tex] = 1
y² = 1 - [tex]\frac{289}{400}[/tex] = [tex]\frac{111}{400}[/tex] ( take square root of both sides )
y = ± [tex]\sqrt{\frac{111}{400} }[/tex] = ± [tex]\frac{\sqrt{111} }{20}[/tex]
since the point is in the third quadrant then y < 0
y = - [tex]\frac{\sqrt{111} }{20}[/tex]
Sandy collected 10 pounds of apples at an apple orchard. She is determined to
eat 20% of the apples remaining every day after the day she went to the orchard.
Write an exponential function to model this scenario and use it to estimate how
many pounds of apples she has left after 1 week.
The weight of apple that Sandy has left after one week is 2.1 pounds.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the number of apple remaining after x days. Sandy collected 10 pounds of apples at an apple orchard and eat 20% daily, hence:
y = 10(1 - 0.2)ˣ
y = 10(0.8)ˣ
After 1 week, x = 7:
y = 10(0.8)⁷ = 2.1 pounds
The weight of apple that Sandy has left after one week is 2.1 pounds.
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A number is multiplied by 20, and that product is added to 10. The sum is equal to the product of 5 and 10. Find the number
Determine d in the equation.
12.6 = −1.8 − 4d
A. d = 2.7
B. d = −2.7
C. d = 3.6
D. d = −3.6
Answer:
D. d= -3.6
Step-by-step explanation:
12.6= -1.8 -4d
Add the negative 1.8 to the left side and then divide by -4
If the price of a business math text rose to $220 and this was 7% more than the original price, what was the original selling price? (Round to the nearest cent.)
Answer:
235.4
Step-by-step explanation:
7% more than 220 would be 235.4
First you would turn 7% as a decimal which would be .07. Then, you would multiply .07 times 220 which would give you 15.4. Lastly, you would add 15.4 plus 220 which would equal 235.4.
7%=.07
.07×220=15.4
15.4+220=235.4
In baseball, a commonly used rate is earned run average (ERA). ERA is a rate of earned runs to a constant number n of innings. In 2020, the pitcher in Example 2 had an ERA of 2.70. Find the value of n.
The value of n which is a constant representing number of innings is equal to 50.
What is ERA or earned run average ?
Earned runs without the help of passed ball, are represented by the earned run average, which is the number of earned runs a pitcher allows per nine innings.
It is given that In 2020, the pitcher had an ERA of 2.70.
A rate of earned runs to a fixed number of innings, n, which is also known as ERA.
Let's check it.
To determine a pitcher's earned run average or (ERA), multiply the runs by nine, then divide it by the number of innings pitched.
The runs earned in 2020 is 15 , let's multiply it by 9.
So , we get 15 × 9 = 135.
Now , divide it by number of innings which is 50.
So , the value of ERA will be equal to : 135 ÷ 50 = 27 which is also given in the question.
Now we will calculate the value of n.
So ,
n = (9 × Earned runs) / ERA
or
n = ( 9 × 15 ) / 2.7
n = 135 / 2.7
n = 50 innings
Therefore , value of n which is a constant representing number of innings is 50.
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K
Assume that adults have IQ scores that are normally distributed with a mear
top 75%. (Hint: Draw a graph.)
The first quartile is
(Type an integer or decimal rounded to one decimal place as needed.)
am from India . Hi .
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What are the specs of your pc
The function f is graphed below.
determine the intervals on which f is increasing and decreasing
The function is decreasing on the interval [-5 < x < -1] (segment 1),
The function is increasing on the interval [-1 < x < 4] (segment 2),
The function is decreasing on the interval [4 < x < 9] (segment 3).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
As per the given graph,
The function is decreasing from the interval from -5 to -1 in its domain
The function is increasing from the interval from -1 to 4 in its domain
The function is decreasing from the interval from 4 to 9 in its domain
Therefore, the function is decreasing on the interval [-5 < x < -1] (segment 1), increasing on the interval [-1 < x < 4] (segment 2), and decreasing on the interval [4 < x < 9] (segment 3).
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In a survey on internet usage , it was found that out of a total of 27 people, 16 use ADSL lines, 15 use wireless internet and 3 use neither of the two . what is the probability that a person chosen at random uses both internet connections
The probability that a person chosen at random uses both internet connections is 1/9
Total number of people = 27
Number of people who use ADSL lines = 16
Number of people who use wireless internet = 15
Number of people who use neither of the two = 3
Let the number of people who use only ADSL lines and wireless internet be denoted by A and B respectively.
Then A + B + A∩B + 3 must be equal to 27
A + B + A∩B = 24
further, we can see that
(A + A∩B) = 16
B + 16 = 24
B = 8
Also, (B + A∩B) = 15
8+ A∩B = 15
A∩B = 7
Thus, the number of people who use both internet connections = 7
Now, P(A∩B) = 7/27
= 1/9
Hence, probability that a person chosen at random uses both internet connections is 1/9.
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convert 3/7 to percent
The percentage is 42.8571%.
what is percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given fraction:
3/7
To convert the fraction into percentage we have multiply 100
3/7*100
=300/7
= 42.8571%
Hence, the percentage of fraction 3/7 is 42.8571%.
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