Answer:
Step-by-step explanation:
13x+2y=1
+ 5x-2y=-19
-------------------
18x=18
x=1
5x1-2y=-19
5-2y=-19
-2y=-19-5
-2y=14
-y=7
y=-7
x=1
y=-7
To solve the system, eliminate variables, find [tex]\( x = -1 \)[/tex], then substitute into an equation to get [tex]\( y = 7 \)[/tex].
To solve the system of equations [tex]\(13x + 2y = 1\)[/tex] and [tex]\(5x - 2y = -19\)[/tex], you can use the method of elimination.
First, let's eliminate one of the variables. We can eliminate [tex]\(y\)[/tex] by adding the two equations together:
[tex]\[ (13x + 2y) + (5x - 2y) = 1 + (-19) \][/tex]
This simplifies to:
[tex]\[ 13x + 5x = -18 \][/tex]
[tex]\[ 18x = -18 \][/tex]
Now, divide both sides by 18:
[tex]\[ x = \frac{-18}{18} \][/tex]
[tex]\[ x = -1 \][/tex]
Now that we have found [tex]\(x\)[/tex], we can substitute it into one of the original equations to find [tex]\(y\)[/tex]. Let's use the first equation:
[tex]\[ 13(-1) + 2y = 1 \][/tex]
[tex]\[ -13 + 2y = 1 \][/tex]
Add 13 to both sides:
[tex]\[ 2y = 1 + 13 \][/tex]
[tex]\[ 2y = 14 \][/tex]
Divide both sides by 2:
[tex]\[ y = \frac{14}{2} \][/tex]
[tex]\[ y = 7 \][/tex]
So, the solution to the system of equations is [tex]\(x = -1\)[/tex] and [tex]\(y = 7\)[/tex].
which expression is equivalent to 45+27
a.) 9(5x3)
b.) 9(5+3)
c.) (9x5)x(9x3)
d.) (9+5)x(9+3)
Answer:
B)
Step-by-step explanation:
1. During a field trip, 60 students are put into equal-sized groups.
- Describe two ways to interpret 60:5 in this context.
- Find the quotient.
- Explain what the quotient would mean in each of the two interpretations you
described.
Help me plzz
The ratio 60:5 can be described as follows :
60 students are divided into equal groups of 5 student each. Groups of 5 students per group totaled up to 60 students. The quotient in both expression is 60:5 = 12 students per group .The ratio expression is a way of expressing the division of numerator by a denominator.
Here,
The total number of students is the numerator = 60
The denominator is the number of students per group = 5
Hence, the quotient is the value of the divison obtained which is (60/2) = 12
Therefore, there are 12 groups of 5 students.
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Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
Answer:
[tex]2x-3y=19[/tex]
Step-by-step explanation:
we have the ordered pairs
(8, –1) and (2, –5)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values in the formula
[tex]m=\frac{-5+1}{2-8}[/tex]
[tex]m=\frac{-4}{-6}[/tex]
simplify
[tex]m=\frac{2}{3}[/tex]
The equation of the line in point slope form is
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{3}[/tex]
[tex]point\ (8,-1)[/tex]
substitute
[tex]y+1=\frac{2}{3}(x-8)[/tex]
Convert to standard form
The equation of the line in standard form is equal
[tex]Ax+By=C[/tex]
where
A is a positive integer
B and C are integers
we have
[tex]y+1=\frac{2}{3}(x-8)[/tex]
Multiply by 3 both sides to remove the fraction
[tex]3y+3=2(x-8)[/tex]
apply distributive property right side
[tex]3y+3=2x-16[/tex]
Group the variables in one side and the constants in the other side
[tex]2x-3y=3+16[/tex]
[tex]2x-3y=19[/tex] ---> equation in standard form
Answer:
The answer is 2x + -3y = 19
Step-by-step explanation:
..
The answer I can’t do it I don’t understand it
Answer: -23 feet to sea level
Step-by-step explanation:
start with 0 (sea level)
he dives twenty, -20
he dives ten more, -20 - 10 = -30
he swims up twelve feet; -18
he goes down 5 more; -23 feet
Answer:
20 + 10 = 30
30 - 12 = 18
18 + 5 = 23
His elevation is 23ft below the sea level
tim and his brother are building towers out of blocks. Tim is using blue blocks that are 6 cm tall and his brother is using green blocks that are 8 cm tall. They both made towers the same height. What is the shortest possible height of the tower? how many of each color block did they use
The shortest possible height of tower is 24 cm.
Tim used 4 blue blocks and his brother used 3 green blocks.
Step-by-step explanation:
Given,
Height of blue block = 6 cm
Height of green block = 8 cm
We will take least common multiple to find the shortest possible height.
6 = 2*3
8 = 2*2*2
LCM = 2*2*2*3 = 24 cm
The shortest possible height of tower is 24 cm.
Number of blue blocks used = [tex]\frac{24}{6} = 4[/tex]
Number of green blocks used = [tex]\frac{24}{8} = 3[/tex]
Tim used 4 blue blocks and his brother used 3 green blocks.
Keywords: LCM, multiplication
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Use the work shown to find the solutions of the quadratic equation. x2 – x –3/4=0 x2 – x = 3/4
Answer:
x = - [tex]\frac{1}{2}[/tex], x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given
x² - x - [tex]\frac{3}{4}[/tex] = 0
Multiply through by 4 to clear the fraction
4x² - 4x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 3 = - 12 and sum = - 4
The factors are + 2 and - 6
Use these factors to split the x- term
4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
The solutions are x = 3 and x = -7.
To solve the quadratic equation, we first need to bring it to the standard form of ax2 + bx + c = 0. In the example given, we have the equation x2 + 4x - 21 = 0, where a = 1, b = 4, and c = -21. To find the solutions for x, we will use the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a).
Substituting the values of a, b, and c into the quadratic formula, we get:
x = (-(4) ± √((4)2 - 4(1)(-21))) / (2(1))
x = (-4 ± √(16 + 84)) / 2
x = (-4 ± √100) / 2
x = (-4 ± 10) / 2
Which gives us two solutions:
x = (6 / 2) = 3
x = (-14 / 2) = -7
Therefore, the solutions to the quadratic equation x2 + 4x - 21 = 0 are x = 3 and x = -7.
Solve the radical equation. q-6=sqrt(27-2q). What is the extraneous solution to the radical equation?
Answer:
the answer is 9
Step-by-step explanation:
the answer is 9
My bed is 3 inches by 2 inches by
What is the volume of my bed?
2
in
6 ins
3
in.
5
in
8 in
Option A
Volume of bed is [tex]2\frac{2}{3}[/tex] cubic inches
Solution:
Given are the dimensions of bed
To find: volume of bed
Since bed is generally of cuboid shape, we can use the volume of cuboid formula
volume of cuboid is given as:
[tex]\text{ volume of cuboid } = l \times w \times h[/tex]
Where, "l" is the length and "w" is the width and "h" is the height of cuboid
From attached figure in question
[tex]l = 2\frac{2}{3} inches = \frac{3 \times 2 + 2}{3} = \frac{8}{3} inches[/tex]
[tex]w = 3 inches[/tex]
[tex]h = \frac{1}{3} inches[/tex]
Substituting the values in formula,
[tex]v = \frac{8}{3} \times 3 \times \frac{1}{3}\\\\v = \frac{8}{3} = 2\frac{2}{3}[/tex]
Therefore volume of bed is [tex]2\frac{2}{3}[/tex] cubic inches
The tables represent the functions fx) and g(x). Which input value produces the same output value for the two functions? X=-3 x=-1 x=0 x=1
Answer: Last option.
Step-by-step explanation:
By definition, a relation is a function if and only if each input value has an unique output value.
For this exercise it is important to remember that the input values are the values of "x" and the ouput values are the values of "y"
Knowing this and given the tables attached which represent the functions [tex]f(x)[/tex], and [tex]g(x)[/tex],, you can identify that:
1. In the table that represents the function [tex]f(x)[/tex], the input value 1 produces the output value 3.
2. In the table that represents the function [tex]g(x)[/tex], the input value 1 produces the output value 3.
Therefore, based on this, you can determine that the input value that produces the same output value for the two functions is:
[tex]x=1[/tex]
A camping leader bought the items listed in the table for his team. What is the average cost of an item in his purchase?
A. $7.75
B.$7.58
C.$6.60
D.$5.44
The right answer is Option D: $5.44
Step-by-step explanation:
Given,
Cost of one sun visor = $6.25
Cost of 11 sun visors = 6.25*11 = $68.75
Cost of one sunglasses = $8.90
Cost of 4 sunglasses = 8.90*4 = $35.60
Cost of one water bottle = $9.50
Cost of 8 water bottles = 9.50*8 = $76
Cost of one whistle = $1.75
Cost of 15 whistles = 1.75*15 = $26.25
Total number of items = 11+4+8+15 = 38
Total cost of items = 68.75+35.60+76+26.25 = $206.60
Average = [tex]\frac{Sum\ of\ prices}{No.\ of\ items}[/tex]
[tex]Average=\frac{206.60}{38}\\Average=\$5.436[/tex]
Rounding off to nearest hundredth
Average = $5.44
The average price of an item is $5.44
The right answer is Option D: $5.44
Keywords: average, sum
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Write as many equivalent expressions to 3/4(4x-8)+1/4(4x-8)
Answer:
4x-8
Step-by-step explanation:
3/4(4x-8)+1/4(4x-8)
12/4x-24/4+4/4x-8/4
3x-6+x-2
3x+x-6-2
4x-8
Answer:
everything is on the sheet
At the beginning of an environmental study a forest cover an area of 1500 km second power since then this area has decreased by 9.8% each year let T be the number of years since the start of the study letter y b the area that the forest covers in km to the second power write an exponential function showing the relationship between Y&T
Answer:
[tex]y=1500\cdot(0.902)^T[/tex]
Step-by-step explanation:
Let T be the number of years since the start of the study and y be the area that the forest covers in [tex]\text{km}^2[/tex].
We have been given that at the beginning of an environmental study a forest cover an area of 1500 [tex]\text{km}^2[/tex]. Since then this area has decreased by 9.8% each year.
We know that an exponential function is in form [tex]y=a\cdot(1-r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Decay rate in decimal form,
x = Time.
Let us convert 9.8% into decimal as:
[tex]9.8\%=\frac{9.8}{100}=0.098[/tex]
We have been given that initial value (a) is [tex]1500[/tex].
Upon substituting our given values, we will get:
[tex]y=1500\cdot(1-0.098)^T[/tex]
[tex]y=1500\cdot(0.902)^T[/tex]
Therefore, our required exponential function would be [tex]y=1500\cdot(0.902)^T[/tex].
-13g+12g+9=15 solve for g
What is the cube root of 27a^12?
answer: 3a^4 is the correct answer
Answer:3a^4
Step-by-step explanation:
A line passes through the point (-8,8) and has a slope of -3/2. Write an equation in point-slope form for a this line.
Answer:
y-8=-3/2(x+8)
Step-by-step explanation:
y-y1=m(x-x1)
y-8=-3/2(x-(-8))
y-8=-3/2(x+8)
Final answer:
The equation of the line in the point-slope form that passes through (-8, 8) with a slope of -3/2 is y - 8 = (-3/2)(x + 8).
Explanation:
To write an equation in point-slope form for a line that passes through a given point with a known slope, we use the formula y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.
For the line that passes through the point (-8, 8) with a slope of -3/2, we substitute these values into the point-slope form equation:
y - 8 = (-3/2)(x + 8)
This equation represents the specific line asked in the problem.
PLEASE HELP ME ASAP!!!!! I NEED SOMEONE REALLY SMART TO HELP ME!!!!!
By what percent will a fraction change if its numerator is decreased by 75% and its denominator is decreased by 50%?
Answer:
The fraction will decrease by 50%.Step-by-step explanation:
[tex]p\%=\dfrac{p}{100}\\\\75\%=\dfrac{75}{100}=0.75\\\\50\%=\dfrac{50}{100}=0.5\\\\\dfrac{n}{d}-\text{a fraction}\to(n-\text{numerator},\ \text{denominator})\\\\\text{numerator is decreased by 75}\%\to n-0.75n=0.25n\\\\\text{denominator is decreased by 50}\%\to d-0.5d=0.5d\\\\\text{new fraction}\ \dfrac{0.25n}{0.5d}=\dfrac{0.25\cdot100}{0.5\cdot100}\cdot\dfrac{n}{d}=\dfrac{25}{50}\cdot\dfrac{n}{d}=\dfrac{1}{2}\cdot\dfrac{n}{d}=0.5\cdot\dfrac{n}{d}\\\\\dfrac{n}{d}-0.5\dfrac{n}{d}=0.5\cdot\dfrac{n}{d}\to\ \text{it's}\ 50\%\ \text{of}\ \dfrac{n}{d}[/tex]
In a study of wait times at an amusement park, the most popular roller coaster has a mean wait time of 17.4 minutes with a standard deviation of 5.2 minutes. If 30 days are randomly selected, find the probability that the mean wait time is greater than 20 minutes.
A: 0.0031
B: 0.1023
C: 0.3207
D: 0.9987
Answer: A: 0.0031
Step-by-step explanation:
Given : In a study of wait times at an amusement park, the most popular roller coaster has a mean wait time of 17.4 minutes with a standard deviation of 5.2 minutes.
i.e. [tex]\mu=17.4[/tex] and [tex]\sigma=5.2[/tex]
We assume that the wait times are normally distributed.
samples size : n= 30
Let x denotes the sample mean wait time.
Then, the probability that the mean wait time is greater than 20 minutes will be :
[tex]P(x>20)=1-P(x\leq20)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{20-17.4}{\dfrac{5.2}{\sqrt{30}}})\\\\=1-P(z\leq2.74)\ \ [\because\ z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9969\ \ [\text{ By z table}]\\\\=0.0031[/tex]
Hence, the probability that the mean wait time is greater than 20 minutes.= 0.0031
Thus , the correct answer is A: 0.0031 .
Answer:
Answer: A: 0.0031
Step-by-step explanation:
What is the answer with the remainder
Answer:
0.0007
Step-by-step explanation:
Captain buys a 100g bar of chocolate. He eats 3/5 of his bar. How many grams of chocolate are left?
Answer:
40g of chocolate are left.
Step-by-step explanation:
3/5*100=300/5=60
100-60=40
Final answer:
To find the amount of chocolate left, subtract the amount eaten from the original 100g bar.
Explanation:
To find the number of grams of chocolate left, you need to subtract the amount Captain ate from the original 100g bar. Captain ate 3/5 of the bar, so you can calculate the amount eaten by multiplying 3/5 by 100g. This gives you 60g. To find the amount left, you subtract 60g from 100g. The answer is 40g.
A park is 4.6 miles long and 2.7 miles wide. If a racecar drove 50 times around the park. How far will it have to go?
The race-car will have to go for 730 miles
Step-by-step explanation:
The given is:
A park is 4.6 miles long and 2.7 miles wideA race-car drove 50 times around the parkWe need to find how far it will have to go
∵ The car will move around the park
- That means it moves the distance equal the perimeter of the park
∵ The dimensions of the park are 4.6 mile long and 2.7 miles wide
∵ The perimeter of the park = 2(length + width)
∴ The perimeter of the park = 2(4.6 + 2.7)
∴ The perimeter of the park = 2(7.3)
∴ The perimeter of the park = 14.6 miles
∵ The car will move around the park 50 times
∵ The distance of one round is 14.6 miles
∴ The distance for 50 rounds = 14.6 × 50
∴ The distance for 50 rounds = 730 miles
The race-car will have to go for 730 miles
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Name two coordinates that are on the line: [tex]y = 12[/tex]
Name two coordinates that are on the line: [tex]x = -5[/tex]
Answer:
(1,12) and (2,12).
(- 5,1) and (- 5, 2).
Step-by-step explanation:
y = 12 is a line that is parallel to the x-axis and at a constant distance of 12 units above the x-axis. Therefore, the points on the line will have any x-coordinate but have a constant y-coordinate i.e. 12.
Therefore, the two points on the line y = 12 can be (1,12) and (2,12).
x = - 5 is a line that is parallel to the y-axis and at a constant distance of 5 units left of the y-axis. Therefore, the points on the line will have any y-coordinate but have a constant x-coordinate i.e. - 5.
Therefore, the two points on the line x = - 5 can be (- 5,1) and (- 5, 2). (Answer)
express the ratio in its simpilest form
4:2:2
To simplify the ratio 4:2:2, divide each part by the greatest common factor, which is 2, resulting in a simplest form of 2:1:1.
To express the ratio 4:2:2 in its simplest form, you need to divide each term of the ratio by the greatest common factor of all the terms. In this case, the greatest common factor of 4, 2, and 2 is 2. Therefore, when you divide each part of the ratio by 2, the simplest form of the ratio is 2:1:1.
Here's a step-by-step breakdown:
Identify the greatest common factor (GCF) of the numbers in the ratio. GCF of 4, 2, and 2 is 2.
Divide each term of the ratio by the GCF. So, 4 divided by 2 is 2, and 2 divided by 2 is 1.
Write down the simplified ratio: 2:1:1.
This method is similar to the way coefficients in a balanced chemical equation can be simplified, or how ratios can be used in genetics to represent phenotypic distribution in a dihybrid cross. In health sciences, ratios such as 1:1000 are expressed in simplest form. Similarly, in engineering, gear ratios like 2:1 are given in the simplest way to indicate how many turns of an input gear will result in one turn of an output gear.
Which option is one important source of public opinion?
the Bill of Rights
mass media
public officials
pollsters
Answer:
Mass Media
Step-by-step explanation:
Answer: Got an (A) on my test, it is (Mass media)
Step-by-step explanation: OOOOFFF is my word
Please help me! I don’t know how to write in as a Compound with Integers.
Answer:
[tex]g \leq -24[/tex] or [tex]g>6[/tex]
Step-by-step explanation:
Lets solve the first inequality by cross multiplying and doing algebra. THe process is shown below:
[tex]\frac{2g+63}{5} \leq 3\\2g+63 \leq 15\\2g \leq 15-63\\2g \leq -48\\g \leq -24[/tex]
Now, lets solve the next inequality with simple algebra. Process shown below:
[tex]13g-34>44\\13g>44+34\\13g>78\\g>6[/tex]
Hence, we can say:
g is less than or equal to -24 AND g is greater than 6
Let f(x) = -4% - 10. Find x when f(x)=10
Answer:
x=-5
Step-by-step explanation:
-4x-10=10
-4x=10+10
-4x=20
x=20/-4
x=-5
Which would you rather have: 21% of $3,876 or 17% of $4,552? choose an inequality sign.
Step-by-step explanation:
21 percent of 3,876 is 813.96$, and 17 percent of 4552 is 773.67$. 813.96>773.67
21% of $3,876 is $813.96, while 17% of $4,552 is $773.84. Therefore, 21% of $3,876 inequality sign is greater than 17% of $4,552.
Explanation:Choosing between 21% of $3,876 or 17% of $4,552 involves calculating each percentage of the given amounts to compare which is greater. To do this:
Calculate 21% of $3,876: 0.21 × 3876 = $813.96.
Calculate 17% of $4,552: 0.17 × 4552 = $773.84.
Comparing these two amounts using an inequality sign, we see that $813.96 is greater than $773.84. So, you would rather have 21% of $3,876 than 17% of $4,552.
The inequality would be written as:
21% of $3,876 > 17% of $4,552
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You prepare 8 scoops of dog food for 4dogs and prepare 12.5 scoops of dog food for 5 dogs is there a propositional relationship between the number of scoops and the number of dogs?
Answer:
The relationship between the number of scoops and the number of dogs is not proportional
Step-by-step explanation:
Let
x ----> the number of scoops
y ----> the number of dogs
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
First situation
You prepare 8 scoops of dog food for 4 dogs
x=8, y=4
Find the constant of proportionality k
[tex]k=\frac{y}{x}[/tex]
substitute the values of x and y
[tex]k=\frac{4}{8}=0.5[/tex]
Second situation
You prepare 12.5 scoops of dog food for 5 dogs
x=12.5, y=5
Find the constant of proportionality k
[tex]k=\frac{y}{x}[/tex]
substitute the values of x and y
[tex]k=\frac{5}{12.5}=0.4[/tex]
Compare the values of k
[tex]0.5\neq 0.4[/tex]
The values of k are not equal
therefore
The relationship between the number of scoops and the number of dogs is not proportional
What is the percent markup on a 300 phone sold for 465
Answer:
55%
Step-by-step explanation:
The percent markup is the percent increase from $300 to $465.
Subtract to find the markup: 465 - 300 = 165
Now we find the percent markup.
Divide: 165/300 = 0.55
Multiply: 0.55 * 100 = 55
Answer: 55%
Markup percentage is 55%
Given that;Old price of phone = 300
New price of phone = 465
Find:Markup percentage
Computation:Markup = [465 - 300] /
Markup = 165 / 300
Markup = 0.55
Markup percentage = 0.55 × 100
Markup percentage = 55%
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5. What is the amplitude of the sinusoidal function? Please help
Answer: 4
Step-by-step explanation:
The amplitude is the distance from the baseline to the maximum.
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Determine whether the pair of solids are similar, congruent, or neither. Figures are not necessarily drawn to scale.
Answer:
Neither
Step-by-step explanation:
Can be determined because there is enough information (Length, width, and height).
Not congruent because from the picture itself, the figures are in different sizes.
Not similar because:
The height ratio is not the same as the ratios of other dimensions.
1 : 4 is not similar to 6 : 12 and 4 : 8