The two numbers given by the algebraic expressions are x = 5 and y = 2.
What is system of equation?A system of equations is a set of two or more equations that are to be solved simultaneously. In other words, a system of equations represents multiple relationships between variables that need to be solved for at the same time. A system of equations can be solved using various methods, such as substitution or elimination. The goal of solving a system of equations is to find the values of the variables that satisfy all of the equations in the system. One common method for solving systems of linear equations is called Gaussian elimination, which involves manipulating the equations in the system to eliminate one variable at a time until a solution is found.
Let us suppose the numbers as x and y.
From the given statement the mathematical expression can be set as:
y = 2x - 8
x + y = 7
Now. substituting the value of y in equation we have:
x + (2x - 8) = 7
3x - 8 = 7
3x = 15
x = 5
Now, for x = 5 the value of y is:
y = 2(5) - 8
y = 2
Hence, the two numbers are x = 5 and y = 2.
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The complete question is:
The number y is 8 less than 2 times another number x, their sum is 7. Find the number.
If something is going 70 km/sec per mpc and its recessional velocity is 49000 km/sec then what is its distance
Step-by-step explanation:
always and you come across a question that needs you to find the time or the distance or the speed the first thing that you need to think of is a triangle based formula so this is what you do you're right DStv in a triangle but you won't include the V therefore it will be DST and you just look at mainly at the formulas and try to identify the one that you're looking for and the way forward for example distance I have already drawn my small triangle and it's revealing that distance is equal to speed times time and speed is equal to a distance divided by time and time is equal to distance divided by speed in this case we're looking for the distance therefore I supposed to say speed time so was supposed to say 70 * 49,000 to get your answer
Please help answer this with good explication and I'll give Thanks , five stars and maybe even brainly.
Andy has X pence. Kelly ha s 7 pence more than Andy . Georgia had a pence less than Andy. Total amount of money they have is 1.48
A) form an equation in terms of x and solve th equation
Let's call the amount of money Andy has "x".
According to the problem, Kelly has 7 pence more than Andy, so Kelly has x + 7 pence.
Georgia has a penny less than Andy, so Georgia has x - 1 pence.
The total amount of money they have is 1.48, which we can write as 148 pence.
So we can set up the equation:
x + (x + 7) + (x - 1) = 148
Simplifying and solving for x:
3x + 6 = 148
3x = 142
x = 47.33
Since we're dealing with pence, we'll round down to the nearest whole number:
x = 47
So Andy has 47 pence, Kelly has 54 pence (47 + 7), and Georgia has 46 pence (47 - 1).
y=-0.8x^2 - 4x please help
The characteristics of the above quadratic unction y=-0.8x^2 - 4x are given as follows.
What are the characteristics of the above function?The vertex is (5, -22).
The axis of symmetry is x = 5.
The function is increasing when x < 5 and decreasing when x > 5.
The x-intercepts are (-5, 0) and (0, 0).
The domain is all real numbers and positive when x < 0.
The range is (-∞, -22].
The function is negative when x > -5.
The y-intercept is (0,0).
The function is negative when x is less than -5/2 and positive when x is greater than -5/2.
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HURRY DUE TONIGHT
Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 21%
B. 3%
Brand B contains 3% saline solution by volume.
The correct option is B.
We have,
Brand A was a six gallon 18% saline solution.
Final, she 18 gallon 8% saline solution mixture.
let the percentage of saline solution in brand B be x.
So, volume of saline solution
= 18% of 6 gallons + x% of (18 - 6) gallons
Then the equation is given as,
0.18(6) + 0.01x(18 - 6) = 0.08(18)
1.08 + 0.12x = 1.44
0.12x = 0.36
x = 3
Thus, the percentage of saline solution in brand B is 3%.
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What is tan(A)?
Remember to rationalize the denominator.
(Please Help)
Answer:
[tex]\frac{2 \sqrt{5}}{5}[/tex]
Step-by-step explanation:
As given by SOH-CAH-TOA
tan is equal to opposite/adjacent.
therefore for A, the opposite would be equal to 2, and adjacent would be equal to [tex]\sqrt{5}[/tex] as the hypotenuse is never referred to as an adjacent side. so the answer would be tan(A) = [tex]\frac{2}{\sqrt{5}}[/tex] however, to rationalize the denominator you must multiply the fraction by [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] .
[tex]\frac{2}{\sqrt{5}} *\frac{\sqrt{5}}{\sqrt{5}} = \frac{2 * \sqrt{5}}{\sqrt{5} *\sqrt{5}}[/tex]
then simplify
[tex]\frac{2 \sqrt{5}}{5}[/tex]
Help, im stuck on another question
According to the information, the probability of missing the first penalty but scoring the second penalty is 3/16.
How to calculate the probability of Evelyn to score first and second penalties?The probability of missing the first penalty is 1/4, and the probability of scoring the second penalty given that she missed the first one is 3/4. Therefore, the probability of missing the first penalty but scoring the second penalty is:
(1/4) * (3/4) = 3/16
So the probability is 3/16, or 0.1875 as a decimal, or 18.75% as a percentage, in its simplest form.
According to the above, the three diagrams would be like this:
------- Score (3/4)
|
------|
|------- Score (3/4)
|
------- Miss (1/4)
|
------- Score (3/4)
|
------- Miss (1/4)
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Find the value of x.
The value of x when the secant intersect is 5.
How to find the length of secant when they intersect?When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.
Therefore,
(4 + 5)4 = (x - 2 + x + 4)(x - 2)
9(4) = (2x + 2)(x - 2)
36 = 2x² - 4x + 2x - 4
2x² - 2x - 4 - 36 = 0
2x² - 2x - 40 = 0
x² - x - 20 = 0
x² - 5x + 4x - 20 = 0
x(x - 5) + 4(x - 5) = 0
(x + 4)(x - 5) = 0
(x - 5)(x + 4) = 0
x = 5 or x = -4
Therefore,
x = 5
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How do you write 843,400 in scientific notation
Answer:
Scientific notation = 8.434 × 10^5
Scientific e notation = 8.434e5
Engineering notation = 843.4 × 10^3 ---> (thousand; prefix kilo- (k) )
Standard form = 8.434 × 10^5
please help me i don’t understand
Answer: the answer is
Step-by-step explanation:
eggs
The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?
Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.
Step-by-step explanation:
To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.
Answer:
the afternoon is the right one
What is the value of the expression −38 − 16 − (−23)?
Answer:
-31
Step-by-step explanation:
Match the appropriate list with the definition
a. reflexive, symmetric, and transitive only
b. congruence and midpoint.
A segment proof is a type of proof that shows the steps used to establish the congruence or equality of two line segments. The goal of a segment proof is to provide a clear and logical argument that demonstrates why the two segments are equal or congruent.
Segment proofs typically involve using a combination of definitions, postulates, and theorems to justify each step of the argument. For example, to prove that two line segments are congruent, one might use the segment addition postulate, the definition of congruence, and the reflexive, symmetric, and transitive properties of congruence.
The appropriate matching is:
1. Segment proofs include the following definitions as justifications/reasons: ⇔ reflexive, symmetric, and transitive only
2. Segment proofs include the following as congruence of segments: ⇔ congruence and midpoint.
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which diagram represents the expression |-5|
How many times does 13 go into 26
Answer: 2
Step-by-step explanation:
please help studying my next grade:
12+6÷(82-33)x66
Answer:
3246
Step-by-step explanation:
To calculate this equation, we need to follow the order of operations, also known as PEMDAS. First, we evaluate anything inside parentheses, which in this case is (82-33), giving us 49. Next, we perform division, so we have 6 ÷ 49. Then, we multiply 49 and 66, resulting in 3234. Finally, we add 12 to 3234, leading to the final answer of 3246. Therefore, the value of the expression 12+6÷(82-33)x66 is 3246.
Answer:
3246
Step-by-step explanation:
You roll a 6-sided die.
What is P(less than 4)?
Write your answer as a fraction or whole number.
The value of the probability of rolling a number less than 4 is 1/2
Calculating the value of P(less than 4)?The probability of rolling a number less than 4 on a fair 6-sided die can be calculated by counting the number of favorable outcomes and dividing it by the total number of possible outcomes.
There are three favorable outcomes: 1, 2, and 3.There are six possible outcomes: 1, 2, 3, 4, 5, and 6.Therefore, the probability of rolling a number less than 4 is:
P(less than 4) = favorable outcomes / total outcomes = 3/6 = 1/2
So the probability of rolling a number less than 4 is 1/2, or 50%.
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if a sample of 32 runners is taken from a population of 201 what is the mean
If a sample of 32 runners is taken from a population of 201, the mean is equal to 201.
What is a population?In Statistics and science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.
What is a sample?In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.
In this context, we can reasonably infer and logically deduce that the mean (μ) could be equal to 201 runners because it represent the average.
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Draw and label a rectangular prism that has a surface area of 96 square meters
There are 2 sides.
First side is 12 by 2 so you would multiply them together which is 24 and since there is another side the same length multiply by 2 which is 48.
Second side small side is 2 by 4 so multiply them together which is 8 and since there is another side the same demension multiply 8 by 2 which is 16.
The last side is 12 by 4 so again multiply them together which is 48. Multiply it by two since there is another side with same dimension which is 96.
Now do 48 + 16 + 96 (the answer gotten after finding the areas for each sides and their identicals) which is 160 ft²
The label for rectangular prism that has a surface area of 96 square meters is in the attached image.
There are x counters in a bag.
15 of the counters are blue.
Hussain takes at random 24 counters from the bag.
6 of these 24 counters are blue.
Work out an estimate for the value of x.
Answer: c=60
Step-by-step explanation: Based on the given conditions, formulate::
15/c= 6/24
By setting up and solving a proportion that represents the ratio of blue counters to total counters in two different scenarios, we find that an estimate for the total number of counters in the bag is 60.
Explanation:We can set up a proportion to solve this problem. In this case, the counters represent the total numbers in different situations. Initially, there are 15 blue counters out of an unknown total 'x'. Meanwhile, Hussain picked 6 blue counters out of 24. As these are similar situations (picking blue counters out of a total), we can express this as a proportion as follows: 15/x = 6/24 .
To solve this proportion, simply cross multiply and solve for x: 15*24 = 6*x. Simplify this to 360 = 6x. Diving both sides by 6 gives the value of x as 60.
So an estimate for the total number of counters in the bag, or 'x', is 60.
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lo Rebecca found the length and width of the garage door. She used the measurements to find the perimeter of the garage door. Which of the following could be the perimeter of Rebecca's garage door? F 48 square feet G 48 square inches H 48 feet J 48 cubic feet
The possible values for the perimeter of Rebecca’s garage door are 48 feet or 48 inches
What is meant by perimeter?
Perimeter is the total length of the boundary of a two-dimensional shape. It is the sum of the lengths of all sides of the shape. The perimeter is commonly used to measure the distance around an object or figure and is often used in geometry to calculate the area of a shape.
According to the given information
The perimeter of a rectangle is calculated by adding the four sides of the rectangle. The formula for the perimeter of a rectangle is given as P = 2 (Length + Width) 12.
Therefore, the possible values for the perimeter of Rebecca’s garage door are 48 feet or 48 inches
Complete question is
Rebecca found the length and width of the 6. garage door. She used the measurements to find the perimeter of the garage door. Which of the following could be the perimeter of Rebecca's garage door? F 48 square feet /G 48 square inches/ H 48 feet/ J 48 cubic feet
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Find the surface area
Round to the nearest tenth
There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.
what is surface area ?The dimensions and shape of the object are taken into account while calculating surface area. The volume of water of a cube, for instance, can be computed by adding the areas of the all six of its equal-sized faces. The surface temperature of something like a sphere, while on the other hand, must be calculated using mathematical methods that take into consideration its radius. The concept of surface area is crucial to many branches of mathematics, science, & engineering.
given
The area of each of the two triangles is [tex](1/2) * 3 * 8 = 12[/tex] square units since each triangle has a base of 3 and a height of 8, respectively.
The trapezium features an 8-inch height, a 6-inch top base, a 12-inch bottom base, and a 10-inch slant height.
two rectangles, each measuring 72 square units: 144 square units (2 x 72)
Four trapezoidal sides, each with a surface area of 12 + 72 = 84 square units 336 square units (4 x 84)
There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.
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If October 15 falls on a Wednesday, then November 11 of that same year falls on which day of the week? (October has 31 days)
Answer:
There are 31 days in October, so there are 31 - 15 = 16 days left in October after October 15.
16 days is equivalent to 2 weeks and 2 days (since there are 7 days in a week), so November 11 is 2 weeks and 2 days after October 15.
Therefore, November 11 falls on a Wednesday + 2 weeks + 2 days = Friday.
So November 11 of that same year falls on a Friday.
Find the area
Round to nearest tenth
The total surface area to paint is 22000 sq. ft.
What is surface area?Surface area is the measurement of the outer surface of an object. It is often used to calculate the area of a three-dimensional object, such as a cube, cylinder, or sphere, and is also used to calculate the area of the faces of a solid object. Surface area is measured in square units such as square centimeters (cm2), square meters (m2), or square inches (in2).
Surface Area = 2(lw + lh + wh)
Surface Area = 2((100' x 50') + (100' x 40') + (50' x 40'))
Surface Area = 2(5000' + 4000' + 2000')
Surface Area = 2(11000')
Surface Area = 22000 sq. ft.
Answer: The total surface area to paint is 22000 sq. ft.
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The graph of f(x)=x2 was transformed to create the graph of g(x)=−f(x−1)+2 Which is the graph of g ?
CAN SOMEONE ANSWER THIS RIGHT PLEASE!!!!!!
For the graph, what is a reasonable constraint so that the function is at least 600?
graph of y equals minus 2 times the square of x plus 40 times x plus 600
0 ≤ x ≤ 20
−10 ≤ x ≤ 30
x ≥ 0
All real numbers
They say 1 and 2 wrong I don’t know what to believe
Please answer right I need it so much
The reasonable constraint so the function is at least 600 would be A. 0 ≤ x ≤ 20.
How to find the reasonable constraint ?Given the function y = -2x² + 40x + 600, we want to find the constraint for x so that the function's value is at least 600.
Since the parabola opens downward (as a is negative), the function will be at least 600 for all values of x within the interval where the parabola is above y = 600. The vertex of the parabola is at its maximum value, so we should look for the interval around the vertex (10, 800).
Looking at the given constraints, the option "0 ≤ x ≤ 20" is a reasonable constraint that ensures the function is at least 600. The parabola starts at a value of 600 at x = 0, reaches its maximum value at the vertex, and then returns to a value of 600 at x = 20.
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A group of employees were asked whether they drive or walk to work.
The probability of being a male and derive from a group of employees were asked whether they drive or walk to work is equal to 0.27.
From the table representing the probabilities of a group of employees.
Employees divided into two groups,
One is male .
Second is female.
While going for work there are two ways .
Derive to walk.
Walk to work.
Different probabilities are as follow,
Male and derive 0.27
Male and walk = 0.27
Female and derive = 0.23
Female and walk = 0.23
The required probability of being a male and derive
= 0.27.
Therefore, the probability of derive and male is equal to 0.27.
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18
If the mean for a data set was 8 and the standard deviation was 1.5, where would most of the data points be located?
A) Above 9.5
B) Between 6.5 and 9.5
Above 12
D) None of these answer choices are correct.
the correct answer is B, between 6.5 and 9.5.The solution of given standard deviations Problem isit is unlikely that most of the data points would be located there.
what is standard deviations?Standard deviation is a statistical measure of the amount of variation or dispersion in a set of data values. It represents the average distance of each data point from the mean of the data set.
According to given informationThe answer to this question can be found using the empirical rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.
Given that the mean is 8 and the standard deviation is 1.5, one standard deviation above the mean would be 8 + 1.5 = 9.5, and one standard deviation below the mean would be 8 - 1.5 = 6.5. Therefore, approximately 68% of the data would be expected to fall between 6.5 and 9.5.
Based on this information, we can eliminate answer choices A and D. Answer choice C is more than two standard deviations above the mean, so it is unlikely that most of the data points would be located there. Therefore, the correct answer is B, between 6.5 and 9.5.
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Question 02/08 The probability that the bus will arrive on time is 0.6 and the probability that it will be late is 0.3. What is the probability that it will arrive early?
The probability that the bus will arrive early is 0.1, or 10%.
To find the probability that it will arrive early
It is possible to calculate the likelihood that the bus will arrive early using the rule that the sum of all possible outcomes must equal 1.
P(on time) + P(late) + P(early) = 1 if P(E) is the likelihood that the bus will arrive early.
Using the probabilities as a replacement, we get:
0.6 + 0.3 + P(E) = 1.
For P(E), use the formula:
P(E) = 1 - 0.6 - 0.3 = 0.1.
Therefore, the probability that the bus will arrive early is 0.1.
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Assume you have a balance of $1200 on a credit card with an APR of 18%, or 1.5% per month. You start making monthly payments of $200, but at the same time you charge an additional $80 per month to the credit card. Assume that interest for a given month is based on the balance for the previous month. The following table shows how you can calculate our monthly balance. Complete and extend the table to show the balance at the end of each month until the debt is paid off. How long does it take to pay off the credit card debt? Fill out the table row by row, and continue until the last full payment. (Round to the nearest cent as needed.) Month Payment Expenses Interest 0 1 $200 $80 0 015 × $1200 = $18.00 2 $200 $80 New Balance $1200 $1200 - $200 ÷ $80 ÷ $18.00 = $1098.00 (0,1) More
Mrs. lang has x amount of students in each class. Ms. easter has 4 less students in each class. If both teachers have 5 classes, write an expression that
shows how many students are in all of Ms. easter’s classes.
If Mrs. Lang has x students in each of her 5 classes, then she has a total of 5x students.
Ms. Easter has 4 less students in each of her classes, so she has x - 4 students in each of her 5 classes.
How many students are in all of Ms. Easter's classes?To find out how many students are in all of Ms. Easter's classes, we can use the expression:
5(x - 4)
This simplifies to:
5x - 20
Therefore, there are 5x - 20 students in all of Ms. Easter's classes.
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