Determine the value of a so that x1-3x3=-3 2x1+ax2-x3=-2 (i)unique solution(ii)no solution(iii)many solutions
Answer:
(i)unique solution
Explanation:
We solve for x1 thus in the first equation:
x1-3x3=-3
x1-9=-3
x1=-3+9
x1= 6
We solve for a thus in the second equation:
2x1+ax2-x3=-2
2+a2-x3=-2
a2-x3=-4
a2=-4+x3
Select the correct answer. dudley is biking. he wants to cover 40 miles. if he travels 30 miles every 2 hours, what is the equation of a line that models y, the number of miles he has left to travel, after biking x hours? a. y = -15x â€" 40 b. y = -30x 40 c. y = -15x 40 d. y = 30x â€" 40
The equation will be y = -15x + 40
Equations help us to understand a particular problem better, they give us possible insights into the situation. Equation Formation is an important aspect of Mathematics. We can form equations on the basis of the information given and then analyze it.
Given:
The biker, Dudley wants to travel 40 miles.
It is given that he travels 30 miles every 2 hours.
Obtaining Equation,
Distance traveled in 2 hours = 30 miles
Then, distance traveled in x hours = \(\frac{30}{2}*x = 15x\)
So, the remaining distance to cover = 40 - 15x
or y = 15x - 40
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Holly earns $30 for babysitting 5 hours. She earns $28 when she does chores for 4 hours. Which compares the unit rates?
A. The unit rate for babysitting is $2 per hour more than the unit rate for doing chores
B. The unit rate for babysitting is $1 per hour more than the unit rate for doing chores
C. The unit rate for doing chores is $1 per hour more than the unit rate for babysitting
D. The unit rate for doing chores is $2 per hour more than the unit rate for babysitting
The population of a county is growing at a rate of 9% per year, compounded continuously. If the county currently has 14,934 people, how many will there be in this county in 10 years? Round to the nearest person.
if the area of a rectangle is 52cm and the lenght 8cm what is its width? what is its perimeter?
29
One side is 8 which means the opposite side it 8, 52cm divided by 8 is 6.5. Add 8+8 then 6.5+6.5. Put those together you get 29 as the perimeter.
agree or desagree ? ..........
Answer:
Disagree.
If you rotate the octagon 90° it will look the same.
good luck, i hope this helps :)
Answer:
Disagree
Step-by-step explanation:
If you have any shape and you rotate it 90 degrees, it moves down and to the right, not onto itself.
Pls help im very desperate i'll defenitely give brainliest
Answer:
-25
Step-by-step explanation:
You can take 10÷-⅖=-25
Answer:
x = -25
Step-by-step explanation:
1. combine all terms into a single fraction
-2x/5 = 10
2. multiply all terms by the same value to eliminate fraction denominators
5 x -2x/5 = -5 x 10
3. cancel multiplied terms that are in the denominator
-2x = -5 x 10
4. multiply the numbers
-2x = -50
5. divide both sides of the equation by the same term
-2x/2 = -50/2
6. simplify
x = -25
sorry if it's a lot to read :) (edit: I didn't see the - sign lol sorry)
The endpoints of line segment. CD are C(-4,7) and D(0,-3). Find the midpoint of
line segment CD.
Given:
The endpoints of line segment CD are C(-4,7) and D(0,-3).
To find:
The midpoint of CD.
Solution:
Midpoint formula:
\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)
Using the midpoint formula, the midpoint of CD is
\(Midpoint=\left(\dfrac{-4+0}{2},\dfrac{7-3}{2}\right)\)
\(Midpoint=\left(\dfrac{-4}{2},\dfrac{4}{2}\right)\)
\(Midpoint=\left(-2,2\right)\)
Therefore, the midpoint of the line segment CD is (-2,2).
Need Help here Please!
Answer:
Step-by-step explanation:
To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:
a) To find the value of \(\sf 3(x - y) \\\):
\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)
b) To find the value of \(\sf 6x - 6y \\\):
\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)
c) To find the value of \(\sf y - x \\\):
\(\sf y - x = - (x - y) = -4 \\\)
Therefore:
a) The value of \(\sf 3(x - y) \\\) is 12.
b) The value of \(\sf 6x - 6y \\\) is 24.
c) The value of \(\sf y - x \\\) is -4.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
A recipe calls for 21 scoops of sugar. Each scoop is 2.5 oz of sugar. How many scoops do you need if the scoop holds 3.5 oz of sugar?
Answer:
you would need 6 scoops of sugar
Answer:
You would need 15 scoops of sugar per 3.5 oz
Step-by-step explanation:
Tavon has a gift card for $85 that loses $3.50 for each 30-day period it is not used. He has another gift card for $75 that loses $3 for each 30-day period it is not used. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal, the determine what the value of each card will be when they have equal value.
Answer:
Each card will have a value of $15 when they equal after 600 days which also is 20 30-day periods.
Step-by-step explanation:
Card1: \(85 - \frac{3.50}{30} x\)
Card2: \(75 - \frac{3}{30} x\)
x is number of days
\(85 - \frac{3.50}{30} x = 75 - \frac{3}{30} x\)
2550 - 3.50x = 2250 - 3x
2550 - 0.50x = 2250
-0.50x = -300
x = 600 days
Card1: \(85 - \frac{3.50}{30} (600)\)
85 - 70 = 15 dollars
Card2: \(75 - \frac{3}{30} (600)\)
75 - 60 = 15 dollars
The value of each card will be when they have equal value is $15.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now, Let x be the number of time periods for which the gift card is not used, then
For the gift card $ 85 if it is not used for x periods, then the amount that will be lost is
85 - 3.50 x---------------------(1)
For the gift card $ 75 if it is not used for x periods, then the amount that will be lost is
75 - 3x---------------------- (2)
Now when both the amount lost is equal
85 - 3.50 x = 75 - 3x
solving the equation, we get
or, 3.50 x - 3x = 85 -75
or, 0.50 x = 10
or, x = 20
Thus the value of gift cards will be equal for 20 ,30 day periods.
Now,the value of each card be when they have equal value
The two cards will have equal value after 20, 30 day periods, this denotes that at this time, the value of each card will be equal.
Then
85 - 3.50 x = 75 - 3x
substituting x = 20, we get
85 - 3.50*20 = 75 - 3*20
85 - 70 = 75 - 60
15 = 15
So, when they have equal value, the value of each card will be $15.
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The box-and-whisker plots show data for the test scores of four groups of students in the same class. Which plot represents data with the greatest range of scores?
Answer:
The answer is B.
Step-by-step explanation:
bag contains seven batteries, all of which are the same size and are equally likely to be selected. each battery is different brand. if you select five batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected. a) with replacement b) without replacement (scroll down for answer!)
The answer would be a) With Replacement 16,807 points will be in the sample space if batteries are selected.
The sample space with replacement would be 7^5 = 16,807 points. This means that when selecting five batteries from a bag of seven with replacement, the total number of points would be 16,807. This is because each of the five batteries could potentially be from the same brand, so the sample space would include all 16,807 possibilities of the combination of 5 batteries from the 7 available.
B) Without Replacement: The sample space without replacement would be 7P5 = 21,053 points. This means that when selecting five batteries from a bag of seven without replacement, the total number of points would be 21,053. This is because each of the five batteries must be from a different brand, so the sample space would include all 21,053 possibilities of the combination of 5 batteries from the 7 available.
In conclusion, the sample space would have more points if the batteries are selected without replacement compared to when the batteries are selected with replacement. This is because when batteries are selected without replacement, each of the five batteries must be from a different brand, whereas when batteries are selected with replacement, the same brand could be chosen multiple times.
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8th grade Mathematics
Please look at picture!
The measure of angels 4 is 120*, and the measure of angle 2 is 35*
What is the measure of angle 5?
A) 95*
B) 105*
C) 130
D) 155
Thank you!
And SCAM “answers” WILL be REPORTED, REPORTING results in a BAN.
Have a great day! :)
Answer: 105
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
the sum of all angles in a triangle is always 180°.
the combination of an inner and an outer angle towards a flat line is always 180°. simply because that line simulates a diameter of a circle with the vertex being the center. and half a circle has 180°.
so,
180 = angle 3 + angle 4 = angle 3 + 120°
angle 3 = 60°
180 = angle 1 + angle 2 + angle 3 = angle 1 + 35 + 60
angle 1 = 180 - 35 - 60 = 85°
180 = angle 1 + angle 5 = 85 + angle 5
angle 5 = 95°
solve the proportion X-16/x+6 = 3/5
Answer:
x = 49
Step-by-step explanation:
Given
\(\frac{x-16}{x+6}\) = \(\frac{3}{5}\) ( cross- multiply )
5(x - 16) = 3(x + 6) ← distribute parenthesis on both sides
5x - 80 = 3x + 18 ( subtract 3x from both sides )
2x - 80 = 18 ( add 80 to both sides )
2x = 98 ( divide both sides by 2 )
x = 49
Answer:
x = - 49
Step-by-step explanation:
Solve for X by cross multiplying.
HELP ASAP DUR AT 11 PM EST
Answer:
I cant see the line also just find out where the Y and the X is and that should help you
Step-by-step explanation:
Answer:
red: 1
blue: 2
purple: 9
orange: 8
green: 4
Step-by-step explanation:
help please!!
Solve for x.
Answer:
x = 9
Step-by-step explanation:
Theorem:
The measure of an exterior angle of triangle equals the sum of the measures of its two remote interior angles.
The angle measuring 12x + 14 is an exterior angle of the triangle.
The angles measuring 76 deg and 1 + 5x are its remote interior angles.
12x + 14 = 1 + 5x + 76
12x + 14 = 5x + 77
7x = 63
x = 9
What is the benefit of using the factored form of a quadratic? aThe factored form gives the vertex of the parabola bThe factored form gives the minimum of the parabola cThe factored form gives the maximum of the parabola dThe factored form gives the zeros of the parabola
Quadratic functions f(x) can be written in three forms.
Factored form, the product of a constant and two linear terms:
\(a.(x-p).(x-q)\text{ or }a(x-p)^2\)The parameters p and q are the roots of the function (the x-intercepts of the graph y=f(x)). Converting a quadratic function to factored form is called factoring.
Hence, The factored form gives the zeros of the parabola
The correct option is D
The pulse rates of 177 randomly selected adult males vary from a low of 40 bpm to a high of 104 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 90% confidence that the sample mean is within 3 bpm of the population mean. Complete parts (a) through (c) below. a. Find the sample size using the range rule of thumb to estimate o n= 77 (Round up to the nearest whole number as needed.) b. Assume that o = 11.3 bpm, based on the value s = 11.3 bpm from the sample of 177 male pulse rates. n= (Round up to the nearest whole number as needed.)
(a) Rounding up to the nearest whole number, the minimum sample size required is n = 90.
(b) Using the given information, the minimum sample size required is 69.
(a) The range rule of thumb states that the range of a sample tends to be about four times the standard deviation of the population. Using this rule, we can estimate the sample size required.
Given that the range of the pulse rates is from 40 bpm to 104 bpm, the range is 104 - 40 = 64 bpm.
According to the range rule of thumb, the range is approximately four times the standard deviation. Therefore, we can estimate the standard deviation as 64 / 4 = 16 bpm.
Using this estimated standard deviation, we can calculate the required sample size using the formula:
n = (Z * σ / E)^2
Where:
Z is the Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of approximately 1.645),
σ is the estimated standard deviation,
E is the desired margin of error (3 bpm).
Plugging in the values, we have:
n = (1.645 * 16 / 3)^2
n ≈ 89.06
Rounding up to the nearest whole number, the minimum sample size required is n = 90.
(b) If we assume that the standard deviation of the population is o = 11.3 bpm (based on the sample of 177 male pulse rates), we can calculate the required sample size using the formula mentioned earlier:
n = (Z * σ / E)^2
Plugging in the values:
n = (1.645 * 11.3 / 3)^2
n ≈ 68.87
Rounding up to the nearest whole number, the minimum sample size required is n = 69.
Therefore, using the given information, the minimum sample size required is 69.
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A car rental offers two options for renting a car. Plan A costs $200 per week plus $0.35 for each mile driven during that week. Plan B costs $180 per week plus $0.55 for each mile driven that week. How many miles of driving would result in both plans costing the same amount for that week
Answer:
100 miles
Step-by-step explanation:
Two plans are being offered for the renting of cars.
Plan A:
Cost per week = $200
Cost for each mile = $0.35
Plan B:
Cost per week = $180
Cost for each mile = $0.55
To find:
Number of miles for which the cost is same ?
Solution:
Let the number of miles driven so that the cost becomes the same = \(m\) miles
First of all, let us find the cost for each plan as per \(m\) miles.
Cost as per plan A = Cost per week + Cost for \(m\) miles = $200 + $0.35\(m\)
Cost as per plan B = Cost per week + Cost for \(m\) miles = $180 + $0.55\(m\)
Now, putting both the costs equal to find the value of \(m\):
\(200 +0.35m = 180 +0.55m\\\Rightarrow 20 = 0.20m\\\Rightarrow m = \bold{100\ miles}\)
Therefore, after 100 miles the cost from each plan will be the same.
PLZ HELLLLLLPPPPPPPP!
WILL MARK BRAINLIEST!!!!!
Answer:
more than one than its a and b but only one than its a
If the two figures are congruent, which statement is true?
A. BCDA ≅ FEHG
B. ABCD ≅ EFGH
C. BADC ≅ EFGH
D. ADCB ≅ HGFE
Answer:
A
Step-by-step explanation:
the order of letter should resemble the same shape
help pls brainliest for whoever helps me ·ω·
Answer:
8
Step-by-step explanation:
Answer:
Answer is 8 :D
Step-by-step explanation:
The common factor of those 2 numbers are 1, 2,4,8 :)
A car rental agency charges $15 a day for driving a car 200 miles or less. If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven. Which of the following functions represents the cost to drive a car from this agency miles x a day?
The function which represents the cost to drive a car from this agency miles x a day is :
C(x) = 15, if 0 ≤ x ≤ 200
= 15 + 0.05x, if x > 200
Given that,
A car rental agency charges $15 a day for driving a car 200 miles or less.
The function can be written as,
C(x) = 15 if 0 ≤ x ≤ 200
If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.
C(x) = 15 + 0.05x, if x > 200
Hence the correct option is D.
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Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I estimate that the probability of my getting married in the next 3 years is 0.7. math
The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.
As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.
In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.
It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.
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5.6+12.9=11.3+[]
complete the missing number
Answer: 7.2
Step-by-step explanation: Cuz 5.6+12.9=18.5, 18.5-11.3=7.2
The missing number is 7.2.
We have the following expression.
5.6 + 12.9 = 11.3 + x
We have to find x.
What is a Decimal Number ?Decimal numbers include those numbers which have a whole number and the fractional part separated by a decimal point.
According to the question -
5.6 + 12.9 = 11.3 + x
x = 18.5 11.3 = 7.2
Hence, the missing number is 7.2
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Find ff 6x²y dA, where R is a region enclosed by 4x − 3y = 0, 4x − 3y = 1, x + 4y = 0, and x + 4y = 2. R Use the change of variables u = 4x − 3y and v = x + 4y. (Use symbolic notation and fractions where needed.) [[ 6x²³y dA= R
∬R 6x^2y dA = ∬R (6(4v + 3u)/25)^2((u - 4v)/25) |J| du dv
= ∬R 36(16v^2 + 24uv + 9u^2)(u - 4v)/625 du dv
Integrating over the new bounds of u and v (0 to 1 for u and 0 to 2 for v), we can evaluate the double integral.
To find the double integral of 6x^2y dA over the region R, where R is enclosed by the lines 4x - 3y = 0, 4x - 3y = 1, x + 4y = 0, and x + 4y = 2, we will perform a change of variables using u = 4x - 3y and v = x + 4y.
First, we need to find the Jacobian determinant of the transformation:
J = ∂(u,v)/∂(x,y) = (4 * 4) - (3 * 1) = 16 - 3 = 13.
Now, we can express x and y in terms of u and v:
4x - 3y = u
x + 4y = v
Solving these equations, we get:
x = (4v + 3u) / 25
y = (u - 4v) / 25
Next, we need to determine the new bounds of integration for u and v. The original region R can be expressed as follows:
0 ≤ 4x - 3y ≤ 1
0 ≤ x + 4y ≤ 2
Substituting the expressions for x and y in terms of u and v, we have:
0 ≤ u ≤ 1
0 ≤ v ≤ 2
Now, we can rewrite the integral in terms of u and v:
∬R 6x^2y dA = ∬R (6(4v + 3u)/25)^2((u - 4v)/25) |J| du dv
= ∬R 36(16v^2 + 24uv + 9u^2)(u - 4v)/625 du dv
Integrating over the new bounds of u and v (0 to 1 for u and 0 to 2 for v), we can evaluate the double integral.
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how many times does 9 go into 18
9 goes into 18 two times.
Here, we have,
To determine how many times 9 goes into 18,
we need to divide 18 by 9.
now, we have,
When we divide 18 by 9, the result is 2.
i.e. 18/9 = 2
This means that 9 goes into 18 exactly 2 times without any remainder.
Therefore, 9 goes into 18 two times.
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Please help need to know the answer
It should be noted that the month when the.price of his phone will be less in website B than website A is D. 8.
How to illustrate the information?It should be noted that there are two websites that have different functions relating to the cost which was illustrated.
Website A = 500(0.85)^t
when t = 8, the cost will be:
50(0.85)^t
= 50(0.85)^8
= $13.6
It should be noted that for website B, the cost is illustrated as:
Website B = 50 - 5t
B = 50 - 5(8)
= 50 - 40
= 10
Therefore, it should be noted that the month when the.price of his phone will be less in website B than website A is 8.
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26) If a = 5 and b= 10, use the formula below to approximate the distance between the planes to the nearest
hundredth.
Answer: 11.18 mi
Step-by-step explanation:
They give us all the information we need to solve. We will be using the Pythagorean theorem to help us solve this question.
Given:
a² + b² = c²
Substitue values:
5² + 10² = c²
Square values:
25 + 100 = c²
Addition:
125 = c²
Square root both sides:
\(\sqrt{125}\) = c
Square root and round at hundredths place:
c ≈ 11.18 mi
Answer:
11.18 miles
Step-by-step explanation:
We see a right triangle here
and a² + b² = c² shows the relationship between all sides of the triangle
c is the hypotenuse and also the distance between the planes.
Let's plug in the values 5 and 10 in the equation to find c
(5)² + (10)² = c²
Solve!
25 + 100 = c²
125 = c²
find the square root of 125
√125 = √c²
c ≈ 11.18 miles