Answer: The answer provided is based on the following calculation:
To make a 75% syrup, Ella should add enough water to the sugar to create a solution that is 25% sugar and 75% water.
To calculate how much water to add, you can use the formula: (desired % of sugar) / (100 - desired % of sugar) * (amount of sugar).
In this case, it would be: (0.75) / (100 - 0.75) * (0.5 lb) = 0.67 lb of water.
To calculate the total amount of syrup, you add the amount of sugar and the amount of water: 0.5 lb + 0.67 lb = 1.17 lb.
So Ella should add 0.67 lb of water to make a 75% syrup and will have a total of 1.17 lb syrup.
Step-by-step explanation:
Answer:
for the 75% syrup: 0.167lbs
For the 1.5% syrup: 32.83 lbs
The cost of packing a box of chocolates is given by 1/4 x^2, where x is the number of chocolates (a box can never have fewer than 3 chocolates). If the weight of a box of
chocolates is given by x + 2, what is the cost of packaging per weight unit
The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.
We have,
To find the cost of packaging per weight unit, we need to calculate the cost of packaging (C) and divide it by the weight of the chocolates (W).
Given:
Cost of packaging (C) = 1/4 x²
Weight of chocolates (W) = x + 2
To find the cost of packaging per weight unit, we can express it as C/W.
Substituting the given expressions:
C/W = (1/4 x²) / (x + 2)
To simplify the expression, we can first simplify the numerator:
C/W = (1/4 x²) / (x + 2)
= (1/4) x (x² / (x + 2))
= (1/4) x (x(x) / (x + 2))
= (1/4) x (x / (x + 2)) * x
Now, we can rewrite the expression as:
C/W = (1/4) x (x / (x + 2)) x
Therefore,
The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.
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If $850 is invested in an account that earns 2.6% yearly interested compounded quarterly, then which of the
following is the worth of this investment after 5 years?
(3) $967.60
(4) $968.25
(1) $960.50
(2) $966.40
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$850\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 850\left(1+\frac{0.026}{4}\right)^{4\cdot 5}\implies A=850(1.0065)^{20} \implies A \approx 967.60[/tex]
Fatoumata has a bag that contains orange chews, apple chews, and watermelon chews. She performs an experiment. Fatoumata randomly removes a chew from the bag, records the result, and returns the chew to the bag. Fatoumata performs the experiment 29 times. The results are shown below: A orange chew was selected 6 times. A apple chew was selected 10 times. A watermelon chew was selected 13 times. Based on these results, express the probability that the next chew Fatoumata removes from the bag will be orange or apple as a percent to the nearest whole number
The probability that the next chew Fatoumata removes from the bag will be orange or apple, rounded to the nearest whole number, is approximately 55%.
To calculate the probability that the next chew Fatoumata removes from the bag will be either orange or apple, we need to determine the total number of times an orange or apple chew was selected.
From the given results, Fatoumata selected an orange chew 6 times and an apple chew 10 times. To find the probability, we add the number of occurrences for each chew:
Orange chews: 6 times
Apple chews: 10 times
Total occurrences of orange or apple chews: 6 + 10 = 16
Fatoumata performed the experiment a total of 29 times. So, the probability of selecting an orange or apple chew can be calculated as:
Probability = (Total occurrences of orange or apple chews) / (Total number of experiments) = 16 / 29
To express this probability as a percentage, we multiply the probability by 100:
Probability (as a decimal) = 16 / 29 ≈ 0.5517
Probability (as a percentage) = 0.5517 × 100 ≈ 55.17%
Therefore, the probability that the next chew Fatoumata removes from the bag will be orange or apple, rounded to the nearest whole number, is approximately 55%.
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The proportional relationship between cost and pints of blueberries is shown in the table. Blueberries (in pints) 4 10 Cost (in dollars) 18.40 46 Describe what a graph of the proportional relationship would look like.
The graph of the proportional relationship is a linear graph, with slope of 4.6 and intercept of zero.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
Hence the graph is a linear function with slope of k and intercept of zero.
The cost of 4 pints is of $18.4, and the cost of 10 pints is of $46, hence the slope of the relation is given as follows:
k = 46/10 = 18.4/4 = 4.6.
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What’s the lateral area of this
Answer:
240 in²
Step-by-step explanation:
You want the lateral area of a triangular prism with triangular base having sides 6 in, 8 in, and 10 in, and a distance between them of 10 in.
Lateral areaThe lateral area of a triangular prism is the area of the three rectangular faces. The width of those faces is the "height" of the prism, given as 10 in. The total length of those faces is the perimeter of the base:
6 in + 8 in + 10 in = 24 in
The lateral area is ...
A = LW = (24 in)(10 in) = 240 in²
<95141404393>
Which graph has the same end behavior as f(x)=(10x^(3)+x^(2)+3)/(2x^(2)+1)?
The graph that has the same end behavior as f(x)= (10x³+x²+3)/(2x²+1) is Option A. See the attached.
What is the end behavior of the above graph?the end behavior of the graph of f(x) is:
As x → +∞ , f(x) → +∞ (approaches positive infinity).
As x → -∞, f(x) → -∞ (approaches negative infinity).
End behavior of a function f defines the behavior of the function's graph at the "ends" of the x- axis.
In other words, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +∞) and the left end of the x -axis (as x approaches - ∞ ).
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
The exact value of sin θ is 9/13.
Option A is the correct answer.
We have,
In trigonometry,
The sine function (sin) represents the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.
The cosecant function (csc) is the reciprocal of the sine function, meaning it is equal to 1 divided by the sine of an angle.
In this case,
We are given that csc θ (the cosecant of θ) is equal to 13/9.
To find the value of sin θ (the sine of θ), we can take the reciprocal of csc θ. So,
sin θ = 1/(csc θ) = 1/(13/9) = 9/13.
Therefore,
The exact value of sin θ is 9/13.
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Ashley got a prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 13 cents per yard. If after that purchase there was $25.06 left on the card, how many yards of ribbon did Ashley buy?
Answer:
38 yards
Step-by-step explanation:
First, subtract to find out how much money was spent.
30 - 25.06
= 4.94
Then divide to find out how many groups of $0.13 are in $4.94.
4.94 ÷ .13
= 38
Ashley bought 38 yards of ribbon.
38 × .13 = 4.94
4.94 + 25.06 = 30
This answer does not consider tax at all. Because it wasn't mentioned in the question and it complicates the problem. So probably don't worry about tax. Unless your teacher /book/program said to consider it. I can edit the answer.
Also, if they said to write an equation:
Let x = yards of ribbon
30 - .13x = 25.06
subtract 30
-.13x = -4.94
divide by -.13
x = 38
can some one
factor 7a10 - 112a2
The factored of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
How to find the factor 7a10 - 112a2To factor the expression [tex]7a^{10} - 112a^2[/tex] we can identify the greatest common factor (GCF) and factor it out. Let's break down the steps:
The coefficients 7 and 112 have a common factor of 7.
The lowest power of "a" in each term.
In this case, the lowest power of "a" is 2.
Factoring out [tex]7a^2[/tex] from both terms, we get:
[tex]7a^2(a^8 - 16)[/tex]
Therefore, the factored form of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
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AC = 3x-10. BD = x+34. Solve for X.
The value of x in the figure is 22 as the diagonals are equal
Diagonals of a parallelogram are the line segments connecting two non-adjacent vertices of a parallelogram
Both the AC and BD are equal
AC=3x-10
BD=x+34
As two diagonals are equal
3x-10=x+34
We have to solve for x
3x-x=10+34
2x=44
Divide both sides by 2
x=22
Hence, the value of x in the figure is 22
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HELPPP
MA.7.DP.1.2
A group of students in the book club are debating whether high school juniors or seniors
spend more time on homework. A random sampling of juniors and seniors at the local high
school were surveyed about the average amount of time they spent per night on homework.
The results are listed in the table below.
Average Amount of Time on Homework Per Night (in minutes)
Juniors 125 90 95
80 100 100 120- 85 95 120 95 85
Seniors 135 70 65 100 35 175 80 80 90 65 120 60
Part A. Calculate and compare the measures of center for the data sets.
Part B. Calculate and compare the variability in each distribution.
Part C. Does the data support juniors or seniors spending more time on homework?
Explain your reasoning.
Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42
Median (Juniors) = (95 + 95) / 2 = 95
Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25
Median (Seniors) = (80 + 80) / 2 = 80
How to solve for the median of centerJuniors: 125, 90, 95, 80, 100, 100, 120, 85, 95, 120, 95, 85
First, sort the data: 80, 85, 85, 90, 95, 95, 95, 100, 100, 120, 120, 125
Sum = 1085
Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42
Median (Juniors) = (95 + 95) / 2 = 95
Seniors: 135, 70, 65, 100, 35, 175, 80, 80, 90, 65, 120, 60
First, sort the data: 35, 65, 65, 70, 80, 80, 90, 100, 120, 120, 135, 175
Sum = 1095
Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25
Median (Seniors) = (80 + 80) / 2 = 80
Variability
Juniors:
Range = max - min = 125 - 80 = 45
Seniors:
Range = max - min = 175 - 35 = 140
C. Based on the mean and median, it appears that seniors spend slightly more time on homework on average (mean ≈ 91.25) compared to juniors (mean ≈ 90.42).
However, the median time spent for seniors (80 minutes) is less than that of juniors (95 minutes), indicating that the data for seniors might be skewed by some outliers.
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Can someone answer this question
The function is a quadratic function, and none of the given options is a factor of the graph of the function.
Here,, we have,
to determine the factor:
The zeros of the function are given as:
-3 and 5
This means that:
x = -3 and x = 5
Rewrite as:
x + 3 = 0 and x - 5 = 0
Multiply both equations
(x + 3)(x -5) = 0 * 0
This gives
(x + 3)(x -5) = 0
Express as a function
f(x) = (x + 3)(x -5)
The above means that the factors of the function are (x + 3) and (x -5)
Hence, none of the given options is a factor of the graph of the function
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complete question:
Graph of a function, f(x), has zeros at - 3, and 5. Which of
following is a factor of f(x)?
(2x - 3)
(2x + 3)
(3x + 2)
(x + 5)
Table 13-15
Labor Output Marginal
Product Variable
Cost Fixed
Cost
0 0 -- $0 $5
1 100 100 $5 $5
2 250 $10 $5
3 350 $15 $5
4 50 $20 $5
5 25 $25 $5
6 430 $30 $5
5. Refer to Table 13-15. What is the marginal product of the second worker?
150
6. Refer to Table 13-15. What is the total output of five workers?
7. Refer to Table 13-15. What is the marginal product of the sixth worker?
8. Refer to Table 13-15. What is the average total cost of producing 425 units of output?
9. Refer to Table 13-15. What is the average variable cost of producing 400 units of output?
10. Refer to Table 13-15. What is the average fixed cost of producing 430 units of output?
1. The marginal product of the second worker is 150 units.
2. The total output of five workers is 75 units.
3. The marginal product of the sixth worker is 405 units.
4. The average total cost of producing 425 units of output is $30.
5. The average variable cost of producing 400 units of output is $20.
6. The average fixed cost of producing 430 units of output is $0.07.
What is the answers to the question?The marginal product of the second worker:
= (Output of 2 workers - Output of 1 worker)
= (250 - 100)
= 150 units
The total output of five workers is:
= Output of 4 workers + Marginal product of the fifth worker
= 50 + 25
= 75 units
The marginal product of the sixth worker is:
= (Output of 6 workers - Output of 5 workers)
= (430 - 25)
= 405 units.
The average total cost to produce 425 units is:
= (Total variable cost + Total fixed cost) / Total output
The total variable cost is $30 * 425 = $12,750
The total fixed cost is $5 * 6 = $30
Total cost = $12,750 + $30 = $12,780
The Average total cost is:
$12,780 / 425
= $30
The average variable cost to produce 400 units is:
= Total variable cost / total output
Total variable cost is $20 * 400 = $8,000
Average variable cost = $8,000 / 400 = $20
The average fixed cost to produce 430 units is:
= Total fixed cost / Total output
Total fixed cost is $5 * 6 = $30
The average fixed cost is:
= $30 / 430
= $0.07.
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please help me solve for x image is attached ive been stuck on it for a few days now
The value of x will be 10.
Given a triangle we need to set a proportion to solve for the value of x,
Therefore, according to the definition of the similar triangles,
x / 5 = 15+5 / x
x² = 5 × 20
x² = 100
x = 10
Hence the value of x will be 10.
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ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
A car's speedometer has a percent error of 5%. The actual speed of the car is 60 mph.
Which statement describes what speed the speedometer could show?
A: The speedometer shows either 57 mph or 63 mph.
B: The speedometer shows either 58 mph or 62 mph.
C: The speedometer shows either 55 mph or 65 mph.
D: The speedometer shows either 30 mph or 90 mph.
Answer:
maybe a
Step-by-step explanation:
as t percent of 60 is 3
so it will show 57 or 63
La siguiente gráfica muestra las calificaciones de un grupo de 40 alumnos que van desde el mínimo 7 hasta el máximo 10 de calificación. ¿Cuántos alumnos sacaron 9?
The specific data points or the Frequency distribution of grades for the 40 students.
The specific information from the graph , the exact number of students who received a grade of 9.
If the graph represents the distribution of grades of 40 students on a scale from 7 to 10, we can estimate the number of students who received a grade of 9 by considering the shape of the graph.
the graph is a normal distribution or bell curve, with the majority of students clustered around the mean (which is likely to be around 8.5 or 9), we can expect a significant number of students to have received a grade of 9. In a typical bell curve distribution, the highest density of scores is around the mean.
without additional information about the shape of the graph or the specific values represented on the x-axis, it is difficult to provide an accurate estimation of the number of students who received a grade of 9. The graph may represent a variety of distributions, such as skewed, bimodal, or uniform.
the exact number of students who received a grade of 9, the specific data points or the frequency distribution of grades for the 40 students.
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Based on the information given regard to the graph, there are 6 students who got 9.
How to explain the valueA graph is a diagram such as a series of one or more points, lines, line segments, curves, or areas which represents the variation of a variable in comparison with that of one or more other variables.
The collection of all points whose coordinates satisfy a given relation such as a function.
The graph shows that there are 4 students who got 7, 8 students who got 8, and 12 students who got 10. This leaves:
40 - 4 - 8 - 12
= 6 students who got 9.
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NO LINKS!! URGENT HELP PLEASE!!!
O is the center of the decagon below. Find its area. Round to the nearest tenth if necessary.
Answer:
752.4
Step-by-step explanation:
Here we are provided with a decagon which has 10 sides.
The total interior angle is 360°.
So each will have 360/10 = 36 degrees
Half of that is 18 degrees inside the triangle.
Refer to the attachment below.
opposite = 16sin(18)
adjacent = 16cos(18)
Find the area of this triangle:
= 1/2 × 16sin(18) × 16cos(18)
= 37.61825
There are 20 triangles just like this so the total area is (37.61825 × 20) = 752.365 ≈ 752.4 unit2
Please help!!! Correct answer gets brainliest!!!
100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!
The given quadrilateral is a parallelogram by the theorem "The diagonals of a parallelogram bisect each other."
Given is a quadrilateral.
We have to determine that the quadrilateral is a parallelogram or not.
From the shape and the drawing given, the quadrilateral is a parallelogram.
A parallelogram has opposite sides parallel to each other.
Here it is parallel.
Here it is given that the diagonals are bisected by each other, that is two parts of the diagonals are of equal length.
We have a theorem that "The diagonals of a parallelogram bisect each other."
A square, rectangle, rhombus can be included in the group of parallelogram.
So this is a parallelogram.
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The following table represents the highest educational attainment of all adult residents in a certain town. If an adult is chosen randomly from the town, what is the probability that they have a high school degree or some college, but have no college degree? Round your answer to the nearest thousandth.
The probability that a random adult has a high school degree or some college, but has no college degree is 53. 50 % .
How to find the probability ?The number of adults with some high school degree or some college would be :
= 3, 561 + 6, 058
= 9, 619 people
The probability that a random adult would have high school degree or some college is therefore :
= Adults with high school degree or some college / Total adults in the town
= 9, 619 / 17, 981
= 53. 50 %
In conclusion, the probability is 53. 50%.
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A person buy a lot of tickets for Rs.136 each execution class ticket cost rupees12 and each local class ticket cost for Rs 4 each make an equation and fine explain possible solutions
Answer:
3.98
Step-by-step explanation:
Answer:
the second method may be through graph
evaluate 3y(9-x) when y=3 and w=7
The numeric value of the expression 3y(9 - x) when y = 3 and x = 7 is given as follows:
18.
How to find the numeric value of a function at a point?To obtain the numeric value of a function or even of an expression, we must substitute each instance of the variable of interest on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The expression in the context of this problem is given as follows:
3y(9 - x).
Hence the numeric value when x = 7 and y = 3 is given as follows:
3 x 3 x (9 - 7) = 3 x 3 x 2 = 18.
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1 secX + 3 = cosX + tanX (2+ sinX)
The solution for X is X ≈ [tex]tan^{(-1)(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.
Given: 1 secX + 3 = cosX + tanX (2 + sinX)
To simplify the equation, let's express secX and tanX in terms of sinX and cosX:
1/cosX + 3 = cosX + sinX/cosX (2 + sinX)
Now, multiply both sides by cosX to eliminate the denominators:
[tex]1 + 3cosX = cos^2X + sinX(2 + sinX)[/tex]
Expanding the equation:
[tex]1 + 3cosX = cos^2X + 2sinX + sin^2X[/tex]
Since [tex]sin^2X + cos^2X[/tex] equals 1 (based on the Pythagorean identity), we can substitute it into the equation:
[tex]1 + 3cosX = 1 + 2sinX + sin^2X[/tex]
Rearranging the terms:
[tex]3cosX = 2sinX + sin^2X[/tex]
Now, let's express cosX in terms of sinX using the Pythagorean identity:
cosX = √(1 - [tex]sin^2X[/tex])
Substituting this into the equation:
3√(1 - [tex]sin^2X) = 2sinX + sin^2X[/tex]
Squaring both sides to eliminate the square root:
[tex]9(1 - sin^2X) = (2sinX + sin^2X)^2[/tex]
Expanding the right side:
[tex]9(1 - sin^2X) = (2sinX)^2 + 2(2sinX)(sin^2X) + (sin^2X)^2\\9 - 9sin^2X = 4sin^2X + 4sin^3X + sin^4X[/tex]
Rearranging the terms:
[tex]sin^4X + 4sin^3X + 4sin^2X + 9sin^2X - 9 = 0[/tex]
Combining like terms:
[tex]sin^4X + 4sin^3X + 13sin^2X - 9 = 0[/tex]
Unfortunately, this equation does not have a simple algebraic solution. It needs to be solved numerically or graphically. Using numerical methods or a graphing calculator, we can find that one solution to this equation is sinX ≈ 0.7429.
Taking the inverse tangent (arctan) of both sides, we have:
X = arctan(0.7429)
Therefore, the solution for X is X ≈ t[tex]an^{(-1)}(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.
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Explain what is meant by a positive relationship between two variables and a negative relationship between two variables. Give an example of a situation in which you would expect to find a positive relationship and when you would expect to find a negative relationship.
Answer: A positive relationship between two variables means that as the value of one variable increases, the value of the other variable also increases. In other words, there is a direct association or correlation between the two variables. Graphically, a positive relationship is represented by an upward-sloping line or curve.
For example, let's consider the relationship between studying time and exam scores. In general, if a student spends more time studying for an exam, their exam score is likely to increase. This implies a positive relationship between studying time and exam scores.
On the other hand, a negative relationship between two variables means that as the value of one variable increases, the value of the other variable decreases. In this case, there is an inverse association or correlation between the two variables. Graphically, a negative relationship is represented by a downward-sloping line or curve.
For instance, let's consider the relationship between hours of sleep and levels of fatigue. As the number of hours of sleep decreases, the level of fatigue tends to increase. This indicates a negative relationship between hours of sleep and levels of fatigue.
It's important to note that these examples describe typical scenarios, but individual variations and other factors can also influence the relationships between variables.
Find the slope of the line.
A. 3/2
B. -2/3
C. 4/3
D. -3/4
Answer:
-3/4, answer D
Step-by-step explanation:
Slope = rise/run. The equation is (y2-y1)/(x2-x1).
So let's pick 2 points. There are pink dots on (-2,2) and (6,-4), so we'll use those points.
slope = (2-(-4))/(-2-6)
slope = (2+4)/(-2-6)
slope = (6)/-8, which we can simplify by dividing the numerator and denominator each by 2.
slope = -3/4
Just as a quick check, this makes sense because as x increases, y decreases so we should expect the slope to be negative.
Answer:
Step-by-step explanation:
Use 2 points from the line: (-2, 2) and (6, -4)
slope = y2 -y1 = -4 - 2 = -6 = - 3
x2 - x1 6 - -2 8 4
The slope is choice D -3/4
Question 8
Match each compound to its correct type.
8.1
CO
hydroxide
8.2
CO₂
carbonate
8.3
SO₂
8.4
CaCO
8.5
NaOH
oxide
trioxide
dioxide
The correct matching of each compound to its type:
8.1 CO - oxide
8.2 CO₂ - dioxide
8.3 SO₂ - dioxide
8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)
8.5 NaOH - hydroxide
8.1 CO - oxide
8.2 CO₂ - dioxide
8.3 SO₂ - dioxide
8.4 CaCO - carbonate
8.5 NaOH - hydroxide
Here is the correct matching of each compound to its type:
8.1 CO - oxide
8.2 CO₂ - dioxide
8.3 SO₂ - dioxide
8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)
8.5 NaOH - hydroxide
Compound 8.4, CaCO, is not correctly represented. It should have a subscript to indicate the number of atoms present in the compound.
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Find g(x), where g(x) is the translation 2 units left and 4 units down of f(x)=x^2.
Write your answer in the form a(x–h)^2+k, where a, h, and k are integers.
g(x) =
The function g(x) in the form a(x-h)^2 + k is: [tex]g(x) = (x + 2)^2 - 4[/tex]
Starting with[tex]f(x) = x^2[/tex], the translation 2 units left and 4 units down would result in the following transformation:
g(x) = f(x + 2) - 4
Substituting[tex]f(x) = x^2:[/tex]
[tex]g(x) = (x + 2)^2 - 4[/tex]
Expanding the square:
[tex]g(x) = x^2 + 4x + 4 - 4[/tex]
Simplifying:
[tex]g(x) = x^2 + 4x[/tex]
Now we need to rewrite this expression in the form [tex]a(x-h)^2 + k.[/tex] To do this, we will complete the square:
[tex]g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4[/tex]
Therefore, the function g(x) in the form a(x-h)^2 + k is:
[tex]g(x) = (x + 2)^2 - 4[/tex]
Where a = 1, h = -2, and k = -4.
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use the linear combination method to solve the system of equations. Explain each step of your solution. 2x-3y=13 x+2y=-4
Answer:
Solution: x = 2, y = -3.
Step-by-step explanation:
Given system of equations:
Equation 1: 2x - 3y = 13
Equation 2: x + 2y = -4
Multiply Equation 2 by 2:
2(x + 2y) = 2(-4)
Simplified: 2x + 4y = -8
Add Equation 1 and Equation 3:
4x + y = 5
Solve Equation 4 for y:
y = 5 - 4x
Substitute y into Equation 2:
x + 2(5 - 4x) = -4
Simplify:
-7x + 10 = -4
Solve for x:
x = 2
Substitute x into Equation 5:
y = 5 - 4(2)
y = -3
Solution: x = 2, y = -3.
Find the gradient of the line segment between the points (-2,3) and (0,2).
Give your answer in its simplest form.
Answer:
[tex]\dfrac{-1}{2}[/tex]
Step-by-step explanation:
Slope or gradient:(-2 , 3) ⇒ x₁ = -2 & y₁ = 3
(0 , 2) ⇒ x₂ = 0 & y₂ = 2
[tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{2-3}{0-[-2]}\\\\\\=\dfrac{-1}{0+2}\\\\=\dfrac{-1}{2}[/tex]
Sarah wants to buy a new laptop. Store A is currently selling the laptop for $1,640 with an additional 20% off. Store B is selling the laptop for $1,500 with an additional 10% off. Which store offers a better deal?
Answer:
Store A
Step-by-step explanation:
If an item is 20% off, then you pay 80% of the price.
If an item is 10% off, then you pay 90% of the price.
Store A
80% of $1640 = 0.8 × $1640 = $1312
Store B
90% of $1500 = 0.9 × $1500 = $1350
Answer: Store A
Answer:
Store A
Step-by-step explanation:
Store A offers a 20% discount which is equivalent to 0.20 x $1,640 = $328.
The laptop is therefore sold for $1,640 - $328 = $1,312 at Store A.
Store B offers a 10% discount which is equivalent to 0.10 x $1,500 = $150.
The laptop is therefore sold for $1,500 - $150 = $1,350 at Store B.
Therefore, Store A offers a better deal at $1,312 compared to Store B at $1,350.