What are the ordered pairs of the
solutions for this system of equations?
f(x) = x2 – 2x + 3; f(x) = –6x
(-3, [?]); ([ ]), ([ ])
Answers
Answer:
[tex] {x}^{2} - 2x + 3 = - 6x \\ = {x}^{2} - 2x + 6x + 3 = 0 \\ \\ = {x}^{2} + 4x + 3 = 0 \\ = (x + 1)(x + 3) \\ = x = - 1and \: x = - 3[/tex]
Related Questions
Write a linear inequality to represent the information given. Shanley would like to give $5 gift cards and $8 teddy bears as party favors. Shanley has $144 to spend on party favors. Enter an inequality to find the number of gift cards x and teddy bears y Shanley could purchase. Give one solution to the inequality.
Answers
16 gift cards and 8 teddys
Solve the system by graphing ツ= 3x ツ = -3x + 6
Answers
Answer:
(1, 3)
Step-by-step explanation:
Using a graphing website like Desmos or a graphing calculator, we can figure out the solution: (1, 3)
wHAT IS THE NEXT NUMBER IN THE FOLLOWING SERIES OF NUMBERS 1,4,8,13,19
Answers
Answer:
26
Step-by-step explanation:
a_n = 1/2 (n^2 + 3 n - 2) (for all terms given)
1, 4, 8, 13, 19, 26, 34, 43, 53, 64, 76, 89, 103, 118, 134, 151, 169, 188, 208, 229, ...
Answer:
26
Step-by-step explanation:
The difference between 1 and 4 is 3
The difference between 4 and 8 is 4
The difference between 8 and 13 is 5
The difference between 13 and 19 is 6
The difference between 19 and 26 is 7
Kara is flying to Hawaii. If her packed suitcase weighs more than 50 pounds
when she checks in at the airport, she will have to pay a fee. Her empty suitcase
weighs 11.3 pounds, and she has to pack all her camera equipment, which
weighs 14.25 pounds. To stay under the weight limit, what is the maximum
possible weight of her other packed items?
Answers
In a sale, normal prices are reduced by 15%. The normal price of a pen is reduced by £1.20 Work out the normal price of the pen.
Answers
Answer:
The normal price of a pen is £8
Step-by-step explanation:
let p be the normal price.
The statement : “normal prices are reduced by 15%. The normal price of a pen is reduced by £1.20”
Means
[tex]p \times \frac{15}{100} = 1.20[/tex]
Then
[tex]p = 1.20 \times \frac{100}{15} = \frac{120}{15} = 8[/tex]
Answer:
The normal price of the pen is £8
Step-by-step explanation:
Reduced by 15%
Reduced by £1.20
Meaning that 15% is £1.20
To find the 100% or the normal price of the pen we find the 1% first then the 100%
So, 1% = £1.20/15
100% =£1.20/15 x 100
= 8
Checking..
If normal price was 8 and reduction is 15%
8(1- R/100) {R = %}
8(1 -15/100) = 6.8 (Reduced price)
8 - 6.8 = £1.20 ( Reduction price aka the 15%)
Therefore, the normal price of the pen is £8.
Savannah takes a car to a title loan business to borrow some money. Savannah is given $2,900.00. She must pay back the $2,900.00 in addition to a $1,375.00 fee in 8 months.
What simple interest rate is she
being charged?
Round to the nearest tenth of a percent and don't forget to include a percent sign, %, in your answer.
Savannah is being charged a simply interest rate of ______.
Answers
Step-by-step explanation:
To find the simple interest rate that Savannah is being charged, we can use the formula for simple interest:
I = P * r * t
where I is the total interest paid, P is the principal (the amount borrowed), r is the interest rate, and t is the time period over which the interest is paid.
Since Savannah must pay back the $2,900.00 principal plus a $1,375.00 fee, the total interest paid is $1,375.00. The time period is 8 months, which is equal to 8/12 = 2/3 of a year. Substituting these values into the formula and solving for r, we get:
$1,375.00 = $2,900.00 * r * (2/3)
r = $1,375.00 / ($2,900.00 * (2/3)) = 0.1429
This is the interest rate that Savannah is being charged. To express this rate as a percentage, we can multiply it by 100% to get:
r = 0.1429 * 100% = 14.3%
Therefore, Savannah is being charged a simple interest rate of approximately 14.3%.
A researcher performs three independent hypothesis tests each at the 5% significance level.
Determine the probability of observing at LEAST one Type I Error. (Round your final answer to the nearest hundredth of a percent)
Answers
The probability of observing at least one Type I Error is 16.67%.
What is probability?Probability is the likelihood of an event occurring, expressed as a number between 0 and 1. It is a measure of how likely it is that something will happen, given the conditions and information available. Probability is the foundation of statistics, which is the science of making decisions when faced with uncertainty. Probability can be used to make predictions about future events and to help us understand how likely various outcomes are.
A Type I Error, also known as a false positive, occurs when an experiment incorrectly rejects a true null hypothesis. This probability can be calculated by multiplying the probability of a Type I Error occurring in each test (0.05) three times, yielding 0.125 (or 12.5%).
We then add 1 minus that probability, which yields 0.167 (or 16.67%). In other words, the probability of observing at least one Type I Error in the three tests is 16.67%.
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what is 10+40-11+100=
Answers
Answer:139 is the answer
Step-by-step explanation:
So the answer is 139
27 POINTS!! The price of 2 items in P and Q come to a ratio of 4:5. When the price of P is increased of $12 and the price of Q is reduced by $6,the items have the same price. Find the original price of P
Answers
The original price P will be $72
To find the ratiosIf we know that the ratio from P to Q is 4:5, we can multiply both sides by y (y = amount multiplied) to get our numbers.
4 × y =?
5 × y =?
We need to input a value in for y.
Let's put 9.
4 × 9 = 36 (P)
5 × 9 = 45 (Q)
Now adding 12 to P, and take away 6 from Q.
36 + 12 = 48
45 - 6 = 39
The numbers aren't the same yet.
Let's use a different value for y.
y = 18
The equations will now look like this:
4 × 18 = 72 (P)
5 × 18 = 90 (Q)
Let's add 12 and 6 to the numbers again.
72 + 12 = 84
90 - 6 = 84
The numbers are now equal
Therefore, the original price of P = $72
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2 3X Find the solution set for each of the following equations. a 20x² + 10x -8=0 b x² − 8x + 15 = 0 3X C
Answers
The Solution set of the given quadratic equations are
1. x = 5 or x = 3
2. x= -3/2 or x = 5
What is quadratic equation?A Quadratic equation is an algebraic expression in which highest degree of the given variable is 2.
Formula used as x² +ax + b = (x + c)(x + d)
Where 'a' is the sum 'c' and 'd' and 'b' is the product of 'c' and 'd'
According to the information, Factorize all the given quadratic equations we get;
1. x² - 8x + 15 =0
Now Split middle term of quadratic equation using formula we get,
x² - 5x - 3x + 15 =0
⇒ x(x- 5) -3(x - 5) =0
⇒(x -5)(x - 3) =0
⇒ x- 5 =0 or x - 3 =0
⇒ x= 5 or x = 3
2. 20x² + 10x -8=0
Now Split middle term of quadratic equation using formula we get,
10x² + 5x - 4 = 0
⇒ 2x(x-5) +3(x-5)=0
⇒(2x+3)(x-5)=0
⇒2x+3 =0 or x-5 =0
⇒ x= -3/2 or x=5
Hence, the solution set are
1. x = 5 or x = 3
2. x= -3/2 or x = 5
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The length of a rectangle is 1 7/9 inches and its width is 3/4 of its length. Find the area of this rectangle.
Answers
Answer:
Area = 2 10/27 inch²
Step-by-step explanation:
Length: 1 7/9 inches
Width: (3/4)(1 7/9 inches)
Area = Length × Width
Area = (1 7/9 inches) × (3/4)(1 7/9 inches)
Area = 16/9 inches × 16/9 inches × 3/4
Area = 768/324 inch²
Area = 256/108 inch²
Area = 128/54 inch²
Area = 64/27 inch²
Area = 2 10/27 inch²
PLEASE HELP ASAP
Three key features of a linear function are described as shown.
• The graph of the function has a y-intercept of (0, 3) .
• The function is increasing over its entire domain.
• The x-intercept of the function is (-4, 0).
Answers
Answer:
y = 3/4 x + 3
Step-by-step explanation:
slope of the line :
(0-3)/(-4-0)
-3/-4
3/4
y = 3/4 x + 3
Please help this is percentages.
Answers
The percentage of boys in the class is 60% and the percentage of girls in the class is 40%.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Total number of students in class = 45
Total number of boys in the class = 27
Then, the percentage of boys in the class will be,
Let the percentage of boys be x.
x% Of 45 = 27
x = (27 × 100)/45
x = 2700/45
x = 60%
Then, total number of girls in the class = 45 - 27 = 18
Assume the percentage of girls in the class be y.
y% Of 45 = 18
y = (18 × 100)/45
y = 1800/45
y = 40%
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Suppose continuous random variable Y has cumulative distribution function FY (y), and density
function fY (y) > 0. Let random variable U = FY (Y ), find the density function of U, and identify its
distribution (name and parameter(s)) if possible.
Answers
Since, U = FY(Y) is uniform distribution (i.e. U(0, 1)).
In the given question, suppose continuous random variable Y has cumulative distribution function FY (y), and density function fY (y) > 0.
Let random variable U = FY (Y ).
We have to find the density function of U, and identify its distribution (name and parameter(s)) if possible.
A random variable Y has cumulative distribution function FY (y).
A random variable Y has density function f(y).
Let U = FY(Y)
Now we have to find the density function of U using cumulative distribution function method
FU(u) = P(U≤u)
FU(u) = P(FY(Y) ≤ u)
FU(u) = P(Y ≤ F (u))
FU(u) = FY(F (u))
FU(u) = u
fU(u) = F'U(u).1
fU(u) = 1
fU(u) = 1, 0<u<1
Here U = FY(Y) is uniform distribution (i.e. U(0, 1)).
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Evaluate the function for the given values of a and b then use the intermediate value theorem to determine which of the statements below is true.
a=-1 and b =0
f(x)=6x^3-9x^2-7x+3
a).f(-1) and f(0) have the same sign, therefore the function f has a real zero between -1 and 0
b.)f(-1) and f(0) have opposite signs, therfore the function f does not have a real zero between -1 and 0
c.) f(-1) and f(0) have the opposite sign, therefore the function f has a real zero between -1 and 0
d.) f(-1) and F(0) have the same sign, therefore intermediate value theorem cannot be used to determine wheter the function f has a real zero between -1 and 0
Answers
The function f has a real zero between -1 and 0. Therefore, statement c) is true.
To evaluate the function for the given values of a and b, we can plug in the values of a and b into the function and solve.
For a=-1, we get:
f(-1) = 6(-1)^3 - 9(-1)^2 - 7(-1) + 3 = 6 - 9 + 7 - 3 = 1For b=0, we get:
f(0) = 6(0)^3 - 9(0)^2 - 7(0) + 3 = 3Therefore, f(-1) and f(0) have opposite signs (one is positive and one is negative).
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3. draw the circuit for an sr flip-flop given the characteristic table, equation and state diagram. (8pts)
Answers
The logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)
What is SR flip-flop?A gated set-reset flip-flop is an SR flip-flop.
The flip-flop is controlled by the S and R inputs when the clock pulse changes from LOW to HIGH.
Till the clock pulse is on a rising edge, the flip-flop won't alter.
There is a chance that the outputs will be HIGH or LOW when S and R are both HIGH at the same time.
A global flip flop with two inputs, the JK flip flop has the letters "J" and "K."
While J and K are not the reduced abbreviated letters for Set and Reset in the SR flip flop, S and R are.
SR flip-flop equation: Qn+1 = S + QnR'
(Refer to the images attached below)
Therefore, the logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)
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1. Anya is at camp and walks 2km due north and then turns and walks another 3km at a bearing angle of 35° . Find her distance back to camp and the bearing angle from her starting point.
Answers
Anya her distance back to camp and the bearing angle from her starting point is 4.78 km North 26.3° West.
Define direction ?
Direction gives the information about the way towards which an object moves or tends.
The angle formed by the 2 km and 3 km is the supplement of the 35 ° angle west of north;
180°- 35° = 145°
We know that the length of two sides and one angle.
The opposite side know angle is the direct distance between the starting and ending points.
Using the law of cosines.
[tex]a^{2} = b^{2} + c^{2} - 2bc (cosA)[/tex]
[tex]a^{2} = 2^{2} + 3^{2} - 2(2)(3)(cos 145)[/tex]
[tex]a^{2} = 4 + 9 - 12 (-0.8192)[/tex]
[tex]a^{2} = 22.83[/tex]
a = 4.78 km
To determine the bearing from the starting point , we must determine the angle between the first leg and the direct path.
Using the law of sines
[tex]\frac{4.78}{sin(145)} = \frac{3}{sin C}[/tex] sin(145°)
4.78 sin C = 3 sin 145°
sin C = [tex]\frac{3 sin (145^ 0)}{4.78}[/tex]
sin C = 0.4438
C = 26.3°
Therefore, the distance and bearing of the end point from the starting point is 4.78 km North 26.3 ° West.
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at what time t is the instaneous velocity equal to the averge equal to the equal to the average velocity of the bug on 0,6 is the bug speeding up or slowing down at t
Answers
At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6], so the bug is neither speeding up nor slowing down.
The instantaneous velocity of a bug at any particular moment in time is the rate at which the bug is changing its position. The average velocity of the bug over a particular interval (in this case, [0,6]) is the average rate at which the bug changes its position over the entire interval. To compare the instantaneous velocity to the average velocity, the two velocities need to be measured at the same time.
At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6]. That means that the bug is neither speeding up nor slowing down.
The Complete the question is :
at what time t is the instaneous velocity equal to the averge equal to the equal to the average velocity of the bug on 0,6 is the bug speeding up or slowing down at t = 0.6
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Can someone evaluate these
1 × ( –6 × – 18 – 8) ÷ 4
–4 – –20 + –5 ×( –11 – –18)
13 – –10 × 16 ÷(14 + –16)
1– –9 × 12 × (–19 + 20)
Answers
Answer:
1 × ( –6 × – 18 – 8) ÷ 4=[tex]\frac{1}{404}[/tex]
–4 – –20 + –5 ×( –11 – –18)=[tex]18[/tex]
13 – –10 × 16 ÷(14 + –16)=[tex]173[/tex]
1– –9 × 12 × (–19 + 20)=[tex]110[/tex]
7. (85D) Richards Park charges an admission fee of
$10 plus an hourly fee for each sport that you
choose to participate in. Which equation
represents the cost C, in terms of the number of
hours, h, you pay to sled?
HELP PLEAAASEEE 20 POINTS
Answers
Answer:
C. C = $10 +$5h
Step-by-step explanation:
The cost is a $10 admission fee plus $5 per hour for sledding. You want an equation representing the cost C in terms of hours h.
CostThe cost is ...
cost = admission fee + hourly charge
The hourly charge is the product of the cost per hour ($5) and the number of hours (h).
C = $10 +$5h
Find the missing side length
Answers
Answer:
8
Step-by-step explanation:
x+7=15 so x=15-7 which is x=8
Answer:
8 ft
Step-by-step explanation:
The length of the shape is 15 ft. The length on the bottom is equal to the length on the top.
We are given 2 "sides" or lines on the bottom. One of them is 7 ft. Find the other "side" length.
x + 7 =15
x = 15 - 7
x = 8
What is the solution and how do I solve this step by step?
Answers
So we can say that…
16x + 8 = 60 + 4x + 8
-8
16x = 60 + 4x
-4x
12x = 60
/12
x = 5
Answer: x = 5
Have a good day ^^
Simplify: 0÷(x−1/3), where x≠1/3.
Answers
Answer:
0
Step-by-step explanation:
0 divided by any nonzero quantity is zero.
The area of a rectangle is 9/10 square meter. The width is 2/5 meter. b. How many times greater is the length than the width? Write your answer in simplest form.
Answers
Using the area of rectangle formula, w = A/l, determine the width of the rectangle first before determining its length.
How do you find the length and width of a rectangle when given the area?In conclusion, you must divide a rectangle's area by its known width in order to determine its length.If you have an area A and a width w, you can calculate the length w using the formula h = A/w.
If you know the perimeter P and the width w, you can calculate the length using the formula h = P/2w.
Given a diagonal (d) and a width (w), its length is given by h = (d2w2).The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape.
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Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, to the water in the tanks that hold the jellyfish.
Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?
A. Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects. B. Randomization will make up for improper experimental design, data collection, and analysis.
C. Randomization makes the analysis easier since the data can be entered into the computer in any order. D. Randomization is required by statistical consultants before they will analyze the experiment.
E. Randomization means that the experiment would not need to be replicated.
Answers
In order to prevent such factors from influencing the treatment's outcomes, randomization tends to reduce the impact of uncontrollable variables like water temperature.
What are variables?
A variable in mathematics is a symbol that designates a mathematical object. A variable can represent any of the following: a number, a vector, a matrix, a function, its argument, a set, or an element of a set. An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed. Because they make up a significant portion of mathematics, variables are crucial.
The impact of water pH on moon jellyfish mating behavior is being studied by researchers. In a scientific experiment, the water in the tanks containing the jellyfish will be randomly assigned to one of three treatments: low pH, medium pH, or high ph.
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The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3. At the instant when dp/dt = 41 and c = 15, what is the value of dc/dtï¼
Answers
The value of dc/dt due to changes in p and c variables is 0.364.
The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3. Now the dp/dt value is 41 and c is 15.
Differentiate the given equation to obtain the following:
2p dp/dt = 3(20-c)^2 dc/dt
Substitute the given values in the equation to obtain the following:
2p (41) = 3(20 - 15)^2 dc/dt
Simplify the equation to obtain the following:
82 = 225 dc/dt
Divide both sides of the equation by 225 to obtain the following:
dc/dt = 82/225
Simplify the equation to obtain the following:
dc/dt = 0.364
Hence, the value of dc/dt is 0.364.
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in a survey of 1,000 adults in a country, 722 said that they had eaten fast food at least once in the past month. create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month. use excel to create the confidence interval, rounding to four decimal places.
Answers
To create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month, we need to first calculate the sample proportion.
The sample proportion is calculated by dividing the number of adults who ate fast food at least once in the past month (722) by the total number of adults surveyed (1000). This gives us a sample proportion of 0.722.
To calculate the confidence interval, we can use the following formula:
Sample proportion +/- 1.96 * sqrt((Sample proportion * (1 - Sample proportion)) / Sample size)Plugging in the values, we get:
0.722 +/- 1.96 * sqrt((0.722 * (1 - 0.722)) / 1000)This gives us a 95% confidence interval of (0.6901, 0.7539). Rounded to four decimal places, the confidence interval is (0.6901, 0.7539).
Note: To calculate the confidence interval using Excel, you can use the following formula:
=CONFIDENCE.NORM(alpha, standard_dev, size)Where "alpha" is the desired confidence level (e.g., 0.95 for a 95% confidence interval), "standard_dev" is the standard deviation of the sample, and "size" is the sample size. To calculate the standard deviation, you can use the STDEV.P function.
For example, to calculate the lower and upper bounds of the 95% confidence interval, you could use the following formulas:
Lower bound: =CONFIDENCE.NORM(0.95, STDEV.P(A1:A1000), 1000) - (1.96 * STDEV.P(A1:A1000))Upper bound: =CONFIDENCE.NORM(0.95, STDEV.P(A1:A1000), 1000) + (1.96 * STDEV.P(A1:A1000))Where A1:A1000 is a range containing the values "1" for those adults who ate fast food at least once in the past month and "0" for those who did not. This will give you the same result as the manual calculation above.
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By first rounding Both number to 1 significant figure estimate the answer to 13 x 378
Answers
The solution is A = 4000
The equation after rounding up numbers is A = 10 x 400 = 4000
What is rounding up numbers?
There are basically two rules while rounding up numbers
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Non-zero digits are always significant
Zeros between non-zero digits are always significant
Leading zeros are never significant
Trailing zeros are only significant if the number contains a decimal point
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be = p
The value of p = 13
Let the second number be = q
The value of q = 378
Rounding the number p to 1 significant figure , p = 10
Rounding the number q to 1 significant number q = 400
So , the equation is A = p x q
Substituting the values in the equation , we get
A = 10 x 400
The value of A = 4000
Hence , The equation after rounding up numbers is A = 10 x 400 = 4000
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If the area of square and rectangle is same and the side of the square is 40cm and width of rectangle is 25cm. So what is the total area of rectangle?
Answers
Answer:
s² = lw
s = 40 w= 25cm
s² = lh
(40cm)² = (25cm)
1 600 cm² = 25cm L
L = 64 cm
The length is 64 cm
Area of Rectangle = length(width)
Area = 64cm(25cm)
Area = 1 600 cm²
Which is correct because the statement is, the area of a square ( 1 600 cm²) is equal to area of the rectangle ( 1 600 cm²)Therefore the area of rectangle is 1 600 cm²Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Tom received a $75 gift certificate for the local sporting goods store. He
bought two baseballs for $1.79 each, a baseball glove for $49.99, and a
baseball bat for $12.19. About how much of his gift certificate will he have
left?
Answers
Answer:
He has $9.24 left of his gift certificate
Step-by-step explanation:
Given that,
He bought two baseballs for $1.79
Baseball= 1.79+1.79 or 1.79 × 2 (because there are two baseballs.
= $3.58
Baseball Glove = $49.99
Baseball Bat = $12.19
Altogether = $3.58 + $49.99 + $12.19
= $65.76
So you subtract $65.76 from the Original amount in the gift certificate,
=> $75 - $65.76
= $9.24