Answer:-1.5
Step-by-step explanation:
first distribute 3
to get 6x + 3= 4x
then -6x on right side to get
3= -2x
then divide by -2
3/-2= x
x= -1.5
Hello !
Answer:
[tex]\Large \boxed{\sf x=-\frac{3}{2}}[/tex]
Step-by-step explanation:
We're looking for the value of x that satisfies the following equation :
[tex]\sf 3 (2x+1) = 4x[/tex]
We need to isolate x.
First, let's expand left side :
[tex]\sf 3\times 2x+3\times1=4x\\6x+3=4x[/tex]
Now let's substract 4x from both sides :
[tex]\sf 6x+3-4x=4x-4x\\2x+3=0[/tex]
Substract 3 from both sides :
[tex]\sf 2x+3-3=0-3\\2x=-3[/tex]
Finally, let's divide both sides by 2 :
[tex]\sf \frac{2x}{2} =-\frac{3}{2} \\\boxed{\sf x=-\frac{3}{2}}[/tex]
Have a nice day ;)
How do I put this in order?
Gina was shopping and saw a t-shirt she really liked, but could not decide which color to buy. The clerk said she would reduce the price by $2.50 per shirt if Gina bought more than one. She purchased 5 shirts all in different colors, for a total of $47.50. Write an equation to find the original cost of one shirt.
Let x represent the original cost of one shirt. The equation is 5x - 47.50 = 0, which can be solved to find that x = $9.50.
Gina was shopping and saw a t-shirt she liked, but couldn't decide which color to buy. The clerk offered to reduce the price by $2.50 per shirt if Gina bought more than one. She decided to purchase 5 shirts in different colors and the total cost of all 5 shirts was $47.50. To find the original cost of one shirt before the discount, we can set up an equation. Let x represent the original cost of one shirt. The equation would be 5x - 47.50 = 0, since the total cost of the 5 shirts was $47.50. When this equation is solved, x = $9.50, which is the original cost of one shirt before the discount. Therefore, the total cost of all 5 shirts was reduced by $2.50 for each shirt, from $9.50 to $7.00.
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someone pls answer this!!
doing more questions after on this topic worth 100 points
do simple working
Answer:
ii. is the answer
hope this helped
If x and y are in direct proportion and y is 30 when x is 6,find y when x is 14
Answer:
70
Step-by-step explanation:
If y=30 when x=6, 5x=y (because they are in direct proportion).
So, when x=14 replace x.
5*14=y
y=70
you can prove this because 70/14=30/6=5
so, the proportions are equal
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t2 + 16t + 480 , where t is the time in seconds and h is the height in feet.
c. Jason hit the water after how many seconds?
How do I do this lol
it takes Jason 6 seconds to hit the water after he jumps off the cliff. To determine when Jason hits the water, we need to find the value of t when h(t) = 0.
This is because the height of Jason is measured in feet and when he hits the water, he will be at a height of zero.
So we can set h(t) equal to zero and solve for t:
[tex]-16t^2 + 16t + 480 = 0[/tex]
Dividing both sides by -16, we get:
[tex]t^2 - t - 30 = 0[/tex]
Now we can use the quadratic formula to solve for t:
t = [-(-1) ± √[tex]((-1)^2[/tex] - 4(1)(-30))] / (2(1))
t = [1 ± √(121)] / 2
t = [1 ± 11] / 2
We get two possible solutions: t = 6 or t = -5. However, since time cannot be negative in this scenario, we can disregard t = -5 and conclude that Jason hits the water after 6 seconds.
Therefore, it takes Jason 6 seconds to hit the water after he jumps off the cliff.
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When playing baseball, Chad misses on 60% of the pitches he receives. Describe
how to use random digits to simulate the probability that he will get a hit on more
than 2 of every 10 pitches he receives.
This proportion represents the estimated probability that Chad will get a hit on more than 2 of every 10 pitches he receives.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To simulate the probability that Chad will get a hit on more than 2 of every 10 pitches he receives using random digits, follow these steps:
1. Divide the pitches into groups of 10. For each group of 10 pitches, record the number of hits that Chad gets.
2. Generate a random digit between 0 and 9 for each pitch in the group. If the digit is 0, 1, 2, or 3, consider it a hit. If the digit is 4, 5, 6, 7, 8, or 9, consider it a miss. Repeat this process for each group of 10 pitches.
3. Count the number of groups of 10 pitches in which Chad gets more than 2 hits.
4. Repeat steps 2 and 3 a large number of times (for example, 1000 times) to get an estimate of the probability that Chad will get a hit on more than 2 of every 10 pitches he receives.
5. Calculate the proportion of times in which Chad gets more than 2 hits in a group of 10 pitches.
Therefore, this proportion represents the estimated probability that Chad will get a hit on more than 2 of every 10 pitches he receives.
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The volume of 1 bottle of water is 250 ml. What is the volume of 20 bottles?
[tex]\frac{2}{3}a + 2 = \frac{1}{3}(4a + 1)[/tex]
solve for "a"
Answer:
a=5/2
Step-by-step explanation:
Answer:
a = [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] a + 2 = [tex]\frac{1}{3}[/tex] (4a + 1)
multiply through by 3 to clear the fractions
2a + 6 = 4a + 1 ( subtract 4a from both sides )
- 2a + 6 = 1 ( subtract 6 from both sides )
- 2a = - 5 ( divide both sides by - 2 )
a = [tex]\frac{-5}{-2}[/tex] = [tex]\frac{5}{2}[/tex]
A bag of marbles contains 12
red, 4
blue, 8
yellow, and 16
green marbles. Keith performed an experiment in which he randomly pulled a marble from the bag, recorded its color, put it back, and then repeated. The following table represents the number of times each color of marble was pulled.
Color Frequency
Red 40
Blue 10
Yellow 20
Green 30
For which colors is the experimental probability the same as the expected probability?
The experimental probability is the same as the expected probability for the blue marble, since the experimental probability of pulling a blue marble is 0.1 and the expected probability is also 0.1.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a mathematical concept that quantifies the chance of an event happening, ranging from 0 (impossible) to 1 (certain). Probability is commonly expressed as a fraction or a decimal between 0 and 1, or as a percentage between 0% and 100%
To determine the expected probability of pulling a certain color from the bag, we need to calculate the ratio of the number of marbles of that color to the total number of marbles in the bag.
Expected probability of pulling a red marble = 12/40 = 0.3
Expected probability of pulling a blue marble = 4/40 = 0.1
Expected probability of pulling a yellow marble = 8/40 = 0.2
Expected probability of pulling a green marble = 16/40 = 0.4
To calculate the experimental probability, we need to divide the frequency of each color by the total number of pulls, which is the sum of all the frequencies:
Experimental probability of pulling a red marble = 40/100 = 0.4
Experimental probability of pulling a blue marble = 10/100 = 0.1
Experimental probability of pulling a yellow marble = 20/100 = 0.2
Experimental probability of pulling a green marble = 30/100 = 0.3
So, the experimental probability is the same as the expected probability for the blue marble, since the experimental probability of pulling a blue marble is 0.1 and the expected probability is also 0.1. For all other colors, the experimental probability is different from the expected probability.
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Find x. Please help I don't know
Probably 26 :P
Because its like almost double of 10 but it is not....
HOPE THAT MADE SENSE!
Answer: well imma said x=19
Step-by-step explanation:
because All the diameter of the circle is equal.
So 14+15=29
And X is
29-10=19
A solid figure having a circular base and one vertex
One tenth of the parts tooled by a machine are rejects. How many parts must be tooled to ensure 4500 acceptable ones?
5000 parts must be tooled by the machine to ensure 4500 are acceptable as One tenth of the parts tooled by a machine are rejects.
One-eighth of the parts tooled by a machine are rejected.
Now, let's take the number of parts made by the machine to be x.
Now, the number of acceptable parts will be:
Total number of parts - number of rejected parts
x - (x/10)
(10x-x)/10
9x/10
Now, we have the number of acceptable parts as 4500.
So, we have:
9x/10 = 4500
9x = 4500*10
x = (4500*10)/9
x = 5000
Hence, the total number of parts tooled by the machine is 5000 in which 4500 are acceptable one.
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. A florist has two arrangements offered at special prices. The first arrangement consists of 5 lilies and 1 rose and costs $19.75. The second arrangement consists of 6 lilies and 3 roses and costs $27.75. What are the costs of each lily and each rose?
The cost of each lily is $3.50, and the cost of each rose is $2.25.
Dimensional analysis problemLet's use the variables L and R to represent the cost of each lily and each rose, respectively.
From the problem, we can write a system of two equations based on the information about the two arrangements:
5L + R = 19.75 (equation 1)
6L + 3R = 27.75 (equation 2)
To solve for L and R, we can use elimination. First, we can multiply equation 1 by 3:
15L + 3R = 59.25 (equation 3)
Then, we can subtract equation 2 from equation 3:
9L = 31.5
Solving for L, we get:
L = 3.50
Now we can substitute this value back into either equation 1 or equation 2 to solve for R. Let's use equation 1:
5L + R = 19.75
5(3.50) + R = 19.75
17.50 + R = 19.75
R = 2.25
Therefore, the cost of each lily is $3.50, and the cost of each rose is $2.25.
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Don't *quite* know how to solve this one. Any help would be great, and please explain your answer ^w^
Answer:
127°
Step-by-step explanation:
I added a photo of my solution
Answer:
x = 127°--------------------------------
The formed quadrilateral has two right angles, because of tangent segments.
One angle is marked as 53°, and the missing angle is x.
We know the sum of interior angles of a quadrilateral is 360°.
Find the missing angle:
x + 53 + 180 = 360x + 233 = 360x = 360 - 233x = 127HELP ASAP
This figure represents a planter
How much soil will it take to fill the planter?
Enter your answer in the box
the amount of soil needed is 27 cubic feet.
Kevin ate 5/12 of a pizza. Which is a better estimate for the amount of pizza that he ate: about half of the pizza or almost all of the pizza?
Answer:
Step-by-step explanation:
answer: about half the pizza as 5/12 is closer to half(6/12) then the full pizza (12/12)
a visitor is staying in a tent that is 9 miles west of the closest point on a shoreline to a rock formation. the rock formation is 3 miles due south of the shoreline. the visitor plans to travel from the tent to the rock formation by running and swimming. if the visitor runs at a rate of 4 mph and swims at a rate of 3 mph, how far should the visitor run to minimize the time it takes to reach the rock formation?
The distance the visitor should run to minimize the time it takes to reach the rock formation is 3/4 miles.
A unitary method is a mathematical technique used to solve problems involving proportional relationships between different quantities.
Let's use the unitary method to find the time it takes to complete the journey.
Time taken to run = Distance / Rate = x / 4
Time taken to swim = Distance / Rate = (3 - x) / 3
Total time taken = Time taken to run + Time taken to swim
= x / 4 + (3 - x) / 3
To minimize the total time taken, we need to find the value of x that minimizes the above expression. Let's differentiate it with respect to x and equate it to zero.
d/dx (x/4 + (3-x)/3) = 1/4 - 1/3 = -1/12
-1/12 = 0 (at minimum)
Solving for x, we get:
x = 3/4
The visitor should run westward along the shoreline until reaching the point 3/4 miles away from the tent, and then swim the remaining 2 1/4 miles to reach the rock formation.
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For each set of points given below, write a possible equation of a quadratic function in standard form.
A: (3/4,0) and (-2,0).
B: (negative square root of 5,0), (square root of 5, 0), and (-3,12)
The equations of the functions from the zeros are f(x) = 4x² + 5x - 6 and f(x) = 3x² - 15
Calculating the equation of the functionsFunction (a)
Given that
(3/4,0) and (-2,0).
Since the two points have the same y-coordinate of 0, the quadratic function is of the form
f(x) = (x - p)(x - q), where p and q are the x-coordinates of the two points.
Plugging in the given values, we get
f(x) = (x - 3/4)(x + 2)
So, we have
f(x) = 4x² + 5x - 6
Function (b)
Here we have
(-√5, 0), (√5, 0) and (-3, 12)
This function can be represented as
f(x) = a(x - p)(x - q)
So, we have
f(x) = a(x - √5)(x + √5)
Expand
f(x) = a(x² - 5)
Using the last point, we have
a((-3)² - 5) = 12
4a = 12
a = 3
So, we have
f(x) = 3(x² - 5)
Expand
f(x) = 3x² - 15
Hence, the function is f(x) = 3x² - 15
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diego earned $1,393.74 commission on weekly sales of $15,486 as a salesperson at the computer store. what is his rate of commission
Answer:
Step-by-step explanation:
Rate of commission = commission / total sales
Rate of commission = $1,393.74 / $15,486
Rate of commission = 0.0898 or 8.98%
Diego's rate of commission is 8.98%.
A family pass to the amusement park costs $54. Using Distributive Property, write an expression that can be used to find the cost in dollars of 8 family passes. (I'm actu
The cost of 8 family passes to the amusement park is $432 when a family pass to the amusement park costs $54.
To find the cost of 8 family passes to the amusement park, we can use the Distributive Property of multiplication over addition. The Distributive Property states that a(b + c) = ab + ac, where a, b, and c are numbers. In this case, we can use the Distributive Property to write:
8 x $54 = (5 x $54) + (3 x $54)
We can see that we have broken 8 down into two smaller numbers that we can multiply by $54 individually, and then add together. The first term, 5 x $54, represents the cost of 5 family passes, while the second term, 3 x $54, represents the cost of 3 family passes. Adding these two values together, we get:
(5 x $54) + (3 x $54) = $270 + $162 = $432
Therefore, the cost of 8 family passes to the amusement park is $432.
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Natalie uses a 50% off coupon when she buys a camera. The original price of the camera is
$46. 00
$46. 0. How much money does Natalie save by using the coupon?
Natalie saved amount $23 by using the coupon.
What is meant by the discount rate?
The discount rate is the interest rate used to determine the present value of future cash flows in a discounted cash flow (DCF) analysis. This helps determine if the future cash flows from a project or investment will be worth more than the capital outlay needed to fund the project or investment in the present.
The data is available from the question is:
The discount through coupon is d = 50%.
The original price of camera is c = $46.00
The discount on the amount is:
[tex]d = (\frac{50}{100}) 46[/tex]
d = 23
Thus, the amount saved is $23.
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PLEASE HELP! What similarity statement can you write relating the three triangles in the diagram?
The answer of the given question based on the finding the similarity statement by relating the three triangle is the three triangles appear to be similar by the Angle-Angle (AA) similarity theorem.
What is Angle-Angle (AA) similarity theorem?The Angle-Angle (AA) similarity theorem is statement used in geometry to determine whether two triangles are similar. It states that if two angles of one triangle are congruent to two angles of another triangle, then two triangles are similar.
More specifically, this theorem states that if two pairs of corresponding angles in two triangles are congruent, then triangles are similar. In other words measure of one angle in one triangle is equal to corresponding angle in other triangle, and measure of another angle in first triangle is equal to corresponding angle in other triangle.
Based on the given diagram, the three triangles appear to be similar by the Angle-Angle (AA) similarity theorem.
In the diagram, we can see that all three triangles have two pairs of congruent angles, which are labeled as angle A and angle B. Therefore, we can conclude that the three triangles are similar by AA similarity.
We can write this similarity statement as: Triangle ABC ~ Triangle DEF, Triangle ABC ~ Triangle GHI, and Triangle DEF ~ Triangle GHI.
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The average of the first 6 scores was 12. The average of the next 12 scores was 36.
What was the overall average ?
Answer:
28
Step-by-step explanation:
Average of first 6 scores is 12, so the total of those 6 scores is 6 × 12 = 72.
Average of next 12 scores is 36, so the total of those 12 scores is 12 × 36 = 432.
Total of all 18 scores is 72 + 432 = 504.
Overall average is 504 ÷ 18 = 28.
i’m really confused on what this is asking.. what does it want me to round to the nearest hundredths?
As a result, the following regression model best fits the data: y ≈ 3.38x + 9.37 rounded to the closest hundredths.
what is linear regression ?The link between a dependent variable and one or more independent variables can be modeled statistically using linear regression. The dependent variable can be treated as a linear function of the independent factors since this sort of regression analysis presupposes a linear relationship between the variables. Finding the line of best fit that minimizes the gap between the observed data points and the anticipated values of the dependent variable is the objective of linear regression. The equation y = mx + b, in which y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept, is represented by the line of best fit, which is a straight line.
given
Using a graphing calculator, we may display the data points and identify the line of best fit in order to determine the regression model that best matches the data.
We obtain the following scatter plot by entering the data into a graphing calculator:
We can observe from the scatter plot that the data seems to have an approximately linear trend. We may utilize the calculator's linear regression tool to determine the line of best fit.
We obtain the following equation by applying a linear regression on the data:
y = 3.38x + 9.37
The regression equation is as follows, rounded to the closest hundredths:
y ≈ 3.38x + 9.37
As a result, the following regression model best fits the data: y ≈ 3.38x + 9.37 rounded to the closest hundredths.
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The complete question is:- Use a graphing calculator to graph the data and to find a regression model that best fits the data. Round values to the nearest hundredths.
A quaffle is thrown into the air during a game of qudditch and modeled by the equation f(x)= -x^2+5x+14
The equation [tex]f(x) = -x^2 + 5x + 14[/tex] models the flight path of a quaffle thrown into the air during a game of quidditch.
The equation [tex]f(x) = -x^2 + 5x + 14[/tex] can be used to model the height of the quaffle, where x represents the time in seconds after the quaffle is thrown.
To find the maximum height of the quaffle, we need to find the vertex of the parabola described by the equation. The following formula can be used to determine the vertex's x-coordinate:
x = -b / 2a
where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c[/tex]. In this case, a = -1, b = 5, and c = 14, so we have:
x = -5 / 2(-1) = 5/2
The y-coordinate of the vertex can be found by plugging this value of x into the equation:
[tex]f(5/2) = -(5/2)^2 + 5(5/2) + 14 = 23.5[/tex]
Therefore, the maximum height of the quaffle is 23.5 feet, and it occurs 2.5 seconds after the quaffle is thrown.
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is 85 a prime number
Answer:
No
Step-by-step explanation:
A prime number cannot be divided exactly by any number other than itself and 1.
For example, 17 is a prime number, since it can only be exactly divided by 17 and 1.
85 is NOT a prime number, since it CAN be divided by 5.
Upper & lower bounds
Brian weighs himself at 84kg to the nearest kg.
What is the most he could weigh?
Give the upper bound as your answer.
Thus, the most he could weigh that is the upper bound of the given condition is 84kg.
What about weigh?
The word "weigh" is not frequently used by itself in arithmetic. The notion of weight or mass, for example, can be used when measuring or comparing quantities. While mass is a measurement of the quantity of matter inside an object, weight is a measure of the gravitational force acting on it. Weight can be viewed as the force a standard gravitational field applies to an object in the setting of measurement. Weight or mass may be denoted in mathematical equations by variables such as "w" or "m," and the units used to measure them may change based on the situation.
Define upper bound:
In mathematics, an upper bound is a number that is greater than or equal to all the elements in a given set. More formally, let S be a set of real numbers. A number u is an upper bound for S if and only if for all x in S, we have x ≤ u.
For example, consider the set S = {2, 4, 6, 8}. The number 10 is an upper bound for S because 2 ≤ 10, 4 ≤ 10, 6 ≤ 10, and 8 ≤ 10. However, the number 7 is not an upper bound for S because 8 > 7.
Note that an upper bound need not be an element of the set S itself. For instance, the set of all negative real numbers does not have any upper bound among the negative real numbers, but 0 is an upper bound for this set.
It's worth noting that an upper bound may or may not be a member of the set S. If an upper bound is a member of S, then it is called a "maximum" or "greatest" element of S. However, if an upper bound is not a member of S, then S has no maximum element.
According to the given information:
Brain weigh himself at 84kg to the nearest kg as (given) , because uses the method of round off.
Thus, the range of weigh:
⇒ 83.5 ≤ Weigh ≤ 84.4.
Thus, the most he could weigh is 84.4kg.
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What is the term-to-term rule of the linear sequence below? 1 , 7 , 13 , 19 , 25
Answer:6n-5
Step-by-step explanation:
1,7,13,19,25
It goes up in 6 each time, so you will need to go back 6 back on the number one, so it will be -5 so the answer will be 6n-5.
6(2)-5 = 7
6(3)-5 =13
Tammy is planning to garden a plot of land in the shape of a right triangle.
The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scale drawing of the plot using a scale of 1 inch to 2 feet. The area of the plot in the scale drawing is
square inches.
Answer: 7.5 square inches
Step-by-step explanation: the ratio is 1:2 meaning we cut the numbers in half, then we can find area normally
5/2=2.5
12/2=6
2.5x6=15
15/2=7.5
A particular type of cell doubles in number every hour.
Write an exponential function that can be used to find
the number of cells present, y, at the end of x hours if
there are initially 4 of these cells?
A particular type of cell doubles in number every hour.Write an exponential function that can be used to findthe number of cells present, y, at the end of x hours ifthere are initially 4 of these cells?The exponential function that can be used to find the number of cells present, y, at the end of x hours, given that there are initially 4 cells is: y = 4 * 2^x This is because the number of cells doubles every hour, so if there are 4 cells to start with, after one hour there will be 8 cells (doubling the initial number), after two hours there will be 16 cells (doubling the number after one hour), and so on. The exponent in the function represents the number of hours elapsed, and the base of the exponent is 2, representing the doubling of cells every hour.