The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)
What is an expression?An expression in maths, a statement involving at least two different numbers (known or unknown) and at least one operation.
Given an expression, -3x²-24x-36;
Factorizing, we get,
-3x²-24x-36 = -3(x²+8x+12)
= -3(x²+6x+2x+12)
= -3[x(x+6)+2(x+6)]
= -3(x+6)(x+2)
Hence, The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)
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Pls someone help I’ll give 100 points pls
Answer:
ST and RQ
Step-by-step explanation:
The 'arrows' on the line segments mean they are parallel
An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If
x engines are made, then the unit cost is given by the function C(x)-0.3x²-192x+47,470. How many engines must be made to minimize the unit cost?
Do not round your answer.
There are 320 engines must be made to minimize the unit cost.
What is an expression?Expression in math's is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The unit cost is given by the function,
⇒ C(x)= 0.3x²- 192x + 47,470
Now,
Since, The unit cost is given by the function,
⇒ C(x)= 0.3x²- 192x + 47,470
Hence, We get;
⇒ dC/dx = 0.6x - 192
Put dC/dx = 0
⇒ 0 = 0.6x - 192
⇒ 0.6x = 192
⇒ x = 320
And, d²C/dx² = - 192 < 0
Hence, This gives the maximum value.
So, The number of engines which must be made to minimize the unit cost = 320
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The number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions. Which equation represents the situation? Let e represent the number of essay questions and m represent the number of multiple choice questions
O m =4e-3
O m=4e +3
O e=3m +4
O e=3-4m
m =4e-3 is the equation represents the number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let the multiple questions be denoted by m.
The essay questions be denoted by e.
The given sentence is the number of multiple-choice questions on a final exam is 3 less than 4 times the number of essay questions.
In the sentence there is less than which means a value is subtracted and it has times which is meant by product.
m =4e-3 is the required equation of the given sentence.
Hence, m =4e-3 is the equation represents the situation.
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Explain why a selection of 10 students from your class can have marks that aren’t normally distributed when the marks of entire class are normally distributed.
What do the graphs indicate about (4, 4) ?
A. It is the only ordered pair that satisfies y = 1/4 * x + 3 it is also the only ordered pair that satisfies . y = 2x - 4
B. It is the only ordered pair that satisfies y = 4x + 3 it is also the only ordered pair that satisfies y = 1/2 * x - 4
C. It is the only ordered pair that satisfies both y = 1/4 * x + 3 and . y = 2x - 4
It is the only ordered pair that satisfies both y = 4x + 3
D. and y = 1/2 * x - 4
Point (4,4) is the only ordered pair that satisfies both equations y = (1/4) x + 3 and y = 2x - 4.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
In the given graph,
The point (4, 4) is the intersection point of the lines.
Since, the point (4, 4) is intersection point,
Therefore, this point will satisfy the equations of line.
From the options, take equations,
y = (1/4) x + 3
Substitute x = 4 and y = 4
4 = (1/4) 4 + 3
4 = 4
y = 2x - 4
Substitute x = 4 and y = 4
4 = 2 × 4 - 4
4 = 4
The point (4,4) satisfies both the equations.
Therefore, (4,4) is the only ordered pair that satisfies both equations y = (1/4) x + 3 and y = 2x - 4.
Option (C) is correct option.
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Determine the x-intercept of the line whose equation is given: y = 4 x + 2 a. (0, 2) b. (negative 2, 0) c. (0, negative one-half) d. (Negative one-half, 0) Please select the best answer from the choices provided A B C D
Answer:
D
Step-by-step explanation:
the x- intercept is the point where the line crosses the x- axis.
any point on the x- axis has a y- coordinate of zero.
let y = 0 in the equation and solve for x , that is
4x + 2 = 0 ( subtract 2 from both sides )
4x = - 2 ( divide both sides by 4 )
x = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex] ← x- intercept
coordinates of x- intercept = (- [tex]\frac{1}{2}[/tex], 0 )
Please help asap will give BRAINLIEST
Solve 2 4/7 X 2/3
1 15/21
2 8/21
2 12/14
3 2/12
Answer:
12
X
7
Step-by-step explanation:
IX.
A sorting machine at an orange processing plant has to sort 720 tons of oranges to meet a
deadline. The machine can process 360 tons of oranges in 50 minutes. Determine how
long it will take the machine to sort 720 tons of oranges.
Proportionately, the sorting machine will take 100 minutes (1 hour and 40 minutes) to process 720 tons if it takes 50 minutes to process 360 tons.
What is proportion?Proportion is the ratio or numerical relationship that one quantity bears to another.
Proportions are equated to each other to find missing variables.
Proportions are fractional values, usually depicted as fractions, decimals, or percentages.
The total number of oranges to sort = 720 tons
Machine processing speed = 360 tons per 50 minutes
Proportionately, the machine can process 7.2 tons per minute (360/50).
The time to sort 720 tons = 100 minutes (720/360 x 50) or (720/7.2)
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Suppose you roll a six-sided die. What is the probability that a 2 or 5 is NOT rolled? (in fraction form)
A) 1/6
B)2/6
C) 3/6
D)4/6
On solving the provided question, we can say that the probability that a 2 or 5 is NOT rolled is - 1- 1/3 = 2/3
What is probability?A branch of mathematics called probability describes the likelihood that an event will occur or that a proposition is true. The probability of an event ranges from 1 to 1, with 1 indicating certainty and numbers in between indicating the difficulty of the event.
to determine the likelihood of rolling a die with a 2 or a 5 on it. The probability formula can be used to do this.
[tex]P(E) = (Number of times event occurs)/(Total number of trials)[/tex]
S = 1, 2, 3, 4, 5, 6 is a sample space of potential results when rolling a dice.
If the likelihood of rolling a die and having a result of 2 or 5 is event E.
Number of occurrences [n(E)] = 2
[n(S)] = 6 trials in all
[tex]P(E) = 2/6 = \frac{1}{3}[/tex]
So, the probability that a 2 or 5 is NOT rolled is - \
1- 1/3 = 2/3
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Pls help will make brainliest thank you
A salon wants to conduct a survey in order to study the consumption pattern of its consumers. The population mean spending on visiting salon per month is unknown with the population standard deviation is assumed to be $200. A random sample of 55 customers is selected and the sample mean spending on visiting salon per month is $800.
(a) Construct a 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month. (3 marks)
(b) It is suggested to do the second round inspection. This time, the sample size is 120. What is the sampling error at 95% confidence level? (2 marks)
a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows: (747, 853).
b) The sampling error at 95% confidence level is of: $35.78.
What is a z-distribution confidence interval?The bounds of the confidence interval are given as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The parameters for this problem are given as follows:
[tex]\overline{x} = 800, \mu = 200, n = 55, z = 1.96[/tex]
Hence the lower bound of the interval is of:
800 - 200 x 1.96/square root of 55 = 747.
The upper bound of the interval is of:
800 + 200 x 1.96/square root of 55 = 853.
The sampling error for a sample size of 120 is calculated as follows:
200 x 1.96/square root of 120 = $35.78.
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what is an equation of the line that passes through the points (2,7) and (8,4)
Answer:
y = - 0.5x + 8
Step-by-step explanation:
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\frac{7-4}{2-8}[/tex]
[tex]\frac{3}{-6}[/tex]
[tex]-\frac{1}{2}[/tex]
m = - 1/2
y = - 1/2x + b
4 = - 0.5(8) + b
4 = - 4 + b
b = 8
y = - 0.5x + 8
PLEASE HELP 50 BRAINLY POINTS IF YOU ANSWER THIS QUESTION CORRECTLY
A probability value is listed at the top of each column. Determine the probability for each situation, then drag and drop each situation into the column under its correct probability.
The list of all probabilities from first to last are 0.5, 0.5, 0.2, 0.4, 0.5,
and 0.2.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
There are a total of 6 possibilities when rolling a die and of which three are even numbers.
P(rolling an even number is) = 3/6 = 1/2 0.5.
There are two possibilities when flipping a coin,
∴ The probability of getting a head is (1/2) = 0.5.
There are a total of (1 + 1 + 3) = 5 possibilities of choosing a block out of which one is red, therefore the probability of choosing a red is = (1/5) = 0.2.
Total 10 marbles and 4 blue marbles, hence the probability of choosing a blue marble is (4/10) = 2/5 = 0.4.
There are a total of 8 balls out of which 4 are soccer balls, hence the probability of choosing a soccer ball is = 4/8 = 1/2 = 0.5.
Total 15 balls out of which 3 tennis balls hence the probability of choosing a tennis ball is = 3/15 = 0.2.
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Can someone please help me with this basic geometry?
The value of side MN is 18.2
What is a Trapezoid?
A quadrilateral is a polygon with four sides.
There are many special types of quadrilateral.
The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
Given data ,
Let the side to be calculated be = MN
Now , the two quadrilaterals are GHIJ and KLMN
And , quadrilaterals GHIJ and KLMN are congruent
So ,
The sides are in the ratio
MN / IJ = NK / JG
On simplifying the equation , we get
Substituting the values in the equation , we get
MN / 47 = 12 / 31
Multiply by 47 on both sides of the equation , we get
MN = ( 12 x 47 ) / 31
On simplifying the equation , we get the value of side MN
MN = 564 / 31
MN = 18.19
On rounding to the nearest tenth , we get
MN = 18.2
Therefore , the value of side MN is 18.2
Hence , The value of side MN is 18.2
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The equation of a line perpendicular to y=3x-1 and goes through (0,2)
Answer:
y = [tex]-\frac{1}{3}[/tex]x + 2
Step-by-step explanation:
Find the reciprocal change the sign of the gradient (m=3):
[tex]-\frac{1}{3}[/tex]
so
y = [tex]-\frac{1}{3}[/tex]x + c
The intersect is 2, so c = 2
Final answer: y = [tex]-\frac{1}{3}[/tex]x + 2
A shirt normally costs £42. If you receive a 15%
discount, how much change will you get from £50?
A-£35.70
B-£23.00
C-£8.00
D- £14.30
to search
1
OE
Answer:
If you receive a 15% discount on a shirt that normally costs £42, the discounted price of the shirt will be £42 - (15/100) * £42 = £35.70. If you pay £50 for the shirt, you will receive £50 - £35.70 = £14.30 in change. Therefore, the correct answer is D- £14.30.
Step-by-step explanation:
i need help with finding the slope
How many real solutions are there to 5x^2+6x+4=0?
The given quadratic equation 5x^2+6x+4=0 has no real roots or 0 real roots.
What is a quadratic equation?A quadratic equation is any algebraic expression that can be expressed in a standard form where x represents an unknown number, a, b, and c represent known values, and where a 0 is true.
So, we have the equation:
5x^2+6x+4=0
Discriminant (D): b² - 4ac
Insert values in the given formula as follows:
b² - 4ac is 6² - 4(5)(4).
= 36 - 80
= - 44 and it is less than zero.
No real roots
Therefore, the given quadratic equation 5x^2+6x+4=0 has no real roots or 0 real roots.
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Help!!!! Urgent pls!!!!
Answer: 34.44
Step-by-step explanation:
Answer:its d
Step-by-step explanation:
Which of the following sets of ordered pairs is a function? Pls look at picture and help me out
Answer: C
Step-by-step explanation:
A function cannot have repeated x value in a set, and c is the only one without repeated x value
consider the following method, which is intended to return the product of 3 and the nonnegative difference between its two int parameters.
Answer: the answer is try hard and if you don’t succeed try try again
Step-by-step explanation:
How do i say uwu please tell me right now now right now
Answer: look it up how to pronounce the word
Step-by-step explanation: go to goggle translate or an app.
9. A park ranger stands a certain distance from an observation tower. Write an equation and then solve for x
53.6 feet
70.0 feet
58.7 feet
37.8 feet.
Using the trigonometry ration, the value of x is 53.6.
In the given question, a park ranger stands a certain distance from an observation tower.
We have to write an equation and then solve for x and choose the right option.
From the diagram we can see that the height of an observation tower is 45 and angle is 40.
To find the value of x we use the trigonometry ratio.
As we know that tangent is the ratio of perpendicular side and adjacent side.
From the given diagram
tan(40)=45/x
Now simplifying
0.8391 = 45/x
Multiply by x on both side, we get
0.8391x = 45
Divide by 0.8391 on both side, we get
x = 53.6 feet
Hence, the value of x is 53.6.
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I need this answer asap
Answer:
x=-8
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x= -8
Step-by-step explanation:
-------------------------
valuate each expression for x = -2 and y = 3.
Evaluating each expression with x = -2 and y = 3 gives
3x²y - x = 38
3y - x = 11
x² - y = 7
x + 2xy = 14
4y - 2xy + 2y = 33
2x - y = -7
6 -x = 8
3x - 2y = -12
3x - 2y + xy = -18
How to evaluate the expressionsThe expressions are evaluated by substituting the values of x and y into the equations and solve
solving the expressions
3x²y - x
substituting x = -2 and y = 3
= 3(-2)² * 3 - (-2)
= 38
3y - x =
substituting x = -2 and y = 3
= 3 * 3 - (-2)
= 11
x² + y
substituting x = -2 and y = 3
= (-2)² + 3
= 7
x + 2xy
substituting x = -2 and y = 3
= -2 + 2 * -2 * 3
= -14
4y - 2xy + 3y
7y - 2xy
substituting x = -2 and y = 3
= 7 * 3 - 2 * -2 * 3
= 21 - (-12)
= 33
2x - y =
substituting x = -2 and y = 3
= 2 * -2 - 3
= -7
6 - x
substituting x = -2
= 6 - (-2)
= 8
3x - 2y
substituting x = -2 and y = 3
= 3 * -2 - 2 * 3
= -6 - 6
= -12
3x - 2y + xy
substituting x = -2 and y = 3
= 3 * -2 - 2 * 3 + -2 * 3
= -6 - 6 + (-6)
= -18
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Two parallel lines are cut by a transversal, as shown. If m 21 = 114°, what is m 22?
help me asap
Answer:
∠ 2 = 66°
Step-by-step explanation:
∠ 1 and ∠ 2 are same- side interior angles and sum to 180° , then
∠ 2 + 114° = 180° ( subtract 114° from both sides )
∠ 2 = 66°
2)
Earings (in dollars)
SALESPERSON'S EARNINGS
500
400
300
200
100
y
0 1 2 3 4 5 6 7 8
Sales (Thousands of dollars)
2a) Explain what x represents. Sales
2 b) Explain what y represents earnings
2 c) Find the slope of the line. Make sure to include units
2 d) Explain what the slope represents for this example.
Use the numbers in your explanation.
The solution is
a) The x represents the number of sales
b) The y represents the total earnings in dollars
c) The slope of the line m = 50 earnings (in dollars) per sale
d ) The slope represents the total earnings per sales and it is $ 50 per sale
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is given by the equation
Let the number of sales be = x
Let the total earnings be = y
Now , let the two points on the graph be A and B
where the value of A = A ( 3 , 200 )
And , the value of B = B ( 5 , 300 )
Now , the slope of the line between the points A and B is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 300 - 200 ) / ( 5 - 3 )
Slope m = 100 / 2
Slope m = 50
So , the slope of the line is given by m = 50 earnings per sales
And , Slope m = $ 50 per sales
The equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 200 = 50 ( x - 3 )
y - 200 = 50x - 150
Adding 200 on both sides of the equation , we get
y = 50x + 50
Therefore , the equation of line is y = 50x + 50
Hence ,
a) The x represents the number of sales
b) The y represents the total earnings in dollars
c) The slope of the line m = 50 earnings (in dollars) per sale
d ) The slope represents the total earnings per sales and it is $ 50 per sale
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Sine, Cosine, Tangent question below
Answer:False
Its just simply incorrect
Find the measure of angle A.
Answer: 32
Step-by-step explanation:
Answer:
25 degrees
Step-by-step explanation:
sum of all three angles of a triangle equal 180
135+5x+4x=180
135+9x=180
-135. -135
9x=45
x=5
angle A is 5x
5(5)
25
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A school sells adult tickets and student tickets for a play. Adult tickets cost $8 each and student ticket cost $4 each. They collect $320 in total
Answer:
The answer is 8a + 4s = $320
Step-by-step explanation:
Let us take a for adult tickets and s for student ticket we get,
8a and 4s
They collect $320 in total
8a + 4s = $320
Thus, The equation represents this relationship is 8a + 4s = $320