Answer:
7.
Step-by-step explanation:
Think of 42/6 as a division question.
42 ÷ 6.
The answer to this equation is 7.
find the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube
The smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5
Perfect cube quotient of a division
The given number is 29160
Note that:
29160 can be factored into 5832
That is, 29160 = 5832 x 5
Take the cube of 5832:
[tex]\sqrt[3]{5832}=18[/tex]
Since it has been confirmed that 5832 is a perfect cube, the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5
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Determine an equation that describes the number of bacteria in both the foods when they are mixed.
The equation that describes the number of bacteria in both the foods when they are mixed is; Option C: 35T₂ + 55T + 450
How to simply quadratic Equations?
We are given the equations that describes the number of bacteria in both the foods when they are mixed.
Equation for first bacteria is;
N₁(T) = 15T₂ + 60T + 300
Equation for second Bacteria is;
N₂(T) = 20T² - 5T + 150
The equation that describes the number of bacteria in both the foods when they are mixed is;
N₁(T) + N₂(T) = 15T₂ + 60T + 300 + 20T² - 5T + 150
⇒ 35T₂ + 55T + 450
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A super sundae ice cream cone has a radius of 0. 5 in and a depth of 4 in. A wonderful waffle cone has a radius 0. 9 in and a depth of 3 in. Which cone holds more ice cream?
The wonderful waffle cone holds more ice cream than super sundae cone.
In this question,
The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.
Volume of ice cream cone = volume of hemisphere + volume of cone
Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]
Volume of super sundae cone:
Radius of hemisphere = height of hemisphere = 0.5 in
Depth of the ice cream cone = 4 in
Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]
⇒ 0.2616+1.0466
⇒ 1.3082 ≈ 1.31 cubic in.
Volume of wonderful waffle cone:
Radius of hemisphere = height of hemisphere = 0.9 in
Depth of the ice cream cone = 3 in
Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]
⇒ 1.526+2.5434
⇒ 4.0694 ≈ 4.07 cubic in.
Thus volume of wonderful waffle cone > volume of super sundae cone.
Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.
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d) y = 3x - 9 7) 2) y-int. m = x-int. 3) -
**Disclaimer** Hi there! I assumed the question to be finding the "y-intercept", "x-intercept", and "slope/gradient" of the equation "y = 3x - 9". The following answering will be according to this understanding. If it is incorrect, please tell me and I will modify my answer.
Answer:
y-intercept = (0, -9)
x-intercept = (3, 0)
slope (m) = 3
Step-by-step explanation:
What is being asked: to find the corresponding values
y-interceptx-interceptSlope/gradientGiven equation
y = 3x - 9
PART I: y-interceptConcept
The y-intercept of a line is on the coordinate of (0, a), where [ a ] is a constant.
Substitute values into the equation
y = 3x - 9
y = 3 (0) - 9
y = 0 - 9
y = -9
Therefore, the y-intercept is [tex]\Large\boxed{(0, -9)}[/tex]
PART II: x-interceptConcept
The x-intercept of a line is on the coordinate of (a, 0), where [ a ] is a constant.
Substitute values into the equation
y = 3x - 9
0 = 3x - 9
Add 9 on both sides
0 + 9 = 3x - 9 + 9
9 = 3x
Divide 3 on both sides
9 / 3 = 3x / 3
x = 3
Therefore, the x-intercept is [tex]\Large\boxed{(3,0)}[/tex]
PART III: Slope/GradientConcept
In the linear formula, y = mx + b, [ m ] is the slope and [ b ] corresponds to the y-intercept.
Determine the slope
Given the equation, y = 3x - 9, when corresponds to the general linear equation formula:
y = mx + b
y = 3x - 9
Therefore, the slope is [tex]\Large\boxed{m=3}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Solve the system of equations.
2x+y = 7
x - 2y = 6
Put your answer as a coordinate point, or use "no solution" or "infinitely many solutions"(aka "the set of all real numbers").
Answer:
Ans: (4,-1)
Step-by-step explanation:
Lets keep:
2x+y=7 --- equation 1
x - 2y=6 ----- equation 2
equation 2 x 2: 2x - 4y=12 -------equation 3
now subtract equation 1 from equation 3
2x - 4y = 12
(-) 2x + y = 7
----> -5y = 5 [ Divide both sides by -5 ]
------> y= -1
Substitute y= -1 into eqaution 1
----> 2x + -1 = 7 [ add 1 to both side]
----> 2x = 8 [Divide by 2 on both sids]
----> x=4
Ans: (4,-1)
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U. Next, draw PT, QU, and RS. Which statements are true
The statements that are true based on the midpoint given in the question include:
m∠P + m∠Q + m∠R = 180°PT, QU, and RS intersect at the same point.What is midpoint?In geometry, the midpoint simply means the middle point of a line segment. The midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Also, it should be noted that the midpoint bisects the segment.
In this case, m∠P + m∠Q + m∠R = 180°. This is because the sum of the angles in a triangle will be equal to 180°. Also, PT, QU, and RS intersect at the same point.
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Complete question:
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.
Next, draw PT, QU, and RS.
Which statements are true?
m∠Q = m∠R
The length of QU is half the length of RP.
m∠P + m∠Q + m∠R = 180°
QU ≅ RS
PT, QU, and RS intersect at the same point.
The sum of the lengths of QU and RS is equal to the length of PT.
Sarita showed the steps to solving the equation. 5 (x minus 3) 7 (x 4) = 73 steps sarita’s solution sarita’s verification 1 5 x minus 15 7 x 28 = 73 5 (5 minus 3) 7 (5 4) = 73. 5 (negative 2) 7 (9) = 73. negative 10 63 = 73. 53 not-equal-to 73. 2 (5 7) x (negative 15 28) = 73 3 12 x 13 = 73 4 12 x 60 5 x = 5 when sarita tried to verify her answer, she found it was wrong. which explains her mistake? sarita’s solution is correct. she made an error in her verification. sarita was supposed to add the 5 and 7 in the first step. sarita added 13 instead of negative 13 in the fourth step. sarita was supposed to use the division property of equality in the third step.
This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).
What is linear equation?
When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it.
Given the following equation:
5(x-3) + 7(x+4) = 73
The steps to solve it are:
Apply the Distributive property:
5x - 15 + 7x + 28 = 73
12x + 13 = 73
Subtract 13 from both side
12x + 13 - 13 = 73 -13
12x = 60
Divide both side by 12
12x/12 = 60/12
x = 5.
To verify it, put the x = 5 in to the equation:
5(5 - 3) + 7(5 + 4) = 73
After solving it, we get
5(2) + 7(9) = 73
10 + 63 = 73
73 = 73
This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).
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Brendan is 30. Anna is 5 years older than Cassie and 10 years younger than Brendan. How old is Cassie
Answer:
20 because Brendan is 30
Sample response: there is a common ratio of 2/3 between the height of the ball at each bounce. so, the bounce heights form a geometric sequence: 27, 18, 12. two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet. what did you include in your response? check all that apply. there is a common ratio between bounce heights. multiply 12 by 2/3. the height on the fourth bounce is 8 feet.
Answer:
Step-by-step explanation:
A Geometric sequence can be used:
To Model this sequence you need to use this formula
A (subscript n) = Ar(n-1)
a = value of the first term
n = the # of the term you want to find (For example, if you want to find the term number 3, it is 12)
r = the common ratio, this is obtained by dividing the second term in the sequence by the first.
So the value of r is = 2/3 because 27 times 2/3 = 18 which is the second term
n = 4 since you want to find the 4th term in the sequence
Plug it in and the results are
4th term = 27(2/3)^(4-1) = 8
The answer is 8
Solve for w, where w is a real number.
Answer:
w= 9
Step-by-step explanation:
[tex] \sqrt{ - 4w + 61} = w - 4[/tex]
Square both sides:
-4w +61= (w -4)²
[tex]\boxed{(a - b)^{2} = a^2 -2ab + b^2 }[/tex]
Expand:
-4w +61= w² -2(w)(4) +4²
-4w +61= w² -8w +16
Simplify:
w² -8w +16 +4w -61= 0
w² -4w -45= 0
Factorize:
(w -9)(w +5)= 0
w -9= 0 or w +5= 0
w= 9 or w= -5 (reject)
Note:
-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.
Why do we use negative square root?
When solving an equation such as x²= 4,
we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.
In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.
However, back to our question, we did not introduce the square root so we should not consider the negative square root value.
Answer: w=9.
Step-by-step explanation:
[tex]\sqrt{-4w+61}=w-4[/tex]
Tolerance range:
[tex]\left \{ {{-4w+61\geq 0} \atop {w-4\geq 0}} \right. \ \ \ \ \left \{ {{4w\leq 61\ |:4} \atop {w\geq 4}} \right. \ \ \ \ \left \{ {{w\leq 15,25} \atop {w\geq 4}} \right. \ \ \ \ \Rightarrow\ \ \ \ \\w\in[4;15,25].[/tex]
Solution:
[tex](\sqrt{-4w+61})^2=(w-4)^2\\-4w+61=w^2-2*w*4+4^2\\-4w+61=w^2-8w+16\\w^2-4w-45=0\\D=(-4)^2-4*1*(-45)\\D=16+4*45\\D=16+180\\D=196.\\\sqrt{D}=\sqrt{196}\\\sqrt{D}=14 \\w_{1,2}=\frac{-(-4)б14}{2} \\w_1=\frac{4-14}{2} \\w_1=\frac{-10}{2} \\w_1=-5\ \notin tolerance\ range.\\w_2=\frac{4+14}{2}\\ w_2=\frac{18}{2} \\w_2=9\ \in tolerance \ range.[/tex]
Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.
Answer:
Step-by-step explanation:
Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.
5 - 3 × (a³-b²)² a=3 and b=5
5 - 3 × (3³ - 5²)² =
5 - 3 × (27 - 25)² =
5 - 3 × (2)² =
5 - 3 × 4 =
5 - 12 =
-7
help me please omg im in a rush
Answer:48
Step-by-step explanation:
When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits, we say the process is
The process is Capable.
According to statement
When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits
and when these conditions are fulfilled then the process is to be called CAPABLE.
So, The process is Capable.
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Brainliest for answer
A quadratic equation is graphed to the left. Which of the following equations could be paired with the graphed equation to create a system of equations whose solution set is comprised of the points (2,-4)and (-4,2)?
The linear function that goes through the points (2,-4) and (-4,2) is:
y = -x + 2.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.A linear function going through the points (2,-4) and (-4,2) would intersect the parabola at these points, hence these points would be the solution for the system of equations.
The slope of the line is:
m = (-4 - 2)/(2 - (-4)) = -1.
The line goes through point (2,-4), that is, when x = 2, y = -4, which we use to find the y-intercept b.
y = -x + b
-4 = -2 + b
b = -2.
Hence the equation is:
y = -x + 2.
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At the trial of a contract dispute, the plaintiff has offered to testify to what she heard the defendant say in a private conversation between the two of them, which the plaintiff secretly recorded on an audiotape that she did not offer in evidence. Is the plaintiff's testimony admissible
The plaintiff's testimony is admissible because plaintiff as personal knowledge of the statement of a party-opponent.
How to illustrate the information?The recording is coincidental with firsthand knowledge. The person could testify based upon firsthand knowledge and could also lay the foundation under Article 9 to authenticate the tape.
In this case, the tape is not required as a matter of the original writing rule, giving the proponent options to offer testimony from memory, and/or the opportunity to corroborate the in-court testimony by a demonstrative exhibit
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The rug for the kitchen has an area of 80 square feet. the width is 40 feet. what is the length?
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises is a "false" statement.
What is circuit training?A circuit workout consists of six or more exercises that are alternated with brief rest intervals and performed for either a predetermined number of reps or a certain duration of time.
Some features of circuit training exercise are-
It is a great approach to increase muscular strength and endurance as well as cardiovascular health. Due to the brief rest times, the use of major muscles in conjunction with smaller ones, and the mix of upper, lower, and whole-body movements in circuit training, your heart rate will increase and remain elevated during the entire circuit.Once all of the selected exercises have been finished, a circuit has been completed. A single training session may involve several circuits.Benefits of doing circuit training exercise-
Training in strength.Cardiovascular Health, Time Efficiency, Friendly Environment, Avoids BoredomTo know more about the circuit training, here
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The complete question is -
In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.(True/False)
Olivia is making 15 bead bracelets for her friends what is the proportional relationship?
5 minutes per bracelet.
because 15/3 = 5 mins.
To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:
constant of proportionality =15/3= 5 minutes.
Now, we're going to consider an example of a proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we'll pay.
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[tex]\sqrt{x}[/tex][tex]\sqrt{x}[/tex]4-[tex]\sqrt{x}[/tex][tex]\sqrt{x}[/tex]7 -[tex]\sqrt{x}[/tex][tex]\sqrt{x}[/tex]4+[tex]\sqrt{x}[/tex]7 +[tex]\sqrt{x}[/tex]2
[tex]4x - 7x - 4x + 7 \sqrt{x} + \sqrt{x} [/tex]
[tex] - 7x + 8 \sqrt{x} [/tex]
PLEASE ANSWER ASAP
What is the solution to the following system of equations?
Answer:
(-3, 1)
Step-by-step explanation:
the easiest thing to do is look at the graph and find the point where the two lines intersect
4. The polynomial-4.9² +40t +20 represents the distance above the ground of an object thrown straight up from an initial height of 20 meters and with an initial speed of 40 meters per second. How long does it take the object to
reach it's maximum height?
20.000 s
8.636 s
4.082 s
101 6330
The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
The height (h) is represented by:
h(t) = -4.9t² + 40t + 20
The maximum height is at h'(t) = 0, hence:
h'(t) = -9,8t + 40
-9.8t + 40 = 0
t = 4.082
The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.
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Which point is a solution to the inequality shown in this graph? (urgent)
Answer: D
Step-by-step explanation:
sorry if its wrong
Find the surface area of the prism. Round to the nearest tenth if necessary.
The surface area of the prism according to the segment labels is; 480mm².
What is the surface area of the prism?The prism given in the task content is five-faced and hence, its surface area can be evaluated as follows;
Surface area = 2(0.5×15×8)+(15×9)+(8×9) + (17×9).
Hence, the surface area of the prism upon evaluation is; 480mm².
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A)x=45
B)x=90
C)x=20
D)x=4.5
Answer:
x=4.5
Step-by-step explanation:
We know that if all sides are congruent then all angles must also be congruent, therefore you can solve for x with the following equation:
[tex]20x=90[/tex]
Solve
[tex]x=4.5[/tex]
The propeller blades on a submarine have a radius of 6 feet. At full speed, they turn at 120 revolutions per minute. What is the angular velocity, in radians per minute, at the tip of the blade? Round your answer to the nearest hundredth.
Using proportions, it is found that the angular velocity at the tip of the blade is of 753.98 radians per minute.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each revolution has [tex]2\pi[/tex] radians, hence in one minute, the 120 revolutions will have a measure in radians of:
M = 120 x 2pi = 240pi = 753.98
Hence the angular velocity is of 753.98 radians per minute.
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A compound inequality is shown below.
x ≤ 3 and x ≥ 0
Which graph represents the solution of the inequality?
Answer:
b
Step-by-step explanation:
edge
A square has a side of length 2xcm. in terms of X, what is the area
Answer:
4x^2
Step-by-step explanation:
2x(2x) It is a square so we multiply the side by the side to get the area.
=2*x*2*x
=4*x2
=4x^2
Given: ABCD is a rectangle.
Prove: ABCD has congruent diagonals.
Rectangle A B C D is shown.
Identify the steps that complete the proof.
♣ =
♦ =
♠ =
By SAS property, ABC ≅ DCB.
How to prove the deductionsIn this question we have to proof ABCD has congruent diagonal. By SAS property and reflexive property it can be proved as follows:
Given:
ABCD is a rectangle.
Prove:
Diagonal AC ≅ Diagonal BD
From the question,
As we can see that, ABCD is a rectangle, it is also a parallelogram.
Thus, ABCD is a parallelogram, opposite sides of a parallelogram are congruent.
⇒ AB ≅ DC
⇒ BC ≅ BC (Reflexive Property of Congruence)
Hence, ∠ABC and ∠DCB are right angles by the definition of rectangle.
∠ABC ≅ ∠DCB (all right angles are congruent)
Therefore, by SAS property, ABC ≅ DCB.
⇒ segment AC ≅ segment BD
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Answer:
♣ = parallelogram side theorem
♦ = SAS
♠ = CPCTC
(Correct On Edgen)
Brett had 3/4 of a family sized pizza. he gave each of his brothers half of this. what fraction of the pizza was each brother given?
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] * [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]
There are 120 students in class 7. it is known that 2 3 out of them like maths, out of which 35 are girls. also, out of total students, 3 5 are boys. (3) (a) what is the number of girls in the class? (b) how many students like maths? (c) how many boys like maths?
maths questions can be solved using unitary method.
Answer:
(a) The total number of girls in the class are 48
(b) The total number of students that like maths are 80
(c) The total number of boys like maths are 45
Solution:
According to the question, [tex]\frac{3}{5}[/tex] of total students are boys
number of boys = [tex]\frac{3}{5}[/tex] × 120 = 72
Also, According to the question, [tex]\frac{2}{3}[/tex] of total students like maths
number of students = [tex]\frac{2}{3}[/tex] × 120 =80
(a) The total number of girls in the class = total number of students - total number of boys
total number of girls in the class = 120 - 72 = 48
(b) The total number of students that like maths are 80
(c) The total number of boys like maths = total number of students that like maths - total number of girls that like maths
total number of boys like maths = 80 - 35 = 45
What is unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
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