The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).
What is a linear equation?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.The equation is referred to as a linear equation in one variable if just one variable is contained in the equation.Now,
We are given the linear equation: [tex]4x + \frac{1}{2}(10x-4)=6[/tex]
4x + 5x -2 = 6 (Distributive property)9x - 2 = 6 (combining the like terms)9x = 8 (additive property of equality)x = 8/9 (division property of equality)Hence, The third and fourth solutions are correct when using the division property of equality, i.e., The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).
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is it possible to have a function f defined on [ 5 , 6 ] and meets the given conditions? f is continuous on [ 5 , 6 ], takes on the values − 5 and 5 but does not take on the value 0.
No.
The intermediate value theorem (IVT) says that if [tex]f(x)[/tex] is continuous on [tex][a,b][/tex], and if [tex]d[/tex] is a number between
[tex]\min\{f(a),f(b)\} \le d \le \max\{f(a),f(b)\}[/tex]
then there is some [tex]c\in(a,b)[/tex] such that [tex]f(c) = d[/tex].
In this case we have for all [tex]x\in[5,6][/tex],
[tex]-5 \le f(x) \le 5[/tex]
0 falls in this range, so by continuity of [tex]f[/tex] and the IVT, there must be some number [tex]x\in(5,6)[/tex] such that [tex]f(x) = 0[/tex].
92.1 divided by 0.03
Answer: 3070
Step-by-step explanation:
2 divded by $1.53 round to the nearest cent
Answer: $0.77
Step-by-step explanation:
1.53/2=
0.765=
0.765=$0.77
Complete the sentence.
3mi ≈ ____ km
The complete sentence is 3 mi ≈ 4.827 km
How to complete the sentence?The open sentence is given as:
3mi ≈ ____ km
In the standard unit of conversion, we have
1 mi ≈ 1.609 km
Multiply both sides by 3
3 * 1 mi ≈ 1.609 km * 3
Evaluate the product
3 mi ≈ 4.827 km
Hence, the complete sentence is 3 mi ≈ 4.827 km
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Find the midpoint of the segment with the given endpoints.
(-5,-7) and (2,4)
Answer:
(-3/2 ; -3/2)
Step-by-step explanation:
Midpoint (x;y)
x = (x1+x2)÷2 = (-5+2)÷2 = -3/2
y = (y1+y2)÷2 = (-7+4)÷2 = -3/2
Therefore midpoint = (-3/2 ; -3/2)
PLEASE
Solve for X
4(5x+6)=12
-3(2x-4)=18
26=2(3x-2)
Answer:
Below in bold.
Step-by-step explanation:
4(5x + 6) = 12
20x + 24 = 12
20x = -12
x = -12/20 = -3/5
-3(2x - 4) = 18
-6x + 12 = 18
-6x = 6
x = -1.
26 = 2(3x - 2)
26 = 6x -4
30 = 6x
x = 30/6 = 5.
Sonny substituted 5 for x in the proportion startfraction 16 over x endfraction = startfraction 48 over 15 endfraction and cross multiplied to get 240 = 240. why is this? because the cross sums of the proportion are equal because the cross differences of the proportion are equal because the cross products of the proportion are equal because the cross quotients of the proportion are equal
Sonny get 240=240 because the cross products of the proportion are equal.
Proportion : Two ratios are said to be in proportion when the two ratios are equal.
For Example , If Smith walks 5 km in 1 hour then he will walk 25 km in 5 hours. denoted by
[tex]\frac{5}{1} =\frac{25}{5} \\ \\ 5=5[/tex].
According to the given question the equation can be written as
[tex]\frac{16}{x} =\frac{48}{15}[/tex]
Sonny substituted 5 for x in the proportion , the equation can be written as
[tex]\frac{16}{5} =\frac{48}{15} \\ \\ Doing .the .cross.product\\ \\ 16*15=48*5\\ \\ 240=240[/tex]
Therefore , Sonny get 240=240 because the cross products of the proportion are equal.
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Find the perimeter of ∠A B C to the nearest hundredth, given the coordinates of its vertices. A(-3,2), B(2,-9), C(0,-10)
The perimeter of the triangle ABC is approximately equal to 35.633 units.
How to determine the perimeter of a triangle
In this problem we find the locations of the three vertices of the triangle and from which we have to calculate the length of each of the three sides. The perimeter is the sum of the three lengths. First, determine the vectors of each side:
AB = (2, - 9) - (- 3, 2)
AB = (5, - 11)
BC = (0, - 10) - (2, - 9)
BC = (- 2, - 1)
AC = (0, - 10) - (- 3, 2)
AC = (3, - 12)
Second, calculate the magnitudes of the three sides:
AB = √[5² + (- 11)²]
AB = √146
BC = √[(- 2)² + (- 11)²]
BC = 5√5
AC = √[3² + (- 12)²]
AC = 3√17
Third, add the three lengths to find the perimeter:
p = √146 + 5√5 + 3√17
p ≈ 35.633
Remark
The statement reports a typing mistake that it would take a triangle for an angle, which is absurd since angles only have one vertex. Correct statement is shown below:
Find the perimeter of Δ ABC to the nearest hundred, given the coordinates of its vertices A(x, y) = (- 3, 2), B(x, y) = (2, - 9) and C(x, y) = (0, - 10).
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What is the greatest common factor of the terms in the expression
3x2y3-48y2+18x³y5?Q
The greatest and the only common factor in the given expression 3x²y³-48y²+18x³y⁵ is 3.
What do we mean by expressions?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent rules. In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.So, 3x²y³-48y²+18x³y⁵:
If we look closely consonants 3, -48, and 18 are divisible by 3.So, we can also write the expression as:
3(x²y³-16y²+6x³y⁵)Therefore, the greatest and the only common factor in the given expression is 3.
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Why might two students have different calculated areas when measuring the same rectangle?
Because of differences in the given dimensions, two students have different calculated areas when measuring the same rectangle.
What is a rectangle?In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.Because all of its angles are equal, it is also known as an equiangular quadrilateral or a parallelogram with a right angle.A square is a rectangle with four equal-length sides.So,
1st students measurement:
Length = 20.70, width = 10.442nd students measurement:
Length = 20.74, width = 10.46The formula of area:
Area = length × width1st students measurement:
Area = 20.70 × 10.44Area = 216.108 cm²2nd students measurement:
Area = 20.74 × 10.46Area = 216.940 cm²Therefore, because of differences in the given dimensions, two students have different calculated areas when measuring the same rectangle.
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The complete question is given below:
Calculating the area of a rectangle
Your measurements Another student's measurements
Length (cm) 20.70 20.74
Width (cm) 10.44 10.46
Area (cm2)
Required:
Why might two students have different calculated areas when measuring the same rectangle?
PLEASEEEE HELP
Select the correct answer from the drop-down menu.
Simplify the expression.
Answer:
2(x^9)(y^2)
Step-by-step explanation:
I just did quick math on this one, but you combine like terms on the top then divide by the bottom terms...
Quelqu’un pourrait m’aider en urgence s’il vous plaît c’est pour demain je n’ai pas réussi pour le x=2 mais pour x=1 oui. Voici l’exercice
Exercice 2:
L'égalité 3x + 4 = 2x+5 est-elle vraie pour x = 2 ? Justifier la réponse.
• L'égalité 3x + 4 = 2x+5 est-elle vraie x = 1 ? Justifier la réponse.
La partie « Exercez-vous »
➺ Exercez-vous
Je m'appelle Catherine… elle est italienne… Il est
anglais. – Et vous, vous êtes française ? – Oui, je suis
française.
➺ Exercez-vous
« vous » entre adultes qui ne se connaissent pas (dessin du haut) – « tu » entre étudiants (dessin du
milieu) quand un adulte s'adresse à un enfant (dessin
du bas).
A solid cylinder has a volume of 454 cm³.
The cylinder has a height of 10 cm.
A similar cylinder has a height of 30 cm.
What is the volume of the larger cylinder?
30 10×3=30 that how you get it
a rectangular prism w a square base with side length(x) and a height of length(y) has a surface area of 100 square feet
The the rectangular solid with maximum volume for given surface area is, in fact, a cube with side 4.5.
Which formula represents the volume of a rectangular prism?
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw .Let x = the side of the square base and y = height
Let V = volume = x2y
The surface area = 2x2 + 4xy = 121.5
Solve the surface area equation for y = (121.5 - 2x2)/4x and substitute this into the volume equation
V = x2(121.5 - 2x2)/4x = x(121.5 - 2x2)/4
the derivative of V with respect to x = (x/4)(-2x) + (1/4)(121.5 - 2x2) = 0 at the maximum
(1/4)(-4x2 + 121.5 - 2x2) = 0'
6x2 = 121.5
x2 = 20.25
x = 4.5
y = (121.5 - 40.5)/(4 * 4.5) =81/18 = 4.5
The the rectangular solid with maximum volume for given surface area is, in fact, a cube with side 4.5.
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Find the weighted average of the points in the line
The weighted average of the points in the line is 7.5
How to find the weighted average of the points in the line?The points are given as
3 and 12
The weighted average of the points in the line is calculated as
Weighted average = Sum/Count
So, we have:
Weighted average = (3 + 12)/2
Evaluate
Weighted average = 7.5
Hence, the weighted average of the points in the line is 7.5
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Cual es la Respuesta de 5a+7a
Answer:
12a
Step-by-step explanation:
1.5 x 10^9 and 1.1 x 10^8 as scientific notation
Answer:
4.875 × 105^5
Step-by-step explanation:
What’s is the answer
Answer:
C
Step-by-step explanation:
Taking a square root of a number that doesn't have a square root like [tex]\sqrt{17}[/tex] will result in an infinite number of random digits which is an irrational number. Hence, C is the answer.
D isn't the answer because even though [tex]\sqrt{5}[/tex] is irrational, you're adding [tex]\sqrt{5}[/tex] and then subtracting [tex]\sqrt{5}[/tex] from the total sum. Hence the total sum would be 5+14.
5+[tex]\sqrt{5}[/tex]+14-[tex]\sqrt{5}[/tex] =5+14+[tex]\sqrt{5}[/tex]-[tex]\sqrt{5}[/tex]= 5+14 ==> 19 is a rational number
4 - 5/3x - 7 = 4 please help solve
Step-by-step explanation:
multiply through by the LCM=3x-7
4(3x-7)-5=4(3x-7)
12x-28-5=12x-28
The integer coefficient of x on both sides of the equation=+12 so there's no integer solution for the equation
Triangle FUN has vertices with coordinates F(-6, 4), U(2, 2), and N(-2, -8). Dilate using the Scale factor of 2. What are the coordinates of the dilated image F’U’N’?
explain
Answer:
F ' (-12, 8)
U ' (4, 4)
N ' (-4, -16)
===================================================
Explanation:
I'm assuming the center of dilation is the origin.
Multiply each coordinate by the scale factor 2.
For point F, the x coordinate goes from -6 to 2*(-6) = -12. The y coordinate goes from 4 to 2*4 = 8
So F(-6,4) moves to F ' (-12, 8)
Use this idea for the other points.
If the center of dilation wasn't the origin, then we can't use this shortcut (not until translating the center to the origin).
Several batches of stew were made yesterday. Each batch required 1 and two-thirds pounds of meat. All together, 10 and StartFraction 5 over 6 EndFraction pounds of meat was used. Janice tried to find the number of batches of stew made. Her work is shown below.
Answer:
Step 2
1 2/3 was converted as 5/2 instead of 5/3
Step-by-step explanation:
Each batch = 1 2/3
Total = 10 5/6
Number of batches
10 5/6 : 1 2/3 =
65/6 : 5/3 =
65/6 * 3/5 =
65/10 =
6.5
Solution by Janice:
10 5/6 : 1 2/3 =
65/6 : 5/2 =
65/6 * 2/5 =
130/30 =
4 1/3
Error made at step 2:
StartFraction 65 over 6 EndFraction divided by five halves = StartFraction 65 over 6 EndFraction times StartFraction 2 over 5
1 2/3 was converted as 5/2 instead of 5/3
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
3m + 4 is the answer obtained after combining like terms
Mei spent $66 buying fabric that costs $7.50 per yard. how many yards of fabric did mei buy? how do you know that your answer is reasonable?
If Mei spent $66 buying fabric that costs $7.50 per yard, then she bought 8.8 yards of fabric
Given,
The total amount Mei spent = $66
Cost of fabric = $7.50 per yard
How many yards of fabric Mei bought= Total amount she spent / Cost of fabric
Substitute the values and divide it
How many yards of fabric Mei bought = [tex]\frac{66}{7.50}[/tex]
=8.8 yards
Hence, if Mei spent $66 buying fabric that costs $7.50 per yard, then she bought 8.8 yards of fabric
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Analysis of data reveals a correlation coefficient of r = 0.77. this is a ______ relationship.
Analysis of data that reveals a correlation coefficient of 0.77 shows a strong relationship between variables.
What is correlation?Correlation can be defined as any statistical relationship, whether causal or not, between two random variables or bivariate data. The type of correlation that we have include;
Positive correlationnegative correlationzero correlationA calculated number greater than 1.0 or less than -1.0 means that there was an error in the correlation measurement while a correlation that is between 0.6 and 0.9 are classified as a strong relationship.
Hence we can conclude that analysis of data that reveals a correlation coefficient of 0.77 shows a strong relationship between variables.
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find the equation of the line passing through the point (-6,4)(−6,4) that is perpendicular to the line 5x 3y
The required equation of line is: [tex](y - 4)= \frac{3}{5}(x+6)[/tex]
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Given:
Equation of line: 5x + 3y = 5New line passes through the point (-6,4)New line perpendicular to given line.To find: Equation of new line
Finding:
Given equation of line: 3y = 5 - 5x=> y = [tex]\frac{5}{3} (1-x) = \frac{-5}{3}(x-1)[/tex]
On comparison with a standard equation of line: [tex](y-y_0) = m(x-x_0)[/tex], where, m = slope of the line[tex](x_0,y_0)[/tex] = coordinates of point through which the line passes.We get: m = -5/3 and [tex](x_0,y_0)[/tex] = (1,0) for the given line.
Now, since the given line is perpendicular to the new line,Slope of the new line = m' = [tex]\frac{-1}{m} = \frac{3}{5}[/tex]
Hence, On substituting the values for [tex](x_0,y_0)[/tex] and m', we get the equation of the new line as:
[tex](y - 4)= \frac{3}{5}(x+6)[/tex]
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Questions 18-30 pls help due tomorrow
Answer:
Step-by-step explanation:
30
Step-by-step explanation:
以下の情報を添えて、このチラシを当社の登録従業員の 1 人に渡してください。 より多くのチラシを提出した先生がピザ パーティーを勝ち取ります。
Two angles of a triangle have measures 45⁰ and 92⁰ . What type of triangle is it?
a. obtuse scalene
b. obtuse isosceles
c. acute scalene
d. acute isosceles
A triangle with two angles measuring 45⁰ and 92⁰ is an obtuse scalene triangle. The answer is A.
A triangle is a two-dimensional shape that has three sides and three angles. The sum of its interior angles is 180⁰.
If two angles of a triangle have measures 45⁰ and 92⁰, solving for the third angle
180⁰ = 45⁰ + 92⁰ + third angle
third angle = 43⁰
If a triangle has an angle greater than 90⁰, then it is an obtuse triangle.
If a triangle has angles less than 90⁰, then it is an acute triangle.
If a triangle has an angle equal to 90⁰, then it is a right triangle.
An isosceles triangle is a triangle with two congruent sides and congruent base angles (2 angles are equal).
An equilateral triangle is a triangle with all three sides equal and all three angles are of equal measures.
A scalene triangle is a triangle with no sides are equal and no angle are equal also.
Since our triangle has 3 unique angles: 43⁰, 45⁰, and 92⁰, with one angle greater than 90⁰, then it is an obtuse scalene triangle.
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HELP ME PLEASE!!!!! I WILL NAME YOU BRAINLIEST
please solve question 2 part b :)
The equivalent of the given expression ( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x ) is (6 1/4)x - 5.
What is the equivalent of the given expression?Given the expression in the question;
( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x )
First, convert the mixed fractions into an improper fractions.
( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x )
( (4×2 + 1/2)x - 3 ) + ( -2 + (1×4 + 3/4)x )
( (8 + 1/2)x - 3 ) + ( -2 + (4 + 3/4)x )
( (9/2)x - 3 ) + ( -2 + (7/4)x )
Now, remove the parenthesis and collect like terms
(9/2)x - 3 + -2 + (7/4)x
(9/2)x + (7/4)x - 3 - 2
9x/2 + 7x/4 - 5
Now, add the two fractions containing x
(9x × 4)+(7x × 2)/8 - 5
( 36x + 14x )/8 - 5
50x/8 - 5
(50/8)x - 5
(25/4)x - 5
Convert 25/4 into an improper fraction
(6 1/4)x - 5
Therefore, the equivalent of the given expression ( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x ) is (6 1/4)x - 5.
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The farmer’s market opens for 2 ⅕ hours in the morning and 3 ⅔ hours in the afternoon. How long is the farmer’s market open in a day?
the lifespans of gorillas in a particular zoo are normally distributed with a mean of 26 years and a standard deviation of 1.5 years. what is the probability that a gorilla will live longer than 26 years?
The probability that a gorilla will live longer than 26 years is between 15.8 and 24.2 years.
What is probability?Likelihood is the part of science concerning mathematical portrayals of how likely an occasion is to happen, or how likely it is that a recommendation is valid.
P (A) is the probability of an event “A”
n (A) is the number of favorable outcomes
n (S) is the total number of events in the sample space
The likelihood of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 shows difficulty of the occasion and 1 demonstrates conviction. The higher the likelihood of an occasion, the almost certain it is that the occasion will happen. A straightforward model is the throwing of a fair coin. Since the coin is fair, the two results are both similarly likely; the likelihood of "heads" approaches the likelihood of "tails"; and since no different results are conceivable, the likelihood of by the same token "heads" or "tails" is 1/2.
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