Andre made a mistake after getting 14x=8x. He divided each side by x, but this is not valid since x may be 0 and dividing by 0 gives an undefined result.
Andre should have collected the like terms in order to have all the variables x on one side before taking the difference.
Inequality expression
Given the inequality expression solved by andre expressed as:
14x + 3 ≤ 8x + 3
Simplify to have:
14x - 8x ≤ 3-3
6x ≤ 0
x ≤ 0
Hence andre should have collected the like terms in order to have all the variables x on one side before taking the difference.
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How many paralellograms are there in the picture?
Correct option is D)
We shall label the figure as shown below:
The simplest parallelograms are ABML, BCNM, COON, DEFO, OFGH, NOHl, MNIJ and LMJK i.e. 8 in number.
The parallelograms composed of two components each are ACNL, BDOM, CEFN, LNIK, MOHJ, NFGI, ABJK, BCLJ, CDHI and DEGH i.e. 10 in number.
The parallelograms composed of three components each are ADOL, BEFM, LOHK and MFGJ i.e. 4 in number.
The parallelograms composed of four components each are AEFL, LFGK, ACIK, BOHJ and CEGI i.e. 5 in number.
The parallelograms composed of six components each are ADHK and BEGJ i.e. 2 in number. AEGK is the only parallelograms composed of eight components.
Total number of parallelograms in the figure =8+10+4+5+2+1=30
Hence, the answer is (D).
Answer:
Option D is correct
Step-by-step explanation:
...
Band members are selling magazines to raise $150 for a field trip. The bar graph below shows the amount six band members have collected so far. Paul, Jim, and Dan are boys and Jane, Mia, and Bryn are girls.
By what percent of the total money raised so far do the girls exceed the boys?
Answer: About 7%
Step-by-step explanation:
I attached th eproblem.
Answer:
[tex]\frac{7}{b+4}[/tex]
Step-by-step explanation:
[tex]\frac{7}{b^2+5b+4}[/tex] × [tex]\frac{b^2+8b+7}{b+7}[/tex] ← factor quadratics on numerator/ denominator
= [tex]\frac{7}{(b+1)(b+4)}[/tex] × [tex]\frac{(b+1)(b+7)}{b+7}[/tex]
cancel factors (b+ 1) and (b + 7) on numerator/ denominator
= [tex]\frac{7}{b+4}[/tex] × 1
= [tex]\frac{7}{b+4}[/tex]
Question 1(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify √5(6-4√3)
09
30√3
06√5-4√15
O√30-20√3
Answer:
6√5 - 4√15
Step-by-step explanation:
√5(6 - 4√3) =
Distribute √5
= 6√5 - 4√3√5
= 6√5 - 4√15
. a survey of first-time home buyers found that the sample mean annual income was $51,000. assume that the survey used a sample of 28 first-time home buyers and that the sample standard deviation was $1,200. compute and explain a 95% confidence interval estimate of the population mean.
The 95% confidence interval estimate of the population mean is between $50,555.51 and $51.444.49.
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x (SD / √n)
where CI = confidence interval
μ = sample mean
z = found by using a z-score table
SD = sample standard deviation
n = sample size
At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.
(100 - 95) / 2 = 2.5
100 - 2.5 = 97.5
Find 0.975 in the z-table to get the value of z.
At p = 0.95, z = 1.96
Plug in the values and solve for the confidence interval.
CI = μ ± z x (SD / √n)
CI = $51,000 ± 1.96 x ($1,200 / √28)
CI = $51,000 ± $444.49
CI = [$50,555.51, $51.444.49]
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A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is 5\%5%5, percent more than the number of shoppers the day before. The total number of shoppers over the first 101010 days is 125812581258.
The population on the first day of the opening of the mall was 7723.66.
Percentage:
A relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Here it is given that there is an increase in the population of the mall by 5%
We have to find the population on the first day.
The population on the 10th day is 12581.
let x be the population on the first day.
Population on the 10th day = x( 1 + 5/100[tex])^{10}[/tex]
12581 = x [tex]1.05^{10}[/tex]
x = 12581/ 1.62889
= 7723.66
Therefore we get the population on the first day of the mall to be 7723.66.
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What is the equation of the function that is graphed as line b?
y = -2 x - 1
y = 1/2x + 1
y = 3 x
y = 2 x - 1
Answer:
A
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line
m = [tex]\frac{-1-1}{0-(-1)}[/tex] = [tex]\frac{-2}{0+1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2
the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = - 2x - 1 ← equation of line b
A bike shop X it costs $1.50 per hour plus a $4.00 deposit to rent a bike. At Bike Shop Z it costs $0.50 per hour plus a $9.00 deposit to rent a bike. The total cost, c, of renting a bike for n hours at either bike shop can be represented by an equation. Write and solve a system of equations to find how many hours you have to rent the bike for the cost to be the same.
Answer:
4+1.5n=c
9+0.5n=c
5 hours
Step-by-step explanation:
(n) represents the number of hours
(c) represents the total cost
Bike shop A) $4+$1.5n=c
Bike shop Z) $9+$0.5n=c
4+1.5n=9+0.5n
n=5 Both shops would charge the same amount at 5 hours.
What is the intermediate step in the form (x+a)^2=b(x+a)
2
=b as a result of completing the square for the following equation?
x^2-28=12x
The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64
Given,
The equation x² - 28 = 12x
We need to find the intermediate step in the form (x + a)² =b as a result of completing the square for the given equation
Equation; x² - 28 = 12x
Arrange the equation;
x² - 12x = 28
Take the coefficient of x
k = -12
Divide it by 2
k/2 = -6
Square both sides
(k/2)² = 36
Add 36 to both sides of x² - 12x = 28
x² - 12x + 36 = 28 + 36
(x - 6)² = 64
Therefore,
The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64
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Do the following rectangle have the ame perimeter, area, or both? A rectangle i labeled 4 centimeter along it left ide and 5 centimeter along it top ide. A rectangle i labeled 4 centimeter along it left ide and 5 centimeter along it top ide. A rectangle i labeled 10 centimeter along it left ide and 2 centimeter along it top ide. A rectangle i labeled 10 centimeter along it left ide and 2 centimeter along it top ide. Chooe 1 anwer: Chooe 1 anwer: (Choice A) A Same area only (Choice B) B Same perimeter only (Choice C) C Same area and perimeter
(Choice A) A Same area only is the correct option about rectangles.
The perimeter and area is calculated using the formula -
Perimeter = 2 (length + breadth)
Area = length × breadth
Now, calculating the perimeter and area of each rectangle
Rectangle with dimensions 5 cm and 4 cm
Perimeter = 2 (5 + 4)
Perimeter = 2 × 9
Perimeter = 18 cm
Area = 5 × 4
Area = 20 cm²
Rectangle with dimensions 2 cm and 10 cm
Perimeter = 2 (2 + 10)
Perimeter = 2 × 12
Perimeter = 24 cm
Area = 2 × 10
Area = 20 cm²
Thus, both the rectangles will have same area.
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A triangle has sides of length of 39 mm 56 mm and 37 mm is it a right triangle
By Pythagoras theorem, The given triangle with sides 37 mm, 39 mm, 56 mm is not a right triangle as the theorem is false in this case.
What is Pythagoras theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The Pythagorean Theorem demonstrates how the side lengths of a right triangle can be calculated from the sum of the areas of three intersecting squares. This theorem is a very helpful tool that serves as the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite.
Here,
We can prove this by Pythagoras theorem,
b²+p²=h²
b=39 mm
p=37 mm
h=56 mm
=39²+37²
=2,890
56²=3,136
As 2890≠3136,
The triangle is not a right triangle. The triangle with sides of 37, 39, and 56 millimeters is not a right triangle according to Pythagoras' theorem because the theorem is incorrect in this case.
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On a number line if A is at 9 and B is at 20. Find the length of AB
Answer:
11units (Brainliest?)
Step-by-step explanation:
(20-9)²
(11)²
(cancel squares by square rooting both sides)
11
In the image below, the m<1 = (x -18)° and the m<2 = (3x+36)°. What is the measure of <3? Show all your work.
The measure of angle 3 is 22.5°.
Given,
∠1 = (x-18)°
∠2 = (3x+36)°
∠1 + ∠2 = 180° (Straight Line)
x - 18 + 3x + 36 = 180
4x + 18 = 180
4x = 180 - 18
4x = 162
x = 162/4
x = 40.5
∠3 = ∠1 (Alternate opposite angles)
= x - 18
= 40.5 - 18
= 22.5
Hence, ∠3 is 22.5°.
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wh at is the smallest number of rectangles, each measuring 2cm by 3cm, which are needed to fit together without overlap to form a rectangle whose sides are in the ratio 5:4 ?
The smallest number of rectangles required will be 30.
Given:- The sides of the rectangle are in the ratio of 5:4
let, length=5x
breadth=4x
Area = 20x²
Area of smaller rectangle =2*3
=6cm²
Now, take numbers which are in the ratio of 5:4;
suppose, Case 1=10:8
Case2 = 15:12
For Case 1;
number of rectangles needed =10*8/2*3
=13.3333
This means it is overlapping hence, not possible.
For Case 2;
number of rectangles needed=15*12/2*3
=30
therefore, the smallest number will be 30.
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The bakery shipped out b boxes of bagels. Each box contained 12 bagels. Write an expression that shows the total number of bagels shipped.
Answer: b=12x
Step-by-step explanation:
The bakery shipped out b boxes of bagels.
Each box contained 12 bagels
b is the number o boxes
x is the number of bagels in each box
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 450 nails. The contractor bought 3 more small boxes than large boxes, which altogether had 2500 nails. Determine the number of small boxes purchased and the number of large boxes purchased.
The total number of small boxes is 1.72 and the large boxes is 5.1.
Given;
To build a house, a contractor has to purchase nails. Both small and large boxes of nails are provided. There are 100 nails in each small box and 450 in each large box. The contractor purchased 3 more tiny boxes—totaling 2500 nails—than large boxes.
To calculate the proportion of small and large boxes that were bought,
Let's assume the small boxes as 's' and the big boxes as '3s'.
∴ s(100) + 3s(450) = 2500
100s + 1350s = 2500
1450s = 2500
s = 2500/1450
s = 1.72
∴ 3s = 1.72 * 3
= 5.1
Hence, the total number of small boxes is 1.72 and the number of large boxes is 5.1.
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The number of small boxes purchased is 7 and the number of large boxes purchased is 4 by the contractor.
Let the number of large boxes purchased = x
then the number of small boxes purchased = x + 3
It is also given that,
small box contains = 100 nails
large box contains = 450 nails
According to the question:
450x + 100(x + 3) = 2500
450x + 100x + 300 = 2500
550x = 2500 - 300 = 2200
x = 2200/550
x = 4
and x + 3 = 4 + 3 = 7.
Thus, Let the number of small boxes purchased = 4 and the number of small boxes purchased = 7.
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find an equation parallel to y=5 and passing through (3,-5)
Using the equation of line, the equation parallel to y=5 and passing through (3,-5) is y+5=0.
In the given question,
We have to find an equation parallel to y=5 and passing through (3,-5).
The equation parallel to y=5.
Point is (3,-5).
We firstly find the slope of y=5
Expressing the equation in the general form
y=0×x+5
On comparing to the y=mx+c, we get slope(m) = 0.
The given point is (3,-5) in which [tex]x_{1}[/tex]=3 and [tex]y_{1}[/tex]= -5
Now finding the equation.
So the Equation of line is
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
Now putting the value
y-(-5)=0(x-3)
Simplifying
y+5=0
Hence, the equation parallel to y=5 and passing through (3,-5) is y+5=0.
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When comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, a one-way anova is appropriate. It is also appropriate in this situation, however, to compare two means at a time using multiple independent two sample t-tests. True or false?.
According one-way ANOVA, the test is false.
In the given question,
When comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, a one-way ANOVA is appropriate. It is also appropriate in this situation, however, to compare two means at a time using multiple independent two sample t-tests. We have to check whether this is true or false.
We firstly learn about one-way ANOVA
"One-Way ANOVA, also known as "analysis of variance," examines the means of two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."
According to the given method it is inappropriate to compare two means at a time using multiple independent two sample t-tests. It will create multiple testing problem and error.
So using one way ANOVA test when comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment and compare two means at a time using multiple independent two sample t-tests is false.
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Please Help Me I'm going to cry If don't get this right ASAP!!!! 100 points Whoever answers gets Brainllest.
Cd is the perpendicular bisector of ab. Ad ≅ bd by definition of a bisector. ∠ cda and ∠ cdb are both right angles based on the definition of perpendicular lines. Cd ≅ cd by the reflexive property of congruence. Δ adc ≅ δ bdc by the _____. So ca ≅ cb because corresponding parts of congruent triangles are congruent.
Answer:
YesTheorem 8.3: If two angles are complementary to the same angle, then these two angles are congruent.
A and B are complementary, and C and B are complementary.
Select all of the equations below that have no solutions.
Select 2 correct answer(s)
3x + 5 = 3x + 8
3(x + 5) = 3x + 15
2(x + 1) = 2x + 1
2x + 1 = 2x + 1
Answer:
3x + 5 =3x + 8
Step-by-step explanation:
3x - 3x = 8-5
x = 3
Step-by-step explanation:
we have to soft the ones that have no solutions.
3x + 5 = 3x + 8
5 = 8
that is never true, and therefore there is no solution.
3(x + 5) = 3x + 15
3x + 15 = 3x + 15
that is always true, and it has therefore infinitely many solutions.
2(x + 1) = 2x + 1
2x + 2 = 2x + 1
2 = 1
this is never true, so, there is no solution.
2x + 1 = 2x + 1
this is always true, so this has infinitely many solutions.
help!!!
Use mental math to decide which equations are true. Drag the true equations into the box.
1.23÷101=0.123
123÷100=1.23
12.3÷100=1.23
0.123÷10=1.23
1,230÷103=1.23
true equations
Which values are part of the solution set based on the result of the inequality?
-4x + 24 < -2x + 2
Step-by-step explanation:
Which values are part of the solution set based on the result of the inequality?
-4x + 24 < -2x + 2
add 2x to both sides:
-4x + 24 + 2x < -2x + 2 + 2x
-2x + 24 < 2
subtract 24 from both sides:
-2x + 24 - 24 < 2 - 24
-2x < -22
divide both sides by -2: [remember to flip the sign direction because you are dividing by a negative number]
-2x/-2 > -22/-2
x > 11
or (11 , ∞)
!!PLEASE HELPPPPPP!!
Answer:
Q29. ∠CAD = (180° - 92°) ÷ 2 (angle sum of triangle; base angles of an isosceles triangle)
= 44°
Q30. Since triangle ACD is an isosceles triangle,
∴ ∠ACD = ∠CAD = 44°
Q31. ∠ACB = 180° - 44° (adjacent angles on a straight line)
= 136°
Q32. ∠ABC = (180 °- 136°) ÷ 2 (angle sum of triangle; base angles of an isosceles triangle)
= 22°
you take a random sample of 605 iphones off an assembly line and find that 0.07 proportion to be defective. what is a lower bound for a 95% confidence interval for the proportion
The lower bound for a 95% confidence interval for the proportion of defective iphones from this assembly line is 0.0524.
With the probability of a success of π , and a confidence level of 1-α, we have the following confidence interval of proportions:
π± z[tex]\sqrt{\frac{\pi (1-\pi }{n} }[/tex]
z is the z-score having a p-value of 1-α/2.
we have η = 605 and ρ = 0.07
So, α = 0.1 and z is the value of Z that has a pvalue of:
1 - 0.1/2 = 0.95
Z= 1.645
Now the lower limit:
π - z[tex]\sqrt{\frac{\pi (1-\pi }{n} }[/tex]
= 0.07-1.645[tex]\sqrt\frac{(0.07*0.93)}{605}[/tex]
= 0.07 - 0.01706
= 0.0524
The lower bound for a 95% confidence interval for the proportion of defective Galaxy phones from this assembly line is 0.0524
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10. Find point W on the y-axis so that VW + XW is a minimum given V(2, 3) and
X(-2, -1).
The point on the y-axis is (0,1) such that the distance is minimum.
Let the coordinate of the point W be (0,a)
We know that the distance from any point on the coordinate place is calculated using the distance formula.
Now let us calculate the distance of VW = √[(2-0)²+(3-a)²]
Distance XW = √[(-2-0)²+(-1-a)²]
Now the sum of the distances is given by:
VW + XW
=√[(-2-0)²+(-1-a)²] + √[(2-0)²+(3-a)²]
This can be written in the form of a function in a such that:
f(a) = √a²+2a+5 + √a²-6a+25
Now we will differentiate with respect to a to get the required first degree
f'(a) = [tex]\frac{a+1}{\sqrt{a^2+3a+5}} + \frac{a-3}{\sqrt{a^2-6a+25}}[/tex]
Now at f'(a)=0
we get a=1.
Hence the required point on the y-axis that is at a minimum distance is (0,1) .
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Solve by the substitution method.
8x-3y=20
5x-y=2
Answer is in ordered pair (x,y)
The ordered pair (x,y) obtained from the linear equations is: (-2,-12)
What is Linear Equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Definition of a Linear Equation: Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason. A linear equation is expressed using the linear equation formula. There are several ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form. To discover how a linear equation is stated in its standard form, let's take an example.
The equation is given:
8x-3y=20
5x-y=2
Using the substitution method for solving the linear equations:
From the equation:
5x-y=2;
we can transform this equation as:
⇒-y = 2-5x;
⇒y = 5x-2;
Now substituting the value of y in the other equation: we get;
⇒8x-3(5x-2)=20
⇒8x -15x+6 = 20;
⇒-7x=14;
x = -2;
Now putting the value of x in the equation to get the value of y;
So,
y = 5(-2) -2;
y = -12;
Hence the value of x and y are -2 and -12 respectively;
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Write an equation in slope-intercept form of the line that passes through (6,
-1) and (3,
-7).
Answer: y = 2x - 13
Step-by-step explanation:
y=mx + b
[tex]m= \frac{-7-(-1)}{3-6}[/tex]
[tex]= \frac{-6}{-3}[/tex]
[tex]m = 2[/tex]
y = 2x + b
(6, -1) <-- use to find "b" by substituting either one of the coordinates
-1 = 2(6) + b
-1 = 12 + b
-13 = b
y = 2x - 13
2(-4x + 2) + 5x - 2 = -19
Solve for x.
Answer:
x = 7
Step-by-step explanation:
2 (-4x + 2) + 5x - 2 = -19 Distribute 2 to -4x and 2
-8x + 4 + 5x - 2 = -19 Combine like terms
-3x + 2 = -19 Subtract 2 from both sides
-3x = -21 To get x by itself, divide -3 on both sides
x = 7
Hi my name is winstead
Answer: Hello winstead. I'm Walter White
Step-by-step explanation:
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