Show that the union of a nonempty directed family of subgroups of a group G is a subgroup of G?
H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.
Let [tex]\mathcal{H}[/tex] be a non-empty directed family of subgroups of a group G. We need to show that the union [tex]H=\bigcup_{H_i\in\mathcal{H}}H_i[/tex] is a subgroup of G.
First, note that H is non-empty since[tex]\mathcal{H}[/tex] is non-empty. We also have [tex]1_G \in H_i[/tex] for all [tex]H_i\in\mathcal{H}[/tex], so [tex]1_G \in H.[/tex]
To show that H is closed under multiplication, let [tex]h_1,h_2\in H[/tex]. Then there exist [tex]H_{i_1},H_{i_2}\in\mathcal{H}[/tex] such that [tex]h_1\in H_{i_1}[/tex] and [tex]h_2\in H_{i_2}.[/tex] Since [tex]\mathcal{H}[/tex] is directed, there exists[tex]H_{i_3}\in\mathcal{H}[/tex] such that [tex]H_{i_1}\cup H_{i_2} \subseteq H_{i_3}[/tex]. Thus, [tex]h_1,h_2\in H_{i_3},[/tex]and since [tex]H_{i_3}[/tex] is a subgroup, we have [tex]h_1h_2\in H_{i_3} \subseteq H[/tex]. Therefore, H is closed under multiplication.
Finally, to show that H is closed under taking inverses, let h\in H. Then there exists [tex]H_i\in\mathcal{H}[/tex] such that [tex]h\in H_i[/tex]. Since [tex]H_i[/tex]is a subgroup, we have [tex]h^{-1}\in H_i \subseteq H[/tex]. Therefore, H is closed under taking inverses.
Since H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.
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Silverton County is home to a declining population of sage grouse, an endangered species of land bird similar to turkeys. Every decade, the Silverton Wildlife Center publishes its estimate of the county's sage grouse population. The most recent estimate, published this year, concluded that there are about 115,000 sage grouse in the county, and the population is expected to decrease by a factor of 1/4 each decade.
Write an exponential equation in the form y=a(b)x that can model the estimated population of sage grouse in Silverton County, y, in x decades.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]
How to write an exponential equation in the form y=a(b)x that can model the estimated population of sage grouse in Silverton CountyGiven that the population is expected to decrease by a factor of 1/4 each decade, we know that the common ratio, b, is 1/4.
Since the most recent estimate is about 115,000 sage grouse, we can assign this value to the initial population, a.
Therefore, the exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]
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The sine of an angle in the third quadrant is -0.5. What is the value of
tan(0)?
Answer:
-0.5. is 5
Step-by-step explanation:
i need the poits
Use the Distributive Property to find (g−7)(g−2) all i need is the answer
Answer: [tex]g^2-9g+14[/tex]
Step-by-step explanation:
(g-7)(g-2)
[tex]g^2 - 2g-7g+14[/tex]
[tex]g^2-9g+14[/tex]
Use FOIL method.
You purchased a home this year for $315,000. You applied for homestead exemption
and were able to take off $50,000 of the appraised value for taxes. The taxes in your
county are 1.22%. What is the monthly payment added to your mortgage for
property taxes? Please round to the nearest cent and do not put a dollar sign or
spaces in your answer.
The monthly payment added to your mortgage for property taxes is $270.25, rounded to the nearest cent. It is a good idea to budget for property taxes when purchasing a home, as they can be a significant expense that should not be overlooked.
To calculate the monthly payment added to your mortgage for property taxes, we can use the following steps:
1) Find the taxable value of the home by subtracting the exemption from the appraised value:
Taxable value = $315,000 - $50,000 = $265,000
2) Calculate the annual property tax by multiplying the taxable value by the tax rate:
Annual property tax = $265,000 x 0.0122 = $3,243
3) Divide the annual property tax by 12 to get the monthly payment:
Monthly property tax payment = $3,243 / 12 = $270.25
It's important to note that property tax rates can vary depending on where you live, so it's a good idea to check with your local tax authority to get an accurate estimate of your property tax bill.
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In Austin TX the cost of housing for a family of four is $1600 per month. How much more would the family need to bring home annually in order to cover the cost of increased housing
The family would need to bring home an additional $2400 annually to cover the increased cost of housing.
The family would need to bring home annually to cover the cost of increased housing need to calculate the total cost of housing for a year and subtract the current annual cost of housing.
The current monthly cost of housing is $1600 so the annual cost is:
$1600/month x 12 months = $19,200/year
Let's assume the family needs to cover an increased housing cost of $200 per month.
The new monthly cost of housing would be:
$1600/month + $200/month = $1800/month
The new annual cost of housing would be:
$1800/month x 12 months = $21,600/year
The family would need to bring home annually to cover this increased cost need to subtract the current annual cost of housing from the new annual cost of housing:
$21,600/year - $19,200/year = $2400/year
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All one question. An electrical firm manufactures light bulbs that have a claimed lifetime with a mean of 1000 hours and a well-established standard deviation of 150 hours. Bulb life is approximately normally distributed.
a) The null hypothesis: H0: μ >= 1000
alternate hypothesis Ha: μ < 1000
b) The value of the test statistic is -3.12.
a) The null hypothesis, denoted by H0, is a statement of no difference or no effect. The alternate hypothesis, denoted by Ha, is a statement of a difference or effect that we want to test.
In this case, the null hypothesis would be that the average bulb life is greater than or equal to 1000 hours:
H0: μ >= 1000
The alternate hypothesis would be that the average bulb life is less than 1000 hours:
Ha: μ < 1000
where μ is the population mean bulb life.
b) To calculate the test statistic, we need to use the formula:
t = (x - μ) / (s / √(n))
where x is the sample mean, μ is the hypothesized population mean (under the null hypothesis), s is the sample standard deviation, and n is the sample size.
Substituting the given values, we get:
t = (950 - 1000) / (160 / √(30))
t = -3.12
Therefore, the value of the test statistic is -3.12.
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Which figure could be the result of dilating this rectangle with a scale factor between 0 and 1? On a coordinate plane, a rectangle has points (0, 0), (0, 3), (6, 3), (6, 0). Group of answer choices On a coordinate plane, a rectangle has points (0, 0), (0, 1), (2, 0), (2, 1). On a coordinate plane, a rectangle has points (0, 0), (0, 4), (8, 4), (8, 0). On a coordinate plane, a rectangle has points (0, 0), (0, 1), (4, 1), (4, 0). On a coordinate plane, a rectangle has points (0, 0), (0, 2), (8, 2), (8, 0).
The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.
Option B is the correct answer.
We have,
Dilation is a transformation that changes the size of an object.
When a figure is dilated with a scale factor between 0 and 1, the resulting figure is smaller than the original.
The scale factor indicates how much smaller the image is compared to the original.
For example, a scale factor of 0.5 would mean that the image is half the size of the original.
Now,
The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.
This is because the side lengths of the second rectangle are half of the side lengths of the first rectangle, which means that the second rectangle is a dilation of the first rectangle with a scale factor of 0.5.
Thus,
The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.
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I need to know how to solve number 4 in order to get a solution
Answer: 11x16x5=880
This means the answer is C
M- What is the exponent for
X in the problem below:
Xy³z²
Step-by-step explanation:
x y^3 z^2 = x^1 y^3 z^2
the x exponent is '1'
In LMN point P in the centroid, and AN = 18. Find AP and NP
The measures of NP and AP equals 8
How to determine the valuesFirst, it is important to note that;
The center of any shape is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. The median is a line that connects the middle of a side to the triangular opposite vertex.From the information given, we have that;
The centroid of the triangle divides AN in the ratio of 1: 2
Hence, the length of AN is twice that of line NP
So;
AN = 2NP
Substitute the value
18 = 2NP
Divide by the coefficient
NP = 9
But;
AN = NP + AP
Substitute the values, we get;
AP = 18 - 9
AP = 9
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PLs help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The area of the triangle is given as follows:
17 cm².
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
Considering the image presented for this problem, the dimensions for the triangle are given as follows:
b = 5 cm, h = 6.8 cm.
Applying the multiplication of these dimensions, the area of the triangle is given as follows:
A = 0.5 x 5 x 6.8
A = 17 cm².
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Actually answer and don't ask for brainliest
A hotel survey showed that nearly 30% of the guests staying at the hotel were there for personal reasons. The remainder of the guests were at the hotel on business.
Use the table of randomly generated letters to answer the questions about this scenario. The letter P represents personal reasons, and B represents business reasons.
BBB PBB BPB PPB BBP
BBP PBB PPB PBB BBP
BBP BPB BBB BBB BBB
PPB BPB PBP BPB BBP
BPB PBP PPB PBB BBB
Based on this data, the estimated probability that exactly two of the three guests randomly picked were not there for personal reasons is .
The estimated probability that it takes at least four guests to find one who is staying for personal reasons is .
Answer:
The estimated probability that exactly two of the three guests randomly picked were not there for personal reasons is 0.25.
The estimated probability that it takes at least four guests to find one who is staying for personal reasons is 0.125.
Books in the clearance section at Reading Central Bookmart cost $6.00 for paperbacks and $12.00 for hardbacks. Which inequality best describes the number of paperback books, p, and the number of hardback books, h, that can be purchased for $53.00 or less?
A.
12p + 6h > 53
B.
6p + 12h < 53
C.
12p + 6h < 53
D.
6p + 12h < 53
13. Lynn is a single mother with two children. She qualifies to file as head of household. Her total income before
deductions was $38,900 last year. Her total deductions were $11,450. Her employer withheld $3,150 from her pay for tax.
Use the tax table below. How much more will Lynn owe in taxes?
a. $570
c. $407
b. $563
d. $399
If line 43
(taxable
income) is -
At
least
But
less
than
And you are-
Single Married Married Head
fing Ning
of a
jointly sepa
house-
hold
Trately
Your tax is
27,000
27,000 27,050 3.653 3,251 3.653 3,481
27,050 27,100 3.660 3.259 3.660
3,489
27,100 27,150 3.668
3.266 1668 3,496
27,150 27,200 3,675 3.274 3.675 3.504
27,200 27,250 3,683 3.281 3,683
27,250 27,300 3,600
3511
3.289 3.600 3519
27,300 27,350 3.008 3.296 1698 3,526
27,350 27,400 3.705
3,304 3,705 3.334
27,400 27,450 3,713 3.311 3,713 3,541
3.549
3,728 3556
3,735 3.564
27,450 27,500 3,720 3319 3,720
27,500 27550 3.728 3.326
3,735 3.334
3,743 3.341 3,743 3,571
27,550 27,600
27,600 27,650
27,650 27,700 3.750 3.349 3,750 3579
27,700 27,750 3,758 3.356 3.758 3,586
27,750 27,800 3.765 3.364 3765 3.994
27,800 27,850 3.773 3.371 3,773 3.601
27,850 27,900 3,780 3379 3,780 3.609
27,900 27,950 3.788 3.386 3.788
3,616
27,950 28,000 3,795
3.394 3.795
3.624
The additional tax (liability) that Lynn owes after her employer withheld $3,150 from her pay is D. $399.
What is the tax liability?Tax liability refers to the amount that a taxpayer owes.
We can determine the tax liability as the difference between the total tax and the employer-withheld tax.
The total tax is computed by applying the rate to the taxable income, which is the difference between the total income and the total deductions.
Lynn's total income last year = $38,900
Total deductions = $11,450
Employer withheld taxes = $3,150
Taxable income = $27,450 ($38,900 - $11,450)
From the tax table, when taxable income is at least $27,450 but less than $27,500, the total tax is $3,549, based on being a head of household.
The tax liability = $399 ($3,549 - $3,150)
Thus, Lynn is expected to remit an additional $399 to settle her tax liability.
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5. What is is mXW based on the figure shown? Assume YWis a diameter of the circle.
M
O
O
60°
120°
78°
42°
W
PRE
Answer:
60°
Step-by-step explanation:
180-78-42=60
The following figure shows a cube. Which expression represents the surface area of the cube? Choose 1 answe B 6-10 5 5-5-5 25 + 25 + 25 + 25 + 25 + 25 5+5+5+5+5+5
The expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25
Calculating the expression that represents the surface area of the cube?From the question, we have the following parameters that can be used in our computation:
The cube
The side length of the cube is
Side length = 5
The surface area of the cube is calculated as
SA = 6 * Side length²
So, we have
SA = 6 * 5²
Expand
SA = 6 * 25
Further expand
SA = 25 + 25 + 25 + 25 + 25 + 25
Hence, the expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25
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Complete question
The following figure shows a cube. Which expression represents the surface area of the cube? Choose 1 answer
(a) 5 5 - 5 - 5
(b) 25 + 25 + 25 + 25 + 25 + 25
(c) 5 + 5 + 5 + 5 + 5 + 5
The figure is attached
please show work I don't understand how to do this
so first I would move -6x to the other side and -2 at the same time it would look like this
24+2=6x+7x
and simplify
26= 13x
divide both sides by 13 to find x
2= x
A company's sales in Seattle were 380000 in 2012, while their sales in Portland were $285000 for the same year. Complete the following statements a) seattles sales were _ % larger than portlands
B) portland sales were _% smaller than seattles
C) Portland sales were_% of seattles
Seattle's sales were approximately 33.33% larger than Portland's.
Portland's sales were approximately 25% smaller than Seattle's.
Portland's sales were approximately 75% of Seattle's sales.
We have,
a)
Seattle's sales were larger than Portland's by:
= (380,000 - 285,000)
= $95,000.
To calculate the percentage difference, we can use the formula:
Percentage difference = (Difference / Original value) x 100
Percentage difference = (95,000 / 285,000) * 100 ≈ 33.33%
b)
Portland's sales were smaller than Seattle's by (380,000 - 285,000) = $95,000.
To calculate the percentage difference, we can use the formula:
Percentage difference = (Difference / Original value) x 100
Percentage difference = (95,000 / 380,000) x 100 ≈ 25%
c)
Portland's sales were a certain percentage of Seattle's sales.
To calculate this percentage, we can use the formula:
Percentage = (Portland sales / Seattle sales) * 100
Percentage = (285,000 / 380,000) * 100 ≈ 75%
Therefore,
Seattle's sales were approximately 33.33% larger than Portland's.
Portland's sales were approximately 25% smaller than Seattle's.
Portland's sales were approximately 75% of Seattle's sales.
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Nicole correctly calculates that the Coach will spend $14,800 after 12 months if he chooses the Five-Year Plan. She then claims the total cost of the Five-Year Plan will be $74,000, because 5x $14,800 $74,000. The Coach says that Nicole made a mistake. Do you agree that Nicole made a mistake? Explain your reasoning. ANSWER FAST WHOEVER GIVES CORRECT ANSWER I WILL GIVE BRAINLIST!
I agree that Nicole made a mistake because the total cost of the Five year plan is $ 34, 000 and not $ 74, 000.
How was the mistake made ?The total cost of the Five year plan would be:
= Payment per month for the five year plan x Number of months in year x number of years + Down payment
= 400 x 12 x 5 + 10, 000
= 4, 800 x 5 + 10, 000
= $ 34, 000
The mistake that Nicole made was to multiply the $ 14, 800 that was the cost of the five year plan in one year, by five years. This was wrong because it meant including a new down payment in every one of the five years instead of just once.
She should have multiplied $4, 800 by 5 years and then added the down payment which is paid just once.
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Find the area of the regular polygon below and round your answer to the nearest tenth.
Explain your reasoning. Show all your work.
1) What is the perimeter of the regular polygon?
2) What is the apothem length? Show all your work and explain how you found the apothem.
3) What is the area of the regular polygon? Show your work.
7 sides each side is 10 in long
The area of the regular polygon is 311.5 in2.
We are given that;
A polygon
Now,
To find the perimeter of the regular polygon, we need to multiply the number of sides by the length of each side. The polygon has 7 sides and each side is 10 in long, so the perimeter is 7 * 10 = 70 in.
To find the apothem length, we need to use some trigonometry.
The central angle is 360/7 degrees, since there are 7 equal angles in a regular polygon. Half of the side length is 5 in, since each side is 10 in long. The apothem is the adjacent side of the right triangle. We can use the tangent function to find the apothem: tan(360/14) = 5/a, where a is the apothem. Solving for a, we get a = 5/tan(360/14) ≈ 8.9 in.
To find the area of the regular polygon, we need to plug in the values of P and a into the formula A = (1/2)P*a.
A = (1/2)708.9 ≈ 311.5 in2.
Therefore, by the area the answer will be 311.5 in2.
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Can someone please answer and provide an explanation for these problems?
Step-by-step explanation:
The way you can think about volume is that we have some cross sectional area times the height of the solid.
27.
The volume of a square based pyramid is
[tex]v = {s}^{2} ( \frac{h}{3} )[/tex]
where h is the height of the pyramid
s is the side length of the square base.
S=7
h=12
[tex]v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196[/tex]
28. The volume of a rectangular prism
[tex]v = l \times w \times h[/tex]
where l is length
w is width
h is height
[tex]v = 11 \times 11 \times 8 = 968[/tex]
29.
Use the same formula in 27
[tex]v = 100(3) = 300[/tex]
30.
Volume of a Cylinder is
[tex]v = \pi {r}^{2} h[/tex]
where r is the radius of the circle
where h is the height
r is half of the diameter
The diameter is 22, thus the radius is 11.
[tex]v = {11}^{2} (8)(\pi)[/tex]
[tex]v = 968\pi[/tex]
pi is approximately 3.14
[tex]v = 3041.06[/tex]
31. Volume of A Sphere
[tex] \frac{4}{3} \pi {r}^{3} = v[/tex]
The radius is half of diamter, thus r=7
[tex] \frac{4}{3} \pi( {7}^{3} ) = 1436.76[/tex]
26. Find the circumference and area. Give exact answers.
The area of a circle is 157 square units and the circumference of a circle is 31.4√2 units.
From the given figure, legs of triangle measure the same, that is 10 units.
Let the diameter of the circle be x.
By using Pythagoras theorem,
x²=10²+10²
x²=100+100
x²=200
x=10√2 units
Radius = 5√2 units
We know that, area of a circle = πr²
= 3.14×(5√2)²
= 3.14×50
= 157 square units
We know that, circumference of a circle = 2πr
= 2×3.14×5√2
= 31.4√2 units
Therefore, the area of a circle is 157 square units and the circumference of a circle is 31.4√2 units.
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Can someone help me with this pls its due td pls
The measures are given as follows:
x = 2.m < A = 110º.m < ABD = 34º.How to obtain the measures?On a parallelogram, the opposite sides are congruent, hence the value of x is obtained as follows:
2x = 4
x = 2.
Opposite angles are congruent, meaning that they have the same measure, hence the measure of angle A is given as follows:
m < A = m < C = 110º.
Consecutive angles are supplementary, meaning that the sum of their measures is of 180º, hence the measure of angle B is given as follows:
m<B = 180º - 110º = 70º.
Considering the angle addition postulate, the measure of angle ABD is given as follows:
m < ABD = 70 - 36
m < ABD = 34º.
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Please help quickly! (Will mark Brainliest)
Hello!
area
= (b x h)/2
= (18in x 7in)/2
= 126in²/2
= 63in²
Answer:
63 in²
Step-by-step explanation:
1/2 bh=area of the triangle
l want the steps.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
The first derivative of the parametric curve is:
dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]
How to solve1. To find the first derivative of the parametric curve x = 1/(t-1) and [tex]y = t^2/(t-1)[/tex], we can use the chain rule.
2. Let's differentiate each component separately.
3. Differentiating x with respect to t, we have:
dx/dt = [tex]-1/(t-1)^2[/tex]
4. Differentiating y with respect to t, we have:
dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2[/tex]
5. Therefore, the first derivative of the parametric curve is:
dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]
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Which of the following is NOT equivalent to x¹⁸
The option that is not equivalent to x ¹⁸ is D. x ¹⁹
How to find the equivalent ?As a means to simplify option 1, we can incorporate the rule of multiplying two powers with an identical base to add their exponents. For instance, by doing x³ × x¹⁵ , we would end up with x¹⁸, which ultimately leads to x ¹⁸ as an equivalent result.
By applying the understood concept that when raising a power to itself,exponents must be multiplied together, option 2 becomes more understandable. Specifically, (x ² ) ⁹ = x ¹⁸,the same equivalence as x¹⁸.
Similarly, option 3 assimilates this approach; (x ⁶ ) ³ = x¹⁸,leading to x¹⁸ once again as an equal resonance.
In contrast, option 4, i.e., x¹⁹, comprises an exponent one higher than x¹⁸ and thus, is dissimilarly unequal in comparison.
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Options for this question are:
x³ × x¹⁵
(x²)⁹
(x⁶)³
x¹⁹
3 pitchers of berry were made and 1/5 serving size how many were made
The total number of berry pitchers made is 15/5 or 3.
If the serving size of berry pitchers is 1/5, it means that each pitcher represents 1/5 of a full serving. To determine the total number of pitchers made, we need to calculate how many times 1/5 fits into the whole serving.
Let's assume that the total number of pitchers made is represented by "x". We can set up the following equation:
x * 1/5 = 3
To solve for "x," we multiply both sides of the equation by 5:
5 * (x * 1/5) = 5 * 3
This simplifies to:
x = 15/5
Thus, the total number of berry pitchers made is 15/5 or 3.
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Jane is converting the given equation in Standard Form to the General Form. At which step did she make her first mistake?
Answer:
Step 4
Step-by-step explanation:
In step 3, 16 + 9 = 25, so step 4 should subtract 25 from both sides. Also, y² became -y² in step 4 which is incorrect.
Answer: Step 4
solve 6x²-42=0 with the exact values of x
Answer:
X=-√7 and √7
Step-by-step explanation:
To solve the equation 6x² - 42 = 0, we can begin by rearranging it to isolate the variable term:
6x² = 42
Then, we can divide both sides by 6:
x² = 7
To get the exact values of x, we need to take the square root of both sides:
x = ±√7
Therefore, the exact values of x are √7 and -√7.