for the square root you must look for a number that multiplied with itself gives you the indicated value
for this case a number that multiplied by itself gives you 100
[tex]10\times10=100[/tex]sothe square root of 100 is:
[tex]10[/tex]Suppose a ray of sunlight bounces off a window at a point P, and that
line mis perpendicular to the window at point P. Angles of inflection
and reflection are created as shown.
Write an equation and then solve for x.
m
-
(3x - 10)°
(2x + 5)°
P
By applying the law of reflection to the ray of sunlight, the value of x is equal to 5.
What is the law of reflection?The law of reflection is a theorem which states that the magnitude of the angle of incidence is equal to the magnitude of the angle of reflection when a ray of light is reflected off a surface such as a plane mirror.
Mathematically, law of reflection can be represented or modelled by this mathematical expression:
sinθi = sinθr
Where:
sinθi represents the angle of incidence.sinθr represents the angle of reflection.By applying the law of reflection to the ray of sunlight (see attachment), we have the following equation:
(3x - 10)° = (2x + 5)°
3x + 2x = 10 + 5
5x = 15
x = 15/3
x = 5.
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a new over-the-counter medicine to treat a sore throat is to be tested for effectiveness. the makers of the medicine take two random samples of 25 individuals showing symptoms of a sore throat. group 1 receives the new medicine and group 2 receives a placebo. after a few days on the medicine, each group is interviewed and asked how they would rate their comfort level 1-10 (1 being the most uncomfortable and 10 being no discomfort at all). the results are below. find the 95% confidence interval in the difference of the mean comfort level. is there sufficient evidence to conclude that the new medicine is effective? assume the data is normally distributed with unequal variances. (round answers to 4 decimal places) make sure you put the 0 in front of the decimal. average group 1
A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence.
In case the 95 % confidence interval would be given by
[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]
What is meant by confidence interval?A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence. It exists often denoted a % whereby a population means lies between an upper and lower interval".
The margin of error exists the range of values below and above the sample statistic in a confidence interval.
Normal distribution, exists a "probability distribution that exist symmetric about the mean, showing that data near the mean exists more frequent in occurrence than data far from the mean".
[tex]$\bar{X}_1=5.84$[/tex] represent the sample mean 1
[tex]$\bar{X}_2=3.96$[/tex] represent the sample mean 2
n 1 = 25 represent the sample 1 size
n 2 = 25 represent the sample 2 size
[tex]$s_1=2.211334$[/tex] sample standard deviation for sample 1
[tex]$s_2=2.35372$[/tex] sample standard deviation for sample 2
[tex]$\mu_1-\mu_2$[/tex] parameter of interest.
The confidence interval for the difference of means exists given by the following formula:
[tex]$\left(\bar{X}_1-\bar{X}_2\right) \pm t_{\alpha / 2} \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} \text \dots{ (1) }$$[/tex]
The point of estimate for [tex]$\mu_1-\mu_2$[/tex] exists just given by:
[tex]$\bar{X}_1-\bar{X}_2=5.84-3.96=1.88$$[/tex]
In order to estimate the critical value [tex]$t_{\alpha / 2}$[/tex] we require to estimate first the degrees of freedom, given by:
[tex]$d f=n_1+n_2-1=25+25-2=48$$[/tex]
Since the Confidence is 0.95 or 95 %, the value of [tex]$\alpha=0.05$[/tex]and α 2 = 0.025, and we can utilize excel, a calculator or a table to estimate the critical value. The excel command would be: " = -T.INV (0.025, 48) ". And we see that [tex]$t_{\alpha / 2}=2.01$[/tex]
In order to replace into formula (1), we get
[tex]$1.88-2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=0.582$[/tex]
[tex]$1.88+2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=3.178$[/tex]
In case the 95 % confidence interval would be given by
[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]
Because all the values for the confidence interval are higher than 0, we may infer that there are significant differences between the means of the two groups in this case, with the mean for group 1 (Medicine) being considerably higher than the mean for group 2 (Placebo) at 5% of significance.
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Please help! Super confused!
Enter the inverse function of f(x) = -9x - 10.
Answer: [tex]f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
Step-by-step explanation:
[tex]f(x)=-9x-10 \implies x=-9f^{-1}(x)-10\\\\x+10=-9f^{-1}(x)\\\\f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
Complete the ratio table.
13 11
22
52 44
55
91 77
The complete table using ratios is:
13, 39, 52, 72, and 91. What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.In mathematics, a ratio shows how frequently one number appears in another.For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.In, the column we can notice the pattern of (×2):
11×2 = 2222×2 = 44Now calculate similarly:
This is a ratio method 13, 39, 52, 72, and 91.Therefore, the complete table using ratios is:
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For a diving event, the highest and the lowest of seven scores are discarded. Next, the total of the remaining scores is multiplied by the degree of difficulty of the dive. That value is then multiplied by 0.6 to determine the final score. Find the final score for the dive.
A drawing of a score board of the event, 3-meter springboard. It shows the scores of the 7 judges as Judge 1, 80; judge 2, 75; judge 3, 90; judge 4, 70; judge 5, 80; judge 6, 85; judge 7, 75. The difficulty level is marked as 3.1.
Answer: 734.7
Step-by-step explanation:
We get rid of 90 and 70 since they are the highest and lowest scores.
80+75+80+85+75 = 395
395 * 3.1 = 1224.5
1224.5*0.6 = 734.7
about 4% of the population has a particular genetic mutation. 300 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 300.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
How to calculate the probability distribution's mean: Steps
change every percentage to a decimal probability.Create a probability distribution table in step two. Multiply each column's values. Combine the outcomes from step 3.A specific genetic mutation affects 4% of the population. 300 persons are chosen at random. Find the standard deviation for the proportion of the 300 groups who have the genetic mutation.
Standard deviation is calculated as follows: 0.04 * 0.93/300 * sqrt(p*(1-p)/n) (0.000124).
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8. A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of
materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality
12n> 170 +3.50n represents the situation in which the artist makes a profit.
a. Will the artist make a profit if he sells 15 necklaces? Show how you know.
b. Solve the inequality and explain what the solution means in regards to the jewelry artist.
By solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. In mathematics, larger than symbol (>), less than symbol (<), less than or equal to a symbol (<), greater than or equal to a symbol (≥), less than or equal to a symbol (≤), and not equal to a symbol (≠).So, is the artist in profit if he sells 15 necklaces:
The cost to rent a booth is $170.The cost of making a necklace is $3.50.The selling price is $12.Inequality is 12n ≥ 170 +3.50n: (let n = 15)
12n ≤ 170 +3.50n12(15) ≤ 170 +3.50(15)180 ≤ 170 + 52.5180 < 222.5Therefore, by solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
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The correct question is given below:
A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality 12n> 170 +3.50n represents the situation in which the artist makes a profit. Will the artist make a profit if he sells 15 necklaces? Show how you know.
-23x^7 + x^9 -6x^3 + 10 + 2x^2
The polynomial is x⁹ - 23x⁷ - 6x³ + 2x² + 10 in the standard form, the degree of the polynomial is nine, and its leading coefficient is 1.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The polynomial below which is given in the question
-23x⁷ + x⁹ -6x³ + 10 + 2x²
To determine the polynomial in the standard form.
⇒ -23x⁷ + x⁹ -6x³ + 10 + 2x²
Rearrange the terms in the descending order of the degree of variables
⇒ x⁹ - 23x⁷ - 6x³ + 2x² + 10
This is the polynomial in the standard form
Here the degree of the polynomial is nine because nine is the highest degree in the above expression and its leading coefficient is 1.
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The question seems to be incomplete the correct question would be:
Write the polynomial in the standard form, and then identify the degree and leading coefficient
-23x⁷ + x⁹ -6x³ + 10 + 2x²
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
SOLUTION:
Step 1:
In this question, we are given the following:
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
Step 2:
This is an application of Boyle's law which states that:
Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.
[tex]\begin{gathered} Mathematically,\text{ we have that:} \\ V\text{ }\propto\text{ }\frac{1}{P} \\ Then,\text{ we have that:} \\ V\text{ =}\frac{k}{P}\text{ \lparen where k is a constant \rparen} \end{gathered}[/tex][tex]when\text{ V = 800 cubic centimetres , then P = 450 mm Hg}[/tex][tex]\begin{gathered} 800\text{ =}\frac{k}{450} \\ cross-multiply,\text{ we have that:} \\ \text{k = 800 x 450 = 360,000} \end{gathered}[/tex][tex]\begin{gathered} Then,\text{ the equation connecting V and P =} \\ \text{ V }=\frac{360,000}{P} \end{gathered}[/tex]Next:
[tex]when\text{ P = 200 mm Hg, we have that:}[/tex][tex]\begin{gathered} V\text{ = }\frac{360,000}{200} \\ \text{V = 1800 cubic centimetres } \end{gathered}[/tex]CONCLUSION:
The volume when the pressure is 200 mm Hg is:
[tex]V\text{ = 1800 cubic centimetres}[/tex]a 2.0 kg box is at rest on a table, The static friction coefficient μs between the box and table is 0.40, and the kinetic friction coefficient μk is 0.2
Then, a 25N horizontal force is applied to the box.
What is the best estimate of the magnitude of the box's acceleration?
The best estimate of the magnitude of the box's acceleration is equal to: B. 11 m/s².
How to determine the box's acceleration?In order to determine the magnitude of the acceleration of this box, we would first of all calculate the magnitude of the kinetic frictional force.
Mathematically, the kinetic frictional force that is acting on a physical body can be calculated by using this equation:
F = μkN = μk(mg)
Where:
μk is the coefficient of kinetic frictional force.N is the normal force.m is the mass.g is the acceleration due to gravity.Substituting the given parameters into the formula, we have;
F = 0.20 × 2.0 × 9.81
F = 3.924 Newton.
By applying Newton's second law of motion, the net force is given by:
∑Fx = Applied force - kinetic frictional force = ma
Acceleration, a = [Applied force - kinetic frictional force]/m
Acceleration, a = [25 - 3.924]/2
Acceleration, a = 21.076/2
Acceleration, a = 10.538 ≈ 11 m/s²
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What is the inequality shown? -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 O 5 6 7 8 9 n
Answer:
Inline range: 2 ≤ n < 8
Interval range: [ - 2, 8 )
Loop: n = - 2; n < 8;
Step-by-step explanation:
The filled circle means inclusive while outlined circle means exclusive.
Answer:
-2 ≤ x > 8
Step-by-step explanation:
x = a possible number based on the diagram
the black-filled-in dot on the line above the number line indicated that it can either be '≤' or '≥'
the empty-not-filled-in dot means that it can be either '<' or '>'
the '≤' means x can be equal or greater to -2
and the '>' means that x must be less than 8
hope this helps!
A parallelogram with coordinates A (-2,3) , B (3,3) , (4,6) , and D (-1 , 6) is first rotated 90 degrees clockwise and the. Translated 4 units left and 2 units down to form quadrilateral A’B’C’D’. What is the distance , in units, between point C’ and point D’ in the resulting figure.
The distance between the translated points C and D is 5 units
How to determine the distance between the translated points?From the question, the coordinates are given as
A (-2,3) , B (3,3) , C (4,6) , and D (-1 , 6)
The sequence of transformations is given as
First rotated 90 degrees clockwiseTranslated 4 units left and 2 units downThe above sequence of transformations are rigid transformations.
This means that the lengths are preserved
In other words,
CD = C'D'
So, we have the distance to be
Distance = √[(x₁ - x₂)² + (y₁ - y₂)²]
Where
(x, y) = C (4,6) , and D (-1 , 6)
So, we have
Distance = √[(4 + 1)² + (6 - 6)²]
Evaluate
Distance = 5
Hence, the distance is 5 units
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provide an appropriate response. the length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 7.0 minutes and a standard deviation of 1 minute. find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.
By the distribution,6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.
Given that,
Finding a parking spot in the library parking lot takes college students an average of 7.0 minutes, with a standard deviation of 1 minute, according to a normal distribution.
Find the window of opportunity that 75.8% of college students miss when looking for a place in the library parking lot.
The following formula calculates the z-score of a measure X of a normally distributed variable with mean μ and standard deviationσ:
Z=(X-μ)/σ
The z-score calculates how far the measure deviates from the mean by standard deviation.
The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.
The cut-off time is the 100th percentile minus 75.8th percentile, or X, for Z = -0.7, so:
Z=(X-μ)/σ
-0.7=(X-7)/1
-0.7=X-7
X=-0.7+7
X=6.3
Therefore, 6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.
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7. It costs $6 to get into the Carnival. Hotdogs cost $1.50 each, Hamburgers cost $1.75 each, French Fries cost $1.05 per
serving, Popcorn cost $1.15 per bag, and Soda is $.75 each. Each ride costs $2.00. How much money would you need to
get into the Carnival and to go on 8 rides, eat 2 hotdogs, 1 order of Fries, 2 bags of Popcorn, and 1 Soda?
Answer: $29.10
Step-by-step explanation:
1. Make a table, like the one shown in the image. You will need the item, its price, and how many are being bought.
2. Multiply the price and quantity of each item that is being bought.
3. Add all of the products together. This should get you the final price.
My steps are in the image. Hope this helps!
What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?
Recall that the formula for the area of a rectangle is, A = l×w where l represents the length of the rectangle and w represents its width.
Find the area of a rectangle that has a length of 3.5 centimeters and a width of 2.2 centimeters. The answer is 7.7
Using the formula for the area of a rectangle is, A = l×w where l represents the length of the rectangle and w represents its width, the area of a rectangle with the length of 3.5 centimeters and a width of 2.2 centimeters will be 7.7 cm^2.
What is the area of a rectangle?The area of the rectangle can be calculated using the formula,
(A = l×w )
and the l = the length of the rectangle
w = represents the width of the rectangle
Then to calculate the area of the rectangle, we can substitute the values that is been given as :
(A = l×w )
A = (2.2 * 3.5) = 7.7 cm^2
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Answer:
7.7
Step-by-step explanation:
The answer was already in the question... He must've edited it or somethin'
Mind doing this too?
The expression that represents the perimeter and area of the rectangle are 10x + 4 and 6x²- 24.
How to find the area and perimeter of a rectangle?The rectangle is a quadrilateral with opposite sides equal to each other.
Opposite sides of a rectangle is also parallel to each other.
Therefore,
perimeter of a rectangle = 2(l + w)
where
l = side lengthw = widthTherefore,
l = 3x + 6
w = 2x - 4
Hence,
perimeter of a rectangle = 2(3x + 6 + 2x - 4)
perimeter of a rectangle = 2(5x + 2)
perimeter of a rectangle = 10x + 4
Let's find the expression that represent the area of the rectangle.
Hence,
area of a rectangle = lw
area of a rectangle = (3x + 6)(2x - 4)
area of a rectangle = 6x² - 12x + 12x - 24
Therefore,
area of a rectangle = 6x²- 24
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Wich is closest to the volume of the cone in cubic feet?
Therefore let us input the values to find the volume of the cone
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\pi r^2h \\ r=\frac{8}{2}=4\text{ ft} \\ h=9ft \\ \text{volume}=\frac{1}{3}\pi r^2h \\ \text{volume}=\frac{1}{3}\times3.14\times4^2\times^{}9 \\ \text{volume}=\frac{1}{3}\times3.14\times16\times9 \\ \text{volume}=\frac{452.16}{3} \\ \text{volume}=\text{ }150.72ft^2 \end{gathered}[/tex]The answer should be A.
When Madison left her house this morning, her cell phone was 80% charged and itthen started to lose 8% charge for each hour thereafter. Write an equation for B, interms of t, representing the charge remaining in Madison's battery, as a percentage, thours after Madison left her house.
Given:
Initially, the cell phone was 80% charged.
Then started to lose 8% charge for each hour thereafter.
To find:
The equation for B in terms t
I Really Need Help..
PHOTO BELOW:
Answer: He is not correct because when simplifying an expression, you can only add like terms together.
Step-by-step explanation:
you are given the expression: x^2 + 4x - 2x
when simplifying an expression, you can only add/subtract like terms (terms that have the same variable which are raised to the same power).
in the expression, you can only subtract 4x - 2x because they have like terms/the same variable.
you cannot add x^2 to 4x because x^2 and x are NOT like terms/the same variable. (If 4x was 4x^2, then you would be able to add them together.
meaning the simplified expression should be: x^2 + 2x and not 3x^2
I used 999 sheets of toilet paper each day for 777 days. The roll had 969696 sheets when it was new. How many sheets of toilet paper have not been used? please get the answer right
The number of sheets of toilet paper that have not been used is 193473.
What is multiplication?Multiplication simply has to do with the product of numbers.
From the information, the roll had 969696 sheets when it was new and the person used 999 sheets of toilet paper each day for 777 days.
Therefore, the sheet left will be:
= Number in the new roll - Sheets used
= 969696 - (777 × 999)
= 969696 - 776223
= 193473
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one student from the school will be selected at random. what is the probability that the student is in the age-group of 6 to 8 years given that the selected student responded joy?
Given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So, the likelihood that a pupil is between the ages of 6 and 8 can be calculated using the techniques below:
Step 1: 89 pupils out of a possible 200 answered with joy, as shown in the table.Step 2 - It is also stated that there were a total of 28 students in the age range of 6 to 8 years who answered positively.Step 3 - Accordingly, the likelihood that the pupil belongs to the 6 to 8-year-old age range is:P = 28/89
Therefore, given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
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The complete question is given below:
Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. The students were classified by their age. The following table summarizes the responses of the students by age group. One student from the school will be selected at random. What is the probability that the student is in the age group of 6 to 8 years given that the selected student responded with joy?
The Winchester Opera House sold 4,600 tickets this year, but it has been experiencing a 10%drop in sales from one year to the next. If this trend continues, then how many tickets willthe opera house sell 8 years from now?
Exponential decay formula:
[tex]y=a(1-r)^t[/tex]y is the number of tickets sold at t years
a is the initial number of tickets sold
r is the rate of drop (in decimal form)
t is the time in years
[tex]y=4600(1-0.1)^t[/tex]8 years from now:
[tex]\begin{gathered} y=4600(1-0.1)^8 \\ \\ y=4600(0.9)^8 \\ \\ y=1980.149 \end{gathered}[/tex]Then, if the trend continues, 8 years from now the number of tickets sell will be approximately 1980-11x-y+3z=-21
(5x-y-5z=-5)
(3x+y+z=13)
Answer: [tex]y=15-5x, z=2x-2[/tex]
Step-by-step explanation:
Subtracting the first equation from the second equation yields [tex]16x-8z=16 \implies 2x-z=2 \implies z=2x-2[/tex].
Substituting this into the first equation,
[tex]-11x-y+3(2x-2)=-21\\\\-11x-y+6x-6=-21\\\\-5x-y-6=-21\\\\-5x-y=-15\\\\5x+y=15\\ \\ y=15-5x[/tex]
A public storage company charges new customers an initial fee of $35.00. Each month of storage costs $18.75. The company uses the formula T = 35.00 + 18.75m to calculate the total charges, where T is the total charges, and m is the number of months of storage. How many months of storage would cost a new customer $260.00?
Answer:
12 months
Explanation:
Given the function that models the total chacrge of a company as T = 35.00 + 18.75m where;
T is the total charges,
m is the number of months of storage
Given
T = $260.00
we are to find the value of m
Substitute
260 = 35 + 18.75m
18.75m = 260 - 35
18.75m = 225
m = 225/18.75
m = 12
Hence it will take 12 months to cost a new custimer $260.00
I have the problem as a picture, can I show u?
corresponding (option D)
Explanation:Since the lines are parallel and a tranversal line cuts the two lines:
The angle 2 at the top of the first line correspods to angle 6 at the top of the second line.
Angle 2 and angle 6 are equal.
Hence. we say angle 2 and angle 6 are corresponding angles (option D)
determine the equation of line from the graph
Answer:
y = 2x
Step-by-step explanation:
The slope is 2. Find a point on the line, to go back to the line, go up two and one to the right. You will be back on the line. This pattern repeats over and over and again.
A restaurant uses four pounds of potatoes for a party of 12 people They are cooking potatoes for a party of 60 people what should I do
Math
Simplify each expression. show your solution
To simplify a phrase, create an equivalent expression without any terms that are identical.The expression will then be rewritten using the fewest terms feasible.
What is an equation to simplify?
A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.The fundamental guidelines and procedures to simplify any algebraic statement are as follows:By multiplying factors, remove any grouping symbols like brackets and parenthesis.If the words contain exponents, use the exponent rule to eliminate grouping.Add or subtract like terms to combine them.Add the constants together. Add numbers
2+1
= 3
2³ = 8
first one 8
2. x²× x°
= x ²+°
3.a6_a4
= a2
4. x×x×y×y
=x²y²
5 x²×x×y×y²
= x³y³
6.(mn)5
= m5N5
7 (abc)²
= a²b²c²
8.(p²q)³
p6q3
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f(x)=4x+2; Find f(8)
We have:
[tex]f(x)=4x+2[/tex]And want to find f(8), for this we simply replace x with 8 and operate:
[tex]f(8)=4(8)+2\Rightarrow f(8)=34[/tex]