To determine if the point (5,1) is part of the line y = 7-2x, we need to substitute x=5 and y=1 into the equation of the line and check if it is a true statement:
y = 7 - 2x
1 = 7 - 2(5)
1 = 7 - 10
1 = -3
Since -3 is not equal to 1, the point (5,1) is not part of the line y = 7-2x.
Una chica mide 5 cm más que su mamá y 8 cm menos que su papá. Si entre los tres miden 3. 45 m. ¿Cuánto mide su papá?
If A girl is 5 cm taller than her mother and 8 cm less than her dad, the height of the girl's dad is 122 cm.
Let's assume that the height of the girl's mother is x cm. Then, according to the given information, the height of the girl would be (x + 5) cm and the height of her dad would be (x + 5 + 8) cm or (x + 13) cm.
Now, we know that the total height of the three individuals is 3.45 m or 345 cm (since 1 m = 100 cm). Therefore, we can write an equation as follows:
x + (x + 5) + (x + 13) = 345
Simplifying the equation, we get:
3x + 18 = 345
Subtracting 18 from both sides, we get:
3x = 327
Dividing both sides by 3, we get:
x = 109
Therefore, the height of the girl's mother is 109 cm, the height of the girl is (109 + 5) cm or 114 cm, and the height of the girl's dad is (109 + 13) cm or 122 cm.
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test the claim that the proportion of teenagers who receive all the recommended doses of the hpv vaccine is not equal to 0.50. in 2018, a random sample of 200 teenagers was obtained. in this sample 110 of the 200 had received all the recommended doses. use a significance level of
To test the claim that the proportion of teenagers who receive all the recommended doses of the HPV vaccine is not equal to 0.50, we can use a hypothesis test.
Let p be the true proportion of teenagers who receive all the recommended doses of the HPV vaccine.
Our null hypothesis is that the true proportion is equal to 0.50, i.e. H0: p = 0.50. Our alternative hypothesis is that the true proportion is not equal to 0.50, i.e. Ha: p ≠ 0.50.
We can use a normal approximation to the binomial distribution to perform the hypothesis test. Under the null hypothesis, the sample proportion of teenagers who received all the recommended doses of the HPV vaccine follows a normal distribution with mean 0.50 and standard deviation σ = √((0.50)(1-0.50)/200) = 0.05.
Using the sample data, the test statistic is:
z = (p' - p) / σ = (0.55 - 0.50) / 0.05 = 1.00
where p' = 110/200 = 0.55 is the sample proportion.
The p-value for a two-sided test with a test statistic of 1.00 is approximately 0.32. Since the p-value is greater than the significance level of α = 0.05, we fail to reject the null hypothesis.
Therefore, we do not have sufficient evidence to conclude that the proportion of teenagers who receive all the recommended doses of the HPV vaccine is different from 0.50 at the 5% significance level.
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members of the stony creek bluebird club monitor nest boxes they've hung for local bluebirds. without disturbing the nest, they keep track of how long it takes the bluebird eggs to hatch after being laid. the table below shows the outcomes they record.days to hatchnumber of eggs122133146154161based on the data, what is the probability that the next bluebird egg laid will take more than 14 days to hatch?write your answer as a fraction or whole number.
The probability of a bluebird egg taking more than 14 days to hatch, based on the data provided, is 6/7 or approximately 0.86.
Probability is a measure of the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
In this case, the event we are interested in is the probability of a bluebird egg taking more than 14 days to hatch. We can calculate this probability by dividing the number of eggs that took more than 14 days to hatch by the total number of eggs.
According to the data provided, there were 6 eggs that took more than 14 days to hatch, out of a total of 7 eggs. Therefore, the probability of a bluebird egg taking more than 14 days to hatch, based on this data, is 6/7 or approximately 0.86.
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If RQ and RS are midsegments of ANOP, what can you conclude about QR and NP? Verify your results by finding x
when QR = 3x + 2 and NP = 2x + 16.
A. QR-NP; x-3
B. QR=2NP; x-9
C. QR-NP:x-3
D. QR=-NP₁ x=9
The conclusion about QR and NP is 2QR = NP; x = 3
Making conclusion about QR and NP?From the question, we have the following parameters that can be used in our computation:
RQ and RS are midsegments of ANOP,
This means that
2QR = NP
So, we have
2 * (3x + 2) = 2x + 16
6x + 4 = 2x + 16
Evaluate the like terms
4x = 12
Divide
x = 3
Hence, the value of x is 3
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7. The table top is a rectangular shape with length (5x - 2) metre and width (x + 2) metre. Mr. Phillip wants to put a piece of glass over the table top. The section of the table top not covered with the glass has a width of (x-3) metre. Determine the area of the table top that is not covered in the form of algebraic expressions.
Answer: The total area of the table top is given by the product of its length and width:
Area of table top = length × width
= (5x - 2)(x + 2)
The width of the section not covered by the glass is (x - 3) metre, which means that the width covered by the glass is (width of table top) - (width of section not covered):
Width covered by glass = (width of table top) - (width of section not covered)
= (x + 2) - (x - 3)
= 5
Therefore, the area of the table top not covered by the glass is:
Area not covered by glass = (length of table top) × (width not covered by glass)
= (5x - 2)(5)
= 25x - 10 square metres
Hence, the area of the table top that is not covered by the glass is 25x - 10 square metres.
Step-by-step explanation:
ABC is an isosceles triangle where AB = BC
Find the length marked q on the diagram
give your answer correct to 1 decimal place
The value of the side q is 2.2
How to determine the valueTo determine the value, we need to take note of the properties of an isosceles triangle. They include;
It has two equal sidesIt has two equal angles, three edges and vertices The sum of interior angles of a triangle equal to 180 degreesUsing the Pythagorean theorem stating that the square of the longest sides of the triangle is equivalent to the sum of the square of the opposite sides as well as the square of the adjacent side.
From the information given, we have;
q² = 2² + 1²
Find the squares
q² = 4 + 1
Add the values, we get;
q² = 5
Find the square root of both sides, we have;
q = 2.2 cm
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Question content area top Part 1 A salesperson at a jewelry store earns 3% commission each week. Last week, Jarrod sold $530 worth of jewelry. How much did he make in commission? How much did the jewelry store make from his sales?
The commission made by Jarrod and total sales done by Jewelry store is equals to $15.90 and $514.10 respectively.
Percent of commission rate earned = 3%
Amount of Jewelry sold last week = $530
Commission Jarrod made last week
= multiply the amount of his sales by the commission rate.
⇒ Commission Jarrod made last week = 3% of $530
⇒ Commission Jarrod made last week = 0.03 x $530
⇒ Commission Jarrod made last week = $15.90
Jarrod made $15.90 in commission last week.
The jewelry store made from Jarrod's sales
= subtract the commission from the total amount of sales.
⇒Store's profit = $530 - $15.90
⇒ Store's profit = $514.10
The jewelry store made $514.10 from Jarrod's sales last week.
Therefore, the amount of commission and sales made by jewelry store is equal to $15.90 and $514.10 respectively.
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A scientist uses a submarine to study ocean life. She begins at sea level, which is at an elevation of 0 feet. She travels straight down for 90 seconds at a speed of 3. 5 feet per second. She then travels directly up for 30 seconds at a speed of 2. 2 feet per second. After this 120-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at the submarine's maximum speed of 4. 8 feet per second? Round your answer to the nearest tenth of a second. Show your work.
The time it will take for "scientist" to "travel-back" to "sea-level" with submarine's maximum speed as 4.8 feet per second is 51.9 seconds.
We know a relationship that : Distance = Speed × time,
For the "First-Travel" :She travels "straight-down" for 90 seconds with speed of 3.5 feet per second,
So, Distance covered is = 90 × 3.5 = 315 ft,
For the Second travel :She then travels "directly-up" for 30 seconds with speed of 2.2 feet per second,
So, Distance covered is = 30 × 2.2 = 66 ft,
The "Net-Change" in position from "sea-level" is = 315 - 66 = 249 ft,
The Maximum speed of submarine is = 4.8 feet per second,
We know that, Time taken = Distance/speed,
⇒ Time taken = 249/4.8 = 51.875 seconds ≈ 51.9 seconds.
Therefore, it will take 51.9 seconds to return to sea level.
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URGENT - Will also give brainliest to simple answer
Answer:
Step-by-step explanation:
A circle has a total angle measurement of 360 degrees.
To find the number of slices given a certain angle, simply perform
360/central angle.
For example, if the central angle is 180, you'll have two sections.
360/180 = 2.
Preferred Products has issued preferred stock with an annual dividend of $6. 50 that will be paid in perpetuity. If the discount rate is 10%, at what price should the preferred sell? Note: Round your answer to 2 decimal places
PLEASE HELP!!! URGENT!!!!
Pictured are curves y=p(x) and y=q(x), together with tangents for x = 2. Let r(x)=p(x)*q(x) and determine r'(2).
Slope Formula:
[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Simply plug in the 2 coordinates into the slope formula to find slope mCalculusDifferentiation
DerivativesDerivative NotationDerivative Rule [Product Rule]:
[tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Let's identify what the problem initially gives us:
We are given the graphs of the curves [tex]\displaystyle y = p(x)[/tex] and [tex]\displaystyle y = q(x)[/tex] along with their tangents for x = 2.This means that they give us the derivative of each respective curve at x = 2, since the definition of a derivative is the slope of the tangent line.
We are also given that some function [tex]\displaystyle r(x)[/tex] is equal to [tex]\displaystyle p(x)q(x)[/tex], where the functions are multiplied by each other.
[tex]\displaystyle r(x) = p(x)q(x)[/tex]We are then asked to find [tex]\displaystyle r'(2)[/tex], which is the derivative of the [tex]\displaystyle r(x)[/tex] function at x = 2.
Step 2: WorkIn order to find the derivative of [tex]\displaystyle r(x)[/tex], we will need to use the Product Rule, which states how to find a derivative of 2 functions being multiplied by each other. Note the equation given under "General Formulas and Concepts":
[tex]\displaystyle \begin{aligned}r(x) & = p(x)q(x) \\r'(x) & = \boxed{ p'(x)q(x) + p(x)q'(x) }\\\end{aligned}[/tex]
∴ the derivative of [tex]\displaystyle r(x)[/tex] is equal to [tex]\displaystyle \boxed{ r'(x) = p'(x)q(x) + p(x)q'(x) }[/tex]
To find the derivative evaluated at x = 2, we substitute in x = 2 into our derivative:
[tex]\displaystyle\begin{aligned}r'(x) & = p'(x)q(x) + p(x)q'(x) \\r'(2) & = p'(2)q(2) + p(2)q'(2) \\\end{aligned}[/tex]
This is where the graphs and their tangent lines come into play.
To find [tex]\displaystyle q(2)[/tex] and [tex]\displaystyle p(2)[/tex], we simply refer to the [tex]\displaystyle y = q(x)[/tex] and [tex]\displaystyle y = p(x)[/tex] graphs, respectively:
[tex]\displaystyle q(2) = \boxed{ -1 }[/tex][tex]\displaystyle p(2) = \boxed{ 3 }[/tex][tex]\displaystyle \begin{aligned}\implies r'(2) & = p'(2)(-1) + 3q'(2) \\& = \boxed{ -p'(2) + 3q'(2) }\end{aligned}[/tex]
We have now simplified our derivative equation [tex]\displaystyle r'(2)[/tex] to be:
[tex]\displaystyle\begin{aligned}r'(x) & = p'(x)q(x) + p(x)q'(x) \\r'(2) & = p'(2)q(2) + p(2)q'(2) \\& = -p'(2) + 3q'(2) \\\end{aligned}[/tex]
To find [tex]\displaystyle p'(2)[/tex] and [tex]\displaystyle q'(2)[/tex], we refer to the tangent lines of the graphs [tex]\displaystyle y = p(x)[/tex] and [tex]\displaystyle y = q(x)[/tex], respectively. We will have to find their slopes (by the definition of a derivative) using the Slope Formula:
[tex]\displaystyle p'(2) = \frac{5 - 1}{3 - 1} = \frac{4}{2} = \boxed{ 2 }[/tex][tex]\displaystyle q'(2) = \frac{-1 - 0}{2 - -1} = \boxed{ \frac{-1}{3} }[/tex][tex]\displaystyle\begin{aligned}\therefore r'(2) & = -p'(2) + 3q'(2) \\ r'(2) & = -2 + 3 \bigg( \frac{-1}{3} \bigg) \\& = -2 - 1 \\& = \boxed{ -3 }\end{aligned}[/tex]
Answer[tex]\displaystyle \therefore \boxed{ r'(2) = -3 }[/tex]
___
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Topic: Calculus
Unit: Derivatives
x + b = c
solve for x
Answer:
x = c-b
the easiest solution is this
roger purchased a pair of pants for 4.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax what was the total for rogers purchased
The total amount purchased by Roger is
$16.11.How to find the total purchasesCalculating the sum of his purchase, Roger's total cost before any discounts or taxes amounted to:
4.50 + 12.00 = 16.50
Taking into account a ten percent discount on this total, the deduction was found to be:
0.10 * 16.50 = 1.65
where 10% = 0.1
Concluding, the total cost after the discount presented was:
16.50 - 1.65 = 14.85
Furthermore, 8.5% tax is determined of 14.85 equalling out to:
0.085 * 14.85 = 1.26
where 8.5% = 0.085
the final total cost for Roger's purchase is solved by addition of the amount after tac and amount after the discount:
14.85 + 1.26 = 16.11
Hence, the complete cost for Roger's acquisition totalled $16.11.
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The center of a circle is at (2, −3) on a coordinate plane. The edge of the circle goes through the point (2, −7).
What is the circumference of the circle?
pls help ill mark you brainliest if you get it right
Step-by-step explanation:
The first one is a linear model for each '1' change of x , the y value changes -3 ( this would be the slope,m, of the linear equation)
The others are not as regular or have two values for a given 'x'
10,10,20,20,20,30,30,30,30,40,40,50 IGR
Answer:IQR=15
Step-by-step explanation:
Jo French s washing line stretches 3 times across her backyard it takes 16. 11 m of line to do this how far is it across the backyard
If Joanna French's washing lines needs 16.11 metres of line to go around her garden three times, we can multiply 16.11 by three to get the length that one stretch. We get 5.37 metres as a result.
The lengths of the three portions of the line must be added up in order to determine the length across the backyard. The entire length of the path is 16.11 metres, which can be calculated by multiplying 5.37 by 3.
The 16.11 metres that separate Jo French's backyard are the result. This figure is predicated on the laundry line being strung across the garden in a straight path without sagging or curving.
It's crucial to keep in mind that the distance over the back yard may vary if the laundry line is not extended in a straight line. This estimate assumes that the laundry line is the only object using space in the backyard, therefore, the real length across the yard may differ if other items or impediments are present.
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please help 30 points
Answer: =[tex]\frac{a}{4(a+2)}[/tex]
Step-by-step explanation:
Let's find common denominator of the the other side first
we have:
2a-4= 2(a-2)
2a²-8 = 2(a²-4) = 2(a-2)(a+2)
a²+2a = a(a+2)
common denominator is 2a(a-2)(a+2)
combine right side:
[tex]\frac{a^{2}(a+2)-a(a^{2}+4)-4(a-2) }{2a(a-2)(a+2}[/tex]
combine like terms on top:
[tex]\frac{a^{3}+2a^{2}-a^{3}-4a-4a+8 }{2a(a-2)(a+2}[/tex]
[tex]\frac{2a^{2}-8x+8 }{2a(a-2)(a+2}[/tex]
lets put the whole problem together.
[tex]\frac{a-2}{4(a^{2}+4a+4) }[/tex] / [tex]\frac{2a^{2}-8x+8 }{2a(a-2)(a+2}[/tex]
When dividing fractions, keep the first, change the sign, flip the 2nd fraction
[tex]\frac{a-2}{4(a^{2}+4a+4) }[/tex] * [tex]\frac{2a(a-2)(a+2}{2(a^{2}-4x+4) }[/tex] simplify more and then reduce
[tex]\frac{a-2}{4(a+2)(a+2) }[/tex] * [tex]\frac{2a(a-2)(a+2}{2(a-2)(a-2) }[/tex]
=[tex]\frac{a}{4(a+2)}[/tex]
people drive an average of 12,000 miles per year with a standard deviation of 2,580 miles per year. what is the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles? does the central limit theorem apply? what is the sampling distribution of the mean?
The probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles is approximately 0.123
This problem involves the sample mean of a set of data, and we can use the central limit theorem to approximate the distribution of sample means, even if the original distribution is not normal.
Let X be the number of miles driven by a single driver in a year. We know that the population mean µ = 12,000 miles and the population standard deviation σ = 2,580 miles. We also know that the sample size n = 36.
The sample mean X is an estimator of the population mean µ. The distribution of sample means is approximately normal with a mean of µ and a standard deviation of σ/√n, according to the central limit theorem
So, the distribution of sample means can be expressed as
X ~ N(µ, σ/√n)
Substituting the given values, we get
X ~ N(12,000, 2,580/√36) = N(12,000, 430)
Now we need to find the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles. This is equivalent to finding the probability that the sample mean is greater than 12,500
P(X > 12,500) = P(Z > (12,500 - 12,000) / 430)
where Z is a standard normal random variable.
P(Z > 1.16) = 1 - P(Z < 1.16) = 1 - 0.877 = 0.123
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The given question is incomplete, the complete question is:
People drive an average of 12,000 miles per year with a standard deviation of 2,580 miles per year. what is the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles?
Please help!!!
What is the “square root” of 25?
Answer: 5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
If one zero of the quadratic polynomial x ^ 2 + kx + 2 is 1, then what is the value of k?
Answer: -3
Step-by-step explanation:
by puggin in 1 to the equation, you get 1^2 + k + 2 = 0, which equals 3 + k; to solve, bring 3 to the other side to get k = -3.
6) Find the sum of 27076 +0.55 +0.004
Answer:
The sum is 27,076.554.
Step-by-step explanation:
The sum of 27076, 0.55, and 0.004 is:
27076 + 0.55 + 0.004 = 27076.554
Therefore, the sum is 27,076.554.
you are predicting when there will be zero married people in the united states. the r^2 value for your trendline equation is 0.9999. you do not believe that there will ever be a time when we have zero married people - someone, somewhere will probably always want to get married! when writing your confidence argument, the level of confidence you would have is:
The high R-squared value indicates that time is a strong predictor of the number of married people in the United States, it is important to consider the limitations of the equation and the uncertainty in the prediction.
First, let's talk about the R-squared value of your trendline equation.
Now, let's talk about your belief that there will never be a time when we have zero married people. This belief is not accounted for in your trendline equation, as it is purely based on your personal belief rather than any data or statistical analysis.
When it comes to confidence level, we need to consider the uncertainty in the prediction. Since we know that there will likely always be some people who want to get married, we can say with a high level of confidence that the number of married people will never actually reach zero.
In mathematical terms, we can use the equation for the confidence interval to determine the range of values within which we can be confident the true value will fall.
This equation takes into account the standard error of the estimate (the degree of variability in the data) and the desired level of confidence (typically 95% or 99%). However, since we know that the true value will never be zero, this equation is not particularly useful in this case.
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Mrs. Campos drives 23 miles each way to visit her daughter every other weekend. Over six weeks, how far does she drive?
Evaluate x^-2y0/x^3y^-2 when x = 2 and y = 5.
Answer:
25/32
Step-by-step explanation:
To evaluate the expression
[tex]\frac{x^{-2}y^{0} }{x^{3}y^{-2} }[/tex]
First we replace x and y by the given values
So x becomes 2 and y becomes 5
[tex]\frac{2^{-2}5^{0} }{2^{3}5^{-2} }[/tex]
Expressions with negative exponents in the numerator always go to the denominator with positive exponent and on the denominator goes to the numerator with positive exponent
[tex]\frac{5^{2}5^{0} }{2^{3} 2^{2} }[/tex]
Simplify
[tex]\frac{25*1 }{8*4 }[/tex]
Which is
[tex]\frac{25}{32}[/tex]
In ΔWXY, y = 600 cm, ∠W=90° and ∠X=12°. Find the area of ΔWXY, to the nearest 10th of a square centimeter.
If in triangle WXY, ∠W is 90° and ∠X is 12°, then the area of ΔWXY is approximately 38260.2 cm².
The measure of angle W is 90° and the measure of angle X is 12°,
So, By using concept of "angle-sum" property of triangle,
⇒ ∠X + ∠Y + ∠Z = 180°,
Substituting the values,
We get,
⇒ 90° + ∠Y + 12° = 180°,
⇒ ∠Y = 180° - (12° + 90°),
⇒ ∠Y = 180° - 102°,
⇒ ∠Y = 78°.
Next, we use the "Sine-Law" to find the length of WY(x),
The length of side "WX" = y = 600cm,
So, y/(SinY) = x/(SinX), ,.....by Sine-Law
⇒ x = (y × SinX)/(SinY) ,
⇒ x = 127.533937..
The Area of the right triangle XYZ is = (1/2)×(WX)×(WY),
Substituting the values of "WX" and "WY",
We get,
⇒ Area = (1/2)×(600)×(127.533937),
⇒ Area = 38260.1811006...
⇒ Area ≈ 38260.2 cm².
Therefore, the required area is 38260.2 cm².
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A chef decides to test the best method to use to make the best pizza. He sets up an
experiment to find the solution to this problem.
Group A
Best PIZZA?
1. the cooking time
2. group B
3. the type of pizza crust
4. the method for cooking the pizza
5. group A
6. the type of toppings
7. the chef who cooked the pizza
Group B
pizzas cooked the same amount of time
the chef is the same
toppings on both are pepperoni and mushrooms
group A pizza is cooked in a brick fire oven
both pizzas have thick crust
the same person tosses both pizza crusts
group B pizza is cooked in a normal oven
a. variable
b. constant
c. control group
d. experimental group
Each of the numbered items is either a constant, a variable, an experimental group, or a
control group.
Working from 1 to 7, find the correct letter for each item. Use all lowercase letters in your
password and do not use any spaces.
The correct letter for each item are: a. variable, b. control group, c. experimental group, d. experimental group, e. control group, f. variable, g. variable
How to determine the correct letter for each itemThe answer to the different components of the experiment are listed below:
a. The cooking time is a variable
b. Group B is control group
c. The type of pizza crust is experimental group
d. The method for cooking the pizza experimental group
e. Group A is control group
f. The type of toppings is a variable
g. The chef who cooked the pizza is a variable
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My question is A bag Contains 12 margoea which 4 are not ripe. What the chance of picking at random aripe mango
The probability of picking up a ripe mango at random from a bag containing 12 mangoes is equal to 2 /3.
Total number of mangoes in the bag = 12
Total number of mangoes in the bag which are not ripe = 4
Then the number of ripe mangoes is equal to,
= 12 - 4
= 8
So, probability of picking a ripe mango at random can be calculated by dividing number of ripe mangoes by total number of mangoes.
This implies,
P(ripe mango)
= Number of ripe mangoes / Total number of mangoes
= 8 / 12
= 2 / 3
≈ 0.667
Therefore, the chance of picking at random a ripe mango is approximately 0.667 or 2/3.
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A right square pyramid is shown,the pyramid has a height of 24. The length of line segment DF is 7. Enter the length of segment AD.
The length of segment AD of the pyramid is approximately 4.95 units.
Since ACD is a right square pyramid, we know that triangle ACD is a right triangle, with DC as its hypotenuse.
Using the Pythagoras theorem, we can write:
AD² + AC² = DC²
Since AC is the length of one side of the square base of the pyramid, and all sides of a square are equal, we know that
AC = DC ÷ √2.
Substituting this into the equation above, we get:
AD² + (DC ÷ √2)² = DC²
Simplifying this equation, we get:
AD² = DC² - (DC ÷ √2)²
AD² = DC² - DC² ÷ 2
AD² = DC² ÷ 2
Now we can substitute the given value of DC into this equation and solve for AD:
AD² = 7² ÷ 2
AD² = 24.5
AD = 4.95
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The correct question is:
A right square pyramid ACD has a height of 24 units. The length of line segment DC is 7 units. Enter the length of segment AD.
can someone help me with 3 and 4 please?
For #3
A quadratic expression is in standard from when written as ax^2 + bx + c = 0. Where, a, b, and c are constants.
The only option that is written in the form above is option C. Where a=-1, b=-5, and c=7.
For #4
First how is 3x^2 in standard form?
Recall that the standard form of a quadratic is ax^2 + bx + c = 0. So lets alter 3x^2 a bit to show that it is in standard form.
3x^2 ==> 3x^2+0x+0
As you can see 3x^2 is in standard form, but the constants b and c are zero.
Second, how is 3x^2 in factored form?
Factored form is written as (a+x)(b+x). So let's alter 3x^2.
3x^2 ==> 3(0+x)(0+x)
3(0+x)(0+x) = 3(x)(x) which is 3x^2
Hence it can be said that 3x^2 is in both standard and factored form.
