Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{9(|x-8|)}{9} < \frac{36}{9} \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}[/tex]
[tex]\underline{\boldsymbol{\sf{Answer}}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x < 12 \ and \ x > 4 \end{gathered}$} }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Therefore,\bf{\underline{the \ correct \ option}} \ \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{"A"}}. \end{gathered}$}[/tex]
Related Questions
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Inequality expressionInequality expressions are expression not separated by an equal sign
Given the following inequality expression
–3(2x – 5) < 5(2 – x)
Expand
-6x + 15 < 10 - 5x
Collect the like terms
-6x + 5x < 10 -15
-x < -5
x > 5
Hence the solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Learn more on inequality here: https://brainly.com/question/24372553
#SPJ1
The lengths of the sides of the right triangle above are a, 3, and c. What is a in terms of c?
Answers
The expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]
Pythagorean theoremFrom the question, we are to determine the expression for a in terms of c
In the given right triangle, we can write that
[tex]c^{2} = a^{2} +3^{2}[/tex] (Pythagorean theorem)
Thus,
[tex]c^{2} = a^{2} +9[/tex]
[tex]a^{2}= c^{2} -9[/tex]
[tex]a^{2}= \sqrt{c^{2} -9}[/tex]
Hence, the expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]
Learn more on Pythagorean theorem here: https://brainly.com/question/23994492
#SPJ1
find the value of x
a) 2:5=8:x
Answers
Step-by-step explanation:
solution:
given,
or, 2:5 = 8:x
or, 2/5 = 8/x [ changing into fraction form ]
or, 2x = 40 [ doing cross-multiplication ]
or, x = 20 [ dividing both sides with 2]
True or false? The graph represents a function.
5
O A. True
O B. False
Answers
order the decimales from leaste to gratest: 72.5, 73.943, 72.1, 73.77,
43.2 43.219 42.1 42.59
38.507 38.507 38.4 28.23 39.5
71.743 71.3 71.3 72.43 72.5
Answers
The decimals would be ordered as:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
How to Order Decimals?To order decimals from the least to the greatest, first state the lowest value, then progress to the highest taking account of the figures that come immediately after each decimal point.
The decimals will be ordered as shown below:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
Learn more about ordering decimals on:
https://brainly.com/question/20603315
#SPJ1
which linear inequality is represented by the graph
Answers
Answer:
The correct awnser is A : )
Step-by-step explanation:
How does the graph of g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3?
A. g(x) is shifted 2 units to the right and 6 units down.
B. g(x) is shifted 2 units to the right and 6 units up.
C. g(x) is shifted 2 units to the left and 6 units down.
D. g(x) is shifted 6 units to the left and 2 units down.
Answers
Answer: B. g(x) is shifted 2 units to the right and 6 units up.
Step-by-step explanation:
See attached image.
a rectangle has horizontal sides of 3 (x-2)ft and vertical sides of 4x-7+(-2x) ft finde the value of x so that the rectangle has a perimeter of 34 ft
Answers
Based on the given horizontal and vertical sides of a rectangle and its perimeter, the value of x in the expression is 6
Perimeter of rectanglePerimeter of rectangle = 2(length + width)
Perimeter of the rectangle = 34 ftLength of the rectangle = 3(x - 2) ft= 3x - 6
Width of the rectangle = 4x - 7 + (-2x)= 4x - 7 - 2x
= 2x - 7
Perimeter of rectangle = 2(length + width)
34 = 2{(3x - 6) + (2x - 7)}
34 = 2(3x - 6 + 2x - 7)
34 = 2(5x - 13)
34 = 10x - 26
34 + 26 = 10x
60 = 10x
x = 60/10
x = 6
Learn more about perimeter of rectangle:
https://brainly.com/question/24571594
#SPJ1
Your friend is helping to raise money for a local charity by participating in a cartwheel-a-thon. Your
friend is 70 inches tall with your friend's arms raised in the air. Your friend is able to complete a
cartwheel in 15 seconds. The charity sponsor supplies a wristband to each participant to assist in
counting the number of cartwheels completed. The wristband is 4 inches from the end of your friend's
arm. Write a model for the height h (in inches) of the wristband as a function of the time (in minutes)
given that the wristband is at the highest point when ; = 0.
Answers
The equation for the height exists h = 31 sin((8π)t + π/2) + 35.
How can the height of the wristband be modeled?The model for the height can be emanated from the general formula of the sine function, then
y = A sin(Bt - C) + D
Maximum point = 70 - 4 = 66 at t = 0
Minimum point = 4
Amplitude, A = (66 - 4) ÷ 2 = 31
D = 4 + 31 = 35
At t = 0, we have;
66 = 31 × sin(B × 0 - C) + 35
31 = 31 × sin(- C)
sin(- C) = 1
C = -π/2
1 minute = 60 seconds
1 second = 1 minute/60
15 seconds = (15/60) minutes
Period = 15 seconds = 15/60 minutes
Period = 2π/B
Therefore, 15/60 = 2π/B
1/4 = 2π/B
B = 2π/(1/4) = 8π
y = Height of the function
Let h denote the height of the wristband.
The equation for the height exists h = 31 sin((8π)t + π/2) + 35.
To learn more about sine function refer to:
brainly.com/question/12102275
#SPJ9
Can someone answer this for me
Answers
The equation of the line in standard form is 6x - 7y = - 11
How to represent linear equation in standard form?The standard form for linear equations in two variables is Ax + By = C.
Therefore, using (-3, -1)(1 / 2, 2)
y = mx + b
where
m = slopeb = y-interceptHence,
m = 2 + 1 / 1 /2 + 3 = 6 / 7
Hence,
-1 = 6 / 7(-3) + b
- 1 = - 18 / 7 + b
-1 + 18 / 7 = b
b = -7 + 18/ 7
b = 11 / 7
Therefore,
y = 6 / 7 x + 11 / 7
Using the standard form,
6 / 7 x - y = - 11 / 7
6x - 7y = - 11
learn more on equation here: https://brainly.com/question/27664510
#SPJ1
The linear equation in standard form is:
6x - 7y = -11
Which is the last option.
How to get the equation of the line?
The line in slope-intercept form is written as:
y = a*x + b
We can see that the line passes through the points (-3, -1) and (1/2, 2), then the slope is:
[tex]a = \frac{2 - (-1)}{1/2 - (-3)} = \frac{3}{3.5} = \frac{6}{7}[/tex]
Then we can write:
y = (6/7)*x + b
To find the value of b, we use the first point. It means that when x = -3, the value of y is -1, then we get:
-1 = (6/7)*-3 + b
-1 + 18/7 = b
-7/7 + 18/7 = b
11/7 = b
Then the equation is:
y = (6/7)*x + 11/7
If we multiply both sides by 7 we get:
7y = 6x + 11
Now we move the term with "x" to the left:
7y - 6x = 11
That is the line in standard form.
If we multiply both sides by -1, we get the last option:
6x - 7y = -11
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Find f(-3) for f(x) = 4(2)^x.
Answers
Answer:
1/2
Step-by-step explanation:
[tex]f( - 3) = 4 {(2)}^{ - 3} = \frac{1}{2} [/tex]
what is 3495 x 30595
Answers
Multiplication of 3495 by 30595 is: 106,929,525.
MultiplicationMultiplication can be defined as the way of multiplying a number by another name.
Using a calculator to multiply 3495 by 30595.
Hence:
Multiplication= 3495×30595
Multiplication= 106,929,525
Therefore Multiplication of 3495 by 30595 is: 106,929,525.
Learn more about multiplication here:https://brainly.com/question/10873737
#SPJ1
What is the domain of the function given below
Answers
Answer:
c. [-1, infinity)
Step-by-step explanation:
the domain the interval or set of valid x values (while the range is the same for the valid y values).
what is the smallest value of x we see for the graph ?
for x values we need to look left and right.
and the more left the value, the smaller it is.
so, in other words, what is the left-most x value e can find ?
x = -1
that is the "starting point" of the function. there is no functional value for any smaller x.
and then clearly, the function goes on and on to the right without any boundary in sight. so, it keeps going to the right in all eternity, that means it goes to infinity.
therefore the answer.
keep in mind that "infinity" is not a number, only a concept. so, when writing "infinity" at an interval end, it is not included (and we use a round bracket).
F(x) =5^2x find the derivative of X
Answers
The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]
Finding the derivative of a functionThe derivative of a function f(x) is the ratio of the change in f(x) to the change in x
The given function is:
[tex]f(x)=5^{2x}[/tex]
Let u = 2x
Find the derivative of u. That is, du/dx
du/dx = 2
f(x) = 5^u
[tex]\frac{df}{du} =5^ulnu[/tex]
Using the chain rule of derivative
[tex]\frac{df}{dx}=\frac{df}{du} \times\frac{du}{dx}[/tex]
[tex]\frac{df}{dx} =5^uln5 \times 2\\\\\frac{df}{dx} =2ln5(5^{2x})[/tex]
The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]
Learn more on the derivative of a function here: https://brainly.com/question/17035616
#SPJ1
Which point is on the graph of f(x) = 5*?
O A. (0, 5)
O B. (0, 0)
• C. (5, 1)
O D. (1, 5)
Answer is (1,5)
Answers
The point that is on the graph of the function [tex]F(x) = 5^x[/tex] is given by:
D. (1,5).
Which points are on the graph of the function?The function is defined by:
[tex]F(x) = 5^x[/tex]
When x = 0, [tex]F(x) = 5^0 = 1[/tex], hence point (0,1) is on the graph of the function.
When x = 1, [tex]F(x) = 5^1 = 5[/tex], hence point (1,5) is on the graph of the function, which means that option D is correct.
When x = 5, [tex]F(x) = 5^5 = 3125[/tex], hence point (5,3125) is on the graph of the function.
More can be learned about functions at https://brainly.com/question/26222939
#SPJ1
The following figure shows the entire graph of a relationship.
See attached!
Answers
The correct answer is Yes. The graph represents a function. The function given is: F(x) = y(-5). Note that the value of x is zero.
What is the graph of a function?A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f might similarly be defined as the graph of the equation y = f. (x).
Thus, the correct answer or function represented in the graph is f(x) = y(-5)
Learn more about functions at;
https://brainly.com/question/3939432
#SPJ1
To the nearest percent how much greater is 8 than 6
Answers
The percent greater of 8 than 6 to the nearest percent is 25%
PercentagePercent greater = difference / higher chance value × 100
= 2/8 × 100
= 0.25 × 100
Percent greater = 25%
Therefore, the percent greater of 8 than 6 to the nearest percent is 25%
Learn more about percentage:
https://brainly.com/question/843074
#SPJ1
Miguelle is deciding which type of heating system to put in his house. An oil system costs $2700 to install and
$900 per year to operate. A solar system costs $9000 to install and $200 per year to operate.
Determine your variables
Let=
Let=
2. Create your equations and number them.
3.Solve the linear system using ELIMINATION OR SUBSTITUTION.
Answers
Answer: (9, 10800)
Step-by-step explanation:
We will first let x be the number of years and y be the total cost.
In that case, let's plug in the values for each into the equation y=mx+b, where m is the slope and b is the y-intercept.
The y-intercept will be the value we start with before any years pass, so it will be the installation cost. The slope is how fast the total cost will increase. Since the operation costs have to be added on every year, it will be our slope.
With that in mind, let's create both of our equations:
y = 900x + 2700 (Oil system)y = 200x + 9000 (Solar system)Since y is solved for in the first equation, we can substitute it into the second equation:
[tex]900x + 2700 = 200x + 9000[/tex]
[tex]700x + 2700 = 9000[/tex] [Subtracting 200x from both sides]
[tex]700x = 6300[/tex] [Subtracting 2700 from both sides]
[tex]x = 9[/tex] [Dividing both sides by 700]
We can now substitute 9 for x in any equation and solve for y. Here I substituted it into the first one:
[tex]y = 900(9) + 2700[/tex]
[tex]y = 8100 + 2700[/tex] [Multiplying]
[tex]y = 10800[/tex] [Adding]
Hence, the solution to this linear system is (9, 10800).
Question 2: Xiulin and Meifang had an equal number of postcards. Meifang gave some of her postcards to Xiulin. After that, Meifang had 76 fewer postcards than Xiulin. Given that Meifang had 72 postcards left, find the number of postcards Xiulin had at first.
Answers
110 postcards Xiulin had at first.
What is algebric equation?Algebric equation is a mathematical statement in which two equation set equal to each other.
Let the number of postcards belonging to Xiulin and Meifang be x.
Let the number of postcard Meifang gave to Xuilin be 'a'
Number of postcard left with meifang
=> x-a = 72
=> x = 72+a
Meifang had 76 fewer postcards than Xiulin.
so, (x+a)-72=76
72+a+a-72=76
2a = 76
a = 38
meifang give 38 cards to xuilin
x = 72+38
= 110
to know more please refer: https://brainly.com/question/4344214
#SPJ9
I need help with this slope
Answers
Answer:
Step-by-step explanation:
First, the y-intercept is -3 so from -3 the slop to the next point is 4/1.
The perimeter of a regular hexagon is 72 inches. Find the length of each of its sides.
Answers
12 inches
Step-by-step explanation:A regular polygon is any 2-D shape where all the sides and angles are congruent.
Regular Hexagon
As denoted by the prefix "hexa-", hexagons have 6 sides and internal angles. The perimeter is equal to all 6 sides added together. However, we know that these sides must be congruent because it is a regular hexagon.
Solving for Perimeter
We can create an equation that describes the perimeter of this shape, with "x" representing the length of one side.
6x = 72Since all the sides are equal we can use multiplication instead of addition. To solve this equation, divide both sides by 6.
x = 12This means that all sides must be 12 inches.
Which equation is the inverse of y = 9x² - 4?
0y= ± √x+4
9
O y = ±₁
+4
9
Oy= 2√x+4
3
INX
+√√√x 2
Oy= 3 3
Answers
[tex]y=9x^2-4\\9x^2=y+4\\x^2=\dfrac{y+4}{9}\\x=\pm\sqrt{\dfrac{y+4}{9}}=\pm\dfrac{\sqrt{y+4}}{3}\\\\\text{inverse: }y=\pm\dfrac{\sqrt{x+4}}{3}[/tex]
The inverse of the function y = 9x² - 4 is y = ±√((x + 4)/9). The correct option is A.
What is the inverse of the function?To find the inverse of a function, we need to swap the positions of the input variable (usually x) and the output variable (usually y), and then solve for y. The resulting equation will be the inverse function.
To find the inverse of the function y = 9x² - 4, we need to swap the positions of x and y and then solve for y.
So, starting with y = 9x² - 4:
y = 9x² - 4
x = 9y² - 4 (swapping x and y)
x + 4 = 9y² (adding 4 to both sides)
y² = (x + 4)/9 (dividing both sides by 9)
y = ±√((x + 4)/9) (taking the square root of both sides, plus or minus)
So the inverse of the function y = 9x² - 4 is:
y = ±√((x + 4)/9)
Note that since we have a plus or minus sign in the expression, this means that the inverse is actually two functions: one that gives the positive square root, and one that gives the negative square root.
To know more about an inverse of the function follow
https://brainly.com/question/3831584
#SPJ5
A machine can pack 5000 articles in 24 hours.How long will 3 such machine take to pack the same number of articles
Answers
The time taken for 3 machines to pack 5000 articles is 8 hours.
What are word problems?Word problems are mathematical problems expressed completely in words.The given problem is the rate of work done kind of word problem.To solve a word problem, first, observe the data given in words and apply the basic algebraic operations.The basic algebraic operations are addition, subtraction, multiplication, and division.How long will 3 such machines take to pack 5000 articles?It is given that,
A machine can pack 5000 articles in 24 hours. I.e,
1 machine → 5000 articles → 24 hours
3 machines → 5000 articles → 24/3 hours
Thus, 3 of such machines can pack the same number of articles in
24 ÷ 3 = 8 hours.
Therefore, 3 of such machines take 8 hours to pack 5000 articles.
Learn more about such a word problem here
https://brainly.com/question/1144815
#SPJ1
Aaron wants to make All-Tournament Team for his high school
basketball team. He needs to average at least 24 points a game
to get selected for All-Tournament Team. They are playing 4
games, in the first 3 games he scored 30, 17, and 25 points.
Answers
Answer:24
Step-by-step explanation:
Answer:
Step-by-step explanation:
A college graduate expects to earn a salary of $55,000 during the first year after graduation and receive a 3% raise every year after that. What is the total income he will have received after ten years?
Answers
Answer:
$73915.40
Step-by-step explanation:
→ Find the multiplier
( 3 + 100 ) ÷ 100 = 1.03
→ Multiply by principal amount and raise it to the power of years
55000 × 1.03¹⁰ = 73915.40
Answer: $630,513.36
Step-by-step explanation:
Making a Formula for His Salary on a Given YearLet's make a table of values to see how much he earns every year after graduation.
1 year -> $55,000
2 years -> 55,000 * 103% = $56,650
3 years -> 56,650 * 103% = 55000 * 103% * 103% = $58,349.50
4 years -> 58349.50 * 103% = 55,000 * 103% * 103% * 103% = 55000(1.03)³
Here, we see that every year, he gets 103% of what he got the previous year, which is also 1.03 times his previous salary.
We also see that we multiply 55000 by 1.03 three times in the fourth year, and two times in the third year. This means that we multiply 55000 by 1.03 n-1 times.
Using this, let's generalize this for n.
n years -> [tex]55000(1.03)^{n-1}[/tex]
Finding the Sum after Ten YearsWe are trying to find his total income after ten years, or the sum of his salary from year 1 to year 10. We can represent this in sigma notation like this
[tex]% Adjusted limits of summation$\displaystyle\sum_{n=1} ^{10} 55000(1.03)^{n-1}$[/tex]
This essentially translates to the sum of the first ten terms in the sequence [tex]55000(1.03)^{n-1}[/tex], starting at n=1.
Since this is a geometric sequence, or a sequence where we need to multiply by the same number to get to the next term, we can find the sum using the sum of geometric series formula. This formula is as follows:
[tex]S_n=a_1\frac{1-r^n}{1-r}[/tex]
where [tex]S_n[/tex] is the sum of the first n terms, [tex]a_1[/tex] is the first term, r is the common ratio, and n is the number of terms. In this question, [tex]S_n[/tex] is the total income after n years, [tex]a_1[/tex] is his salary after the first year, r is how much his salary increases by each year, and n is the number of years we are calculating the sum for.
[tex]a_1[/tex] -> 55000
r -> 1.03
n -> 10
Now that we have the values for each variable, let's plug them in and solve
[tex]S_{10}=55000(\frac{1-1.03^{10}}{1-1.03})\\S_{10}=630513.36[/tex]
The total income he will have received after ten years is $630,513.36.
A company's cost formula for its salaries and wages cost is $2,850 per month plus $317 per job. For the
month of February, the company planned for activity of 16 jobs, but the actual level of activity was 14
jobs. The actual salaries and wages cost for the month was $7,640. The spending variance for salaries
and wages cost in February would be closest to:
$352 F
$352 U
O $282 F
$282 U
Answers
The spending variance for salaries and wages cost in February would be closest to; $282 F.
What is the spending variance in February?The spending variance as the name implies is the difference between the budgeted cost and actual cost paid for an item. It therefore follows from the definition above that for the month of February;
Spending variance = $7,640 - (2850 + (16×317))
Spending variance = $7,640 - (7922)
Spending variance is therefore; $282 F.
Read more on spending variance;
https://brainly.com/question/25801623
#SPJ1
An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.
H0: The product does not change the height of the plant.
Ha: The product makes the plant grow taller.
Is the following an example of a type I or type II error?
The sample suggests that the product does not change the height of the plant, but it actually does make the plant grow taller.
Answers
It is an example of Type I error.
About Type I error
The rejection of a null hypothesis (H0) when it is actually true is a Type I error. It is represented by the following condition,
Failure to reject a null hypothesis when it is true that it is false which is a Type II error.
How is this an example of Type I error?
The given case's hypothesis is described as follows:
H₀: The product has no effect on the plant's height.
Hₐ: The substance causes the plant to enlarge.
The sample claims that the product causes the plant to grow taller, however in reality, it has no effect on the plant's height.
Therefore, the sample recommends rejecting the null hypothesis even though it is true. Consequently, a result, this error is a Type I error.
Learn more about Type I error here:
https://brainly.com/question/24320889
#SPJ1
root of polynomial function f(x)=(x-3)^4(x+6)^2
Answers
What is the most precise name for quadrilateral ABCD with vertices
A(-1,0), B(4, 0), C(5, 4), and D(0, 4)?
A. rhombus
B. rectangle
C. square
D. parallelogram
Answers
Parallelogram is the quadilateral ABCD with vertices A(-1,0), B(4, 0),
C(5, 4), and D(0, 4)
What is parallelogram?A parallelogram is a quadrilateral whose opposite sides are parallel and equal.
first, find the length of the sides of the quadilateral.
AB = [tex]\sqrt{(4-(-1))^2+0-0^2} \\[/tex]= [tex]\sqrt{5^2+0}[/tex] = [tex]\sqrt{25}[/tex] = 5
BC = [tex]\sqrt{(5-4)^2+(4-0)^2}[/tex] = [tex]\sqrt{1^2+4^2}[/tex] = [tex]\sqrt{1+16} = \sqrt{17}[/tex]
CD = [tex]\sqrt{(0-5)^2+(4-4)^2} = \sqrt{(-5)^2+0} = \sqrt{25-0} = 5[/tex]
DA = [tex]\sqrt{(-1-0)^2+(0-4)^2} = \sqrt{(-1)^2+(-4)^2} = \sqrt{1+16} = \sqrt{17}[/tex]
opposite side length is equal.
so quadilateral is parallelogram.
to learn more please refer: https://brainly.com/question/970600
#SPJ9
The most precise name for quadrilateral ABCD with vertices
A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is parallelogram.
What is the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4)?The most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is parallelogram.The parallelogram has opposite parallel sides.A parallelogram is a flat 2d shape that has four angles.The opposite interior angles are equal.If the parallelogram has anyone of the angles is a right angle, then all the other angles will be at a right angle.Hence, the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is a parallelogram.
To learn more about parallelogram, refer to:
https://brainly.com/question/970600
#SPJ9
WILL GIVE BRAINLIEST!!! If [tex]\frac{a}{b} =2[/tex] what is the value of [tex]\frac{a}{a-b}[/tex]?
Could the answer be D) or is it C)?
A) -2
B) 1
C) 2
D) It cannot be determined from the given information
Answers
Considering the given proportion, the value of [tex]\frac{a}{a - b}[/tex] is:
C) 2
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportion between a and b is given by:
a/b = 2.
Then:
a = 2b.
The expression is:
[tex]\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2[/tex]
Hence option C is correct.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1