6.) find a formula for the area of a rhombus ( see figure 12.52) in terms of the good distances between opposite vertices. Explain why your formula is valid.
Answers
For the Rhombus you know that:
The opposite sides are parallel
All sides have equal length
Its diagonals bisect each other in right angles
You can calculate the area of the Rhombus by either mutiplying its whide by its length, and sice its 4 sides are of equal lenght, the area will be equal to the square of one of it's sides (s):
[tex]A=s^2[/tex]Or using its diagonals (d1 and d2) you can calculate its area as:
[tex]A=\frac{(d_1\cdot d_2)}{2}[/tex]Related Questions
What is the length of the hypotenuse of the right triangle with coordinates:(-2, -1), (-6,5), and (4, 3)?
Answers
ANSWER:
10.2 units
STEP-BY-STEP EXPLANATION:
The first thing is to make a sketch of the triangle formed in the Cartesian plane, like this:
The hypotenuse is the side opposite the right angle, therefore, it would be the side from the point (-6, 5) to the point (4, 3).
We calculate the distance between these two points using the following formula:
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]We replace and calculate the length of the hypotenuse:
[tex]\begin{gathered} d=\sqrt{\left(4-\left(-6\right)\right)^2+\left(3-5\right)^2} \\ d=\sqrt[]{(4+6)^2+(3-5)^2} \\ d=\sqrt[]{(10)^2+(-2)^2} \\ d=\sqrt[]{100+4} \\ d=\sqrt[]{104} \\ d\cong10.2 \end{gathered}[/tex]The length of the hypotenuse is 10.2 units.
Cindy has a jacket with the first letter of her school's name on it. determine the area of the letter on Cindy's jacket.
Answers
To find the area of the letter, use the area of a rectangle formula below:
Area = Length x Width
Find the
Total area = ( 10 x 2) + (6 x 2) + (6 x 2)
= 20 + 12 + 12
= 44 in²
Therefore, the area of the letter on Cindy's jacket is 44 in²
ANSWER:
44 in²
The baghrams make regular monthly deposits in a savings account. The graph shows the relationship between the numbers x of months and the amount y in dollars in the account.what is the equation for the deposit?A- y/x = $40/monthB- y/x = $25/monthC- y/x = $50/monthD- y/x = $75/month
Answers
The two point throught which line passes are (2,100) and (4,200).
Determine the equation of line passes through the points.
[tex]\begin{gathered} y-100=\frac{200-100}{4-2}(x-2) \\ y-100=50(x-2) \\ y=50x-100+100 \\ y=50x \\ \frac{y}{x}=50 \end{gathered}[/tex]T
For each row of the table, choose the equivalent expression
Answers
Ok, so:
Let's make all operations and then choose the equivalent expression for each one.
Let's start in order:
a. 4/12 + 4/12 = 8/12
b. 1/12 + (3/12 + 3/12) = 7/12
c. 4/12 + 5/12 = 9/12
d. 2/12 + 2/12 + 2/12 = 6/12.
Notice that the last operations are the columns of the table.
So, let's do it the same with the upper rows:
e. 5/12 + 4/12 = 9/12
f. (1/12 + 3/12) + 3/12 = 7/12
g. 1/12 + 2/12 + 3/12 = 6/12
h. 15/12 - 7/12 = 8/12.
Now, let me draw the table to make this problem more understandable.
This is the order you have to put the answer:
Bea crió algunas vacas y algunos pavos. Crió un total de 28 vacas y pavo. habia 96 patas en total cuantas vacas y cuantos pavos crió bea?
Answers
1) Coletando los datos:
Vacas: v
Pavos: p
p+v =28
2p+4v=96 Como las vacas tienen 4 patas e los pavos tienen 2 patas
2) Multiplicando por - 2, la primera ecuación
-2p -2v =-56
2p +4v =96
-------------------
2v = 40
v= 20
3) Substituindo en la primera ecuación
p +20 =28
p =28 -20
p=8
Entonces, había 20 vacas y 8 perus
Which information is not enough to prove quadrilateral ABCD is a parallelogram?
Answers
To prove :
ABCD is a parallelogram
For parallelogram, if one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram.
Thus, in option (2) their is not enought information to prove that ABCD is a parallelogram because AB and CD are given congruent but not given parallel.
Similarly, BC and DA are given congruent but not given parallel.
So, the correct option is (2)
The y-value of which function’s y-intercept is larger, f or h?
Answers
Answer:
h
Explanation:
The y-value of the y-intercept is the value of y when x is equal to 0, so for the first function, we need to calculate f(x) for x = 0 as:
[tex]\begin{gathered} f(x)=\log _2(x+8) \\ f(0)=\log _2(0+8) \\ f(0)=\log _2(8) \\ f(0)=3 \end{gathered}[/tex]So, the y-value of the first function's y-intercept is 3.
On the other hand, for the second function, when x = 0, h(x) is 4. It means that the y-value of the second function's y-intercept is 4.
Since 4 is larger than 3, the function with the largest y-value in its y-intercept is h(x). So, the answer is h(x)
what is the area of triangle Givenchy height 137 and base 203
Answers
the area is calculated according to:
[tex]area=\frac{1}{2}\times203\times137=13,905.5[/tex]
Decide whether the relation defines y as a function of x. Give the domain. x+2y=——— 5A) Does the equation describe y as a function of x?1. Yes2. NoB) Give the domainThe domain is _____
Answers
Answer:
A) 1.yes
B) The domain is All real numbers.
Explanation:
The problem gives us a relationship:
[tex]y=\frac{x+2}{5}[/tex]For this relationship to be a function, for each value of x, we should get a single value of y. We can see that this is true, given a value of x, we get a unique value of y. Thus, A is true.
Now, we need to find the domain. The domain is the set of all values of x for which the function is defined. In this case, the function is a line:
[tex]\begin{gathered} y=\frac{x+2}{5} \\ . \\ y=\frac{x}{5}+\frac{2}{5} \\ . \\ y=\frac{1}{5}x+\frac{2}{5} \end{gathered}[/tex]The equation is a line with slope 1/5 and y-intercept 2/5. We know that any line is defined for all real numbers.
Thus, the domain is all real numbers.
i start at (3,2). You move down 1 unit and left 3 units. Where do u end
Answers
Given the initial coordinate: (3,2)
Moving down 1 unit means a negative displacement of 1 unit to the y-axis.
Moving left 3 units means a negative displacement of 3 units to the x-axis.
We get,
[tex](x^{\prime},y^{\prime})\text{ = (x + A,y + B) = (3 - 3, 2 - 1) = (0, 1)}[/tex]Therefore, after moving down 1 unit and left 3 units, you end at coordinate 0,1.
write a linear equation that has m=4 and has an x intercept of (5,0)
Answers
the equation is of the form y = mx + b, then
for b:
[tex]\begin{gathered} 0=4(5)+b \\ 0=20+b \\ 0-20=20+b-20 \\ b=-20 \end{gathered}[/tex]the equation is:
[tex]y=4x-20[/tex]what property do we use to check that our factored form is equivalent to the standard form
Answers
Lets solve an example:
[tex]\begin{gathered} y=x^2+6x+8 \\ \end{gathered}[/tex]this quadratic polynomial is in standard form. We can write the same polynomial in factored form as
[tex]y=(x+4)(x+2)[/tex]In the case of quadratic polynomials, a fast check is
that is, 4 plus 2 must be equal to 6 in the term 6x and
4 times 2 must be 8 in the constant term, which is 8.
In the diagram, GH bisects ∠FGI.Solve for x and find m∠FGH.a. X=b. Find m∠HGI.C. Find m∠FGI.(Simplify your answer.)
Answers
Answer:
(a)19 degrees
(b)29 degrees
(c)58 degrees
Explanation:
If GH bisects ∠FGI, it means it divides it into two equal parts ∠FGH and ∠HGI.
[tex]\begin{gathered} m\angle FGH=m\angle\text{HGI} \\ (2x-9)^0=(3x-28)^0 \end{gathered}[/tex](a)We solve the equation above for x.
[tex]\begin{gathered} 3x-2x=-9+28 \\ x=19 \end{gathered}[/tex](b)
[tex]\begin{gathered} m\angle HGI=3x-28 \\ =3(19)-28 \\ =57-28 \\ =29^0 \end{gathered}[/tex](c)
[tex]\begin{gathered} m\angle FGI=2\times m\angle HGI \\ =2\times29^0 \\ =58^0 \end{gathered}[/tex]Jeff receive six dollars for each hour he babysits how much money will just make after six hours eight hours 10 hours in 12 hours right the function and then find each answer to the correct function table that matches this situation
Answers
Jeff receive six dollars for each hour he babysits
Function:
f(x) = 6x
Where x is the number of hours
for 6 hours:
F(6) = 6(6) = 36
For 8 hours:
F(8)= 6(8) = 48
For 10 hours:
F(10)= 6(10)= 60
For 12 hours:
F(12)=6(12)=72
The diameter of a circle is 12 meters. What is the area of a sector bounded by a 102° arc?Give the exact answer in simplest form.
Answers
Answer:
The area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]Explanation:
The Area of a sector can be calculated using the formula;
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]Where:
A = area of the sector
Angle theta = the angle bounding the sector
r = radius
Given:
[tex]\begin{gathered} \theta=102^0 \\ r=\frac{\text{diameter}}{\text{2}}=\frac{12m}{2}=6m \\ r=6m \end{gathered}[/tex]substituting the given values, we have;
[tex]\begin{gathered} A=\frac{102}{360}\times\pi(6^2) \\ A=10.2\pi m^2 \\ A=32.04m^2 \end{gathered}[/tex]Therefore, the area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]
11. Reflect quadrilateral CONE with C(5,1), 0(1,6),N(-7,0) and E(-2,-4) in the line y = -2.
Answers
Step 1
y = -2 is the mirror line.
Step 2
The graph below shows the result after reflection about y = -2.
Joni took out a loan for $21,912. To pay it back, she will make 42 monthly paymentsof $931. How much will he pay in interest? Round answer to a whole number.
Answers
Given:
Loan of $21,912
42 monthly payments of $931.
Find amount of interest.
First, find the total amount that Joni will pay.
[tex]42\times\$931=\$39,102[/tex]Next, subtract the result by the amount of loan
[tex]\$39,102-$\$21,912=$\$17,190[/tex]Therefore, Joni will pay $17,190 in interest.
Ezra is finding the perimeter of different-sized regular pentagons. There is a proportional relationship between the side length of the regular pentagon in inches, x, and the perimeter of the regular pentagon in inches, y. The equation that models this relationship is y=5x. What is the perimeter of a regular pentagon with a side length of 2 inches? Write your answer as a whole number or decimal.
Answers
The perimeter of the regular pentagon Ezra is finding is 10m inches
How to find the perimeter of a regular pentagon with a side length of 2 inchesPerimeter refers to the total outside length of an object,
The equation given in the problem is
y = 5x
where
the side length of the regular pentagon in inches, x,
the perimeter of the regular pentagon in inches, y
if the side length is 5, we plug in 2 into the equation above
y = 5x
y = 5 * 2
y = 10 inches
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given the definitions of f(x) and g(x) below find the value of g(f(1)).f (x)= -3x + 4 g(x)= x squared + 7x + 5
Answers
f(x) = -3x + 4
g(x) = x^2 + 7x + 5
g(f(x)) = put x = f(x) in equation g(x)
g(f(x)) = (-3x + 4)^2 + 7(-3x + 4) + 5
put x = 1
g(f(1)) = (-3(1) + 4)^2 + 7(-3(1) + 4) + 5
= (-3+4)^2 + 7(-3 + 4) + 5
= 1^2 + 7(1) + 5
= 1 + 7 + 5
= 13
so the answer is 13
Perform the indicated operation numbers be sure to express your answer in reduced form
Answers
We need to calculate the following sum:
[tex]\frac{8}{15}+\frac{7}{25}[/tex]The first step is to calculate the least common multiplier between the two denominators. This is done below:
[tex]\begin{gathered} 15=3\cdot5 \\ 25=5\cdot5 \end{gathered}[/tex]We broke down the two denominators into their factors, now we need to multiply the factors that are unique. This is done below:
[tex]\text{LCM}=3\cdot5\cdot5=75[/tex]Now we have to replace the denominators by 75 and calculate new numerators. The new numerators must be calculated as follows:
1 - Divide the LCM by the old denominator
2 - Multiply the result of 1 by the old numerator.
This is done below:
[tex]\begin{gathered} \frac{5\cdot8}{75}+\frac{3\cdot7}{75} \\ \frac{40}{75}+\frac{21}{75} \end{gathered}[/tex]Since both fractions have their denominators with the same value, we can just directly add them.
[tex]\frac{40+21}{75}=\frac{61}{75}[/tex]The fraction is already in its most reductable form, therefore the answer is 61/75.
1. Here is an inequality below: Select ALL of the values that are a solutionto the inequality.*72 +62<3r+2X=-3X-2X = -1X=0x= 1x = 2X = 3
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given inequality
[tex]\frac{7x+6}{2}\le3x+2[/tex]STEP 2: Solve for x
[tex]\begin{gathered} \frac{7x+6}{2}\le3x+2 \\ \mathrm{Multiply\: both\: sides\: by\: }2 \\ 7x+6\le2(3x+2) \\ 7x+6\le\: 6x+4 \\ \mathrm{Subtract\: }6\mathrm{\: from\: both\: sides} \\ 7x+6-6\le\: 6x+4-6 \\ \text{By simplification,} \\ 7x\le\: 6x-2 \\ \mathrm{Subtract\: }6x\mathrm{\: from\: both\: sides} \\ 7x-6x\le\: 6x-2-6x \\ x\le\: -2 \end{gathered}[/tex]STEP 3: Select the values that are a solution to the inequality
[tex]\begin{gathered} \text{ Since }x\le-2,\text{ this means that x is less than or equal to -2} \\ \text{This implies that all values less than or equal to 2 are a solution to the inequality} \\ \text{Looking at the options, the values that are less than or equal to 2 are:} \\ x=-3,x=-2 \end{gathered}[/tex]Hence, the values that are a solution to the inequality are:
help me Plss Im begging you
Answers
Answer:
2:1
Step-by-step explanation:
No of hydrogen atoms = 4
No of carbon atoms = 2
Ratio of hydrogen atoms to carbon atoms mean that the no of hydrogen atoms need to be divided by the no of Carbon atoms
that is 4/2 = 2/1 = 2 : 1
There are 23 students in a class, and 6 of them will be chosen to go on a field trip. How many ways can these students be chosen?
Answers
To find how many ways a group of 23 students can be chosen from a group of 6, we use combinations, where the order doesn't matter.
Combinations are found with the next formula:
[tex]\text{nCr}=\frac{n!}{r!(n-r)!}[/tex]Where n is the total of persons and r is the sample asked.
Therefore:
n=23 and r=6
Replacing the values:
[tex]23C6=\frac{23!}{6!(23-6)!}[/tex]Then:
[tex]23C6=100947[/tex]Hence, there are 100947 ways that 23 students can be chosen from a group of 6.
Hi i have uploaded the question in the image. Equation no. 2 (ii).
Answers
Let's determine if g(x) is a factor of f(x).
[tex]\text{ f(x) }=\text{ }x^3\text{ }-3x^2+4x-4[/tex][tex]\text{ g(x) = }x\text{ - 2}[/tex]Given that g(x) = x - 2, at x = 2, let's check the value of f(x) at x = 2, If f(x) = 0, then g(x) is a factor, otherwise, g(x) is not a factor of f(x).
We get,
At x = 2,
[tex]\begin{gathered} \text{ f(x) }=\text{ }x^3\text{ }-3x^2+4x-4 \\ \text{ f(2) = (2)}^3-3(2)^2\text{ + 4(2) - }4 \\ \text{ f(2) = 8 - 12 + 8 - }4 \\ \text{ f(2) = 16 - 1}6 \\ \text{ f(2) = 0} \end{gathered}[/tex]Therefore, g(x) is a factor of f(x).
determine whether the line is a tangent, secant, a secant that contains the diameter, or none of these. Graph the circle using your calculator or online calculator or graph paper. Then graph this line.
Answers
As suggested, we will use a diagram that includes the circle and the line to decide what type of chord is the line to the circle.
The graph of the circle and the line is:
From the above graph, we get that the line is exterior to the circle and never touches it. Therefore, the line is not a tangent, a secant, or a secant that contains the diameter.
Answer:
None
Find the amount of interest and the monthly payment for the loan described.
Purchase of a living room set for $2,700 at 12% add-on interest for 3 years
Answers
The amount of interest is $972 and monthly payment is $102.
What is Simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
Given that, a loan described as purchase of a living room set for $2,700 at 12% add-on interest for 3 years
SI = P*R*T/100
SI = 2700*12*3/100 = $972
Amount to be paid = $972+$2,700 = $3672
Amount to be paid monthly = $3672/3*12 = $102
Hence, The amount of interest is $972 and monthly payment is $102.
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find the length of each chord. horizontal chord and vertical
Answers
Consider the circle
we have the intersecting chords theorem, which states that
[tex]a\cdot b=c\cdot d[/tex]In our case we have a=x, b=12, c=6 and d=x+4. So we have
[tex]12\cdot x=6\cdot(x+4)[/tex]distributing on the right side we get
[tex]12\cdot x=6x+6\cdot4=6x+24[/tex]Subtracting 6x on both sides, we get
[tex]24=12x\text{ -6x=6x}[/tex]Dividing boht sides by 6, we get
[tex]x=\frac{24}{6}=4[/tex]So, the value of x is 4. Now we replace this value to find the length of each chord, so we have
x---->4
12---->12
x+4----->4+4=8
6----->6
A polynomial has one root that equals 2 + i. Name one other root of thispolynomial.
Answers
In a polynomial, if it has an imaginary root, then it also has the conjugate of that root. In this case, since 2 + i, is a root then 2 - i, is also a root.
Question 2 (5 points) (04.01 LC) Simplify +5x+6 X+2
A x²+1
B x²-1
C X +3
D X-3
Answers
[tex]\bf{\dfrac{x^{2} +5x+6 }{x+2} }[/tex]
Rewrite the term.
x² + 2x + 3x + 6
Group the terms into two fractional parts.
(x² + 2x + (3x + 6)
Factor the expression
x(x + 2) + 3 (x + 2)
[tex]\boldsymbol{\sf{\dfrac{(\not{x+2)(x+3)}}{\not{x+2}}=x+3 \to Option \ C }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{\cfrac{x {}^{2} + 5 x + 6 }{x + 2} }[/tex]
Answer :
Note: To solve a problem like this, we must first determine which of the two numbers add 5 and multiply 6, we know that they are 2 and 3 and then we must Rewrite the expression using the above.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{(x+2)(x+3)}[/tex]
Now, we must put a fraction since we can more easily solve the problem posed.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \cfrac{(x + 2)(x + 3)}{x + 2} }[/tex]
Now the last thing we have to do is Cancel [tex]\bold{x+2}[/tex] to have a final result that is the following:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x+3}[/tex]
Select the recursive and explicit formula for the Arnold family 2 answer
Answers
ANSWER:
[tex]\begin{gathered} A\left(n\right)=a_{n-1}\times 2 \\ A\left(n\right)=0.05\cdot\left(2\right)^{n-1} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the Arnolds family are going to save a nickel on the first day of the month and then double the amount each day.
One nickel is equal to $0.05, therefore, we can make an recursive formula, it is a geometric sequence where the initial value is 0.05 and the ratio is equal to 2, because it doubles every day, therefore:
[tex]A(n)=0.05\cdot(2)^{n-1}[/tex]Now, from the above we can deduce the explicit formula, since the next value will be double the previous value, therefore, the explicit formula would be:
[tex]A(n)=a_{n-1}\times2[/tex]Therefore, the correct answers are the 1st and 4th options.