____________________________________________________
Answer:
$203.5
____________________________________________________
Step-by-step explanation:
In order to find the answer to your question, we would need to find how much money she made when selling the collars.
Lets gather the important information:
$4.75 for small collar
$7.75 for large collar
With the information above, we can solve the problem.
What we would do is multiply the amount of collars that was sold to the right price.
Therefore, we would multiply 4.75 by 20, since small collars cost 4.75 and she sold 20 of them. We would also multiply 7.75 by 14, since large collars cost 7.75 and she sold 14 of them.
Lets calculate:
[tex]4.75*20=95\\\\7.75*14= 108.50[/tex]
Now, we would add the final prices together in order to find how much revenue she made off of the collars.
[tex]95+108.50=203.5[/tex]
When you're done soplving, you should get 203.5.
This means that her revenue last month was $203.5.
$203.5 should be your FINAL answer.
____________________________________________________
Answer:
205.50
Step-by-step explanation:
9 is subtracted from 5 times 3 and 10 is added
The final answer is 16
What is subtraction?The act or process of taking one number away from another is called subtraction.
How to now the final value after subtraction?According to the problem,
9 is subtracted from 5 times 3 and 10 is addedThis can be written as (5 x 3) + 10- 9
= 16
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What is the surface area of this composite solid?
square feet
let's take a peek
we really have a rectangular prism below a square pyramid.
the prism has a front, back, left and right of a rectangle 2x11 .
its bottom or base is an 11x11 square.
the pyramid 4 triangles, each one has a base of 11 and a height of 7.
[tex]\bf \stackrel{\textit{front, back, left, right}}{4(2\cdot 11)}~~+~~\stackrel{\textit{base}}{(11\cdot 11)}~~+~~\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(11)(7) \right]} \\\\\\ 88+121+154\implies 363[/tex]
Answer:
The surface area of composite solid = 363 ft²
Step-by-step explanation:
Points to remember
Area of rectangle = Length * Breadth
Area of triangle = bh/2
Where b - Base and h - Height
To find the surface area of composite solid
Surface area = Base area + side area + area of 4 triangles
= (11 * 11) + 4(11 * 2) + 4(11 * 7)/2
= 121 + 88 + 154
= 363 ft²
Therefore the surface area of composite solid = 363 ft²
At a summer camp, there are 50 girls out of 80 campers.What is this ratio writtin as a fraction in simplest form?
The ratio is 5:8 campers
Answer:
50
--- Ratio: 50:80
80
Step-by-step explanation:
50 would be how many girls were that the summer camp. And the 80 is how many students all together at the summer camp.
Hoped This Helped You
Have A Wonderful day
What is f(x) + f(x) + f(x)?
3f(x) =
Evaluate 3f(2) =
.
Answer:
the answer on e2020 is 12.
The required answer is,
f(x) + f(x) + f(x) = 3ax² + 3bx + 3c
3f(x) = 3ax² + 3bx + 3c
3f(2) = 12a + 6b + 3c
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Now let the function be,
f(x) = ax² + bx + c
To find,
f(x) + f(x) + f(x)
we have,
f(x) + f(x) + f(x) = (ax² + bx + c) + (ax² + bx + c) + (ax² + bx + c)
⇒ f(x) + f(x) + f(x) = 3(ax² + bx + c)
or, f(x) + f(x) + f(x) = 3ax² + 3bx + 3c
Similarly,
3f(x) = 3(ax² + bx + c)
or, 3f(x) = 3ax² + 3bx + 3c
now to find f(2), put x = 2 in f(x). we get,
f(2) = a2² + b2 + c
or, f(2) = 4a + 2b + c
Therefore,
3f(2) = 3(4a + 2b + c)
or, 3f(2) = 12a + 6b + 3c
hence, the required answer is,
f(x) + f(x) + f(x) = 3ax² + 3bx + 3c
3f(x) = 3ax² + 3bx + 3c
3f(2) = 12a + 6b + 3c
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what is the location of the point on the number line that is 2/5 of the way from A=-6 to B=9?
Answer:
0
Step-by-step explanation:
Between -6 and 9 are 15 units.
2/5 of 15 units is 6 units. Add this to -6 to obtain 0.
0 is the answer to this question
Step-by-step explanation:
I'm not sure but I think its like the distance between -6 and 9 is 15 or something and 15 divided by 5 is 3 and 2/5 is 6 so 6-6 is 0 and that's that point.
there are 48 heads and 134 legs how many sheep is there
Answer:
48
Step-by-step explanation:
48 heads =48sheep. .i guess. .......
Something's odd with this question: each sheep has one head, so if you see 48 heads there are 48 sheeps.
But each sheep has also 4 legs, so if you have 48 sheeps you should see
[tex]48\cdot 4 = 192\text{ legs}[/tex]
So, unless you have some sheeps with missing legs, there must be a mistake in the question.
Can someone help me out with this question plz
Answer:
[tex]\left(s\cdot t\right)\left(x\right)=2x^2+12x+16[/tex]
[tex]\left(s-t\right)\left(x\right)=-x[/tex]
[tex]\left(s+t\right)\left(4\right)=20[/tex]
Step-by-step explanation:
Given functions are:
[tex]s\left(x\right)=x+4[/tex]
[tex]t\left(x\right)=2x+4[/tex]
Then [tex]\left(s\cdot t\right)\left(x\right)=s\left(x\right)\cdot t\left(x\right)[/tex]
or [tex]\left(s\cdot t\right)\left(x\right)=\left(x+4\right)\left(2x+4\right)[/tex]
or [tex]\left(s\cdot t\right)\left(x\right)=2x^2+4x+8x+16[/tex]
or [tex]\left(s\cdot t\right)\left(x\right)=2x^2+12x+16[/tex]
---------
Similarly
[tex]\left(s-t\right)\left(x\right)=s\left(x\right)-t\left(x\right)[/tex]
or [tex]\left(s-t\right)\left(x\right)=\left(x+4\right)-\left(2x+4\right)=x+4-2x-4[/tex]
or [tex]\left(s-t\right)\left(x\right)=-x[/tex]
---------
Similarly
[tex]\left(s+t\right)\left(4\right)=s\left(4\right)+t\left(4\right)=\left(4+4\right)+\left(2\left(4\right)+4\right)=\left(8\right)+\left(12\right)=20[/tex]
[tex]\left(s+t\right)\left(4\right)=20[/tex]
If m1 = 110°, an arc with a measure of 250°.
BC
BCA
CTA
Answer:
the correct answer is BCA
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: [tex]m\angle 1=110^{\circ}[/tex].
It is given that [tex]m\angle 1=110^{\circ}[/tex], so arc(BA)=110° and the central angle of arc BCA is
[tex]Arc(BCA)=360^{\circ}-Arc(BA)[/tex]
[tex]Arc(BCA)=360^{\circ}-110^{\circ}[/tex]
[tex]Arc(BCA)=250^{\circ}[/tex]
The measure of arc BC is
[tex]180^{\circ}-110^{\circ}=70^{\circ}[/tex]
The measure of arc CTA is 180° because AC is the diameter.
It means options 1 and 3 are incorrect.
The measure of arc BCA is 250°. Therefore the correct option is 2.
The mapping diagram shows a function R(x).
Which mapping diagram shows the inverse of R(x)?
Answer:
C
Step-by-step explanation
The mapping diagram which shows the inverse of R(x) is Option (C).
What is a mapping diagram ?A function is a special type of relation in which each element of the domain is paired with exactly one element in the range . A mapping diagram shows how the elements are paired. Its like a flow chart for a function, showing the input and output values. A mapping diagram consists of two parallel columns.
How to find the mapping diagram which contains the inverse of a function ?To identify the mapping diagram for inverse of a function, we simply just change the values of first set of columns into the second set of columns.
This is because if [tex]f(x) = y[/tex] , then [tex]f^{-1}(y) = x[/tex]
For the given function R(x) , values are 6,7,8,9 in first column and 9,10,11,12 in the second column . Thus for the inverse function, 6,7,8,9 will be in the second column and 9,10,11,12 will be in the first column.
From the given Options, Option (C) is the correct mapping of inverse of R(x).
Thus, the mapping diagram which shows the inverse of R(x) is Option (C).
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11-30x+24. what is this answer
Answer:
-30x+35
Step-by-step explanation:
Add 11 and 24
What is the x-intercept of the graph?
Answer:
-3
Step-by-step explanation:
The x-intercept is the plot point where y = 0.
Answer:
-3
Step-by-step explanation:
the x-intercept is the point on the graph where the ploted line crosses the x axes
What is the solution to the equation?
(A) d = –4 and d = 2
(B) d = –2 and d = 4
(C) d = 1
(D) d = 2
MY LAST QUESTION HELP.
ANSWER
(C) d=1
EXPLANATION
The given equation is
[tex] \frac{ - 3d}{ {d}^{2} - 2d - 8} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]
Factor the first fraction to get,
[tex] \frac{ - 3d}{(d + 2)(d - 4)} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]
Multiply through by (d+2)(d-4)
[tex] - 3d + 3(d + 2) = - 2(d - 4)[/tex]
Expand:
[tex] - 3d + 3d + 6 = - 2d + 8[/tex]
[tex] 6 = - 2d + 8[/tex]
[tex]6 - 8= - 2d[/tex]
[tex] - 2 = - 2d[/tex]
divide both sides by -2
[tex]d = 1[/tex]
The correct answer is (B) [tex]\( d = -2 \)[/tex] and [tex]\( d = 4 \)[/tex].
To find the solution to the given quadratic equation, we can factor it or use the quadratic formula. The equation is not provided in the conversation, but based on the options given, it seems that the equation could be in the form [tex]\( (d - a)(d - b) = 0 \)[/tex], where [tex]a[/tex] and [tex]b[/tex]are the roots of the equation.
The quadratic equation can be written as [tex]\( d^2 - (a+b)d + ab = 0 \)[/tex]. To have the sum of the roots [tex]\( a + b \)[/tex] equal to 0 and the product of the roots [tex]\( ab \)[/tex] equal to -8, we can set up the following system of equations:
1. [tex]\( a + b = 0 \)[/tex]
2. [tex]\( ab = -8 \)[/tex]
From equation 1, we can express [tex]\( b \)[/tex] in terms of [tex]\( a \): \( b = -a \).[/tex]
Substituting [tex]\( b \)[/tex] into equation 2, we get:
[tex]\( a(-a) = -8 \)[/tex]
[tex]\( -a^2 = -8 \)[/tex]
[tex]\( a^2 = 8 \)[/tex]
Taking the square root of both sides, we find:
[tex]\( a = \pm\sqrt{8} \)[/tex]
[tex]\( a = \pm2\sqrt{2} \)[/tex]
Since [tex]\( b = -a \),[/tex] we have:
[tex]\( a = 2\sqrt{2} \) and \( b = -2\sqrt{2} \)[/tex]
[tex]\( a = -2\sqrt{2} \) and \( b = 2\sqrt{2} \)[/tex]
However, these are not the exact values given in the options. We need to find the exact integer values for [tex]a[/tex] and [tex]b[/tex]. Since the product [tex]\( ab \)[/tex] is -8, we can look for two numbers that multiply to -8 and add up to 0. These numbers are -2 and 4.
Therefore, the solutions to the equation are [tex]\( d = -2 \)[/tex] and [tex]\( d = 4 \)[/tex], which corresponds to option (B).
Question: An arithmetic sequence is a sequence with a common difference. It can be represented by the recursive formula a1 = a (where a is the first term of the sequence); an = an - 1 + d. a) Create your own arithmetic sequence. Write out the first 3 terms. b) What is the common difference of your sequence? c) Write the recursive formula representing your sequence. Use the underscore symbol to indicate a subscript. For example, the recursive formula would be written like a1 = a; a_n = a_(n – 1) + d
Answer:
a) 3,6,9,12,15,..
b) Common Ratio is 3
c) Recursive Formula : aₙ= aₙ₋₁ + d where a₁=3 and d= 3
Step-by-step explanation:
a) Create your own arithmetic sequence. Write out the first 3 terms.
Consider the sequence: 3,6,9,12,15,..
a₁ = 3
a₂ = 6
a₃ = 9
b) What is the common difference of your sequence?
6-3 = 3
9-6 = 3
12 -9 =3
So, common difference is 3
c) Write the recursive formula representing your sequence.
a₁ = 3
a₂ = aₙ₋₁ + d
= a₁ + d
= 3+ 3 = 6
a₃ = aₙ₋₁ + d
= a₂ + d
= 6+3 = 9
so, recursive formula is aₙ = aₙ₋₁ + d where a₁ = 3 and d= 3
An example of an arithmetic sequence can be created with a starting value (a1) of 2 and a common difference (d) of 3. The sequence's terms would be 2, 5, 8, etc. Its recursive formula would be a1 = 2; a_n = a_(n–1) + 3.
Explanation:
Let's create an arithmetic sequence, starting with the first term (a1) of 2 and a common difference (d) of 3. So, the first three terms of the sequence would be 2, 2+3=5, and 5+3=8.
The common difference of this arithmetic sequence is 3 as each term is 3 greater than the previous term.
The recursive formula for this sequence is a1 = 2; a_n = a_(n–1) + 3. What this formula means is that the first term is 2, and each subsequent term (an) is the previous term (an-1) added to the common difference (3).
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Solve the Equation
2x-3=14
-x+3y=-6
Step-by-step explanation:
If you lost "y" in the first equation.
[tex]\underline{+\left\{\begin{array}{ccc}2x-3y=14\\-x+3y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\\\.\qquad x=8\\\\\text{Put the value of x to the first equation:}\\\\2(8)-3y=14\\16-3y=14\qquad\text{subtract 16 from both sides}\\-3y=-2\qquad\text{divide both sides by (-3)}\\y=\dfrac{2}{3}\\\boxed{x=8,\ y=\dfrac{2}{3}}[/tex]
If first equation is correct.
[tex]2x-3=14\qquad\text{add 3 to both sides}\\2x=17\qquad\text{divide both sides by 2}\\x=8.5\\\\\text{Put the value of x to the second equation:}\\-8.5+3y=-6\qquad\text{add 8.5 to both sides}\\3y=2.5\qquad\text{divide both sides by 3}\\y=\dfrac{2.5}{3}\\y=\dfrac{25}{30}\\y=\dfrac{5}{6}\\\\\boxed{x=8.5,\ y=\dfrac{5}{6}}[/tex]
fill in the missing exponents in each box (9^4)?=9^1
x=1/4 because, 1/4 will multiply with 4 to cancel out to have an exponent of 1
[tex]\bf (9^4)^{?}=9^1\implies 9^{4\cdot ?}=9^1\implies \stackrel{\textit{same base, the exponents must also be the same}}{4?=1\implies ?=\cfrac{1}{4}}[/tex]
if tanØ = 3/4, Find sinØ
a. SinØ=1/2
b. sinØ = 3/5
c. sinØ = 2
d sin Ø = 8/5
Answer: This is some information I have gathered to help you since I cannot answer this directly sin θ + (cot θ)(cos θ)
= sin θ + (cos θ / sin θ)(cos θ)
= sin θ + cos² θ / sin θ
Since cos² θ = 1 - sin² θ,
= sin θ + (1 - sin² θ) / sin θ
= sin θ + 1 / sin θ - sin θ
= 1 / sin θ
= csc θ ∎ Sin(x) = tan(x) / [sqrt(1 + tan^2(x)]
Sin(theta) =3/4 / sqrt[1 + .75^2]
Sin(theta) =0.75 / sqrt[ 1.5625 ]
Sin(theta) =0.75 / 1.25
Sin(theta) = 0.60
Taxes are used for which of the following?
Depending on the country, most democracies use taxes for:
-public programs (any governmentally run or funded services)
-infrastructure (roads, bridges, etc)
-the military
-schools
-governmental departments (EPA, Department of Homeland Security, etc)
-government employee paychecks
And SOMETIMES:
-universal healthcare
-college/university
-etc.
Taxes are used to fund government services, reduce income inequalities, and support state and local government activities.
Explanation:Taxes are used for a variety of purposes. They are primarily used to fund government services such as military, police, education, infrastructure, and social security. Taxes are also used to reduce income and wealth inequalities by transferring income to lower income groups. Additionally, taxes are used to support state and local government activities and services.
For example, in the United States, the federal government raises revenue through income taxes, corporate earnings taxes, and sales taxes on goods such as gasoline, alcohol, and tobacco. State and local governments also collect taxes, including income, property, and sales taxes, which fund activities like maintaining public parks and providing a police force.
Overall, taxes play a crucial role in financing government operations and essential public services that benefit communities.
The values for three different sets of data are shown below.
Without calculating any statistics, Jadyn knows that data set 1 would have the least mean absolute deviation among the
three sets. Which statement explains how she knows?
Answer:
I'd say C Sets 2 and 3 contain outliers.
Step-by-step explanation:
Set 2 has an outlier of 90, while set 3 has an outlier of 40. 40 isn't as much of an outlier as 90 is, so I'm not absolutely sure. Cmakes the most sense though.
Answer: Third option.
Step-by-step explanation:
The standard deviation increases as we have more values that are far away from the mean.
For example, in data set 2, we can see that most of hour points are between 38 and 49, but we also have a point with a value of 90, so we may expect that this data set has a big standard deviation.
The data set 3 is similar, most of our points are between 24 and 31, and we have a value that is on 40, so again we have an outlier that increases the value of the standard deviation.
Noticing it we can conclude that data set 2 and data set 3 have a greater standard deviation than set 1.
The correct option is the third option.
The histogram shows the weekly attendance of participants in a school's study skills program. Student attendance numbers were the same during which two weeks of the workshop?
A.
weeks 1 and 2
B.
weeks 2 and 4
C.
weeks 5 and 6
D.
weeks 4 and 6
That would be week 2 and 4 (B). They are both at 12 students attending
Hope this helped!
Answer:
The correct option is B. weeks 2 and 4.
Step-by-step explanation:
Consider the provided histogram.
The histogram shows the weekly attendance of participants in a school's study skills program.
Now, consider the Histogram.
In week 1 the Student attendance was 8.
In week 2 the Student attendance was 12.
In week 3 the Student attendance was 15.
In week 4 the Student attendance was 12.
In week 5 the Student attendance was 18.
In week 6 the Student attendance was 16.
Hence the Student attendance numbers were the same during week 2 and week 4 of the workshop.
Therefore, the correct option is B. weeks 2 and 4
(b)
5 cm
5 cm
108
cm
1080
1080
5 cm
5 cm
108°
1089
5 cm
Answer:
(b)
5 cm
5 cm
108
cm
1080
1080
5 cm
5 cm
108°
1089
5 cm
Step-by-step explanation:
Ummmmm. :)
well hope it helped you!
Answer:
Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements.
Triangle JKL is congruent to triangle .
Side LK corresponds to sides .
Angle JLK corresponds to angles .
Step-by-step explanation:
In history class, Colin takes a multiple-choice quiz. There are 10 questions. Each question has five possible answers. To the nearest percentage, what is the probability that Colin will get exactly 3 questions correct if he guesses an answer to each question?
Answer:
[tex]P = 0.201[/tex]
Step-by-step explanation:
If the discrete random variable X represents the number of correct Colin responses then X can be represented by a binomial distribution with parameters p, n, x.
In this case p represents the probability that colin gets a correct answer, n represents the number of questions.
So the probability that Colin receives x correct questions is:
[tex]P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}[/tex]
Where:
[tex]p=\frac{1}{5}[/tex]
[tex]n=10[/tex]
[tex]x=3[/tex]
[tex]P(x=3) = \frac{10!}{3!(10-3)!}*(\frac{1}{5})^3*(1-\frac{1}{5})^{10-3}[/tex]
[tex]P(x=3) = \frac{10!}{3!*7!}*\frac{1}{125}*(\frac{4}{5})^{7}[/tex]
[tex]P = 0.201[/tex]
Given the system of equations, match the following items.
2 x - y = 0
x + y = -3
[0 -1
-3 1]
[2 0
1 -3]
[2 -1
1 1]
The x - determinant of the equation is [tex]\left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right][/tex]
The y - determinant of the equation is [tex]\left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right][/tex]
The system determinant is [tex]\left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right][/tex]
How to find the determinants of x, y and the entire system?
The given system of equation include the following;
2x - y = 0
x + y = - 3
The x - determinant of the equation will be obtained by replacing coefficient of x with the constant terms.
[tex]\Delta x = \left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right][/tex]
The y - determinant of the equation will be obtained by replacing coefficient of y with the constant terms.
[tex]\Delta y = \left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right][/tex]
The system determinant is obtained by removing the constant term and writing only the x and y coefficient in the matrix;
[tex]\Delta = \left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right][/tex]
The distance between two cities is 500 miles. On a map, they are 4 inches apart. What is the scale of the map?
500/4 = x/1
125 = x
125 miles per inch.
6(3x–5)–5(2x+7)=25 help me
Answer:
18x-30-10x-35=25
8x-65=25
8x-65+65=25+65
8x=90
Divide by 8 for 8x and 90
x=90/8 or 45/4 or 11 1/4 ( Answers)
The table shows the effect of education on annual income. Based on the data in the table, how much more does a person with an Bachelor’s degree earn than a person with only a high school diploma over 10 years?
A) $20,800
B) $29,690
C) $208,000
D)$290,690
B is the correct answer
which expression is equivalent to (64y^100)^1/2
Answer:
8y^50
Step-by-step explanation:
Answer:
8y^50
Step-by-step explanation:
At which point(s) do the graphs of y = x + 1 and y = 2x intersect?
Answer:
(1,2)
Step-by-step explanation:
I just used a graphing calculator
which will result in a difference of squares?
Answer:
C
Step-by-step explanation:
Answer:
The correct option is 3.
Step-by-step explanation:
The difference of squares is defined as
[tex]a^2-b^2=(a-b)(a+b)[/tex]
In option 1,
[tex](-7x+4)(-7x+4)=(-7x+4)^2[/tex]
This expression is a perfect square, therefore this is not the difference of squares. Option 1 is incorrect.
In option 2,
[tex](-7x+4)(4-7x)=(-7x+4)(-7x+4)=(-7x+4)^2[/tex]
This expression is a perfect square, therefore this is not the difference of squares. Option 2 is incorrect.
In option 3,
[tex](-7x+4)(-7x-4)=(-7x)^2-(4)^2[/tex]
This expression is the difference of squares., therefore Option 3 is correct.
In option 4,
[tex](-7x+4)(7x-4)=-(-7x+4)(-7x+4)=-(-7x+4)^2[/tex]
This expression is a perfect square, therefore this is not the difference of squares. Option 4 is incorrect.
Which of the following are equations for the line shown below? Check all that
apply
(-1,5)
O
A. y-2 = -0.75(x-3)
B. y-5 = -0.75(x-1)
C. y-3 = -0.75(x - 2)
D. y-5-0.75(x+1)
The answer is:
The correct options are:
A) [tex]y-2=-0.75(x-3)[/tex]
and
D) [tex]y-5=-0.75(x+1)[/tex]
Why?To find the correct answers, we need to find a equation that meet the following charactheristics:
From the graph we can se that the function:
- Has a negative slope (is decreasing)
- Pass throught the points: (-1,5) and (3,2)
Now, discarding from the given options, we have:
A.[tex]y-2=-0.75(x-3)[/tex]
We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).
Evaluating the points, we have:
Evaluating (-1,5)
[tex]5-2=-0.75(-1-3)[/tex]
[tex]3=-0.75(-4)[/tex]
[tex]3=3[/tex]
Evaluating (3,2):
[tex]2-2=-0.75(3-3)[/tex]
[tex]0=-0.75(0)[/tex]
[tex]0=0[/tex]
We have that the equation is satisfied, so, the line pass through the given points.
Hence, we have that the equation A is an equation of the line shown.
B.[tex]y-5=-0.75(x-1)[/tex]
We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).
Evaluating the points, we have:
Evaluating (-1,5)
[tex]5-5=-0.75(-1-1)[/tex]
[tex]0=-3.5[/tex]
Hence, we have that since the equation is not satisfied, the line shown is not passing through the point (-1,5) meaning that the equation is not an equation of the line shown.
So, we have that the equation B is not equation of the line shown.
C.[tex]y-3=-0.75(x-2)[/tex]
We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).
Evaluating the points, we have:
Evaluating (-1,5)
[tex]5-3=-0.75(-1-2)[/tex]
[tex]2=-0.75(-3)[/tex]
[tex]2=2.25[/tex]
Hence, we have that since the equation is not satisfied, the line shown is not passing through the point (-1,5) meaning that the equation is not an equation of the line shown.
So, we have that the equation B is not equation of the line shown.
D.(assuming you committed a mistake writing the options and the equality sign is missing)
[tex]y-5=-0.75(x+1)[/tex]
We have that the coefficient of the linear term is negative (-0.75), so, the slope is negative (the function is decreasing).
Evaluating the points, we have:
Evaluating (-1,5)
[tex]5-5=-0.75(-1+1)[/tex]
[tex]0=-0.75(0)[/tex]
[tex]0=0[/tex]
Evaluating (3,2)
[tex]2-5=-0.75(3+1)[/tex]
[tex]-3=-0.75(4)[/tex]
[tex]-3=-3[/tex]
We have that the equation is satisfied, so, the line pass through the given points.
Hence, we have that the equation B is an equation of the line shown.
Finally, we have that the correct options are:
A) [tex]y-2=-0.75(x-3)[/tex]
and
D) [tex]y-5=-0.75(x+1)[/tex]
Have a nice day!
what are the solutions of this equation 16-2x^2=-64
Answer:
x = ± 2[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Given
16 - 2x² = - 64 ( subtract 16 from both sides )
- 2x² = - 80 ( divide both sides by - 2 )
x² = 40 ( take the square root of both sides )
x = ± [tex]\sqrt{40}[/tex] = ± [tex]\sqrt{4(10)}[/tex] = ± 2[tex]\sqrt{10}[/tex]