28. Overhead Projectors Your teacher draws a circle on an overhead projector.
The projector then displays an enlargement of the circle on the wall. The circle
drawn has a radius of 3 inches. The circle on the wall has a diameter of 4 feet.
What is the scale factor of the enlargement?
a
A scale factor is a factor that can be used to either increase or decrease the size of a given figure. Therefore, the scale factor of the enlargement is [tex]\frac{1}{8}[/tex].
Scale drawing is a type of drawing that requires the use of a factor to either enlarge or reduce the size of a given figure. The factor required is called a scale factor. It can be expressed as:
scale factor = [tex]\frac{length of side of image}{length of side of object}[/tex]
In the given question, the radius of the circle drawn is 3 inches, while that on the wall has a diameter of 4 feet.
Thus;
diameter of circle = 2 * 3
= 6 inches
But;
1 feet = 12 inches
So that;
x = 6 inches
⇒ x = [tex]\frac{6}{12}[/tex]
= [tex]\frac{1}{2}[/tex]
x = 0.5 feet
Thus, the diameter of the circle is 0.5 feet.
So that;
scale factor = [tex]\frac{0.5 feet}{4 feet}[/tex]
= 0.125
scale factor = [tex]\frac{1}{8}[/tex]
The scale factor of the enlargement is [tex]\frac{1}{8}[/tex].
For more on scale factor, visit: https://brainly.com/question/10253650
What does this graph represent?
Question options:
not moving
acceleration
constant speed
Answer:
A or C
Step-by-step explanation:
miggy ask to solved the given quadratic equation x²+8x-20=0 using the quadratic formula,Help miggy to determine the following
roots of the quadratic 3
discriminant
nature of roots
sum of the roots
product of the roots
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
roots of the quadratic equation ~
[tex]2 \: \: \: \:a nd \: \: - 10[/tex]discriminant ~
[tex]144[/tex]nature of roots ~
[tex]real[/tex]sum of the roots ~
[tex] - 8[/tex]product of the roots ~
[tex] - 20[/tex][tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's solve he given quadratic equation using quadratic formula ~
Let's consider the following values ~
b (Coefficient of x) = 8 a (Coefficient of x²) = 1 c (Constant term) = -20According to quadratic formula, the roots are ~
[tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]where, ( b² - 4ac ) is known as it's discriminant ~
that is equal to ~
[tex](8) {}^{2} - (4 \times 1 \times - 20)[/tex][tex]64 - ( - 80)[/tex][tex]64 + 80[/tex][tex]144[/tex]Hence, Discriminant = 144
And since discriminant is positive, then the roots of the quadratic polynomial are real .
Let's find the roots now ~
[tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac} }{2a} [/tex][tex] \dfrac{ - 8 \pm \sqrt{144} }{2 \times 1}[/tex][tex] \dfrac{ - 8 \pm12}{2} [/tex][tex] \dfrac{ 2( - 4 \pm6)}{2} [/tex][tex] - 4 \pm6[/tex]So, the two roots are ~
[tex] - 4 + 6[/tex][tex]2[/tex]and
[tex] - 4 - 6[/tex][tex] - 10[/tex]Sum of roots ~
[tex] - 10 + 2[/tex][tex] -8[/tex]product of roots ~
[tex] - 10 \times 2[/tex][tex] - 20[/tex]You bought for hamburgers you gave the cashier $50 bill and get $22 change how much was each hamburger
!!!!!!!!5 step plan please!!!!!!!!
Please help geometry question
Answer:
D) QR≅ST
The answer follows from basic AAS congruences
Answer:
line PQ≅line SU
Step-by-step explanation:
∆PQR ∆UST
P corresponds to U
Q corresponds to S
R corresponds to T
line PQ to line US
line QR to line ST
line PR to line UT
Select all the equations that have {6} as its solution set.
15−x=54x
8+3x=6x−10
x2+2=7x−4
43−4x=3x−1
ANSWER:
The ANSWER IS 2. if two solutions are allowed then 2. AND 3. and if your rounding, then 2. 3. and 4.
Step-by-step explanation:
For the first one it is: 0.27... or 3/11
For the second one it is: 6
For the third one it is: 1 or 6, meaning it has two solutions
For the fourth one it is: 6.285714, or 44/7
for the first one: 15-x=54x -> add x to both sides: 15=55x -> then divide both sides by 55: x=3/11
for the second one: 8+3x=6x-10 -> subtract 6x from both sides: 8-3x=-10 -> subtract 8 from both sides: -3x=-18 -> divide both sides by -3: x=6
I'm actually supposed to be doing school, so I don't have time to explain the last two, but I wanted to help, so please give 4 stars or brainliest. and thanks for waiting patiently.
The equation 8+3x=6x−10 has {6} as its solution set. Option B is correct.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
The equations that have {6} as its solution set is,
We have to solve the equation in order to find the value of x,
Equation 1,
15−x=54x
54x+x=15
55x=15
x=0.27
Equation 2,
8+3x=6x−10
6x-3x=-10+8
3x=18
x=6
Equation 3,
x²+2=7x−4
x²-7x+6=0
x²+6x+x+6=0
x(x+6)+1(x+6)=0
(x+1)=0 , x=-1
(x+6)=0, x=-6
Equation 4,
43−4x=3x−1
4x+3x=43+1
7x=44
x=44/7
x=6.285
Thus, the equation 8+3x=6x−10 has {6} as its solution set. Option B is correct.
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ2
Pls help and explain, will give brainliest!
-5+3 + (-1/6)+ 5/6 in fractions form
Answer:
Step-by-step explanation:
-5+3 + (-1/6)+ 5/6
-2 - 1/6 + 5/6
-2 + 4/6 (do this boring math)
Answer:
[tex]-1\frac{1}{3}[/tex] aka [tex]\frac{-4}{3}[/tex]
Step-by-step explanation:
-5+3+(-1/6)+ 5/6
Ok soo -5+3 is -2 So then
-2-[tex]\frac{1}{6}[/tex]+[tex]\frac{5}{6}[/tex]
-2+(-[tex]\frac{1}{6}[/tex]+[tex]\frac{5}{6}[/tex])
-[tex]\frac{1}{6}[/tex]+[tex]\frac{5}{6}[/tex]=[tex]\frac{4}{6}[/tex] or [tex]\frac{2}{3}[/tex]
-2+[tex]\frac{2}{3}[/tex]=-1[tex]\frac{1}{3}[/tex]
Need help fast i have a test tomorrow and i need to get ready
Question there asking:examine (a), (b), and (c) and select the best answer.
(a) 1 / 5 of 30 (b) 1 / 4 of 20 (c) 1 / 3 of 15
Answer:
a) 6
b) 5
c) 5
Step-by-step explanation:
In this context, "of" means "times."
a) 1/5 of 30 = 1/5×30 = 30/5 = 6
b) 1/4 of 20 = 1/4×20 = 20/4 = 5
c) 1/3 of 15 = 1/3×15 = 15/3 = 5
Pg 118 #11 - 13, 15, 16
We can't get the answer if there's no problem?
9. Using a twenty sided number cube, what is the probability that you will roll an even number or
an odd prime number? The number 1 isn't an odd prime. Round to three decimals.
(1 point)
Answer:
0.85
Step-by-step explanation:
total samples cases = 20
chances that are even or odd prime are 17 chances
2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20
probability = 17/20
= 0.85
Diana made 143 treats for her visit to the nursing home. There are 37 patients and she wants each person to get the same number of treats. How many more treats will she need to make in order for each patient to receive 4 treats?
Answer:
5 more treats
Step-by-step explanation:
The total number of treats if she gives each person 4 treats is
. 37 people * 4 treats = 148 treats
Subtract 143 (number of treats she has) from 148 (total number of treats to give out)
. 148 treats - 143 treats = 5 treats
143 treats
37 patients
to find:how many treats will she need to make in order for each patient to receive 4 treats.
solution:[tex]4 \times 37[/tex]
[tex] = 148[/tex]
[tex] = 148 - 143[/tex]
[tex] = 5[/tex]
therefore, she'll have to make 5 treats more in order for each patient to receive 4 treats
answer= option D
5. Find the triangle similar to AABC at the right.
Answer:
the answer is b
Step-by-step explanation:
W/11+10=10 w/11=0. W=
Answer:
w/11+10=10w/11=0•w=10
What is the equation of this line in slope intercept form? -x- 5y = 10
A) y= -1/5x-2
B) y= -1/5x + 10
C) y= 1/5x + 10
D) y= 5x - 2
NO FILES NO LINKS PLEASE
Answer:
D 22ilsjjssiksksksksksksks
Step-by-step explanation:
212
a car travels 30m in 2 minutes whats the speed
Answer:
15
Step-by-step explanation:
speed is distance over time so its 30 devided by 2
Consider the function given by the graph. What are
these values?
fl-2) =
10) =
f(4) =
Answer:
f(-2) = 2
f(0) = 4
f(4) = -1
Step-by-step explanation:
Given the graph of a piecewise function:
[tex]\displaystyle\mathsf{f(x) = \left \{ {{x\:+\:4\quad if\:\:x\leq \:0} \atop {-\frac{1}{2}x\:+\:1\quad if\:\:x\: >\:0}} \right.}\\[/tex]
Side note:
I used the method of finding the linear equations in slope-intercept form to establish the piecewise function. First, I solved for the slope by choosing two points in each defined interval. Then, I plugged in the y-intercepts of each interval, for f(x) = x + 4: the y-intercept is (0, 4) where b = 4; for f(x) = -½x + 1, the y-intercept is (0, 1) where b = 1.
Explanation:There are two methods for determining the range values of the given domain values.
Method 1: The first method is using the graph to find the corresponding range values of the given domain {-2, 0, 4}.
Method 2: Alternatively, we could use the rules provided by the piecewise function in evaluating the following domain values. This post will use the second method (using the piecewise function) to evaluate the input values.
Regardless of the method used, the results will remain the same.
f(-2)Since the input value is x = -2, then we must use the function, f(x) = x + 4:
f(x) = x + 4
f(-2) = -2 + 4
f(-2) = 2
Therefore, the range value given the domain, x = -2 is 2, or simply: f(-2) = 2.
f(0)
Given the input value is x = 0, then we must also use the function, f(x) = x + 4:
f(x) = x + 4
f(0) = 0 + 4
f(0) = 4
Therefore, the range value given the domain, x = 0 is 4, or f(0) = 4.
f(4)
Since the input value is x = 4, then we must use the function, f(x) = -½x + 1:
f(x) = -½x + 1
f(4) = -½(4) + 1
f(4) = -2 + 1
f(4) = -1
Therefore, the range value given the domain, x = 4 is -1, or f(4) = -1.
Part A
In "Primary Lessons" from Silent Dancing: A Partial Remembrance of a Puerto Rican Childhood, what can the reader infer about how the narrator will ultimately feel about going to school?
She will misbehave there constantly to punish her mother for sending her.
She will become used to it, knowing everyone must go.
She will become an academic herself as she begins a lifelong quest for learning.
She will remain upset and fight her mother every single day.
Question 2
Part B
Which sentence in the text best supports the answer in Part A?
"It was my final argument, and it failed miserably because I was shouting my defiance in the language I claimed not to speak."
"How could she send me to school to learn Spanish when we would be returning to Paterson in just a few months?"
"I guess most children can intuit their loss of childhood’s freedom on that first day of school."
"The sight of my cousins in similar straits comforted me."
Answer:
a) she will become used to it, knowing everyone must go.
b) i guess most children can intuit their loss of childhood's freedom on that first day of school.
Explanation: i took the quiz
Q.10). ABC is a triangle right angled at C. A line through mid point M of hypotenuse AB and parallel to BC intersects AC at D.
Show that:
(I) D is the mid point of AC.
(ii) MD ⏊ AC.
(iii) CM = MA = 1/2 AB
Answer:
In attachment I have answered this problem.↑↑
Hope this helps.
If you have any doubt, then you can ask me in the comments.
Solve the system of linear equations by elimination.
3x−30=y
7y−6=3x
Solve the system of linear equations by elimination.
3x−30=y
7y−6=3x
can we represent any number on number line
Answer:
Rational numbers can be depicted on the number line. The centre of the number line is called Origin (O). Positive rational numbers are illustrated on the right side of zero (called origin), and negative on left side of origin. The representation of rational numbers on the number line depends on the type of fraction.
Step-by-step explanation:
The numbers on the number line increase as one moves from left to right and decrease on moving from right to left. Here, fractions and decimals have been represented on the number line. A number line can also be used to represent both positive and negative integers as well.
60 divided by the ratio of 7:3
Please help help and thank you
Answer:
The first option you have selected should be correct. if any doubt comment.
6 friends paid for a parking ticket each. Each ticket had a surcharge extra of $11 per ticket. The total they paid for their parking was $186. What was the price of each ticket without the surcharge?
Answer:
$20
Step-by-step explanation:
Money paid with surcharge by 6 friends = $ 186
Money paid with surcharge by a friend = 186 ÷ 6 = $ 31
Money paid by each friend without surcharge = 31 - 11 = $ 20
question:To make a certain shade of paint, Anya mixed 2/3 cups of white paint with 2 2/3 cups of blue paint
How many cups of blue paint should she mix with 3 cups of white paint to make the same shade?
Step-by-step explanation:
2/3 cups white paint mix with 2 2/3 cups = 8/3 cups blue paint.
so, 2/3 / 8/3 = 2×3 / 3×8 = 6/24 = 1/4.
therefore, the mix ratio white/blue paint is 1/4 (1 part white, 4 parts blue).
so, for 3 cups of white paint we need 3×4 = 12 cups of blue paint.
I really really really need help with this please I’ll give brainlist
Roy works in the shipping department of a toy factory that makes radio-controlled helicopters. Small helicopters weigh 1 kilogram each, and are shipped in a container that weighs 6 kilograms. Large ones, on the other hand, weigh 2 kilograms apiece, and are shipped in a container that weighs 5 kilograms. If these boxes can hold a certain number of helicopters each, all of the packed containers will have the same shipping weight. How many helicopters would fit in either container? What would the total weight be
for the small one there would be six small helicopters and two big ones
and the total weight would be 11 for the two containers like one container of large helicopters and one container of small helicopters
if it's wrong i'm very sorry i'm bad at word problems
simplify this addition x+(-x)+r
You have already saved $75 dollars for a new TV. You are
week from now on. Write an equation to model the amount of your savings.
If the TV costs $250, how many weeks will you need to save?
find the the equations of the circle passing through (1, 4) and having the diameters of 3x-4y=1 and 2x+y=8?
Answer:
In order to write the equation of a circle, we need two things their centre as well as the radius. so….diameter always intersect each other at the centre of the circle, hence after solving the equation of diameter, we get the intersecting point(x, y)=(3,2). now, we have already given one point…and as per the question circle passing through that point itself. so by applying distance formula, we can obtain the value of radius. thus we get radius 2√2. now we have required things to get the equation of a circle. we know the standard equation of circle having centre =(x1,y1) and radius = r is (x-x1)²+(y-y1)²=r² hence we can find the equation of circle by putting the coordinate (x1,y1)=(3,2) and radius =2√2 in the above mentioned standard equation.
Step-by-step explanation:
:3
What is the quotient of 1.155 x 10^5 and 1.65 x 102 expressed in scientific
notation?
Answer: 7.00x10^2
Step-by-step explanation:
Are you asking for the quotient of (1.155 x 10^5)/(1.65 x 10^2)?
If so, divide (1.155/1.65) = 0.7000.
Then subtract 2 (the bottom exponent from [tex]10^{2}[/tex]) from the top exponent: [tex]10^{5}[/tex] becomes [tex]10^{3}[/tex].
Combine the two: 0.7000x10^3
Move the decimal point to the right by one: 7.00x10^2 (to 3 sig figs).
7 x 10² is the quotient of 1.155 x 10⁵ and 1.65 x 10² expressed in scientific
notation.
To find the quotient of these two numbers in scientific notation, you divide the two significant figures and then subtract the exponents of 10. The calculation would be as follows:
(1.155 x 10⁵) / (1.65 x 10²)
Dividing the significant figures:
1.155 / 1.65
= 0.7
Subtracting the exponents:
5 - 2 = 3
So, the quotient in scientific notation is approximately:
0.7 x 10³
Which can also be written as:
7 x 10²
Hence, the quotient of 1.155 x 10⁵ and 1.65 x 10² expressed in scientific
notation is 7 x 10².
To learn more on Number system click:
https://brainly.com/question/1763119
#SPJ3
Matilda and Nancy are miles apart, bicycling toward each other on the same road. Matilda rides miles per hour and Nancy rides at miles per hour. In how many hours will they meet
Answer:
it will take 3 hours For them to cover 60 miles and meet
Step-by-step explanation:
In pic
(Hope this helps can I pls have brainlist (crown)☺️)