Answer:
The correct answer is option 2: 32 cm
Step-by-step explanation:
Let l be the length of the picture frame and w be the width
Then according to given statements, the system of equations will be
[tex]2l+2w = 100\ \ \ Eqn\ 1\\w = 2l-4\ \ \ Eqn\ 2[/tex]
Putting w = 2l-4 in equation 1
[tex]2l+2(2l-4) = 100\\2l+4l-8=100\\6l-8 = 100\\6l = 100+8\\6l=108\\\frac{6l}{6}=\frac{108}{6}\\l = 18[/tex]
Putting the value of l in equation 2
[tex]w = 2(18)-4\\w = 36-4\\w = 32[/tex]
The width is 32 cm
Hence,
The correct answer is option 2: 32 cm
In the figure below, APQR is a reflection of ATSA.
Two students describe the given triangles as shown:
Student I: Because reflections preserve side lengths, OR a SR, PO TS, and PR TR.SO APORATSR by SSS.
Student II: Because reflections preserve both side lengths and angle measures, ZROP ZRST, OR SR. and PO = TS. SO APOA - ATSR by SAS.
Who has proven APOR - ATSR correctly?
only studenti
only student II
o
both student I and student II
o
neither student I nor student II
Answer:
both student one and student two
Step-by-step explanation:
With the properties of congruent triangle we conclude that the statement of both student I and student II are correct.
Congruent triangle-If the sides of two triangle measure same lengths and the angle have same measures then the two triangle are said to be congruent.
Given-
Statement of student 1-Because reflections preserve side lengths,
[tex]QR \cong SR[/tex],
[tex]PQ \cong TS[/tex],
[tex]PR \cong TR.[/tex] so,
[tex]\bigtriangleup PQR \cong \bigtriangleup TSR[/tex]
In all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangle are said to be congruent by the side side side (SSS) rule. Hence, the above statement is correct.
Statement of student 2- Because reflections preserve both side lengths and angle measures,
[tex]\angle RQP \cong \angle RST[/tex]
[tex]QR \cong SR[/tex]
[tex]PQ \cong TS[/tex]
[tex]\bigtriangleup PQR \cong \bigtriangleup TSR[/tex]
In any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangle are said to be congruent by the side angle side (SAS) rule. Hence the above statement is correct.
Hence, with the properties of congruent triangle we conclude that the statement of both student I and student II are correct.
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In the news you hear tuition was expected to increase from $1200 to $2350 over the next 10 years. This represents a ___% increase from current tuition. Round answers to two decimal places.
Answer:
93.83%
Step-by-step explanation:
2350 - 1200 = 1150
1150/1200 * 100 = 95.83%
Find the slope of the line in the given graph.
Answer:
option A, 3/4
Step-by-step explanation:
slope / gradient formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
use the 2 coordinates from the graph
i) (-2,3)
x1 = -2
y1 = 3
ii) (2,6)
x2 = 2
y2 = 6
[tex] \frac{y 2 - y1}{x2 - x1} [/tex]
[tex] \frac{6 - 3}{2 - ( - 2)} [/tex]
[tex] \frac{3}{2 + 2} [/tex]
[tex] \frac{3}{4} [/tex]
Bea's catering charges $3 per person and a $60 clean-up fee to cater banquets. Write an equation to find the number of students (n) that could attend the French clubs banquet if they had a budgeted $200 for catering
Answer:
The required equation will be:
200 = 3n + 60Step-by-step explanation:
We know the slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where 'm' is the slope or rate of change and 'b' is the y-intercept of the equation
Let 'n' represents the number of students (n).Let 'c' represents the cost budget.Given that Bea's catering charges $3 per person.
Thus, the slope or rate of change = m = 3 dollars per personGiven that the clean-up fee to cater banquets = $60
In other words, $60 is the initial condition or y-intercept.
Thus, the y-intercept b = 60Given that the cost budget = c = $200
Thus, the equation becomes
c = mn+b
substituting c = 200, m = rate of cgange = 3, b = 60
200 = 3n + 60 ∵ comparing with y = mx+b
Thus, the required equation will be:
200 = 3n + 60The equation that determines the no of students should be 200 = 3n + 60
Equation need to be used:Here we assume n be the number of students
And, c be the the cost budget.
So, we know the equation should be formed by applying the following expression
c = mn+b
Here c = 200, m = r = 3, b = 60
Therefore, the equation is 200 = 3n + 60
Hence, The equation that determines the no of students should be 200 = 3n + 60
Learn more about an equation here; https://brainly.com/question/18510004
help asaap dont use me for points please
Answer:
-1.5
Step-by-step explanation:
You were on the free points page
The inequality x ≥ -3 is satisfied by point (0, -2). True False
please explain!!
Answer:
true
Step-by-step explanation:
x [tex]\geq[/tex] -3, when graphed, is a vertical line which crosses the x-axis at -3
The solution area is then shaded either to the left of that line or to the right
Look at the point (0, -2); the x-coordinate is zero, which is greater than -3
Therefore, if graphing, you would shade the area to the right of the line and every point contained in this area is a solution to x [tex]\geq[/tex] -3
25 yd. 4 in. Divided by 8
Answer:
113 inches or 3.13889 yards
can u pls help me with this question
2. Which of the following is the correct value of (0.22) - (0.4)? Show your reasoning. c. 0.088 d. 0.0088 w
Answer:
C
Step-by-step explanation:
there would have to be one more zero between 0 and 8 for both of them
2x squared times 6 =
A:10x squared
B:8x squared
C:12x squared
Answer:
C: 12x squared
Step-by-step explanation:
the equation would look like [tex]2x^{2}[/tex] · [tex]6[/tex] or [tex]6(2x^{2})[/tex]
you only multiply the coefficients, leave the exponent alone for this one
so 2 times 6 would be 12 and the [tex]x^{2}[/tex] remains the same giving you [tex]12x^{2}[/tex]
put the numbers in order from least to greatest.
5 * 10^6
4000000
5 * 10^5
0.6 * 10^7
75 * 10^5
66 and 2/3% as a fraction and decimal
Answer:
Answer are right here
Step-by-step explanation:
66 as a fraction is 33/50 and as a decimal, it would be 0.66
2/3 as a fraction would be 2/3 and as decimal it would be 0.66666667
Two airplanes leave Columbus at the same time and fly in opposite directions. One plane travels 70 miles per hour faster than the other plane. After 4 hours they are 3800 miles apart. What is the rate of each plane?
Hint: Distance equals rate times time. (d = r t)
Answer:
it goes 4233 miles
Step-by-step explanation:
sorry if am wrong luv!
What is the domain of the function graphed below? Hurry pls I’m being timed
There were 350 apples on the tree in March. By September there were 420 apples on the tree. What was the percentage of change of apples on the tree? Round your answer to the nearest tenth.
Answer:
them some fast growing apples
Step-by-step explanation:
realy
1. An iPhone is on sale for $780. It originally cost $1000.00. What is the percent of change?
Answer:
your answer is going to be 220.
What is the value of p in the proportion below?
StartFraction 20 over 6 EndFraction = StartFraction p over 12 EndFraction
Answer:
20/6=p/12
cross multiply
20*12=6p
240=6p
divide both sides by 6
p=40
Answer:
C - 40
Step-by-step explanation:
Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.
a. y=
b. y=
Answer:
(a). y = - 4x + 19 ; (b). y = [tex]\frac{1}{4}[/tex] x + 2
Step-by-step explanation:
Slope "m" of given line is
m = - 4
Slope of parallel line is ( - 4) and perpendicular line is [tex]\frac{1}{4}[/tex]
P(4, 3)
y - [tex]y_{P}[/tex] = m( x - [tex]x_{P}[/tex] )
(a). y - 3 = - 4 (x - 4)
y = - 4x + 19
(b). y - 3 = [tex]\frac{1}{4}[/tex] ( x - 4 )
y = [tex]\frac{1}{4}[/tex] x + 2
Drew wants to buy sports equipment that costs $140. The sales tax is 8%. What is the total cost of the equipment with the tax?
Answer: $151.20
Step-by-step explanation: 8 percent of 140. Add this number to 140.
[tex]\frac{x}{140} = \frac{8}{100}[/tex]
100x=112
x=11.2
1
For every 2 teaspoons of white vinegar in a jar of homemade glue, there are 5 tablespoons of
cornstarch. How many teaspoons of white vinegar are there for every tablespoon of cornstarch?
A. 1
5
В.
C 1
D. 5
The number of teaspoons of white vinegar are there for every tablespoon of cornstarch is 0.4.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, for every 2 teaspoons of white vinegar in a jar of homemade glue, there are 5 tablespoons of cornstarch.
The number of teaspoons of white vinegar are there for every tablespoon of cornstarch = 2/5
= 0.4
Therefore, the number of teaspoons of white vinegar are there for every tablespoon of cornstarch is 0.4.
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Solve the proportion for X.
0.666/5=х/15 x3
x= 2
x=3
x= 5
x = 10
Answer:
x = 2
Step-by-step explanation:
0.666/5 = (2/3)/5 = 2/15
Therefore, x = 2.
Gabriel earned $238.40 at His job when he word for 16 hours what was his hourly wage in dollars per hour?
Answer:
$14.9
Step-by-step explanation:
238.40 / 16 = $14.9 hourly
Answer:
Gabriel earns $14.90 per hour
Step-by-step explanation:
238.4 divided by 16 gives you 14.9
Hope this helps
please solve needed asap
Answer:
x = 56°
Step-by-step explanation:
Base angles of an isosceles triangle are equal.
This:
The angle of the triangle to our right, which is the third unequal angle = 180 - 2(31)
= 180 - 62
= 118°
The base angle of the triangle to our left = 180 - 118 (angles on a straight line)
= 62°
x = 180 - 2(62)
x = 180 - 124
x = 56°
Help
w(a)=a-1; find w(0)
Answer:
Step-by-step explanation:
w(0) = 0-1
w(0) = 0-1
w(0) = -1
Since w(0), this basically means that a = 0.
So, plug 0 into anywhere a is.
The value of the function w(a) = a - 1 at a = 0 will be negative 1.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
w(a) = a - 1
The value of the function at a = 0 will be
w(0) = 0 - 1
w(0) = - 1
The value of the function w(a) = a - 1 at a = 0 will be negative 1.
More about the value of expression link is given below.
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Need help with this one will mark brainliest
Answer:
circle 3
Step-by-step explanation:
If the imput is -8 then what is the output of y=3x+7
Answer:
output is -17
Step-by-step explanation:
x is input, y is output. You do y = -24 + 7
then y = -17
A yoga instructor offers two options for classes. Option 1: $40 joining fee and $20 per class Option 2$0 joining fee and $25 per class After how many classes will both options have the same cost?
Answer:
The indifference point is 8 classes.
Step-by-step explanation:
Giving the following information:
Option 1:
$40 joining fee and $20 per class
Option 2:
$0 joining fee and $25 per class
First, we establish the total cost formulas:
Option 1= 40 + 20x
Option 2= 0 + 25x
x= number of classes
Now, we equal both formulas and isolate x:
40 + 20x = 25x
40=5x
8=x
The indifference point is 8 classes.
Prove:
Option 1= 40 + 20*8= $200
Option 2= 0 + 25*8= $200
I just want ppl to check, extra points too!
Answer:
thats correct
Step-by-step explanation:
i had that on my test and i ot it right
What is the least common multiple of the two denominators 6/8, 4/32
Answer:
32
Step-by-step explanation:
The highest recorded temperature in the world is 120°F. The lowest recorded temperature in the world is -129.6°F. What is the difference in the two temperatures?
Group of answer choices
9.6 degrees
29.6 degrees
229.6 degrees
249.6