The most appropriate choice for linear equation will be given by -
Length of the rectangle is 80 inches
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Let the length of the pegboard be l inches
Width of the pegboard = [tex]\frac{1}{2}l - 8[/tex]
Perimeter =
[tex]2(l + \frac{1}{2}l - 8 )\\2(\frac{3l}{2} - 8)\\[/tex]
[tex](3l - 16)[/tex] inches
But the problem,
[tex]3l - 16 = 224\\3l = 224 +16\\3l = 240\\l = \frac{240}{3}\\[/tex]
[tex]l = 80[/tex] inches
The length of the rectangle is 80 inches.
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One of your friends is working on their math homework. They decide to translate the phrase "subtract 3 from 5" like this:
3-5
Which statements below give a reason why your friend's expression is incorrect?
Select ALL that apply.
A.The expression is written with the wrong operation.
B.in subtraction, order matters and the expression in the incorrect order.
C.the expression should be written as an addition expression with the 5 being added to the 3
D. The expression was written in the order from the phrase which is incorrect
Answer:
B
Step-by-step explanation:
When you are taking 3 away from 5 it would be 5-3, when you are taking 5 away from 3 it would be 3-5, but in this case it is not so the answer would be B as the order is incorrect.
Is the function linear? (actual answers please, i know someone could easily say yes or no)
Answer:
Obviously yes...
Step-by-step explanation:
Because there is not a single curve, hence the fn is linear.
Had it been if there are some curves, it may result in having more than one zeroes...
Cuz there's no curve it has only one zero, which made the fn linear..
Thanks.
Rewrite in simplest terms: −4(8f+g)+9g−5(−2g+6f)
1 - 3x = 3x + 1
what does x equal?
Answer:
the value of x is -6
Step-by-step explanation:
1-3x= 3x+1
-3x -3x =1-1
-6x=0
-x=6
x= -6
Why can it help to line up the decimal
points before comparing and ordering
numbers with decimals?
Answer: Why it makes sense: When we compare or order decimals we need to compare place values just like we do with whole numbers. When the edges are “jagged” it makes it harder to compare each decimal place. Adding a zero in an empty place value makes it easier to compare the numbers.
Step-by-step explanation:
Answer:
you need to line them up to tell what place value each are in. if u don't the you won't known exactly what the product is equivalent to.
1. how do we change a similar fraction?
2. how do we add the similar fraction?
Answer:
You add similar fraction by adding the numerators together but since the denominators are the same u keep them as they are
1. Similar fractions are those which have the same denominator. To change dissimilar fraction to similar fractions, you express them as a equivalent with a common denominator. For example 2/12, 3/12
2. To add similar fraction one should ensure that both the numerator are same and then add the numerator and put that on the denominator. If there is need to simply the fraction then you should first simplify the fraction.
For example:- 1/4+4/4= 5/4
Here as we see that bot number denominator are same so it's addition is done easily
The graph shows the velocity f(t) of a runner during a certain time interval:
Graph of line segment going through ordered pairs 0, 4 and 4, 8. Graph of another line segment going through ordered pairs 4, 8 and 8, 0. Label on the x axis is time in seconds, and label on the y axis is velocity in meters per second.
Which of the following describes the intercepts on the graph?
The initial velocity of the runner was 4 m/s, and the runner stopped after 8 seconds.
The initial velocity of the runner was 8 m/s, and the runner stopped after 4 seconds.
The initial acceleration of the runner was 4 m/s2, and the runner stopped after 8 seconds.
The initial acceleration of the runner was 8 m/s2, and the runner stopped after 4 second
The description of the intercepts of the Graph segments passing through the points (0, 4), (4, 8), (4, 8) and (8, 0) is given by the option;
The initial velocity of the runner was 4 m/s and the runner stopped after 8 secondsWhat is a velocity time graph?A velocity time graph is a graph that shows how the velocity of an object changes with time
The given information on the graph are;
The coordinates of the points on the Graph of the first line segment = (0, 4) and (4, 8)
On Graph of the second line segment, the coordinates of the points = (4, 8), (8, 0)
The label of the axis of the graph are;
X–axis label = Time in seconds (s)
Y–axis label = Velocity in m/s
Required; The option that gives the description of the intercepts of the graph
Solution; The x and y–intercept are given as follows;
At the x–intercept the y–value is 0, which gives the x–intercept of the graph as the point (8, 0)
Given that the y–value which is the value of the velocity, is 0, it means that the runner stops at the point (8, 0), or after 8 seconds
At the y–intercept, the x–value is 0. The y–intercept is therefore the point (0, 4)
The 0 in the y–intercept means that the time is 0 seconds, which is the starting or initial time, while the 4 means that the velocity is 4 m/s.
Therefore, the y–intercept (0, 4) can be described as the initial velocity of the runner is 4 m/s
The description of the intercepts on the graph are therefore;
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Answer:
The initial velocity of the runner was 4 m/s, and the runner stopped after 4 seconds and then again after 8 seconds. Option A is the correct answer
Step-by-step explanation:
The intercepts on the graph can be described as follows:- The y-intercept is the point at which the line intersects the y-axis, and it represents the initial velocity of the runner. In this case, the y-intercept is at (0, 4), which means that the initial velocity of the runner was 4 m/s.- The x-intercept is the point at which the line intersects the x-axis, and it represents the time at which the runner stopped. In this case, there are two x-intercepts: one at (4, 8) and another at (8, 0).
This means that the runner stopped twice, once after 4 seconds and again after 8 seconds.
Therefore, the correct description of the intercepts on the graph is: The initial velocity of the runner was 4 m/s, and the runner stopped after 4 seconds and then again after 8 seconds. Option A is the correct answer.
Estimate the quotient of 41 ÷ 7.94.
4
5
6
7
Select all the equations where x = -2 is a solution.
(Select all that apply.)
a. 3x - 5 = 1
b. 19 = 2(x-6)+3
c. 5 + 3x = -1
d. 2(x+5)=x+8
e. 4x = 4 + 2x
the leters c and d are correct for this equation
PLS HELP QUICK!!!
help me solve 3<2p-3≤ 12 and graph the solution
The solution to the given inequalities is 3 < p and p ≤ 7.5. That is 3 < p ≤ 7.5.
The graph of the solution is shown below.
Solving Linear InequalitiesFrom the question, we are to solve the given inequalities
The given inequalities are
3 < 2p - 3 ≤ 12
We will solve the inequalities separately
That is
3 < 2p - 3 and 2p - 3 ≤ 12
Solve 3 < 2p - 3
3 < 2p - 3
3 + 3 < 2p
6 < 2p
6/2 < p
3 < p
Solve 2p - 3 ≤ 12
2p ≤ 12 + 3
2p ≤ 15
p ≤ 15/2
p ≤ 7.5
Hence,
Joining the two solutions together, the solution is 3 < p ≤ 7.5.
The graph is shown below.
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Which diagram shows parallel lines cut by a transversal?
#2 The number of bacteria in a refrigerated food is given by N(T)=20T2-20T+120 for -2T14 Tand where T is the temperature of the food in Celsius.
(a)Explain the meaning of -2T14 in this context
(b)Determine the temperature the number of bacteria will be minimal?
(c)Find number of bacteria in a above
(d) Sketch a graph
From the given quadratic function, it is found that:
a) The interval -2 ≤ T ≤ 14 gives the range of the temperature of the food in Celsius.
b) The number of bacteria will be minimal for a temperature of 0.5 ºC.
c) The minimum number of bacteria is of 115.
d) The graph that models the situation is sketched at the end of the answer.
What does the quadratic function models in this problem?The quadratic function is given as follows:
N(T) = 20T² - 20T + 120, -2 ≤ T ≤ 14.
In which:
T is the temperature in Celsius of the food.N(T) is the number of bacteria in the food.The function has a domain of -2 ≤ T ≤ 14, meaning that these are the possible temperatures of the food.
For a concave up quadratic function, the minimum value happens when the input is of:
Tm = -b/2a.
For this problem, the coefficients of the quadratic function are as follows:
b = -20, a = 20.
Hence the temperature in which the number of bacteria will be minimal is of:
Tm = 20/40 = 0.5 ºC.
The number of bacteria with this temperature is given by the numeric value of the function when T = 0.5, that is, each instance of T in the function is replaced by 0.5, hence:
N(0.5) = 20(0.5)² - 20(0.5) + 120 = 115 bacteria.
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On the axes below, make an appropriate scale and graph exactly one cycle of the trigonometric function y=16sin 1/2 x
For the given trigonometric function y =16sin1/2 x the graph shows the amplitude of 16 , graph of exactly one cycle is with period 4π , with no vertical and phase shift.
As given in the question,
Given trigonometric function :
y = 16sin 1/2 x
Attached graph of the given trigonometric function with
Amplitude = 16
Period = 4π
Vertical shift = None
Phase shift = none
Table for the required trigonometric function values which represent appropriate scale and graph exactly one cycle of the trigonometric function
x : 0 π 2π 3π 4π
y : 0 16 0 -16 0
Therefore, graph of trigonometric function y =16sin1/2 x shows the amplitude of 16 , graph of exactly one cycle is with period 4π , with no vertical and phase shift.
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MODELING REAL LIFE You can use at most 5 gigabytes of data per month on your cell phone. Your data usage so far for the month is 1.24 gigabytes. What are the possible amounts of data you can use for the remainder of the month?
Answer:3.76 gigabytes
Step-by-step explanation:
You subtract the 5.00 by the 1.24
THIS IS EASY!!!!!!!!!!!!!!!
In ΔFGH, the measure of ∠H=90°, GF = 29, FH = 20, and HG = 21. What is the value of the sine of ∠F to the nearest hundredth?
The value of the sine of ∠F to the nearest hundredth is 0.72
Sine rule
A triangle is a figure that has 3 sides and angles. Given the following parameters;
∠H=90°
GF = 29
FH = 20
HG = 21.
Using the SOH CAH TOA identity;
sin theta = opposite/hypotenuse
sin ∠F = HG/GF
Substitute the given parameters
sin ∠F= 21/29
sin ∠F = 0.72
This gives the required value of sin ∠F to the nearest hundredth
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The three inside angles (A, B and C) of a right-angled triangle are in the ratio 7/18 / 11 The smallest angle is 35 deg Work out angles A, B and C.
A polygon with the three edges and three vertices is called a triangle. It is one of fundamental geometric shapes. The symbol for a triangle containing the vertices A, B, and C is ABC, measures of the right triangles are 35, 90 and 55.
What is a triangle?A polygon with the three edges and three vertices is called a triangle. It is one of fundamental geometric shapes. The symbol for a triangle containing the vertices A, B, and C is ABC.
In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All the triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses the triangles in Euclidean geometry, namely the Euclidean plane.
Which is the smallest angle, which is the right angle, and which is the third angle of the triangle are the three inner angles (A, B, C) of a right angled triangle.
sum of the interior angles of a triangle = 180
ratio 7:18:11
so
7+18+11 = 36
180 / 36 = 5
7 x 5 = 35
18 x 5 = 90
11 x 5 = 55
measures of the right triangles are 35, 90 and 55
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What is the best estimate of 31 3/4 X 4 1/7 = ? Help Me?!!
The best estimate of fraction is 131.445.
What is fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is [tex]\frac{1}{2}[/tex]
Given Data
31[tex]\frac{3}{4}[/tex] × 4[tex]\frac{1}{7}[/tex]
Solving mixed fractions
[tex]\frac{127}{4}[/tex] × [tex]\frac{29}{7}[/tex]
31.75 × 4.14
Multiplying
131.445
The best estimate of fraction is 131.445.
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Write the equation of the line whose slope is -6 and y intercept is (0, -2)
Answer: y = -6x-2
Step-by-step explanation:
y=mx+b
-2=(-6)(0)+b
b= -2
y=-6x - 2
Create an equivalent expression for 17^-7 • 17^5.
Answer:
Answer is in fraction.--> 1/289.
Step-by-step explanation:
[tex]17^{-7} =17^{-7+5}=17^{-2} =\frac{1}{17^{2} } = \frac{1}{289}[/tex]
Which graph represents the function f(x)=√x+4-2?
Answer:
the top right graph
Step-by-step explanation:
I assume you mean the function is
f(x) = sqrt(x + 4) - 2
because for your function as you wrote it
f(x) = sqrt(x) + 4 - 2 = sqrt(x) + 2
none of the graphs apply.
to find the correct one we look at some specific points.
like x = 0, and when the square root will be 0 (x = -4).
normally we can see the right graph latest here already, but if not, then we have to pick a few more points.
so,
for x = 0 we get
sqrt(0 + 4) - 2 = 2 - 2 = 0
that means
f(0) = 0
now, when we look at the graphs, we see we are already finished. there is only one graph that goes through (0, 0).
the top right graph.
In Exercises 7-10, determine whether the table represents a linear or nonlinear function. Explain. (See Exam
8.
7.
X
X
y
4
y 16.8
1
5
2
12.6
10
8 12
7.4
3
15
16
1.2
4
20
10.
x 5
y
-9
X
y
-1
35
7
-3
9
-1
11
3
0
1
2
20 5 -10 pls help me
Answer:
every number has a correlating value
Step-by-step explanation:
9. Describe and correct the error in performing the operation.
X 4x²(3x - 2x² + 7) = 12x³ - 8x + 28x²
Answer:
12[tex]x^{3}[/tex]-8[tex]x^{4}[/tex]+ 28[tex]x^{2}[/tex]
Step-by-step explanation:
the second term should not be -8x, it should be -8[tex]x^{4}[/tex]
The product of powers principle tells us that when we are multiplying powers with the same bases, we add the exponents. 4[tex]x^{2}[/tex](2[tex]x^{2}[/tex]) is 8 but then we add the exponents 2 + 2 = 4
Find the volume of this solid.
Answer:
128m²
Step-by-step explanation:
separate the two solids.The cube and the cuboid
find the volume of the cube i.e.5³=115m²
find the volume of the cuboid i.e 1×1×3=3m²
add the two volumes
Answer:
128m²
Explanation:
Add all volumes, 5+5+4+6+3, then times that by the volume below.
The value for x that makes the equation 4×-2+3×-7=51 true
The value of x that makes the equation true is 60/7.
The given equation is:-
4x - 2 + 3x - 7 = 51
The given equation is a linear equation in one variable.
Linear equation in one variable
A linear equation in one variable is of the form of ax + b = 0, where a and b are any two integers and x is an unknown variable having only one solution. Example : 5x + 3 = 10.
We have to find the value of x that makes the equation true.
Simplifying the given equation, we get
(4x + 3x) - (2 + 7) = 51
7x - 9 = 51
7x = 51 + 9
7x = 60
x = 60/7
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need help on this question
The coordinates of the vertex B' is (2,3)
Given,
The vertices of triangle ABC are
A = (-4,4)
B = (-2,3)
C = (-5,2)
and, reflected across the y-axis to produce the image of triangle A'B'C'
To find the coordinate of the vertex B'
Now, According to the question
For reflection across y-axis, the rule is:
(x, y) → (-x, y)
So, the image of B is:
(-2, 3) → (-(-2), 3)
(-2,3) → (2, 3)
Hence, The coordinates of the vertex B' is (2,3)
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. Calculate the circumference of a circle with a radius of 15 inches. Use 3.14 for pi.
Round answer to the nearest tenth, if necessary.
Answer: 94.2
Step-by-step explanation:
C = 2 πr
C = 2 x 3.14 x 15
C = 30 * 3.14
C = 94.2
Please answer the question in the photo
Answer: 8
Step-by-step explanation:
180 degrees in a triangle, so 180 - 92 - 48 = 40
So, the missing angle is 40, which is equal to 5t, so
40 = 5t
t = 8
can some one help i will give 100 points and brainliest can you show your work step by step?
What is the equation for the line that passes through the coordinates (-4,-12)and(16,3)
The equation of the line that passes through these coordinates is 3x-4y= 36
How to calculate slope?
If you have the coordinates of two points on a line, you can use the slope formula to determine that line's slope. m=(y2-y1)/(x2-x1), or the ratio of the change in the y values to the change in the x values, is the slope formula.
To find the equation of the line we first have to find the slope which is represented by m.
The slope or m is given by : y₂ - y₁ / x₂ - x₁
thus, m= 3-(-12)/ 16-(-4)
m= 3+12/ 16+4 = 15/20
m= 3/4
The equation of a slope is y-y₁=m (x-x₁)
y- (-12) = 3/4 (x- (-4))
y+12 = 3/4 (x+4)
On solving it further we get:
4y+48= 3x+12
3x-4y= 36
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$10,000 for 5 years at 4% interest
Simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
As given in the question,
Simple Interest:
The simple interest is an amount that is paid for loan or borrowed money over a certain period at a fixed percentage of borrowed money.
Principal amount:
Principal amount is the money that is taken as loan or borrowed.
Formula of Simple Interest:
Simple interest = Principal amount × Rate × Time
Since,
Principal amount = $10,000
Rate = 4% per year
Time = 5 years
Then,
Simple interest = 10,000 × 4 × 5
Simple interest = $ 12000
Total value after 5 years = $ 12000
Principal amount = $ 10000
Interest Earned = (Total value) - (Principal amount)
Interest Earned = $ 12000 - $ 10000
Interest Earned = $ 2000
Therefore, simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
The complete question is:
Fabian is taking out a loan in the amount of $10,000. His choices for the loan are a 5-year loan at 4% rate of interest .What is the amount of simple interest and interest earned Fabian would have to pay?
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