Elisa's distance from home (in miles) equals her walking speed (2 mph) multiplied by time spent walking (t hours).
To model Elisa's distance from home based on the time spent walking, we can use the formula for distance, which is:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\\[/tex]
Given that Elisa walks at a steady pace of 2 miles per hour, her rate (or speed) is 2 miles per hour. Let's denote this rate as [tex]\( r = 2 \)[/tex] mph.
The time Elisa spends walking can vary, so let's denote it as [tex]\( t \)[/tex] (in hours).
Now, to find Elisa's distance from home, we'll substitute the values into the formula:
[tex]\[ \text{Distance} = r \times t \]\[ \text{Distance} = 2 \times t \][/tex]
Since Elisa's distance from home is what we're interested in, this equation models her distance from home based on the time spent walking. It shows that her distance from home increases linearly with time as she walks at a steady pace.
If s(x) = x-7 and f(x) = 4x? – X+3, which expression is equivalent to (tos)(x)?
04(x-7)2 – X-7 + 3
0 4(x-7)2 – (x-7) + 3
(4x2 - x + 3)-7
0 (4x2 – x+3)(x-7)
Answer:
4(x-7)^2-(x-7)+3 (Assuming t is f)
Step-by-step explanation:
Let s(x)=x-7 and t(x)=4x^2-x+3 .
(t o s)(x)=t(s(x))=t(x-7)
Before I continue this means replace the orginal x in t with x-7.
This will then give you
4(x-7)^2-(x-7)+3
Lightning travels much faster than thunder so lightning is seen before thunder is heard. Using inductive reasoning and graph if you count 45 s between the lightning and thunder how far away is the storm?
Answer:
9 seconds.
Step-by-step explanation:
On your graph, use a ruler and your eye to get the best fitting line.
Then find the time in seconds (45) which is between 40 and 50 on the x axis.
Go across to the y axis. You will find it is about 9 seconds.
Based on the information depicted by the graph, the distance of the storm 45 seconds between Lightning and Thunder will be 9 miles
From the graph, we can create a proportional relationship thus :
Distance from storm = Seconds between Thunder
4 miles = 20 seconds
Let the miles traveled by Storm between 45 seconds = s
Hence, we have ;
4 miles = 20 seconds
s miles = 45 seconds
Cross multiply :
20s = 45 × 4
20s = 180
Divide both sides by 20
s = 180 / 20
s = 9 miles
Therefore, the storm will be 9 miles away.
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In the diagram below, what is the length of ST?
Check the picture below.
If sides SX=5,SY=10,XU=4,YT=x then the length of ST=18.
What is triangle?A triangle is a two dimensional figure having three sides, three angles, three vertex. Th sum of all the angles is equal to 180°.
How to find length?We have been given SX=5, XU=4,SY=10 and we are required to find the length of ST. We can write the sides as under:
SX/SU=SY/T
SX=5,SU=5+4=9,SY=10,ST=10+x
5/9=10/(10+x)
Solving this for the value of x.
5(10+x)=10*9
50+5x=90
5x=90-50
x=40/5
x=8
We know that ST=10+x.
We have to put the value of x in ST.
ST=10+8
=18
Hence if sides are SX=5,SY=10,XU=4,YT=x then the length of ST=18.
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For O D, find mCBE.
A. 311.1°
B. 311.20
C.352 29
D. 332.19
Check the picture below.
Answer:
i think its d
Step-by-step explanation:
A 5inch x 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame?
4x+12
8x+24
2x^2+24
4x^2+24x+35
Answer:
8x + 24
Step-by-step explanation:
Given photograph length L = 7" and width W = 5"
Also that the frame is 2x" longer and 2x" wider
hence,
new length = ( 7 + 2x) inches
new width= ( 5 + 2x) inches
Hence perimeter of frame,
= 2 x ( new length + new width)
= 2 [( 7 + 2x) + ( 5 + 2x)]
= 2 (4x + 12)
= 8x + 24 (Answer)
In polygon QRST, what is the name of the angle that is included between sides SR and SQ?
In the polygon QRST, the angle that is formed between sides SR and SQ is known as the angle RSQ.
Explanation:In the polygon QRST, the angle included between sides SR and SQ is named as the angle RSQ. In polygons, the included angle between two sides is the angle that both sides share. Here, sides SR and SQ share vertex S, so the included angle is at S, formed by extending from R through S to Q. Hence, we denote this angle as RSQ.
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Find the average rate of change of f(x) = 2x2 – 7x from x = 2 to x=6.
Simplify your answer as much as possible.
Answer:
-6Step-by-step explanation:
[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}\\\\f(x)=2x^2-7x\\\\\text{Put the values of x = 2 and x = 6 to the equation of the function:}\\\\f(2)=2(2^2)-7(2)=2(4)-14=8-14=-6\\f(6)=2(6^2)-7(6)=2(36)-42=72-42=-30\\\\\dfrac{f(6)-f(2)}{6-2}=\dfrac{-30-(-6)}{4}=\dfrac{-24}{4}=-6[/tex]
A line passes through the points (9, 30) and (18, 30). Which statement is true about the line?
Answer:
the line is horizontal
Step-by-step explanation:
Note the y- coordinates of the 2 points the line passes through are equal.
This indicates that the line is horizontal and parallel to the x- axis
The equation of a horizontal line is y = c
where c is the value of the y- coordinates the line passes through.
Here the y- coordinates are 30, hence
Equation of horizontal line is y = 30
Answer:
It has a slope of zero because the change in the y-values is 0.
Step-by-step explanation:
if 1 liter cost $12 how much does 0.7 liters cost
Answer:
$8.40
Step-by-step explanation:
You multiply $12 by 0.7 and get $8.40
Answer:
$8.40
Step-by-step explanation:
Since 1 Liter costs $12, you can multiply 12 by 0.7 (L) to get the answer.
Answer is 8.4, so it's $8.40
Which is the best definition of a scalene triangle?
Answer:
B A triangle in which no two sides are congruent is scalene
Step-by-step explanation:
A triangle that has 3 congruent sides is an equilateral triangle
A triangle in which no two sides are congruent ( no sides are the same) is a scalene triangle
A triangle that has at least two congruent sides is an isosceles triangle
Answer:
a triangle in which no two sides are congruent
Step-by-step explanation:
please help i'd really appreciate it.
Answer:
y = [tex]\frac{1}{4}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4x + 3 ← is in slope- intercept form
with slope m = - 4
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (8, 1 ) into the partial equation
1 = 2 + c ⇒ c = 1 - 2 = - 1
y = [tex]\frac{1}{4}[/tex] x - 1 ← equation of perpendicular line
P(A) = 0.60, P(B) = 0.20, and P(A and B) = 0.15. What is P(A or B)?
Answer:
P(A or B) = 0.65
Step-by-step explanation:
Given that P(A) = 0.60, P(B) = 0.20, and P(A and B) = 0.15
We have to find P(A or B)
Apply the formula:
P(A or B) = P(A)+P(B)- P(A and B)
Now substitute the values in the formula:
P(A or B) = 0.60 + 0.20 - 0.15
P(A or B) = 0.80 - 0.15
P(A or B) = 0.65
Thus P(A or B) = 0.65 ....
Answer:
0.65 ~apex
Step-by-step explanation:
The temperature is 50°F The temperature will decrease by 4°F each hour. Let
h be the number of hours,
When will the temperature be below 32°F?
Write an inequality for this problem,
A. 50 - 4h: 32
B. 50 - 4h32
c. 50 + 4h3 32
D. 50 + 4h+ 32
Answer:
50-4h<32
Step-by-step explanation:
If the temperature starts at 50 and the temperature is decreased by 4 per each hour, then:
1) after the first hour, the temperature is 50-4 or 46
1) after the second hour, the temperature is 46-4 or (50-4)-4 or 50-4(2).
So what I'm trying to show you that if I continue this pattern our equation for what happens h hours later is: 50-4h.
We want to know when is the temperature below 32 so less than 32.
Temperature<32
Put in our variable expression for temperature.
50-4h<32
The question is about using algebra to solve a real-life problem of temperature decrease. The correct inequality for the given problem is '50 - 4h < 32', which shows the number of hours it takes for the temperature (50 and decreasing 4 every hour) to be less than 32 degrees.
Explanation:The subject matter of this question is mathematics, specifically algebra and inequalities. The question provides that the temperature in degrees Fahrenheit is reducing by 4 each hour from a starting point of 50°F and seeks to find the number of hours (h) it takes for the temperature to decrease below 32°F.
We can represent this situation as an inequality: 50 - 4h < 32. In English, this states that the temperature (50, decreasing by 4 each hour) should be less than 32 degrees. So, to answer your question, option B with '50 - 4h < 32' is the correct inequality for this problem.
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Find the inverse of the following function f(x)= cubed root of x+12
Answer:
[tex]x^{3} -12[/tex]
Step-by-step explanation:
[tex]y=\sqrt[3]{x+12}[/tex]
Replace x with y to get
[tex]x=\sqrt[3]{y+12}[/tex]
Cube both side
[tex]x^{3}=y+12[/tex]
Subract 12 from both sides
[tex]x^3-12=y[/tex]
the area of triangle ABC is 95 square feet. What is the value of b, to the nearest foot?
A) 7 ft
B) 8 ft
C) 13 ft
D) 16 ft
Answer:
D
Step-by-step explanation:
The area (A) of a triangle is calculated using
A = 0.5 absinC
Here a = 13 and ∠C = 65°, hence
A = 0.5 × 13 × b × sin65° = 95, that is
6.5b × sin65° = 95 ( divide both sides by 6.5sin65° )
b = [tex]\frac{95}{6.5sin65}[/tex] ≈ 16 ft ( to the nearest foot )
Given the area of 95 square feet and side AC of 13 feet, the value of side b, opposite the 65° angle, is 7 feet rounded to the nearest foot. Thus, the correct option is A.
From the image, we see that triangle ABC is a right triangle with a right angle at C. We are given that the area of the triangle is 95 square feet and that the length of side AC is 13 feet. We want to find the length of side b, which is opposite the 65° angle.
To find the area of a right triangle, we use the formula:
Area = (1/2) * base * height
In this case, the base is side b and the height is side AC. We are given that the area is 95 square feet and that AC is 13 feet, so we can plug these values into the formula to solve for b:
95 = (1/2) * b * 13
b = 95 * 2 / 13
b = 7.3 feet
Since we are asked to round the answer to the nearest foot, we round 7.3 feet up to 7 feet.
Therefore, the value of b, to the nearest foot, is 7 ft.
Use the diagram to find the measure of the given angle.
Given angle: PRQ
Answer:
∠PRQ = 85°
Step-by-step explanation:
∠PRS and ∠TRQ are vertical angles and congruent, thus
4x + 15 = 3x + 35 ( subtract 3x from both sides )
x + 15 = 35 ( subtract 15 from both sides )
x = 20
Hence ∠PRS = (3 × 20) + 35 = 60 + 35 = 95°
∠PRQ and ∠PRS form a straight angle and are supplementary, hence
∠PRQ = 180° - 95° = 85°
Answer:
Angle QRP = 85
Step-by-step explanation:
Hopefully you can see QRS and TRP both equal 180 degrees, we will use this.
QRS is the same as QRP and PRS added together. Just like TRP is TRQ and QRP. We will call QRP R for simplicities sake, and we are given a formula for PRS and TRQ. PRS = 3x+35 and TRQ = 4x+15.
So now we have two equations.
180 = QRP + PRS = R + 3x + 35
180 = TRQ + QRP = 4x + 15 + R
So it's basically a system of equations.
180 = 35 + R + 3x
145 = R + 3x
R = 145 - 3x
180 = 4x + 15 + R
Replace R with what we found in the last equation
180 = 4x + 15 + 145 - 3x
180 = x +160
x = 20
Now go back to the first equation and plug 20 in for x
R = 145 - 3x
R = 145 -3(20)
R = 145 - 60
R = 85
So Angle QRP = 85
Let em know if something doesn't make sense.
Which equation is equivalent to: 11r+4=55
A.- 11r=55+4
B.- 11r=55-4
C.- -11r=55-4
D.- -11r=55+4
The equation 11r + 4 = 55 is equivalent to the equation 11r = 55 – 4. Then the correct option is B.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The equation is given below.
11r + 4 = 55
Then the equation can be written as
11r = 55 – 4
Then the correct option is B.
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I need help with this problem please ! Evaluate 3/7r + 5/8s when r=14 and s=8.
Answer:
11
Step-by-step explanation:
It is given that:
r = 14 & s = 8
Plug in the corresponding numbers to the corresponding variables:
(3/7)(14) + (5/8)(8)
Solve. Remember to simplify. Do multiplication & division first, then add:
(3/7)(14) + (5/8)(8)
(3 * 14)/7 + (5 * 8)/8
(3 * 2) + 5
(6) + 5
11
11 is your answer.
~
14 points!!
Is this shape a polygon?
Answer:
TRUEStep-by-step explanation:
A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit.
What is the value of x?
2
3
6
7
Answer:
2
Step-by-step explanation:
So we are going to do
(sum of parts of the secant)(part on outside)=(sum of parts of the secant)(part on outside) .
This is what you get from doing that:
(1+x+4)(x+4)=(11+x+1)(x+1)
Simplifying:
(x+5)(x+4)=(x+12)(x+1)
We could see which value of x makes both side the same.
Choice 1: Plug in 2 for x:
(2+5)(2+4)=(2+12)(2+1)
(7 )(6 )=( 14 )(3)
42 = 42
This equation is true.
Choice 2: Plug in 3 for x:
(3+5)(3+4)=(3+12)(3+1)
( 8)( 7)=( 15)( 4)
56 = 60
This equation is not true.
Choice 3: Plug in 6 for x:
(6+5)(6+4)=(6+12)(6+1)
( 11 )( 10 )=( 18 )(7 )
110 = 126
This equation is not true.
Choice 4: Plug in 7 for x:
(7+5)(7+4)=(7+12)(7+1)
(12 )( 11 )=( 19 )(8)
132 =152
This equation is not true.
Answer:
The answer is A or "2"
Step-by-step explanation:
if 8 markers cost $20 what is the cost of 12 markers
Answer:
$30
Step-by-step explanation:
Find the cost per marker.
Given: 8 markers = $20
Divide 8 from both sides.
Let x = amount of markers.
(8x)/8 = (20)/8
x = 2.5
Each marker costs $2.50
Now, multiply 12 with $2.50
2.50 x 12 = 30
$30 is the cost of 12 markers.
~
What is the solution to this equation?
x- 12 = 9
Answer:
x = 21
Step-by-step explanation:
x- 12 = 9
Add 12 to each side
x- 12+12 = 9+12
x = 21
Answer:
[tex]\huge \boxed{x=21}[/tex]
Step-by-step explanation:
[tex]\Huge\textnormal{Add 12 from both sides of the equation.}[/tex]
[tex]\displaystyle x-12+12=9+12[/tex]
[tex]\Huge \textnormal{Simplify and solve to find the answer.}[/tex]
[tex]\displaystyle 9+12=21[/tex]
[tex]\huge \boxed{x=21}[/tex], which is our answer.
If A = (7,9) and B = (3, 12), what is the length of AB?
A. 4 units
B. 5 units
c. 7 units
D. 6 units
Answer:
B. 5 units
Step-by-step explanation:
[tex]\tt |AB|=\sqrt{(3-7)^2+(12-9)^2}=\sqrt{16+9}=\sqrt{25}=5 \ \ units[/tex]
The length of AB is 5 units.
What is length?Length is defined as the measurement or extent of something from end to end.
In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects.
Given that there are two points A = (7,9) and B = (3, 12),
So, we need to find the distance between them,
We know that the distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by,
D = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
D = [tex]\sqrt{(3-7)^2 + (9-12)^2}[/tex]
D = [tex]\sqrt{4^2+3^2}[/tex]
D = 5
Hence the length of AB is 5 units.
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graph 10x +20y >/= -9
Answer:
(see attached)
Step-by-step explanation:
Rearrange the equation in the form y (≥ or ≤) mx + c , so that you get:
y ≥ (-1/2)x - (9/20)
Graph this equation.
Test a random point on either side of the line to see which side is valid (and shade)
we try the origin (0,0)
This makes the equation :
(0) ≥ (-1/2)(0) - (9/20)
0 ≥ - (9/20) (this inequality is valid, so that means the point we picked (0,0) falls on the valid side. Shade that side. (in this case the region above the line)
Find the standard equation and graph of a parabola that matches the given set of characteristics. vertex (0, 0) focus (-2, 0)
The standard equation of a parabola with vertex (0, 0) and focus (-2, 0) is y^2 = -8x. It opens to the left with the directrix x = 2.
To find the standard equation of a parabola with vertex (0, 0) and focus (-2, 0), we can use the definition of a parabola as the set of all points equidistant from a point (the focus) and a line (the directrix).
Since the focus is at (-2, 0), the directrix is a vertical line equidistant from the vertex on the opposite side of the focus, which is x = 2. The distance between the vertex and the focus (or the vertex and the directrix) is 2 units, so q = 2. This means that the parabola opens to the left.
The standard equation for a parabola that opens horizontally is of the form (y - k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus. Here, p = -2 because the parabola opens to the left.
Therefore, the standard equation for the given parabola is y^2 = -4(2)x or y^2 = -8x.
The graph of which equation has the same slope as the graph of y = 4x + 2
A. y = -2x + 3
B. y = 2x - 3
C. y = -4x + 2
D. y = 4x - 2
Please include a detailed explanation thank you
Answer:
D.
Step-by-step explanation:
The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.
The slope of y=4x+2 is 4.
Let's look at the choices:
A) The slope of y=-2x+3 is -2.
B) The slope of y=2x-3 is 2.
C) The slope of y=-4x+2 is -4.
D) The slope of y=4x-2 is 4.
So we are looking for a line that has the same slope as the given line which is 4.
The answer is D.
Answer:
D.
Y = mx + b is the equation for a straight line. "B" is called the y intercept. "M" is the value of the slope of the line. "X" is the value where the line intercepts the x axis.
so the reason the awnser is D is because the M=4 in both equations, meaning that they have the same slope
Someone please help me with this question. I would greatly appreciate it. Please and thank you.
[tex]\dfrac{15(15-1)}{2}=\dfrac{15\cdot14}{2}=15\cdot7=105[/tex]
Can somebody help thanks if you do
Answer:
It is A i believe.
Step-by-step explanation:
Because, 15/100 = 0.15 and y is your regular price so;
y - 0.15
Sorry had to rewrite what i did, but i hope my answer has helped you.
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
Answer:
All real numbers
Step-by-step explanation:
we have
f(x) = 3x +9
The linear function has a range of all real numbers -------> (-∞, ∞)
f(x) can take any real value.
Please see attached image below, for more information
Answer:
I think its B because K is = to Y
So if K is 9 then the asymptote would be 9
Limiting the Y to the to be only greater than 9
Step-by-step explanation:
in a gymnastics competition an athletes final score is calculated by taking 75% of the average technical score and adding 25% of the artistic score all scores are out of 10 and one gymnast has a 7.6 average technical score what artistic score does the gymnast need to have a final score of at least 8.0
Answer:
x ≥ 9.2
Step-by-step explanation:
If in a gymnastics competition an athletes final score is calculated by taking 75% of the average technical score and adding 25% of the artistic score all scores are out of 10 and one gymnast has a 7.6 average technical score, the gymnast needs x ≥ 9.2 to have a final score of at least 8.0.
7.6 x 75 / 100 = 5.7
Final answer:
The gymnast requires an artistic score of at least 9.2 to achieve a final score of at least 8.0, calculated by taking 75% of their average technical score and adding 25% of their artistic score.
Explanation:
To find out what artistic score the gymnast needs to achieve a final score of at least 8.0, we use the given information that the final score is composed of 75% of the average technical score plus 25% of the artistic score. Let's represent the artistic score as A.
First, calculate 75% of the average technical score:
0.75 × 7.6 = 5.7
Now, set up the equation using the required final score (8.0) and the known technical score (5.7):
5.7 + 0.25A ≥ 8.0
To find the minimum artistic score (A), we subtract 5.7 from both sides of the equation:
0.25A ≥ 8.0 - 5.7
0.25A ≥ 2.3
Finally, divide by 0.25 to solve for A:
A ≥ ÷ 0.25
A ≥ 9.2
So, the gymnast would need an artistic score of at least 9.2 to achieve a final score of at least 8.0.