Answers
To determine the initial length, we have to evaluate the given equation at x=0. Evaluating the equation, we get:
[tex]y=3\cdot0+59.[/tex]Therefore, the initial length of the road was 59 miles.
Now, notice that the given equation is a linear equation in slope-intercept form y=mx+b, where b is the slope, recall that the slope of a line represents the change of y compared to the change in x, in this case, miles per day.
Therefore, the change per day in the road's length is 3 miles.
Answer:
a) 59 miles.
b) 3 miles.
Related Questions
Which equation represents the line whose slope is 6 and whose y- intercept is 2?
Steps please
Answers
y=−2x+6
Explanation:
the equation of a line in
slope-intercept form
is.
∙xy=mx+b
where m is the slope and b the y-intercept
here m=−2and b=6
⇒y=−2x+6←
is the equation
If a1=8 and an= 5an-1 + 5 then find the value of a5
Answers
a_5 =5780
1) Given the 1st term a_1 =8 and the Recursive formula for this Sequence, let's find the 5th term by plugging and finding each term. Like this:
[tex]\begin{gathered} a_n=5a_{n-1}+5 \\ a_2=5(8)\text{ +5}\Rightarrow a_2=45 \\ a_3=5(45)+5\Rightarrow a_3=230 \\ a_4=5(230)+5\Rightarrow a_4=1155 \\ a_5=5(1155)+5\Rightarrow a_5=5780 \\ (8,\text{ 45, 230, 1155, 5780)} \end{gathered}[/tex]2) Since it is a Recursive Formula we need to recur to the previous term to find the subsequent one. So
[tex]a_5=5780[/tex]help me pleaseeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
Answer:
Domain: [tex][2, \infty)[/tex], Range: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
a pirate keeps 2/3 of his coins in a treasure chest and distributes the rest equally among three crew members. if each crew member receives 25 coins, how many coins did the pirate keep
Answers
ANSWER:
150 coins
STEP-BY-STEP EXPLANATION:
We know that of the total that the pirate initially had 2/3 I keep them in a chest and the rest he distributed, the rest corresponds to 1/3 of the total.
Now, if each one received 25 coins, and 3 three members, it means that 1/3 is equivalent to 3 times 25 coins, that is, 75 coins.
Now, if 1/3 is 75 coins, 2/3 proportionally would be:
[tex]\begin{gathered} \frac{75}{\frac{1}{3}}=\frac{x}{\frac{2}{3}} \\ \text{ solving for x} \\ 225=\frac{3x}{2} \\ x=\frac{225}{3}\cdot2 \\ x=150 \end{gathered}[/tex]Which means that the pirate kept 150 coins in the chest
the quotiant of a number and 3 is 8
Answers
the quotiant of a number and 3 is 8:
[tex]\begin{gathered} \frac{x}{3}=8 \\ \text{Solve for x:} \\ \text{Multiply both sides by 3:} \\ x=8\times3 \\ x=24 \end{gathered}[/tex]nine times a number is -63:
[tex]undefined[/tex]Please help I need this for a text ASAP.
Answers
The values of x and y are 45 and 8.
What is a Linear Pair of Angles?When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.
Given:
Measures of two linear pairs of angles which are of equal measures are 2x and 11y + 2.
As the sum of linear pair of angles is 180°, and if they are of equal measures, each angle must be equal to 90°.
To determine the values of x and y we equate the given angles to 90°.
2x = 90°
⇒ x = 45
And 11y+2 = 90°
⇒ 11y = 90-2 = 88
⇒ y = 8
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2 (02.05)John bought 15 cookies and ate 3 of them. He ate% of the cookies. (Makpoints)3. (02.05)had $125 to spend at the ma. She spent
Answers
You have the following information:
- John bought 15 cookies
- John ate 3 of the 15 cookies
In order to calculate the percentage associated to the 3 cookies John ate, respect to the total cookies, you proceed as follow:
[tex]\frac{3}{15}(100)=\frac{300}{15}=20[/tex]Hence, John ate 30% of the total number of cookies.
Find the value of EF in the triangle below.H8FE4O 472O 43O8V2
Answers
From the triangle shown, we have three important informations:
- It is a right triangle, because it has a right angle, mHEF.
- Its hypotenuse has length 8, HF = 8.
- Its two legs has the same length, HE = EF.
Because it is a right triangle, we can use the Pythagora's Theorem:
[tex]HE^2+EF^2=HF^2[/tex]And we know that:
[tex]\begin{gathered} HE=EF \\ HF=8 \end{gathered}[/tex]Thus:
[tex]\begin{gathered} EF^2+EF^2=8^2 \\ 2EF^2=64 \\ EF^2=32 \\ EF=\sqrt[]{32} \\ EF=\sqrt[]{2^5} \\ EF=4\sqrt[]{2} \end{gathered}[/tex]This graph represents a linear or exponential function?A linearB exponential
Answers
As the graph is a straight line hence the it is a linear function.
Candice and Porter each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Candice has 21 signatures, and Porter has 18. Candice is collecting signatures at an average rate of 2 per day, whereas Porter is averaging 5 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?
In ______ days, Candice and Porter will each have collected ________ signatures.
Answers
In 1 day, Candice and Porter will have collected 23 signatures each, using a system of equations.
What are equations?Equations are mathematical statements that claim that two expressions are equal or equivalent.
Equality is depicted using the equation sign (=).
Candice Porter
The number of signatures collected for nomination 21 18
Average collection of signatures per day 2 5
Let the total signatures collected by Candice on day x = 21 + 2x
Let the total signatures collected by Porter on day x = 18 + 5x
The day the two candidates will have collected the same signatures is set as equality:
21 + 2x = 18 + 5x
21 - 18 = 5x - 2x
3 = 3x
x = 1
Check:
Total signatures collected by on day 1:
Candice = 21 + 2x = 21 + 2(1) = 23
Porter = 18 + 5x = 18 + 5(1) = 23
Thus, for Candice and Porter to have collected the same number of signatures, it will take them 1 day and each will have 23 signatures, using a system of equations.
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On the following table, which best reflects the values of a function g for which lim g (x) =5?
Answers
We have the following limit:
[tex]\lim_{n\to9}g(x)=5.[/tex]To determine which table best reflects function g(x) values, we analyse the limit.
0. x → 9 means that we must analyze the function g(x) in the range of values of x very near the value x = 9.
,1. lim = 5 means that for the values of x very near to x = 9, the value of the function must be a number near to 5.
1) From point 1, we can discard the second option because the table shows values of x near x = 5, not x = 9.
2) From point 2, we can discard the first and fourth options:
• the first option shows a jump up from the value y = 4.997 to y = 10.030,
,• the fourth option shows a jump down from the value y = 100.00 to y = 4.570.
3) The third option is the correct one. It has values of y near to y = 5 for values of x near to x = 9.
AnswerThird option
Answer:
Third one
Step-by-step explanation:
The third one down has g(x) values across the board that are just about '5' for any value of x, thus g(x) = 5
the others have widely varying values not close to 5
One angle of an isosceles triangle measures 42°. what measures are possible for the other two angles? choose all that apply.
Answers
The measure of second angle and third angle of the isosceles triangle will be equal to 69° each.
What is an isosceles triangle ?
An isosceles triangle is a triangle which has two equal sides and two equal angles.
It is given that the first angle of an isosceles triangle is 42°. In a triangle sum of all angles is equal to 180°.
We know that in an isosceles triangle the measure of two angles and two sides are equal.
The measure of first angle is 42°. Let's assume the measure of second angle is x this meant the measure of third angle will be x too.
∵ Sum of three angles of a triangle = 180°
∴ 42 ° + ( x + x ) = 180°
or
42 ° + ( 2x ) = 180°
2x = 180° - 42°
2x = 138°
or
x = 69°
As measure of both unknown angles is same , so second angle and third angle will have a measure of 69° each.
Therefore , the measure of second angle and third angle of the isosceles triangle will be equal to 69° each.
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Sarah used 3.5 cups of cheese in a dish that serves 10 people. What constant of proportionality relates the number of servings to cups of cheese?
Group of answer choices
0.35
0.05
0.5
0.25
Answers
B. 0.05
pls mark brainleist
Which pair of numbers has a GCF of 5? A.15 and 30 C.45 and 9 B.5 and 21 D.20 and 55
Answers
Answer:
D
Step-by-step explanation:
The GCF in answer choice A is 15.
The GCF in answer choice B is none.
The GCF in answer choice C is 9 since 45 is divisible by 9 and 9 is divisible by itself
D is correct as 55/5 = 11 and cannot be divided anymore. And 20 is divisible by 5
there were 943 tornadoes in 2013 and 897 in 2014. what% decrease was that using 2 decimal places?
Answers
decrease in tornadoes = 943-897 = 46
% decrease in tornadoes = (decrease in tornadoes) / (initial amount of tornadoes) x 100%
[tex]\begin{gathered} \frac{46}{943}\text{ }\times\text{ 100 = }\frac{460}{943}\text{ = 4.87805} \\ \approx\text{ 4.88 ( 2 decimal places )} \end{gathered}[/tex]write a two column proof
Answers
The two-column method is used to prove that AB = CD as follows;
Statement [tex]{}[/tex] Reasons
1. B is the midpoint of [tex]\overline{AC}[/tex] [tex]{}[/tex] Given
C is the midpoint of [tex]\overline{BD}[/tex] [tex]{}[/tex]
2. [tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 2. Definition of midpoint
3. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 3. Definition of midpoint to a segment
4. [tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 4. Transitive property of congruency
5. [tex]\overline{AB}[/tex] = [tex]\overline{CD}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 5. Definition of congruent segments
What are the details of the definitions, and properties used to prove that the segments [tex]\overline{AB}[/tex] = [tex]\overline{CD}[/tex]?The midpoint of a segment in geometry is the point that bisects the line into two equal parts and serves as the centroid of the line. The distance from both ends of the segment to the midpoint are the same.
The transitive property of equality states that if a variable a equals a variable b and if the variable b equals the variable c then the variable a also equals the variable c.
Mathematically; If a = b, and b = c, then a = c
Two, segments, figures, or shapes in geometry are congruent if they have the same shape and size.
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A rancher has a pen shown on the grid, where 1 unit represents 1
meter. The rancher needs a larger pen to be a dilation of the
smaller pen by a scale factor of 3.5 with the origin as the center of
dilation.
Answers
The coordinates of the vertices of the rectangle are A'(x, y) = (3.5, 3.5), B'(x, y) = (3.5, 7), C'(x, y) = (10.5, 7) and D'(x, y) = (3.5, 10.5). The graph of the new pen is shown below.
What is the representation of a pen by using a scale factor?
We find a representation of a original pen, whose vertices are shown on Cartesian plane. The new pen is the result of dilating the original one by a scale factor of 3.5 and with center at the origin. The expression that describes the transformation is:
P'(x, y) = k · P(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointk - Scale factorIf we know that A(x, y) = (1, 1), B(x, y) = (1, 2), C(x, y) = (3, 2), D(x, y) = (1, 1) and k = 3.5, then the coordinates of the resulting point are:
A'(x, y) = 3.5 · (1, 1)
A'(x, y) = (3.5, 3.5)
B'(x, y) = 3.5 · (1, 2)
B'(x, y) = (3.5, 7)
C'(x, y) = 3.5 · (3, 2)
C'(x, y) = (10.5, 7)
D'(x, y) = 3.5 · (1, 3)
D'(x, y) = (3.5, 10.5)
The graph of the resulting rectangle is shown below.
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Consider the line -9x-4y=-2.What is the slope of a line parallel to this line?What is the slope of a line perpendicular to this line?Would the perpendicular slope be -4/9 and the parallel line be 9/4?
Answers
first we solve the equation for y
[tex]\begin{gathered} -4y=-2+9x \\ \\ y=\frac{-2+9x}{-4} \\ \\ y=\frac{1}{2}-\frac{9}{4}x \end{gathered}[/tex]on this line the slope is the coefficient of x, so the number that accompanies the variable x
the slope is
[tex]-\frac{9}{4}[/tex]for a line to be perpendicular to it, it must have the inverted fraction and the opposite sign to the original slope
then
[tex]-\frac{9}{4}\longrightarrow\frac{4}{9}[/tex]the slope of the perpedicular line is 4/9
and the slope of a parallel line must be the same slope, so
[tex]-\frac{9}{4}[/tex]help me please
thank you
Answers
Answer:
(-7, 3)
Step-by-step explanation:
Since the endpoints of the interval are not included, use parentheses.
Indicate whether the terms are like or unlike. The two terms 3,3 and – x3 arelike terms unlike tems
Answers
The given terms are
[tex]\begin{gathered} 3,3 \\ x^3 \end{gathered}[/tex]Notice that these terms are not like terms because one has variable and the other one doesn't.
Remember that like terms are those terms that have the same variable with the same exponent.
Therefore, the given terms are unlike terms.In a recent study, 50 males used a new weight-loss supplement, and all but 15 of them lost weight. In the same study, 100 females used the supplement, and
all but 45 of them lost weight.
Fill in the blanks below to make the statement the most reasonable possible.
The new weight-loss supplement was less effective on [(choose one) in the study because % of them failed to lose weight, whereas only
% of the [(choose one) failed to lose weight.
Answers
Answer: The new weight-loss supplement was less effective on females because 45% of the females failed to lose weight.
Step-by-step explanation:
30% of the males didn't lose weight and 45% of the females didn't lose weight out of 100.
on the males 30% out of 100% did not lose weight
on the females 45% out of 100% did not lose weight
Hope this is helpful or correct.
For a certain company, the cost for producing x items is 40x+300 and the revenue for selling x items is 80x−0.5x2 . The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.) Part b: Find two values of x that will create a profit of $300 Part c: Is it possible for the company to make a profit of $15,000 ?
Answers
Given that
The cost for producing items is 40x + 300 and the revenue collected is 80x - 0.5x^2
And we have to write an equation for the profit and also we have to find the profit.
Explanation -
The profit is basically the difference between revenue and cost.
So the profit will be
[tex]Profit=Revenue-cost[/tex]Substituting the values
[tex]\begin{gathered} Profit=80x-0.5x^2-(40x+300) \\ Profit=80x-0.5x^2-40x-300 \\ P=40x-0.5x^2-300 \end{gathered}[/tex](a). The profit equation will be, P = 40x - 0.5x^2 - 300
(b). Here the profit given is $300 (P=300) and we have to find the values of x.
Then,
[tex]\begin{gathered} 300=40x-0.5x^2-300 \\ 600=40x-0.5x^2 \\ 0.5x^2-40x+600=0 \\ Dividing\text{ by 0.5 we have} \\ x^2-80x+1200=0 \\ x^2-60x-20x+1200=0 \\ x(x-60)-20(x-60)=0 \\ (x-20)(x-60)=0 \\ x=20\text{ and x = 60} \end{gathered}[/tex]So the two values of x are 20 and 60.
(c). Now we have to check whether the profit can be $15000 or not.
For this, we have to put P = 15000 in the quadratic equation and if we get a solution for x then it is possible otherwise it is not.
So, substituting P = 15000
[tex]\begin{gathered} 15000=40x-0.5x^2-300 \\ 0.5x^2-40x+15300=0 \\ Dividing\text{ by 0.5 in the above equation} \\ x^2-80x+30600=0 \\ \end{gathered}[/tex]The solution to this equation is not possible. So Company cannot make a profit of $15000.
Hence the final answers are(a). P = 40x - 0.5x^2 - 300(b). 20 and 60(c). Nois econometrics science or commerce related
Answers
Answer:
Yes,econometrics science and commerce are related
A plane is beginning its descent to the ground. After 3
minutes, the plane is at an altitude of 31,275', and after 7
minutes it is at an altitude of 22,975'. At what rate, in feet
per minute, is the plane descending?
Answers
Answer:
2075 ft/minute
Step-by-step explanation:
31,275 - 22,975 = 8300, this is the decrease in altitude over 4 minutes.
By dividing the change in position by time you can find the rate of change.
8300/4
= 2075 ft/minute
Solve: 9(x-9) + 8 = -19
Answers
we have the equation
[tex]9\left(x-9\right)+8=-19[/tex]Solve for x
step 1
Apply distributive property on the left side
[tex]\begin{gathered} 9\left(x)-9(9\right)+8=-19 \\ 9x-81+8=-19 \end{gathered}[/tex]Combine similar terms on the left side
[tex]9x-73=-19[/tex]step 2
Adds 73 on both sides
[tex]\begin{gathered} 9x-73+73=-19+73 \\ simplify \\ 9x=54 \end{gathered}[/tex]step 3
Divide both sides by 9
[tex]\begin{gathered} \frac{9x}{9}=\frac{54}{9} \\ \\ x=6 \end{gathered}[/tex]The answer is x=6We do that by isolating the variable by dividing each side by factors without the variable in this case X.
Fatima us on the track team. One day at practice, it took her 19 minutes to run2 miles ,select the expression that gives this as a unit rate
Answers
The unit rate expression is 19/2 or 7.5 units.
What is unitary Method?A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilise this technique for math computations. This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
This approach allows us to calculate both the value of many units from the value of one unit and the value of one unit from the value of many unit.
Given:
Total time taken= 19 minutes
Total distance = 2 miles
Now, find the unit rate we have to divide the
unit rate = 19/2
= 7.5
Hence, the unit rate is 7.5 units.
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If QR = 13 and PT = 8, find QT.
Answers
Since the diagram is symmetric ,
so,
[tex]\begin{gathered} QR=QP \\ QP=13 \end{gathered}[/tex]Considering the triangle PQT is,
Using the pythagoras theorem on triangle PQT,
[tex]\begin{gathered} QP^2=PT^2+QT^2 \\ 13^2=8^2+QT^2 \\ QT^2=13^2-8^2 \\ ^{}QT^2=169-64 \\ QT^2=105 \\ QT=\sqrt[]{105} \\ QT=\text{ 10.24 } \end{gathered}[/tex]Hence, the value of QT is 10.24
Find the slope of the line that is perpendicular to the line that passes through the following pair of points: (12, -16) and (-2, -11)
Answers
,First we need to find the slope of the line that passes through (12, -16) and (-2, -11)
the slope can be calculated using these points
(12, -16)=(x1,y1)
(-2, -11)=(x2,y2)
the formula to calculate the slope is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]we substitute the values
[tex]m=\frac{-11+16}{-2+12}=\frac{5}{10}=\frac{1}{2}[/tex]The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1 / m
so if m=1/2
the slope of a perpendicular line will be m=-2
a. What is the center of dilation?
b. What is the shape that was dilated?
c. Is the scale factor one-third, two, or three?
Answers
Answer:
well I can answer b the shape here is a 3D Hexagonal pyramid
Which expression should you simplify to find the 90% confidence interval,given a sample of 50 people with a sample proportion of 0.65?
Answers
Answer
Explanation
The confidence interval
