Answers
The height of the tree in 30 months given the linear equation is 16m.
What is the height of the tree?The given equation is a linear equation. A linear equation is an equation that changes at a constant rate. The change can either be an increase or a decrease. A linear equation usually has an intercept and a slope. The intercept is the value of the equation when x is zero. The slope is the rate of change of the equation.
H (x) = 10 + 0.20x
10 = intercept
0.20 = slope
In order to determine the height of the tree after 30 months, substitute for x in the above linear equation.
H(x) = 10 + (0.2 x 30)
H(x) = 10 + 6
H(x) = 16
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Related Questions
Line AB formed by (2,3) and (-1,4)Line CD formed by (-5,3) and (-4,6)Parallel perpendicular or neither
Answers
To check whether the lines are perpendicular or parallel, we will use the following rules:
1) For parallel lines, the slopes are equal.
2) For perpendicular lines, the product of the slopes is equal to -1.
Slope of line AB:
Using
[tex]\begin{gathered} (x_1,y_1)=(2,3) \\ (x_2,y_2)=(-1,4) \end{gathered}[/tex]The slope is given as
[tex]\begin{gathered} m_A=\frac{y_2-y_1}{x_2-x_1} \\ m_A=\frac{4-3}{-1-2} \\ m_A=-\frac{1}{3} \end{gathered}[/tex]Slope of line CD:
Using
[tex]\begin{gathered} (x_1,y_1)=(-5,3) \\ (x_2,y_2)=(-4,6) \end{gathered}[/tex]The slope is given as
[tex]\begin{gathered} m_B=\frac{y_2-y_1}{x_2-x_1} \\ m_B=\frac{6-3}{-4-(-5)} \\ m_B=\frac{3}{-4+5} \\ m_B=3 \end{gathered}[/tex]Comparing both slopes, we can observe that
[tex]\begin{gathered} m_A\times m_B=-1 \\ \text{Given that} \\ -\frac{1}{3}\times3=-1 \end{gathered}[/tex]Therefore, both lines are PERPENDICULAR.
The scatter plot shows the number of roses (x) and daisies (y) a florist sold at a flower
show. How many roses did the florist who sold 125 daisies sell?
100
200
80
170
Answers
The number of roses that the florist sold who sold 125 daisies is; 200
How to Interpret Scatter Plots?Scatter plots are the graphs that present the relationship between two variables in a data-set.
From the given scatter plots, we see that the x and y axes are marked in intervals of 50 like 0, 50, 100, 150, 200,...e.t.c
Now, from the scatter plot, we see a couple of coordinates and we are told that the x-axis shows the number of roses sold at a flower show while the y-axis shows the number of daises sold at the flower show.
Now, from the scatter plot, we see that when the number of daises sold is 125, we can trace that the number of roses sold was 200 roses.
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Mary has 13 1/3 feet of material. She needs to divide the material into 4 sections of equal length. What will be the length of each new section?
Answers
The answer is 3 1/3 feet
Solution :
Total length of material : 13 1/3 feet
Number of sections needed : 4
so the length of new sections = Total length ÷ No. of section
= 13 1/3 ÷ 4
13 1/3 = 40/3
so, 40/3 ÷ 6
that is 40/3 × 1/6
= 40/12
= 3.33 or 3 1/3
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Consider the equation 8x - 2y= 24. Select True or False for each statement.
Answers
8y - 2y = 24
a)
The x intercept is when y = 0; if we use the equation when y = 0:
8x - 2(0) = 24 ==> 8x = 24 ==> x = 24/8 ==> x = 3
So the fist answer is TRUE
b)
The y intercept is when x = 0; if we use the equation with x = 0:
8(0) - 2y = 24 ==> -2y = 24 ==> y = 24/(-2) ==> y = -12
So the second answer is FALSE
c)
if we take the equation and solve it for y:
8x - 2y = 24 ==> 8x - 24 = 2y ==> (8x - 24)/2 = y ==> 4x - 12 = y ==> y = 4x -12
So the third answer is TRUE
y = 2x - 3
I need to find the y-int and the slope for the graph
Answers
Answer:
y-int = (0,-3)
slope = 2
Step-by-step explanation:
The slope is found by the number before x. If its just x then the slope is 1. The y-int is found by the number all the way at the end. In this case its -3. So the y-int is (0,-3)
Answer:
Step-by-step explanation:
y
=
2
x
+
3
The slope-intercept form is
y
=
m
x
+
b
, where
m
is the slope and
b
is the y-intercept.
y
=
m
x
+
b
Find the values of
m
and
b
using the form
y
=
m
x
+
b
.
m
=
2
b
=
3
The slope of the line is the value of
m
, and the y-intercept is the value of
b
.
Slope:
2
y-intercept:
(
0
,
3
)
Please help me solve this algebra problem on my homework
Answers
We need to determine a few characteristics of the following linear equation:
[tex]y-5=-\frac{1}{2}(x-2)[/tex]The first step we need to take is to isolate the "y" variable on the left side.
[tex]\begin{gathered} y=\frac{-1}{2}(x-2)+5 \\ y=\frac{-1}{2}\cdot x+1+5 \\ y=\frac{-1}{2}\cdot x+6 \end{gathered}[/tex]Now we need to analyze this function and provide the necessary characteristics.
First is the Domain. The Domain of a function is the group of all numbers that can be used as an input (x), in this case the Domain is the whole Real group.
Second is the Range, which is the group of numbers that can be the output of the function (y), for this case we also have the whole Real group as Range.
Then we need to find the "Zero". Which is the value at which the function crosses the x-axis, to calculate it we must make "y=0" and solve for x.
[tex]\begin{gathered} 0=\frac{-x}{2}+6 \\ \frac{x}{2}=6 \\ x=12 \end{gathered}[/tex]The zero is equal to 12.
The slope of the function is the number multiplying "x", in this case it is -1/2.
The slope is negative, decrescent.
To find the value of f(8), we need to replace x by 8 and solve for y.
[tex]\begin{gathered} f(8)=\frac{-8}{2}+6 \\ f(8)=-4+6=2 \end{gathered}[/tex]The value of f(8) = 2.
To determine the value of x where f(x) is equal to 5, we need to replace f(x) by 5 and solve for x.
[tex]\begin{gathered} 5=\frac{-x}{2}+6 \\ \frac{-x}{2}=5-6 \\ \frac{-x}{2}=-1 \\ -x=-2 \\ x=2 \end{gathered}[/tex]The value of x for which f(x) is equal to 5, is 2.
Now we need to graph the equation, for that we have to use two of the points we found before, we will use (8, 2) and (2,5). We need to mark these points at the coordinate plane and draw a line between them:
A 25-foot ladder is leaning against the side of a building and is positioned such that the base of the ladder is 15 feet from the base of the building. How far above the ground is the point where the ladder touches the building?
Answers
Let us use a diagram to demonstrate the event .
From the diagram we are asked to find the value h. The value h can be found using pythagora's theorem.
[tex]\begin{gathered} h^2=25^2-15^2 \\ h^2=625-225 \\ h^2=400 \\ \text{square root both sides} \\ h=\sqrt[]{400} \\ h=20\text{ ft} \end{gathered}[/tex]Quadrilateral PQRS is dilated by a scale factor of to
form quadrilateral P'Q'R'S'. What is the measure of side
QR?
Answers
Answer: 24 units
Step-by-step explanation:
If you are multiplying a shape by a scale factor, the dimensions are also multiplied by the scale factor.
QR= x
Q'R'= (1/2)(X)
12=(1/2)(X)
(2)12= 1/2x(2)
24=X
If you're multiplying QR by 1/2 you would get 12. 12 is a half of QR. Therefore, QR is 24.
Solve with substitution method: 3x+5y=10 and 9y+3x=15
Answers
The value of x and y using the substitution method are 5/4 and 5/4.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Two equations:
3x + 5y = 10 _____(1)
9y + 3x = 15 ______(2)
From (1) we get,
3x = 10 - 5y
x = (10 - 5y) / 3 ______(3)
Putting (3) in (2) we get,
9y + 3 x [(10 - 5y) / 3] = 15
9y + 10 - 5y = 15
4y = 15 - 10
4y = 5
y = 5/4
Putting y = 5/4 in (3) we get,
x = (10 - 5 x 5/4) / 3
x = (10 - 25/4) / 3
x = (40 - 25) / (4 x 3)
x = 15 / 12
x = 3x5 / 3x4
x = 5/4
Thus,
The value of x and y using the substitution method are 5/4 and 5/4.
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A music store sold for 10³ CDs and 10² CD players. If each CD costs $12
and each CD player costs $35, what was the store's total earnings?
Answers
The total earning of the store from the formed equation is: 15,500 dollars.
What is equation?
In mathematics, the statement based problems can be solved by forming the equation. And it consists of dependent variable as well as independent variable.
According to the question, the given parameter states that the music store sold 1000 CDs and 100 CD players. And the cost of each CD is $12 and each CD player is $35.
Now, to calculate the total earning by forming the equation for the given statement and it is as follows:
(1000)(12) + (100)(35) = 12,000 + 3500 = 15,500 dollars
Hence, the total earning of the store from the formed equation is: 15,500 dollars.
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Two angles form a linear pair. The measure of one angle is z and the measure of the other angle is 2.4 times z plus 10°. Find the measure of each angle.
Answers
Two angles form a linear pair.
so, the sum of the angles are 180
the measure of the angles are z and (2.4 * z + 10)
so,
z + (2.4 * z + 10) = 180
solve for z
so,
z + 2.4 * z + 10 = 180
3.4 z = 180 - 10
3.4 * z = 170
divide both sides by 3.4
so, z = 170/3.4 = 50
so, the angles are 50 and 130
Cheyenne is playing a board game. Her score was −175 at the start of her turn, and at the end of her turn her score was −325. What was the change in Cheyenne’s score from the start of her turn to the end of her turn? How did you determine your answer?
Enter the correct answers in the boxes.
points
I subtracted
from
.
Answers
Answer: -150
Step-by-step explanation:
To find the change in the score we need to find the difference between the two scores. To do this easily, we can add 175 to -325.
-325 + 175 = -150
By doing this we get the difference and the answer to the question.
Answer: -150
Step-by-step explanation: I subtracted from -325.
A 6 ft tall tent standing next to a cardboard
box casts a 9 ft shadow. If the cardboard
box casts a shadow that is 6 ft long then how
tall is it?
Answers
Answer: 4
Step-by-step explanation:
9/6=3/2(1.5)
6/1.5= 4
Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
(show as much details upon answering)
Answers
Answer:
linear equations;15m+10=w
15 pages written for every month for 5 months plus the 10 pages she has already written is equal to the total number of pages written in 5 months m=number months written in this case it is 5 months.
w=number of pages written in 5 months 15(5)+10=w
75+10=w
85 Pages written=w
will have written 85 Pages in 5 months
He following cards are dealt to three people at random, so that everyone gets the same number of cards. what is the probability that everyone gets a red card?
Answers
The probability that everyone will get a red card is 0.5.
What probability exactly is?Probability is a branch of mathematics that deals with numerical representations of the probability that an event will happen or that a statement is true.The probability of an event is a number between 0 and 1, with 0 roughly denoting impossibility and 1 denoting certainty.The probability is the likelihood that something will happen, to put it simply.The likelihood or likelihood of various outcomes can be discussed when we don't know how an event will turn out.The study of events that fit into a probability distribution is known as statistics.So, the probability that everyone gets a red card:
Probability formula: P(E) = Favourable events/Total number of eventsAs cards are distributed to 3 people, divide both favorable events and total events by 3.Then,
P(E) = Favourable events/Total number of eventsP(E) = (26/3)/(52/3)P(E) = 26/3 × 3/52P(E) = 26/52P(E) = 0.5Therefore, the probability that everyone will get a red card is 0.5.
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4 × logx -(2 × logv + 3 × logy)
Answers
Simplifying the given logarithmic equation, the expression is obtained as log([tex]\frac{x^{4} }{v^{2} y^{3} }[/tex]).
The objective is to find the resultant expression for 4 × logx -(2 × logv + 3 × logy)
According to logarithmic results,
The product of an integer constant and a logarithm term of a number is equivalent to the logarithm of the number raised to the power of the particular integer constant.
That is, b × log(a) = log([tex]a^{b}[/tex])
Hence, 4 × log(x) = log([tex]x^{4}[/tex]),
2 × log(v) = log([tex]v^{2}[/tex])
and, 3 × log(y) = log([tex]y^{3}[/tex])
So, the equation can be rewritten as log([tex]x^{4}[/tex]) - (log([tex]v^{2}[/tex]) + log([tex]y^{3}[/tex]))
The sum of the logarithms of two numbers is equivalent to the logarithm of their product.
That is, log(a) + log(b) = log(a×b)
Hence, log([tex]v^{2}[/tex]) + log([tex]y^{3}[/tex]) = log([tex]v^{2}[/tex][tex]y^{3}[/tex])
So, the equation can be rewritten as log([tex]x^{4}[/tex]) - log([tex]v^{2}[/tex][tex]y^{3}[/tex])
The difference in the logarithms of two numbers is equivalent to the logarithm of their fraction.
That is, log(a) - log(b) = log(a÷b)
Hence, log([tex]x^{4}[/tex]) - log([tex]v^{2}[/tex][tex]y^{3}[/tex]) = log([tex]\frac{x^{4} }{v^{2} y^{3} }[/tex])
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Calculate rates (backwards)
If pipe costs $30, at $6 / m, how many metres would you get?
Answers
Answer:
5 m
Step-by-step explanation:
$30 divided by $6 a m
30/6=5 m
Samuel wants to save enough money to buy a new couch, but isn’t sure which bank’s savings account he should sign up for. Wells Fargo has a yearly interest rate of 6%. Chase has an interest rate of 0.5% compounded monthly. If Samuel deposits $3000 at the beginning of the year and makes no additional deposits or withdrawals, which bank would have the higher balance after one year?
Answers
wells Fargo would have a higher balance after one year
Step-by-step explanation:
wells Fargo would have a higher balance after one year
Identify the reason that would be used to justify step 2 in the proof below.
Converse of the Consecutive Interior Angle Theorem
Corresponding Angles Postulate
Alternate Exterior Angle Theorem
Vertical Angles Theorem
Answers
The reason that would be used to justify step 2 in the proof below is: Corresponding Angles Postulate (Option B).
What is A corresponding Angle Postulate?Congruence and likeness tests in geometry require comparing corresponding sides and angles of polygons. In these tests, each side and angle of one polygon are matched with a side or angle of the second polygon, with care taken to maintain the order of adjacency.
A mathematical proof is an inductive explanation for a mathematical assertion that demonstrates that the provided assumptions logically ensure the conclusion.
There are several methods for demonstrating anything. There are three of them:
direct proof, proof by contradiction, and proof by induction. We'll go through each of these proofs and when and how they're utilized.Learn more about Corresponding Angles:
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Write an equation for the line that is
perpendicular to the line y = 4x + 9
and goes through the point (2, 8).
Answers
Answer:
[tex]\sf y =\dfrac{-1}{4}x+\dfrac{17}{2}[/tex]
Step-by-step explanation:
Equation of the line: y =mx + bwhere m is slope and b is y-intercept.
y = 4x + 9
Slope = m₁ = 4
[tex]\sf \text{Slope of the perpendicular line = $\dfrac{-1}{m_1}$}[/tex]
[tex]\sf \boxed{m = \dfrac{-1}{4}}[/tex]
[tex]\sf y =\dfrac{-1}{4}x +b[/tex]
The point (2,8) passes through the line. Substitute in the above equation to find 'b'.
[tex]\sf 8 = \dfrac{-1}{4}*2+b\\\\\\ 8 = \dfrac{-1}{2}+b\\\\[/tex]
[tex]\sf 8+\dfrac{1}{2}=b\\\\ \dfrac{16}{2}+\dfrac{1}{2}=b\\\\ \boxed{b=\dfrac{17}{2}}[/tex]
Equation of the line:
[tex]\sf y =\dfrac{-1}{4}x + \dfrac{17}{2}[/tex]
kelly sold 35 books at £1.40 each. 28 bracelets at £1.50 each. some badges at 80p each. She got a total of £115. Work out how many badges Kelly sold
Answers
Answer:
the answer is 30 !! :)
Step-by-step explanation:
115-(35*1.40)-(28*1.50)= 24
24/.8 = 30
Can someone help me, please
Answers
The quadratic equation that Olivia is solving is y = x² + 4x + 6
Any expression that can be changed into standard form, such as the ones below, is considered to be a quadratic equation in algebra:
y = ax² + bx +c
With a = 0 (and b = 0), the equation is linear rather than quadratic since the ax² term is omitted, and x symbolizes an unknown whereas a, b, and c denote known quantities.The quadratic coefficient, linear coefficient, and constant or free term are the three coefficients of an equation, indicated by the numbers a, b, and c, respectively.The values of x that satisfy the equation are represented by the roots or zeros of the equation on the left side of the equation.We know that the quadratic formula to solve a quadratic equation is:[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]Now from the given step and by using the quadratic formula we can ascertain that the values of a ,b and c are 1 ,4 and 6 respectively.
hence the quadratic equation is y = x² + 4x + 6.
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Select the correct answer.
Which expression is equivalent to 2x² . √16x, if x>0?
Answers
The expression is equivalent to option A, 8x[tex]\sqrt[6]{x}[/tex].
Option A is correct
How do expressions work?Variables, constants, and mathematical operators make up an expression, which is a mathematical statement.
How can one locate equivalent expressions?Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation. The x-term is typically put before constants when arranging the terms in the same sequence. It is said that two expressions are equivalent if every phrase in them is the same.
The expression is 2[tex]\sqrt[3]{x^2}[/tex]
The expression can be simplified as
= 2.4[tex]x^{2/3}[/tex][tex]x^{1/2}[/tex]
= 8[tex]x^{7/6}[/tex]
= 8x[tex]x^{1/6}[/tex]
= 8x[tex]\sqrt[6]{x}[/tex]
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The prime factor tree for 6 is shown
below.
Complete the prime factor tree for 15 and
use it to help you find the lowest common
multiple (LCM) of 6 and 15.
2
6
3
15
Answers
Answer: 3
Step-by-step explanation:
6 - 2, 3
15- 3, 5
i need help with the first question in this picture
Answers
Initial price of the TV = $899
discount in % = 25 % = 0.25
First, we will find the amount discounted:
[tex]\begin{gathered} Amount\text{ discounted = }25\text{ \% }\times\text{ 899} \\ Amount\text{ discounted = }0.25\text{ }\times\text{ 899} \\ Amount\text{ discounted = \$224.75} \end{gathered}[/tex]sales price after the discount was removed:
[tex]\begin{gathered} sales\text{ price = }initial\text{ price - amount discounted} \\ sales\text{ price = 899 - 224.75} \\ sales\text{ price before }Tax\text{ = \$674.25} \end{gathered}[/tex][tex]\begin{gathered} \text{Sales tax = 8.125 \% = 0.08125} \\ \text{Tax = sales price before tax }\times\text{ sales tax} \\ \text{Tax = 674.25 }\times\text{ 0.08125} \\ \text{Tax = \$}54.78 \end{gathered}[/tex][tex]\begin{gathered} \text{Sales price with tax = sales price before tax + Tax} \\ \text{Sales price with tax = 674.25 + 54.78} \\ \text{Sales price with tax = \$729.03} \end{gathered}[/tex]x>-4
except the greater than symbol has a line under. Graph each inequality and write the solution set using both set-builder notation and interval notation.
Answers
The solution set of the inequality x ≥ - 4 using set builder notation and interval notation is {x | x ∈ Z, - 4 ≤ x ≤ ∞ } and [ - 4, ∞ ) respectively.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.
Interval Notation: A set of real numbers known as an interval contains all real numbers that fall inside any two of the set's numbers.
Consider the inequality,
x ≥ - 4
In the number line, the value of x is equal to and greater than - 4 increasing to infinity.
Therefore,
The solution set using the set builder notation is:
{x | x ∈ Z, - 4 ≤ x ≤ ∞ }
The solution set of the inequality using the interval notation is:
[ - 4, ∞ )
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33 percent of 300
And 24 percent of 300 PLSS
Answers
the first one is 99 and the second one is 72
Hope this helped
Answer:
33% of 300 is about 99, and 24% of 300 is about 72
Step-by-step explanation:
Hope this helps.
I need some help... I am very confused.
Answers
The base of the triangle shown is 12 millimeters
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
Given that:
A is the area of the triangleb is the base of the triangleh is the heightb = 2A/h
For the triangle, A = 36 mm², h = 6 mm
Substituting:
b = 2(36)/6
Simplifying gives:
b = 12 mm
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Moses makes a school spirit flag. He has 1/3 as many yards of red fabric as blue
fabric. He buys 2 2/3 yards more red fabric. Now he has equal amounts of red and
blue fabric. Use x to represent the amount of blue fabric. Which equations could
you use to find the amount of red fabric Moses has? Select all that apply.
Answers
Answer:
1/3+2 2/3=3/2=1 1/2 yards or x=3/2
To solve 1-variable equations and inequalities, we use additive inverses and/or multiplicative inverses to isolate the variable.
Options:
True
False
The multiplicative inverse of 0.1
Options:
1/10
-10
10
-0.1
The multiplicative inverse of 2/6 is 3.
Options:
True
False
The additive inverse of 80.
Options:
80
1/80
-80
8
The multiplicative inverse of 13.
Options:
-13
0.13
1/13
13/1
1 of 5 questions saved
Answers
Answer:
false 1/10 false 80 13/1
