Answers
The gradients for each line are given as follows:
Line A: m = 4.Line B: m = -2.How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The gradient of each line represents the slope, hence they are given as follows:
Line A: m = 4, as when x increases by one, y increases by four.Line B: m = -2, as when x increases by one, y decays by two.More can be learned about linear functions at https://brainly.com/question/24808124
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Related Questions
9. Find m DF
m
140°
DF:
=
E
44°
20. Find
mZPQR.
131*
m/POR=
Need done asap please show work
Answers
According to the angles between intersecting secant and tangent, the value of
angle DF is 52 degrees
angle PQR = 49 degrees
How to solve for angle DFThe value of angle DF is solved using the angles of intersecting secant out side the circle
The theorem give the formula in the form
44 = 1/2 (140 - DF)
88 = 140 - DF
DF = 140 - 88
DF = 52 degrees
Using intersection of tangents, for the second figure
exterior angle = 1/2 (major arc - minor arc)
major arc = 360 - 131 = 229
PQR = 1/2 (229 - 131)
PQR = 49 degrees
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Determine the x coordinate of the center of a circle if its diameter's endpoints are located at (7,-2) and (9,5).
Answers
Answer:
(2,8)
Step-by-step explanation:
Where does 1/6 land on a number line
Answers
Answer:
On a number line, 1/6 would land in the exact middle between 0 and 2/6
Step-by-step explanation:
Not too sure what your question meant, but I hope my answer helped!
If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)
A normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95. Find the z-score of 235.90.
Answers
The z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.
What is mean?The mean of the set of data is equal to the sum of all the quantities in the data, and divide by the no of quantities.
Given:
The standard deviation, d = 182.56,
The mean, m = 265.95,
The observation value, X = 235.90
Calculate the z score by the following formula given below,
Z = (X - m) / d,
Here, Z is the Z score,
Z = 235.90 - 265.95 / 182.56
Z = -0.165
Therefore, the z-score of 235.90, if a normal distribution of scores has a standard deviation of 182.56 and a mean of 265.95, is -0.165.
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12.874 rounded to the nearest tenth
Answers
I think it might be 12.9
NO LINKS!!! URGENT HELP PLEASE!!!
Solve ΔABC using the Law of Sines
1. A = 29°, C = 63°, c = 24
2. A = 72°, B= 35°, c = 21
Answers
Answer:
1) B = 88°, a = 13.1, b = 26.9
2) C = 73°, a = 20.9, b = 12.6
Step-by-step explanation:
To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
Question 1Given values:
A = 29°C = 63°c = 24As the interior angles of a triangle sum to 180°:
\(\implies A+B+C=180^{\circ}\)
\(\implies B=180^{\circ}-A-C\)
\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)
\(\implies B=88^{\circ}\)
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)
\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)
Solve for a:
\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)
\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)
\(\implies a=13.0876493...\)
\(\implies a=13.1\)
Solve for b:
\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)
\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)
\(\implies b=26.9194211...\)
\(\implies b=26.9\)
\(\hrulefill\)
Question 2Given values:
A = 72°B = 35°c = 21As the interior angles of a triangle sum to 180°:
\(\implies A+B+C=180^{\circ}\)
\(\implies C=180^{\circ}-A-B\)
\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)
\(\implies C=73^{\circ}\)
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)
\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)
Solve for a:
\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)
\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)
\(\implies a=20.8847511...\)
\(\implies a=20.9\)
Solve for b:
\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)
\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)
\(\implies b=12.5954671...\)
\(\implies b=12.6\)
describe all the numbers that when rounded to the nearest thousand are 41000
Answers
Answer:
40,900 40,800 40,700 40,600 40,500
Step-by-step explanation:
The 4 will stay the same, it doesn't need to change because you are focusing on the number after it which is 1. a number has to be over 5 to round up the number. If we are trying to make a 1 , the previous number must be either a 5, a 6, a 7, an 8, or a 9
please fast if could
Answers
Answer:9/41
SOH = opposite over hypotenuse
Step-by-step explanation:
The side of a triangle are in the ratio 4:4:3 what kind of triangle is it (b) calculate the smallest angle of the triangle to the nearest degree
Answers
The smallest angle of the equilateral triangle is 60 degrees
If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.
To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.
For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:
Smallest angle \(= \frac{180}{3} = 60\)\) degrees.
Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).
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(6,3) and (2,7) the midpoint formula
Answers
Answer: (4,5)
Step-by-step explanation:
3+7=10/2=5 y=5
(4,5)
Prove the Converse of the Pythagorean Theorem
In this activity, you will prove and apply the converse of the Pythagorean theorem. Recall that the
converse states that if the square of the length of the longest side of a triangle is equal to the sum of
the squares of the other two sides, then the triangle is a right triangle.
Open the GeoGebra activity to complete each step below. For help, watch these short videos about
using GeoGebra to measure and create points, lines, and anglese.
Question 1
Part A
Draw AABC with vertices at A(1,6), B(1, 1) and C(5,1). In this triangle, AB²+ BC² = AC².
Next, use the GeoGebra tools to draw ADEF such that AB = DE, m/E
Paste a picture of your drawing in the answer box.
= 90°, and EF
BC.
B I U X² X2 15px
AVA
E E g = = 三 四 V 田
=
Answers
The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.
To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.
AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5
BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4
AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)
Now, let's check if AB^2 + BC^2 = AC^2:
AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41
AC^2 = (2sqrt(10))^2 = 4(10) = 40
Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.
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Help!! Please photo art attached below
Answers
Answer:
C
Step-by-step explanation:
180 degrees + 30 =210 degrees
210 degrees equals 7π/6
4x^2-19x-5=0
Solve by factoring
Answers
Answer:
x= −1/4 or x = 5
Step-by-step explanation:
Step 1: Factor left side of equation.
(4x+1)(x−5)=0
Step 2: Set factors equal to 0.
4x+1=0 or x−5=0
Answer:
x= −1/4 or x = 5
The factored form of the equation 4x²- 19x - 5 = 0 is (4x+1)(x-5).
The given equation is 4x²- 19x - 5 = 0.
To factor the quadratic expression on the left-hand side into two binomials.
The binomial factors will have the form (ax + b)(cx + d).
We need to find two numbers whose product is equal to ac (the coefficient of x² term) multiplied by d (the constant term), which is (4)(-5) = -20, and whose sum is equal to the coefficient of the x term, -19.
After considering different factor pairs of -20, we find that -20 and +1 satisfy the requirements.
(4x² - 20x) + (x - 5) = 0.
4x(x - 5) + (x - 5) = 0.
(4x+1)(x-5)=0
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anyone nervous about semester exams
Answers
Answer:
YES
Step-by-step explanation:
I am literally trying to fit in as much studying as possible but I keep getting distracted ;-;
find-5/6÷(-1/2) write the answer in the lowest terms.
Answers
-5/6 x -2/1
The negatives cancel, giving you a positive answer:
10/6
Simplified to 5/3 or 1 and 2/3 if you use mixed fractions.
12.403 in expanded form
Answers
12.403 can be expanded in the following manner -
\(10 + 2 + \frac{4}{10} + \frac{0}{100} + \frac{3}{1000} \\ \)
hope helpful! ;-;
Answer:
10 + 2 + 4/10 + 3/1000
Step-by-step explanation:
Hope it helps! =D
x−1.2=3 what is x
HELP ASAP K-12 8TH GRADE
Answers
hi! here is ur answer
x-1.2=3
x=3+1.2
x=4.2
hope it helps you!
Hello! :)
To find what is x we will add 1.2 to both sides
x - 1.2 + 1.2 = 3 + 1.2
x = 4.2
Hope this helped you!
THEDIPER
6x+7=3x+16 ?
5x-4=9x ?
-54-8x=-2x ?
5+30=x+10 ?
8x-15x=-44-12 ?
7x-5=8x+24 ?
3x+1=12x+10 ?
-8+10=-6x+6 ?
Answers
b) x = -1
c) x = -9
d) x = 25
e) x = 8
f) x = -29
g) x = -1
h) x = 4/6
Answer:
x = 3
x = -1
x = -9
x = 25
x = 8
x = -29
x = -1
x = 4/6
Step-by-step explanation:
For each of these, you simply subtract the similars from each other. Basically meaning, the number with variables will be subtracted from each other while the constants will be substrates from each other. In the first case, you’ll subtract 3x from 6x and be left with 3x. Then it’d be 3x + 7 = 16. Now you don’t want to subtract 16 from 7 as to not leave the right side empty but rather to have one coefficient with it’s variable on one side and a constant on the other, you’ll subtract 7 from 16 and get 9. 3x = 9. Then to get the x by itself, you’d divide because (3x) is multiplication, basically (3*x) so to rid one value from a multiplication problem, you’d have to divide. So you’d divide 3 from both sides. And get x = 3.
for each parallel lines. you are given the measure of one angle
Answers
Answer:
The question is not complete
Which graph represents the following system of inequalities?
y <-2 +4
y < x + 3
x < 3
Answers
Answer: I think it’s D is
Step-by-step explanation:I put it in Desmos and it didn’t show the same answer as A. B. or C.
10. (04.02 LC)
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation? (1 point)
2x + y = 8
-x - 3y = -12
3y + 12
-3y + 12
3y - 12
-3y - 12
Answers
If you isolated x in the second equation to use the substitution method. -3y + 12 expression we substitute into the first equation.
What is Substitution Method ?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
The substitution method has three straightforward steps, which are listed below:
In any equation, determine the value of any one variable in terms of the other variable.Replace that in the other equation, then solve it.In any of the equations, replace the value of the second variable once more.2x + y = 8
-x - 3y = -12
__________
-3y + 12
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The solution to an inequality is represented by the number line.
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
How can this same solution be written using set-builder notation?
Answers
The set builder notation of the solution inequality represented on the number line is; {x: 3< x <=5}.
What is the set builder notation representation of the solution?It follows from the task content that at point positive 3, there's an open circle which signifies that the number 3 is less than the solution.
And since the number line is shaded from positive 3 to 5, it follows that the maximum value in the solution set is 5.
The representation is therefore; {x: 3< x <=5}.
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On the number line, the solution inequality is represented by the notation x: 3=5, which is the set builder notation of the inequality.
This is further explained below.
What does the answer look like when represented using set builder notation?Given the information provided in the job, it is logical to conclude that at point positive 3, there will be an open circle. This will indicate that the number 3 will be lower than the answer.
And since the shading on the number line goes from positive 3 to 5, it follows that the highest value that can be found in the set of solutions is 5.
As a result, the representation is written as:
"x: 3 x = 5."
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the soccer team manager plans to have 2 gallons of water for every 4 players on the team during practice. determine whether the statements about ratios are true or false.
A. The team manager needs 1 gallon of water for every 1 player
` true or false
B. The ratio of number of players to gallons of water is 2:1
` true or false
C. The team manager ould need 4 gallons of water for 10 players
` true or false
D. For 30 players, the team manager would need 15 gallons of water ` true or false
Answers
Answer:
A.=False
B.=True
C.=False
D.=True
Step-by-step explanation:
The original ration is 2 gallons of water for 4 players.
Each player requires 1/2 gallon of water.
To get the amount of water needed multiply 1/2 by the amount of players.
1*(1/2) does not equal 1
2*(1/2) equals 1
10*(1/2) does not equal 4
30*(1/2) equals 15
Find the volume of cuboid of dimension 16cm X 10m x 6cm.
Answers
The given values are
length=16cm, width w=10cm and height h=6cm.
Recall that the formula for the volume of the cuboid is
\(V=l\times w\times h\)Substitute length=16cm, width w=10cm and height h=6cm, we get
\(V=16\times10\times6\)Multiplying 16,10 and 6, we get
\(V=960m^3\)Hence the volume of the given cuboid is
\(V=960m^3\)The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4.5 square imeters / m * inute . At what rate is the base of the triangle changing when the altitude is 10 centimeters and the area is 95 square centimeters?
Answers
Solution:
The area of a triangle is expressed as
\(\begin{gathered} A=\frac{1}{2}bh\text{ ----- equation 1} \\ where \\ A\Rightarrow area \\ b\Rightarrow base \\ h\Rightarrow altitude \end{gathered}\)By taking the derivative of equation 1 with respect to time t, we have
\(\frac{dA}{dt}=\frac{1}{2}b\frac{dh}{dt}+\frac{1}{2}h\frac{db}{dt}\text{ ---- equation 2}\)Given that the altitude of the triangle is increasing at a rate of 1 cm/minute while the area of the triangle is increasing at a rate of 4.5 square cm/minute, this implies that
\(\begin{gathered} \frac{dh}{dt}=\text{ 1 cm/minute} \\ \frac{dA}{dt}=4.5\text{ cm}^2\text{ per minute} \end{gathered}\)Given that the altitude and area are 10 centimeters and 95 square centimeters, this implies that
\(\begin{gathered} h=10\text{ cm} \\ A=\text{ 95 cm}^2 \end{gathered}\)We can evaluate the base of the triangle from equation 1 as
\(\begin{gathered} 95=\frac{1}{2}\times b\times10 \\ \Rightarrow5b=95 \\ divide\text{ both sides by 5} \\ \frac{5b}{5}=\frac{95}{5} \\ \Rightarrow b=19\text{ cm} \end{gathered}\)By substituting these values into equation 2, we have
\(\begin{gathered} 4.5=\frac{1}{2}(19)(1)+\frac{1}{2}(10)(\frac{db}{dt}) \\ \Rightarrow4.5=9.5+5\frac{db}{dt} \\ add\text{ -9.5 to both sides} \\ -9.5+4.5=-9.5+9.5+5\frac{db}{dt} \\ \Rightarrow-5=5\frac{db}{dt} \\ thus, \\ \frac{db}{dt}=-1\text{ cm per minute} \end{gathered}\)Hence, the base is changing at the rate of
\(\frac{db}{dt}=-1\text{ centimeters per minute}\)You invested $4000 between two accounts paying 3% and 4% annual interest. If the total interest earned for the year was $130, how much was invested at each rate?
Answers
You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.
Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.
To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).
According to the given information, the total interest earned from both investments is $130. So we can set up the equation:
0.03x + 0.04($4000 - x) = $130
Simplifying the equation:
0.03x + 0.04($4000 - x) = $130
0.03x + $160 - 0.04x = $130
-0.01x = $130 - $160
-0.01x = -$30
x = -$30 / -0.01
x = $3000
Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.
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Does anyone know this I don’t know what to put
Answers
Answer:
110
Step-by-step explanation:
3x+5+2x=180
Step 1: Simplify both sides of the equation.
3x+5+2x=180
(3x+2x)+(5)=180(Combine Like Terms)
5x+5=180
5x+5=180
Step 2: Subtract 5 from both sides.
5x+5−5=180−5
5x=175
Step 3: Divide both sides by 5.
x=35
35*3+5=110
AB congruent CD. Find the length of BD.
Answers
Answer:
8
Step-by-step explanation:
2x+5x+7=3x-4+5x+7
7x+7=8x+3
x=4
BD=3(4)-4=12-4=8
Hope this helps!
Answer:
BD=4
Step-by-step explanation:
Since AB and CD are congruent (or the same length) we can equal the corresponding equations for the two:
2x+5x+7=5x+7+3x-4
(simplify)
7x+7=8x+3
(get variables to one side)
7x+7-8x=3
7x-8x=3-7
(simplify)
-x=-4
(multiply by -1 to get x by itself)
x=4
Now, plug x=4 into the BD equation (3x-4)...
3(4)-4=BD
12-4=BD
8=BD
You would like to have $20,000 to use a down payment for a home in five years by making regular, end-of-month deposits into an annuity that pays 6% interest compounded monthly.
How much should you deposit each month?
Round your answer to the nearest cent. Do not include the dollar sign in the answer box below.
Answers
The calculation of this can be done by first determining the future value of the monthly payments of $327.50
The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,
which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.
The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35
This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.
Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.
for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).
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Derrick's dinner bill, including an 18% tip, is $15.34.
What was the amount of the bill before the tip?
Enter your answer in the box. I WILL GIVE BRANLIEST IF ASWERED CORRECTLY
Answers
Answer:
The amount before the tip was $12.58
Step-by-step explanation:
Answer:
The amount before the tip was $12.58
Step-by-step explanation: