Answer:
40:60:80
Step-by-step explanation:
1. add the ratio first 2+3+4 =9, then divide the amount by the total number of parts
2. multiply the quotient by each part (20×2, 20×3 and 20×4)
Increase R245 in the ratio 5:6.
Answer:
To increase R245 in the ratio 5:6, you can add an amount proportional to the ratio 5:6 to R245.
Let's say you want to increase R245 by x.
The new value for 5 parts will be 5x + 245, and the new value for 6 parts will be 6x + 245.
So, the new ratio would be (5x + 245) : (6x + 245), which is still 5:6.
Therefore, to increase R245 in the ratio 5:6, you would add x to R245.
The table shows the parts of powder and water used to make gelatin.
Boxes of Gelatin Powder (oz) Water (cups)
3 9 6
8
At this rate, how much powder and water will Jeff use to make 8 boxes of gelatin?
To make 8 boxes of gelatin Jeff used 24 oz of gelatin powder and 16 cups of water.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the given table, we have
Boxes Gelatin Powder (oz) Water (cups)
3 9 6
Here,
Gelatin Powder = 3 × Boxes
Water = 2 × Boxes
The equations for 8 boxes is
Gelatin Powder = 3 × 8
= 24 oz
Water = 2 × 8
= 16 cups
Hence, to make 8 boxes of gelatin Jeff used 24 oz of gelatin powder and 16 cups of water.
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A Statistics Primer A researcher is interested in handedness in ants. (Here, handedness refers to the propensity of individuals to turn more often in one direction than another.) He hypothesizes that if ants show handedness they should be more likely to turn into the right or left arms of a T-maze. He plans to place 20 ants into a maze and use a binomial test to evaluate this hypothesis. When the 20 ants were placed into the maze he observed that 16 of the ants walked into the right arm and that three ants walked into the left arm (one ant managed to crawl over the edge of the maze before it went down either of the arms). (1 point) 5. What is the probability that exactly 16 of the ants enter the right arm when the null hypothesis is true? (1 point) 6. What outcomes are equally extraordinary or more extraordinary than the outcome observed under conditions in which the null hypothesis is true? (Example of a more extraordinary outcome: The outcome in which all 19 ants turn into the right arm and no ants turn into the left arm (19R, OL) is more extraordinary than the outcome he observed.] (1 point) 7. What are the probabilities associated with the outcomes identified in Problem 5 under conditions in which the null hypothesis is true? (Probability for example given in Problem 6: 1 (1 point) 8. What is the probability that an outcome as extraordinary or more extraordinary than the outcome observed would occur when the null hypothesis is true? Be sure to include the observed outcome in this calculation! (This is the P value for the binomial test.) (1 point) 9. Does the observed outcome indicate that the null hypothesis should be rejected at a rejection criterion of 0.05? What do you conclude?
The observed data indicates that the null hypothesis should be rejected at a rejection criterion of 0.05. This means that the data supports the researcher's hypothesis that ants show handedness, and that they are more likely to turn into the right or left arms of a T-maze.
The researcher is interested in determining if ants show handedness.
The researcher is hypothesizing that if ants show handedness, they will be more likely to turn into the right or left arms of a T-maze.The researcher placed 20 ants into the maze and observed that 16 of the ants walked into the right arm and 3 into the left arm (one ant managed to crawl over the edge of the maze before it went down either of the arms). The probability that exactly 16 of the ants enter the right arm when the null hypothesis is true is 0.368. This is calculated using the binomial formula, P(x=16) = (20 choose 16) * (0.5)^16 * (0.5)^4, where 0.5 is the probability of each ant turning into either arm.Outcomes that are equally extraordinary or more extraordinary than the outcome observed under conditions in which the null hypothesis is true include: 17R, 3L; 18R, 2L; 19R, 1L; and 19R, OL.The probabilities associated with the outcomes identified in Problem 5 under conditions in which the null hypothesis is true are: 0.246 for 17R, 3L; 0.127 for 18R, 2L; 0.052 for 19R, 1L; and 0.026 for 19R, OL.The probability that an outcome as extraordinary or more extraordinary than the outcome observed would occur when the null hypothesis is true is 0.451. This is calculated by adding up the probabilities associated with each of the outcomes identified in Problem 5 (0.368 for 16R, 4L, 0.246 for 17R, 3L, 0.127 for 18R, 2L, 0.052 for 19R, 1L, and 0.026 for 19R, OL).
The observed outcome does not indicate that the null hypothesis should be rejected at a rejection criterion of 0.05 since the P value for the binomial test (0.451) is greater than 0.05. Therefore, we cannot reject the null hypothesis and conclude that ants do not show handedness.
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2. În triunghiul ABC, AB=3√7 cm, BC = sqrt(17) cm şi AC= 4√5 cm. Verificați dacă triunghiul este dreptunghic cu catetele AB şi BC.
Answer: it’s b
Step-by-step explanation:
your welcome
draw a triangle in which angleXYZ=30degree, angleYZX=75degree and side YZ=8.5cm
Answer:
see attached
Step-by-step explanation:
You want to draw a triangle with angle measures 30° and 75° at vertices Y and Z, and the length of YZ as 8.5 cm.
Third angleThe third angle of the triangle will be 180° -30° -75° = 75°. This means the triangle is isosceles, and the two congruent sides are both 8.5 cm.
ProtractorOnce you measure the length YZ as 8.5 cm, you can draw angles at 30° and 75° from points Y and Z, respectively. A protractor is a suitable tool for the purpose. The point of intersection of these rays is X, giving you the desired triangle XYZ.
ConstructionA right triangle with hypotenuse 8.5 cm will have the leg opposite the 30° angle as 4.25 cm, half the hypotenuse. This offers opportunities to construct the triangle several ways.
Here's one. Draw an arc (or circle) of radius 8.5 cm centered at point Y. Mark a point Z on the arc. Using the same radius, draw an arc that intersects the first one at point A. Angle ZYA is 60°, as is angle YZA. Now, you can bisect angle ZYA, or segment ZA, or you can simply measure off 4.25 cm on segment ZA. The point halfway between Z and A can be marked point B. Where ray YB intersects the original arc (or circle) centered at Y, is point X of your triangle XYZ.
__
Additional comment
We used a geometry program to draw the triangle in the attachment. It conveniently provided angles with the necessary measures. In terms of the construction described above, the vertex of the right angle is point B.
Another way to start is by identifying right angle lines BZ and BY on grid paper. Once you locate point Z 4.25 cm from B, you can draw an arc centered at Z with radius 8.5 cm that intersects line BY at Y. Then an arc with the same radius centered at Y will identify the location of point X.
Evaluate the expression and write your answer in the form a+bi.
√−25
The express in the form of a + bi would be 0 + 5i.
What is meant by Complex numbers?Complex numbers are those expressed as a + ib, where a, b are real numbers and 'i' is a fictitious number called a "iota." i is equal to (√-1). A pair of real and imaginary numbers combined in the form a + bi.
When a and b are real numbers, a complex number is one with the formula a + bi. The complex number has two parts: real component (a) and imaginary part (b). If both the real and imaginary components of two complex numbers are identical, only then are the two complex numbers equal.
Let the given expression be [tex]$\sqrt{-25}$$[/tex].
We have to evaluate the expression.
[tex]$$\begin{aligned}\sqrt{-25} & =\sqrt{-1 \cdot 25} \\& =\sqrt{-1} \sqrt{25} \\& =i(5) \\& =5 i\end{aligned}$$[/tex]
The express in the form of a + bi = 0 + 5i.
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a function satisfies the differential equation (a) what are the constant solutions of this equation? separate your answers by commas.
The solutions are decreasing when y is in the set (1,3).
(A) Equilibrium solutions, also known as constant solutions, fulfill dy/dx=0.
When the right-hand side of the equation is taken into account, we have
dy/dx equals y2(y-1) (y-3). We get the constant solutions y=0, y=1, and y=3 by setting the right side to zero.
(b) Solutions rise when dy/dx exceeds 0. For the set of y values (-,0) (0,1) (3,) see that dy/dx > 0. Therefore, when y in is the set (-,0) (0,1) (3,), solutions are growing.
(c) When dy/dx 0, solutions are decreasing, and dy/dx 0 when 1 y 3. That is, while y is in the set, solutions are decreasing (1,3).
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What is the sum of the first 20 multiples of five?
Answer:
1050
Step-by-step explanation:
Answer:
the answer is: 1050
Step-by-step explanation:
hope it helped you mark brainliest
. Taylor can cut a standard size lawn in 3 hours. Jamie can do the same job in 2 hours.
If Taylor works twice as many hours as Jamie and they complete 4 lawns, how many hours
does Taylor work?
Let's call the number of hours Jamie works "J" and the number of hours Taylor works "T".
We know from the problem that T = 2 * J, because Taylor works twice as many hours as Jamie.
We also know that J + T = 4 * (3 + 2), because they are working together to complete 4 lawns and it takes 3 hours for Taylor and 2 hours for Jamie to complete one lawn.
So we can substitute the first equation into the second equation:
2J + J = 4 * (3 + 2)
3J = 4 * 5
J = 4
So Jamie works 4 hours and Taylor works 2 * 4 = 8 hours.
Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.
y = 5 (2 Superscript x Baseline)
a.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 1) and approaches x = 1 in quadrant 1.
y-intercept = 1
c.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 2) and approaches x = 1 in quadrant 1.
y-intercept = 1
b.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 1) and (2, 4) in quadrant 1.
y-intercept = 2
d.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 5) through quadrant 1.
Answer: The equation y = 5 * 2^x represents an exponential function where the base is 2 and the y-intercept is 5.
The graph that best fits this equation is:
d. On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 5) through quadrant 1.
y-intercept = 5
So, the correct answer is d.
Step-by-step explanation:
The table below shows how far a person driving in their car was able to go over different intervals of time. Perform a regression to model the data, using the form y = kx + h. What is your value for k? (Round your answer to the nearest tenth.)
Answer:
kxh is the answer to this question
When a chartered accountant (CA) provided his services to Mr. Rao in filing his income
returns, his bill for services was ₹8260 inclusive of 18% GST. What is the original
amount of the bill? How much is the GST paid to the State Government by the CA
The original amount of the bill was $7000 and the GST paid to the State Government by the CA is $1260.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
The bill services including the GST = 8260
and, Rate of GST= 18%
So, let the original amount was x
x+ 18% of x= 8260
x + 0.18x = 8260
1.18x= 8260
x= $7000
and, the GST paid to Govt. = 8260 -7000 = $1260.
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coins are tossed. a. give an example of a simple event. b. give an example of a joint event. c. what is the complement of getting on the coin? d. what does the sample space consist of?
Coin tossing has a simple event of heads or tails, a joint event of multiple coin combinations, the complement of heads is tails, and sample space is {heads, tails}.
a. A simple event in coin tossing is getting either heads or tails on a single coin flip.
b. A joint event in coin tossing is getting heads on one coin and tails on another coin, for example.
c. The complement of getting heads on a coin flip is getting tails. The complement of getting tails is getting heads.
d. The sample space in coin tossing consists of all the possible outcomes of a single coin flip. This can be represented as a set, such as {heads, tails}. The sample space is the set of all possible outcomes of the experiment.
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which expressions are equivalent to 5(x+7)+7(x+5)
Equivalent to 5(x+7)+7(x+5) is expression 12x + 70 .
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given expression
5(x+7)+7(x+5)
Using distributive property
= 5x + 35 + 7x + 35
Adding like terms
= 12x + 70
Hence, expression 12x + 70 is equivalent to 5(x+7)+7(x+5).
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Suppose the demand curve for pencils is QD = 200 - 4P. What is the exact own price elasticity of demand at P-$30?A. -0.67B. -10.67C. -0.09D. -1.5
The exact own price elasticity of demand is (A) -0.67.
The own price elasticity of demand measures the responsiveness of the quantity demanded to changes in price. It can be calculated using the formula:
epsilon = (dQ/dP) * (P/Q)
where dQ/dP is the derivative of the demand curve with respect to price and P/Q is the price elasticity of demand.
In this case, the demand curve is QD = 200 - 4P, so dQ/dP = -4. When P=$30, Q = 200 - 4 * 30 = 140. So,
epsilon = (-4) * (30/140) = -0.67
Hence, the exact own price elasticity of demand at P=$30 is -0.67, so the answer is A. -0.67.
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Write the equation for the linear function shown in the table
Answer:
y = 6x
Step-by-step explanation:
Each value of x is multiplied by 6 to get the corresponding y value
a soup can has a diameter of 278 inches and a height of 414 inches. how many square inches of metal are required to make the soup can?
Are required 482,972.60 in^2 of metal to make the soup can
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2
The formula and procedure to solve this geometry exercise is:
A= (2* π *r * h) + (2 * π * r²)
Where:
A = areah = height r = radiusProblem information:
d = 278 inh = 414 inA = ?Using the formula of the cylinder area we get:
A= (2* π *r * h) + (2 * π * r²)
A= [2* π *(278/2) * 414] + [2 * π * (278/2)²]
A= [2* π *(139) * 414] + [2 * π * (139)²]
A= [2* π *(139) * 414] + [2 * π * (139)²]
A = 361575.18 in^2 + 121397.42 in^2
A = 482,972.60 in^2
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evaluate the expression 4(3-2)^3+2(-8) and justify each step
Answer:-12
Step-by-step explanation: First you will have to deal with the things in parenthesis and the exponent. So after cubing the 3 and 2 the equation you will then multiply and then add them rest of the numbers to get -12
0.800 in fraction form
Answer:8/
Step-by-step explanation: It is because any number after decimal point contains zero at it's end then the number is considered as it is. For example here 0.800 so after decimal point is 8, and after 8 there are zero's. So numerically, it is 0.8 or 0.800 both are same . Hence it's fraction form would be 8/ 10.
Answer:
4/5
Step-by-step explanation:
0.800 = 800/1000 = 8/10 = 4/5
consider a game of nim with four piles, of sizes 9, 10, 11, 12. (a) is this position a win for the next player or the previous player (assuming optimal play)? describe the winning first move. (b) consider the same initial position, but suppose that each player is allowed to remove at most 9 chips in a single move (other rules of nim remain in force). is this an n- or p-position?
This is a position a win for the next player; the first player's winning move is to remove 2 chips from the pile with size 11, and if each player is allowed to remove at most 9 chips in a single move, then this is a P-position, and the previous player has won.
(a) The outcome of a game of Nim depends on the XOR (exclusive or) of the sizes of the piles. The XOR of 9, 10, 11, and 12 is 2, which means that this is a P-position (i.e., the previous player has won).
To determine the winning first move, we must find a combination of pile sizes that results in a new XOR of 0. One way to do this is to remove 2 chips from the pile with size 11, resulting in 9, 10, 9, and 12. The XOR of these new pile sizes is 0, which means that this is an N-position (i.e., the next player will win).
The first player's winning move is to remove 2 chips from the pile with size 11.
(b) The maximum number of chips that can be removed in a single move is 9, so the players are restricted in the amount they can remove. However, the outcome of the game still depends on the XOR of the pile sizes. In this case, the XOR of 9, 10, 11, and 12 is 2, which means that this is still a P-position and the previous player has won.
The winning first move, as described above, would still be to remove 2 chips from the pile with size 11.
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help me pleaseeee i need help
Answer:
see below
Step-by-step explanation:
z+66+z+69+43z=180
so 45z=180-66-69 = 45
so z=1
so angle U= 43 its opposite side length ST is the smallest
same logic for the other 2.
66+1=67
69+1=70
so ST<US <TU
the radius of earth is 6371 km. how many times longer is the diameter of earth than the piece of wood's length? use scientific notation.
The [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.
The radius of earth is 6371 km.
Let's say the length of the piece of wood is L.
The diameter of the Earth is 2 times its radius
The radius of our planet, The Earth, is the distance from the center of the Earth to a point on or near its surface, and it ranges from nearly 6,378 km to nearly 6,357 km.
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. The area and circumference of a circle are also measured in terms of radius.The diameter of a circle is the length of the line starting from one point on a circle to another point and passing through the center of the circle. It is equal to twice the radius of the circle. It is usually denoted by ‘d’ or ‘D’.
Diameter = 2 x RadiusThe diameter of the Earth is 2 times its radius, or 2 x 6371 km = 12742 km.
The diameter of the Earth is 12742 km / L times longer than the length of the piece of wood.
In scientific notation, we can express this as:
12742 km / L = [tex]1.2742*10^4 km / L[/tex]
The [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.
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Yvonne is using Triangle PQR with Altitude QS¯¯¯¯¯ shown below to prove the Pythagorean Theorem.
Given △PQR∼△QSR∼△PSQ, which conclusion about these triangles could Yvonne use in her proof of the Pythagorean Theorem?
Responses
PQQR=QSPS and QRPR=RSQR
P Q Q R = Q S P S and Q R P R = R S Q R
PQPR=PSPQ and QRPR=RSQS
P Q P R = P S P Q and Q R P R = R S Q S
PQPR=PSPQ and QRPR=RSQR
P Q P R = P S P Q and Q R P R = R S Q R
PQQR=QSSR and QSSR=PSQS
P Q Q R = Q S S R and Q S S R = P S Q S
The conclusions with regards to the similar right triangles, Yvonne needs to prove the Pythagorean Theorem are;
PQ/PR = PS/PQ and QR/PR = RS/QR
What is the Pythagorean Theorem?Pythagorean Theorem outlines the relationship between the length of the hypotenuse side and the lengths of the legs of a right triangle. The theorem states that the sum of the squares of the lengths of the legs of a right triangle, is equivalent to the square of the length of the hypotenuse side.
The specified similar triangles are;
ΔPQR ~ ΔQSR ~ ΔPSQ
PQ/PS = PR/PQ...(1)
(PQ)² = PS·PR
QR/RS = PR/QR...(2)
(QR)² = RS·PR
(PQ)² + (QR)² = PS·PR + PR/RS = PR·(PS + RS) = PR×PR = (PR)²
(PQ)² + (QR)² = (PR)²
Equations (1) and (2), can be expressed as follows;
PQ/PS = PR/PQ...(1)
Multiply both sides by PS/PR
PQ/PS × (PS/PR) = PR/PQ × (PS/PR)
PQ/PS × (PS/PR) = PQ/PR
PR/PQ × (PS/PR) = PS/PQ
Therefore;
PQ/PR = PS/PQQR/RS = PR/QR...(2)
Multiplying both sides by (SR/PR). we get;
QR/SR × (RS/PR) = QR/PR
PR/QR × (RS/PR) = RS/QR
QR/PR = RS/QRTherefore, the conclusions about the triangles, Yvonne can use in her proof of the Pythagorean Theorem are;
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write the equation with the least degree and integer coefficients that has the roots listed
3, 2 +-3i
The polynomial function is f(x) = (x - 3)((x - 2)² + 9)
How to determine the polynomial from the zeros?From the question, we have the following parameters that can be used in our computation:
Zeros: x=3, 2 +-3i
The polynomial can be repesented as
f(x) = product of (x - zeros)
using the above as a guide, we have the following:
f(x) = (x - 3)(x - (2 - 3i))(x - (2 + 3i))
This can be expressed as
f(x) = (x - 3)((x - 2)² + 9)
hence, the polynomial is f(x) = (x - 3)((x - 2)² + 9)
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5x - 6 = 44. what is x
Answer:
[tex]5x - 6 = 44 \\ \longrightarrow \: 5x = 44 + 6 \\ \longrightarrow \: 5x = 50 \\ dividing \: both \: sides \: by \: 5 \: \\ \\ \longrightarrow \: \cancel\frac{5x}{5} = \cancel\frac{50}{5} \\ \\ \longrightarrow \:\boxed{ x = 10}[/tex]
hope helpful! :)
Answer:
x = 10
Step-by-step explanation:
5x - 6 = 44. what is x
5x - 6 = 44
add 6 on both sides5x = 50
divide each side by 5x = 10
---------------------
check
5 x 10 - 6 = 44 (remember pemdas)
44 = 44
the answer is good
What is the area of rhombus KLMN? Rhombus 467.4 in 387.6 in 289 in 287.3 in
The area of rhombus KLMN is 287.3 in²
What are rhombuses?A quadrilateral called a rhombus has four equal-length sides. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
Given:
Since, the diagonals of a rhombus bisects each other at a right angle,
Let they bisect at O,
so, KM = 2MO = 2KO = 2×11.4 = 22.8 in
Thus, Δ KON is a right triangle,
Using Pythagoras theorem,
KN² = KO² + ON²
ON = √17²-11.4²
ON = 12.611 in
LN = 2×12.611
LN = 25.22 in
Then, Area of a rhombus = 1/2 × diagonal 1 × diagonal 2
Area = 1/2 × 25.22 × 22.8
= 287.3 in²
Hence, the area of rhombus KLMN is 287.3 in²
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d is inversely proportional to r.
d = 7 when r = = 8
a) Use the information above to write an
equation for d in terms of r.
b) What is the value of d when r =
Give any decimal answers to 1 d.p.
= 5?
Answer: 11.2
Step-by-step explanation:
a) d= k/r
=> 7= k/8
=> k= 7x8
therefore, k=56
b) d=k/r
=> d=56/ 5
so, d= 11.2
The value of d is 7 when r = 5.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
d is inversely proportional to r.
This can be written as,
d ∝ 1/r
d = k/r
Now,
d = 7 when r = = 8
This means.
7 = k/8
k = 56
Now,
Substituting r = 8.
d = 56/8
d = 7
Thus,
d = 7.
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Can anyone factor these equations?
7) The factors of the expression (x² + 17x + 60) is, (x + 5) (x + 12)
8) The factors of the expression (x² - 6x - 27) is, (x + 3) (x - 9)
9) The factors of the expression (2x² - 18x + 28) is, 2 (x - 2) (x - 7)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We can factor as;
7) The factors of the expression (x² + 17x + 60) is,
⇒ x² + 17x + 60
By using quadratic formula as;
⇒ x = - 17 ± √(17² - 4×1×60 / 2
⇒ x = - 17 ± √289 - 240 / 2
⇒ x = - 17 ± √49 / 2
⇒ x = - 17 ± 7 / 2
⇒ x = - 17 + 7 / 2
⇒ x = - 10/2
⇒ x = - 5
And, x = - 17 - 7 / 2
⇒ x = - 24/2
⇒ x = - 12
Thus, The factors of the expression (x² + 17x + 60) is,
⇒ (x + 5) (x + 12)
8) The factors of the expression (x² - 6x - 27) is,
⇒ x² - 6x - 27
⇒ x² - 9x + 3x - 27
⇒ x (x - 9) + 3 (x - 9)
⇒ (x + 3) (x - 9)
Thus, The factors of the expression (x² - 6x - 27) is,
⇒ (x + 3) (x - 9)
9) The factors of the expression (2x² - 18x + 28) is,
⇒ 2x² - 18x + 28
⇒ 2 (x² - 9x + 14)
⇒ 2 (x² - 7x - 2x + 14)
⇒ 2 (x (x - 7) - 2 (x - 7))
⇒ 2 (x - 2) (x - 7)
Thus, The factors of the expression (2x² - 18x + 28) is,
⇒ 2 (x - 2) (x - 7)
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A home was bought 4 years ago. The purchase price was $92,000 and the buyer made a down payment of $11,000. The current loan balance is $79,000. The house was recently appraised for $116,000. What is the equity?
a)13,000
b)24,000
c)35,000
d)37,000
If the current loan balance is $79,000 and the house was recently appraised for $116,000, the equity in the house would be worth d) $37,000.
The home was bought at a price of $92,000 and a down payment of $11,000 was made. It is also given that the current loan balance is $79,000.
Also, the house was recently appraised for $116,000. We are asked to calculate the equity.
Now, equity is defined as the sum of money the owner of an item would receive if they sold it and all associated debts were settled is known as equity. For example, if one person owns a house which has a value of $100,000 and he has a mortgage of $40,000. Then, the equity in the home would be worth $60,000.
Here, in this question, the current debt is $79,000 and the current value of the house is $116,000.
So, the equity in the home would be:
Equity = 116,000 - 79000 = $37,000
Hence, the equity in the house would be worth $37,000.
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Work out the equation of the line shown below.
Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.
An equation of the line shown above in slope-intercept form is y = x/8 + 5/2.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided in the graph above, we have the following data points on its line:
Points on the x-axis = (60, 140).Points on the y-axis = (10, 20).At data point (60, 10), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 10 = (20 - 10)/(140 - 60)(x - 60)
y - 10 = 1/8(x - 60)
y = x/8 - 7.5 + 10
y = x/8 + 5/2
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