The slope-intercept equation of line is -1 and equation will be y = -x - 1.
What is the slope?
m = (y2 - y1) / (x2 - x1) is the formula for calculating slope from two points on a line, (x1, y1) and (x2, y2). Here,
m = the line's slope
x1 is equal to the initial point's x-coordinate.
y1 is the first point's y-coordinate.
x2 is equal to the second point's x-coordinate.
The second point's x-coordinate is equal to y2.
x1 = -3, y1 = 4; x2= -2, y2=3
m = (3-4)/(-2 - (-3))
= -1 / (-2+3)
= -1/1
m = -1
Substitute the value in given equation:
y = -x + (-1)
y = -x - 1
Hence, the slope-intercept equation of line is -1 and equation will be y = -x - 1.
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Can someone help me with this, please?
Learning Task 2: Try to solve the following problem. Use the block model
to help you. Write your answer in your notebook.
1) Ruben can paint square meters per hour. At the same rate, how
many square meters can he paint in an hour.
1
2 6
1
2 2
2) The lot has a length of meters and a width of meters. The
piece of lot per square unit is ₱ 850. 0. What is the total value of the lot?
Answer: Problems Involving FractionsIn solving word problems, first, identify what is asked. Then, look for the given facts. Establish the number sentence and the operation/s to be used. Make sure that the operation/s used will bring out the correct answer. Check the answer using the number sentence and see if it will satisfy the given condition.
Step-by-step explanation: Learning Task 2:Answers:16 1/4 square meters₱322,362.50Step-by-step explanation:Solutions:1. Given: 6 1/2 square meters - area which Ruben can paint in an hour
what is the range and domain of y = 3x^2 + 2?
The domain of the function is (-∞, ∞) and the range of the function is [2, ∞).
Define range!In mathematics, the range of a function refers to the set of all possible output values (dependent variable) that the function can produce for its corresponding input values (independent variable).
According to question:The given function is y = 3x² + 2.
The domain of a function is the set of all possible values of the independent variable (x) for which the function is defined. Since the given function is a polynomial function, it is defined for all real numbers.
Therefore, the domain of the function y = 3x² + 2 is (-∞, ∞), which means that the function is defined for all real values of x.
The range of a function is the set of all possible values of the dependent variable (y) that the function can take. In this case, the function is a quadratic function with a leading coefficient of 3, which means that the parabola opens upwards and its vertex is at the point (0,2).
Since the minimum value of the function is 2, the range of the function is [2, ∞).
Therefore, the domain of the function is (-∞, ∞) and the range of the function is [2, ∞).
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When adding or subtracting mixed numbers with like denominators, the numerators ___ , but the denominators ______ .
A. Stay the same
B. change
Answer:
Yo, when you adding or subtracting mixed numbers with the same denominators, the numerators stay chill, they don't change, bro.
But the denominators, they also stay the same, man. It's like keeping things consistent, ya feel me? So the answer is A, dude. Numerators stay put, denominators stay put. It's all good vibes, bro! ✌️
a scientist claims that the mean gestation period for a fox is more than 48.9 weeks. if a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? g
The rejection of the null hypothesis in a hypothesis test that claims the mean gestation period for a fox is more than 48.9 weeks implies there is sufficient evidence to support the claim, indicating a statistically significant difference between the observed sample mean and the hypothesized mean.
If a hypothesis test is performed that rejects the null hypothesis that the mean gestation period for a fox is 48.9 weeks or less, it means that there is sufficient evidence to support the claim that the mean gestation period for a fox is more than 48.9 weeks.
The rejection of the null hypothesis implies that the observed sample mean is significantly different from the hypothesized mean, and this difference is unlikely to have occurred by chance alone. The statistical test used to evaluate the hypothesis would have produced a p-value less than the significance level, indicating that the evidence against the null hypothesis is strong.
Therefore, the scientist can conclude that there is evidence to support their claim that the mean gestation period for a fox is more than 48.9 weeks, and this finding could have important implications for understanding fox reproductive biology and management.
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write an integral that quantifies the change in the area of the surface of a cube when its side length quadruples from s unit to 4s units.
Answer:
Step-by-step explanation:
Let A be the area of the surface of the cube.
When the side length changes from s to 4s, the new area A' can be calculated as:
A' = 6(4s)^2 = 96s^2
The change in area is then:
ΔA = A' - A = 96s^2 - 6s^2 = 90s^2
To find the integral that quantifies the change in area, we can integrate the expression for ΔA with respect to s, from s to 4s:
∫(90s^2)ds from s to 4s
= [30s^3] from s to 4s
= 30(4s)^3 - 30s^3
= 1920s^3 - 30s^3
= 1890s^3
Therefore, the integral that quantifies the change in area of the surface of a cube when its side length quadruples from s units to 4s units is:
∫(90s^2)ds from s to 4s
= 1890s^3 from s to 4s
= 1890(4s)^3 - 1890s^3
= 477,840s^3 - 1890s^3
Solve for X, please write an explanation.
Step-by-step explanation:
2x+20 and 2x-4 are supplementary angles...they form a straight line and thus = 180 degrees when added together
2x+20 + 2x-4 = 180 simplify
4x + 16 = 180 subtract 16 from both sides
4x = 164 divide both sides by 4
x = 41 degrees
Find the distance, d, of AB.
The distance between A and B is approximately 8.06 units.
In order to find the distance, d, of AB, we need to use the distance formula. The distance formula gives us the distance between two points in a coordinate plane. It is given as:$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where (x1, y1) and (x2, y2) are the coordinates of the two points in question.
In this case, A and B are the two points for which we need to find the distance. Let's assume that the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2).
Then the distance formula becomes:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
$$d = \sqrt{((8 + 4) - 2)^2 + ((5 - 1) - 3)^2}$$
$$d = \sqrt{(10 - 2)^2 + (4 - 3)^2}$$
$$d = \sqrt{(8)^2 + (1)^2}$$
$$d = \sqrt{64 + 1}$$
$$d \approx \sqrt{65}$$
$$d \approx 8.06$$
Therefore, the distance between A and B is approximately 8.06 units.
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When x is 2, what is the value of the expression 124+3(8−x)12
12
4
+
3
(
8
−
x
)
12
?
When x is 2, the value of the expression is 9.
Describe Algebraic Expression?An algebraic expression is a mathematical phrase that contains one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can also contain exponents, roots, and trigonometric functions.
Algebraic expressions are used to represent mathematical relationships and solve problems in a wide range of fields, including physics, engineering, finance, and statistics. They can be used to model real-world phenomena and to make predictions based on data.
Algebraic expressions can be simplified by combining like terms and using mathematical rules and properties. They can also be evaluated by substituting values for the variables and simplifying the expression. Solving equations involving algebraic expressions often involves manipulating the expression to isolate a variable and find its value.
When x is 2, the value of the expression 12/4+3(8−x)-12 can be found by substituting 2 for x and simplifying the expression:
12/4 + 3(8 - 2) - 12
= 3 + 3(6) - 12
= 3 + 18 - 12
= 9
Therefore, when x is 2, the value of the expression is 9.
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The complete question is :
When x is 2, what is the value of the expression 12/4+3(8−x)-12?
HLEP me please with math
For the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.
Explain about the scale factor:On a map, scales are frequently present. The scale factor in geography usually applies to how accurately the scale depicted on the map reflects actual distance. Find the corresponding sides upon that two figures before obtaining the scale factor.
Then, divide the new figure's measurement by the old figure's measurement. Your scale factor, i.e., how many times bigger or less than your new image is in comparison to the old, is the consequence.
From the diagram:
coordinate of A = (1,1)
coordinate of A' = (5,5)
Thus, the coordinates of A is multiplied by 5 to get the coordinates of A'
Same applies with the coordinates of B, C and D.
Thus, for the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.
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5 × (10 + 7) = (5 × 10) + (5 ×7)
Answer:
Same equation just using the assocaitive property
Step-by-step explanation:
For example, 8 + (2 + 3) = (8 + 2) + 3 = 13
Hope this helps! =D
Solve Triangle
Because I Need Answer My Assignment:-)
Good Perfect Complete=Brainlist
Copy Wrong Incomplete=Report
Good Luck Answer Brainly Users:-)
Answer:
x = 4√5 ≈ 8.94 (2 d.p.)
y = 8√5 ≈ 17.89 (2 d.p.)
Step-by-step explanation:
To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).
Geometric Mean Theorem (Leg Rule)The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.
[tex]\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}[/tex]
From inspection of the given right triangle RST:
Altitude = SVHypotenuse = RT = 20Leg 1 = RS = ySegment 1 = RV = 16Leg 2 = ST = xSegment 2 = VT = 4Substitute the values into the formulas:
[tex]\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}[/tex]
Solve the equation for x:
[tex]\implies \dfrac{20}{x}=\dfrac{x}{4}[/tex]
[tex]\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}[/tex]
[tex]\implies 80=x^2[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{80}[/tex]
[tex]\implies x=\sqrt{80}[/tex]
[tex]\implies x=\sqrt{4^2\cdot 5}[/tex]
[tex]\implies x=\sqrt{4^2}\sqrt{5}[/tex]
[tex]\implies x=4\sqrt{5}[/tex]
Solve the equation for y:
[tex]\implies \dfrac{20}{y}=\dfrac{y}{16}[/tex]
[tex]\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}[/tex]
[tex]\implies 320=y^2[/tex]
[tex]\implies \sqrt{y^2}=\sqrt{320}[/tex]
[tex]\implies y=\sqrt{320}[/tex]
[tex]\implies y=\sqrt{8^2\cdot 5}[/tex]
[tex]\implies y=\sqrt{8^2}\sqrt{5}[/tex]
[tex]\implies y=8\sqrt{5}[/tex]
A rock of radioactive material has 500 atoms in it. The number of atoms decreases at a rate of 11% a day. Write an exponential function that models this situation. f(x) type your answer... (1 choose your answer... choose your answer... ✓)^x
Answer:
[tex]f(x) = 500( {.89}^{x} )[/tex]
PLEASE HELP!! ITS TIMED! WILL GIVE BRAINIEST TO THE FIRST CORRECT ANSWER!
Elijah bought earrings to give to his mother for her birthday. The earrings are in a case
shaped like a rectangular prism that is 2 inches long, 1½ inches wide, and 1 inches tall. He
doesn't want his mother to guess what the gift is, so he put the case in a larger, cube-shaped
gift box. The gift box is 4 inches along each edge.
What is the volume of the extra space left in the gift?
Answer:
The answer is 59 ½
Step-by-step explanation:
4×4×4-2×1 ½×1 ½
= 64 - 2× 3/2 × 3/2
= 64 - 9/2
= 128/2 - 9/2
= 119/2
= 59 ½ in3
Hope this helped :)
The equation ( x + 6)^2 + ( y + 4) ^2 = 36 models the position and range of the source of a radio signal.
1. Where is the signal located?
2. What is the range of the signal? Only enter numerical values.
1) The equation (x + 6)² + (y + 4)² = 36 represents a circle centered at the point (-6, -4) with a radius of 6. Therefore, the signal is located at the point (-6, -4).
What is the range of the signal?2) The range of the signal refers to the maximum distance that the signal can travel before it becomes too weak to be detected. In this case, the range of the signal is equal to the radius of the circle, which is 6. This means that any point on the circle (x + 6)² + (y + 4)² = 36 is 6 units away from the signal located at (-6, -4).
To visualize this, imagine the signal as a point source located at (-6, -4), and the range of the signal as a circle centered at the signal with a radius of 6. Any point on this circle represents the farthest distance that the signal can reach and still be detected.
In summary, the signal is located at (-6, -4) and its range is 6 units, as represented by the circle (x + 6)² + (y + 4)² = 36.
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If you watch from ground level, a child riding on a merry-go-round will seem to be undergoing simple harmonic motion from side to side. Assume the merry-go-round is 10.6 feet across and the child completes 8 rotations in 120 seconds. Write a sine function that describes d, the child's apparent distance from the center of the merry-go-round, as a function of time t.
The sine function that describes the child's apparent distance from the center of the merry-go-round is d(t) = 5.3 sin(2π/15 * t)
How to write a sine function that describes the child's apparent distance?To write a sine function that describes the child's apparent distance from the center of the merry-go-round as a function of time t, we can start by finding the amplitude, period, and phase shift of the motion.
Amplitude:
The amplitude of the motion is half the diameter of the merry-go-round, which is 10.6/2 = 5.3 feet. This is because the child moves back and forth across the diameter of the merry-go-round.
Period:
The period of the motion is the time it takes for the child to complete one full cycle of back-and-forth motion, which is equal to the time it takes for the merry-go-round to complete one full rotation.
From the given information, the child completes 8 rotations in 120 seconds, so the period is T = 120/8 = 15 seconds.
Phase shift:
The phase shift of the motion is the amount of time by which the sine function is shifted horizontally (to the right or left).
In this case, the child starts at one end of the diameter and moves to the other end, so the sine function starts at its maximum value when t = 0. Thus, the phase shift is 0.
With these values, we can write the sine function that describes the child's apparent distance from the center of the merry-go-round as:
d(t) = 5.3 sin(2π/15 * t)
where d is the child's distance from the center of the merry-go-round in feet, and t is the time in seconds. The factor 2π/15 is the angular frequency of the motion, which is equal to 2π/T.
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answer the following
Answer:
6 inches
Step-by-step explanation:
Using the graph, determine the equation of the axis of symmetry.
Step-by-step explanation:
x = -4 ( the value of the x-coordinate of the vertex is the axis of symmetry for normal up or down opening parabolas)
Chase is moving and must rent a truck. There is an initial charge of $35 for the rental plus a fee of $2.50 per mile driven. Make a table of values and then write an equation for C,C, in terms of m,m, representing the total cost of renting the truck if Chase were to drive m miles.
The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
What is the equation?Equation: A declaration that two expressions with variables or integers are equal.
In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
The equation would be:
C is the total cost and m is the miles driven.
We know that:
Charge of the truck: $35
Charge per mile: $2.50
Then, form the equation as follows:
C = 35 + 2.50m
Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
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Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians. (Enter your answers as a comma-separated list.)
(a)
3/4
The two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.
What is coterminal angles ?Coterminal angles are two or more angles that have the same initial and terminal sides, but differ by a multiple of 360 degrees or 2π radians. In other words, coterminal angles are angles that overlap each other when drawn in standard position (with their initial side on the positive x-axis).
To find two coterminal angles with 3/4 radians, we can add or subtract multiples of 2π radians (which is equivalent to a full circle).
One positive coterminal angle is obtained by adding 2π radians to 3/4 radians:
3/4 + 2π = 3/4 + 8π/4 = 3/4 + 2π
Simplifying, we get:
3/4 + 2π = (3π + 4)/4
Therefore, one positive coterminal angle is (3π + 4)/4 radians.
One negative coterminal angle is obtained by subtracting 2π radians from 3/4 radians:
3/4 - 2π = 3/4 - 8π/4 = 3/4 - 2π
Simplifying, we get:
3/4 - 2π = (-5π + 4)/4
Therefore, one negative coterminal angle is (-5π + 4)/4 radians.
Hence, the two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.
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Select the correct answer. Sides of three square rooms measure 14 feet each, and sides of two square rooms measure 17 feet each. Which expression shows the total area of these five rooms? A. (3 × 14^2) + (2 × 17^2) B. (2 × 14^3) + (2 × 17^2) C. (3 × 17^2) + (2 × 14^2) D. (3 × 14^2) × (2 × 17^2) Reset Next
The correct expression showing the total area of the five rooms is A. (3 x 14²) + (2 x 17²), which simplifies to 1918 square feet.
What is expression?An expression is a combination of numbers, symbols, and operators (such as addition, subtraction, multiplication, and division) that represent a mathematical calculation. An expression can be a single number, a variable, or a combination of both, and can be used to represent mathematical formulas, equations, or relationships.
In the given question,
C. (3 × 17²) + (2 × 14²)
To find the total area of the five rooms, we need to add the area of each room. The area of a square is found by squaring the length of one side.
For the three rooms with sides of 14 feet each, the area of each room is:
14^2 = 196 square feet
So the total area of these three rooms is:
3 × 196 = 588 square feet
For the two rooms with sides of 17 feet each, the area of each room is:
17^2 = 289 square feet
So the total area of these two rooms is:
2 × 289 = 578 square feet
Therefore, the total area of all five rooms is:
588 + 578 = 1166 square feet
Option C, (3 × 17²) + (2 × 14²), gives the correct expression for this calculation.
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what minus 1 1/2 equals 3 3/4
Answer:
5 1/4
Step-by-step explanation:
Graph Y = 1/2x - 4 on the coordinate plane
The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.
Describe Coordinate Plane?Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.
Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.
For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.
The graph is shown below when y=1.
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Graph attached below,
The coordinates of the plane is
x y
1 -3.5
2 -3
4 -2
6 -1.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is y = [tex]\frac{1}{2}x-4[/tex].
Now put x= 1 then y = [tex]\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5[/tex]
Now put x=2 then [tex]y=\frac{1}{2}\times2-4=1-4=-3[/tex]
Now put x=4 then [tex]y=\frac{1}{2}\times4-4=2-4=-2[/tex]
Now put x=6 then [tex]y=\frac{1}{2}\times6-4=3-4=-1[/tex]
Then coordinates of the plane is
x y
1 -3.5
2 -3
4 -2
6 -1.
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Determine the density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm3.
The density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm³ is 0.5 grams.
What do you mean by the density of an object?Density is a fundamental physical property that measures the amount of matter (mass) packed into a particular space (volume). The mathematical definition of density is simply the mass of an object divided by its volume. Density is typically measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). One crucial aspect of density is that it is an intrinsic property of a substance, meaning it is a characteristic that depends solely on the material and is not affected by the amount of the substance. By using density, we can identify the material a particular object is made of. For example, a piece of gold will have a higher density than a piece of silver because gold is a more dense metal. Additionally, the density of an object can be used to determine its buoyancy in a fluid. Objects with a higher density will sink in a fluid with a lower density, while objects with a lower density will float.
Density is defined as the amount of mass per unit of volume. Mathematically, it can be represented as:
Density = Mass/Volume
Substituting the given values, we get:
Density = 6 grams/12 cm³
Density = 0.5 grams/cm³
Therefore, the density of the sample is 0.5 grams/cm³.
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Maggie spent $18. 00 Of $30. 00 In her wallet which decimal represents the fraction of the $30. 00 Maggie spent
The decimal that represents the fraction of the $30.00 Maggie spent is 0.6.
Now, let's talk about decimals. Decimals are a way of expressing parts of a whole number in a fraction of 10. For example, 0.5 is the same as 1/2. In your situation, Maggie spent $18.00 out of $30.00. To figure out what decimal represents the fraction of the $30.00 Maggie spent, we need to divide the amount she spent by the total amount she had.
So, we can write this as a fraction:
$18.00 / $30.00
To turn this fraction into a decimal, we divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.
$18.00 / $30.00 = 0.6
Another way to say this is that Maggie spent 60% of the money she had in her wallet.
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Find the measures of angle a and B. Round to the
nearest degree.
The measure of angle A and B is 29° and 61° respectively
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
The opposite is 6 and the adjascent = 11
Therefore tan (tetha) = 11/6 = 1.833
tetha = tan^-1( 1.833)
= 61°( nearest degree)
The sum of angle in a triangle is 180°
therefore,
angle A = 180-( 61+90)
= 180-151
= 29°
therefore the measure of angle A and B is 29° and 61° respectively.
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I don’t know what to write for the equation.
fraction wise, a whole is always simplified to 1, so
[tex]\cfrac{4}{4}\implies \cfrac{1000}{1000}\implies \cfrac{9999}{9999}\implies \cfrac{17}{17}\implies \text{\LARGE 1} ~~ whole[/tex]
so, we can say the whole of the players, namely all of them, expressed in fourth is well, 4/4, that's the whole lot, and we also know that 3/4 of that is 12, the guys who chose the bottle of water
[tex]\begin{array}{ccll} fraction&value\\ \cline{1-2} \frac{4}{4}&p\\[1em] \frac{3}{4}&12 \end{array}\implies \cfrac{~~ \frac{4 }{4 } ~~}{\frac{3}{4}}~~ = ~~\cfrac{p}{12}\implies \cfrac{~~ 1 ~~}{\frac{3}{4}} = \cfrac{p}{12}\implies \cfrac{4}{3}=\cfrac{p}{12} \\\\\\ (4)(12)=3p\implies \cfrac{(4)(12)}{3}=p\implies 16=p[/tex]
If anyone is reading this, rn i would be so flipping happy if u got this for me ive been waiting for so long and got nothing please answer correctly please
Answer: The answer is A.
Step-by-step explanation: Because I am smart don't underestimate me.
Answer:
C
Step-by-step explanation: (look at attachment)
3x + 4 = -2x -2
By looking at the y-intercepts, you automatically know the answer is C.
The y-intercept of the pink line is 4 because of 3x + 4.
The y-intercept of the blue line is -2, because of -2x - 2.
Need help ASAP
there are 600 poetry books at the library.Of the poetry books,8 1/2% are for children.How many poetry books at the library are for children
The answer is 24. To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.
What is number?Numbers are often used to measure and compare objects, and they can be used to solve problems and make predictions.
8 1/2% is equal to 0.04.
To calculate the number of poetry books for children, multiply 0.04 by 600.
0.04 x 600 = 24
To find the number of poetry books for children, the decimal equivalent of 8 1/2% needs to be multiplied by the total number of poetry books.
In conclusion, 8 1/2% of 600 poetry books is equal to 24 books.
To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.
Then, the decimal needs to be multiplied by the total number of poetry books. This will give the answer, which can be rounded down if necessary.
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April is considering a 7/23 balloon mortgage with an interest rate of 4.15% to
purchase a house for $197,000. What will be her balloon payment at the end
of 7 years?
OA. $173,819.97
OB. $170,118.49
OC. $225,368.29
OD. $170,245.98
SUBMIT
The balloon payment at the end of 7 years would be $173,819.97, which is option A.
How to find the balloon payment at the end of 7 yearsA 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.
To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:
n = 23 * 12 = 276 (total number of payments)
r = 4.15% / 12 = 0.003458 (monthly interest rate)
P = (r * PV) / (1 - (1 + r)^(-n))
where
PV is the present value of the loan (the loan amount)n is the total number of paymentsr is the monthly interest ratePV = $197,000
P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)
Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.
Using the formula for the remaining balance of a loan after t payments:
B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)
Where
B is the remaining balancePV is the initial loan amount r is the monthly interest rateP is the monthly payment t is the number of payments madet = 84 (number of payments made)
B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)
B = $173,819.97
Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.
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Alfred buys a car for £13960 which depreciates in value at a rate of 0.75% per year.
Work out how much Alfred's car will be worth in 12 years.
Answer:
£12063.57
Step-by-step explanation:
The value of Alfred’s car after 12 years can be calculated using the formula for exponential decay: Final Value = Initial Value * (1 - rate of depreciation)^(number of years). Plugging in the values we get: Final Value = 13960 * (1 - 0.0075)^12. Therefore, after 12 years, Alfred’s car will be worth approximately £12063.57.