Using proportions, the coordinates of the point 3/10 of the way from (-3,-8) to (12,6) are: (1.5, -3.8).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
We want a point C 3/10 of the way from A(-3,-8) to B(12,6), hence:
C - A = 3/10(B - A).
The x-coordinate of the point is found as follows:
x + 3 = 3/10(12 + 3)
x + 3 = 4.5
x = 1.5.
The y-coordinate of the point is found as follows:
y + 8 = 3/10(6 + 8)
y + 8 = 4.2
y = -3.8.
Hence the coordinates are: (1.5, -3.8).
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The depth and the corresponding pressure form an arithmetic sequence, where the depth
represents the number of the term and the corresponding distance represents the value of
the term. What is the pressure, in pounds per square inch, that a scuba diver will
experience when they are 130 feet underwater?
Answer:
40 psi
Step-by-step explanation:
We can see that the relationship is linear with pressure increasing by 5 psi for every extra 15 feet depth
The data is given from depth of 40 feet
At 40 feet, pressure = 10 psi
At 55 feet, pressure = 15 psi
At 70 feet pressure = 20 psi
We have to use 40 as the base depth since there are no measurements less than that value. So relative depth is d - 40 and since for every 15', there is an increase of 5psi, the relative increase in pressure per 15' is [tex]= \dfrac{d-40}{15}\cdot 5[/tex]
But the base pressure is 10psi not 0 so we have to add 10 to this equation to get the absolute psi
So the equation that connects depth (d) and pressure (p) is:
[tex]p = \dfrac{d - 40}{15}\cdot 5 + 10\\\\\textrm{At 130' depth},\\p = \dfrac{130-40}{15}\cdot 5 + 10\\= \dfrac{90}{15}\cdot 5 + 10\\\\= 30 + 10 = 40 psi\\[/tex]
If we plot these values, we can see they fit a straight line with slope = 1/3 and y-intercept = -10/3
Hope that helps
Type in one, none or infinite
What is 4x -2 = -12
[tex]4x-2=-12\\\\4x=-10\\\\\frac{4x}{4} =\frac{-10}{4} \\\\x=\boxed{-\frac{5}{2} }[/tex]
Simplify each expression. 3[2(x-3)+2]+5(x-3)
The simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3) is 12x - 63.
According to the given question.
We have an expression 3[2(x - 3) + 2] + 5(x - 3).
To simplify the above expression we will use the distributive law and add and subtract the like terms.
Therefore,
3[2(x - 3) + 2] + 5(x - 3)
= 3[2x - 6 + 5x - 15] (distributive rule)
= 3[7x - 21] (adding the like terms)
= 21x - 63
Therefore, the simplified form of the given expression 3[2(x - 3) + 2] + 5(x - 3) is 12x - 63.
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5. A rock is thrown straight up from a 224-foot tall cliff. The height of the rock as a
function of time is given by the equation h(t) = -16t² + 80t+224. How many
seconds until the rock hits the ground?
By finding the positive root of the quadratic equation, we conclude that the rock will hit the ground 7 seconds after it is thrown.
How many seconds until the rock hits the ground?
We know that a rock is thrown from a cliff whose height is 224 ft. And the equation that models the height of the rock as is the quadratic equation:
h(t) = -16t² + 80t + 224
The rock will reach the ground when its height is equal to zero, so what we need to find is the positive root of the quadratic equation, so what we need to solve is:
-16t² + 80t + 224 = 0
Solving it we get:
t = (-80 ± √(80² - 4*(-16)*224)/(2*-16)
t = (-80 ± 144)/(-32)
The positive solution is:
t = (-80 - 144)/(-32) = 7
This means that the rock will hit the ground 7 seconds after it is thrown.
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The equation 8x − 12 = 4x represents two cars traveling in opposite directions, where x represents the distance in miles between the cars. what is the distance, in miles, between the cars? x = 48 x = 30 x = 3 x = 1
Answer:
its option C: x = 3
Step-by-step explanation:
The distance between the cars, x = 3 miles
The equation representing two cars traveling in opposite directions is given by, 8x-12 = 4x,
where 'x' is the distance (in miles) between the cars.
We need to find 'x'.
The equation given is a linear equation in x. So we will solve for 'x'.
8x-12 = 4x
⇒ 8x-4x = 12
⇒ 4x = 12
⇒ x = 12/4
⇒ x = 3
So the distance between the cars = 3 miles
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What is the probability that a randomly chosen diameter is greater than or equal to 10?
probability that a randomly chosen colony diameter is greater than or equal to 10 =P(10<X<12)+P(12<X<14)
=0.14+0.02 = 0.16
What is probability?
Probability is basically how likely something is to happen. Whenever we're uncertain around the outcome of an occasion, ready to talk approximately the probabilities of certain outcomes—how likely they are. The analysis of occasions administered by probability is called statistics.
Probability may be a measure of the probability of an event to occur. Numerous events cannot be predicted with add up to certainty. Able to predict as it were the chance of an occasion to happen i.e. how likely they are to happen, using it.
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Solve each system by substitution.
4y - 6 = 2x , y - 3x = 9
Using substitution method, the solution of the given system of equations is (-3,0)
A system of equation can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations:
4y - 6 = 2x ............ (1)
y - 3x = 9 .............. (2)
We need to find the solution using substitution method.
In equation (2), add 3x to both sides:
y - 3x + 3x = 9 + 3x
y = 9 + 3x ........ (3)
Substitute y = 9 + 3x into equation (1):
4y - 6 = 2x
4.(9 + 3x) - 6 = 2x
36 + 12x - 6 = 2x
12x - 2x = 6 - 36
10x = -30
x = -3
Substitute back x = -3 into equation (3)
y = 9 + 3x
= 9 + 3.(-3)
= 9 + (-9) = 0
Hence, the solution is (-3, 0)
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(5x + 9) + (8x - 30) = 180
Hello and Good Morning Afternoon:
Let's take this problem step-by-step:
[tex](5x + 9) + (8x-30)=180\\\\\text{Take out the parentheses as they are unnecessary to solve this problem}\\5x + 9+8x-30=180\\\\\text{Combine like terms like variables to variables and constants to constants}\\5x + 8x + 9-30 = 180\\13x - 21=180\\13x = 201\\x = 15.46 \text{ or }\dfrac{201}{13}[/tex]
Answer: 15.46 or 201/13
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Which angles are obtuse?
D
AB
C
Check all that apply.
A. ZMLK
B. ZGFE
C. ZDBC
D. ZOBA
K
G
24
H
PREVIOUS
M
SUBMIT
Answer:
dbc
Step-by-step explanation:
thats the only one that is obtuse
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.
The given statement is False. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.
Euclidean geometry a mathematical system in which we study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid.
Parallel Postulate is one of the five postulates of Euclidean geometry. It is Euclid's fifth postulate which states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.
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Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 10+7+4+ . . . ; n=5
The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.
The given arithmetic series is 10+7+4+ . . .
The summation notion of given series is ∑10-3n , here n starts from 0.
The sum of arithmetic series can be written as,
[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]
n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.
We have, n=5, [tex]a_{1}[/tex] = 10
To calculate sum of arithmetic series, we need to find [tex]a_{5}[/tex] .
[tex]a_{5} = a_{1} + (n-1)d[/tex]
d = -3 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{5}[/tex] = 10 + (5-1)(-3)
[tex]a_{5}[/tex] = 10-12 =-2
On substituting values in sum of arithmetic series formula, we get
[tex]S_{5}[/tex] = (5(10 + (-2)))/2 = 20
The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.
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Find the sum: 435,098 + 37,987
Answer:
473085 is the answer
Step-by-step explanation:
Hope it helps you
28-6x+4=30-3x what is the answer ?
Answer: x=2/3
Step-by-step explanation:
Solve z3 = 27.
please help due in 1 hour
whoever gets it right gets a crown
Answer:
z = 9
Step-by-step explanation:
Divide both sides by 3 to get z by itself
What 8.1+2.53 with shown work
Answer:
10.63
Step-by-step explanation:
Simplify each rational expression. State any restrictions on the variable. x²+4 x+3 / x²-3 x-4
Just like polynomials and other expressions, you can perform basic arithmetic operations on rational expressions: addition, subtraction, multiplication, and division. A rational expression is a fraction whose numerator and the denominator is a polynomial. If f is a logical expression, then we can write f in the form of p/q, where p and q are polynomials.
Solution:
To find the restriction on a variable in the denominator, we Set the denominator equal to zero. Then we solve for X
So,
X+1 = 0
X = -1
X-4 = 0
X = 4
When we put the X= -1 or X= 4, we get 0 in the denominator, so these are restrictions variables
= (x2+4x+3)/(x2-3x-4)
= (x+1) (x+3)/(x+1) (x-4)
Now cancel the common factor (x+1)
= x+3x-4
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Which angles of rotation will map the figure onto itself? Explain your reasoning
and/or show your work.
The graph of the equation y= f(x) passes through the points (0,2), (2,4), (4,6), and (7,9). What is the value of y in the equation y= f(2)
The answer is 4. The generalized equation is y = f(x). So when the coordinate of x is 4, value of y is 2
Graph of the equation y= f(x) passes through the points (0,2), (2,4), (4,6), and (7,9).
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
The coordinate plane comprises a horizontal line (x-axis) and a vertical line (y-axis), and it is divided into four quadrants named using roman numbers (I, II, III and IV).
The different points in a graph have coordinates written as ordered pairs (pairs of numbers within parentheses separated by a comma). The first number in an ordered pair (x, y) represents the value of x, and the second one represents the value of y for a given point.
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Mohammad leaves home walks 5 blocks to the library. he then walks 2 blocks toward home to meet up with his friend. together, he and his friend walk to the library together. how far did mohammad walk?
If Mohammad leaves home walks 5 blocks to the library and he then walks 2 blocks toward home to meet up with his friend and then together, he and his friend walk to the library together, then Mohammad walked for 9 blocks.
To calculate how far Mohammad walked we use addition.
Total blocks Mohammad walked = blocks to the library + blocks towards home to meet up with friend + blocks back to the library together
blocks to the library = 5
blocks towards the home to meet up with friend = 2
blocks back to the library together = 2 (As he walked 2 blocks towards home from the library, he will walk the same number of blocks again to reach the library)
Therefore,
total blocks Mohammad walked = 5 + 2 + 2
total blocks Mohammad walked = 9
Hence, the number of blocks Mohammad walked for is calculated to be 9.
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A triangle has vertex coordinates (0,0) and (a, 0) . If the coordinates of the third vertex are in terms of at, and the triangle is isosceles, identify the coordinates and position the triangle on the coordinate plane.
The coordinate of another point will be (a/2,y) where y can be any value.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
An isosceles triangle is a triangle whose two sides are equal.
Let's say AB = AC
So,
Distance associate to AB = Distance associate to AC
(x- 0)² + (y - 0)² = (x - a)² + (y - 0)²
x² + y² = (x - a)² + y²
x = a/2
So the coordinate of the third vertex is (a/2,y)
Hence "The coordinate of another point will be (a/2,y) where y can be any value".
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HELP ME WITH THIS QUESTION PLS
Answer:
49π in²
Step-by-step explanation:
Formula for Area of a Circle: A = πr²
The image shows the radius (r) = 7in
A = πr² → A = π(7)²→ A = π(49)
A = 153.94 in²
Step-by-step explanation:
Area of circle with radius of r is given by:
[tex] a = \pi {r}^{2} \\ a = 49\pi {(in)}^{2} \\ or \: \: a = 153.9 \: {(in)}^{2} [/tex]
Kelly is designing a new quilt. It will be made of squares that are sewn together at the sides with a circle sewn on top of each square. a. Kelly decides that the quilt will be a rectangle 7ft 4in by 6ft 5in. How many squares will she need to make for the quilt? Round the answer to the nearest tenth, if necessary.
Answer:
14ft 8in by 12ft 10in
Solve the equation x²+10 x+40=5 by completing the square.
So we are provided with the equation,
x2 + 10x + 40 = 5
To simplify it, we will first reorder the terms,
40 + 10x + x2 = 5
Now we will solve the equation to find the value of the unknown variable that we declared here as x.
40 + 10x + x2 = 5
Solving for variable 'x.'
40 + -5 + 10x + x2 = 5 + -5
We will combine similar terms; the variables and the constants.
40 + -5 = 35
35 + 10x + x2 = 5 + -5
Combine the like terms again:
5 + -5 = 0
35 + 10x + x2 = 0
Adding -35 on both sides
35 + 10x + -35 + x2 = 0 + -35
35 + -35 + 10x + x2 = 0 + -35
35 + -35 = 0
0 + 10x + x2 = 0 + -35
10x + x2 = 0 + -35
0 + -35 = -35
10x + x2 = -35
The x term is 10x.
Take half its coefficient (5) to make it a perfect square.
Square it (25) and add it to both sides.
10x + 25 + x2 = -35 + 25
25 + 10x + x2 = -35 + 25
-35 + 25 = -10
25 + 10x + x2 = -10
Perfect square on the left side:
(x + 5) (x + 5) = -10
We can see that the Square root of the right side can’t be calculated.
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An angle is a figure formed by two rays with a common initial point called a
of the angle.
An angle is a figure formed by two rays with a common initial point called a of the angle.
What does a math angle mean?
When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.What is type of angle ?
There are three different types of angles in geometry: acute angles, which range from 0 to 90 degrees. Right angle, or a 90° angle. A 90–180 degree angle is referred to as an obtuse angle. a 180 degree angle, or a straight angle.What is acute angle?
Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.Learn more about acute angle
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Please can someone help me? It’s due trmw
Answer:
Yes OFC
Step-by-step explanation:
As you can see at the 12-second mark the graph shows 1466 wave length for air so the density of the mass will be subtracted from the height
Please help!! ;-; I cannot figure this out
to get the equation of any straight line, we simply need two points off of it, let's use the points from the table in the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 3 }\implies -1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-x+2\implies {\LARGE \begin{array}{llll} y=-x+6 \end{array}}[/tex]
Which of the following functions is graphed below?
Answer:
The answer is A because both equations are true
[tex] a) \: {x}^{3} - 2 = {1}^{3} - 2 \\ = 1 - 2 \\ = - 1 \\ \\ b) \: {x}^{2} + 4 = {1}^{2} + 4 \\ = 1 + 4 \\ = 5 \\ \\ [/tex]
The expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped. What is the distance the object falls during each time?
10 seconds
If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance the object falls during 10 seconds is 1600 foot
Given,
The algebraic expression of the distance in feet that an object falls = [tex]16t^{2}[/tex]
Where t is the time in seconds
Here,
time t = 10 seconds
Substitute the value in the expression
[tex]16t^{2}=16(10)^{2}[/tex]
=1600 foot
Hence, If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance the object falls during 10 seconds is 1600 foot
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question in the picture
Answers:
14 rides: 52
and
r rides: 3r + 10
Step-by-step explanation:
3(14) + 10
52
For each rational function, find any points of discontinuity.
y=2x-1 / x²+4
In rational functions, the discontinuities are caused by the denominator terms. Since the denominator of a fraction is non-zero, any term multiplied by the denominator is also non-zero.
To find the discontinuities, we need to factor the polynomial below. Once we have the two binomials, we set each to 0. This way, you can find the value that produces 0 in the denominator.
If x = -2 then (x^2) + 4 is 0.
So, the discontinuities are shown as x = -2
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