The equation in standard form is x - y = 9
How to determine the equation in standard form?From the question, we have the following parameters that can be used in our computation:
Points = (8, –1) and (2, –5)
Point-slope form is y + 1 = (x – 8).
Recall that the point-slope form is y + 1 = (x – 8).
So, we have
y + 1 = (x – 8)
Open the brackets
y + 1 = x – 8
Subtract 1 from both sides
y = x - 9
Rewrite as
-x + y = -9
Multiply through by -1
x - y = 9
Hence, the equation is x - y = 9
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Trigonometry find the length of AC
Give your answer to the nearest decimal
The length AC of the triangle will be 10.6 units
What are trigonometric functions?
The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given is a right angled ΔABC as shown in the figure.
We have the image as shown in the figure. In the right angled triangle -
Sin(62°) = CA/CB
Sin(62°) = CA/12
CA = 12 x Sin(62°)
CA = 12 x 0.88
CA = 10.6
Therefore, the length AC of the triangle will be 10.6 units
Therefore, by following the steps above, we can plot the graph of →
y = 5 cos(2x + π/3) - 1
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[Refer to image attached for full question]
A couple buys a $290000 home, making a down payment of 15%. The couple finances the purchase with a 15
year mortgage at an annual rate of 3.4%. Find the monthly payment.
per month.
If the couple decides to increase their monthly payment to $1950, find the number of payments.
payments (give 2 decimal places)
which we would round up to
total payments.
The monthly payment for the first condition is $1750.11 and the total number of payments is 156.
What is the monthly payment?
Monthly payment is defined as the amount paid every month depending on the terms of the mortgage loan. This includes the principal, which is the actual balance on the loan, and the interest on the loan.
The formula for monthly payments on the mortgage is given:
[tex]MP = \frac{P(\frac{r}{n}) }{1- (1+\frac{r}{n})^{-nt} }[/tex]
where, MP = monthly payment
P = principal amount
r = rate of interest
n = number of payments per year
t = number of years
Given, a couple buys a house for $290000 and makes a down payment of 15%
Down payment = 0.15*290000 = $ 43500
First condition,
Present value of loan (P) = $290000 - $43500 = $246500
rate of interest (r) = 3.4% = 0.034
number of payments per year (n) = 12
number of years (t) = 15 years
Then, the monthly payment is calculated by:
[tex]MP = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*15} } = 1750.11[/tex]
Therefore, monthly payment = $1750.11
Second condition,
monthly payment (MP) = $1950
Present value of loan (P) = $290000 - $43500 = $246500
rate of interest (r) = 3.4% = 0.034
number of payments per year (n) = 12
time in years (t) = x years
Then,
or, [tex]1950 = \frac{246500(\frac{0.034}{12}) }{1- (1+\frac{0.034}{12})^{-12*x} }[/tex]
or, [tex]x = 13.06 = 13[/tex]
So, the total number of payments = 13*12 = 156
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the per capita consumption of meat by people in the united states in a recent year was normally distributed with a mean of 218.4 pounds and standard deviation of 42 pounds. a random selection of 30 people was taken. what is the probability that the sample mean is less than 200 pounds? (notice i used the words sample mean!)
The probability that the sample mean is less than 200 pounds is 33% or 0.33
Given that,
The average annual meat consumption in the United States was 218.4 pounds, with a standard deviation of 42 pounds, and was normally distributed. A random sample of 30 individuals was chosen.
Mean (μ) = 218.4
Standard deviation (σ) =42
Probability = P(X< 200) = P[(X-μ ) / σ < (200-218.4) /42 ]
= P(z <-0.44 )
Using z table
=0.3300
Probability=0.3300
Therefore, 33% or 0.33 of the time, the sample mean will weigh less than 200 pounds.
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Is there any evidence to prove m and n are parallel
Find the values of x and y that satisfy the equation.
22 + 1/5yi = 2x - 2
Answer:
[tex]x=12, y=0[/tex]
Step-by-step explanation:
[tex]22+\frac{1}{5}yi=2x-2 \\ \\ (24-2x)+\frac{1}{5}yi[/tex]=0[/tex]
Setting the real and imaginary parts of the left hand side equal to 0,
[tex]24-2x=0 \implies x=12 \\ \\ \frac{1}{5}y=0 \implies y=0[/tex]
Pls help asap
Number 3
Answer:
No
Step-by-step explanation:
The value that corresponds with the other value on a data (34 to 2, 51 to 3, 68 to 5 etc.) needs to have the same quotient (or ratio) when you compare them.
34/2 = 51/3 ? Yes (but you can't stop here because you need to test ALL the values, what I mean is ALL the values UNTIL you found one that is not equal to each other, if all of them are equal, then the data are proportional.
34/2 = 68/5 ? No (Now you can stop here and say it's not proportional because we already found one pair that are not equal).
will mark brainliest
Find the x-intercept and the y-intercept of the graph of the equation.
4x + 5y = 20
The x-intercept is
The y-intercept is
(Type an integer.)
(Type an integer.)
The x-intercept and y-intercept of the graph is (5,0) and (0,4)
How to find the intercept ?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.
1. To find the x-intercept we put y=0
The equation becomes
4x + 5(0) = 20
4x = 20
x = [tex]\frac{20}{4}[/tex]
x = 5
∴ The x-intercept is (5,0)
2. To find the y-intercept we put x=0
The equation becomes
4(0) + 5y = 20
5y = 20
y = [tex]\frac{20}{5}[/tex]
y = 4
∴ The y-intercept is (0,4)
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Find the product of 3 1/4 and 1/2
The product of the improper fraction 3 1/4 and 1/2 is 1 5/8.
What is mixed fraction?
A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. a fraction when the denominator (bottom number) and the numerator (top number) are both more than or equal (the bottom number). When the numerator is equal to or more than the denominator, the fraction is said to be improper fraction. It always has a value of one or higher.
Here the given fraction 3 1/4 convert into 13/4.
Now the product of the fractions is
=> 13/4 × 1/2
=> 13/8
=> 1 5/8.
Therefore product of the given fraction is 1 5/8.
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Expand and Simplify (x+5)(x-2)
Answer:
[tex]x^2+3x-10[/tex]
Step-by-step explanation:
To expand you must do this:
[tex]x*x+(-2x)+(5x)-10\\x^2-2x+5x-10\\x^2+3x-10[/tex]
Find the length and the width.
Answer:
Length would be 6ft
Width would be 4ft
Step-by-step explanation:
24ft^2 is the area as we know 6x4 = 24 and 4 is two less than 6, therefor your answer is 4 and 6.
The sum of three consecutive even numbers is 558. What is the 1st number?
The sum of three consecutive even numbers is 558, The first number is 184.
The Sum of three consecutive even numbers is 558
We have to find the first number
Let the three consecutive even numbers be:
First number = x
Second number = x + 2
Third number = x + 4
Since their sum is 558
Therefore,
x + x + 2 + x + 4 = 558
3x + 6 = 558
3x = 558 - 6
3x = 552
Divide both sides by 3
Then the first number is 184.
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Dad fills the car's gas tank when it is about 1/2 empty. Later, he fills the tank when it is about 3/4 empty. He bought a total of 18 1/2 gallons of gas on those two days. How many gallons does the tank hold?
Dad's car's gas tank holds 14.8 gallons of the gas.
Define the term mixed fraction?A mixed fraction is one generated by integrating a whole number as well as a fraction.
When the car's gas tank is nearly half full, Dad fills it up. Later, when the tank is about 3/4 full, he fills it. Total gas purchased = 18 1/2 gallons of gas.Changed the mixed fraction in decimal.
Total gas purchased = 37/2 = 18.5 gallons of gas.
Let x be the gallons of gas tank contains.
Then,
(1/2)x + (3/4)x = 18.5
Multiply both sides by 4,
2x + 3x = 74
5x = 74
x = 14.8 gallons
Thus, Dad's car's gas tank holds 14.8 gallons of the gas.
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[tex]\sqrt{|x|^2} =x[/tex]
Answer?
The solution to the equation given as √|x|² = x is x ≥ 0
How to solve the equation?From the question, the representation of the equation is given as
√|x|² = x
To start with;
We evaluate the square root expression in the equation
So, we have the following representation
|x| = x
The above implies that the absolute value of a number equals the number
As a general rule of absolute values, the absolute value of a number is positive
This can be represented as
x ≥ 0
Hence, the solution to the equation is x ≥ 0
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She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 41 seconds at a speed of 4.9 feet per second.
She then ascends for 49 seconds at a speed of 3.2 feet per second.
After this 90-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at 3.6 feet per second?
The scientist will take 23 seconds to get back to the sea level.
Let us calculate the distance covered by the scientist at the given speeds and at the specified times.
She travels down for 41 seconds at speed of 4.9 feet per second.
Distance travelled = 41 × 4.9 = 200.9 feet
Elevation = -200.9 feet
She then goes up for 49 seconds at speed of 3.2 feet per second.
Distance travelled = 49 × 3.2 = 156.8 feet
Elevation = -222.9 + 156.8 = -44.1
So she is at a depth of 44.1 feet below the sea level.
Time taken = 44.1 / 3.6 = 12.25 seconds
Therefore it will take her about 12.25 seconds to go back to the sea level.
The average surface level of one or more of the Earth's coastal bodies of water is known as mean sea level (MSL), which can be used to calculate heights like elevation.
There are several terminologies that describe the ebb and flow of the relationship between sea level and dry land.
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Can anyone write the equation of this graph?
The absolute value equation graphed is defined by the rule given as follows:
y = |x - 3| + 6.
What is the function graphed?The function graphed is an absolute value equation, due to it's v format.
The equation that represents an absolute value function with vertex (h,k) is given by the rule presented as follows:
y = |x - h| + k.
On the graph, this vertex is the turning point of the absolute value function.
For the graphed function, the coordinates of the vertex are given as follows:
x = 3, as the turning point of the graphed function has an horizontal coordinate of 3, hence h = x = 3.y = 6, as the turning point of the graphed function has a vertical coordinate of 6, hence k = y = 6.Then the coordinates of the vertex are:
(3,6).
The equation of the graphed absolute value function is:
y = |x - 3| + 6.
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What is the value of y in the equation 2(2y − 16) = 0? (5 points)
a 4
b 6
c 8
d 9
Answer:
the options are wrong
Step-by-step explanation:
open the bracket2(2y)2(-16)=04y-32=0make y the subject of formulary=-32÷4y=-8Answer:
C. 8
Step-by-step explanation:
2 x 8 = 16
16 - 16 = 0
2 x 0 = 0
Dividing the polynomial P(x) by x + 2 yields a quotient Q(x) and a remainder of 8. If Q(2) = 5, find P(-2) and p(2)
================================================
Explanation:
Part A) Find P(-2)
We'll divide P(x) over (x+2) to get a quotient Q(x) and remainder 8 like so
P(x)/(x+2) = quotient + remainder/(x+2)
P(x)/(x+2) = Q(x) + 8/(x+2)
When multiplying both sides by (x+2), it clears out the fractions and we're left with this
P(x) = (x+2)*Q(x) + 8
From here, plug in x = -2 and simplify
P(x) = (x+2)*Q(x) + 8
P(-2) = (-2+2)*Q(-2) + 8
P(-2) = (0)*Q(-2) + 8
P(-2) = 0 + 8
P(-2) = 8
Luckily we don't need the value of Q(-2) since it cancels out with the zero.
-----------------------------------
Part B) Find P(2)
This time we'll plug in x = 2 and we'll get...
P(x) = (x+2)*Q(x) + 8
P(2) = (2+2)*Q(2) + 8
P(2) = 4*Q(2) + 8
P(2) = 4*5 + 8
P(2) = 20+8
P(2) = 28
Add/Subtract Rational Numbers :
Add ; -1/2 + 2/3 (Simplify)
Evaluate ; -1/8 - (-5/6) (Simplify)
Two planes are parallel and each plane contains a line. Are the two lines skew? Explain your reasoning.
If Two planes are parallel and each plane contains a line, the two lines are not skew because In the event that any two lines fall on a single plane, they will either intersect or be parallel to one another. Both instances violate the concept of a skew line because the skew lines are neither parallel nor intersect.
Do two parallel lines on a plane have a skew?Infinitely many lines cross through, yet only one of them is parallel to. Lines that never intersect and are in distinct planes are known as skew lines. Parallel lines and skew lines are distinguished by the fact that they both reside in the same plane, whereas skew lines do not.
The two lines would overlap at some point if the two planes on which they are located weren't parallel, which again defies the definition of skew lines.
Therefore, The skew lines are thus present if and only if both lines fall on a pair of parallel planes.
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The graph represents a one-to-one function because every x-value is paired with only one y-value.
The graph represents a one-to-one function because it is defined for all x-values.
The graph does not represent a one-to-one function because it does not pass through the origin.
The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
The correct statement regarding whether the graph is a one-to-one function is:
The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
What is an one-to-one function?An one-to-one function is a function in which each output is related to only one input, that is, there are no horizontally aligned points.
These horizontally aligned points happen when an horizontal line is traced on the graph of the function, and crosses the function more than once.
From the graph of the function given by the image at the end of the answer, it can be seen that this line would cross the function twice for values of y between 0 and 2, hence the correct option is:
The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
Missing InformationThe problem asks for the correct statement regarding the function given on the image at the end of the answer.
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Help!! In two or more sentences , explain how to find the time it takes for a rocket following the path h(x)= -4x^2 + 16x to hit the ground
The time it takes for a rocket following the path h(x)= -4x² + 16x to hit the ground is 4 seconds.
How to find the time for a rocket to hit the ground?
The given path equation is a function of x which is a time variable here. When the rocket hits ground, height of the rocket gets zero.
Hence equating the equation of height to zero and solving for x will give the time required for the rocket to hit the ground.
According to the given question:
We are given equation for height as
h(x) = -4x² + 16x
where x is the time in seconds
When object hits the ground the height becomes 0
So, we can set h(x) = 0 and then we can solve for x
-4x² + 16x = 0
Dividing by -4x from both sides
x - 4 = 0
x = 4 sec
So, the time it takes for a rocket to hit the ground is 4 seconds.
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sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1
Answer:
sin(2x)cos(7x) - cos(2x)sin(7x)= -0.1
pls help me with this
Answer:
31-6/1-1
=25/0
=undefined
Lol help quick pleaseeeeeeeeee
The answer to be entered in the boxes for the area model is 17, 0 and 17
How to find the division problem the area model represents?
An area model is a rectangular diagram or model used for solving multiplication and division problems, in which the quotient and divisor define the length and width of the rectangle
Given:
....60.....1.............
36|2160 | 36 | 17
2160 ÷ 36 = 60 R 0
36 ÷ 36 = 1 R 0
17 ÷ 36 = 0 R 17
Note: (0 x 36) + 17 = 17
Therefore, the answer to be entered in the boxes is 17, 0 and 17 respectively
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The shaded area below is 79 m².
Work out the area of the smaller rectangle.
If your answer is a decimal, give it to 2 d.p.
x+4 m
x + 3 m
x+2m
2x+5 m
Not drawn accurately
Answer:
[tex](x + 4)(2x + 5) - (x + 3)(x + 2) = 79 \\ 2x {}^{2} + 5x + 8x + 20 - {x}^{2} - 2x - 3x - 6 = 79 \\ {x}^{2} + 8x + 14 = 79 \\ {x}^{2} + 8x - 65 = 0 \\ {x}^{2} + 13x - 5x - 65 = 0 \\ x(x + 13) - 5( x + 13) = 0 \\ (x - 5)(x + 13) = 0[/tex]
x-5=0
x=5
the length of smaller rectangle= 8 m
and breadth of s. rectangle= 7 m
l x b = 8 x 7
[tex]56 {m}^{2} [/tex]
hopefully this will u
multiply
(−5 2/5) ⋅ 3 7/10.
a. −19 49/50
b. −15 7/25
c. −9 1/10
d. −1 7/10
Answer: -19 49/50 ==> a
Step-by-step explanation:
(−5 2/5) ⋅ 3 7/10=
(−5 - 2/5) ⋅ (3 + 7/10)=
(−25/5 - 2/5) ⋅ (30/10 + 7/10)= ==> make the terms have like denominators
((-25-2)/5) ⋅ ((30+7)/10)=
-27/5 ⋅ 37/10 =
-27 ⋅ 37 / (5 ⋅ 10) =
-999/50=
(-950-49)/50=
-950/50 - 49/50=
-19 - 49/50=-19 49/50 ==> a
16 divided by the sum of 2 and 6
Answer:
Step-by-step explanation:
16/(2+6)
16/8=2
please help what is the answer and how do you do it
The dimensions of two rectangular prisms are shown below. How much more volume does the larger prism have than the smaller prism?
Answer:16/25 :D
Step-by-step explanation:does that help :3
Slope:
Y-intercept
Equation:
y-intercept: (0,60)
This is given in the table.
Slope: [tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Using (1,50) and (2,40):
[tex]m = \dfrac{40 - 50}{2-1} = \dfrac{-10}{1} = -10[/tex]
The slope is -10.
Using the slope-intercept form (y=mx+b) and the fact that we found m=-10 and b=60 from the table, the equation is:
y = -10x + 60
