The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.
what is slope ?A line's slope determines how steep it is. A mathematical expression for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two points. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is used to represent it. The y-intercept is located at a point where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).
given
for parallel their slope will be equal
y1= 1x/2 + 3/8 .... eq1
y2= kx/4 + 5k/4 ..... eq2
y1 = y2
1x/2 + 3/8 = kx/4 + 5k/4
1/2 + 3/8 = k/4 + 5k/4
7/8 = 6k/4
k = 7/12
for perpendicular product of their slope is 1
y1 * y2 = 1
1x/2 + 3/8 * kx/4 + 5k/4 = 1
1/2 + 3/8 * k/4 + 5k/4 = 1
k = 1/21
so The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.
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Given:
f(x) = x² + x − 6
g(x) = x + 3
Find: (f/g)(x)
Answer:
x–2, x ≠ -3
Step-by-step explanation:
Solution in the diagram
Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
X
6
-
X
The equation has Select an option
0
attempt 1 out of 2
The equation has one solution.
A value of x that makes the equation true is 6 which when substituted into the equation and simplified makes the equation turn into x = 0.
A value of x that makes the equation false is 8 which when substituted into the equation and simplified makes the equation turn into x = 2.
How to evaluate the equation?From the information provided, we have the following equation:
x - 6 = 6 - x
Rearranging the equation by collecting like terms, we have the following solution:
x + x = 6 + 6
2x = 12
x = 12/2
x = 6
Substituting the value "6" into the equation, we have the following solution;
x - 6 = 6 - 6
x - 6 = 0
Assuming x = 8, we have the following solution;
x - 6 = 8 - 6
x - 6 = 2
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Complete Question:
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
x - 6 = 6 - x
The equation has _____.
A value of x that makes the equation true is ___ which when substituted into the equation and simplified makes the equation turn into ____.
A value of x that makes the equation false is ___ which when substituted into the equation and simplified makes the equation turn into ___.
1. This week Tony practiced basketball 2 hours on Tuesday, 1 hours Wednesday, and 2 hours on Friday. Next
week Tony will practice basketball for the same number of hours Tuesday, Wednesday, and Friday. What is
the total number of hours Tony will practice basketball over the 2 weeks?
For 2 weeks tony will spent time for practice basketball is 10 hours.
How do you find time in math problems?The equation for calculating time is [Time = Distance Speed]. The distance may be calculated using the time formula [Distance = Speed Time].Work completed equals Time x Rate of Work. Work Rate is equal to One/Time. Time = 1 divided by the rate of work. If a task is completed across x days, then the amount of work completed in a single day is equal to 1/x.The Greenwich hour angle, abbreviated GHA, is used to define the Equation of Time as E = GHA (apparent Sun) - GHA (mean Sun) (1). E = right ascension of the fictional mean Sun - right ascension of the apparent (real) Sun is a different formula that is frequently used in textbooks.Given data :
1st week
= Tuesday = 2 hours
= Wednesday = 1 hour
= Friday = 2 hours
same for 2nd week
so total hours = 1st week + 2nd week
= 2 + 1 + 2 + 2 + 1 + 2
= 10 hours
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What is the equation of the line that passes through the point (7, -4) and has an
undefined slope?
A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,240 ft Determine the flag's width and length if the length is 460 ft greater than the width.
Answer:
the flag is 50 feet long and 160 feet wide
Answer: The width is 330 feet and the length is 790 feet.
Step-by-step explanation:
We will write a system of equations to help us solve. Let w be the width and l be the length.
2w + 2l = 2,240 ft
l = 460 ft + w
Now, we will solve for w, the width, by substituting one equation into the other.
2w + 2l = 2,240 ft, l = 460 ft + w
2w + 2(460 ft + w) = 2,240 ft
2w + 920 ft + 2w = 2,240 ft
4w + 920 ft = 2,240 ft
4w = 1,320 ft
w = 330 ft
The width is 330 feet.
Now, we will solve for l, the length.
l = 460 ft + w, w = 330 ft
l = 460 ft + 330 ft
l = 790 ft
The length is 790 feet.
whats 2+2 pls i have a test tomorrow i need to pass it
Solve for : -3(x+8)=30
Answer: -18
Step-by-step explanation:
Distribute the -3 to the values inside the parentheses, (x and 8) which equals -3x-24.
Then, use inverse operations by adding 24 on both sides (it will cancel on the left) to get -3x=53
Then divide -3 on both sides to get x by itself
Answer:
-18
Step-by-step explanation:
-3(x+8)=30
by dividing 3 from both sides
-(x+8)=10
by multiplying -1 for both sides
(x+8)= -10
by subtracting 8 from both sides
x = -18
Illustrate the effect that a decrease in the price of milk and input to ice cream would have on the market for ice cream
The effect that a decrease in the price of milk and input to ice cream would have on the market for ice cream is that there will be more production and demand in the market.
What is Market?This is referred to as a place where buyers and sellers can meet to facilitate the exchange or transaction of goods and services.
A decrease in the price of milk and input to ice cream means that production costs would fall, which will cause the suppliers to produce more thereby shifting the supply curve to the right with the demand for the goods being increased which is therefore the effect on the market.
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Solve 2 < n +1| ≤ 7. Explain your reasoning and graph
the solution set.
Let n = the number
The solution set is {x | x > 10}. 2. 5 ≥ 7 + y.
What is the value of N?It's used to refer to the collection of all natural numbers. Positive whole numbers that are not zero make up the natural numbers. N = 1 , 2 , 3 , 4 . By multiplying the integers from 1 to n, the factorial of n is calculated and denoted by the symbol n!. n! = n (n - 1)! is the formula for n factorial. Example: What is9! if8, which is40,320, is?The sample size, or n, is the number of data points. described in Chapter 2 here. in a probability experiment using a binomial model, the total number of trials.Instead of the product n n, which is typically pronounced"n squared," the equivalent exponentiation n2 is used to represent a number's square.To learn more about exponentiation refer to:
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If QR = 8, RS = x + 2, and QS = 6x, what is QS?
Answer:
QS = 12
Step-by-step explanation:
Hello!
We can see that QS is the sum of QR and RS, which is equal to 6x.
We can substitute the given values to solve for x, and then use that to find QS.
Solve for xQS = QR + RS6x = 8 + x + 2 Substitute values6x = 10 + x Combine like terms5x = 10 Subtract xx = 2 Divide by 2The value of x is 2. We can now find QS by substituting 2 for x in 6x.
QS = 12.
B. Higher Order Thinking For keeping business records, every three months of a year is called a quarter. How many months are equal to three-quarters of a year? Explain how you found your answer.
Answer:
9 months
Step-by-step explanation:
1 quarter is 3 months
3 quarters is 3 times 1 quarter, so it is 3 times 3 months.
3 x 3 months = 9 months
Answer: 9 months
Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.
The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.
What does rate of change mean?
An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then the rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.
Surafce area of a prism is equal to
2(Area of base) + (perimeter of base)(height)
2b^2+4bh
[tex]S=2b^2+4bh[/tex]
[tex]\frac{ds}{dt}=4b\frac{db}{dt} + 4b\frac{db}{dt} + 4h\frac{db}{dt} \\[/tex]
It is given that db/dt= -7 and dh/dt -=10.
At a particular instant b= 4km, h=9 km.
Now we will substitute the values in this formula:
[tex]\frac{ds}{dt}=-4*4*7-4*4*7+ 4*9*10\\\frac{ds}{dt}=136[/tex]
The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.
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Shana wants to buy a music player. She has $100 cash.
1. Can she afford a $79 unit plus HST? Yes or No?
Provide an estimate or a calculation to support your answer:
Answer:
Yes
Step-by-step explanation:
A $79 unit plus HST will be 89.27
Convert to rectangular
When convert it into rectangular form we get x=-1/2 and y=0.
How to convert polar to rectangular form?To convert a point in polar coordinates (r, θ) to rectangular coordinates (x, y), you can use the following formulas:
[tex]x = r * cos(θ) \\y = r * sin(θ)[/tex]
Where r is the distance from the origin to the point, and θ is the angle in radians between the positive x-axis and the line connecting the point to the origin.
Alternatively, you can also convert from rectangular to polar coordinates using the following formulas:
[tex]r = sqrt(x^2 + y^2)\\θ = atan2(y, x)[/tex]
Where x, y are the rectangular coordinates and atan2 is a function that computes the angle of a point in a cartesian plane.
In general, it's worth noting that the polar coordinates are often used in some physics and engineering problems, while the rectangular coordinates are often used in computer graphics, analytic geometry and other fields.
What is 1 in polar co-ordinate?The angle of 1's inverse tangent is 45°. This is the outcome of translating to polar coordinates in the form (r,theta).
To convert it into rectangle equation we have
[tex]x=rcos(theta)\\y=rsin(theta)\\r=1\\theta= 3*pi/2\\x= cos(3*pi/2)\\x= -1/2\\y=sin(3*pi/2)\\y=0[/tex]
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Write the equation of the ellipse with a center at (5,-2), one vertex at (2, -2) and a focus at
(5+ √5,-2)
On solving the provided question we can say that - the value of the ellipse will be (5+ , root5)
what is ellipse?In mathematics, an ellipse is a planar curve that encompasses two focus points and ensures that the sum of the two distances from any point on the curve to the focal points is constant. In doing so, the circle—a particular variety of ellipse with two equal focus points—is generalized. The ellipse, whose eccentricity is less than 1, indicates the area containing the points whose distances from its two foci add up to a certain amount. Running tracks in sporting arenas and 2D egg forms are two straightforward examples of ellipses in daily life.
here we have,
center at (5,-2), one vertex at (2, -2) and a focus at
(5+ √5,-2)
so the answer is (5+ , root5)
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got a prepaid debit card with $15 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 24 cents per yard. If after that purchase there was $3.48 left on the card, how many yards of ribbon did
The length of ribbon is 48 yards.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Kala got a prepaid debit card with $15.
Price of Ribbon = 24 cents per yard.
After purchase money left $3.48.
So, Price of Ribbon purchased = 15 - 3.48 = $11.52 = 1152 cents
length of ribbon = 1152/ 24
= 48 yards
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All of the quadrilaterals in the shape below are squares. Find the area of the shaded
region.
Answer: I don't remember how to solve, but, I figured out the lengths of each side in the shaded region:
11, 11, 7, 7, 4, 4
Step-by-step explanation:
Hope this helps!! :D
A student made two patterns to show multiplication of a decimal by powers of ten. the equations shown for both patterns are incorrect. pattern A
3.675. 10 =3.7650
3.675. 100= 3.67500
3.675.1,000= 3.675000
pattern B
3.675. 10=3.0675
3.675.0.01= 3.00675
3.675. 0.001= 3.000675
explain why the equations in each of the patterns are false. Include in your explanation the values that should appear on the right side of each equation in both patterns to make the equations true.
If a student made two patterns to show multiplication of a decimal by powers of ten. All the value are incorrect. The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
How to find the correct value?Pattern A
3.675×10 =3.7650 Incorrect
3.675×10 = 36.75 Correct
3.675× 100= 3.67500 Incorrect
3.675×100= 367.5 Correct
3.675×1,000= 3.675000 Incorrect
3.675×1,000 = 3,675 Correct
Pattern B
3.675×10=3.0675 Incorrect
3.675× 10= 36.75 Correct
3.675×0.01= 3.00675 Incorrect
3.675×0.01= 0.03675 Correct
3.675×0.001= 3.000675 Incorrect
3.675×0.001= 0.003675 Correct
The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
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Find the volume of a cone with a base radius of 3in and a height of 11in. Use the value 3.14 for π, and do not do anu rounding. Be Sure to include the correct unit in your answer.
So the formula to find the volume of a cone is,
[tex]V = \pi r^{2} \frac{h}{3}[/tex]
Given,
Base of the cone is 3 inchesHeight of the cone is given as 11 inchesTo Find : The Volume of the cone
Applying the values we get,
[tex]V = 3.14X(3)^{2} X \frac{11}{3}[/tex]
[tex]V = 28.26X\frac{11}{3}[/tex]
[tex]V = 103.62in^{3}[/tex]
Hence , the volume of the cone is 103.62in³
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
What is the equation of C(t)?
C(t) = −(x − 5)2
C(t) = (x − 5)2
C(t) = −x2 + 5
C(t) = x2 + 5
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,
C(t) = a(t - 0)² + 5
C(t) = at² + 5
The equation is passing through the point (1, 4), then we have
4 = a (1²) + 5
4 = a + 5
a = - 1
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
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At a bakery, 55 chocolate chip cookies were burned. if that was 15% of the day's production, how many total cookie did they make that day?
The total number of cookies that was made that day given that 55 which is 15% was burnt is 360.
How to solve for the number of cookies madeWe know that the number of burned cookies is 55, and that this represents 15% of the total production for the day.
We can use this information to set up a proportion to find the total number of cookies made that day.
Burned cookies / Total cookies = 15% / 100%
55 / X = 15/100
To find the total number of cookies made, we can cross-multiply and divide:
X = (55 * 100) / 15
X = 365
So, the bakery made a total of 365 cookies that day.
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Cones A and B both have volume 48pi cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B.
The possible radius and height for Cone B are 3 units and 16 units respectively
How to determine the radius and height of the cone
The formula for calculating the volume of a cone is expressed mathematically;
Volume = 1/3 πr²h
Given that;
π takes the value 3.1 4r is the radius of the coneh is the height of the coneFrom the information given, we have that;
Both cone A and B have volume of 48πCone A has 6 units and height of 4 unitsNow, let the height of cone B be 16 units
Substitute the value into the formula, we have;
48π = 1/ 3 × π × r² × 16
multiply the values, we have
48 = 16r²/3
cross multiply
16r² = 144
Divide both sides by 16
r² = 144/16
r² =9
Find the square root of both sides
r = 3units
Hence, the values are 3 units and 16 units
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Perry borrows $150 from his brother to fix his car. His brother doesn't like lending Perry money and so charges him 7% interest per month. a. Write a rule in the "y=..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments.
Answer: Let's say,
y = the amount of money Perry will owe his brother after n months.
x = the principal (the initial amount borrowed) = 150
r = the interest rate per month = 7/100 = 0.07
n = number of months.
We know that Interest on a loan is calculated by multiplying the principal by the interest rate.
Therefore, the interest for n months is (0.07*x)*n
So to find the total amount Perry will owe his brother after n months, we need to add the interest to the principal amount.
y = x + interest
y = x + (r*x)n
y = x(1 + rn)
Therefore, the rule in the "y =..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments is:
y = 150(1 + 0.07*n)
It's worth noting that this formula can be used to calculate the amount he will owe after any number of months by changing the value of n, and It's assuming he doesn't make any payments, meaning if he makes any payments, the total amount he will owe will change.
Step-by-step explanation:
y 10- 9 8 6 5 4 2 1 2 3 4 5 6 7 8 9 10 What is the equation of the blue line? X
Therefore , the solution of this is the required system of equation is,
y=-x+6 and y=x+10.
Explain the equation.A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.
Here,
(0,6) and the blue line pass through them (-2,8). You may figure out the equation for the blue line as,
=> y-6/x-0 = 8-6 /-2-0
=>y-6/x = 2/-2
=> y-6=-1(x)
y=-x+6
(-2, 8) and the red line pass through them (-3,7). The red line's equation can be calculated as,
y-8/x- (-2) = 8-7 /-2-(-3)
y-8 /x+2 = 1
y-8=x+2
y = x + 10
Thus, the required system of equations is,
y=-x+6 and y=x+10.
Therefore , the solution of this is the required system of equations is,
y=-x+6 and y=x+10.
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Refer to the diagram shown.
I need help with this please help me
Answer: Angle-Side-Angle Theorem
Step-by-step explanation:
The two triangles are shown to have congruent angles. By the Reflexive Property of Congruence, Side PM is shared and congruent between the two.
Because the angles are on either side (left and right) of the shared side, the triangles are congruent by the Angle-Side-Angle Theorem.
1.171875 as a fraction
false
it is a decimal not a fraction
Click on a factor pair of 32
Factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)
⇒ Firstly find the factors of 32
How Do You Work Out Factors of 32?
Step 1: Let's start with the whole number 1 and work our way up to the factors of 32. 32 ÷ 1= 32
Step 2: Now divide 32 by two. 32 ÷ 2= 16
Step 3: Then we get. 32 ÷ 4= 8
Step 4: Similarly, we calculate all the 32 factors.
32 factors = 1, 2, 4, 8, 16, and 32.
⇒ Secondly, find factor pairs of 32
The two numbers that, when multiplied together, give 32 are the factors of 32 in pairs. The factors of 32 are listed below in pairs.
Products of 32 Factor pair of 32
1 × 32 = 32 (1, 32)
2 × 16= 32 (2 ,16)
4 × 8 = 32 (4, 8)
∴Therefore, factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)
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Maya went shopping for a new video game because of a sale. The store was offering a 40% discount. If the price on the tag was pp, which expression does NOT represent the price after the discount but before tax?
The expression that represents the price of the video game after the discount is
p - 0.4p
Where p is the original price of the video game.
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Price of the video game = p
Discount = 40%
The price of the video game after the discount.
= p - (40% of p)
= p - (40/100)p
= p - 0.4p
Thus,
The expression is p - 0.4p.
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An engine spins a wheel with radius 5 inches at 800 rpm. How fast is this wheel spinning in miles per hour?
The wheel is spinning at 23.80 miles per hour
How determine how fast the wheel spinning in miles per hour?The wheel speed in miles per hour can be calculated using the expression below:
Speed in miles per hour = Wheels RPM × 2 × π × r × (60 / 63360),
where r is the radius of wheel , 60 converts minute to hour and 63360
converts inches to miles
Speed in miles per hour = 800 × 2 × π × 5 × (60 / 63360)
Speed in miles per hour = 23.80 miles per hour
Thus, the wheel spins at 23.80 miles per hour
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i’m not sure if the first one right but i need help
The formula is written as (3x+9)(x+9) of + 36x + 81 = 0. A second-degree polynomial equation can be used to define quadratics.
A quadratic equation is defined.Multiplying a variable by itself is the mathematical operation known as "squaring," which is frequently used to refer to a quadratic issue. This vocabulary is based on the notion that a square's area is equal to the sum of its side lengths. The word "quadratic" derives from the Latin quadratum, which meaning square.
here ,
[tex]= + 36x + 81 = 0\\= 3x^2 + 27x + 9x + 81\\= 3x(x+9) + 9(x+9)\\= (3x+9)(x+9)\\= 3(x+3)(x+9)[/tex]
factorized form is [tex](3x+9)(x+9) of + 36x + 81 = 0 .[/tex]
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