The general equation of the line is 7x+8y−65=0 when the line equation is 7x+8y=16 and the point is (7,2) and is perpendicular to the given line.
What is line?A line is a one-dimensional figure with no width and only length. A line is made up of a series of points that extend in opposite directions indefinitely. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.
here, the given equation is 7x+8y=16 and point is (7,2).
by the relation y = mx + c we will find the value of slope for the line.
8y=-7x+16
y=(-7/8 ) x+16
on comparing relation,
m=[tex]\frac{-7}{8}[/tex]
y=mx+b
b=y1-m.x1
b=2-(-7/8).7
b=65/8
y=(-7/8)x+65/8
final equation,
7x+8y=65
The required equation of the line is 7x+8y=65 for the given point and line.
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ROYAL ACADEMY TUTORS Empowering you to conquer your world Question 21 To travel overseas, Mr. Leeto borrows an account of money after 20 months (period), he pays back a once-off amount of R15 000 (FV) How much did he borrow (PV) (to two decimal places) if interest rate is 13% (interest rate) per annum compounded monthly (P/YR)
The amount that he borrow (PV) if interest rate is 13% (interest rate) per annum compounded monthly (P/YR) is: $12,235.90.
How to find the amount borrowed?First step is find to the number of months
n = 20 months / 12
n = 1.66666666
Now let find the amount borrowed
A= P/ ( 1+ r) ^ n
Where:
A = Amount
P = Principal
r = interest rate
n = time
Hence.
A = 15,000 / ( 1+ 0.13) ^ 1.66666666
A = 15,000 / (1.13)^ 1.66666666
A = 15,000 / 1.2259
A = $12,235.90
Therefore $12,235.90 is the amount borrowed.
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Three pencils are on sale for $0.45 at this rate what is the cost per pencil
1) Gathering the data
3 pencils ----------- $0.45
how would I answer and what would be the answer?
there is a zero at x = 1 (option D)
Explanation:
a) The graph shows it is going up (increasing towards both the y axis and x axis).
This graph will give a positive leading coefficient.
As a result, the equation will have a positive leading coefficient not a negative one.
b) zeros of a polynomial are the values of x when the line crossses the x axis.
From our graph, the line doesn't cross the x axis at x = 6.
As a result, there is no zero of -6.
Multiplicity tells us the number of times the number of times a factor occurs.
Since part of the statement is wrong, it makes the whole statement wrong
c) The degree of this graph is odd. Its equation is 3rd degree
d) From the graph, the line crosses the x axis at x = 1 (2nd tick line)
Each tick line represents 0.5
The zero is the value of x when it crosses the x axis
As a result the polynomial has a zero at x = 1
The correct option is there is a zero at x = 1 (option D)
The diameter of the moon is
3,474,000 meters. Which is the
best estimate of the diameter of the
moon?
The best estimate of the diameter of the moon is 3.474×10⁶.
The best estimate of the diameter will be calculated by converting the number into scientific notation. To convert the number into scientific notation it is broken into two parts.
First number is coefficient which has to range between 1 and 10. So, as per the digits, 3.474 will be the coefficient.
The 10 will be written along with exponent. There are three digits after the decimal followed by three zeroes. Therefore, the 10 and exponent will be written as 10⁶.
So, the complete number estimating the diameter of moon is 3.474×10⁶.
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X centimetersThe perimeter of a geometric figure is the sum of the lengths of its sides. The perimeter ofthe pentagon (five-sided figure) on the right is 54 centimeters.a. Write an equation for perimeter.b. Solve the equation in part (a).c. Find the length of each side.X centimetersx centimeters3x centimeters3x centimetersa. Choose the correct answer below.O A. x + x + x + 3x + 3x = 54OB. 9x5 = 54O C. X + x + x + x + x = 54OD. X + x + x + 3x + 3x = 9
The perimeter of a geometric figure is the sum of it's side lengths.
We have a pentagon with side lengths equal to:
x, x, x, 3x, and 3x
a)
The perimeter of this pentagon is:
P = x + x + x + 3x + 3x
Since the perimeter is given as 54 cm:
x + x + x + 3x + 3x = 54
Answer: Option A
b) Solve the equation in part a)
Collecting all like terms:
9x = 54
Dividing by 9:
x = 54 / 9
x = 6 cm
c) Find the length of each side.
The sides are
x=9 cm
x=9 cm
x=9 cm
3x=27 cm
3x=27 cm
PLS HELP!! WILL MARK BRANLIEST What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?
Make sure to use decimals, if necessary, and write with no spaces in the format (x,y) with you solving for x and y.
When we want to determine the midpoint of two points on a line segment, we must first determine the coordinates of the two points. Then we divide the sum of the abscissa [tex](x)[/tex] by [tex]2[/tex] to find the abscissa of the midpoint and divide the sum of the ordinates [tex](y)[/tex] by [tex]2[/tex] to find the ordinate of the midpoint.
Let the coordinates of our midpoint be [tex]F(a,b)[/tex].
[tex]F(a)=\frac{4+(-2)}{2}=1[/tex][tex]F(b)=\frac{7+(-2)}{2} =\frac{5}{2}=2.5[/tex]We found our midpoint.
[tex]F(a,b)=(1,2.5)[/tex]Find the x-intercepts of the polynomial y = a2 + 16a + 64
Given the polynomial:
[tex]y=a^2+16a+64[/tex]The x-intercepts are the points in which the polynomial crosses the x-axis. That is, are the points (x, 0).
To find these points, use the quadratic formula according to the steps below.
Step 01: Substitute the values in the quadratic formula.
For a equation y = ax² + bx + c, the x-intercepts are:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this question,
a = 1
b = 16
c = 64
Substituting the values:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-16\pm\sqrt[]{16^2-4\cdot1\cdot64}}{2\cdot1} \end{gathered}[/tex]Step 02: Solve the equation above.
Begin by solving the square and the multiplications:
[tex]x=\frac{-16\pm\sqrt[]{256^{}-256}}{2}[/tex]Now, subtract the values inside the root.
[tex]x=\frac{-16\pm\sqrt[]{0}}{2}[/tex]Solve the root:
[tex]x=\frac{-16\pm0}{2}[/tex]And find the values of x:
[tex]\begin{gathered} x_1=\frac{-16-0}{2}=-\frac{16}{2}=-8 \\ x_2=\frac{-16+0}{2}=-\frac{16}{2}=-8 \end{gathered}[/tex]Answer: The x-intercepts are: (-8, 0), (-8, 0).
2 is subtracted from the square of a numberWrite as an algebraic expression.
Answer:
x²-2
Explanation:
Let the number be x.
The square of the number = x²
If 2 is subtracted from the square of the number, we have:
[tex]x^2-2[/tex]Therefore, an algebraic expression for the statement "2 is subtracted from the square of a number" is x²-2.
the economys real gdp was 100 billion in 2019 and 240 billion in 2020. its population was 15 million in 2019 and 15 million in 2020. what is the growth rate of real gdp per capita from 2019 to 2020
The growth rate of real gdp per capita from 2019 to 2020 is 40%
Given,
The real gdp of an economy in 2019 = 100 billion = 100, 000, 000, 000
The real gdp of an economy in 2020 = 240 billion = 240, 000, 000, 000
The population in 2019 = 15 million = 15, 000, 000
The population in 2020 = 15 million = 15, 000, 000
Growth rate of real gdp per capita =( increased gdp × 100) / (initial gdp)
Here,
Initial gdp = 100,000,000,000 / 15,000,000 = 6666.67
Increased gdp = 240,000,000,000 / 15, 000, 000 = 16000
Now,
Growth rate of real gdp per capita =( increased gdp × 100) / (initial gdp)
Growth rate of real gdp per capita = (16000 × 100) / 6666.67 = 240
That is,
The growth rate of real gdp per capita from 2019 to 2020 is 40%
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An item costs $430 before tax, and the sales tax is $8.60.
Find the sales tax rate. Write your answer as a percentage.
The sales tax rate of an item which cost $430 and tax of $8.60 is 2%
How to find the sales tax rate?Sales tax refers to local or state tax imposed as a percentage of the selling price of goods or services payable by the customer. The tax is not recognized as the seller's earnings as the seller only collects the tax and transmits it to local or state authorities.
Cost of item before tax = $430Sales tax = $8.60Sales tax rate = Sales tax / Cost of item before tax × 100
= $8.60 / $430 × 100
= 0.02 × 100
= 2%
In conclusion, the sales tax rate of the item is given by 2%.
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Dave's wardrobe contains 25 T-shirts, of which 13 are gray. Dave selects a T-shirt at random.
What is the probability that Dave will select a gray T-shirt?
Enter a reduced fraction
What are the odds in favor of Dave selecting a gray T-shirt?
Enter the ratio in lowest terms
The probability that Dave will select a gray T-shirt is 13 / 25.
The odds in favor of picking a gray T-shirt is 13 : 25
What is the probability?
Probability is used to calculate the odds that are in favor or against a random event happening. The odds in favor or against a random event happening has a probability value that lies between 0 and 1. The higher the odds that are in favor of the event happening, the closer the probability value would be to 1.
The probability that Dave will select a gray T-shirt = number of gray T-shirts / total number of T-shirts
13 / 25
Ratio is used to compare two or more numbers together.
The odds in favor of picking a gray T-shirt = number of gray T-shirt : total number of T-shirts = 13 : 25
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The heights of ten-year-old males are normally distributed with a mean of 57.4 inches and a standard deviation of 5.1 inches. If a pediatrician selects a random sample of 46 ten-year-old males from his patient population, what is the probability that the mean height of this sample will be greater than 57 inches?Round your answer to at least three decimal places
Given:
[tex]Means,\text{ }\mu=57.4[/tex][tex]Standard\text{ deviation, }\sigma=5.1[/tex][tex]The\text{ sample size, n=46.}[/tex]Required:
We need to find the probability that the mean height of this sample will be greater than 57 inches,
[tex]P(x>57).[/tex]Explanation:
Consider the formula to find the z-score.
[tex]z=\frac{\mu-x}{\frac{\sigma}{\sqrt{n}}}[/tex][tex]Subst\text{itue }\mu=57.4\text{, }\sigma=5.1,\text{ n=46 and x=57 in the formula.}[/tex][tex]z=\frac{57-57.4}{\frac{5.1}{\sqrt{46}}}[/tex][tex]z=\frac{-0.4}{\frac{5.1}{\sqrt{46}}}[/tex][tex]z=-0.4\times\frac{\sqrt{46}}{5.1}[/tex][tex]z=-0.5319[/tex]From the z table, we get
[tex]P(x<57)=0.2974[/tex][tex]\text{We know that }P(x>57)=1-P(x<57).[/tex][tex]Substitut\text{e }P(x<57)=0.2974\text{ in the equation.}[/tex][tex]P(x>57)=1-0.2974.[/tex][tex]P(x>57)=0.7026.[/tex][tex]P(x>57)=0.703.[/tex]
Final answer:
The probability that the mean height of this sample will be greater than 57 inches is 0.703.
And also state the vertex and the axis of symmetry. I need help with number 2
In order to complete the square remember that
[tex](x\pm a)^2=x^2\pm2\cdot x\cdot a+a^2[/tex]first, equal the expression divide all the expressions by 2,
[tex]\begin{gathered} f(x)=2x^2+4x+7 \\ 2x^2+4x+7=0 \\ 2x^2+4x=-7 \\ x^2+2x=-\frac{7}{2} \end{gathered}[/tex]then, we can find "a" using the second portion of the definition
[tex]\begin{gathered} 2\cdot x\cdot a=2x \\ a=\frac{2x}{2x} \\ a=1 \end{gathered}[/tex]then,
[tex]a^2=1^2=1[/tex]add 1 on both sides
[tex]\begin{gathered} x^2+2x+1=-\frac{7}{2}+1 \\ x^2+2x+1=-\frac{5}{2} \end{gathered}[/tex]rewrite as a square expression on the left,
[tex](x+1)^2=-\frac{5}{2}[/tex]multiply both sides by 2
[tex]2(x+1)^2=-5[/tex]bring all to the left side and equal to f(x)
[tex]\begin{gathered} f(x)=2(x+1)^2+5 \\ \text{The vertex is at (-1,5)} \\ \text{the axis of symmetry is x=-1} \end{gathered}[/tex]How do you write a point slope form equation from this graph?
Answer: y-1=3(x-3)
this in the correct answer. you take one point on the line and substitues x and y of the point into the equation. M is your slope. y-y1=m(x-x1)
A parallelogram has one angle that measures 24°. What are the measures of the other three angles in the parallelogram?°, °, and °
Answer:
[tex]24\degree,156\degree,\text{ and 156}\degree[/tex]Explanation:
Here, we want to get the measure of the other three angles in a parallelogram
The angle rules in a parallelogram are:
i) Opposite angles are equal to each other
ii) The two adjacent angles add up to 180 degrees
From what we have, one of the angles is 24 degrees
The measure of the last two angles would be:
[tex]180-24\text{ =156}\degree[/tex]The product of two consecutive
odd positive integers is one hundred forty-three. Find the integers.
The integers are 71 and 72 respectively
What is an algebraic expression?An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, factors and constants.
They are also known to be composed of mathematical operations such as;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcFrom the information given , we have;
x + 1 + x + 2 = 143
collect like terms
2x = 143 - 3
Subtract like terms
2x = 140
Make 'x' the subject
x = 140/2
x = 70
The numbers are;
x + 1 = 70 + 1 = 71
x + 2 = 70 + 2 = 72
Hence, the numbers are 71 and 72
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Write +/99 +/44 in the form avb where a and b are integers.
Step-by-step explanation:
[tex] \sqrt{99} = 3 \sqrt{11} \\ \sqrt{44} = 2 \sqrt{11} \\ 3 \sqrt{11} + 2 \sqrt{11} = 5 \sqrt{11} [/tex]
Answer:
[tex]3 \sqrt{11} [/tex]
[tex]4 \sqrt{11} [/tex]
because we rewrite it as integer statements
help l need to finish this
Answer:
Your answer is [tex]y = 2x - 2[/tex]
Step-by-step explanation:
Just test it out on all of them, it fits.
For any positive numbers, a, b and d, with b = 1, logb = d•log b a
The exponent multiplies the logarithm of the base
So:
[tex]\log_ba^d=d\log_ba[/tex]The answer is option C
Kendall rode her bike 7 miles in 45 minutes. If she maintains this speed, how far can she ride in 2 hours? Round your answer to the nearest tenth of a mile.
Kendall can ride about ___ miles in 2 hours.
Answer:
18.7 miles
Step-by-step explanation:
You want to know how far Kendall can ride her bike in 2 hours if she rides at the speed of 7 miles in 45 minutes.
ProportionThe question assumes that distance is proportional to time, so the distance (d) of interest can be written in the proportion ...
miles/minutes = 7/45 = d/120 . . . . . . 120 minutes is 2 hours
Multiplying by 120, we have ...
d = 120(7/45) = 7(8/3) = 18 2/3 ≈ 18.7
Kendall can ride about 18.7 miles in 2 hours.
all you need is on the photo this is homework please i really needed heeeeelp
the zeros of the graph tell us the time needed for the tank to be drain.
(2t-7)(2t-9)
Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s. For example, che value of a particular rocking chair is well approximated byV = 60(1.25)^twhere V is in dollars and t is the number of years since 1975. Find the rate, in dollars per year, at which the price is increasing.Rate= ____ dollars/yr
SOLUTION:
Step 1:
In this question, we are given the following:
Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s.
For example, the value of a particular rocking chair is well approximated by:
[tex]V=60(1.25)^t[/tex]where V is in dollars and t is the number of years since 1975.
Find the rate, in dollars per year, at which the price is increasing.
Step 2:
Next,
[tex]\begin{gathered} \text{Given,} \\ V=\text{ }60(1.25)^t \\ \text{Calculating the rate, } \\ we\text{ ne}ed\text{ to differentiate V with respect to t, we have that:} \\ \frac{dV}{\differentialDt t}=(1.25)^t\ln (1.25)\text{ 60} \end{gathered}[/tex]
Now, we need to evaluate:
[tex]\begin{gathered} \ln (1.25)60\text{ = 13. 38861308 }\approx\text{ 13. 3886} \\ \end{gathered}[/tex]Hence, the rate, in dollars per year since 1975, at which the price is increasing is:
[tex]\frac{dV}{\differentialDt t}=13.3886(1.25)^t[/tex]
Determine the magnitude and direction of vector a = (3,8) Round to the nearest tenths. |a| =theta =
Recall the definitions of the magnitude and direction of a vector:
[tex]\begin{gathered} \parallel a\parallel=\sqrt[]{3^2+8^2}=\sqrt[]{73}=8.5 \\ \theta=\tan ^{-1}(\frac{8}{3})=69.4^{\circ} \end{gathered}[/tex]Someone please help I’m stuck. The question is 13. (L4)
Donna is right. 115° angle and ∠3 are supplementary.
From the figure, we are discussing about the 115° angle and ∠3.
Donna says that m∠3 = 65° because the 115° angle and ∠3 are supplementary. That is their sum = 180°.
From the figure, it is clear that the 115° angle and ∠2 are supplementary.
So ∠2 = 180° -115° = 65°.
Now ∠2 and ∠3 are corresponding angles formed between the parallel lines m and q. Since corresponding angles are equal, m∠2 = m∠3.
Thus m∠3 = 65°.
Thus 115° + m∠3 = 115° + 65° = 180°
As the sum of the 115° angle and m∠3 = 180°, they are supplementary.
Hence Donna is correct.
Luis said that 115° and ∠3 are alternate but they are not. Alternate angles are those which are formed in the interior and on the opposite sides of the transversal cutting two parallel lines. They are of same size. But here, m∠3 ≠ 115°.
So Luis is not right.
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please help me ASAP!!!
This is the correct answer, this is because it only function that the inverse is correctly represented
[tex]\begin{gathered} y\text{ = }\sqrt[3]{x+3} \\ y^3=\text{ x+3} \\ x=y^3-3 \\ f^{-1}(x)=x^3-3 \end{gathered}[/tex]Which of the statements is true for the two equations below?
Explanation:
Equation A
[tex]undefined[/tex]Deriving the equation of parabola given its focus and directrix
The equation of the parabola from its focus and vertex is 5x = 4y² .
A parabola is a mirror-symmetrical, roughly U-shaped planar curve. The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.
A line and a point (the focus) are two components of one definition of a parabola (the directrix). There is less emphasis on the directrix. The parabola is the location of the endpoints in that plane that are equally spaced away from the directrix and the focus.
Another approach to define a parabola is as a conic section formed by the union of a right circular conical area with a plane parallel to another axis perpendicular to the conical surface.
from the figure the parabola is opening on the right side.
Hence the general equation of the parabola is is y² = 4ax
Now from the focus we get 4a = 5
or, a = 5/4
Hence the equation of the parabola is 5x = 4y².
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8 Real life /
and are blue.
Rasheed and Kamal did a survey on car colours.
Problem-solving Approximately of cars in the UK are silver
a Rasheed found 120 people had silver cars.
How many people could he have asked?
b Kamal found 120 people had blue cars.
How many people could he have asked?
Using proportions, it is found that the number of people that each asked is given as follows:
a) Rasheed: 571 people.
b) Kamal: 667 people.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication and division, with the unit rates or percentages of the problem.
For Rasheed, since he was counting people with silver cars, we have that 21% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:
0.21n = 120
n = 120/0.21
n = 571 people. (rounding)
For Kamal, since he was counting people with blue cars, we have that 18% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:
0.18n = 120
n = 120/0.18
n = 667 people. (rounding)
Missing informationThe percentages of car colors in the UK are mussing and are given as follows:
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Write an equation of the parabola that passes through the point (-9, 2) and has vertex (-3,1).
Answer:
[tex]\textsf{Vertex form}: \quad y=\dfrac{1}{36}(x+3)^2+1[/tex]
[tex]\textsf{Standard form}: \quad y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Given:
Vertex = (-3, 1)Point = (-9, 2)Substitute the given vertex and point into the formula and solve for a:
[tex]\begin{aligned}y&=a(x-h)^2+k\\\\\implies 2&=a(-9-(-3))^2+1\\2&=a(-6)^2+1\\2&=36a+1\\36a&=1\\a&=\dfrac{1}{36}\end{aligned}[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]\boxed{y=\dfrac{1}{36}(x+3)^2+1}[/tex]
In standard form:
[tex]\implies y=\dfrac{1}{36}(x+3)(x+3)+1[/tex]
[tex]\implies y=\dfrac{1}{36}(x^2+6x+9)+1[/tex]
[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{6}{36}x+\dfrac{9}{36}+1[/tex]
[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]
If the point (2,-5) is reflected in the line y=x, then the image is:
Answer:
(-5, 2)
Explanation:
If a point (x,y) is reflected in the line y=x, the x-coordinate and y-coordinate change places.
That is:
[tex](x,y)\to(y,x)[/tex]Therefore, the image of (2, -5) when reflected in the line y=x is:
[tex](-5,2)[/tex]