In ΔPQR, \overline{PR} PR is extended through point R to point S, \text{m}\angle QRS = (7x+8)^{\circ}m∠QRS=(7x+8) ∘ , \text{m}\angle RPQ = (x+12)^{\circ}m∠RPQ=(x+12) ∘ , and \text{m}\angle PQR = (3x+20)^{\circ}m∠PQR=(3x+20) ∘ . Find \text{m}\angle RPQ.m∠RPQ.
Answers
The measurement of ∠RPQ is 20°.
What is the meaning of extended point?
A polygon's extended side or sideline in plane geometry is the line that contains one of the polygon's sides. Several situations call for the extension of a side.
Given that,
In ΔPQR, the side PR is extended to the point S.
The measurement of ∠RPQ is (x+12)°, ∠QRS is (7x+8)°, and ∠PQR is (3x+20)°.
We know that, the exterior angle of triangle is equal to the sum of opposite interior angles.
Therefore,
∠QRS = ∠RPQ + ∠PQR
Putting the value of ∠QRS, ∠RPQ, ∠PQR in the above equation:
(7x+8)° = (x+12)° + (3x+20)°
7x + 8 = 4x + 32
Subtract 4x from both sides:
3x + 8 = 32
Subtract 8 from both sides:
3x = 24
Divide both sides by 3:
x = 8
Putting x = 8 in ∠RPQ = (x+12)°
∠RPQ = (8+12)° = 20°
To learn more about exterior angle, click on below link:
https://brainly.com/question/22073609
#SPJ1
Related Questions
e throw a fair die three times. if we observe the first throw is a 4, what is the probability that there is at least two 4s in the three throws?
Answers
The probability that there is at least two 4s in the three throws is 0.05 or 5%
Probability
In statistics, probability deals with the possibility of happening of the events.
Given,
Here we know that the throw a fair die three times. if we observe the first throw is a 4.
And we need to find the probability that there is at least two 4s in the three throws.
According to the given question, we know that the dice is thrown 3 time.
Then the sample space of the given event is 216.
Here we know that the first throw has 4.
And we need to find the probability of getting two 4s in the 3 throws,
So, the possible number of events are.
=> {444, 441, 442, 443, 445, 446, 414, 424, 434, 454, 464}
So, the total possible number is 11.
Then the probability is,
=> 11/216
=> 0.05 or 5%
To know more about Probability here.
https://brainly.com/question/11234923
#SPJ4
A stone is thrown vertically upward from a platform that is 20 feet height at a rate of 160 ft/sec. Use the quadratic function h(t) = −16t^2 + 160t + 20 to find how long it will take the stone to reach its maximum height, and then find the maximum height.
Answers
Check the picture below.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+160}x\stackrel{\stackrel{c}{\downarrow }}{+20} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 160}{2(-16)}~~~~ ,~~~~ 20-\cfrac{ (160)^2}{4(-16)}\right) \implies \left( - \cfrac{ 160 }{ -32 }~~,~~20 - \cfrac{ 25600 }{ -64 } \right) \\\\\\ \left( 5 ~~~~ ,~~~~ 20 +400 \right)\implies (\stackrel{seconds}{5}~~,~~\stackrel{feet}{420})[/tex]
3√y^2=6√x y=n√x
Find n
Answers
Answer:
n = 4
Step-by-step explanation:
Given equation:
[tex]\sqrt[3]{y^2} =\sqrt[6]{x}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies y^{\frac{2}{3}}=x^{\frac{1}{6}[/tex]
Take both sides of the equation to the power of ³/₂:
[tex]\implies \left(y^{\frac{2}{3}}\right)^\frac{3}{2} =\left(x^{\frac{1}{6}\right)^\frac{3}{2}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies y^{\frac{2}{3} \cdot \frac{3}{2}}=x^{\frac{1}{6} \cdot \frac{3}{2}}[/tex]
Simplify:
[tex]\implies y^{\frac{6}{6}}=x^{\frac{3}{12}[/tex]
[tex]\implies y^1=x^{\frac{1}{4}[/tex]
Apply exponent rule a¹ = a :
[tex]\implies y=x^{\frac{1}{4}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]
[tex]\implies y=\sqrt[4]{x}[/tex]
if f(x)=2x²-6, then find f(4)
Answers
Answer:
Substitute x = 4 into the equation.
f(4) = 2(4)² - 6
= 2(16) - 6
= 32 - 6
= 26
if triangle pqrs is similar to triangle wxyz find the value of x?
Answers
Answer:
x=60
Step-by-step explanation:
these shapes seem to be flipped
side WZ seems to be similar to PS
and Side ZY seems to be similar to RS
ewe can make ratios on the side lengths
40/75=32/x
cross multiply
40x=75(32)
40x=2400
/40. /40
x= 60
hopes this helps please mark brainliest
Consider the monthly payment formula M = (Pr(1+r)^n/(1+r)^n-1 What is the name of the formula you get if you solve for P?
What about if you solve for n? What special function do you need to use when solving for n?
I will give brainliest if correct.
Answers
In the given formula we have variables:
M - monthly payment,P - principal,r - interest rate,n - number of payments.If we have to solve it for P then it should be called 'Principal' or 'Loan amount'.
If we have to solve it for n then it should be called 'Number of payments' or 'Number of installments'.
Since n is the power of a number we need logarithm to solve it for n.
Answer:
"Principal (loan amount)"
"Term of the loan (in months)" or "Number of monthly payments"
Logarithms
Step-by-step explanation:
Monthly Payment Formula
[tex]M=\dfrac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}[/tex]
where:
M = monthly payment.P = principal loan amount.r = interest rate per month (in decimal form).n = term of the loan (in months).If we solve for P, the name of the formula is "Principal (loan amount)".
If we solve for n, the name of the formula is "Term of the loan (in months)" or "Number of monthly payments".
When solving for n, we need to use logarithms:
[tex]\boxed{\begin{aligned}M&=\frac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\\\\M(\left(1+r\right)^n-1)&=Pr\left(1+r\right)^n\\\\\frac{\left(1+r\right)^n-1}{\left(1+r\right)^n}&=\frac{Pr}{M}\\\\1-\frac{1}{\left(r+1\right)^n}&=\frac{Pr}{M}\\\\\frac{1}{\left(r+1\right)^n}&=1-\frac{Pr}{M}\\\\\left(r+1\right)^{-n}&=1-\frac{Pr}{M}\\\\\ln \left(r+1\right)^{-n}&=\ln \left(1-\frac{Pr}{M}\right)\\\\-n\ln(r+1)&=\ln\left(1-\frac{Pr}{M}\right)\\\\n&=\frac{-\ln\left(1-\frac{Pr}{M}\right)}{\ln(r+1)}\end{aligned}}[/tex]
You start at (4, 0). You move up 10 units. Where do you end?
Answers
Answer: (4, 10)
Step-by-step explanation:
The first number, 4, is the number on the x axis, the horizontal axis. The second number 0 is the number on the y axis, the vertical axis.
If you move up you would moving on the y axis, therefore the second number, 0, would change.
You moved 10 units so starting at 0 move up 10 units. 0 + 10 = 10
Now you're at (4, 10)
the lifetime in months of a transistor in a certain application is random with probability density function
Answers
The chance density characteristic of lifetime in months of a transistor in a positive utility is:
[tex]f(x)=0.4cdot e^x > 0f(x)=0.4⋅e −0.4x ;x>0[/tex]
The chance density characteristic shows that the random variable X follows a exponential characteristic with parameter λ = 0.4.
Compute the suggest lifetime as follows:
[tex]mu=frac=2.5μ= λ1 = 0.401 =2.5[/tex]
Thus, the suggest lifetime is months.
Compute the usual deviation of the lifetimes as follows:
[tex]sigma=2.5σ= λ 2 1 = 0.40 2 1 =2.5.[/tex]
Thus, the usual deviation of the lifetimes is 2.5 months.
Compute the sixtieth percentile of the lifetime as follows:
Thus, the sixtieth percentile of the lifetime is 2.3 months.
Read more about density:
https://brainly.com/question/1354972
#SPJ4
What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?
a. The 90% C.I. is wider and includes more values than the 95% C.I.
b. The 95% C.I. is more precise in estimating a mean than the 90% C.I.
c. The 90% C.I. is more precise in estimating a mean than the 95% C.I.
d. The 95% C.I. is narrower and includes less values than the 90% C.I.
Answers
The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.
You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.
The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.
To learn more about confidence interval here:
https://brainly.com/question/24131141
#SPJ4
21) Submarine A is sent to explore the ocean floor in the Atlantic Ocean. It descends to 126
feet below sea level, For the next 4 ½ hours, it descends further at a rate of 15 feet per hour
and then reaches its destination.
Submarine B is sent to explore the ocean floor in the Pacific Ocean. It begins its descent at
sea level and reaches the same elevation as Submarine A over the course of 6.5 hours. At
what rate does Submarine B descend? Show and explain your thinking.
Answers
The rate at which Submarine B descends is 29.8 feet per hour.
What is the rate?The rate refers to the average speed of an object in motion from one point to another.
The rate can be determined by dividing the distance by the time.
The rate or average speed is the quotient between distance and time.
The distance descended by Submarine A = 193.5 feet (126 + 4 ½ x 15)
The time Submarine B descends = 6.5 hours
Submarine B's rate of descent = 29.77 feet (193.5/6.5) per hour
= 29.8 feet
Thus, we can conclude that Submarine B descends at the rate of 29.8 feet every hour, whereas, Submarine A descends 15 feet per hour.
Learn more about the average speed at https://brainly.com/question/4931057
#SPJ1
a landscaper is designing a flower garden in the shape of a trapezoid he wants the shorter base to be 2 yards greater than the height of the trapezoid h and the longer base to be
Answers
The length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.
What is a Trapezoid?A quadrilateral with at least one set of parallel sides is called a trapezoid in American and Canadian English.
In British and other varieties of English, it is termed a trapezium.
In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.
The parallel sides are called the basis of the trapezoid.
So, we have:
The height should be 3 yards higher than the shorter base.
b₁=h+3
The height should be 3 yards higher than the shorter base.
b₂=h+7
Formula for Area of trapezoid = 1/2(b₁+b₂)h
Now, using the formula, calculate as follows:
150=1/2(h+3+h+7)h
150=(2h+10)h/2
150=2h²+10h/2
150=2h²+5h
h²+5h-150=0
h²+15h-10h-150=0
h(h+15)-10(h+15)=0
(h-10)(h+15)=0
h=10 or h-15
h should be positive:
b₁=h+3=15+3=18
b₂=h+7=15+7=22
Therefore, the length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.
Know more about a Trapezoid here:
https://brainly.com/question/1410008
#SPJ4
Complete question:
A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answers
The required choice for inequality is Option 2.
What is inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.
Given, 3(8 – 4x) < 6(x – 5)
or, 24 - 12x < 6x - 30
or, 24 + 30 < 6x + 12x
or, 54 < 18x
or, 18x > 54
or, x > 3 means x is greater than positive 3 and pointing to the right.
Hence, the required choice for inequality is Option 2.
To learn more about inequality
https://brainly.com/question/25275758
#SPJ1
Answer: b
Step-by-step explanation:
g the correlation between two variables a and b is .10 with a p value of .01 what should we conclude
Answers
We can conclude that there is a statistically significant correlation between the two variables, a and b. The correlation coefficient is .10, which indicates a weak positive relationship.
A correlation coefficient of .10 indicates that there is a weak positive relationship between the two variables, a and b. A p-value of .01 indicates that the correlation between the two variables is statistically significant, meaning that it is unlikely to be due to chance. This suggests that there is a real relationship between the two variables, even though it is weak.
To calculate the correlation coefficient, you can use the formula where x and y are the two variables in question. In this case, the correlation coefficient is .10. This can be determined by plugging in the values for x and y and doing the necessary calculations.
Learn more about correlation here
https://brainly.com/question/28898177
#SPJ4
what are the steps to -3+7x-9+8x=54
Answers
Answer: 67/15
Step-by-step explanation:
-3+7x-9+8x=54
-12 + 15x = 54
15x = 67
x = 67/15
Each minute, a faucet allows 4/7 gallons of water to enter a large tub, and the drain allows 5/7 gallons to leave the tub.
What is the change in the amount of liquid in the tub after 1/4 minute?
Enter your answer as a fraction in lowest terms in the box.
gal.
Answers
Answer: -1/28 gallon
Step-by-step explanation:
divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)
Answer: -1/28 gallon
Step-by-step explanation:
There are two option for tickets & admission to the carnival. Option #1 requires you to pay a $5 admission fee plus $0.30 per ride ticket. Option #2 requires you to pay a $3 admission fee plus $0.80 per ride ticket. Garrett chose option #1 and Meagan chose option #2. If they wound up paying the same amount of money, how many tickets did they each purchase?
Answers
The number of tickets they purchased is 4.
How many tickets did they purchase?The expression that would b used to represent the total cost at the carnival is a linear expression. A linear expression is an expression that has a single variable that is raised to the power of one.
The form of the linear expressions that can be used to represent the total cost at the carnival is:
Total cost = admission fee + (price per ride x number of rides)
Total cost in option 1 = $5 + 0.30r
Total cost in option 2 = $3 + $0.80r
Where r = number of rides
When they pay the same amount of money, the linear functions would be equal:
$5 + 0.30r = $3 + $0.80r
$5 - $3 = $0.80r - 0.30r
$2 = $0.50r
r = 2 / 0.5
r = 4
To learn more about cost, please check: https://brainly.com/question/12125744
#SPJ1
Marcus monthly salary is $1,500 plus 10% of sales. How much could Marcus earn per month with salary and 9% sales? Please explain your answer.
pls
Answers
If Marcus monthly salary is $1,500 plus 10% of sale, then he could earn 1500 + 0.09x per month with salary and 9% sales
Monthly salary of Marcus = $1500
The percentage incentives for sales = 10%
If the percentage of incentive for sales is 9 %
Consider the amount of sales is $x
Therefore the monthly salary of Marcus = Monthly salary of Marcus + (The amount of sales × 9/100)
Substitute the values in the equation
The monthly salary of Marcus = 1500 + (x×9/100)
Divide the numbers in the equation
= 1500 + (x × 0.09)
Multiply the numbers the numbers
= 1500 + 0.09x
Therefore, the monthly salary of Marcus will be 1500 + 0.09x
Learn more about percentage here
brainly.com/question/12715980
#SPJ4
the test statistics for one-way anova follows the _______.
Answers
The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.
Z-test definition:On data that is dispersed normally, the Z test is a parametric process that is applied. The z-test can be applied to proportions, two samples, or one sample to test hypotheses. When the population variance is known, it is possible to determine whether the means of two significant groups differ.
The second is one-way analysis of variance (ANOVA), which checks if three or more samples originate from populations with the same mean using the F-distribution.
The test statistic should be compared to the crucial value. If the test statistic is more extreme in favor of the alternative than the crucial value, the alternative hypothesis should be considered instead of the null hypothesis. If the test statistic is not as extreme as the crucial value, the null hypothesis should not be disregarded.
Therefore,
The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.
To learn more about One-way Anova visit : brainly.com/question/29554661
#SPJ4
In his free time, Gary spends 9 hours per week on the Internet and 12 hours per week playing video games. If Gary has five hours of free time per day, what percent of his free time is spent on the Internet and playing video games
Answers
Answer: 11.64%
Step-by-step explanation:
On a coordinate grid, line j passes through points (8, 2) and (-2,-2). On the same grid, line k
passes through points (-4, 3) and (-6, 8). Are lines j and k parallel, perpendicular, or neither?
Answers
Answer: lines j and k are perpendicular
Step-by-step explanation:
Let's find the equations of lines j and k
[tex]\displaystyle\\\boxed{\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
Line j: (8,2) (-2,-2)
x₁= 8 x₂=-2 y₁=2 y₂=-2
[tex]\displaystyle\\\frac{x-8}{-2-8}=\frac{y-2}{-2-2} \\\\\frac{x-8}{-10}=\frac{y-2}{-4} \\\\[/tex]
Multiply both parts of the equation by -4:
[tex]\displaystyle\\\frac{2}{5} (x-8)=y-2\\\\\frac{2}{5} x-\frac{16}{5} =y-2\\\\\frac{2}{5} x-3.2+2=y-2+2\\\\\frac{2}{5}x-1.2=y\\\\ Thus,\ y=\frac{2}{5}x-1.2[/tex]
Line k: (-4,3) (-6,8)
x₁=-4 x₂=-6 y₁=3 y₂=8
[tex]\displaystyle\\\frac{x-(-4)}{-6-(-4)} =\frac{y-3}{8-3} \\\\\frac{x+4}{-6+4}=\frac{y-3}{5} \\\\\frac{x+4}{-2} =\frac{y-3}{5}[/tex]
Multiply both parts of the equation by 5:
[tex]\displaystyle\\-\frac{5}{2}(x+4)=y-3\\\\ -\frac{5}{2}x-10=y-3\\\\ -\frac{5}{2}x-10+3=y-3+3\\ -\frac{5}{2}x-7=y\\Thus,\ y=-\frac{5}{2} x-7[/tex]
Hence, lines j and k are perpendicular
Which of the following congruence does not occur * A SSS B SAS C SSA D RHS?
Answers
Answer:
Answer Option C: SSA
How do you simplify 24 ⋅ 2^ − 2 ?
Answers
Answer:
Step-by-step explanation:
We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:24⋅2−2=24⋅12+2=244=6
Answer:
We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:
24⋅2−2= 24⋅1/2 OVER +2= 24/4= 6
Step-by-step explanation:
For a project in her Geometry class, Addison uses a mirror on the ground to measure
the height of her school's football goalpost. She walks a distance of 13.25 meters from
the goalpost, then places a mirror on flat on the ground, marked with an X at the
center. She then steps 1.3 meters to the other side of the mirror, until she can see the
top of the goalpost clearly marked in the X. Her partner measures the distance from
her eyes to the ground to be 1.55 meters. How tall is the goalpost? Round your answer
to the nearest hundredth of a meter.
1q
1.55 m
1.
13 m-
13.25 m
Answers
Answer:
the height of the goalpost is approximately 10.48 meters.
Step-by-step explanation:
To find the height of the goalpost, Addison needs to use the distance from the mirror to the goalpost, the distance from her eyes to the ground, and the angle formed by the goalpost, the mirror, and her eyes. She can use the law of cosines to solve for the height of the goalpost.
Let "a" be the distance from the goalpost to the mirror, "b" be the distance from the mirror to Addison's eyes, and "c" be the distance from Addison's eyes to the ground.
The law of cosines states that: c^2 = a^2 + b^2 - 2ab * cos(C), where C is the angle formed by the goalpost, the mirror, and Addison's eyes.
In this case, a = 13.25 meters, b = 1.3 meters, and c = 1.55 meters. We can substitute these values into the formula to solve for the angle C:
1.55^2 = 13.25^2 + 1.3^2 - 2 * 13.25 * 1.3 * cos(C)
Solving for cos(C) and using the inverse cosine function (arccos), we find that C = 52.22 degrees.
Now that we know the angle C, we can use the law of sines to solve for the height of the goalpost. The law of sines states that:
sin(C) / a = sin(A) / h, where A is the angle formed by the ground, the mirror, and the goalpost, and h is the height of the goalpost.
In this case, A = 180 - C - 90 = 180 - 52.22 - 90 = 37.78 degrees, and a = 13.25 meters. We can substitute these values into the formula to solve for h:
sin(52.22) / 13.25 = sin(37.78) / h
Solving for h, we find that the height of the goalpost is approximately 10.48 meters.
Therefore, the height of the goalpost is approximately 10.48 meters.
a jet airliner travels 1680 miles in 3 hours with a tail wind. the return trip, into the wind, takes 3.5 hours. write a system of equations whose solution is the ground speed of the airplane and the wind speed.
Answers
A system of equation is 1680mi3hr = p−w×600×2hr -p + w for a jet airliner travels 1680 miles in 3hours with a tail wind.
Let p be the speed of the jet airliner
and w be the speed of the tail wind
It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get
1680mi3hr = p−w×600×2hr = p + w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation, we use
200mph = p - w
Add w to both sides:
p = 200mph + w
Using the value of x, we can found the value of w using system of equations.
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
On dividing by 2:
50mph = w
So the speed of the tail wind is 50mph.
Therefore, 200mph = p - 50mph
Add 50mph on both sides:
250mph = p
Hence, speed of jet airliner is 250mph.
To know more about System of equation, visit here:
https://brainly.com/question/21620502
#SPJ4
Given the equation 8x = 4y + 16, generate a plan to rewrite it in slope-intercept form. Which variable do you solve for?
Answer: Convert the equation to slope-intercept form by solving for the variable y. Use the properties of equality to subtract 16 from both sides, and then divide both sides by 4.
This is for future people who don't want to watch adds or have hit their daily limit, have a nice day!
Answers
The slope-intercept form of the equation 8x = 4y + 16 will be y = 2x -4.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation given is 8x = 4y + 16.
We must solve for y as follows;
8x = 4y + 16
4y = 8x -16
By dividing through by 4; we have;
y = 2x -16
Hence the equation for both lines will be y = x +3 and y = x+13
Learn more about straight line, by the following link
https://brainly.com/question/16949303
#SPJ1
you are bored at a lunch meeting and surreptitiously place a raisin in your glass of water. the raisin swells to twice its original size. relative to the water, the raisin must have been:
Answers
If the raisin swells to twice its original size, relative to the water, the raisin must have been a)hypertonic solution. So, correct option is a.
Hypertonic alludes to an answer with higher osmotic strain than another arrangement. At the end of the day, a hypertonic arrangement is one in which there is a more noteworthy fixation or number of solute particles outside a layer than there are inside it.
A hypertonic arrangement is one which has a higher solute fixation than another arrangement.An illustration of a hypertonic arrangement is the inside of a red platelet contrasted and the solute centralization of new water.At the point when two arrangements are in touch, solute or dissolvable moves until the arrangements arrive at harmony and become isotonic concerning one another.Hence, correct option is a.
To know more about hypertonic solution, visit here:
https://brainly.com/question/29309024
#SPJ4
(Complete question) is:
You are bored at a lunch meeting and surreptitiously place a raisin in your glass of iced tea. The raisin shrinks to half its original size. The raisin must have been a __?__ solution.
a)hypertonic
b)aquatonic
c)hypotonic
d)isotonic
henry wants to earn at least trimming trees. he charges per hour and pays in equipment fees. what are the possible numbers of hours henry could trim trees?
Answers
The possible number of hours Henry could trim trees is t > 10.
The given information represents a scenario which demonstrates an inequality statement as Henry wants to earn at least $ 56, which means the amount earned should be greater than 56.
Let t be the possible number of hours Henry trim trees. As his per hour charge is $6 and he pays $4 in equipment fee, the inequality statement is:
6t – 4 > 56
Solving,
6t > 56 + 4
6t > 60
t > 10.
In order to earn at least $56, Henry must trim trees for at least 10 hours or more.
Note: The question is incomplete. The complete question probably is: Henry wants to earn more than $56 trimming trees. He charges $6 per hour and pays $4 in equipment rental fees. What are the possible number of hours Henry could trim trees?
Learn more about Inequality:
https://brainly.com/question/24372553
#SPJ4
the sum of the age of father and son at present iz 45 year.if both live on until the son age become equal to the father present age the sum of their agr then become 95 years .find the present ages.
Answers
Answer:
10 yrs old and 35 yrs old
Step-by-step explanation:
I figured it out by trial and error but here's the thinking process.
10 + 35= 45
Son becomes dad's age so 35-10=25, so plus 25 year to each age.
10+25=35
35+25= 60
35+60=95
I hope that makes enough sense!
a group of veterinarians at a major veterinary hospital was interested in investigating a possible link between enteroliths, stones that form in the colon of horses, and diet. they decided to conduct a survey of feeding practices of horses in the hospital's state. they created a survey questionnaire and decided to administer it to the owners of every fifth horse being treated at the hospital. the sample is a:
Answers
Fron the given question, we can say that systematic sample because not all sample are possible.
What is Systematic sampling?Using the probabilistic sampling technique known as systematic sampling, researchers periodically choose individuals from a community. Choose each 15th of her, for instance, from the population list. You can simulate the advantages of straightforward random sampling by randomly sorting the population.
[tex]Since every 100th horse is selected in the sample. Thus, Systematic Sampling is used.[/tex]
Further,
Sampling method is said to be Simple Random Sampling if unit from the population are picked randomly without any criteria, so that each unit as similar chance of selection.
If any criteria are used to select every sample, such as selecting every fourth unit, the sampling technique is said to be systematic sampling.
If the population is divided into various groups that share the same characteristic, the sampling method is said to be stratified sampling. Additionally, units are chosen at random from these groups.
To know more about Systematic Sampling visit:
https://brainly.com/question/24317913
#SPJ4
How do you determine whether the sequence a_n=(2^n+3^n) / (2^n−3^n) converges, if so how do you find the limit?
Answers
You determine the limit by [tex]\lim_{n \to \infty} a_n = -1[/tex].
A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. The concept of limit, which is founded on the idea of closeness, is largely used to give values to some functions at points when none are defined in a way that is consistent with values close by.
Divide the denominator and numerator by 3n as shown.
[tex]\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{2^n+3^n}{2^n-3^n\\}[/tex]
[tex]= \lim_{n \to \infty} \frac{(\frac{2}{3})^n+1 }{(\frac{2}{3})^n-1 } \\=\frac{0+1}{0-1} \\=-1[/tex]
To learn more about limits, refer:-
https://brainly.com/question/12211820
#SPJ4
