Answer:
Step-by-step explanation:
First let us determine the perpendicular line by remembering that a perpendicular line that intersects with the current line must have the opposite reciprocal slope as it. Meaning... the current slope is -1/2 and the opposite reciprocal is +2 or 2.
To clarify...
*opposite= the opposite sign ex. the opposite of +3 is -3 and the opposite of -1 is +1
*reciprocal=put simply, the reciprocal is the flipped version of the current number ex. the reciprocal of 1/2 is 2/1 or 2 and the reciprocal of 3 or 3/1 is 1/3
After we determine the slope of the perpendicular line, we are also know the point it must pass through.
Given that, we can find the equation.
Using y=mx+b
Plug in known varibles
y=-5
x=-4
m=2
b=?
-5=2(-4)+b
b=3
So now that we have b, we can put the equation in standard form.
y=2x+3
Hope this helps!!!
What is the domain of function f?
Answer:
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set.
Answer:
B. -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞
Step-by-step explanation:
The domain of a graph is all the x-values it covers. Since this graph does not have any arrows at its end or beginning points, we can assume it goes on forever. Lines that go on forever always have an infinite domain.
Eva is solving the equation 4(x+32)=8
She says, “I can subtract 32 from each side to get 4x=132 and then divide by 4 to get x=138."
Dakota says, “I think you made a mistake.”
Determine the correct value for x.
x=
Answer:
The correct answer is -30
Step-by-step explanation:
4(x+32)=8 basically you multiply 4 times the numbers that are in the parentesis which that will equals to 4x+128 because 4x1= 4x and 4x32 = 128. then you subtract 128 from 8 which equals to -120. you divide -120 by 4 which equals to -30.
Solid A and Solid B are similar. The surface area of Solid A is 675 m² and the surface area of
Solid B is 432 m2. If the volume of Solid B is 960 m3, find the volume of Solid A.
The Volume of solid A that is similar to solid B is: 960 × 1.25 = 1,200 m³.
What is the Surface Area and Volume of Similar Shapes?If two solids, A and B, are given and have corresponding dimensions as a and b respectively, we would have the following:
Surface area of solid A/Surface area of solid B = a²/b²
Volume of solid A/Volume of solid B = a³/b³
Given that solid A and solid B are similar, and:
Surface area of solid A = 675 m²Surface area of solid B = 432 m²Volume of solid B = 960 m³.Find their corresponding dimensions, a and b:
Surface area of solid A/Surface area of solid B = a²/b²
Substitute
675/432 = a²/b²
√(675/432) = a/b
1.25 = a/b
Scale factor of Solid A to Solid B is 1.25.
Multiply 1.25 by 960 to get the volume of solid A.
Volume of solid A = 960 × 1.25 = 1,200 m³.
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Write a mixed number between 5 and 6, and then write its reciprocal.
Answer: 11/2
Reciprocal: 2/11
Step-by-step explanation: 11/2 is 5.5 (between 5 and 6) the reciprocal or 11/2 is 2/11
Jade wants to buy a $200,000 term life insurance policy. she is 34 years old. using the premium table, what is her annual premium for a 10 year policy? a 5-column table with 6 rows titled annual life insurance premium (per 1,000 dollars of face value). column 1 is labeled age with entries 30, 31, 32, 33, 34, 35. column 2 is labeled 5-year term male with entries 3.98, 4.08, 4.19, 4.30, 4.42, 4.54. column 3 is labeled 5 year term female with entries 3.66, 3.76, 3.87, 3.98, 4.10, 4.22. column 4 is labeled 10-year term male with entries 6.06, 6.13, 6.30, 6.38, 6.45, 6.53. column 5 is labeled female with entries 5.72, 5.79, 5.85, 5.93, 6.01, 6.09. a. $1,290 b. $1,202 c. $6,010 d. $820
Premium rates are often referred to as premium per fixed face value. Jade's annual premium for a 10-year policy of $200,000 is $1,202.
How to calculate the total annual premium for $x?
When it's given that the annual premium is $p per $y face value, then we can calculate the annual premium for $1 face value and then use it to calculate the annual premium for $x. Therefore using proportions, we can write,
$y face value : $p annual premium
[tex]\text{\$1 face value} : \$\dfrac{P}{y}\ \rm annual\ premium[/tex]
[tex]\text{\$x face value} : \$\dfrac{P\times x}{y}\ \rm annual\ premium[/tex]
In the given case, from the tables, we see that for age 34, and 10-year life insurance for the female gender, there is an annual premium of 6.01 per $1000 face value.
Therefore, we will get the value of p = 6.01, and y = 1000.
As mentioned that Jade wants to buy Life insurance for $200,000, therefore, x = $200,000
Putting it in the above-derived formula, we get:
[tex]\text{\$x face value} : \$\dfrac{P\times x}{y}\ \rm annual\ premium[/tex]
[tex]\text{\$200,000 face value} : \$\dfrac{6.01\times 200,000}{1,000}\ \rm annual\ premium = \$1,202\ \rm annual\ premium[/tex]
Hence, Jade's annual premium for a 10-year policy of $200,000 is $1,202.
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Answer:
b 1,202 on edge 2022
Step-by-step explanation:
Find the 10th term of the following geometric sequence 6,24,96,384,…
Answer:
1572864
Step-by-step explanation:
the nth term of a geoemtric series can be calculated using the following rule : [tex]a_n=a_1(r)^n^-^1[/tex]
where an = nth term, a1 = first term , r = common ratio and n = term position.
here, the first term is 6, the common ratio is 4 and the term position is 10 ( because we want to find the 10th term )
so a1 = 6 , r = 4 and n = 10
using these values we plug them into the rule
recall rule : [tex]a_n=a_1(r)^n^-^1[/tex]
==> plug in a1 = 6 , r = 4 and n - 10
[tex]a_1_0=6(4)^1^0^-^1[/tex]
==> subtract 10 and 1
[tex]a_1_0=6(4)^9[/tex]
==> simplify exponent
[tex]a_1_0=6(262144)[/tex]
==> simplify multiplication
[tex]a_1_0=1572864[/tex]
and we are done!
Note:
the common ration was found by dividing the first term by the next term
how do you find the circumference, radius, and diameter in area?
Answer:
Sample Respond: Let's assume it's equal to 14 cm. Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm . You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm² . Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm .
Step-by-step explanation:
I got 100% on the quiz
Prism M is a dilation of Prism N. The height of Prism M is 4 3/4 ft, and the volume of Prism M is 68 2/5 ft³. The height of Prism N is 2 3/8 ft. What is the volume of Prism N?Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
8 11/20 ft³
Step-by-step explanation:
For dilated figures, the ratio of volumes is the cube of the ratio of corresponding linear dimensions.
Vn/Vm = (Hn/Hm)³
Vn = Vm(Hn/Hm)³ = (68 2/5 ft³)((2 3/8 ft)/(4 3/4 ft))³
Vn = (342/5 ft³)((19/8)/(19/4))³ = (342/5 ft³)(1/2)³ = 342/40 ft³
Vn = 8 11/20 ft³
The volume of Prism N is 8 11/20 ft³.
Answer:
The answer is 8 11/20.
Complete a Proportion Web for the following situation
A candy-wrapping robot can wrap 434 pieces of candy in 5 minutes. How many pieces of candy can it wrap in and number of minutes
Answer:
It can produce about 86 candy.
Step-by-step explanation:
434 divided by 5 = 86 with a remainder of 0.8
What is the solution of X+8/5x-1
-> O?
5
X5-8 or
x>
O x<-8 or x>5
0x
X
col-
0 -85x<5
0 -8 < x < 1 / 3
x - inf - 8 1/5 + inf
x+8 - 0 + +
5x-1 - - 0 +
result + 0 - ║ +
x+8/(5x-1) > 0 if x € ] -inf ; - 8[ U ] 1/5 ; + inf [
=> x < - 8 and x > 1/5
The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:
x ∈ (-∞, -8] ∪ [1/5, ∞)
We have,
To solve the inequality (x + 8)/(5x - 1) ≤ 0,
We can use the following steps:
Step 1:
Find the critical values of x where the expression (x + 8)/(5x - 1) is equal to zero or undefined.
The expression is undefined when the denominator is equal to zero:
5x - 1 = 0
x = 1/5
The expression is equal to zero when the numerator is equal to zero:
x + 8 = 0
x = -8
Therefore,
The critical values are x = -8 and x = 1/5.
Step 2:
Create a sign chart to determine the sign of the expression (x + 8)/(5x - 1) for each interval between the critical values.
On the interval (-∞, -8), the expression (x + 8)/(5x - 1) is negative if x + 8 is negative, which means x < -8.
On the interval (-8, 1/5), the expression (x + 8)/(5x - 1) is positive if both the numerator and denominator are negative, or if both are positive.
The numerator is negative on this interval, so the expression is positive if the denominator is negative, which means x < 1/5.
On the interval (1/5, ∞), the expression (x + 8)/(5x - 1) is negative if the numerator is negative and the denominator is positive, which means x > 1/5.
Step 3:
Write the solution in interval notation.
Therefore,
The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:
x ∈ (-∞, -8] ∪ [1/5, ∞)
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plllsss hhhheelllppp mee pllllsss
Answer:
The theoretical probability states that it should be equal. That is should be 50/50 but the experimental results show that the coin favoured heads.
you flip a coin and draw a marble at random from a bag containing two purple marbles and one white marble . what is the probability you flip a heads on the coin and draw a purple marble
Answer:
1/3 probability
Step-by-step explanation:
The probability that you flip heads is 1/2, one heads out of two possible (heads and tails).
The probability that you draw a purple marble is 2/3, two purples and three total (2 p +1 w).
To find the probability of both happening, multiply the probabilities together:
(1/2) * (2/3) = (2/6) = (1/3)
If you are asked to factorize only, can you also expand the brackets ? Or you can’t u less you are asked to? Please answer..
What is the slope of a line that is perpendicular to line m ?
Answer:
b) -b/a
Step-by-step explanation:
Slopes of perpendicular lines are negative reciprocals. That means to flip the fraction and change the sign. :-)
HELP HELP HELP HELO HELP HELP HELP
This function is Exponential
Reason: Exponential graphs tend to get very big quickly, and though they start out smaller than polynomial functions or vice versa
Hope that helps!
If remove the zero from 0.76 would it change the value of the number
If remove the zero from 10.25 would it change the value of the number
PLS HELP THIS WAS ON SHORT NOTICE AND I NEED IT DONE IN 30 MINUTES
!!!
Question 1:
Answer: The number does not changeRemoving the zero from 0.76 leads to .76 which is the same as before. Both lead to [tex]7.6 \times 10^{-1}[/tex] in scientific notation.
Personally I prefer the zero up front to make the decimal point stand out easier. Of course it's just a preference, so its up to you to decide which you prefer.
===========================================
Question 2:
Answer: Yes the number changesTaking the zero out of 10.25 leads to 1.25 which is definitely a different number (and smaller). Therefore, this zero is a significant digit compared to before.
The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $1.90. Today they made $78.60 from the 57 wraps sold. How many of the wraps so ld were vegetarian?
2. A football is punted into the air. Its height h, in metres, after t seconds is given by the equation
h(t) = -4.91? + 24.5t + 1
a) How high is the ball after 1 second?
b) Find the maximum height of the ball to one decimal place.
c) When does the ball reach its maximum height?
d) When does the ball hit the ground?
Answer:
I'll assume the ? is supposed to be t^2
See the answers below.
Step-by-step explanation:
h(t) = -4.91t^2 + 24.5t + 1
a) How high is the ball after 1 second?
h(1) = -4.91*(1)^2 + 24.5*(1) + 1
h(1) = 20.59 meters
b) Find the maximum height of the ball to one decimal place.
We can find the maximum height by graphing or by taking the first derivative and setting it equal to zero (the slope is zero at the top of the curve):
First Derivative
h(t) = -4.91*(t)^2 + 24.5*(t) + 1
'h(t) = -9.82*(t) + 24.5
0 = -9.82*(t) + 24.5
9.82t = 24.5
t = 2.49 seconds is the time the ball reaches maximum height. Use that is the equation to find the height:
h(2.49) = -4.91*(2.49)^2 + 24.5*(2.49) + 1
h(2.49) = 31.6 meters
Graph
See attached graph. The maximum height occurs at t = 2.49 seconds and the height is 31.6 meters.
c) When does the ball reach its maximum height?
From the first derivative calculation above, t = 2.49 seconds to reach maximum height. The graph also shows 2.49 seconds. Better hurry.
d) When does the ball hit the ground?
The can be determined by either direct calculation of from the graph (attached).
Calculation:
h(t) = -4.91t^2 + 24.5t + 1
0 (ground) = -4.91t^2 + 24.5t + 1
4.91t^2 - 24.5t - 1 = 0 Solve with the quadratic equation. I get t = 5.04 seconds
Graph:
The graph shows 4.95 seconds. Both agree when rounded to one decimal point: 5.0 seconds.
find the area of the shape below
Answer:
396 cm²
Step-by-step explanation:
Let us break this shape into two parts.
The left part:
27 cm² * 10 cm² = 270 cm²
The right part:
24 cm² - 10 cm² = 14 cm²
14 cm² * 9 cm² = 126 cm²
Total area:
270 cm² + 126 cm² = 396 cm²
What is the solution to the inequality?
12 < 8 + x
O A. x < 20
O B. x>4
O c. x> 20
O D. x<4
Answer:
B. x > 4
Step-by-step explanation:
12 < 8 + x
12-8 < 8-8 +x
12-8 < x
4 <x
x > 4
What is the sale price of jeans which regularly cost $32, but now are 10% off?
Answer:
$28.80
Step-by-step explanation:
32 x 0.1 = 3.2
32 - 3.2 =28.8
Hope this helps :)
Answer:
$28.8
Step-by-step explanation:
10% of 32 is 3.2
32 - 3.2 = 28.8
Given that x is an acute angle and cos x=2√5÷5,find without using mathematical tables or a calculator , tan(90-x)°.
Answer: 2
Step-by-step explanation:
Fill in the table and graph the parametric equation
Answer:
Shown above
Step-by-step explanation:
Sorry for my untidy handwriting
How do you find the area of a triangle when given only the lengths of three sides?
Answer:
Use Heron's formula; see below.
Step-by-step explanation:
Use Heron's formula.
Let the sides of the triangle have lengths a, b, and c.
[tex] s = \dfrac{a + b + c}{2} [/tex]
[tex] area = \sqrt{s(s - a)(s - b)(s - c)} [/tex]
Example:
A triangle has side lengths 3, 4, and 5 units.
Find the area of the triangle.
[tex] s = \dfrac{a + b + c}{2} [/tex]
[tex] s = \dfrac{3 + 4 + 5}{2} [/tex]
[tex] s = 6 [/tex]
[tex] area = \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex] area = \sqrt{6(6 - 3)(6 - 4)(6 - 5)} [/tex]
[tex] area = \sqrt{6(3)(2)(1)} [/tex]
[tex] area = \sqrt{36} [/tex]
[tex] area = 6 [/tex]
Micheal is planting a garden in the shape of a right triangle. He wants 4 plants for each square meter area. How many plants does Michael want in the garden?
PLEASE answer this today because it is due tomorrow
Hence, required answer is 336
See the picture for the solution
X+6y=10 x+5y=9
Use elimination to solve the following equations
Answer:
(4, 1 )
Step-by-step explanation:
x + 6y = 10 → (1)
x + 5y = 9 → (2)
subtract (2) from (1) term by term to eliminate x
0 + y = 1
y = 1
substitute y = 1 into either of the 2 equations and solve for x
substituting into (1)
x + 6(1) = 10
x + 6 = 10 ( subtract 6 from both sides )
x = 4
solution is (4, 1 )
A survey of 600 people was conducted to find thier favorite book genre. The survey results are shown in the table o the right. Adventure:102, Comedy: 114, Mystery:84, Romance:132
Part A: How many people responed with a genre other than one of the genres listed?
Part B: Develop a complete probabiliy model to describe all possible reasons, including 'other' as one response.
PLEASE HELP ASAP
The probability shows that the number of people who responed with a genre other than one of the genres listed is 168.
How to calculate the probability?The number of people who responded with a genre other than one of the genres listed will be:
= 600 - (102 + 114 + 84 + 132)
= 600 - 332
= 168
The probability for adventure = 102/600 = 0.17
The probability for comedy = 114/600 = 0.19.
The probability for mystery = 84/600 = 014
The probability for romance = 132/600 = 0.22
The probability for others = 168/600 = 0.28
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Make x the subject a(x-a)=a^2
Answer:
x = 2a
Step-by-step explanation:
a(x - a) = a² ( divide both sides by a )
x - a = a ( add a to both sides )
x = 2a
Answer:
x = 2a
Step-by-step explanation:
Given equation
[tex]\sf a(x-a)=a^2[/tex]
Make x the subject
expand brackets:
[tex]\sf \implies ax-a^2=a^2[/tex]
Add [tex]\sf a^2[/tex] to both sides:
[tex]\sf \implies ax-a^2+a^2=a^2+a^2[/tex]
[tex]\sf \implies ax=2a^2[/tex]
Divide both sides by a:
[tex]\sf \implies \dfrac{ax}{a}=\dfrac{2a^2}{a}[/tex]
[tex]\sf \implies x=2a[/tex]
Final solution
[tex]\sf x=2a[/tex]
Solve 34x−5<8. Round your answer to the nearest thousandth
Answer:
x < 0.382
Step-by-step explanation:
because we know that 34x is smaller than 13. therefore after division we can find out that x must be smaller than 0.382
Jocelyn is pregnant and needs to eat at least 500 more calories a day than usual. when buying groceries one day with a
budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150
calories each. the bananas cost $0. 35 each and the granola bars cost $2. 50 each.