Final answer:
The correct answer is C. outside 45 degrees. In this question, we are asked to identify which directions are NOT vector directions. Options A, B, and D all describe vector directions, but option C does not.
Explanation:
The correct answer is C. outside 45 degrees.
In this question, we are asked to identify which directions are NOT vector directions. A vector direction is a specific direction or angle that describes the orientation of a vector.
Options A, B, and D all describe vector directions:
A. 35 degrees north of east: This describes a vector direction that is 35 degrees north of the east direction.
B. north: This is a vector direction that points directly north.
D. 35 degrees inside: This describes a vector direction that is 35 degrees inside the reference angle.
Option C, outside 45 degrees, does not describe a specific vector direction. It is not clear whether the direction is outside 45 degrees to the left or right. Therefore, option C is NOT a vector direction.
What is the measure of angle A ?
Answer:25%
It's spit into fourths so yeah
Step-by-step explanation:
Answer: 88 degrees
===========================================
Explanation:
Sides AC and AB are tangents to the circle, so 90 degree angles form at points C and B.
Angle O = 92
Angle B = 90
Angle C = 90
Angle A = unknown
----------
The four interior angles of any convex quadrilateral always add to 360 degrees
(angle O) + (angle A) + (angle B) + (angle C) = 360
92 + A + 90 + 90 = 360
A + 272 = 360
A+272-272 = 360-272
A = 88
-----------
A shortcut is to subtract angle O from 180
angle A = 180 - (angle O) = 180 - 92 = 88
we get the same answer
help me??? please????
Answer:
∠2 = 78°
Step-by-step explanation:
Angle of a straight line is 180°.
So, that would mean ∠1 + ∠2 = 180°.
⇒ ∠2 = 180° - ∠1
⇒ ∠2 = 180° - 102°
⇒ ∠2 = 78°
Hence, the answer.
y-3=3(x+1)
what is the equation in standard form of a perpendicular line that passes through (5,-1)
Answer: x + 3y = 2
Step-by-step explanation:
Given:
y - 3 = 3 ( x + 1 )
y - 3 = 3x + 3
y = 3x + 3 + 3
y = 3x +6
comparing the equation with the formula for finding equation of line in slope - intercept form
y = mx + c , where m is the slope and c is the y - intercept. This means that the slope of the line above is 3
Two lines are said to be perpendicular if the product of their slope = -1, that is , if [tex]m_{1}[/tex] is the slope of the first line and [tex]m_{2}[/tex] is the slope of the second line , if they are perpendicular , then [tex]m_{1}[/tex][tex]m_{2}[/tex] = -1
Considering this rule , this means that the slope of the line we are to find = [tex]\frac{-1}{3}[/tex]
Using the formula : y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) to find the equation of the line , we have
y - (-1 ) = [tex]\frac{-1}{3}[/tex] ( x - 5 )
y + 1 = [tex]\frac{-1}{3}[/tex] ( x - 5 )
multiplying through by 3 , we have
3 ( y + 1 ) = -1 ( x - 5)
Expanding , we have
3y + 3 = -x + 5
writing the equation in standard form , we have
3y + x = 5 - 3
Therefore :
x + 3y = 2
a windscreen wiper of a vehicle of length 30 cm clears out an angle of 180 degrees what is the area of the screen cleared take pie=22/7
Final Answer:
The area of the screen cleared IS 9900/7 cm² or about 1414.29 cm².
Explanation:
The question asks about finding the area cleared by a windscreen wiper that sweeps out an angle of 180 degrees (or a semi-circle) with a length (or radius) of 30 cm. We can calculate the area cleared using the formula for the area of a circle, A = πr², but since the wiper covers only half the circle, we'll divide the result by 2.
Given the radius (r) is 30 cm, and using π as 22/7, we calculate the area as follows:
First, calculate the area of the full circle: A = πr² = (22/7) * (30)²
Then, since the wiper clears half the circle, we divide this result by 2.
Substituting the values:
A = (22/7) * 900 = 19800/7 cm²
Half of that area is 19800/7 / 2 = 9900/7 cm²
Therefore, the area of the screen cleared by the windscreen wiper is 9900/7 cm² which is approximately 1414.29 cm².
The area cleared by the windscreen wiper is approximately 86 square centimeters.
To find the area cleared by the windscreen wiper, we first need to determine the area of the sector formed by the angle cleared (108°) and then subtract the area of the triangle formed by the radius of the wiper (30 cm) and the two radii that define the angle cleared.
Given:
- Radius of the wiper, r = 30 cm
- Angle cleared by the wiper, [tex]\( \theta = 108° \)[/tex]
- Value of π, [tex]\( \pi = \frac{22}{7} \)[/tex]
Let's break down the solution step by step:
1. Calculate the area of the sector:
The formula to calculate the area of a sector of a circle is:
[tex]\[ \text{Area of sector} = \frac{\theta}{360°} \times \pi r^2 \]\\[/tex]
where [tex]\( \theta \)[/tex] is the angle in degrees,[tex]\( \pi \)[/tex] is the constant pi, and r is the radius of the circle.
Substituting the given values:
[tex]\[ \text{Area of sector} = \frac{108°}{360°} \times \frac{22}{7} \times (30)^2 \][/tex]
2. Calculate the area of the triangle:
The area of a triangle can be calculated using Heron's formula, which states:
[tex]\[ \text{Area of triangle} = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]
where s is the semi-perimeter of the triangle, and a , b , and c are the lengths of its sides.
In this case, the sides of the triangle are all equal to the radius of the wiper, r = 30 cm, so a = b = c = 30 cm.
The semi-perimeter s can be calculated as [tex]\( s = \frac{3r}{2} \).[/tex]
3. Subtract the area of the triangle from the area of the sector:
[tex]\[ \text{Area cleared} = \text{Area of sector} - \text{Area of triangle} \][/tex]
Let's perform the calculations:
1. Calculate the area of the sector:
[tex]\[ \text{Area of sector} = \frac{108}{360} \times \frac{22}{7} \times (30)^2 \][/tex]
[tex]\[ = \frac{108}{360} \times \frac{22}{7} \times 900 \][/tex]
[tex]\[ = \frac{108}{360} \times 286 \][/tex]
[tex]\[ = 102 \text{ cm}^2 \][/tex]
2. Calculate the area of the triangle:
[tex]\[ s = \frac{3r}{2} = \frac{3 \times 30}{2} = 45 \text{ cm} \][/tex]
[tex]\[ \text{Area of triangle} = \sqrt{45(45 - 30)(45 - 30)(45 - 30)} \][/tex]
[tex]\[ = \sqrt{45 \times 15 \times 15 \times 15} \][/tex]
[tex]\[ = \sqrt{506250} \][/tex]
[tex]\[ = 225 \text{ cm}^2 \][/tex]
3. Subtract the area of the triangle from the area of the sector:
[tex]\[ \text{Area cleared} = 102 \text{ cm}^2 - 225 \text{ cm}^2 \][/tex]
[tex]\[ = -123 \text{ cm}^2 \][/tex]
The negative value indicates that the area of the triangle is greater than the area of the sector. This suggests an error in calculation or reasoning. Let's recheck the calculations.
Upon reviewing, it seems there was a mistake in the calculation of the area of the triangle. We should not have taken the square root of the semi-perimeter. Instead, we should have used the correct Heron's formula without the square root. Let's correct this:
[tex]\[ \text{Area of triangle} = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]
[tex]\[ = \sqrt{45(45 - 30)(45 - 30)(45 - 30)} \][/tex]
[tex]\[ = \sqrt{45 \times 15 \times 15 \times 15} \][/tex]
[tex]\[ = 337.5 \text{ cm}^2 \][/tex]
Now, let's subtract the corrected area of the triangle from the area of the sector:
[tex]\[ \text{Area cleared} = 102 \text{ cm}^2 - 337.5 \text{ cm}^2 \][/tex]
[tex]\[ = -235.5 \text{ cm}^2 \][/tex]
It seems that there is an error in the calculation, as the area cannot be negative. Let's reassess the approach and correct any errors.
Upon reevaluation, it appears that we should not subtract the area of the triangle from the area of the sector, as the triangle represents the area covered by the wiper itself, not the area cleared on the windscreen. Instead, we should calculate the area of the sector and use it as the area cleared by the windscreen wiper.
Let's correct the approach and recalculate the area of the sector:
1. Calculate the area of the sector:
[tex]\[ \text{Area of sector} = \frac{\theta}{360°} \times \pi r^2 \][/tex]
[tex]\[ = \frac{108°}{360°} \times \frac{22}{7} \times (30)^2 \][/tex]
[tex]\[ = \frac{108}{360} \times \frac{22}{7} \times 900 \][/tex]
[tex]\[ = \frac{108}{360} \times 286 \][/tex]
[tex]\[ = 86 \text{ cm}^2 \][/tex]
So, the corrected area cleared by the windscreen wiper is[tex]\( 86 \, \text{cm}^2 \).[/tex]
In summary, the area cleared by the windscreen wiper is [tex]\( 86 \, \text{cm}^2 \).[/tex]
The Correct Question is:
A windscreen wiper of a vehicle of length 30 cm clears out an angle of 108° as shown in the diagram below. What is the area of 6 the screen cleared? (Take π =22/7)?
[tex]2 + \frac{5}{6} \sqrt{6} = 2 + \sqrt{6}y [/tex]
Answer:
Therefore,
[tex]y=\dfrac{5}{6}[/tex]
Step-by-step explanation:
Given:
[tex]2+\dfrac{5}{6}\sqrt{6}=2+\sqrt{6}y[/tex]
To Find:
x = ?
Solution:
[tex]2+\dfrac{5}{6}\sqrt{6}=2+\sqrt{6}y[/tex]
Subtract 2 from both the side.
[tex]2-2+\dfrac{5}{6}\sqrt{6}=2-2+\sqrt{6}y[/tex]
Then we have
[tex]\dfrac{5}{6}\sqrt{6}=\sqrt{6}y[/tex]
Divide [tex]\sqrt{6} [/tex]on both the side
[tex]\dfrac{5}{6}\dfrac{\sqrt{6}}{\sqrt{6}}=\dfrac{\sqrt{6}}{\sqrt{6}}=y[/tex]
Then we have
[tex]\dfrac{5}{6}=y[/tex]
Therefore,
[tex]y=\dfrac{5}{6}[/tex]
Simplify the expression and combine like terms.
2 (x+6) + 3x + 4
Answer:
x = 16/5
Step-by-step explanation:
2x+12+3x+45x+16 x = 16/5What is the solution set to the inequality 7z+5>47
Answer:
[tex]z>6[/tex]
Step-by-step explanation:7z+5>47
Remove the 5:
[tex]7z+5-5>47-5\\7z>42[/tex]
Divide by 7 to get z by itself:
[tex]\frac{7z}{7} >\frac{42}{7} \\z>6[/tex]
A boat rental charges $7.50 for the first hour and $2 for each additional hour. Which rule gives the cost for x hours of renting a boat?
c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat
Solution:Given that a boat rental charges $7.50 for the first hour and $2 for each additional hour.
To find: Rule that gives the cost for x hours of renting a boat
Let "x" be the total hours of renting a boat
[tex]c = f + (v \times x - 1)[/tex]
"c" is the total cost for the boat rent
"f" is the fixed cost for boat rent for first hour
"v" is the cost for each additional hours of rent
"x" is the total hours of renting a boat
In the expression we have used "x - 1" to represent the additional hour of boat rent after first hour
Here f = $ 7.50
v = $ 2
[tex]c = 7.50 + 2 \times x - 1\\\\c = 7.50 + 2(x - 1)[/tex]
Thus c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat
The cost for renting a boat for x hours can be found using the formula y = 7.50 + 2(x - 1), where y is the total cost and x is the number of hours.
Explanation:Based on the given information, the boat rental company charges $7.50 for the first hour and then an additional $2 for each subsequent hour. Therefore, if x is the number of hours you rent the boat, the total cost would be calculated using the formula y = 7.50 + 2(x - 1). Here, y represents the total cost of renting the boat for x hours. The formula subtracts the one-hour charge included in the initial payment.
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If two angles are complementary and one angle is 10∘greater than the other, then the smaller angle of the two is?
Answer:
the smaller angle = 40
Step-by-step explanation:
Let x be the smaller angle.
Other angle = x + 10
x + x+ 10 = 90
2x = 90 - 10
2x= 80
x = 80/2
x = 40
Answer:
40 degrees. A set of complementary angles make up 90 degrees. 90 - 40 is 50, which is 10 more than forty.
What value of x makes this equation TRUE? 4x + 2 = −14
4x + 2 = -14
4x = -16
x = -4
4(-4) + 2 = -14
-16 + 2 = -14
-14 = -14
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(1.5x 109) (3.5 x 109)
well,I am not sure about the answer.
PLEASE HELP godbless 20 points
Another term for measurement data is
A) quantitative data.
B) categorical data.
C) qualitative data.
D) bivariate data.
Answer:
A) quantitative data.
Step-by-step explanation:
'quantitative' derives from 'quantity', almost synonymous with a measure or measurement.
the units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than the original number. What is the original number?
Answer:
36
Step-by-step explanation:
Here is the correct and complete question: The units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than twice the original number. What is the original number?
Lets assume the original number be"10y+x". (x is unit digit and y is 10th digit)
∴ if number is reversed then resulting number be "10x+y".
As given: x= 2y
and [tex]10x+y= 2(10y+x)-9[/tex]
Now, solving the equation to get original number.
[tex]10x+y= 2(10y+x)-9[/tex]
Distributing 2 to 10y and x, then opening the parenthesis.
⇒ [tex]10x+y= 20y+2x-9[/tex]
subtracting by (2x+y) on both side.
⇒ [tex]8x= 19y-9[/tex]
subtituting the value of "x", which is equal to 2y.
∴ [tex]8\times 2y= 19y-9[/tex]
⇒ [tex]16y=19y-9[/tex]
subtracting both side by (16y-9)
⇒ [tex]3y= 9[/tex]
cross multiplying
We get, [tex]y= 3[/tex]
y=3
∵x= 2y
[tex]x=2\times 3= 6[/tex]
∴ x= 6
Therefore, the original number will be 36 as x is the unit number and y as tenth number.
Choose the word phrase (greater than, less than, or equal to) to make the statements true.
Each paper clip can be traded for three matches.
Each pencil can be traded for six paper clips.
Twenty-two paper clips are worth sixty-seven matches.
In the problem, one paper clip equals three matches, one pencil is greater than one paper clip, and twenty-two paper clips are greater than sixty-seven matches.
Explanation:In this scenario, one paper clip is equivalent, or equal to, three matches. This is ascertained from the first sentence which states that each paper clip can be traded for three matches. Similarly, one pencil is greater than a single paper clip as it can be traded for six paper clips. This conclusion is drawn from the second sentence. Lastly, the value of twenty-two paper clips is greater than sixty-seven matches since one paper clip is equal to three matches, hence twenty-two paper clips would be worth sixty-six matches, but since we have sixty-seven matches, twenty-two paper clips are worth more.
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Simplify the rationsl expression 6x(x+3)(x-2)/3(x-2)(x+9)
Answer:
The simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex].
Step-by-step explanation:
Given rational expression is
[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]
Now to simplify the given rational expression:
[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]
[In the above expression 6 and 3 cancelled and the result is 2, (x-2) and (x-2) getting cancelled each other]
[tex]=\frac{2x(x+3)}{x+9}[/tex]
Now applying distributive property to the above expression
[tex]=\frac{2x^2+6x}{x+9}[/tex]
Therefore [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]
Therefore the simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]
solve my factoring:f(x)=2x^2+5x-3.Multiply the smaller x-intercept by -4
Answer:
(-3)(-4) = 12Step-by-step explanation:
[tex]f(x)=2x^2+5x-3\\\\x-\text{intercept for}\ f(x)=0\\\\2x^2+5x-3=0\\\\2x^2+6x-x-3=0\\\\2x(x+3)-1(x+3)=0\\\\(x+3)(2x-1)=0\iff x+3=0\ \vee\ 2x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\\boxed{x=-3}\\\\2x-1=0\qquad\text{add 1 to both sides}\\2x=1\qquad\text{divide both sides by 2}\\\boxed{x=0.5}\\\\-3<0.5[/tex]
A freight train made a trip to a repair. On the trip there it travelers 25 mph and on the return trip it went 20 mph. How long did there take if the return trip took 15 hours?
Answer:
Time taken by train in onward journey = 12 hours.
Step-by-step explanation:
Given:
Speed of train making a trip to a repair = 25 mph
Speed of train on return trip = 20 mph
Time taken for return trip = 15 hours
To find the time taken on the on wards trip.
Solution:
The distance traveled by the train on the trip and return trip is the same as the y are of same trips in opposite directions.
Distance can be calculated by using the data for the return trip.
Distance= [tex]Speed\times Time[/tex]
Distance= [tex]20\ mph\times 15\ h=300\ miles[/tex]
Speed of train for on ward trip = 25 mph
Time taken = [tex]\frac{Distance}{Speed}[/tex]
Time taken = [tex]\frac{300\ miles}{25\ mph}= 12\ h[/tex]
Thus, time taken by train in onward journey = 12 hours.
7(2 + 4) - 3(6)+2(3+5)
Simplify the numerical expression
Final answer:
To simplify the expression 7(2 + 4) - 3(6) + 2(3 + 5), calculate within the parentheses, do the multiplications, and then the additions and subtractions to get the result, which is 40.
Explanation:
To simplify the numerical expression 7(2 + 4) - 3(6) + 2(3 + 5), you need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Here's how you simplify the expression step by step:
First, calculate the expressions within the parentheses: (2 + 4) and (3 + 5).
Then, multiply each result by the number outside the parentheses.
Afterward, complete any multiplication or division from left to right.
Finally, perform the addition and subtraction from left to right.
Now let's apply these steps to the expression:
Calculate the expressions inside the parentheses: 2 + 4 = 6 and 3 + 5 = 8.
Multiply each result by the respective number outside the parentheses: 7 * 6 = 42 and -3 * 6 = -18 and 2 * 8 = 16.
Now rewrite the expression with these calculated values: 42 - 18 + 16.
Now it's just addition and subtraction: 42 - 18 = 24, and 24 + 16 = 40.
Therefore, the simplified expression is 40.
1. Geoff rode his bike along an 8-mile path and lost his cell phone at some random location
somewhere along the way. Geoff searched from mile 4.5 to mile 7. What is the probability
that he found his phone?
I need help!!
Answer:
0.3125
Step-by-step explanation:
Use definition of geometric probability:
[tex]P=\dfrac{\text{Desired Length}}{\text{Total Length}}[/tex]
In your case,
Total Length = 8 miles
Desired Length = 7 - 4.5 = 2.5 miles,
so the probability is
[tex]P=\dfrac{2.5}{8}=\dfrac{25}{80}=\dfrac{5}{16}=0.3125[/tex]
Final answer:
The probability of finding the lost cell phone by searching from mile 4.5 to mile 7 along an 8-mile path is 0.3125 or 31.25%.
Explanation:
The student's question deals with the probability of finding a lost cell phone on an 8-mile path by searching between the 4.5 and 7 mile markers.
To calculate this probability, we consider the length of the path where the phone could potentially be found (the search area) and the total length of the path.
The search area is from mile 4.5 to mile 7, which is 2.5 miles long. Since the phone could be anywhere along the 8-mile path, the probability of finding the phone is the length of the search area divided by the total path length:
Probability = Length of Search Area / Total Path Length = 2.5 miles / 8 miles = 0.3125 or 31.25%.
Find the distance between union and sun valley if they are 4cm apart on a map with a scale of 2 cm : 16m
Answer:
32 meters
Step-by-step explanation:
we know that
The scale is [tex]\frac{2}{16} \ \frac{cm}{m}[/tex]
That means ----> 2 cm on a map represent 16 m in the actual
so
using proportion
Find out the distance between union and sun valley if they are 4 cm apart on a map
[tex]\frac{2}{16} \ \frac{cm}{m}=\frac{4}{x} \ \frac{cm}{m}\\\\x=16(4)/2\\\\x=32\ m[/tex]
Samantha is measuring the snowfall in a snow Gog for her science project. The first week she measured 3 3/4 inches of snow the second week she measured twice as much snow, and the third weekShe measured half as much snow as the first week. It did not snow at all in the fourth week. How much snowfall did Samantha measure for the entire month? Explain
[tex]\frac{105}{8}[/tex] inches of snowfall measured for entire month
Solution:
Given that first week she measured [tex]3\frac{3}{4}[/tex] inches of snow
Second week she measured twice as much snow, and the third week she measured half as much snow as the first week
It did not snow at all in the fourth week
To find: Amount of snowfall measured for entire month
First week:
[tex]\text{ first week } = 3\frac{3}{4} = \frca{4 \times 3 + 3}{4} = \frac{15}{4} inches[/tex]
Second week:
She measured twice as much snow as the first week
[tex]\text{ second week } = 2 \times \frac{15}{4} = \frac{15}{2} inches[/tex]
Third week:
The third week She measured half as much snow as the first week
[tex]\text{ third week } = \frac{1}{2} \times \frac{15}{4} = \frac{15}{8} inches[/tex]
Fourth week:
It did not snow at all in the fourth week
fourth week = 0
Total snowfall for entire month:
Total snowfall = first week + second week + third week + fourth week
[tex]\rightarrow \frac{15}{4} + \frac{15}{2} + \frac{15}{8} + 0\\\\\rightarrow 15(\frac{1}{4} + \frac{1}{2} + \frac{1}{8} )\\\\\rightarrow 15(\frac{2+4+1}{8})\\\\\rightarrow 15 \times \frac{7}{8} = \frac{105}{8}[/tex]
Therefore [tex]\frac{105}{8}[/tex] inches of snowfall measured for entire month
The list price for a dress is $90 if a discount of $10.80 was given for paying cash what percent of the list price was the discount
Answer:
12% discount
Step-by-step explanation:
the sum of three numbers is 50 the second number is three times the first number and the third number is twice the second number what are the numbers
Answer:1st is 5 2nd is 15 last is 30
Step-by-step explanation:
1st = 5
2nd = 3 x 5 = 15
3rd = 15 x 2 = 30
5 + 15 + 30 = 50
The three numbers in question are 5, 15, and 30. This has been achieved by setting up and solving algebraic equations based on the given conditions.
Explanation:To solve this problem, we should set up equations based on the information given. Let's define:
First number = x
Second number = 3x (since it is three times the first number)
Third number = 2 * 3x = 6x (since it is twice the second number)
According to the problem, the sum of these three numbers is 50. Therefore, we can write the equation as:
x + 3x + 6x = 50
Solve for x:
10x = 50
x = 50 / 10 = 5
So, the three numbers are:
First number = x = 5
Second number = 3x = 3 * 5 = 15
Third number = 6x = 6 * 5 = 30
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y = 5- 2
1-3x + y = -12
What is the value of x and y ?
Answer:
x=5.333
y=3
Step-by-step explanation:
given, y=5-2............(1)
1-3x+y=-12...............(2)
y=5-2=3
put y=3 in equ (2)
1-3x+3=-12
1+3+12=3x
3x=16
x=[tex]\frac{16}{3}[/tex]
x=5.333
hence, x=5.333
y=3 answer
11x - 3y=8
9x +4y=13
Answer:
y=1
x=1
Step-by-step explanation:
$13,957 is invested, part at 7% and the rest at 6%. If the interest earned from the amount invested at 7% exceeds the interest earned from the amount invested at 6% by $833.73, how much is invested at each rate?
Answer:
The Amount invested at 7% interest is $12,855
The Amount invested at 6% interest = $1,102
Step-by-step explanation:
Given as :
The Total money invested = $13,957
Let The money invested at 7% = [tex]p_1[/tex] = $A
And The money invested at 6% = [tex]p_2[/tex] = $13957 - $A
Let The interest earn at 7% = [tex]I_1[/tex]
And The interest earn at 6% = [tex]I_2[/tex]
[tex]I_1[/tex] - [tex]I_2[/tex] = $833.73
Let The time period = 1 year
Now, From Simple Interest method
Simple Interest = [tex]\dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}[/tex]
Or, [tex]I_1[/tex] = [tex]\dfrac{\textrm p_1\times \textrm 7\times \textrm 1}{100}[/tex]
Or, [tex]I_1[/tex] = [tex]\dfrac{\textrm A\times \textrm 7\times \textrm 1}{100}[/tex]
And
[tex]I_2[/tex] = [tex]\dfrac{\textrm p_2\times \textrm 6\times \textrm 1}{100}[/tex]
Or, [tex]I_2[/tex] = [tex]\dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100}[/tex]
∵ [tex]I_1[/tex] - [tex]I_2[/tex] = $833.73
So, [tex]\dfrac{\textrm A\times \textrm 7\times \textrm 1}{100}[/tex] - [tex]\dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100}[/tex] = $833.73
Or, 7 A - 6 (13,957 - A) = $833.73 × 100
Or, 7 A - $83,742 + 6 A = $83373
Or, 13 A = $83373 + $83742
Or, 13 A = $167,115
∴ A = [tex]\dfrac{167115}{13}[/tex]
i.e A = $12,855
So, The Amount invested at 7% interest = A = $12,855
And The Amount invested at 6% interest = ($13,957 - A) = $13,957 - $12,855
I.e The Amount invested at 6% interest = $1,102
Hence,The Amount invested at 7% interest is $12,855
And The Amount invested at 6% interest = $1,102 . Answer
Final answer:
The total amount invested and the difference in interest earned. Then, using algebraic techniques such as substitution or elimination, we solve for the amounts invested at 7% and at 6%.
Explanation:
To solve the problem of allocating investments at different interest rates, we can set up a system of equations. Let's designate x as the amount invested at 7% and y as the amount invested at 6%. Given the total investment is $13,957, our first equation will be:
x + y = 13,957 (1)
The interest from the amount invested at 7% exceeds the interest from the amount invested at 6% by $833.73. The second equation, reflecting the interest earned, will be:
0.07x - 0.06y = 833.73 (2)
y = 13,957 - x (3)
Now, substitute equation (3) into equation (2) and solve for x:
0.07x - 0.06(13,957 - x) = 833.73
Simplify and solve this equation to find the value of x.
Once we have the value for x, we can use equation (3) to find the corresponding value for y, giving us the amount invested at each interest rate.
CAN SOMEONE PLEASE HELP MEEE
Graph y = –4/3x + 1
Answer:
Step-by-step explanation:
y = -4/3x + 1
in y = mx + b form, the number in the b is the y intercept...so ur y intercept is
(0,1).....this is where ur line crosses the y axis
to find ur x axis, sub in 0 for y and solve for x
y = -4/3x + 1
0 = -4/3x + 1
4/3x = 1
x = 1 / (4/3)
x = 1 * 3/4
x = 3/4........and ur x intercept is (3/4,0)...this is where ur line crosses the x axis.
in y = mx + b form, the letter m represents ur slope....so ur slope is
-4/3.....that negative means ur line is descending.....so when we graph, we will start at the y int.
go ahead and plot ur intercepts.......(0,1) and (3/4,0)....now look at ur slope -4/3.....the numerator (either go up or down)....the denominator (go right)
if the numerator is negative....go down....if it was positive u would go up.
so start at (0,1).....slope is -4/3.....so go down 4 and to the right 3...plot that point......then go down 4 and to the right 3...plot that...ur gonna keep on going down 4 and to the right 3 as far as u need to...connect ur points and u have ur line
if it helps, ur line will be going through points (3,-3), (6,-7),(-3,5), (-6,9).....those are some whole number points.....its kinda hard to graph when ur intercepts dont fall on whole numbers
The graph of the function y = -4/3x + 1 is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = -4/3x + 1
The above function is a linear function that has been transformed as follows
Vertically stretched by a factor of -4/3Shifted up by 1 unitNext, we plot the graph using a graphing tool by taking note of the above transformations
The graph of the function is added as an attachment
Read more about functions at
brainly.com/question/2456547
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Find the equation of the image of a line y=3x-8 after reflection over the x-axis
Answer:
The required image line is 3x + y = 8
Step-by-step explanation:
We have to find two points on the given straight line then find their reflection points over the x-axis and then finally the straight line passing through those two image points will give the required straight line.
Now, the given straight line is y = 3x - 8.
Now, two any points on this straight line are say (1,-5) and (2,-2).
So, the image of (1,-5) point reflecting over the x-axis will be (1,5) and the image of the point (2,-2) reflecting over the x-axis will be (2,2).
Therefore, the straight line passing through those two image points will have equation
[tex]\frac{y - 5}{5 - 2} = \frac{x - 1}{1 - 2}[/tex]
⇒ y - 5 = 3(1 - x)
⇒ y - 5 = 3 - 3x
⇒ 3x + y = 8
Hence, the required image line is 3x + y = 8 (Answer)
in the triangle abc the side length side are bc=14 and ac=7 whats b
hope this helps you mate
Net of cuboid having lengh, breadth and height 5,4 and 3 find the area of all faces
Answer:
The area of all faces of the cuboid is 94 square units
Step-by-step explanation:
Given:
Length = 5
Breadth = 4
Height = 3
To Find :
The area of all faces = ?
Solution:
The area of all the faces = surface area of the cuboid
The surface area of the cuboid = 2(LB + BH + HL)
where
L is the length
B is the breadth
H is the height
Now substituting the values,
The surface area of the cuboid
=> [tex]2(5 \times 4 + 4\times 3 + 3\times 5)[/tex]
=> [tex]2(20 + 12+ 15)[/tex]
=> [tex]2(47)[/tex]
=>94 square units