The total distance ran by Johnny after he left the house is D = 31 miles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as D
Now , the value of D is
Substituting the values in the equation , we get
Let the total distance ran by Johnny be D = ran 2 miles north, 6 miles west, 3 miles north, 10 miles south, 8 miles east, and then 2 miles
So , D = 2 + 6 + 3 + 10 + 8 + 2
On simplifying the equation , we get
D = 31 miles
Hence , the distance is D = 31 miles
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
please help and show work
Answer:
see explanation
Step-by-step explanation:
(3)
The opposite sides of a parallelogram are congruent, so
6x = 3x + 15 ( subtract 3x from both sides )
3x = 15 ( divide both sides by 3 )
x = 5
and
2y - 10 = y + 5 ( subtract 5 from both sides )
y - 10 = 5 ( add 10 to both sides )
y = 15
Then x = 5 and y = 15
-------------------------------------------------------------------------
(4)
The diagonals of a parallelogram bisect each other, thus
y = 4x - 6 → (1)
9x - 25 = 2y → (2)
Substitute y = 4x - 6 into (2)
9x - 25 = 2(4x - 6)
9x - 25 = 8x - 12 ( subtract 8x from both sides )
x - 25 = - 12 ( add 25 to both sides )
x = 13
Substitute x = 13 into (1)
y = 4(13) - 6 = 52 - 6 = 46
Then x = 13 and y = 46
Faye borrowed $9600 at 8% per anum compound interest.
(a) Calculate the interest on the loan for the first year.
At the end of the last year,she repaid $4368.
(b) How much did she still owe at the beginning of the year?
(c)Calculate the interest on the remaining balance for the second year.
Answer:
(a) $768
Step-by-step explanation:
Faye borrowed $9600 at 8% interest compounded per annum.
Solution for question (a):
Amount accumulated is given by;
A = P(1 + [tex]\frac{r}{n}[/tex][tex])^{nt}[/tex]
Where A is the amount, P is the pricipal, r is the rate, n is the number of times in a year, and t is the number of years.
So the amount after one year was;
A = 9600(1 + [tex]\frac{8}{1 * 100}[/tex][tex])^{1 * 1}[/tex] = 9600 × 1.08 = 10368
Interest = Amount - Principal = $10368 - $9600 = $768
a. The interest on the loan for the first year is $768.
b. The amount she still owe at the beginning of the year is $6,000.
c. The interest on the remaining balance for the second year is $480.
a. Interest on loan:
Interest on loan=$9600 × 8%
Interest on loan=$768
b. Amount owed
Amount owed=$9,600+$768-$4368
Amount owed=$6,000
c. Interest on remaining balance :
Interest on remaining balance=$6,000×8%
Interest on remaining balance=$480
Inconclusion the interest is $768, amount owe is $6,000 and Interest on remaining balance is $480.
Learn more about interest here:https://brainly.com/question/16134508
Solve the triangle.
B = 36°, a = 41, c = 20
choices:
b ≈ 27.5, C ≈ 115.5, A ≈ 28.5
b ≈ 45.3, C ≈ 25.5, A ≈ 118.5
b ≈ 45.3, C ≈ 29.5, A ≈ 114.5
b ≈ 27.5, C ≈ 25.5, A ≈ 118.5
The triangle solve for B = 36°, a = 41, c = 20 is:
b ≈ 27.5, C ≈ 115.5, A ≈ 28.5
TriangleTo solve the triangle, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and angles A, B, and C opposite those sides,
c² = a² + b² - 2ab cos(C)
We can use this formula to find the length of the missing side b:
b² = a² + c² - 2ac cos(B)
b² = 41² + 20² - 2(41)(20) cos(36°)
b² ≈ 1074.12
b ≈ 32.8
Now that we have found the length of side b, we can use the Law of Sines to find the measures of angles A and C:
sin(A) / a = sin(B) / b
sin(A) / 41 = sin(36°) / 32.8
sin(A) ≈ 0.274
A ≈ 16.5°
We know that the angles in a triangle add up to 180°, so C = 180° - A - B ≈ 127.5°.
The closest choice to these values is:
b ≈ 27.5, C ≈ 115.5, A ≈ 28.5
Learn more about Triangle solved here:
https://brainly.com/question/26489558
#SPJ1
Beth has had her car for a while and knows that it gets pretty good gas mileage On a recent business trip she used 16.25 gallons of gas and drove 471 miles. To the nearest tenth of a mile, what was her gas mileage? OA) 29 0 mpg OB) 30 0 mpg OC) 28.5 mpg OD) 270 mpg
Answer:
A) 29.0 mpg
you divide 471 by 16.25
plot the x- intercept and y- intercept. then write the intercepts as ordered pairs
Answer:
x-intercept = 4
y-intercept = -1
As ordered pairs they would be ( 4, 0) and ( 0, -1)
Step-by-step explanation:
The line goes through 4 on the x line and goes through -1 on the y line.
As an ordered pair you just put the numbers in their x and y spots being ( x, y )
With 4 being on the X and -1 being on the Y it would make them ( 4, 0) and
( 0, -1).
Please help me ASAP!!
Answer:
First one is 6
Second on is 45
Find the midpoint of CD If C(12, 6) and D(0, 3)
( ? , ? )
Answer:
(6, 4.5)
Step-by-step explanation:
6 if halfway between 12 and 0 and 4.5 is halfway between 6 and 3
i hope this helped :))
Answer:
The anser is (5, 4) oh and thank you for the points, i am very greatful for them
Help please & thanks!
Answer:
D
Step-by-step explanation:
Just add all the number together.
What number is 40% of 160?
Try to explain
Answer: 64
Step-by-step explanation:
40% of 160
40/100 x 160
6400/100
64
Did I explain this well?
Answer: 64
Step-by-step explanation: So you would start off with the ratio of 40:100 other known as in fraction form 40/100 and you know of means to multiply so you grab the numbers 160 and 40 and mulitiply those digits together and you get 6400. This is where the 100 comes to place and you divide the 6400 by 100 and you get 64.
please help and show work if you can
Answer:
25. a = 60
26. a = 17
Step-by-step explanation:
In these two problems we are going to use a property of parallelograms that says: opposite angles have equal measure
so we have
25.
[tex]6a+10=130\\\\6a=130-10\\\\6a=120\\\\a=60[/tex]
and for 26 we have
[tex]4a-4=2a+30\\\\4a=2a+30+4\\\\4a=2a+34\\\\4a-2a=34\\\\2a=34\\\\a=17[/tex]
Which is a graph of y=-1/2x- 2?
Answer:
the first one
y-intercept (0,-2)
x-intercept (-4,0)
7th grade math please help me will give brainliest
Answer: 67.27
Step-by-step explanation:
7.1 x 7.1 for the square = 50.41
7.1 divided by 2 = 3.55
3.55 x 4.75= 16.86
Normally here you would divide by 2, but you don’t need two because there is 2 triangles that are the same
Add the 50.41 and the 16.86 and you have your answer!
Answer:
16.86 square units
Step-by-step explanation:
I think this is the answer.
Find the distance between a and b
For each situation, write an expression answering the question. The expression should only
use multiplication,
a. A person's salary is $2,500 per month. She receives a 10% raise. What is her new salary,
in dollars per month?
b. A test had 40 questions. A student answered 85% of the questions correctly. How many
questions did the student answer correctly?
C. A telephone cost $250. The sales tax is 7.5%. What was the cost of the telephone
including sales tax?
Answer:
The expressions for each statement are as follows:
a: 2500+(0.10*2500)
b: 40 * 0.85
c: 250 + (0.075*250)
Step-by-step explanation:
Part a:
Given
Salary = $2500
Percentage of raise = 10%
The new salary will be:
[tex]= 2500+ (10\%\ of\ 2500)\\=2500 + (0.10*2500)\\=2500+250\\=\$ 2750[/tex]
Part b:
Given
Total questions = 40
Percentage of correct answers = 85%
The required expression for correct answers is:
[tex]= 85\%\ of\ 40\\= 0.85*40\\=34[/tex]
Part c:
Given
Price of phone = $250
Percentage of sales tax = 7.5%
The required expression is:
[tex]Cost\ with\ sales\ tax = 250 + (7.5\%\ of\ 250) \\= 250 + (0.075*250)\\=250+18.75\\=268.75[/tex]
Hence,
The expressions for each statement are as follows:
a: 2500+(0.10*2500)
b: 40 * 0.85
c: 250 + (0.075*250)
4 of 6
© As an estimation we are told £3 is €4.
Convert €44.80 to pounds.
Give your answer rounded to 2 DP.
What is the answer
Answer- 44.60
Step-by-step explanation:
After swimming 55 feet below the surface of the water, a
fish swims up 30 feet. Use a number line to help you create
an equation that shows the new location of the fish in
relation to the water's surface.
-80 -70 -60 -50 40 -30 -20 -10 0
10
Interpret the sum in the context of the problem.
Answer:
c.
Step-by-step explanation:
when the fish swam down 55, you moved 55 to the left of zero. then when he swam 30 up, you take that 55 and move it 30 towards to the right. since -55 is greater than 30, your answer is still negative. -55+30=-25.
Answer:
C
Step-by-step explanation:
i need help please answer for me ... Logan drove from New Orleans to Nashville to visit friends. Logan drove the speed limit which was 60 miles/hour. If Logan's driving time for the trip was 9 hours, how many miles did Logan drive?
please help!
"a line intercepts the point (3, -4) and has a slope of 17. what is the slope-intercept equation for this line?"
then it has the partially filled out equation:
y=17x+__
Answer:
-55 = b
Step-by-step explanation:
If you fill in the x and the y with the equation you have below, you would get:
-4 = 17(3)+b
Multiply 17 and 3
-4 = 51 + b
-55 = b
Answer:
y=17x-55
Step-by-step explanation:
4 = 17(3)+b
-4 = 51 + b Subtract 51 both sides
-55 = b
Hope this helps :)
g− 3/7=2/7
solve.
G=?
thx!
Answer: g = 5/7
=======================================================
Work Shown:
Let's move the -3/7 to the other side, to fully isolate g.
We do so by adding 3/7 to both sides (to undo the subtraction)
[tex]g - \frac{3}{7} = \frac{2}{7}\\\\g - \frac{3}{7}+\frac{3}{7} = \frac{2}{7}+\frac{3}{7}\\\\g = \frac{2+3}{7}\\\\g = \frac{5}{7}\\\\[/tex]
Luckily all of the denominators are the same (7), so we can add the fractions by adding the numerators to place that sum over the common denominator.
Find the slope of the line that passes through the points (-2, 6) and (9, -5).
Answer:
slope = -1
Step-by-step explanation:
Use the slope formula [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex] to find the slope. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point, and the [tex]x_2[/tex] and [tex]y_2[/tex] represent the x and y values of another point. So, we'll use the points given in the question, (-2,6) and (9, -5). Substitute -2 for [tex]x_1[/tex], 6 for [tex]y_1[/tex], 9 for [tex]x_2[/tex], and -5 for [tex]y_2[/tex]. Then, solve:
[tex]\frac{(-5)-(6)}{(9)-(-2)} \\= \frac{-5-6}{9+2} \\= \frac{-11}{11} \\= -1\\[/tex]
Therefore, the slope is -1.
The slope of the line that passes through the points (-2, 6) and (9, -5) is -1.
A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
Given the coordinates of the two points on the graph is (-2, 6) and (9, -5). Therefore, the slope of the line that passes through this point is,
Slope = [6 - (-5)] / [-2 - 9]
Slope = (11) / (-11)
Slope = -1
Hence, the slope of the line will be -1.
Learn more about Slope of Line here:
https://brainly.com/question/14511992
#SPJ2
PLEASE HELP ME dhdjdbjfjf
Answer:
Option A
Step-by-step explanation:
Since X,Y and Z are on the same line, The gradient is the same so far as the point chosen are on the same line.
What is (4-4) k I need help
Answer:
zero
Step-by-step explanation:
1.12 unit test
Enter an inequality that represents the graph in the box.
Answer:
45
Step-by-step explanation:
it is blah blah this is the best you multiply by 5 add 40 subtract 5 and add 5 again
Which expressions are in their simplest form? Check all that apply.
Answer:
The first one is the only one in simplest form.
Answer: this is answerrrr
A C Dpeace
Solve -1/2 + (3/4 x 4/9) = ?
Answer:
=-1/6
Step-by-step explanation:
-1/2 + (3/4 * 4/9)
3/4 * 4/9 = 12/36
12/36 simplify to 1/3
-1/2 + 1/3 = -1/6
triangle ABC has perimeter 22cm
AB= 8cm
BC= 5cm
by calculation deduce whether triangle ABC is right-angled triangle
9514 1404 393
Answer:
not a right triangle
Step-by-step explanation:
The perimeter is 22, so we have ...
AB +BC +CA = 22
8 + 5 + CA = 22
CA = 22 -13 = 9
If this is a right triangle, the sum of the squares of the short sides will be equal to the square of the long side.
AB² +BC² = 8² +5² = 64 +25 = 89
This is not the same as ...
CA² = 9² = 81
The triangle is not a right triangle.
_____
Additional comment
If you're familiar with a few Pythagorean triples, you know that a couple involving a side length 5 are (3, 4, 5) and (5, 12, 13). That is, (5, 8, 9) is NOT a Pythagorean triple, so you know immediately that those side lengths do not form a right triangle. (No calculation is necessary.)
the diameter of each circular hole in a paint palette is 42 milliliters m Use 3.14 as an approximation
Answer:
Hmm your answer would be (19)
Step-by-step explanation
Im not 100% sure but good luck
Mikah is proving the base angles of this triangle are congruent.
In isosceles triangle QRS, RT is the angle bisector of ∠QRS. Mikah begins the proof by stating ∠1≅∠2. What is a valid reason for this statement?
A. Definition of Angle Bisector
B. Reflexive Property of Congruence
C. Symmetric Property of Congruence
D. Corresponding angles are congruent.
Answer:
its B
Step-by-step explanation:
Which statement is not true?
Answer:
C
Step-by-step explanation:
There can be multiple solutions when two lines intersect.
What is the quotient? ?
-22
O
O
11
11
50
O
22.
Answer:
Didn't get it!
write correctly please!