Answer:
Mary has $1120
Step-by-step explanation:
money mary has at first : x
money jane has at first : y
Mary brought twice as much money as Jane : x=2y
Mary had spent $800 and Jane had spent $240, they had equal amount of money left : x-800=y-240
=> [tex]\left \{ {{x=2y} \atop {x-800=y-240}} \right.[/tex]
=> x=1120
y=560
Answer:
Mary had $1,120Step-by-step explanation:
Let the amount mary and jane had be 2x and x respectively.
Let the equal amount be y:
[tex]mary \: (y = 2x - 800) \\ jane \: (y = x - 240)[/tex]
Using the simultaneous equation method, multiply the first equation by the coefficient of x(1) of the second equation and the second equation by the coefficient of x(2) of the first equation:
[tex]y = 2x - 800 \\ 2y = 2x - 480[/tex]
Subtract the second equation from the first equation:
[tex] - y = - 320 \\ y = 320[/tex]
$320 was their equal amount.
Substitute 320 for y in any equation:
[tex]y = x - 240 \\ 320 = x - 240 \\ x = 320 + 240 \\ x = 560 \\ \\ 2x = 1120[/tex]
Therefore, Jane had $560 at first and Mary had $1120 at first.
Find the measures of the interior angles that maximize the area of an isosceles trapezoid
where the length of the non-parallel sides are each 4 inches and the length the shorter of
the two bases is 6 inches.
The measure of the angle that would maximize the area of this isosceles trapezoid is equal to 0.4395 rad.
Given the following data:
Base length = 6 inches.Sides length = 4 inches.How to calculate the area of a trapezium.Mathematically, the area of a trapezium is given by this formula:
A = ½ × (a + b) × h
A = ½ × (12 + 2l) × h
A = h(6 + l)
Next, we would derive a mathematical expression for A in terms of h as follows;
Let l = 4sinθ Let h = 4cosθA = (6 + 4sin(θ)) × 4cosθ
In order to determine the value of θ for which the area of this isosceles trapezoid is maximized, we would differentiate the area (A) with respect to angle (θ):
Note: sin²θ + cos²θ = 1 ⇒ cos²θ = 1 - sin²θ.
[tex]\frac{dA}{d\theta} =16 cos^{2} \theta - 4sin \theta(6+4sin \theta)\\\\\frac{dA}{d\theta} = 16 cos^{2} \theta - 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} =16(1-sin^{2} \theta)- 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} = - 32 sin^{2} \theta - 24sin\theta+16\\\\32 sin^{2} \theta + 24sin\theta-16=0[/tex]
Next, we would use the quadratic formula to solve for the value of sinθ.
Mathematically, the quadratic formula is given by this equation:
[tex]sin\theta = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Where:
a = 32.b = 24.c = -16.Substituting the parameters into the formula, we have;
[tex]sin\theta = \frac{-24\; \pm\; \sqrt{24^2 - 4(32)(-16)}}{2(32)}\\\\sin\theta = \frac{-24\; \pm\; \sqrt{2624}}{64}\\\\sin\theta = \frac{-24\; \pm\; 51.23}{64}\\\\sin\theta = \frac{-24\;+\; 51.23}{64}\\\\sin\theta = \frac{27.23}{64}\\\\sin\theta = 0.4255\\\\\theta = sin^{-1}(0.4255)[/tex]
θ = 0.4395 rad.
Note: We would only consider the positive value of the quadratic root.
For the obtuse interior angles of the trapezoid, we have [tex](\frac{\pi}{2} +0.4395)[/tex]
Similarly, the measure of the acute interior angles of the trapezoid is [tex](\frac{\pi}{2} -0.4395)[/tex]
Read more on isosceles trapezoid here: https://brainly.com/question/4758162
A square pyramid has a base with a side length of 7.5 feet and lateral faces with heights of 16 feet. Write an expression that can be used to find the surface area, in square feet, of the square pyramid.
Please provide an expression, not just the surface area please :)
Check the picture below.
so the surface area of the pyramid will be the sum of the areas of the base and the four triangular faces.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{4 triangular faces}}{4\left[ \cfrac{1}{2}(7.5)(16) \right]}~~ + ~~\stackrel{\textit{rectangular base}}{(7.5)(7.5)}}\implies 240~~ + ~~56.25\implies 296.25~ft^2[/tex]
l need help with this pls
Answer:
50°
Step-by-step explanation:
In a parallelogram opposite angles have the same measure. Angle ABC has then the same measure of angle ADC, which is 38°+12°=50°
What is the area in polynomial form
Answer:
[tex] \orange{ \boxed{ \sf{ ( \: {x}^{2} + 11x + 18 \: ) \: sq. \: units}}}[/tex]
Solution :
Area = lenght x widthLenght = x + 9
Width = x + 2
[tex] \sf \green{area \: = \: (x + 9)(x + 2)} \\ \sf \green{ = \: { {x}^{2} + 11x + 18}} [/tex]
Answer:
[tex]x^2+11x+18\: \sf(square\:units)[/tex]
Step-by-step explanation:
To use the area model of solving multiplication and division problems, calculate the area of each of the colored rectangles and add them together.
Area of a rectangle = Length × Width
Area of blue rectangle: [tex]x \times x = x^2[/tex]
Area of pink rectangle: [tex]x \times 9 = 9x[/tex]
Area of green rectangle: [tex]2 \times x=2x[/tex]
Area of orange rectangle: [tex]2 \times 9=18[/tex]
Area of entire rectangle = blue + pink + green + orange
= [tex]x^2+9x+2x+18[/tex]
= [tex]x^2+11x+18\: \sf(square\:units)[/tex]
Find the value of each variable in the parallelogram.
Answer:
h=9
g=61
Step-by-step explanation:
16-h=7
g+4=65
&
Opposite angles and sides are equal in a paralleogram
g+4=65g=65-4g=61Amd
16-h=7h=16-7h=9can someone please help me with this
Answer:
"4 or less, let it rest. 5 or more, raise the score."
Step-by-step explanation:
1) 5.57, 5.62, 5.59
2) 2.349, 2.352, 2.346, 2.354
3)
0.7
0.3
1.5
3.4
4)
3.74
0.93
0.33
1.56
I hope this helps! Have a lovely day!! :)
(I would appreciate brainliest!!)
how many positive integers are between 28/3 and 83/5
Answer: ur dad
Step-by-step explanation:
lol
There are 7 positive integers in between 28/3 and 83/5.
What is an integer?
An integer is a whole number (not a fractional number) that can be positive, negative or zero.
Given that;
Two fractions are;
28/3 and 83/5.
Now, Write fraction into decimal form as;
28/3 = 9.33
83/5 = 16.6
So, All Integers in between 9.33 and 16.6 are;
⇒ 10, 11, 12, 13, 14, 15, 16
Thus, There are 7 positive integers in between 28/3 and 83/5.
Learn more about the integers visit:
https://brainly.com/question/24653557
#SPJ2
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x)=x2 to the number of x-intercepts in the graph of g(x)= (x+2)2 -7
Work out the length of x.
Give your answer rounded to 3 significant figures.
х
16.5 mm
6.6 mm
Answer:
x=17.771mm
Step-by-step explanation:
given a right triangle
to find vslue of x
solution (perpendicular) ² + (base) ² =(hypotenus) ²
using pythagorus theorem
(16.5)²+(6.6)²=(x)²
272.25+43.56=(x)²
315.81=(x)²
√315.81=x
x=17.771mm
Answer:
By Pythagoras theorem
H^2=P^2+B^2
x^2=(6.6)^2+(16.5)^2
x^2=43.56+272.25
x^2=315.81
x=√315.81
x=17.771mm
What is the answer for this question?
Answer:
is this from flvs?
Step-by-step explanation:
The number 9 is a common factor of _________.
A) 6 and 9
B) 9 and 36
C) 16 and 27
Answer:
Step-by-step explanation:
B) 9 and 36
================================================
9 is a common factor of
9 and 36.
Here's why:
6 is not evenly divisible by 9
16 is not divisible evenly by 9 (it is divisible by 8)
All the other numbers are divisible by 9.
=============================================
note:-Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer. :)
What is a Semicircle?
Answer:
half a circle
Please help me to answer this
the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 56 in, find its length and width
Answer:
Step-by-step explanation:
Let the width of the rectangle = x
As length is 5 inches longer than width, we have to add 5 to width
Length = x + 5
Perimeter of ractangle = 56 in
2* (length + width) = 56
2*( x + 5 + x) = 56
2* (2x + 5) = 56
Use distributive property: a*(b +c) =(a*b) + (a * c)
2*2x + 2*5 = 56
4x + 10 = 56
Subtract 10 from both sides
4x = 56- 10
4x = 46
Divide both sides by 4
x = 46/4
x = 11.5
Width = 11.5 in
length = 11.5 + 5
= 16.5 in
Solve | x + 6| - 7 = 8
A: x= -9 and x = -21
B: x = 9 and x = -9
C: x = -9 and x = 21
D: x = 9 and x = -21
Answer:
x = 9,-21
Step-by-step explanation:
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Cancel absolute sign and add plus-minus to 15:
[tex]\displaystyle \large{x+6=\pm 15}[/tex]
Transport 6 to subtract ±15:
[tex]\displaystyle \large{x=\pm 15-6}[/tex]
Consider:
[tex]\displaystyle \large{x= 15-6}[/tex] or [tex]\displaystyle \large{x = -15-6}[/tex]
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x = 9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Second Method
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Absolute Function Property:
[tex]\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}[/tex]
Consider both intervals:
When x ≥ a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}[/tex]
Transport 6 to subtract 15:
[tex]\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}[/tex]
When x < a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}[/tex]
Transport -6 to add 15:
[tex]\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}[/tex]
Transport negative sign to 21:
[tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!
What is the least common multiple of 324 and 245?
the lcm would be 79380
Step-by-step explanation:
5×7×7
2×2
×3×3×3×3
muliply all the 3 numbers and then you get 79380
Pam’s monthly food budget is equal to 40% of her monthly rent payment. If her food budget is $200 a month, how much is her rent payment each month?
so we know that 40% for the rent payment is for food, and we also know that those 40% are really 200 bucks, so what would it be for the 100%?
[tex]\begin{array}{ccll} \%&amount\\ \cline{1-2} 40 & 200\\ 100& x \end{array} \implies \cfrac{40}{100}=\cfrac{200}{x}\implies \cfrac{2}{5}=\cfrac{200}{x} \\\\\\ 2x=1000\implies x=\cfrac{1000}{2}\implies x=500[/tex]
PLEASE HELP WILL GIVE BRANLIEST
Carly needs $149 to buy a skateboard. She already has $52. She earns money washing cars for $20 a car.
Carly says that if she washes 5 cars she will have enough money to buy the skateboard.
Use the drop-down menus to explain how to solve this problem.
First multiply
Choose...
× $20 to find how much money Carly will earn washing cars. Then add this amount to
Choose...
to find how much money Carly has in all. Finally,
Choose...
the total to the cost of the skateboard.
Answer:
$149 - skateboard price
$52 - carly's money
$20 × 5 cars = $100
$100 + $52 = $152
$152 - $149 = $3 left
Factor completely 4a^2-b^2-2a+b GUYS HELP THERE ARENT ANY CORRECT ANSWERS ON BRAINLY URGENT
Answer:
(2a-b)(2a+b-1)
Step-by-step explanation:
Robin got home from school
at 3:45. She spent 2 hours
working on her homework, a
half an hour walking the dog,
and forty-five minutes eating
dinner with her family. Then
she began reading her book.
At what time was she finished
eating dinner?
Answer:
She was finished with dinner at 6:50
Step-by-step explanation:
3:45 + 2 = 5:45
5:45 + 30 = 6:05
6:05 + 45 = 6:50
Fatima has 3 packs of batteries. Each pack contains 4 batteries. She gives her brother 8 batteries to put in his toy robot.
Let b represent the number of batteries Fatima has left.
Which equation could be used to find the value of b?
3×4−8=b
3+4−8=b
3 × 4 + 8 = b
3 + 4 + 8 = b
Using a system of equations, it is found that the equation that could be used to find the value of b is given by:
3×4−8=b
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
Fatima has 3 packs of batteries. Each pack contains 4 batteries, hence:
b = 3 x 4
She gives her brother 8 batteries to put in his toy robot, hence:
b = 3 x 4 - 8
Which means that the first expression is correct.
More can be learned about a system of equations at https://brainly.com/question/24342899
2) Jose bought a magazine for $10 and some erasers for $2 per eraser. He spent a total of $26. How many erasers
he buy?
I can solve it i just need to know the equation with X
Please help solve by elimination I hope its not blurry Have a nice day and Goodnight
Answer:
[tex]\displaystyle \textcolor{black}{4.}\:[-3, -5][/tex]
[tex]\displaystyle \textcolor{black}{3.}\:[8, -1][/tex]
[tex]\displaystyle \textcolor{black}{2.}\:[4, -7][/tex]
[tex]\displaystyle \textcolor{black}{1.}\:[3, -2][/tex]
Step-by-step explanation:
When using the Elimination method, you eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:
[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-5x - 3y = 30}} \right.[/tex]
{2x - 3y = 9
{⅖[−5x - 3y = 30]
[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-2x - 1\frac{1}{5}y = 12}} \right. \\ \\ \frac{-4\frac{1}{5}y}{-4\frac{1}{5}} = \frac{21}{-4\frac{1}{5}} \\ \\ \boxed{y = -5, x = -3}[/tex]
------------------------------------------------------------------------------------------
[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {x + 3y = 5}} \right.[/tex]
{x - 2y = 10
{⅔[x + 3y = 5]
[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {\frac{2}{3}x + 2y = 3\frac{1}{3}}} \right. \\ \\ \frac{1\frac{2}{3}x}{1\frac{2}{3}} = \frac{13\frac{1}{3}}{1\frac{2}{3}} \\ \\ \boxed{x = 8, y = -1}[/tex]
_______________________________________________
[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {y = -8x + 25}} \right.[/tex]
{y = −3x + 5
{−⅜[y = −8x + 25]
[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {-\frac{3}{8}y = 3x - 9\frac{3}{8}}} \right. \\ \\ \frac{\frac{5}{8}y}{\frac{5}{8}} = \frac{-4\frac{3}{8}}{\frac{5}{8}} \\ \\ \boxed{y = -7, x = 4}[/tex]
------------------------------------------------------------------------------------------
[tex]\displaystyle \left \{ {{y = -x + 1} \atop {y = 4x - 14}} \right.[/tex]
{y = −x + 1
{¼[y = 4x - 14]
[tex]\displaystyle \left \{ {{y = -x + 1} \atop {\frac{1}{4}y = x - 3\frac{1}{2}}} \right. \\ \\ \frac{1\frac{1}{4}y}{1\frac{1}{4}} = \frac{-2\frac{1}{2}}{1\frac{1}{4}} \\ \\ \boxed{y = -2, x = 3}[/tex]
_______________________________________________
I am joyous to assist you at any time.
PLEASE ANSWER THIS ASAP IT'S DUE IN 5 MINUTES!!!!
1. The rule for an arithmetic sequence is: __________?
2. The rule for a geometric sequence is: __________?
Answer:
an = a1 + d (n - 1)
aⁿ = a₁ˣ⁻1
A student was asked to simplify the expression 2(x+3)+(4x−8)−7x.
Identify the line which contains the initial error.
1: 2(x+3)+(4x−8)−7x
2: 2x+6+4x+8−7x
3: (2x+4x−7x)+(6+8)
4: −x+14
Answer:
Line 2
Step-by-step explanation:
When factoring the second bracket, 1 x -8 is -8.
Answer:
4
Step-by-step explanation:
2{x+3}+{4x_8}_7x is same2x+6+4x+8_7x the first bracket was multiply by 2 {2x+4x_7x}+{6+8} the like term was collected and grouped with bracketsNO LINKS!!!
Part 3: Figure A is a dilated image of Figure B. Find the scale factor. #5 and 6
Answer:
Step-by-step explanation:
Scale:- 1box=1units
So
Take one side of each
B=6unitsA=10unitsScale factor(A to B)
[tex]\\ \rm\rightarrowtail \dfrac{6}{10}=\dfrac{3}{5}[/tex]
Scale factor (B to A) is 5/3#6
B=12A=6Scale factor (A to B)
[tex]\\ \rm\rightarrowtail \dfrac{12}{6}=2[/tex]
Scale factor (B to A)
[tex]\\ \rm\rightarrowtail \dfrac{6}{12}=0.5[/tex]
Pls help pls pls help me pls pls help pls
Answer:
D should be the answer because the rate of Mason and Evan is 3 pages per a minute because three goes into both like so 30÷10=3 and 12÷4=3. Which is why D is your answer.
Palil used 6 pieces of ribbon that were each 9 inches long on a project.
How many inches of ribbon did he use?
Use the bar diagram to show how many inches of ribbon Palil used.
Drag the numbers to the bar diagram. Numbers may be used once, more than once, or not at all.
Answer:
54
Step-by-step explanation:
9x6=54
For each of the following, draw a diagram or use words to explain your answer.
A. How many 2/3 are in 2?
B. How many 1/10 are in 3?
Answer:
A. 3. B. 20
Step-by-step explanation:
2 divided by 2/3 is 2/ 2/3 or 6/2 which is 3.
3 divided by 1/10 is 3/ 1/10 or 30.