Answer:
2 hours
Step-by-step explanation:
You can express each person's total earning as the formula for a line. (y=mx+b) Use the amount per hour that can be earned as the slope (m) and the amount already earned as the y intercept (b)
Sophie: y=4x+7
Marcos: y=6x+3
Since y is the total amount of money saved and you know that both people need to earn the same amount of money, we know that y is the same in both equations so we can use substitution to substitute one of the equations in for y in the other equation like this:
4x+7=6x+3
From here, solve algebraically
Subtract 3
4x+4=6x
Subtract 5x
4=2x
Divide by 2
x=2
So they will have the same amount of money after 2 hours.
8x + y = -16
-3x + y = -5
Answer:
Graph= (-1,-8)
y= -8
x=-1
Step-by-step explanation:
I NEED THIS ASAP…. mathematician simplifies the expression mentally.
12(-72) +41(-3-32)
What is the best estimate of the value of the expression?
А
-2,100
B
-700
C 700
D D 2,100
Answer:
The answer is exactly -2,299. But since this is a mental math question it's okay if it's not the exact answer. The answer would be "A"
What’s the distance between (-5,-3) and (-2,11)
Answer: 14.3178210633
Step-by-step explanation: d=√((x_2-x_1)²+(y_2-y_1)²)
Mathematics question (Optional math)
Answer:
Hi mate!
To prove:-[tex] \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} } = \sec( \theta) - \tan( \theta) [/tex]
Step-by-step explanation:
By taking LHS,
[tex] \maltese \: \: \large \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} } [/tex]
By rationalisation method,[tex] : \longrightarrow \bf \sqrt{ \frac{1 + \sin( \theta)}{1 - \sin( \theta)} \times \frac{1 + \sin( \theta)}{1 + \sin( \theta)} } \\ \\ : \longrightarrow \frac{ {( \sqrt{1 + \sin\theta }) }^{2} }{( \sqrt{1 - \sin( \theta)})(\sqrt{1 + \sin( \theta)}) } \\ \\ : \longrightarrow \frac{ {( \sqrt{1 + \sin\theta }) }^{2} }{ \sqrt{ {1}^{2} - { \sin}^{2} \theta } } \: \\ \\ : \longrightarrow \: \frac{1 + \sin \theta}{ \cos \theta } \\ \\ \longrightarrow \: \frac{1}{ \cos \theta } + \frac{ \sin \theta}{ \cos \theta} [/tex]
[tex] \: \: \: \: \: \bigg\lgroup \because \: \frac{1}{ \cos \theta }\: = \sec \theta \: \\ \: \: \: \: \: \: \: \: \: \: \: \frac{ \sin \theta}{ \cos \theta} = \tan \theta \bigg \rgroup[/tex]
[tex] \implies \boxed{\pink{ \sec \theta + \tan \theta }}[/tex]
Now taking RHS
[tex] \sf \sec \theta + \tan \theta [/tex]
[tex]\implies \: \: \frac{1}{ \cos \theta } + \frac{ \sin \theta}{ \cos \theta} \\ \\ \implies \frac{1 + \sin \theta }{ \cos \theta } [/tex]
Hence, proved
Answer:
[tex]\large{\pink{\underline\textsf{To Prove :-}}}[/tex]
[tex] \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } = \sec \theta + \tan \theta[/tex]
[tex] \huge{\orange{\underline{\textsf{Solution :-}}}}[/tex]
[tex] \sf \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } [/tex]
First we have to rationalize it to remove the square rootNow we will multiply √1+sinθ both sides[tex] \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } \times \sqrt{ \frac{1 + \sin \theta }{1 - \sin \theta } } \\ \sqrt{ \frac{ {(1 + \sin \theta) }^{2} }{(1 + \sin \theta)(1 - \sin \theta) } } \\ \sqrt{ \frac{ {(1 + \sin \theta) }^{2} }{1 - { { \sin}^{2} \theta } } }[/tex]
We know that sin²θ + cos²θ = 1so cos²θ = 1 - sin²θ[tex] \sqrt{ \frac{( {1 + \sin \theta })^{2} }{ { \cos}^{2} \theta} } \\ \frac{1 + \sin \theta }{ \cos \theta } \\ \frac{1}{ \cos \theta} + \frac{ \sin \theta }{ \cos \theta } [/tex]
[tex]\sf{\red { \sec \theta + \tan \theta}}[/tex]
[tex] \sf \huge \purple {HENCE \: \: PROVED! }[/tex]
Find the median and mean
40, 4, 12, 15, 45, 16
Answer:
15.5 is the median.
The mean of the data is 22
Step-by-step explanation:
First, the median of a data set is found by sorting the numbers in order, from least to greatest. Then you count inwards one at a time on both sides until you reach a center number.
4 , 12, 15, 16, 40, 45
12, 15, 16, 40
15, 16
15.5
This means, 15.5 is the median
Next, to find the mean, you add up all the numbers and divide it by however many numbers there are. In this case there are 6 numbers, so we divide the total by 6.
40 + 4 + 12 + 15 + 45 + 16 = 132
132 / 6 = 22
The mean of the data is 22
Answer:
Mean: 22
Median: 15.5
Step-by-step explanation:
hope this helps :)
A 4-column table with 3 rows. the first column has no label with entries students, teachers, total. the second column is labeled wear glasses with entries 32, 4, 36. the third column is labeled do not wear glasses with entries 97, 2, 99. the fourth column is labeled total with entries 129, 6, 135. which statements are correct about the two-way frequency table? check all that apply. the table displays qualitative data. the row categories are "wears glasses" and "do not wear glasses." two teachers do not wear glasses. thirty-six students wear glasses. a total of 6 teachers were polled.
The correct statements about the two-way frequency table are:
Option A, Option C, and Option E.
What is a two-way frequency table?In Mathematics and statistics, A two-way frequency table is a tabular method for displaying relative data for two categories of variables. (See the attached).
The question (attached) shows that:
The frequency of teachers that don't wear glasses is two.The table indicates that the data is qualitative data because it is collected via surveys,The table also shows that a total of 6 teachers were surveyed.Learn more about a two-way frequency table at:
https://brainly.com/question/17284360
Answer:
The answer is a,c, e
Step-by-step explanation:
what is the value of x?
Answer:
k=10
Step-by-step explanation:
The reason is that we should solve the following equation:
4k+5 + 6k+10 + (180-115) = 180
by doing some basic algebra we get:
10k = 100
thus: k=10
Lisa built a rectangular flower garden that is 444 meters wide and has a perimeter of 262626 meters.What is the length of Lisa's flower garden
Answer:
9
Step-by-step explanation:
4+4=8, 26-8=18, 18 / 2 = 9, and this is 100% right becuase I got it right on Khan Academy
MATH
THIS
IS URGENT PLS
3a. Area = 2 (5×7 + 5×3 + 7×3)
3b. Area = 2 (6×6 + 6×5 + 6×5)
3c. Area = 2 (6.5×10 + 6.5×3 + 3×10)
4a. Area = 2(1/2 × 4 × 6) + 2(7×5) + 7×6
4b. Area = 2(1/2 × 6 × 6) + 2(10×8.5) + 10×6
4c. Area = 2(1/2 × 10.2 × 3.6) + 15×8.3 + 15×4.5 + 10.2×15
16. Higher Order Thinking
a. Find the value of x given that rls.
m21 = (63 - x)º
m22 = (72 - 2x)
2
b. Find mz1 and m22.
Answer:
[tex]\red{ \bold{m \angle \: 1 = 54 \degree}} \\\: \purple{ \bold{m \angle \: 2 = 54 \degree}} [/tex]
Step-by-step explanation:
[tex](a) \: \: \: \\ r || s \: \: \: (given) \\ \implies \: m \angle \: 1 = m \: \angle \: 2 \\ (corresponding \: \angle s) \\ \implies \: (63 - x) \degree = (72 - 2x) \degree \\ \implies \: 63 - x = 72 - 2x \\ \implies \: 2x - x = 72 - 63 \\ \implies \: \huge \orange{ x = 9} \\ \\ (b) \\ m \angle \: 1 = (63 - x) \degree \\ \implies \: m \angle \: 1 = (63 - 9) \degree \\ \implies \: \red{ \bold{m \angle \: 1 = 54 \degree}} \\ \implies \: \purple{ \bold{m \angle \: 2 = 54 \degree}} \\ ( \because \: m \angle \: 1 = m \: \angle \: 2)[/tex]
Simplify the following (x+3y)(x-3y)
Answer:x^2-9y^2
Step-by-step explanation:
x timesx +x(-3y)+3yx+3y(-3y)
Then simplify
X^2-9y^2
Find the equation of a line that passes through the point (-3,-4) and has a gradient of 5.
Leave your answer in the form
y=mx+c
i will mark brainly
Answer:
Y=5X+11Step-by-step explanation:
x1= -3
y1= -4
m=5
y-y1=m(x-x1)
y-(-4)=5(x-(-3))
y+4=5(x+3)
y+4=5x+15
y=5x+15-4
y=5x+11
An equation has solutions of m = –5 and m = 9. which could be the equation? (m 5)(m – 9) = 0 (m – 5)(m 9) = 0 m2 – 5m 9 = 0 m2 5m – 9 = 0
An equation is formed of two equal expressions. The equation that has solutions of m=–5 and m=9 is (m+5)(m-9)=0.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
As it is given that the solution of m is -5 and 9. Therefore, the equation which will represent the solution of m as -5 and 9 is
(m+5)(m-9)=0
Hence, the equation that has solutions of m=–5 and m=9 is (m+5)(m-9)=0.
Learn more about Equation:
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A dealership paid $8,000 for a car at an
auction. A salesman at the dealership sold
the car for 40% more than the auction
price. If he received a 15% commission on
the difference between the auction price
and sales price, what was his commission?
A. $415
B. $430
C. $465
D. $480
Answer:
D
Step-by-step explanation:
[tex]1.40(8000) = 11200[/tex]
[tex].15(11200 - 8000) = .15(3200) = 480[/tex]
Find Mitch's mistake.
Answer:
C
Step-by-step explanation:
Step 1
7.7 - 2 = w - 2 + 2Step 2
LHS ⇒ 7.7 - 2 = 5.7RHS ⇒ w - 2 + 2 = w [-2 and 2 cancel out = 0]⇒ 5.7 = 2Mitch did not make a mistake6 - v = 260
Solve for V.
Answer:
............
Step-by-step explanation:
Melissa is driving a sports utility vehicle along the interstate at a constant speed of 55 mph. A sports car one-half mile behind her that is moving at a constant speed passes her in 60 seconds. How many miles per hour is the speed of the sports car
Using proportions, it is found that the speed of the sports car is of 85 miles per hour.
What is a proportion?A proportion is a fraction of a total amount.
The cars are moving in the same direction, hence their relative speed is the difference of them.
The sports car is 0.5 miles faster over one minute, hence over one hour the difference is:
60 x 0.5 = 30 miles per hour.
Considering that the utility vehicle has a speed of 55 mph, the speed of the sports car is given by:
55 + 30 = 85 miles per hour.
More can be learned about proportions at https://brainly.com/question/24372153
The length of a rectangle is 5 inches longer than the width. The perimeter of the rectangle is 40 inches. What is the width of the rectangle?
Explain or show work please
Step-by-step explanation:
Set the parameters,
Let the width be 'X' inhes
Therefore,
Length = "5X" inches
According to the given condition,
Perimeter = sum of the sides = 2(l+b) = 40 inches,
Equation = 2(5X+X) = 40
2(6X) = 40
12X= 40
X= 3.33
Therefore,
Width = X = 3.33 inches
MARK ME AS BRAINLIST30 points Helppppp!! Find the value of
x
xx in the triangle shown below.
x
=
x=x, equals
∘
∘
degrees
Answer:
please see photo above for details
What is the area of the figure?
Step-by-step explanation:
take the rectangle as whole with dimensions 16*8
area = 128 in^2
area of rectangle of dimensions 10*2 =20
required area = 108 in^2
Nic is making chocolate chip cookies. The recipe requires 3/4 cups of brown sugar and 1 1/8 teaspoons of salt. Nic wants to make the recipe using 1 cup of brown sugar. To maintain the ratio, how much salt is required when 1 cup of brown sugar is used?
To maintain the ratio, the amount of salt required when 1 cup of brown sugar is used is 1.5teaspoon
Ratio and proportion
Fractions are written as a ratio of two integers.
From the gven question, we are told that a recipe requires 3/4 cups of brown sugar and 1 1/8 teaspoons of salt, this can be expressed as:
3/4 cups = 1 1/8 teaspoons
To maintain the ratio, the amount of salt that is required when 1 cup of brown sugar is used is given as:
amount of salt required = (1 1/8)/3/4
amount of salt required =9/8 * 4/3
amount of salt required = 3/2
amount of salt required = 1 1/2 teaspoon
Hence to maintain the ratio, the amount of salt required when 1 cup of brown sugar is used is 1.5teaspoon
Learn more on ratio and proportion here: https://brainly.com/question/2914376
Donald bought 2 game controllers at Gamestop for $36. Each one cost the same amount. What is the unit rate for a single controller? & Jake was offered the following amounts of an entire pizza: 0.6, 4/5, or 0.75. Jake really likes pizza and wants the largest amount of pizza he can get. Which of the amounts should he select?
Don’t add all together
There’s two answers
Answer:
Answer to question 1 is 18
Answer to question 2 is 4/5
Step-by-step explanation:
Question one simply asks how much one controller is
Being that both controllers = 36$
And to find one controller price you would just divide the price by the number of units
36/2= 18
The second question asks how much pizza would be more .6, 4/5 or .8, or .75
Since .8 has the most value or in this case pizza 4/5ths is the answer
A shark's depth in meters relative to sea level over time in minutes, x, is modeled as a parabola. At time 1 minute the shark is swimming upwards and is at a depth of 7 meters. The shark continues to swim toward the surface for another minute and then turns and begins to swim downwards and returns to a depth of 7 meters at time 3 minutes. What is the axis of symmetry of the graph of the parabola?
Answer:
The axis of symmetry of the graph of the parabola is -2
Step-by-step explanation:
Since the sharks depth in meters is relative to sea level over time in minutes we need to model this as x= 7-2x so 2 times 3 is 6 7-6=1
1 plus 1 equals 2
Levi just started a running plan where he runs 8 miles the first week and then
increases the number of miles he runs by 5% each week. If he keeps up this plan for
19 weeks, how many total miles would Levi have run, to the nearest whole number?
Answer:
244 miles (nearest whole number)
Step-by-step explanation:
We can model this as a geometric series.
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common difference)
Given information:
Miles run in first week = 8Weekly increase of miles = 5%Total number of weeks in plan = 19Therefore:
[tex]a[/tex] = 8[tex]r[/tex] = 1.05[tex]n[/tex] = 19Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Therefore, sum of the first 19 terms:
[tex]\implies S_{19}=\dfrac{8(1-1.05^{19})}{1-1.05}[/tex]
[tex]\implies S_{19}=244.3120313...[/tex]
So Levi ran a total of 244 miles (to the nearest whole number)
For every $1 increase in the price per scarf, Sofie's profit changes by an average of $
Answer:
True, because if price changes, dod oes average of money. So if you get 5 bucks per 10 scarfs, you'll get 5.50$ for 11 scarfs
Step-by-step explanation:
Lets just say she gets half of what the actual cost is. In total.
Answer:
This is true
Step-by-step explanation:
.......................
Please help me with this math problem!! Will give brainliest!! NO LINKS PLEASE!! Thanks!! :)
Answer:
The sum of all the sides to this quadrilateral will equal a total of 20 inches, so you set up the equation:
2 + 2x + 7 + x + 2 = 20
Solve for x by combining like terms;
(2 + 7 + 2) + (2x + x) = 20
Which simplifies to;
11 + 3x = 20
Get rid of constants;
-11 -11
3x = 9
Isolate x by getting rid of it's coefficient;
/3 /3
x = 3
Now, to find the length of PQ, we plug in the value of x(3) into the equation that contains the line PQ.
x + 2
3 + 2
= 5 inches.
Now, to find the length of RS, we plug in the value of x(3) into the equation that contains the line RS.
2x
2(3)
= 6 inches.
Complete the equation so that it has solutions of –5 and 7. x2 x = 0
The equation it has solutions of –5 and 7 is x^2-2x-37=0
We have equation
solutions of equation are –5 and 7.
We have to find complete the equation.
We have given that solutions of the equation are -5, 7.
The standard form of a quadratic equation.
What is the factor of the quadratic equation?
[tex](x -\alpha) (x- \beta)[/tex]
Where we have
[tex]p = -(\alpha+\beta) and q = (\alpha\times \beta)[/tex]
So, roots are
[tex]( x- (-5)) (x-7)[/tex]
[tex]p = -( -5+7)[/tex] , [tex]q =(-5)(7).[/tex]
[tex]p = -2 and q = -35.[/tex]
On substituting p and q in equation
[tex]x^2+(-2)x-37=0[/tex]
[tex]x^2-2x-37=0[/tex]
Therefore,x^2-2x-37=0 is the equation of solution -5,7.
To learn more about the quadratic factor visit:
https://brainly.com/question/472337
Answer:
-2, -35
Step-by-step explanation:
Write a paragraph describing your zipline. Include the 5 components below. * Zipline's Name *Setting *Description of point A and how the zipliner would get to that height. (climbing ladder , higher ground , etc) Zipline Safety Landing (How would the zipliner land safely? Stop block, brakes, etc) *Names of Three Locations for points A, B and C. The zipliner will move through these 3 locations marked by these 3 points. A:(5, 25), B / (65, 19) and C: (105, 14) .
Answer:
A
Step-by-step explanation:
because it A because I can done that fast
What is the area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn? (2π 28) mm2 (2π 32) mm2 (2π 40) mm2 (2π 48) mm2
The area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn is (2π + 40) mm².
What is the area of the semicircle?The area of a semicircle is the space contained by the circle. The area is the number of square units enclosed by the sides of the shape.
The area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn is given by adding an area of MKCD , area of ABCD, area of a semi-circle with AB as diameter.
Area of the composite figure = area of MKCD + area of ABCD + area of a semi-circle with AB as diameter.
The area of the composite figure is;
Area A = (DC + MK)/2 × DN + AB² + (1/2)×π×2²
Area A = (4 + 8)/2 × 4 + 4² + (1/2)×π×4
Area A = 24 + 16 + 2π = (2π + 40) mm²
Hence, the area of the composite figure if ab ≅ bc ≅ cd ≅ da ≅ dn is (2π + 40) mm².
To know more about the area of the semicircle click the link given below.
https://brainly.com/question/17098710