[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} \stackrel{-3\cdot 2}{-6}&2\\ \stackrel{-3\cdot 3}{-9}&3\\ \stackrel{-3\cdot 5}{-15}&5\\ \cline{1-2} \end{array}~\hspace{5em}\textit{we know that } \begin{cases} y=3\\ x=-9 \end{cases}\implies 3=k(-9) \\\\\\ \cfrac{3}{-9}=k\implies -\cfrac{1}{3}=k\qquad therefore\qquad \blacktriangleright y=-\cfrac{1}{3}x \blacktriangleleft[/tex]
as you can see above, we can see that "x" can be a product of whatever "y" happens to be, so we know each variable is just a factor away from the other.
Answer:
Direct variation; k = -3; y = -3x
Step-by-step explanation:
The formula for direct variation is
y = kx Divide both sides by x
k = y/x
For x = -6, y = 2:
k = -6/2
k = -3
=====
For x = -9, y = 3:
k = -9/3
k = -3
=====
For x = -15, y = 5:
k = -15/5
k = -3
y = -3x
y and x are always in the same ratio, so y varies directly with x.
Jeff Jones earns $1,200 per week. He's married and claims four withholding allowances. The social security rate is 6.2% on $118,500, and Medicare is 1.45%. Each paycheck, his employer also deducts $42.50 for health insurance. What's his net pay?
Jeff's net pay is $1,065.70 per week.
To calculate Jeff Jones's net pay, we need to consider several deductions from his gross pay.
1. Gross Pay: Jeff earns $1,200 per week.
2. Social Security Deduction: Social Security tax is 6.2% of the first $118,500 of earnings. Jeff's earnings are below this threshold, so his Social Security deduction is 6.2% of his gross pay.
Social Security deduction = 6.2% of $1,200 = 0.062 * $1,200 = $74.40
3. Medicare Deduction: Medicare tax is 1.45% of all earnings.
Medicare deduction = 1.45% of $1,200 = 0.0145 * $1,200 = $17.40
4. Health Insurance Deduction: $42.50 is deducted for health insurance.
5. Total Deductions: Add up all deductions.
Total deductions = Social Security deduction + Medicare deduction + Health insurance deduction
= $74.40 + $17.40 + $42.50
= $134.30
6. Net Pay: Subtract total deductions from gross pay.
Net pay = Gross pay - Total deductions
= $1,200 - $134.30
= $1,065.70
Therefore, Jeff's net pay is $1,065.70 per week.
Hello! Can someone please help me with this? There are four answers in total. :D
Problem 1
a) y = 8 and c) x = 2 are perpendicular lines to one another. The first is horizontal and the second is vertical.
The other two lines are not perpendicular because their slopes (1/8 and 8) do not multiply to -1. This rule only applies to lines that are neither horizontal nor vertical.
Answers: A and C.
============================================
Problem 2
Equations b) y = (-1/2)x - 4 and c) y-4 = 2(x+3) are perpendicular. Equation B has a slope of -1/2, while equation C has a slope of 2. Those two values multiply to -1. One slope is the negative reciprocal of the other. It might help to think of 2 as 2/1.
The other two equations are not perpendicular to each other, nor are they perpendicular to B or C. Equation A has a slope of 0. Equation D has a slope of -2.
Answers: B and C
Molly ran 2/3 of a mile in 8 minutes. If Molly runs at the same speed, how long will it take her to run one mile
Answer:
It will take 12 minutes
Step-by-step explanation:
We can use ratio's to solve the problem
2/3 mile 1 miles
------------ = ------------------
8 minutes x minutes
Using cross products
2/3 * x = 8*1
Multiply each side by 3/2 to isolate x
3/2 * 2/3 x = 3/2 * 8
x = 12
Is the system of equations consistent, consistent and coincident, or inconsistent? y=3x+4y=3x+3 Select the correct answer from the drop-down menu.
Answer: Inconsistent
Step-by-step explanation:
y = 3x + 4 → m = 3, b = 4
y = 3x + 3 → m = 3, b = 3
These equations have the same slope but different y-intercepts so they are parallel lines which means they will never intersect.
NOTES
one solution: consistent & independent lines crossinfinite solutions: consistent & dependent same lineno solution: inconsistent parallel linesAnswer:
Inconsistent
Step-by-step explanation:
Three bricklayers from the Emerald Construction Company are working on the new addition to an office building. The first bricklayer laid 8,792 bricks; the second laid 9,491 bricks; and the third laid 9,629 bricks this week. How many bricks did they lay in all?
This question is asking us to find the sum.
8,792 + 9,491 + 9,629 = 27, 912
They lay 27, 912 bricks in all.
Hope helps!-Aparri
Answer: Three bricklayers from the Emerald Construction Company are working on the new addition to an office building. The first bricklayer laid 8,792 bricks; the second laid 9,491 bricks; and the third laid 9,629 bricks this week. They lay a total of 8,792 + 9,491 + 9,629 = 27, 912 bricks.
Step-by-step explanation:
First Brick Layer Laid: 8,792
Second Brick Layer Laid: 9,491
and lastly the
Third Brick Layer Laid 9,629
Now if you take all the bricks that each Brick layer has laid and add them all up (break down)
8,792+9,491+9,629= 27,912 bricks laid in all
that's the break down I hope this helps you all
Mr. Jensen is a salesperson for an insurance company. His monthly paycheck includes a base salary of $2,175 and a commission of $250 for each policy he sells. Write an equation, in slope-intercept form, that represents the total amount, y, in dollars, of Mr. Jensen's paycheck in a month when he sells x policies. Do not include dollar signs in the equation.
Answer:
y = 250x + 2175
Step-by-step explanation:
Mr. Jensen month pay = 2175
Commission per policy = 250
Let "x" be the number of policy he sells and "y" is the total paycheck including the commission.
y = 250x + 2175
Thank you.
Answer:
y = 250x + 2175
Step-by-step explanation:
Factorize 21x^2 - 16-7x / 3x^2-4 = 5
Answer: [tex]\bold{(12x - 7 - i\sqrt{47})(12x - 7 + i\sqrt{47})=0}[/tex]
Step-by-step explanation:
[tex]\dfrac{21x^2-7x - 16}{3x^2-4}=5[/tex]
cross multiply: 21x² - 7x - 16 = 15x² - 20
set equal to 0: 6x² - 7x + 4 = 0
Use quadratic formula to find the roots:
a=6, b=-7, c=4
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(6)(4)}}{2(6)}[/tex]
[tex]=\dfrac{7 \pm \sqrt{49-96}}{12}[/tex]
[tex]=\dfrac{7 \pm \sqrt{-47}}{12}[/tex]
[tex]=\dfrac{7 \pm i\sqrt{47}}{12}[/tex]
[tex]x_1 =\dfrac{7 + i\sqrt{47}}{12} \qquad >>\qquad (12x - 7 - i\sqrt{47})= 0[/tex]
[tex]x_2 =\dfrac{7 - i\sqrt{47}}{12} \qquad >>\qquad (12x - 7 + i\sqrt{47})= 0[/tex]
plz help me with these two questions :)
The Science Club went on a two-day field trip. The first day the members paid $30 for transportation plus $12 per ticket to the planetarium. The second day they paid $90 for transportation plus $9 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club.
Answer: Total: 30 + 20y + 85 + 17y This is the not simplified version.
37y+115 This is the simplified version. Hope this helps
Step-by-step explanation: I really don't know the steps.?
Jill bought a 9 pound bag of cat food for her cats. She had used 4/5 of the bag. How many pounds has she used?
A. 9 4/5
B. 8 4/5
C. 8 3/5
D. 7 1/5
Answer:
D. 7 1/5
Step-by-step explanation:
We would calculate the amount of pounds she used by multiplying the total amount of cat food = 9 to the amount she has used = 4/5
= [tex]9 * \frac{4}{5}[/tex]
= [tex]\frac{36}{5}[/tex]
= [tex]7 \frac{1}{5}[/tex]
(An image is attached for the calculation)
what is 3w - 60 if the perimiter is 449 yards?
Answer:
sooo sorry im in the third grade and notised that this is not my onw level but i really thought i could help u sorry ;(
Step-by-step explanation:
The jones family drove 1,200 miles in 3 days on the first day they traveled 1/4 of the total distance how many miles did they travel the first day
Answer:
They drove 300 miles on the first day
Step-by-step explanation:
They drove 1200 miles
They drove 1/4 on the first day
1200 * 1/4 = 300 miles
They drove 300 miles on the first day
18 × 106) + (5 × 104)
Answer:
2,428
Step-by-step explanation:
(18 × 106) + (5 × 104)
1908 + 520
= 2,428
I'm really sorry if this isn't what you meant... but if it is then... Hope this helps you! :)
What is the diameter of a circle with a circumference of 66 ft? Use 22/7 for pie
Answer:
21 ft
Step-by-step explanation:
Diameter = Circumference/Pi
Diameter = 66/(22/7)
Diameter = 21
What are the x–coordinates of the three points where the graphs of the equations intersect? x3 – 10x = x2 – 6
Answer:
(- 3, 0), (2 + [tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)
Step-by-step explanation:
rearrange the equation equating to zero
x³ - x² - 10x + 6 = 0
note that when x = - 3
(- 3)³ - (- 3)² - 10(- 3) + 6 = - 27 - 9 + 30 + 6 = 0, hence
x = - 3 is a root and (x + 3) is a factor of the polynomial
dividing x³ - x² - 10x + 6 ÷ (x + 3) gives
(x + 3)(x² - 4x + 2) = 0
solve x² - 4x + 2 = 0 using the quadratic formula
with a = 1, b= - 4 and c = 2
x = (4 ± [tex]\sqrt{16-(4(1)(2)}[/tex])/ 2
= (4 ± [tex]\sqrt{8}[/tex]) / 2
= (4 ± 2[tex]\sqrt{2}[/tex]) / 2
= 2 ±[tex]\sqrt{2}[/tex], hence
x = 2 + [tex]\sqrt{2}[/tex], x = 2 - [tex]\sqrt{2}[/tex]
intersect at (- 3, 0), (2 +[tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)
Answer: [tex]\bold{x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2} }}[/tex]
Step-by-step explanation:
First, move all terms to one side with zero on the other side so the Zero Product Property can be applied:
x³ - x² - 10x + 6 = 0 Possible rational roots are: ±{1, 2, 3, 6}
Use synthetic division to find one of the roots. Let's try x = -3
-3 | 1 -1 -10 6
| ↓ -3 12 -6
1 -4 2 0 ← remainder is zero, so x = -3 is a root/intercept
Next, evaluate the reduced polynomial x² - 4x + 2 = 0
This can not be factored so use the quadratic formula to find the remaining roots/intercepts: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 1, b = -4, c = 2
[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)}}{2(1)}[/tex]
[tex]=\dfrac{4\pm\sqrt{16-8}}{2}[/tex]
[tex]=\dfrac{4\pm\sqrt{8}}{2}[/tex]
[tex]=\dfrac{4\pm2\sqrt{2}}{2}[/tex]
[tex]=2\pm\sqrt{2}[/tex]
[tex]x=2+\sqrt{2}\qquad x=2-\sqrt{2}[/tex]
Intercepts are [tex]x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2}}[/tex]
How would u convert 5 feet 6 inches in inches
1 feet is 12 inches.
We have 5 feet and 6 inches. First, let's convert the feet to inches. 5 times 12 is 60, so 5 feet is 60 inches.
Now add 60 inches to the 6 inches that we didn't mention. 60 plus 6 is 66. Thus, 5 feet and 6 inches is 66 inches.
Answer:
The answer is 66
Step-by-step explanation: 1 foot is 12 inches so you do 12 times 5 and get 60 and then add the next 6 inches... :)
solve the following system of equations by graphing y=2x+2y=x-1
y = 2x + 2
for x = 0 → y = 2(0) + 2 = 0 + 2 = 2 → (0, 2)
for x = -1 → y = 2(-1) + 2 = -2 + 2 = 0 → (-1, 0)
y = x - 1
for x = 0 → y = 0 - 1 = -1 → (0, -1)
for x = 1 → y = 1 - 1 = 0 → (1, 0)
Look at the picture.
Answer: (-3, -4) → x = -3 and y = -4.Given: ABCD is a trapezoid, AB=CD, MN is a midsegment, MN=30, BC=17, AB=26 Find: m∠A, m∠B, m∠C, and m∠D
Answer:
m∠A=m∠D=60°, m∠B=m∠C=120°
Step-by-step explanation:
Consider isosceles trapezoid ABCD with midsegment MN. Draw two trapezoid heights BF and CE. Then quadrilateral FBCE is rectangle and EF=BC=17 units.
By the trapezoid midsegment theorem,
[tex]MN=\dfrac{AD+BC}{2},\\ \\30=\dfrac{AD+17}{2},\\ \\60=AD+17,\\ \\AD=60-17=43\ units.[/tex]
Segments FA and ED are equal to [tex]\dfrac{43-17}{2}=13\ units.[/tex]
In right triangle ABF, the hypotenuse AB is twice greater than the leg FA, then m∠FBA=30°.
m∠B=m∠FBA+m∠CBF=30°+90°=120°.
In isosceles trapezoid
m∠B=m∠C=120°,
m∠A=m∠D and m∠A=180°-m∠B=180°-120°=60°=m∠D.
In a trapezoid with equal bases and a midsegment, the angle measures of the trapezoid can be determined using the properties of the figure. In this case, the angle measures are 90 degrees for each angle.
Explanation:In a trapezoid ABCD, the midsegment MN is parallel to the bases AB and CD, and its length is equal to the average of the lengths of the bases. Given that AB = 26, CD = 26, and MN = 30, we can set up the equation: MN = (AB + CD) / 2. Substituting the given values, we get 30 = (26 + 26) / 2. Solving for the angle measures, we can use the fact that the opposite angles in a trapezoid are congruent. So, m∠A = m∠C and m∠B = m∠D. Since the sum of the interior angles of a trapezoid is always 360 degrees, we can use the equation: m∠A + m∠B + m∠C + m∠D = 360. Substituting the angle measures we found, we get 2(m∠A) + 2(m∠B) = 360. Solving for the angle measures, we get m∠A = m∠C = 90 degrees and m∠B = m∠D = 90 degrees.
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what is the value of the lower quartile?
a.0
b.8
c.6
d.2
thank you!
Answer:
D
Step-by-step explanation:
From the box- plot the left hand side of the box represents the lower quartile
that is [tex]Q_{1}[/tex] = 2 → D
5y - 10 = -25
ok try this one buster.
Answer:
Y= -3
Step-by-step explanation:
5y-10=-25 Add 10 on both sides
5y=-15 Divide by 5 on both sides
y=-3
20 POINTS ANSWER SOON PLEASE
Which table represents a proportional situation?
x f(x)
–1 –3
0 0
1 3
4 12
x f(x)
–2 2
0 4
2 6
3 7
x f(x)
–1 –5
0 –2
1 1
2 4
x f(x)
–1 5
0 1
1 –1
2 –3
Answer:
78
Step-by-step explanation:
The coordinates of the vertices of JKL are J(-5, -1), K(0, 1) , and L(2, -5). Which statement correctly describes whether JKL is a right triangle?
Answer:
It is NOT a right triangle.
Step-by-step explanation:
You must figure out the slopes of the segments of the triangle to see if it is a right triangle. If they are perpendicular (meaning the slopes are negative reciprocals of each other), they form a right angle, making it a right triangle.
[tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex] This formula finds slope using two points.
Let's figure out the slope of JK.
(-1-1)/(-5-0) = m
Simplify.
-2/-5 = m
A negative divided by a negative makes a positive.
2/5 = m
Now LK.
(-5-1)/(2-0) = m
Simplify.
-6/2 = m
Divide.
-3/1 = m
Now JL.
(-1+5)/(-5-2) = m
Simplify.
4/-3 = m
None of these slopes are negative reciprocals of each other, thus deeming it not a right triangle.
Four friends went to a local amusement park. Three of the friends bought ride tickets for x dollars, plus a game pass for $10. The other friend bought just a ride ticket. Write and simplify an expression showing the amount of total money spent.
Answer:
4X + 30 = TOTAL AMOUNT OF MONEY
Step-by-step explanation:
All of them bought a ride ticket (that explains the 4x)
3 of them also bought a game pass thet costs $10 each. That explains the 30
going deeper: If the total amount of money was $70
The tickets would've costed $10 each.
Look:
4x + $30 = $70
4x = 70 - 30
4x = 40
x = 40/4
x =$10
will give brainliest
What is the simplified form of 72x16/50x36 ? Assume x ≠ 0.
Answer:
72 / 50 = 36/25
x^16 / x^36
= x^-20
Answer:
[tex]\frac{36}{25x^{20} }[/tex]
Step-by-step explanation:
In order to simplify this function, we have to divide by the maximum common divisor:
[tex]\frac{72x^{16} }{50x^{36} }\\ 72/2=36\\50/2=25\\\frac{36}{25} \\(x^{16} )(x^{-36})=x^{-20}=\frac{1}{x^{20} } \\\frac{36}{25x^{20} }[/tex]
By doing this you can simplify the function into the simplified form.
What is the approximate area that is shaded red?
A.
42 in2
B.
54 in2
C.
66 in2
D.
396 in2
To find the area that is shaded red, you find the area of the rectangle and subtract it by the area of the triangle.
Area of a rectangle:
A = l × w [ l = 11 in ; w = 6in ] Plug these numbers into the equation
A = 11 · 6
A = 66 in²
Area of a triangle:
[tex]A=\frac{1}{2}bh[/tex] [ b = 4 in ; h = 6 in ] Plug these #s into the equation
[tex]A = \frac{1}{2}(4)(6)[/tex]
[tex]A=\frac{24}{2}[/tex]
A = 12 in²
Area of rectangle - Area of triangle = Area of the shaded region
66 in² - 12 in ² = 54 in²
Your answer is B
The required red shaded region has the area of 54 in²
What is a rectangle?A figure bounded by 4 sides in which the opposite sides are equal and all the internal angles are 90 ° is called a rectangle.
What is a triangle?A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.
What is a right angled triangle?A triangle in which one angle in 90° is called a right angled triangle.The side opposite to the right angle is called the hypotenuse which is the longest side of the triangle.Area of the right angled triangle can be found with the formula :Area = (1/2)(base)(height)
How to find the area of the red shaded region?In the given problem, there is a rectangle with in which there is a white colored right angled triangle.The required area will be (Area of the rectangle) - (Area of the triangle).Area of the rectangle = (11 x 6) in² = 66 in²
Area of the right angled triangle = (1/2)(6 x 4) in² = 12 in²
∴ Area of the red shaded region = (66 - 12) in² = 54 in²
Option B is correct.
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can you factories them
For each part A through D below, the idea is to find the common factor between the terms, which you'll then use the distributive property to pull out.
==================================
Part A
3x + 18 = 3(x+6)
Note how we pulled out a 3. If we distribute it back in, we end up with 3x+18 again. The other problems are done in a similar fashion
==================================
Part B
2x - 14 = 2(x - 7)
==================================
Part C
6x + 4 = 2(3x + 2)
==================================
Part D
9x - 15 = 3(3x - 5)
Select the two binomials that are factors of this trinomial x^2+4x-32
So to factor this expression, I'm going to be factoring by grouping. Firstly, what two terms have a sum of 4x and a product of -32x²? That's going to be 8x and -4x. Replace 4x with 8x - 4x:
[tex]x^2+8x-4x-32[/tex]
Now, factor x² + 8x and -4x - 32 separately. Make sure that they have the same quantity on the inside of the parentheses:
[tex]x(x+8)-4(x+8)[/tex]
Now you can rewrite the expression as:
[tex](x-4)(x+8)[/tex]
Answer:In short, the two binomial factors are (x - 4) and (x + 8).
Answer:
x-4 and x+8
Step-by-step explanation:
Factoring a quadratic equation of the form x^2+bx+c:
Divide b into two numbers p and q, so that p+q = b and p*q = c
8 + (-4) = 4 = b
8 * (-4) = -32 = c
x^2+8x-4x-32
Factor by grouping
(x^2+8x)+ (-4x-32) =
x*(x+8) + -4* (x+8) = (x-4)(x+8)
(10 points)Julia exercises at the gym. For every
3 minutes she spends running, she spends
5 minutes lifting weights. Choose 2 answers♾
Answer:
The answer is B and E
Step-by-step explanation:
Julia runs 5 time and lifts 5 times in B. She also runs 10 times and lifts 10 times in E.
Julie drew a picture of her rectangular garden,. In her picture,the length of her garden is 7/8 inches and the width is 3/4 inches. She thinks the area of her picture is 21/32 inches. do you agree or disagree with Julie ? JUSTIFY YOUR ANSWER.(Area=Length X Width)
Answer:
21/32 square inches.
Step-by-step explanation:
The area of a rectangle = length x width
The area of her picture = length x widht
= 7/8 x 3/4
= 21/32
The area of her picture is 21/32 square inches.
Yes, I agree the area of the picture is 21/32 square inches.
The area must be in square inches. So she need to specify it.
Thank you.
Terry bakes bread. He uses the equation 3x-18=y to find the profit, y , in dollars. He paid $18 for supplies and earns $3 for each loaf he sells. What does x represent?
Answer:
The number of loaves sold
Step-by-step explanation: