Answer:
2/3
Step-by-step explanation:
The formula for the slope is:
[tex]\frac{y2-y1}{x2-x1}[/tex]
Plug in (7,1) and (10, 3):
[tex]\frac{3-1}{10-7} = 2/3[/tex]
Santa and his elves had a workshop that allowed them to produce 22{,}912{,}546{,}99222,912,546,99222, comma, 912, comma, 546, comma, 992 toys each year.
The world population increased, so they built a new workshop. The new workshop allows them to produce 4{,}134{,}232{,}638{,}9374,134,232,638,9374, comma, 134, comma, 232, comma, 638, comma, 937 toys each year.
Approximately how many times as many toys can the new workshop produce each year compared to the old workshop?
Choose 1 answer:
Choose 1 answer:
The new workshop can produce as many as 180 toys each year compared to the old workshop
What is the approximation of a number?The approximation of numbers is the estimates of the said number.
This means that the approximation of a number is close to the said number, but it has a slight different value
How to determine the approximate number of times?The given parameters are:
Old capacity = 22,912,546,992 toys per year
New capacity = 4,134,232,638,937 toys per year
The approximate number of times is calculated as
Number of times = New capacity/Old capacity
Substitute the known values in the above equation
So, we have
Number of times = 4,134,232,638,937 toys per year/22,912,546,992 toys per year
Remove the units
So, we have
Number of times = 4,134,232,638,937/22,912,546,992
Evaluate the quotient
So, we have
Number of times = 180.435315217
Approximate
Number of times = 180
Hence. the approximate number of times is 180
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please! Is for today!! HELP!!
The given pairs of lines have been identified as parallel, perpendicular lines or neither as explained below.
How to Determine if Two Lines are Parallel or Perpendicular?Two lines are parallel if they have the same slope (m), while they are perpendicular to each other if their slopes are negative reciprocal of each other.
The slope in a given equation of a line that is in slope-intercept form, y = mx + b, is represented as "m" in the equation.
1. y = 3x - 7 and y = 3x + 1 both have the same slope (m) of 3. They are parallel lines.
2. y = -2/5x + 3 and y = 2/5x + 8 both have the different slope (m), which are not negative reciprocal to each other. They are neither parallel nor perpendicular lines.
3. The slope of y = -1/4x is -1/4. The slope of y = 4x - 5 is 4. -1/4 is the negative reciprocal of 4. Therefore, the lines are perpendicular.
4. 2x + 7y = 28 can be rewritten as y = -2/7x + 4, the slope (m) is -2/7.
7x - 2y = 4 can be rewritten as y = 7/2x - 2, the slope (m) is 7/2.
-2/7 and 7/2 are negative reciprocals.
They are perpendicular lines.
5. The slope of y = -5x + 1 is -5.
x - 5y = 30 can be rewritten as y = 1/5x - 6, the slope is 1/5.
The lines are perpendicular.
6. 3x + 2y = 8 can be rewritten as y = -3/2x + 4, the slope (m) is -3/2.
2x + 3y = -12 can be rewritten as y = -2/3x - 4, the slope (m) is -2/3.
The lines are neither.
7. The slope of y = -4x - 1 is -4.
8x + 2y = 14 can be rewritten as y = -4x + 7, the slope is -4.
They are therefore parallel lines.
8. x + y = 7 can be rewritten as y = -x + 7, the slope (m) is -1.
x - y = 9 can be rewritten as y = x - 9, the slope (m) is 1.
The lines are perpendicular.
9. They have the same slope of 1/3. They are parallel lines.
10. They have different slopes that are not negative reciprocals, therefore, they are neither.
11. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.
12. They have the same slope of 3/4. They are parallel lines.
13. They have the same slope of 1. They are parallel lines.
14. Their slopes are -5/4 and 4/5. Therefore, they are perpendicular lines.
15. Their slopes are not negative reciprocals and are not the same, therefore, they are neither.
16. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.
17. They are both vertical lines, therefore they are neither.
18. x = 1 is a vertical line while y = -8 is a horizontal line that meets perpendicularly. Therefore, the lines are perpendicular.
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Which is the following numbers is the closest to six
38
34
33
37?
Robin’s favorite pound cake recipe needs 2 1/3 cups of flour. She plans to make 2 cakes for a picnic. She has 4 1/2 cups of flour in her cabinet. How much more flour does she need to make the 2 cakes
Answer: 1/6
Step-by-step explanation:
Please help, thanks
Answer:
13. x = 3∛2
14 x = ± 4√6 = ± 4√2 √3
15. x = 2∛11
16 x = -4∛2
17 x = ± 10√3
18. x = ± 4 √3 √5
Step-by-step explanation:
13. x³ = 54
x = ∛4
Factor 54: 2 x 27
∛54 = ∛2 x ∛27
∛27 = 3
answer: 3∛2
14. x² = 96
x = ±√96
96 = 6 x 16
√16 = 4
√6
√96 = ± 4√6 = ± 4√2√3
15. x³ = 88
x = ∛88
88 = 8 x 11
∛88 = ∛8 x ∛11 = 2∛11
16. x³ = -128 means x has to be negative
x = -∛128
128 = 64 x 2
∛128 = ∛64 x ∛2 = 4∛2
So x = -4∛2
17. x² = 300
=> x = ± √300
300 = 100 x 3
√300 = √100 x √3 = 10√3
x = ± 10√3
18. x² = 240
x = ±√240
240 = 16 x 15
√240 = ± (√16 x √15)
= ± 4 √3 √5
Order from least to greatest .003 3.03 33.03 .303 .383 .030
Answer:
0.003, 0.03, 0.303, 0.383, 3.03, 33.03
Step-by-step explanation:
You spin a spinner, Flip a coin, then spin the spinner again. Find the probability of the compound event, write your answer as a fraction or percent. If necessary round your answer to the nearest hundredth.The probability of spinning blue, flipping heads, then spinning a one is _
The probability is given by:
[tex]P=\frac{numb\text{er of favourable outcomes}}{\text{total number }of\text{ outcomes}}[/tex]Therefore:
- The probability of spinning blue is:
Favorable outcomes = 1 (blue color)
Total outcomes = 3 (red, blue, and yellow)
[tex]P(\text{spinning blue)}=\frac{1}{3}[/tex]- The probability of flipping heads is:
Favorable outcomes = 1 (head)
Total outcomes = 2 (head and tail)
[tex]P(\text{flipping head)=}\frac{1}{2}[/tex]- The probability of spinning a one is:
Favorable outcomes = 1 (number 1)
Total outcomes = 3 (numbers 1, 2 and 3)
[tex]P(\text{spinning a one)=}\frac{1}{3}[/tex]Next, the probability of the compound event:
[tex]P(\text{compound event)=}\frac{1}{3}\times\frac{1}{2}\times\frac{1}{3}=\frac{1\times1\times1}{3\times2\times3}=\frac{1}{18}[/tex]Answer: the probability of the compound event is 1/18
help asap pls!!!!!!!!!
Answer:
z=70 y=98
Step-by-step explanation:
180-110=70=z
70+87+105=262
360-262=98=y
For every 500 g of reactants, 3.1 g of catalyst were required. How much catalyst was
required for 900 g of reactants?
For every 500 g of reactants, 3.1 g of catalyst were required. The catalyst that was required for 900 g of reactant was 5.58g
What do you mean by a catalyst?The process of catalysis involves introducing a catalyst to chemical reaction to speed up the process. Catalysts are not destroyed during reaction and are unaffected by it. Very little amounts of catalyst are frequently sufficient when the reaction is swift and the catalyst recycles quickly; the velocity of the reaction is greatly influenced by mixing, surface area, and temperature. In most cases, catalysts interact with one or more reactants to produce intermediates that ultimately lead to the final reaction product, regenerating the catalyst in the process.
Homogeneous catalysis, in which all of the components are dispersed in the same phase as the reactant (often a gas or liquid), and heterogeneous catalysis, in which the components are not. It's common to think of enzymes and other biocatalysts as a a third category.
In all branches of the chemical business, catalysis is commonplace. 90% of all chemical compounds manufactured for commercial purposes are thought to use catalysts at some point during the manufacturing process.
500g of reactants = 3.1g of catalyst
1g of reactants = 3.1g of catalyst / 500g of reactants
900g of reactants = [tex]\frac{3.1}{500} * 900[/tex] = 5.58g
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Find the measure of angles 1 and 2
I really need to get this done by today!
The unknown angles are as follows:
∠1 = 118°∠2 = 62°How to find measures of angles?The measures of angle 1 and 2 can be found as follows:
When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.
Therefore,
∠1 + ∠2 = 180(sum of angle on a straight line)
∠1 = 118(alternate angles)
118 + ∠2 = 180
∠2 = 180 - 118
∠2 = 62 degrees
Therefore,
∠1 = 118 degrees
∠2 = 62 degrees.
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Can someone please help i will give brainliest
The given function g(x) is positive for all real values of x, and increasing for the interval (-3,∞) , decreasing for the interval (-∞,-3) and
the end behavior is that g(x) → ∞ as x → -∞ an g(x) → ∞ as x → ∞ .
In the question ,
the graph of the function g(x) is shown ,
we see that ,No part of the graph of function g(x) is below the x axis ,
So, the negative of the function g(x) does not exist .
Also from the graph we can see that the graph is above the x axis for all values of x,
So , the function g(x) is positive for all real values of x .
the graph shows that the function is decreasing for x<-3 means
function g(x) is decreasing in the interval (-∞,-3) .
the graph shows that the function is increasing for x>-3 means
function g(x) is increasing in the interval (-3,∞) .
From the graph ,
the end behavior of the function g(x) is that g(x) → ∞ as x → -∞ and g(x) → ∞ as x → ∞
Therefore , the given function g(x) is positive for all real values , and increasing for the interval (-3,∞) , decreasing for the interval (-∞,-3) and
the end behavior is that g(x) → ∞ as x → -∞ and g(x) → ∞ as x → ∞ .
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Lizzy is tiling a kitchen floor for the first time. She had a tough time at first and placed only 5 tiles the first day. She started to go faster, and by the end of day 4, she had placed 35 tiles. She worked at a steady rate after the first day. Use an equation in point-slope form to determine how many days Lizzy took to place all of the 100 tiles needed to finish the floor.
y - y1 = m (x - x1)
It will take 11 days to place all of the 100 tiles needed to finish the floor.
What is point slope form?The slope of a line and any points it contains determine the point-slope form of the line. When a point on the line and the slope are provided, the form's objective is to represent the equation of the complete line.
Given Data
She had a tough time at first and placed only 5 tiles the first day. She started to go faster, and by the end of day 4, she had placed 35 tiles.
Points are:
(1,5) (4,35)
Slope = [tex]\frac{30}{3}[/tex]
Slope = 10
y - y₁ = m(x -x₁)
y - 5 = m(x- 1)
For 100, it will need,
100 - 35 = 10(x-4)
65 = 10x - 40
105 = 10x
x = 10.5
It will take 11 days to place all of the 100 tiles needed to finish the floor.
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A career counselor decides to make monthly payments of $150 on credit card debt of $3,482.46 and discontinue using that credit card. Assuming the monthly interest rate is 1.55%, it will take the counselor approximately 30 months to repay the debt. How many fewer months would it take to repay the debt if the counselor makes monthly payments of $200? (Round your answer to the nearest month.)
The $150 monthly payment on the $3,482.46 credit card loan at 1.55% monthly interest rate gives the number of fewer months it would take to repay the loan if the monthly payment is $200 as 10 months
What is a monthly interest rate?A monthly interest rate is obtained from an annual interest rate by dividing it by 12.
The monthly payment formula is presented as follows;
[tex] \displaystyle{M = \frac{P \cdot r \cdot (1 + r)^{n} }{ (1 + r)^{n} - 1}} [/tex]
Where;
M = The monthly payments = $150
P = The loan amount = $3,482.46
r = The monthly interest rate = 1.55% = 0.0155
n = The number of periods (monthly payments) = 30
When the monthly payment, M = $150, it takes the career councilor approximately 30 months for the debt to be repaid.
When the monthly payment, M = $200, we have;
[tex]\displaystyle{200 \approx \frac{3482.46 \times 0.0155 \times (1 + 0.0155)^{n} }{ (1 + 0.0155)^{n} - 1}} [/tex]
Which gives;
[tex] \displaystyle{200 \times ((1 + 0.0155)^{n} - 1)= 3482.76 \times 0.0155 \times (1 + 0.0155)^{n}} [/tex]
[tex] \displaystyle{200 \times (1.0155)^{n} - 200 = 53.98278 \times (1.0155)^{n}} [/tex]
[tex]\displaystyle{ 146.017 \times (1.0155)^{n} = 200 }[/tex]
n•ln(1.0155) ≈ ln(1.3697)
[tex] n = \frac{ln(1.3697)}{ln(1.0155)} \approx 20.45[/tex]
The number of months it will take to pay back the loan using a monthly payment of $200 is therefore approximately 20 months
The number of fewer months it takes to repay the loan is therefore;
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what is 71.04 in expanded form
Answer:
(7 x 10) + (1 x 1) + (0/10) + (4/100)
70 + 1 + 0.04
70 + 1 + 4/100
Step-by-step explanation:
Here are all the expanded forms I can think of off the top of my head, sorry if this didn’t help much!
We can find the remainder for the quotient using either substitution or synthetic division. Using either method, explain whether or not we can conclude that x - 5 is a factor of the polynomial f(x)=x^3-x^2-17x-15. (Your answer must include what that remainder value is and what it indicates
We may get the same conclusion using either approach, which is that x—5 is a factor of the polynomial.
This will be discussed in further detail below.
Can you explain what the polynomial is?Explain, taking into account the fact that, using either method, whether or not we can think of x-5 as a factor in the polynomial based on the given information.
Generally, the equation for the problem is mathematically given as
f(x)=x^3-x^2-17 x-15
Therefore, If (x-5) is factor of f(x) then at x=5 ,f(x)=0 then apply this
[tex]\begin{aligned}f(x) &=5^3-5^2-17 \times 5-15 \\&=125-25-85-15 \\&=0\end{aligned}[/tex]
In conclusion,Since f(x) is equal to 0 when x = 5, the factor of f is (x-5) (x).
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Solve for x -
[tex]\sf 5x-6=3x-8[/tex]
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]\textsf{Given equation}:[/tex]
[tex]5x-6=3x-8[/tex]
[tex]\textsf{Subtract $3x$ from both sides}:[/tex]
[tex]\implies 5x-6-3x=3x-8-3x[/tex]
[tex]\implies 2x-6=-8[/tex]
[tex]\textsf{Add $6$ to both sides}:[/tex]
[tex]\implies 2x-6+6=-8+6[/tex]
[tex]\implies 2x=-2[/tex]
[tex]\textsf{Divide both sides by $2$}:[/tex]
[tex]\implies \dfrac{2x}{2}=\dfrac{-2}{2}[/tex]
[tex]\implies x=-1[/tex]
Which number rounds to 32.6 when rounded to the nearest tenth?
1 32.58 2 32.65 3 32.68 4 32.75
multiply. what is the product (3 x 10^9) x (2 x 10^17) in scientific notation
Answer:
600000000000000000000000000[tex]x^{2}[/tex]
Stuck with this question, I hope it goes right but I put in 15 points so
Have a good day and thanks in advance to anyone who helps me.
Write an equation of the line that passes through point (2, −4) and has the slope m=.5. y=
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Since slope is 5, equation is y = 5x + c.
Substitute (2,-4) into the equation to find c.
-4 = 5(2) + c
c = -14
Hence equation of line is y = 5x - 14
Chang invested his savings in two investment funds. the $3000 that he invested in fund a returned a 2% profit. the amount that he invested in fund b returned a 7% profit. how much did he invest in fund b, if both funds together returned a 4% profit?
Using algebraic expression and equation, he invested $2000 in fund b.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Let x = amount he invested in fund b
If both funds together returned a 4% profit, then the sum of the profit in each investment is equal to 4% of the total investment.
$3000(0.02) + x(0.07) = (3000 + x)(0.04)
Solving for x,
$3000(0.02) + x(0.07) = (3000 + x)(0.04)
$60 + 0.07x = $120 + 0.04x
0.07x - 0.04x = $120 - $60
0.03x = $60
x = $2000
amount he invested in fund b = $2000
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x² - 7x-18 = 0
What is the set of all values of x that satisfy the equation above?
A. (-9,2)
B. (-6, 3)
C. (6, 3)
D. (9,-2)
method 1.
[tex] {x}^{2} - 7x - 18 = 0[/tex]
simplify:
[tex](x - 9)(x + 2) = 0[/tex]
so the answer is (D) x =9 or x = -2
method 2.
if
[tex] {a}^{2}x+ bx + c = 0[/tex]
[tex]x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \: or \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
so
[tex]x = \frac{ - ( - 7) + \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)} or\frac{ - ( - 7) - \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)}[/tex]
[tex]x = \frac{ 7 + \sqrt{ 121 } }{2}or\frac{ 7 - \sqrt{ 121 } }{2}[/tex]
[tex]x = 9 \: \: \: \: or - 2[/tex]
Kindly help and mention which one youve solved
The value of m²+n²+p² is 46.
What is algebraic identities?In mathematics, an identical element, also known as a neutral element, is an element of a set that, when subjected to a binary operation, leaves each element of the set intact. In algebraic structures like groups and rings, this idea is applied. Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.
Given Data
m + n+ p= 10
mn + np + mp = 27
For m² + n²+ p²
Using algebraic identities,
(m+ n +p)² = m² + n² + p² +2(mn + np + pm)
(10)² = m² +n² + p² + 2(27)
100 = m² + n² + p² + 54
100 - 54 = m² + n² + p²
46 = m²+n²+p²
The value of m²+n²+p² is 46.
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1. Shelley comparó el número de robles al número de arces como parte de un estudio sobre árboles de madera dura en una arboleda. Ella contó 9 árboles de arce por cada 5 árboles de roble. Más adelante en el año hubo un problema de insectos y muchos árboles murieron. Se plantaron nuevos árboles para asegurarse de que hubiera el mismo número de árboles que antes del problema de insectos. La nueva razón del número de árboles de arce al número de árboles de roble es 3:11. Después de plantar nuevos árboles, habia 132 robles. ¿Cuántos árboles de arce más había en la arboleda antes del problema de insectos que después del problema de insectos? Explica.
Answer:
Step-by-step explanation:
855555555555fhhhhhhhhhhhhhhhhg6
What is the special angle pair relationship between 2 and 3?
The special angle pair relationship between ∠2 and ∠3 is same-side interior angles.
How to find angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the angle pair relationship between angle 2 and 3 are same side interior angles.
The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary.
Supplementary angles are those angles that sum up to 180 degrees. In other words, If the measures of two angles sum up to 180°, they are called supplementary angles.
Therefore, same side interior angles are supplementary angles.
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can y’all help me out with this worksheet?
Value of x [tex]\frac{36}{5}[/tex]
value of m∠3 = [tex]\frac{462}{5}[/tex]
Define angles.When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolized by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees. A figure made up of two rays meeting at the vertex of the angle can be referred to as an angle.
Given Data
m∠3 = 17x - 30
m∠6 = 12x +6
Angle pair - exterior alternate angle
For the value of x,
17x - 30 = 12x + 6
17x - 12x = 6 + 30
5x = 36
x = [tex]\frac{36}{5}[/tex]
For m∠3,
17x - 30
Equating value of x,
17([tex]\frac{36}{5}[/tex]) - 30
[tex]\frac{612-150}{5}[/tex]
[tex]\frac{462}{5}[/tex]
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Every year, Reba's family runs the sand castle contest during the Fun in the Sun beach festival. Reba's job is to deliver empty buckets to the teams. This year, Reba hands out the same number of buckets to each of the 12 teams in the contest. Each team gets 6 buckets.
Use an equation to find the total number of buckets Reba delivers.
If this year, Reba hands out the same number of buckets to each of the 12 teams in the contest. Each team gets 6 buckets. the total number of buckets Reba delivers is 72 buckets.
Total number of bucketsLet x represent the total number of buckets Reba delivers.
The equation to find the total number is:
x / 6 = 12
Let solve for x, to get the total number of buckets Reba delivers.
x = 12 × 6
x = 72 buckets
Therefore the total number of buckets is 72.
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On Monday, a local hamburger shop sold a combined total of 416 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Monday?
(Will mark brainliest plus 100 points)
A nearby hamburger joint sold 416 hamburgers and cheeseburgers in total on Monday. 104 hamburgers were sold.
Given that,
A nearby hamburger joint sold 416 hamburgers and cheeseburgers in total on Monday. Three times as many cheeseburgers were sold as regular hamburgers.
We have to find on Monday, how many hamburgers were sold.
Let us take hamburgers were sold as h and cheeseburgers were sold as c.
Quantity equation is h+c=416
c=3h
Substitute c =3h in h+c=416
h+3h=416
4h=416
h=104
Now,
Substitute h=104 in c=3h
c=3×104
c=312
Therefore, 104 hamburgers were sold.
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5. A rocket is launched from atop a 68-foot cliff with an initial velocity of 139 feet per
second. The height of the rocket t seconds after launch is given by the equation
h=-16t² + 139t+ 68. How long after the rocket is launched will it be 12 feet from the
ground? Round to the nearest hundredth of a second.
Answer: Its t=
32
−
23673−64h
+139
Step-by-step explanation:
convert -5C into fehrenheit