Answer:
5x - 8y = -2
Step-by-step explanation:
m = 5/8, x = 0, y = 1/4
so y = mx + b
1/4 = 5/8(0) + b
b = 1/4
so y = 5/8x + 1/4
8y = 5x + 2
5x - 8y = -2
Find all the numbers that satisfy the fol-
lowing descriptions:
The number has seven digits.
The number is between 1,000 and
10,000.
The digit in the tenths place is 150%
of the digit in the thousandths place.
The digit in the hundredths place is
of the sum of the digit in the
tenths place and the digit in the
thousandths place.
The sum of all the digits in the num-
ber is 17.
None of the digits are zero.
There is no number which is satisfying the given conditions.
The first condition is that the number has seven digits.
The second condition is that the number lies between 1000 and 10000.
From these two conditions, we can conclude that there is no number which satisfies all the given conditions. Because there is no seven-digit number which is less than 10000.
Let us assume that the second condition is the number lies between 1000000 and 10000000.
And let the required number be "abcdefg".
The third condition is the digit in the tenth place is 150% of the digit in the thousandth place.
⇒ f = 150 × (d) / 100 = 1.5 × d
The fourth condition is the digit in the hundredth place is the sum of the digit in the tenth place and the digit in the thousandth place.
⇒ e = f + d = 1.5d + d = 2.5d
The fifth condition is the sum of all the digits in the number is 17.
⇒ a + b + c + d + e + f + g = 17
⇒ a + b + c + d + 2.5d + 1.5d + g = 17
⇒ a + b + c + 5d + g = 17
And the last condition is none of the digits is zero.
Using the last condition the possible values for d are either 1 or 2.
Because, if d is 3, then if we take the least possible digit(1) for others, the sum on the LHS is 19, which is greater than 17.
And d can not be 1. Because, if d is 1, then f and e are 1.5 and 2.5 respectively. 1.5 and 2.5 are not valid digits.
Therefore, the value of d = 2.
f = 1.5d = 3
e = 2.5d = 5
If d = 2, then we get a + b + c + g + 10 = 17
⇒ a + b + c + g = 17 - 10
⇒ a + b + c + g = 7
⇒ The possible values for (a, b, c, g) are (4, 1, 1, 1), (1, 4, 1, 1), (1, 1, 4, 1), (1, 1, 1, 4), (2, 2, 2, 1), (2, 2, 1, 2), (2, 1, 2, 2), (1, 2, 2, 2), (2, 3, 1, 1), (3, 2, 1, 1), (1, 1, 2, 3), and (1, 1, 3, 2)...
Therefore there are more than 12 possible answers that satisfy the assumption made.
411253114125311142531111253422225312212532212253212225322312531321253112325311322531Learn more about number here:
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Write 4,000,000 in scientific notation
4 × 10 then put a 6 by the 10 as an exponent.
Rory has 6 pounds of ground beef to make meatballs. He uses 5/8 pound per meatball to make 9 meatballs. How many 1/8 pound meatballs can Rory make with the remaining beef?
Rory can make 43 metaballs from the remaining beef.
What are maths operations?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations. A zero-arity operation, also known as a nullary operation, is a constant. The mixed product is an example of an arity 3 operation, also known as a ternary operation.Rory has 6 pounds of ground beef on hand for making meatballs.
He makes 9 meatballs with 5/8 pounds of meat per meatball.
We must subtract 5/8 from 6.
6 - 5/848-5/843/8There are 43/8 pounds of ground beef remaining.
As a result, the number of 1/8 pound meatballs produced from 21/8 pound ground beef can be calculated as follows:
43/8 ÷ 1/843/8 × 8/1= 43Therefore, Rory can make 43 metaballs from the remaining beef.
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Find the domain and range of the function F(t) = sec(3.14t/4)
The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].
The Domain of a function f(x) is the set of all values for which the function is defined.
The Range of a function is the set of all values that f takes.
As, [tex]sec x=\frac{1}{cos x}[/tex] , so sec x is defined where [tex]cos x \neq 0[/tex].
It implies, sec(3.14t/4) is defined where [tex]cos(3.14t/4)\neq 0[/tex].
The cosine is 0 at [tex](2n+1)\frac{\pi }{2}[/tex] , where n is any integer.
Now, [tex]\frac{3.14t}{4} =\frac{(2n+1)\pi }{2}[/tex]
[tex]\frac{\pi t}{4} =\frac{(2n+1)\pi }{2}[/tex]
[tex]t=2(2n+1)\\t=2+4n[/tex]
Since, the range of cos x is [-1,1], so sec x will never be less than 1, but can grow infinitely large as cos x approaches 0.
Thus, The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].
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4. What is the probability of pulling either a fork or a spoon out of the bag?
We the Probability of pulling either fork or spoon as 1.
We are given that:
We have a fork and a spoon in a bag.
Total number of items in a bag = 1 + 1 = 2
Now, we need to tell the probability of either pulling a fork or a spoon.
Now,
Probability of pulling a fork = 1 / 2 = 0.5
Probability of pulling a spoon = 1 / 2 = 0.5
So, the Probability of pulling either of them will be = 1 / 2 + 1 / 2 = 1
Therefore, we the Probability of pulling either fork or spoon as 1.
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Determine which integer in the solution set will make the equation true.
3s − 12 = −9
S: {−1, 0, 1, 2}
A: −1
B: 0
C: 1
D: 2
Answer:
c) 1
Step-by-step explanation:
Solving for the value of s,
→ 3s - 12 = -9
→ 3s = -9 + 12
→ s = 3/3
→ [ s = 1 ]
Thus, option (c) is correct.
Jared estimates that his houseplant is as heavy as a 5 kilogram bowling ball. Draw a tape diagram to estimate the weight of 3 houseplants.
3 houseplants will weigh 15 kg (Refer to the tape diagram below).
What is a tape diagram?A tape diagram is a visual model that looks like a piece of tape and is used to aid in the calculation of ratios, addition, subtraction, and, most commonly, multiplication. It is also referred to as a divided bar model, a fraction strip model, a length model, or a strip diagram. It is used in elementary school mathematics education to solve word problems.The weight of 3 household plants will be about 15 kg.
5 kg × 3 = 15 kg(Refer to the tape diagram given below)Therefore, the weight of 3 household plants will be about 15 kg (Refer to the tape diagram below).
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geometry someone help
Answer:
D. F
Step-by-step explanation:
Both F and G are not on plane P
Shawn reads 5 pages in 20 minutes. He spends the same amount of time per page. How long will it take him to read 11 pages?
Answer:
44
Step-by-step explanation:
20 ÷ 5 = 4 minutes per page
4 x 11 pages = 44
What is the approximate length of the diameter, d?
7in
14in
22in
44in
Answer:
14 in
Step-by-step explanation:
the formula for the circumference of a circle is
2×pi×r
or (because the diameter is 2×r)
pi×d
with r being the radius and d being the diameter.
44 = pi×d
d = 44/pi = 14.00563499... in ≈ 14 in
4 D
A bear can run 400 feet in 8 seconds.
A horse can run 290 feet in 5 seconds?
Which animal runs at the faster rate?
Horse runs at the faster rate i.e. at the rate of 58 feet per seconds.
According to the given question.
A bear can run 400 feet in 8 seconds.
A horse can run 290 feet in 5 seconds.
As we know that, the measurement of the speed at which something happens is called rate.
Therefore, form distance rate formula (rate = distance/time)
The rate of the bear = 400/8 = 50 feet/sec
And the rate of the horse = 290/5 = 58 feet/sec
Therefore, horse can run faster than bear.
Hence, horse runs at the faster rate i.e. at the rate of 58 feet per seconds.
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beth and ann are joking that their combined ages equal sams age. if beth is twice anns age and sam is 69. what are beth and anns age
Answer: ann is 69 and beth is 138
Step-by-step explanation:
if a(x + 1) = 2x + 3a, and a ≠ 0, then what is x in terms of a
Answer:
[tex]x = \frac{2a}{a - 2} [/tex]
What is the factored form of 82+12?
O 442+80)
O4(2x+3)
O ax(x+4)
O 8x(+4)
Answer:
Option 2
Step-by-step explanation:
TRAIN STATIONS A train travels a straight route from Rolesville to Townsend. The railway would like to build a station along the route so that the ratio of the distance from Rolesville to the station and the distance from the station to Townsend is 3:4 . If the coordinates of Rolesville and Townsend on the map are R(1, 2) and T(8, 23) , respectively, what should be the coordinates of the new station?
coordinates of the new station= (5,98/4)
When two lines intersect at a point then the angle between them can be expressed in terms of their slopes and is given by the following formula:
tan θ = |
|where
are the slopes of the line AB and CD respectively.
If
is positive then the angle between the lines is acute. If
is negative then the angle between the lines is obtuse.
Slope of Vertical Lines
Vertical lines have no slope, as they do not have any steepness. Or it can be said, we cannot define the steepness of vertical lines.
A vertical line will have no values for x-coordinates. So, as per the formula of slope of the line,
Slope, m = (y2 – y1)/(x2 – x1)
But for vertical lines, x2 = x1 = 0
Therefore,
m = (y2 – y1)/0 = undefined
In the same way, the slope of horizontal line is equal to 0, since the y-coordinates are zero.
m = 0/(x2 – x1) = 0 [for horizontal line]
Positive and Negative Slope
If the value of slope of a line is positive, it shows that line goes up as we move along or the rise over run is positive.
If the value of slope is negative, then the line goes done in the graph as we move along the x-axis.
Let R,Q,T be the points that divide the line into 3:4 equal parts
Let the Q = (x,y)
R(1, 2) and T(8, 23) ,
x = m1x1+m2x2/m1+m2
y = m1y1+m2y2/m1+m2
X= 3.1+4.8/7
x= 3+32/7
x=35/7
x=5
y=2.3+23.4/3+4
y= 6+92/4
y=98/4
y= 24.5
(x,y) = (5,98/4)
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can anyone help me with this I am stuck
Using integrals, the desired probabilities and measures are given as follows:
a) P(X < 6) = 0.84375 = 84.375%.
b) P(X < 13) = 1 = 100%.
c) P(6 < X < 8) = 0.15625 = 15.625%.
d) P(X > 5) = 0.31641 = 31.641%.
e) x = 6.434.
What is the probability distribution?The distribution is given as follows, simplifying the operations:
f(x) = 0.09375x - 0.01171875x², 0 ≤ x ≤ 8.
Hence the density function is:
[tex]\int_{a}^{b} f(x) dx[/tex]
[tex]\int_{a}^{b} (0.09375x - 0.01171875x^2) dx[/tex]
[tex]0.046875x^2 - 0.00390625x^3|_{x=a}^{x = b}[/tex]
Applying the Fundamental Theorem of Calculus:
P(a < X < b) = 0.046875b² - 0.00390625b³ - 0.046875a² + 0.00390625a³
Hence, for item a:
P(X < 6) = 0.046875(6)² - 0.00390625(6)³.
P(X < 6) = 0.84375 = 84.375%.
For item b, the entire distribution is below 13, hence:
P(X < 13) = 1 = 100%.
For item c:
P(6 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(6)² + 0.00390625(6)³.
P(6 < X < 8) = 0.15625 = 15.625%.
For item d:
P(5 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(5)² + 0.00390625(5)³.
P(X > 5) = 0.31641 = 31.641%.
For item e:
We have to find b when a = 0 and P(X < b) = 0.9, hence:
0.046875b² - 0.00390625b³ = 0.9.
Using a calculator, the solution in the range of the distribution is given by:
b = x = 6.434.
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Select the part of speech for the underlined words below. I WAS afraid of roller coasters when I was younger, but I AM a huge fan of them now. preposition, adverb, verb, adjective
Answer: I'm pretty sure its a verb
Step-by-step explanation:
Let f(x) = -3x+5 and g(x)=x²-2. Find the difference (g - f)(x).
(g-f)(x) =
Answer: f(x^2) = x^2 - 5
The sum of an integer and 7 times the next consecutive odd integer is 6. Find the value of the greater integer.
The value of the integer number is -1
How to find the value of the greater integer?The statement is given as:
The sum of an integer and 7 times the next consecutive odd integer is 6
Let the integer value be x
So, the next consecutive odd integer is x + 2
When represented as an equation, we have
x + 7(x + 2) = 6
Open the bracket
x + 7x + 14 = 6
Evaluate the like terms
8x = -8
Divide both sides by 8
x = -1
Hence, the value of the integer number is -1
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Find the sum of (6.9 × 106) and (5.9 × 105). Write the final answer in scientific notation.
The sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11
Scientific notation(6.9 × 10^6) and (5.9 × 10^5)
Sum
= (6.9 × 10^6) + (5.9 × 10^5)
= (6.9 + 5.9) × 10^(6+5)
= 12.8 × 10^11
Therefore, the sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11
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Josue is the youngest of three siblings whose ages are consecutive even integers. If
the sum of their ages is 78, find Josue's age.
Answer:
39 is the sum of their ages
Step-by-step explanation:
Hope this helps :)
help me with this Select all the expressions that are equivalent to 78 • 7.
73 • 73
71879
(73)3
74 + 75
74 • 75
The expressions that are equal to 7⁸ x 7 are:
B. For (7¹⁸)/7⁹
C. For (7³)³
E. For 7⁴ x 7⁵
What are the fundamentals of exponential functions?Exponential functions now have formula f(x) = bx, where b > 0 and b 1. As in any exponential expression, b serves termed the base and x is called its exponent. The proliferation of bacteria is an example of such an exponential function.
According to the given data:A. For 7³ x 7³
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7³ ⁺ ³
Calculate the sum or difference: 7⁶
Calculate power : 117649
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: False
Solution: False
B. For (7¹⁸)/7⁹
Reduce the fraction: 7⁹
Calculate power : 40353607
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: True
Solution: True
C. For (7³)³
simplify using exponent power rule : 7⁹
Calculate power : 40353607
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: True
Solution: True
D. For 7⁴ + 7⁵:
Calculate the power: 2401 + 16807
Calculate the sum or difference: 19208
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: False
Solution: False
E. For 7⁴ x 7⁵:
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁴ ⁺ ⁵
Calculate the sum or difference: 7⁶
Calculate power : 40353607
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: True
Solution: True
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I understand that the question you are looking for is:
Select all the expressions that are equivalent to 7⁸ x 7.
A. For 7³ x 7³
B. For (7¹⁸)/7⁹
C. For (7³)³
D. For 7⁴ + 7⁵:
E. For 7⁴ x 7⁵
Answer:
none
Step-by-step explanation:
point steeler
Evaluate.
Remember Order of Operations!
(PEMDAS)
(-7+3²) × 8
Answer:
16
Step-by-step explanation:
[tex]-7+3^2\\3^2\\=9\\=-7+9\\=-7+9 = 2\\=2\times \:8\\2\times \:8=16\\\boxed{16}[/tex]
what set M is the set of months hauling 31 days?
The set of months having 31 days will be S = { January, March, May, July, August, October, December }.
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
We know that there are 12 months in a year.
From these months, we get that the months that have 31 days are:
January
March
May
July
August
October
December
The set of months having 31 days will be:
S = { January, March, May, July, August, October, December }
Therefore, we get that, the set of months having 31 days will be S = { January, March, May, July, August, October, December }.
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Rewrite as a simplified fraction 0.7 repeating
Answer:
7/10
Step-by-step explanation:
Rewriting 0.7 as a fraction would be 7/10. 0.7 can also be 0.70, and 70/100
(100 POINTS ASAP)
Triangle EFG is shown in the graph.
The triangle will be reflected across the x-axis and then dilated by a scale factor of 2 with respect to the origin, resulting in triangle E'F'G'.
What will be the coordinates of G'?
Answer:
The coordinates of G' will be (8, 4)Step-by-step explanation:
Point G has coordinates (4, -2).
After reflection across the x-axis it s coordinates will change as per rule:
(x, y) → (x, - y)Applied to point G:
(4, - 2) → (4, 2)After dilation by a scale factor of 2 the coordinates will change as per rule:
(x, y) → (2x, 2y)Applied to point G:
(4, 2) → (2*4 = 8, 2*2 = 4)G' = (8, 4)Zan needs 28 centimeters of ribbon for each bow she makes. What is the greatest number of bows Zan can make with 9 feet of ribbon?
Answer:
3
Step-by-step explanation:
i think its 3 because 28 divided by 9 is 3
12345678901234567890
Yes; The construction demonstrates how to bisect an angle correctly using technology because Circles D & E have the same radius
How to properly bisect an angle?
In construction of angles and lines, bisection means dividing either a given angle or line segment into two equal parts. This means after the construction, the two parts must have equal measure.
The steps to bisect a line segment are as follows;
1. Draw the required length of the line segment AB.
2. With point A and radius of the compass greater than half of AB, describe arcs above and below the segment.
3. With the same radius as in step 2 and point B, describe two arcs above and below the segment. These would intersect that of step 2 at C and D.
4. Join the points of intersection of the arcs with a straight line CD.
Now, in this given question with the circle, we can see that line AG is the line that bisects the angle EAD.
Now, we see that circles C and D have the same radius and as such the construction demonstrated is correct for that very reason.
Answer: yes
Step-by-step explanation: the construction correctly shows how to bisect an angle using technology because circles D and E have the same radius.
The graph of f(x) is shown.
How many horizontal tangent lines does f(x) have?
0
1
2
3
4
Check the picture below.
in the grid below what is the distance between point a and b. round to the nearest tenth