Answer:x=21
Step-by-step explanation:
10/14=15/x
5/7=15x^-1
(5/7)/15=ans
ans=x^-1
ans^-1=21
Answer: x=21
Step-by-step explanation:
[tex]\frac{10}{14} =\frac{15}{x}[/tex]
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 14x, the least common multiple of 14,x.
x×10=14×15
Multiply 14 and 15 to get 210.
x×10=210
Divide both sides by 10.
x=
10
210
Divide 210 by 10 to get 21.
x=21
Victoria drew a diagram of her laptop that she uses at school. It is in the shape of a rectangle. The dimensions are as follows:
Length: 13x - 9 units
Width: 4.5x + 8 units
If the length is greater than the width, which inequality represents this situation?
The inequality that represents the given situation is 13x - 9 > 4.5x + 8
Writing an InequalityFrom the question, we are to determine the inequality that represents the given situation
From the given information, we have that
The length of the laptop is given by 13x - 9 units
and
The width of the laptop is given by 4.5x + 8 units
If the length is greater than the width, then we can write that
13x -9 > 4.5x + 8
Hence, the inequality is 13x - 9 > 4.5x + 8
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In Exercises 4 and 5, find the area of the polygon with the given vertices.
4. P(1,1) Q(-2,1), R(-1,-4)
5. A(3,7), B(5,7), C(3,-7), D(5,-7)
Answer:
#4: 7.5
#5: 28
Step-by-step explanation:
Polygon in #4
is a triangle
base = 1 - (-2) = 1+2 = 3
height = 1-(-4) = 1 + 4 = 5
Area of a triangle with base b and height h = (1/2)b.h
So area of this triangle = (1/2) (3) (5) = 15/2 = 7.5
Polygon in #5
is a rectangle with length = 7 - (-7) = 7 +7 = 14
and width = 5-3 = 2
Area of a rectangle with length l and width w = lw
Area of this rectangle = 14 x 2 = 28
Hope that helps
The area of the polygon for exercise 4 is 7.5 square units and for exercise 5 the area is 28 square units.
What is an area?The space occupied by the object in two-dimensional space is called as the area.
For a triangle, the area will be calculated as,
base = 1 - (-2) = 1+2 = 3
height = 1-(-4) = 1 + 4 = 5
Area of a triangle with base b and height,
h = (1/2)b.h
Area of this triangle,
A = (1/2) (3) (5) = 15/2 = 7.5
Rectangle with length = 7 - (-7) = 7 +7 = 14
Rectangle width = 5-3 = 2
Area of a rectangle with length l and width w = lw
Area of this rectangle = 14 x 2 = 28 square units
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solve -8n+4(1+5n)=-6n-14
A family plans to have 3 children. For each birth, assume that the probability of a boy is the same as the probability of a girl. What is the probability that they will have at least one boy and at least one girl?.
Probability of having at least one boy and at least one girl is 0.75
There are two possibilities of a child, it could be a girl or a boy.
Since, the family plans to have 3 children.
∴ Total outcomes are = 2³
Total outcomes are = 8 outcomes
The total possible outcomes are: BBB, BBG, BGB, GBB, GBG, BGG, GGB, GGG
So, there are 8 possible outcomes.
Now, probability of having at least one boy and at least one girl= 1 - (Probability of having all girls, Probability of having all boys)
Probability of having all girls i.e., GGG = 1/8
Probability of having all boys i.e., BBB = 1/8
P(at least one boy and at least one girl) = 1 - (1/8 + 1/8)
= 1 - (2/8)
= 6/8
= 0.75
∴ P(at least one boy and at least one girl) = 0.75
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1. Identify as algebraic expression, numerical expression or equation:
a) 3x+1
b) 3+x=5
c) 2²-6(347),
Answer:
a) algebraic expression
b) equation
c) numerical expression
Step-by-step explanation:
Hope this helps......if not then sorry for wasting your time and may God bless you<3
How to simplify it as a fraction?
0.7 bar can be expressed as 7/9 in fraction.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.
In mathematics, a fraction is referred to as a portion of a whole. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.
Part of a whole number and a means of dividing a number into equal parts are represented by fractions. The numerator, also known as the number of equally divided parts, is how it is written.
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SOMEONE HELP PLEASE ME
1) The converse of the function is; If not q, then p
2) The Inverse of the function is; If not p, then q.
3) The contrapositive of the function is; If q, then not p
How to Interpret Conditional Statements?
Suppose we have a conditional statement, If it is raining, we will not play. Let, A: It is raining and B: we will not play. Then; If A is true, that is, it is raining and B is false, that is, we played, then the statement A implies B is false.
The conditional statement is given as;
If p, then not q.
1) The converse of the function is; If not q, then p
2) The Inverse of the function is; If not p, then q.
3) The contrapositive of the function is; If q, then not p
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Please helppppp no wowo
Answer:
d-(8,15)
Step-by-step explanation:
69497694646946464646463434644
ZA and ZB are vertical angles. If mA = (6x – 16)° and mZB = (4x + 22)°,
then find the measure of ZB.
As A and B are vertical angles, the measures of angle A and B is 98° each.
What in geometry are Vertical Angles?When two lines collide, vertical angles are created. The angles that are directly opposite one another, out of the four that are generated, are vertical angles. Additionally, they are known as "vertically opposed angles." All of these angles are equal.
Vertical angles are created when two straight lines cross. Angles vertically are consistently congruent and equal. As the two sets of non-adjacent angles created by crossing two lines superimpose on one another, vertical angles are congruent.
As A and B are vertical angles,
6x - 16 = 4x + 22
⇒ 2x = 38
⇒ x = 19
Measure of Angle A is 98°
Measure of Angle B is 98°
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cuantos enteros hay en 384/135
Evaluate
5.7 x 0.049 / 0.681
Give your answer rounded to 2 DP.
Answer:
0.41
Step-by-step explanation:
A high school decided to spend $ 750 on student academic achievement awards. At least 5 awards will be given, they should be equal in value, and each award should not be less than $ 50 . Write and sketch a function that models the relationship between the number a of awards and the cost c of each award. What are the domain and range of the function?
a. Which equation describes the relationship between a and c ?
Equation that describes the relationship between a and c is c = 750 / a
The domain of the function is - 5 ≤ a ≤ 50
The range of the function is - 50 ≤ c ≤ 150
Given,
Total money spent is = $750
Thus, our equation become,
ca = 750
solving for c,
c = 750 / a
The domain and range of function is -
a ≤ 5
Now, each award should be less than 50.
= 50 ≤ c
using equation, ac = 750
maximum value for a = 75.
we can say that domain is
5 ≤ a ≤ 50
Finally, by substituting a = 5 we can see that the maximum for c is 150.
This gives range for c as -
50 ≤ c ≤ 150
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The denominator of a rational number is greater than its numerator by 2. If 5
is subtracted from the numerator and 5 is added to its denominator, the new
number becomes 1
4
. Find the number.
Based on the word problem, the number is 9
What is a Rational Number?This refers to the type of number that is expressed as the ratio of two integers that has a non-zero denominator.
Calculations and ParametersLet the numerator be x
Let the denominator be x+2
If 5 is subtracted from the numerator
x - 5
If 5 is added to the denominator
x +2 + 5
x-5/x+7= 1/4
Cross multiply the values
It becomes
4x- 20 = x+ 7
3x= 27
x= 9
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You have $28, and you want to get half-dollar from the bank to give to children who come into
your store. How many half-dollar coins are in $28?
The total number of half-dollar coins are in $28 given to children who come into your store is 56.
What is arithmetic?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
You have $28, and you want to get half-dollar from the bank to give to children who come into your store.
According to given question we have
Half-dollar from the bank= $28
1/2 =28
1=28*2
1=56
So, the total number of half-dollar coins given to children who come into
your store is 56.
Therefore, the total number of half-dollar coins are in $28 given to children who come into your store is 56.
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A number which was tripled and added to 4, totals 40. What is the number?
Answer:
x=12
Step-by-step explanation:
Our equation: 3x + 4= 40
40-4=36. 36/3 = 12
Subtract. 10,000 - 6,128
Answer:
3872
Step-by-step explanation:
10,000 - 6,128 = 3872
use calculator man
Makayla is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday and flips a coin?
The different possible outcomes are there if she spins a spinner with 5 equal-sized sections-
So, there are are total 10 outcomes of flipping a coin
A coin has two faces head and tail . On flipping a coin there are total 2 outcomes i.e. a head and a tail.
There is a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday.
On Spinning a spinner with 5 equal-sized sections there are total 5 outcomes . They are Monday, Tuesday, Wednesday, Thursday, Friday.
So there are two events flipping a coin and spinning a spinner.
possible outcomes are
(Head, Monday) (Tail , Monday) (Head, Tuesday) (Tail, Tuesday)
(Head, Wednesday) (Tail , Wednesday) (Head, Thursday) (Tail, Thursday)
(Head, Friday) (Tail, Friday)
So, there are are total 10 outcomes.
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ethans cooking recipe uses 3 cups of sugar to make 21 cookies mias recipe uses 4 cups to make 28 cookies which has a greater sugar/cookie ratio
Find the sum of (6-t-t²) and (10t + t²).
and write the sum from the question too
Space Use the formula for maximum velocity v=-0.0098 t+c ln R . Find the mass ratio of a rocket with an exhaust velocity of 3.1km/s, a firing time of 50s, and a maximum shuttle velocity of 6.9km/s .
The mass ratio of the rocket is 10.8468 kg/C.
What is mass ratio of a rocket?An indicator of a rocket's effectiveness is its mass ratio. It describes the ratio of the rocket's wet mass to its dry mass, or how much more massive the vehicle is with propellant than without.Given:
v = - 0.0098(t) + c (ln (R) ), where:v = maximum shuttle velocityt = firing timec = velocity of exhaustR = mass ratioHere, c = 3.1 km/s, t = 50s, v = 6.9km/sTo find: Mass ratio (R) = ?
Finding:
On substituting the values of 'c', 't', 'v', we get:
6.9 = - 0.0098 (50) + 3.1 (ln (R) )
=> 6.9 + 0.49 = 3.1 (ln (R) )
=> 7.39 = 3.1 (ln (R) )
=> ln (R) = [tex]\frac{7.39}{3.1}[/tex]
=> R = [tex]e^{\frac{739}{310}}[/tex] ≈ 10.8468
Hence, the mass ratio of the rocket is 10.8468 kg/C.
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Two rectangles have the exact same area.The measurements of the first rectangle is 3k by 3.Calculate the value of k
In the area of the rectangle the value of the k is 6.
According to the statement
We have to find that the value of the k in the area of rectangle.
So, For this purpose, we know that the
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
From the given information:
Two rectangles have the exact same area.The measurements of the first rectangle is 3k by 3 and the measurements of the second rectangle is k+3 by 6.
Then
The area of the first rectangle = 3k*3
The area of the first rectangle = 9k
And
The area of the second rectangle = 6(k+3)
The area of the second rectangle = 6k+18
Then
Compare the both values of the area
6k+18 = 9k
9k - 6k = 18
3k = 18
k = 18/3
k = 6.
So, In the area of the rectangle the value of the k is 6.
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Write an absolute value equation representing all numbers x whose distance from 5 is 3 units.
The absolute value equation representing all numbers x whose distance from 5 is 3 units.eiol be x = (-3, 8).
How to illustrate the information?It should be noted that from the information, we are to write an absolute value equation representing all numbers x whose distance from 5 is 3 units.
Therefore, the absolute value equation representing all numbers x will be illustrated as:
x - 3 = 5.
It should be noted that we will solve for x
Therefore, x - 3 = 5
Collect like terms
x = 5 + 3.
x = 8
Therefore, the absolute value equation representing all numbers x whose distance from 5 is 3 units.eiol be x = (-3, 8).
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What is the x -intercept of f(x)=x³-x²+1 ? Round the answer to the nearest hundredth.
The x -intercept of f(x)=x³-x²-1 is x=1.46557.
What are Cubic polynomials?Cubic polynomials are polynomials with the highest degree of three. A cubic polynomial can only have three roots or solutions. We must find the X intercept for the given cubic polynomial in the given example.So, to find the x-intercept of f(x)=x³-x²-1:
To find the x-intercept, substitute y = 0.
Using the long division method, we obtain:
x³-x²-1/x-1.46557 = x²+0.46557x+0.68232x = 1.46577 and x²+0.46557x+0.68232 = 0x = -0.2328 ± 0.7925i ∉ RTherefore, the x -intercept of f(x)=x³-x²-1 is x=1.46557.
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The correct question is given below:
What is the x-intercept of f(x)=x³-x²-1? Round the answer to the nearest hundredth.
Where's the bus? Jayden takes the same bus to
work every morning. The amount of time (in min-
utes) that he has to wait for the bus to arrive can be
modeled by a uniform distribution on the interval
from 0 minutes to 10 minutes.
a) draw a density curve to model the amount of time that Jayden has to wait for the bus. Be sure to include scales on both axes.
b) on what percent of days does Jayden wait more than 7 minutes for the bus?
c) find the 38th percentile of this distribution.
Using the uniform distribution, we have that:
a) The graph is given at the end of the answer.
b) Jayden waits more than 7 minutes 30% of the days.
c) The 38th percentile is of 3.8 minutes.
What is the uniform probability distribution?It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
For this problem, the bounds are given as follows:
a = 0, b = 10.
As shown in the graph at the end of the answer.
The probability of waiting more than 7 minutes is:
[tex]P(X > 7) = \frac{10 - 7}{10 - 0} = 0.7[/tex]
Jayden waits more than 7 minutes 30% of the days.
The 38th percentile is x for which P(X < x) = 0.38, hence:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
0.38 = x/10
x = 3.8.
The 38th percentile is of 3.8 minutes.
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How do we solve the formula for the indicated variable
Answer:
z = Fn +s.
Step-by-step explanation:
F = (z - s)/n
z - s = Fn
z = Fn +s.
five balls are randomly chosen, without replacement, from an urn that contains 5 red, 6 white, and 7 blue balls. find the probability that at least one ball of each color is chosen.
The probability that at least one ball of each color is chosen is 105/8568.
Given that:-
Number of red balls in the urn = 5
Number of white balls in the urn = 6
Number of blue balls in the urn = 7
We have to find the probability that at least one ball of each color is chosen.
Let us consider the that 1 ball of each color has been chosen.
Hence, we are left with 4 red balls, 5 white balls and 6 blue balls.
Now we have to choose 2 balls from them.
Hence,
Number of ways in which we can choose 2 balls from (4+5+6) that is 15 balls = [tex]^{15}C_2=105[/tex]
Total number of ways in which we can choose 5 balls from 18 balls =
[tex]^{18}C_5=8568[/tex]
Hence,
Probability that at least one ball of each color is chosen = 105/8568
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Angle 2 is an____angle and is_____to angle 1.
Angle 5 is an____angle and is_____to angle 8.
Answer:
Angle 2: Acute, supplementary
Angle 5: Obtuse, congruent
Step-by-step explanation:
An acute angle is less than 90 degrees. An obtuse angle is more than 90 degrees. A supplementary angle is an angle equal to 180 degrees when added to another angle. (Angle 1 + angle 2 = 180 degrees.) Congruent angles are equal to each other in degrees. (Angle 5 = angle 8.)
A toy helicopter flies forward with a force of 15 N into an oncoming wind of 10 N. The force of gravity pulls the helicopter down
with a force of 5 N, but the propeller is providing an upward force of 10 N.
Which of the following accurately describes the helicopter's force?
(1 point)
O The toy helicopter is flying forward with a force of 15 N.
O The toy helicopter is flying forward with a force of 10 N and upward with a force of 5 N.
O The toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.
O The toy helicopter is flying forward with a force of 15 N and upward with a force of 10 N.
The statement which accurately describes the helicopter's force is: C. the toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.
What is Newton's Third Law of Motion?Newton's Third Law of Motion states that for every action there is an equal but opposite reaction. This ultimately implies that, in every interaction, there is a pair of forces acting on the two interacting objects.
Next, we would determine the resultant forces in the two scenarios as follows:
Resultant force A = Forward force - Wind force
Resultant force A = 15 N - 10 N
Resultant force A = 5 Newton.
Resultant force B = Upward force - Force of gravity
Resultant force B = 10 N - 5 N
Resultant force B = 5 Newton.
In this context, we can reasonably infer and logically deduce that the toy helicopter is flying forward with a force of 5 N and upward with a force of 5 N.
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HELP ME PLS
Use f(x) = |x|
f(x) is shifted left 5 and shifted up 2 to create
te g(x). Write the equation g(x)
Answer:
g(x) = | x + 5 | + 2
Step-by-step explanation:
given f(x) then f(x ± h ) represents a horizontal translation of f(x)
• if x > 0 then a shift to the left of h units
• if x < 0 then a shift to the right of h units
here f(x) is shifted left by 5 units , then
g(x) = | x + 5 |
given f(x) then f(x) + k represents a vertical translation of f(x)
• if k > 0 then a shift up of k units
• if k < 0 then a shift down of k units
here f(x) is shifted up 2 units , then
g(x) = | x + 5 | + 2
Evaluate the expression if x = 6, y = 4, and z = 2: xy + z
The value of the expression xy + z is 26 when x = 6, y = 4, and z = 2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the expression?The expression is given as
xy + z
The values are given as
x = 6, y = 4, and z = 2
The expression can then be represented as
xy + z = 6 * 4 + 2
Evaluate the product
So, we have
xy + z = 24 + 2
Evaluate the sum
So, we have
xy + z = 26
Hence, the value of the expression xy + z is 26 when x = 6, y = 4, and z = 2
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