If y varies directly as x, and y=24, when x=6, find y when x=4 8, -2, 4 or 16
Answer:
Step-by-step explanation:
is x equals 48, y might be 2, since 24x2=48, & when 6x8=48.
The sum of three numbers is 20. The third is 3 more than 12 times the second. 9 times the first is 11 less than 10 times the second. Find the numbers.
A three-number total equals twenty. The third is three times as much as the second. From the equation numbers area 0.1, 1.2 and 17.4.
Given that,
A three-number total equals twenty.
The third is three times as much as the second.
11 less than 10 times the second is 9 times the first.
We have to find the numbers.
First take the 3 numbers as a,b and c
A three-number total equals twenty.
We can write as,
a+b+c=20→ equation(1)
The third is three times as much as the second.
c=12b+3→equation(2)
11 less than 10 times the second is 9 times the first.
9a=10b-11→equation(3)
Now,
From equation(3) we get,
a=(10b-11)/9=10/9b-11/9
From equation(2) we get,
c=12b+3
Substitute value a and c in equation(1),
10/9b-11/9+b+12b+3=20
10b-11+9b+108b+27=20×9
127b+16=180
127b=180-16
127b=164
b=164/127
b=1.2
Substitute the b value in equation (2) and (3)
Equation(2)
c=12b+3
c=12(1.2)+3
c=14.4+3
c=17.4
Equation(3)
a=10/9b-11/9
a=10/9(1.2)-11/9
a=1.3-1.2
a=0.1
Therefore, the numbers are 0.1, 1.2 and 17.4.
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Estimate Jupiter’s mass using a one-digit whole number times a power of 10. Be sure to include units.
The most appropriate choice for exponent will be given by-
Mass of jupiter = 1.898 [tex]\times[/tex] [tex]10^{27}[/tex] kg
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a\times a \times a\times....\times a[/tex] (m times), a is the base and m is the index.
The laws of index are
[tex]a^m \times a^n = a^{m+n}\\\\\frac{a^m}{a^n} = a^{m - n}\\\\a^0=1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m =\frac{a^m}{b^m}\\\\a^{-m} = \frac{1}{a^m}[/tex]
Here,
Mass of jupiter = 1.898 [tex]\times[/tex] [tex]10^{27}[/tex] kg
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What are the vertex and x-intercepts of the graph of the function given below?
y = x^2 – 2x – 35
Answer: x = 7 0r x -5
Step-by-step explanation:
Question
POSSIBLE POINTS: 1.25
Rewrite the following equation in Slope-Intercept Form (y=mx+b), then use your equation to complete the table and find the slope, the y-intercept, and the x-intercept.
6x−2y=12
Equation:
Table:
x y
-2
-1
0
1
2
y-intercept: (
,
)
x-intercept: (
,
)
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The slope–intercept form of the equation, 6•x - 2•y = 12, is y = 3•x - 6, the completed table is therefore;
x; -2, -1, 0, 1, 2
y; -12, -9, -6, -3, 0
The slope of the equation is 3
The y–intercept of the graph of the equation is (0, -6)
The x–intercept is (2, 0)
What is the slope–intercept form of a straight line equation?The slope–intercept form of a straight line equation is the form; y = m•x + c, which shows (indicates) the slope, m and the y–intercept, c
The given equation is; 6•x - 2•y = 12
Required;
To rewrite the equation in the slope–intercept form of a straight line equation, y = m•x + c
Solution;
6•x - 2•y = 12
Rearranging the above equation gives;
6•x - 12 = 2•y
From the symmetric property of equality, we have;
2•y = 6•x - 12
Dividing both sides of the equation by 2 gives;
y = (6•x - 12) ÷ 2 = 3•x - 6
Therefore;
y = 3•x - 6
The above equation is in the slope–intercept form, y = m•x + c
Where;
The slope, m = 3The y–intercept, c = -6Which gives the y–intercept as the point (0, -6)
The table of values can therefore be completed as follows;
x; -2, -1, 0, 1, 2
When x = -2, y = 3×(-2) - 6 = -12
When x = -1, y = 3×(-1) - 6 = -9
At the point, x = 0, y = 3×(0) - 6 = -6
The point where x = 1, gives; y = 3×(1) - 6 = -3
At the point where x = 2, y = 3×(2) - 6 = 0
Which gives the completed table as follows;
x; -2, -1, 0, 1, 2
y; -12, -9, -6, -3, 0
The x–intercept is the point where the y–value is 0, which from the completed table gives the x–intercept as the point (2, 0)
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which statement is true regarding the graphed functions
The option A that f(-3)=g(-4) will be the correct option for the given graph of set of intersecting line meeting at point (-3,-4).
What is Intersecting line?When two or more lines intersect in a plane, they are referred to as intersecting lines. The intersecting lines share a common point, which exists on all of them and is known as the point of intersection.
What are the properties of intersecting lines?The intersecting lines (two or more) always meet at one point.
The intersecting lines may cross at any angle. This formed angle is always greater than 0° but less than 180°.
A pair of vertical angles is formed by two intersecting lines. Vertical angles are opposite angles that share a vertex (which is the point of intersection).
In the graph we can see that lines are meeting at (-3,-4) that is why the option A f(-3)=g(-4) is most suitable option.
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Which expression is equivalent to 3x+4(3x+2)
Responses
An object is moving at a speed of 7300 inches every 3 seconds. Express this speed in miles per day. Round your answer to the nearest whole number.
The speed in miles per day 3318.18miles/day
What is Speed?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.
Given,
Object moving in speed of 7300inches in 3 sec
Object moving in 1 sec = 7300/3
= 2433.33inches/sec
Converting inches/sec into miles/day
Since,
1inches/sec = 1.36364miles/day
Then ,
2433.33inches/sec = 2433.33 x 1.36364
= 3318.18miles/day
Hence, speed in miles per day is 3318.18miles/day
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An object is moving at a speed of 3 kilometers every 5 days. Express this speed in yards per hour.
An object is moving at a speed of 27.3 yards per hour.
How to find the speed in yards?3 kilometers must first be converted to yards.
1 m = 1.09 yards.
1 Km = 1093.61
3 km to yards is 3280.84
Currently, we must convert 5 days to hours. There are 24 hours every day, we shall multiply that number by 5 to find the number of hours in 5 days.
5 * 24 = 120 hours
To determine the speed in yards per hour, divide 3280.84 by 120.
3208.4/120
= 27.34 yards per hour
27.34 is 27.3 approximately.
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Is this triangle congruent?
Answer:
I'm not sure if this is right but I'm gonna say no, the tip of each triangle seems off by just a bit
A sequence is defined by the term-to-term rule
Un+1 = U²₁ - 3U₁ + 1
Given that u, = 3,
a) find u₂
b) find us
c) find u₁
The solution of the given sequence is :
Putting n = 0
a ) u1 = u0 ^3 + 2 = - 27 + 2 = - 25
b) un+1=un^3+2
c ) u2 = u1^3 + 2 = - 15625 + 2 = - 15623
What is an arithmetic sequence ?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
Starting with a number and repeatedly adding a fixed constant (d) to it is an easy technique to create a series. An arithmetic sequence is this kind of sequence. An arithmetic sequence is one that has the following formula: a, a + d, a + 2d, a + 3d, a + 4d.
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In p.e. class the boys and girls were asked about their favorite sport. for every three boys who stated they like basketball, two boys liked kickball. when the girls were surveyed, for every four girls that like basketball, one liked kickball. if 36 girls said they liked basketball. how many boys like each sport?
The total number of the boys and girls in that class were equal, then 27 boys stated that they liked basketball while 18 stated that they liked kickball.
As per the question statement, in a P.E. class, when the boys and girls were asked about their favorite sport, for every three boys who stated they like basketball, two boys liked kickball, while the girls' survey reported that, for every four girls that like basketball, one liked kickball, and 36 girls said they liked basketball.
Since there is no other information provided in the question statement, we are assuming that the total number of the boys and girls in that class were equal.
Based on the question mentioned conditions and above stated assumptions, we are required to calculate the number of boys who like each sport separately.
Here, given that, "for every four girls that like basketball, one liked kickball", i.e.,
The ratio of the number of girls who liked basketball to that of kickball is (4 : 1).
Now, let us assume that the total number of girls in that class is "x"
Therefore, as per the condition that, "36 girls said they liked basketball",
we can write [{(4/5) * x} = 36]
Or, [x = {36 * (5/4)}]
Or, [x = (9 * 5)]
Or, (x = 45)
That is, the total number of girls in that class is 45.
And as per our assumptions, the total number of boys in that class is also 45.
Also given in the question statement that, "for every three boys who stated they like basketball, two boys liked kickball", i.e.,
The ratio of the number of boys who liked basketball to that of kickball is (3 : 2).
Therefore, number of boys who like basketball = (3/5) * 45] = (3 * 9) = 27.
And the number of boys who like kickball = (45 - 27) = 18.
Ratio: In Mathematics, a ratio is a term that is used to compare two or more numbers, specifically used to indicate how big or small a quantity is when compared to another.
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How many clusters are in the scatter plot?
2
3
0
1
From the information given in the scatter plot, we can infer that the number of clusters given is three in number. (Option B) See attached image and explanation below.
What is a scatter plot?A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.
A scatter plot is a graph that displays data points linking two variables. Each item of data is represented by a separate point on the scatter plot, and the points are not linked.
In a scatter plot, a cluster is a group of dots that follow the same basic pattern. They might follow a straight route or a curved line. Many points can be found in a cluster.
Given the patterns identified in the scatter plot, it is correct to infer that there are three clusters.
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The price of a cell phone is x dollars. sandy bought the phone for x+0.07x dollars after an additional 7%sales tax. what is another expression that represents the same amount, in dollars, that sandy had to pay to buy the cell phone?
The amount that Sandy has to pay to buy the cell phone is 1.07x dollars.
This is a question of percentages.
Percentage
Percentage means a number or a ratio expressed in terms of fractions of 100. It is denoted using the percentage sign “%”.
It is given in the question that:-
Price of cell phone = x dollars
Additional sales tax = 7 %
We have to find the amount, in dollars, that Sandy had to pay to buy the cell phone.
Total amount Sandy had to pay for the cell phone = x + 7 % of x
x + (7/100)x = x + 0.07x = 1.07x dollars.
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Help please I really need help
Answer:
x=18
Step-by-step explanation:
Using proportion reasoning:
6/12=9/x
6x=108
x=18.
24% of a value is £84. Work out the original value. Give your answer in pounds (£).
A 28-sided die exists rolled 3 times then the different possible outcomes exist £350.
What is meant by original value?The sales price of the property used as collateral for the mortgage, as stated in the contract, or the appraised value at the time the relevant residential mortgage transaction was completed, whichever is less, is referred to as the "original value" with respect to a residential mortgage transaction.
The value of a mortgaged property is determined by an appraisal that was done in conjunction with the loan's origination.
Based on the given conditions, formulate:
28 × 3 = 84 then
£84 / 24%
simplifying the above equation, we get
= £350
Therefore, different possible outcomes exist for £350.
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Very easy 7th grade math please answer both questions 10 points!!!!
Answer:
28:
The Greatest Common Factor (GCF) of 10 and 35 is 5.
10/5 = 2
35/5 = 7
Take the GCF out and keep your divided values in the brackets:
5(2x+7)
29:
n = number of times Thalia has made cookies
c = cups of flour used
c = 12 - 2n
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2+(45+92)63 so how do I solve this
Answer:
8363
Step-by-step explanation:
Solve this using BODMAS (Brackets of Division, Multiplication, Addition, Subtraction)
=> 2 + (45 + 92)63
=> 2 + (137)63
=> 2 + 8361
=> 8363
function notation of g(x)-3x-8;g(-3)
The value of the function at -3 is g(-3) = -17 .
A function from set X to set Y is created by assigning an element from set Y to each element in set X. The function's domain and codomain are respectively referred to as the sets X and Y as a whole.
A function from the set X to the set Y assigns each element of X exactly one element of Y. The function's domain and codomain are respectively referred to as the sets X and Y as a whole.The collection of all pairings (x, f (x)) that distinctively represent a function is known as the graph of a function, which is a typical technique for lighting the function.We know that g(x) = 3x-8
Therefore we substitute the value of x with -3 to get g(x) .
g(-3) = 3(-3)-8 = -9 - 8 = -17
Therefore the value of the function is -17.
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What is a simplified expression for (x- y) - (x -y)?
Answer:
0
Step-by-step explanation:
if you distribute the negative through the second part, you get x-y-x+y, so the x and y will both cancel to 0.
Answer:
Step-by-step explanation:
( x + y ) - ( x - y )
x + y - x + y
x - x + y + y
2y AnsAt the end of 10 years, Alan has $4220 in his savings account. This account compounds monthly. If Alan’s initial deposit was $2100, what is the rate at which the account compounds
Answer:
Step-by-step explanation:
Which value, if any, from the set {4, 5, 6} makes 15f = 85 true?
A. 5
B. 4
C. None of these values
D. 6
I need to know the answer please…
Find the value of x in the given figure of a triangle
In the triangle ABE
step 1
Find out the measure of angle AEB
m by form a linear pair
mm
step 2
Find out the measure of angle ABE
m by alternate interior angles
step 3
Find out the measure of angle x
Remember that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
msubstitute given values
x+100+30=180
x=180-130
x=50 degreesWhat is the slope of the line that passes through the points (-9, 0) and (-17, 4)?
Write your answer in simplest form.
Answer:
m = -1/2Step-by-step explanation:
Use the slope formula of y^2-y^1 over x^2-x^1
(-9,0)
x^1 ,y^1
(-17,4)
x^2,y^2
4-0 over -17-(-9) ----> 4/-8
Simplify 4/-8 by dividing the numerator and denominator by 4
= -1/2it is 76 degrees at the 6000 foot level of a mountain and 49 degrees at the 12000 foot level of the mountain. write a linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet
The linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet will be T = (-9/2)x +103.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that, it is 76 degrees at the 6000-foot level of a mountain and 49 degrees at the 12000-foot level of the mountain.
As we know the linear equation in the slope-intercept is found as,
y =mx + b
Replace m with the c,y with the T, and b with the k as
T = cx + k
From the given data,
76 = c(6) + k
76 = 6c + k
⇒ k = 76 - 6c
For condition 2,
49 = c(12) + k
49 = 12c + k
Substitute the value of k in the above equation,
49 = 12c + (76 - 6c)
49 = 12c + 76 - 6c
49 - 76 = 6c
6c = -27
c=-9/2
Put the value of c in the equation,
K = 76 -6c
K = 76 -6(9/2)
K = 76+27
k = 103
Put the value of c and k in the equation below,
T = cx + k
T = (-9/2)x+103
Thus, the linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet will be T = (-9/2)x +103.
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What type of god is Kronos?
Answer:
Kronos is a Titan Deity.
Step-by-step explanation:
He was a very powerful "Titan Deity" that was the King of the Titans and the Heavens.
i hope this helps c: <3
A ball manufacturer wants to stack three balls, each with an 8-centimeter diameter, in a box that is an equilateral triangular prism. The diagram shows the dimensions of the bases. Will the balls fit in the box? Explain how you know.
Considering the volumes of the ball and of the box, it is found that the balls will not fit into the box.
Volume of the ballThe ball is spherical, with a diameter of 8 inches = radius of 4 inches.
The volume of an sphere of radius r is given by:
V = 4/3πr³.
Hence the volume of each ball is given by:
V = 4/3π x 4³ = 267.4 cm³.
The volume of the three balls is:
V = 3 x 267.4 cm³ = 802.2 cm³.
Volume of the boxThe box is a triangular prism, hence the volume is given by the multiplication of the base area by the height, as follows:
V = Ab x h.
The height of the box is of 9 cm, however we have to find the base area.
From the bisection, at the right side of the triangle, we have that half the side of the equilateral triangle is of 7.8 cm, hence the side length is of:
s = 2 x 7.8 = 15.6 cm.
Hence, bisecting the base triangle to find the height, it will have:
Height h. (side of a right triangle).Side of 7.8 cm (another side of a right triangle).Angle of 30º between them.Then the height can be found as follows:
tan(30º) = h/7.8 (tangent = opposite side/adjacent side)
h = 7.8 x tan(30º)
h = 4.5 cm.
The area of a triangle is half the multiplication of the side length and the height, hence the base area is:
A = 0.5 x 15.6 x 4.5 = 35.1 cm².
Then the volume of the box is:
V = 35.1 x 9 = 315.9 cm³.
The volume of the three balls is of 802.2 cm³ > 315.9 cm³, hence the three balls will not fit into the box.
What is the missing information?The box is missing and is given by the image at the end of the answer.
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Answer:
an inscribed, sides, 4.5,cm , greater, will
Solve for x. Write both solutions, separated by
a comma.
3x² + 7x-6=0
Answer:
- 3, 2/3
Step-by-step explanation:
Given:
3·x² + 7·x - 6 = 0
General Equation:
a·x² + b·x + c = 0
a = 3;
b = 7;
c = - 6.
Discriminant:
D = b² - 4·a·c = 7² - 4·3·(-6) = 49 + 72 = 121
√ (D) = √ (121) = 11
Solution:
x₁₂ = ( - b ± √(D) ) / (2·a);
x₁ = ( - 7 - 11 ) / (2·3) = ( - 18) / 6 = -3
x₂ = ( - 7 + 11 ) / (2·3) = 4 / 6 = 2 / 3
Which expressions are equivalent to the one below? Check ALL that apply. log2 - log8
using properties of log (a/b) = log (a) - log (b)
in this case log 2 - log 8 = log (2/8) = log (1/4)
first option
