let
the smaller number = x
the larger number = y
x + y = 30
4y + 6x = 128
[tex]\begin{gathered} x+y=30 \\ 4y+6x=128 \\ x=30-y \\ 4y+6(30-y)=128 \\ 4y+180-6y=128 \\ -2y=128-180 \\ -2y=-52 \\ y=\frac{52}{2} \\ y=26 \\ x+y=30 \\ x+26=30 \\ x=30-26 \\ x=4 \end{gathered}[/tex]
The numbers are 4 and 26.
Identify the graphs that represent a linear function. Check all that apply.On a coordinate plane, a line has a positive slope.On a coordinate plane, a curve opens down.On a coordinate plane, a graph decreases, increases, and then decreases again.On a coordinate plane, a line has a negative slope.
A linear function is represented by a straight line, that means the right answers are those graph with straight lines.
Therefore, the right graphs are the first and the last one.• The first graph represents a linear function with a positive slope.
,• The last graph represents a linear function with a negative slope.
First and last one.
uhh yeah its right i jus tried it
probability experiment4.4 Given that a spinner lands on a prime number, find the probability that the arrow will land on an odd number.
To determine the probability of an event to occur, the formula is:
[tex]P(x)=\frac{noof\text{ favorable outcomes}}{no.\text{ of total possible outcomes}}[/tex]In the spinner, there are 6 possible outcomes. The arrow can either point from 1 to 6.
4.1. In the spinner, there are 3 prime numbers. These are 2, 3, and 5. Hence, there are 3 favorable outcomes if we want to have a prime number as a result after the spin. The probability of that happening will be:
[tex]P(x)=\frac{3}{6}=\frac{1}{2}=0.5[/tex]The probability of spinning a prime number is 1/2 or 0.5 or 50%.
4.2. We have already mentioned that there are 3 prime numbers (2, 3, 5). For odd numbers, we also have 3 and these are 1, 3, and 5. Combining the two, we get {1, 2, 3, 5} as either prime or odd numbers. As we can see, there are 4 favorable outcomes. Therefore, the probability is:
[tex]P(x)=\frac{4}{6}=\frac{2}{3}[/tex]The probability of spinning a prime number or an odd number is 2/3.
4.3. We have already mentioned that there are 3 prime numbers (2, 3, 5). For multiple of 3, we only have {3, 6}. Since the given operation is AND, that means, we have to find the intersection or what's common of both data. As we can see, only {3} is common. This means, only 3 is both a prime number and a multiple of 3. There is only 1 favorable outcome. The probability is:
[tex]P(x)=\frac{1}{6}[/tex]The probability of spinning a prime number and a multiple of 3 is 1/6.
4.4. If it has been already given that the number lands on a prime number, this means that we only have 3 choices or 3 possible outcomes. It's either 2, 3, or 5. Out of the 3 prime numbers, there are only 2 odd numbers and these are 3 and 5. Hence, the probability is:
[tex]P(x)=2\text{ out of 3}=\frac{2}{3}[/tex]Given that a spinner lands on a prime number, the probability of spinning an odd number is 2/3.
Which of the following graphs to the probability that z-score is between 0 and 1?
The z-score of a measure is given by the following formula
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x represents the measure, mu represents the mean of the distribution, and sigma represents the standard deviation.
If we have a z-score equal to zero, our measure will be
[tex]\begin{gathered} 0=\frac{x-\mu}{\sigma} \\ 0=x-\mu \\ x=\mu \end{gathered}[/tex]a z-score equal to zero represents the mean of the distribution.
For a z-score equal to 1, we have
[tex]\begin{gathered} 1=\frac{x-\mu}{\sigma} \\ \sigma=x-\mu \\ x=\mu+\sigma \end{gathered}[/tex]Then, the interval between z = 0 and z = 1 is the interval between the mean and one positive standard deviation.
[tex](\mu,\mu+\sigma)[/tex]The graph that represents this interval is the first graph.
In what they call “Year Zero," a group of 26 people started a settlement. Every yearthe population changes as babies are born, people move in, and people move out.Generally, the population increases by an average of 2.6 people a year.At the same time, a nearby established community discovered that their populationcould be described by the following function, where f(x) is the population, inpeople, and x is the time, in years, from "year zero."f(x) = -5.3x + 256Part AUsing your knowledge of functions, explain specifically why both communities' waysof expressing their populations represent functions. Provide evidence to supportyour answerPart BAnalyze the functions and compare the populations for the two communities overtime by describing in detail under what conditions one community's population isgreater than the other's population. Provide evidence to support your answer.
Solution
In the first paragraph,
It is given that a group of 26 people started a settlement and the population increased by an average of 2.6 people a year.
We can represent the population function as ;
g(x) = 26 + 2.6 x
Where x denotes the number of years and g(x) is the population after some certain years.
At a nearby community, it was discovered that the population can be written as;
f(x) = -5.3x + 256
Part A.
The population can be expressed as a function because the population at a particular time depends on the number of years x.
Specifically, it can be represented as a linear function because the rate at which the population increases per year is constant.
Part B.
Equating the functions
-5.3x + 256 = 26 + 2.6x
=> 5.3x + 2.6x = 256 - 26
=> 7.9x = 230
=> x = 29
Therefore, if the number of years is less than 29
The population of the first community will be less than the population of the second community
If the number of years is greater than 29
The population of the first community will be greater than the population of the second community
5g + h =g solve for g
You have the following equation:
5g + h = g
In order to solve for g, you first organize the previous equation, as follow:
5g + h = g substract g both sides and substract h both sides too
5g - g = -h
4g = -h dive by 4 both sides
g = -h/g
Then, the answer is g = -h/g
If a line has slope a, what is the slope of its reflection across the line y=x?Question content area bottomPart 1The slope of its reflection across the line y=x will be
By definition, let m be the slope a line, then m can be calculated by the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}^{}[/tex]Given that (x1, y1) and (x2, y2) are known points of the line. By reflecting all the points of the line across the line y = x
What is the mean? 8 3 9 8 6 8
The mean of 8 3 9 8 6 8 is
[tex]\frac{8+3+9+8+6+8}{6}=\text{ 7}[/tex]The mean is 7
2х +8y = 16 -3х +6y = 30determine the number of solutions
Given: The system of equation below
[tex]\begin{gathered} 2x+8y=16 \\ -3x+6y=30 \end{gathered}[/tex]To Determine: The number of solutions
Solution
Combine the two equations and solve
[tex]\begin{gathered} equation1:2x+8y=16 \\ equation2:-3x+6y=30 \end{gathered}[/tex]Multiply equation by 3 and equation 2 by 2
[tex]\begin{gathered} 3(2x+8y=16)=6x+24y=48==equation3 \\ 2(-3x+6y=30)=-6x+12y=60==equation4 \end{gathered}[/tex]Add equation 3 and 4
[tex]\begin{gathered} 6x-6x+24y+12y=48+60 \\ 36y=108 \\ y=\frac{108}{36} \\ y=3 \end{gathered}[/tex]Substitute y in equation 1
[tex]\begin{gathered} 2x+8y=16 \\ 2x+8(3)=16 \\ 2x+24=16 \\ 2x=16-24 \\ 2x=-8 \\ x=-\frac{8}{2} \\ x=-4 \end{gathered}[/tex]Hence, x = -4, y = 3
Find the upper quartile of the first ten natural numbers.
Answer:
8
Explanation:
The first ten natural numbers are:
[tex]1,2,3,4,5,6,7,8,9,10[/tex]To find the upper quartile, separate the numbers into two halves:
• Lower Half: 1,2,3,4,5
,• Upper Half: 6,7,8,9,10
The upper quartile is the number in the middle of the upper half.
The number in the middle of the upper half = 8
Therefore, the upper quartile of the first ten natural numbers is 8.
Write the coordinates of the vertices after a translation 2 units left and 1 unit up. 10 D E F -10 0 10 -10 D(-6, 4) → E(0,4) → Ell F(-4, 2) + FIC D
We need to subtract 2 from our x-coordinate and add 1 to our y-coodrinate. Doing this gives us
[tex]D(-6,4)\rightarrow D(-8,5)[/tex][tex]E(0,4)\rightarrow E(-2,5)[/tex][tex]F(-4,2)\rightarrow F(-6,3)[/tex]And hence, we have correctly given the coordinates of our translated points.
Find the two positive consecutive odd integers whose product is 63.3 and 217 and 89 and 117 and 9
Given: Two positive consecutive odd integers.
Required: To find two positive consecutive odd integers whose product is 63.
Explanation: Let x be a positive odd integer. Then (x+2) is the consecutive positive odd integer. Now according to the question
[tex]x(x+2)=63[/tex]Or
[tex]x^2+2x-63=0[/tex]which can be factorized as follows
[tex](x+9)(x-7)=0[/tex]Which gives
[tex]\begin{gathered} x=7\text{ or } \\ x=-9 \end{gathered}[/tex]Since x is a positive odd integer,
[tex]x\ne-9\text{ }[/tex]Hence the two required integers are
[tex]\begin{gathered} x=7\text{ and } \\ x+2=9 \end{gathered}[/tex]We can also verify our result as the product of 7 and 9 is 63.
Final Answer: Option D is correct.
The set of all nunbers, including all rational and irrational number?
Rational numbers are type of real numbers that can be represented as a simple fraction. Rational numbers can be formed by dividing 2 integers, Rational number can be represented in this form x/y. Where y is not equal to zero.
Example of rational numbers are as follows
[tex]r=1.5,5,\frac{3}{4}[/tex]Solve the right triangle with a= 1.42 and b=17.1 . Round off the results according to the table below
A)
[tex]\begin{gathered} c=17.159 \\ A=4.747\text{\operatorname{\degree}} \\ B=85.253\operatorname{\degree} \end{gathered}[/tex]Explanation
Explanation
Step 1
c) to find the measure of the hypotenuse we can use the Pythagorean theorem, it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
[tex]a^2+b^2=c^2[/tex]Step 1
a) Let
[tex]\begin{gathered} a=1.42 \\ b=17.1 \end{gathered}[/tex]b) now, replace and solve for c
[tex]\begin{gathered} a^2+b^2=c^2 \\ 1.42^2+17.1^2=c^2 \\ 294.4264=c^2 \\ c=\sqrt{294.4264} \\ c=17.15885 \\ rounded \\ c=17.159 \end{gathered}[/tex]Step 2
angle A
to solve for angle A we can use tan function, so
[tex]tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}}[/tex]replace
[tex]\begin{gathered} tan\text{ A=}\frac{a}{b} \\ tanA=\frac{1.42}{17.1} \\ A=\tan^{-1}(\frac{1.42}{17.1}) \\ A=4.747\text{ \degree} \end{gathered}[/tex]Step 3
for angle B we can use tan function
let
[tex]\begin{gathered} opposit\text{ side=b} \\ adjacent\text{ side=a} \end{gathered}[/tex]replace and solve for angle B
[tex]\begin{gathered} tan\text{ B=}\frac{b}{a} \\ tanB=\frac{17.1}{1.42} \\ B=\tan^{-1}(\frac{17.1}{1.42}) \\ B=85.252\text{ \degree} \\ \end{gathered}[/tex]I hope this helps you
The circle below has center P.The point (x, y) is on the circle as shown.12-(a) Find the following.1110-unitsRadius: 0Center: 0987Value of a:(Choose one)(x,y)351Value of b:(Choose one)4a32(b) Use the Pythagorean Theorem to write an equationrelating the side lengths of the right triangle. Writeyour answer in terms of x and y (with no otherletters)+
Given:
Center of the circle = P
Let's determine the following:
a) Radius.
Here, the radius of the circle is the hypotenuse of the triangle.
Therefore, the radius of the circle is 3 units
b) Center:
To find the point at the center of the circle, let's locate the point P on the graph.
On the graph, the point P is at (x, y) ==> (9, 4)
Therefore, the center (h, k) is (9, 4)
c) Value of a:
To find the value of a, let's first find the value of b.
Value of b = 6 - 4 = 2
Apply Pythagorean Theorem to find the value of a:
[tex]c^2=a^2+b^2[/tex]Where:
c is the hypotenuse = 3
b = 2
Thus, we have:
[tex]\begin{gathered} 3^2=a^2+2^2 \\ \\ 9=a^2+4 \\ \\ \text{Subtract 4 from both sides:} \\ 9-4=a^2+4-4 \\ \\ 5=a^2 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{5}=\sqrt[]{a^2} \\ \\ 2.2=a \\ \\ a=2.2 \end{gathered}[/tex]Therefore, the value of a is 2.2 units
d) Value of b.
The value of b is 2 units
ANSWERS:
• Radius: , 3 units
,• Center: , (9, 4)
,• Value of a = , 2.2 units
,• Value of b = , 2 units
b. What is the sample space if you spin the spinner TWO TIMES?RedYellowBlueRedYellowBluec. One spin, P(red)(fraction)d. Two spins, Pared then blue)(decimal to 2 places)e. Two spins, P(yellow or red)=% (percent to 1 decimal place)
Hanna, this is the solution:
As you can see there are three equal sectors colored yellow, blue, red, therefore, the sample space for spinning the spinner two time is:
{yellow-yellow, blue-yellow, red-yellow, red-blue, red-red, blue-blue}
Spin the spinner one time:
• Red = 1/3 or 0.33
,• Blue = 1/3 or 0.33
,• Yellow = 1/3 or 0.33
Spin the spinner a second time:
• Red - Red = 1/3 * 1/3 = 1/9 or 0.11
,• Red - Blue = 1/3 * 1/3 = 1/9 or 0.11
,• Red - Yellow = 1/3 * 1/3 = 1/9 or 0.11
,• Blue - Blue = 1/3 * 1/3 = 1/9 or 0.11
,• Blue - Red = 1/3 * 1/3 = 1/9 or 0.11
,• Blue - Yellow =1/3 * 1/3 = 1/9 or 0.11
,• Yellow - Yellow = 1/3 * 1/3 = 1/9 or 0.11
,• Yellow - Red = 1/3 * 1/3 = 1/9 or 0.11
,• Yellow - Blue = 1/3 * 1/3 = 1/9 or 0.11
,•
George is a salesperson in a jewelry store and earns $100 per week, plus 10% of his weekly sales. If George makes $425 in one week , what are his sales for that week? $5,250$4,250$4,000$3,250
Since George earns $100 per week plus 10% of his weekly sales
Assume that his weekly sales are $x
Then he earns 100 + 10% of x
Since he makes $425 in a week, then
[tex]\begin{gathered} 100+\frac{10}{100}\times x=425 \\ 100+0.1x=425 \end{gathered}[/tex]Subtract 100 from both sides
[tex]\begin{gathered} 100-100+0.1x=425-100 \\ 0.1x=325 \end{gathered}[/tex]Divide both sides by 0.1
[tex]\begin{gathered} \frac{0.1x}{0.1}=\frac{325}{0.1} \\ x=3250 \end{gathered}[/tex]His sales for that week are $3250
The answer is D
Which polynomial function is graphed below?-10A. (x) = (x – 3yº (x + 2)B. f(x) = (x - 2y(x +3)C. (*) - (x - 2)(x+3)D. *(x) = (x-3)(x + 2y4
Every polynomial can be written in the form:
[tex]f(x)=(x-a_1)(x-a_2)\ldots_{}[/tex]The a_1, a_2.... are the roots of the polynomial, meaning that f(a_1) = f(a_2) = ... = 0. This happens wen the graph of the polynomial intersects or tangency the x-axis. Whe it only tangecy the x-axis, it means that you have two of the root.
In this case, we have the polynomial tangency the x-axis in x = -2 and intersect the x-axis in x = 3. This means that the polynomial has roots -2, -2 (again) and 3. So:
[tex]\begin{gathered} f(x)=(x-(-2))(x-(-2))(x-3) \\ f(x)=(x+2)(x+2)(x-2) \\ f(x)=(x+2)^2(x-3) \end{gathered}[/tex]Since the order doesn't metter, we can right in this way:
[tex]f(x)=(x-3)(x+2)^2[/tex]Which corresponds to alternative D.
134TIME REMAINING22:39Which statements about the diagram are true? Selectthree optionsDE+EF > DFD A DEF is an isosceles triangle5
Statements that are true:
DE + EF > DF
DEF is an scalene triangle
5 < DF < 13
which of these answers are in standard for of the linear equation?
hello
the standard linear equation can be written as
[tex]\begin{gathered} x+y=z \\ \text{where z = any variable} \end{gathered}[/tex]in the question here, the options that corresponds to the answer here are
[tex]\begin{gathered} 3x+y=8 \\ x+4y=12 \\ 5x+24y=544 \end{gathered}[/tex]The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone. The formula for the surface area S of the cone S=piR2+piRL where R id the radius and the base and L is slant higher find the hight of the cone
hello
to find the height of the cone, we can simply use pythagorean theorem here since we know two sides of the triangle formed
using pythagorean theorem,
[tex]\begin{gathered} x^2=y^2+z^2 \\ 15^2=y^2+6^2 \\ 225=y^2+36 \\ \text{collect like terms } \\ y^2=225-36 \\ y^2=189 \\ \text{take square roots of both sides} \\ y=\sqrt[]{189} \\ y=13.747\approx13.75 \end{gathered}[/tex]from the calculations above, the height of the cone is 13.75cm
If ƒ (7) = 22, thenf-¹(f(7)) = [?]
Remember the following property of invertible functions:
[tex]f(x)=y\qquad\Leftrightarrow\quad f^{-1}(y)=x[/tex]Then:
[tex]f^{-1}(f(x))=x\qquad\forall x[/tex]Then:
[tex]f^{-1}(f(7))=7[/tex]Therefore, the answer is: 7.
determine if the following sequence is Arithmetic if so what is the common difference 77 44 16 -12
Answer:
The sequence is not an arithmetic sequence.
Explanation:
Given the sequence:
[tex]77,44,16,-12,\ldots[/tex]Calculate the difference between the terms below:
[tex]\begin{gathered} 44-77=-33 \\ 16-44=-28 \\ -12-16=-28 \end{gathered}[/tex]Observe that the differences between the terms are not the same all through.
Thus, there is no common difference which implies that the sequence is not an arithmetic sequence.
Hello, I need help with this problem. Picture will be included . Thank youu!
Solve for the missing equivalent rational expressions
[tex]\begin{gathered} \frac{-7}{w}=\frac{\square}{4w^8} \\ \\ \text{Swap left and right side of equations} \\ \frac{\square}{4w^8}=\frac{-7}{w} \\ \\ \text{Multiply both sides by }4w^8\text{ to cancel out the denominator on the left side} \\ \frac{\square}{4w^8}=\frac{-7}{w} \\ \frac{\square}{4w^8}\cdot4w^8=\frac{-7}{w}\cdot4w^8 \\ \frac{\square}{\cancel{4w^8}}\cdot\cancel{4w^8}=\frac{-28w^8}{w} \\ \square=\frac{-28w^8}{w} \\ \\ \text{Simplify the right side of the equation} \\ \square=\frac{-28w^8}{w} \\ \square=-28w^{8-1} \\ \square=-28w^7 \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ \frac{-7}{w}=\frac{-28w^7}{4w^8} \end{gathered}[/tex]Consider the circle Which instructions can be used to find the circle correctly
Answer:
Explanation:
Given a circle, we want to identify its center
A way to do this is to draw two chords at any part of the circle
A chord is a line inside the circle that joins two points on the circumference
The next thing to do here is to draw a perpendicular bisector through each of these chords
Now, the point at which these perpendicular bisectors intersect is the center of the circle
This mean option B is the correct answer choice
How many times smaller is 2 x 10^-12 than 4 x 10^-10?
the ratio is,
[tex]=\frac{4\times10^{-10}}{2\times10^{-12}}[/tex][tex]\begin{gathered} =2\times10^{12-10} \\ =2\times10^2 \\ =200 \end{gathered}[/tex]so 2 x 10 ^-12 is 200 times smaller than 4 x 10 ^-10
Eleanor had an average daily balance of $250.82 in her chargeaccount. She paid 1.7% interest on that amount. Compute her financecharge.a. $254.58b. $.13c. $37.63d. $4.26
For an daily balance of P in her charge account and an interest paid at a rate of r, her finance charge is given by the expression:
F = r*P
For r = 1.7% and P = $250.82, we have:
F = 0.017*250.82
F = $4.26
Answer: d
The enrollment at a local college increased 3% over last year's enrollment of 500. Find the current enrollment.
Given:
Last year's enrollment is 500.
Enrollment increased percentage is 3%
[tex]\begin{gathered} \text{Increased enrollment=500}\times\frac{3}{100} \\ \text{Increased enrollment=}5\times3 \\ \text{Increased enrollment=}15 \end{gathered}[/tex][tex]\begin{gathered} \text{Current enrollment=500+15} \\ \text{Current enrollment=}515 \end{gathered}[/tex]I need some help, this one is hard
Arithmetic progression: -25, -37, -49
d = - 12
General formula
An = -25 + (n -1)*(-12)
A85 = - 25 + 84*(-12) = -1033
a hot air balloon ascended to a height of 35 meters 2 minutes after launch after some time the ballons altitude began to change by -3¼ meters every 9 minutes to avoid a tree the hot air ballon flew up by 5½ meters what is the new altitude of the hot air balloon
Our objective for this case is find the final altitude for this problem
The first distance is x1=35 m after 2 min =120 sec
The second distance is :
[tex]x_2=-\frac{13}{4}\frac{m}{mi}\cdot9\min =-\frac{117}{4}m[/tex]Then flight up:
[tex]x_3=5\frac{1}{2}m=\frac{11}{2}m[/tex]Then the final altitude would be:
[tex]x_1+x_2+x_3[/tex]And replacing we got:
[tex]35m-\frac{117}{4}m+\frac{11}{2}m[/tex]And after we operate we got:
[tex]\frac{45}{4}m=11.25m[/tex]In the sketch below, A ABC is similar to AXY Z. Find the length of side x
From geometry, we know that if two triangles are similar, then their corresponding sides are in proportion.
From the statement, we know that ΔABC is similar to ΔXYZ.
From the diagram, we see that:
• AB = 15 is the corresponding side to XY = 10,
,• BC = 9 is the corresponding side to YZ = x.
So we must have the equality:
[tex]\begin{gathered} \frac{AB}{XY}=\frac{BC}{YZ}, \\ \frac{15}{10}=\frac{9}{x}, \\ 1.5=\frac{9}{x}. \end{gathered}[/tex]Solving for x, we get:
[tex]\begin{gathered} 1.5x=9, \\ x=\frac{9}{1.5}=6. \end{gathered}[/tex]Answerx = 6