Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?-5-4-3-2 -1 01+4123on++at-5-2+ o+1-1234501-5-4-3+o-2-1+1N+W+A+5++-5-4-3-2+o-1NT1345
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To find the solution, lets first simplify the inequality:
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Charles is 16 years older than his sister Michelle. In 8 years, he will be twice as old as Michelle. How old is each of them now?
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Charles is now 24 years old and Michell 8 years old
1) In this problem, let's turn that information into an equation so that we can solve it using Algebra.
2) The first equation is:
Charles: x+16
Michelle: x
After 8 years, since Charles is going to be twice older than Michelle, we'll have:
[tex]\begin{gathered} C=x+16 \\ M=x \\ --- \\ x+16+8=2(x+8) \\ x+24=2x+16 \\ x-2x=-24+16 \\ -x=-8 \\ x=8 \end{gathered}[/tex]Note that we equated the age of Charles plus 8 to the double of x, Michelle's age.
3) Let's now find the age of them now:
[tex]\begin{gathered} C=8+16 \\ C=24 \\ M=8 \end{gathered}[/tex]Plugging back into the first equations, we can see that Charles is now 24 yrs old and Michell 8 yrs old
how to find arc for circles or angle indicated
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Given data:
The given image of the circle.
The given diagram can be redrawn as,
Here, Triangle JOK is an isosceles triangle in which OJ and OK are radii, the expression for the angle sum property is,
[tex]undefined[/tex]In a study of 200 students under 25 years old, 5% have not yet learned to drive. Howmany of the students cannot drive?
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We can write 5% in decimal form as 5/100=0.05.
So if a 5% of the 200 students under 25 years old have not yet learned to drive, we can calculate the number of students that have not yet learned to drive as:
[tex]n=\frac{5}{100}\cdot200=5\cdot2=10[/tex]10 students out of the group of 200 can not drive.
consider a cone with a base radius of 3 ft and height of 10 ft. Find the volume of the cone
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The volume V of a cone with radius r and height h is given by the formula:
[tex]V=\frac{1}{3}\pi r^2\times h[/tex]Substitute r=3ft and h=10ft to find the volume of the cone:
[tex]\begin{gathered} V=\frac{1}{3}\pi\times(3ft)^2\times10ft \\ =\frac{1}{3}\pi\times90ft^3 \\ =\pi\times30ft^3 \\ =94.24777961\ldots ft^3 \end{gathered}[/tex]Therefore, the volume of the cone is 30π cubic feet, which is equal to 94 cubic feet (to the nearest whole number).
Find the quotient and the remainder using the long division method
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The question is to evaluate the quotient and remainder of the division using the long division method:
[tex]\frac{-3x^3+13x^2-14x+9}{x-3}[/tex]Step 1: Write out the problem in the long division format
Step 2: Divide the leading term of the dividend by the leading term of the divisor. Write down the calculated result in the upper part of the table. Multiply it by the divisor and subtract the dividend from the obtained result
[tex]\begin{gathered} \frac{-3x^3}{x}=-3x^2 \\ -3x^2(x-3)=-3x^3+9x^2 \end{gathered}[/tex]Step 3: Apply the steps from 2 above to the remainder at the bottom
[tex]\begin{gathered} \frac{4x^2}{x}=4x \\ 4x(x-3)=4x^2-12x \end{gathered}[/tex]Step 4: Apply the steps from 3 above
[tex]\begin{gathered} \frac{-2x}{x}=-2 \\ -2(x-3)=-2x+6 \end{gathered}[/tex]Step 5: Since the degree of the remainder is less than that of the divisor, we are done with the division. The quotient is the polynomial at the top and the remainder is at the bottom
[tex]\frac{-3x^3+13x^2-14x+9}{x-3}=-3x^2+4x-2+\frac{3}{x-3}[/tex]ANSWER
The quotient is:
[tex]-3x^2+4x-2[/tex]The remainder is
[tex]3[/tex]The 8 foot diameter circular table has a 4 foot wide extension.1. What is the total area with the extension?2. How does the area compare to the area o4 ft.O8 ft. table with extension10 ft. table
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1.- Area
[tex]\begin{gathered} \text{Area of the circle = 3.14 x (4)}^2 \\ \text{Area of the circle = 50.24 ft}^2 \end{gathered}[/tex]2.- Area of the extended table
Area = 50.24 + (8 x 4)
Area = 50.24 + 32
Area = 82.24 ft^2
Second question
Area = 3.14 x (5)^2
Area = 25 x 3.14
Area = 78.5 ft^2
The area of the larger circle is smaller than the area of the table with the extension.
3. Find the surface area of each object to the nearest tenth of a square unit. d=2.5 cm b) d=0.003 m 16cm wooden rod 16 m flag pole 62 MHD
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The formula for the surface area of a cylinder is given:
[tex]A=2\cdot\pi\cdot r\cdot h+2\cdot\pi\cdot r^2[/tex]then, since the information given is a diameter, rewrite the expression using the diameter.
[tex]\begin{gathered} D=2\cdot r \\ r=\frac{D}{2} \\ \text{then, } \\ A=D\cdot\pi\cdot h+2\cdot\pi\cdot(\frac{D}{2})^2 \end{gathered}[/tex]Replace with the data given
[tex]\begin{gathered} A=(2.5)\cdot(\pi)\cdot(16)+2\cdot\pi\cdot(\frac{2.5}{2})^2 \\ A=40\pi+3.125\pi \\ A=43.125\pi \end{gathered}[/tex]can someone please help me find the area of the following?
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Mya, this is the solution:
Let's recall that the formula to solve for the surface area of a cylinder is:
A = 2 * π * r * h + 2 * π * r²
In our exercise, we have:
r = 8 cm
h = 7 cm
In consequence, replacing these values in the formula:
A = 2π * 7 * 8 + 2π * 8²
A = 2π * 56 + 2π * 64
A = 112π + 128π
A = 240π cm²
The correct answer is D. 240π cm²
Write the equation of the linear relationship in slope Intercept form, using decimals as needed. 0 2.5 100 200 300 375 725 1075 Enter the equation of the relationship.
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Let us first calculate the slope of the function. We need 2 points (0,2.5) and (100,37.5)
so the slope is
[tex]m=\frac{37.5-2.5}{100-0}=\frac{35}{100}=\frac{7}{20}=0.35[/tex]So the equation is
[tex]y=0.35x+2.5[/tex]Triangle ABC has vertices at A: (0,7), B: (0, 2), and C: (4,2). What is the perimeter in units?Round your answer to the nearest tenth (one decimal place).
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Given that
A = (0, 7)
B = (0 2)
C = (4, 2)
[tex]undefined[/tex]i need help with this question parts 1 - 4
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Given:
Given data points are (950,100) and (1000,40).
Required:
To find the linear model for this data.
Explanation:
The standard form of linear equation is
[tex]y=mx+b[/tex]Where
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{40-100}{1000-950} \\ \\ m=-\frac{60}{50} \\ \\ m=-\frac{6}{5} \end{gathered}[/tex]Now
[tex]y=-\frac{6}{5}x+b[/tex]Now we have to find b using the points (950,1000), we get
[tex]\begin{gathered} 1000=-\frac{6}{5}(950)+b \\ \\ 1000=-6\times190+b \\ \\ 1000=-1140+b \\ \\ b=1000+1140 \\ \\ b=2140 \end{gathered}[/tex][tex]y=-\frac{6}{5}x+2140[/tex]Final Answer:
[tex]y=-\frac{6}{5}x+2,140[/tex]i have a question on one of my assignments i need to do its homework
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the initial height is when the number of days is 0 from the graph we can notice is 4Cm
The graph is relationship lineal because is a line
The graph is relationship proportional because if time increases the size also increases
Josh and Daniel each want to save $600 to attend a sports camp. Josh has saved 60% ofthe amount. Daniel has saved $320. Who has saved more money? How much more?
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The total amount to save is $600
Josh saved 60%. This is the same as below
[tex]\begin{gathered} 60\text{ \% of \$600} \\ =\frac{60}{100}\times600 \\ =\frac{36000}{100} \\ =360 \end{gathered}[/tex][tex]\begin{gathered} \text{ 60\% } \\ =\frac{60}{100}=\frac{360}{600} \end{gathered}[/tex]Josh has saved $360.
Daniel has saved $320
It can be observed that $360 is more than $320, so Josh saved more money
The difference tells how much more
[tex]\begin{gathered} \text{ \$360 - \$320} \\ =\text{ \$40} \end{gathered}[/tex]Hence,
1. 60/100= x/600
2. Multiply both sides by 600
3. Josh has saved $360
4. Josh saved more money. Josh saved $40 more than Daniel
Use definitions of right-hand and left-hand limits to prove the limit statement.lim-1|x|X>0Since x approaches 0 from the left, x<0, (x = []).
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First we need to understand what |x| means or what values it repressents
[tex]|x|=\begin{cases}x,x\ge0 \\ \\ -x,x<0\end{cases}[/tex]|x| indicates the absolute value of x, this is, x is always going to be positive, for example,
when x = 1 -> |x| = 1 , but also when x = -1 , then |x| = 1
Since, in this case, we need to find the limit when X approaches 0 from the left we are going to use |x| = -x , for x<0
this is...
[tex]\lim _{x\rightarrow0-}\frac{x}{|x|}=\lim _{x\rightarrow0-}\frac{x}{-x}=\lim _{x\rightarrow0-}(-1)=-1[/tex]At this point we have proved the limit statement.
So, in order to answer the question in the lower part... x approaches to 0 from the left, x<0, |x| = -x
In the graph you can see, whenever X<0 the value of the funcion will be negative and when it approaches 0 it becomes -1
On the other hand, when the function approaches to 0 from the right, the value of the function is +1. This is a discontinuity
[tex]\lim _{x\rightarrow0-}\frac{x}{|x|}=\lim _{x\rightarrow0-}\frac{x}{-x}[/tex]This way we eliminate the absolute value, because, remember, when x<0, |x| = -x
Would appreciate your help with this algebra question. Thank you!
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The above function is to be used if the value of x is between 0 and 8. On the other hand, the function to be used when x ≥ 8 is -5x + 11.
Since the interval to be checked is from 2 to 7, we will be using the first function which is -2x + 4.
To determine the rate of change between those intervals, we have the formula below:
[tex]\text{rate of change = }\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]Let's solve f(x₂) first. Our x₂ = 7. Let's substitute the function above with x = 7.
[tex]\begin{gathered} f(x)=-2x+4 \\ f(7)=-2(7)+4 \\ f(7)=-14+4 \\ f(7)=-10 \end{gathered}[/tex]Let's solve f(x₁) first. Our x₁ = 2. Let's substitute the function above with x = 2.
[tex]\begin{gathered} f(x)=-2x+4 \\ f(2)=-2(2)+4 \\ f(2)=-4+4 \\ f(2)=0 \end{gathered}[/tex]So, we now have the value of f(x₂) = -10, and f(x₁) = 0. Let's use these values to the formula of the rate of change above.
[tex]\begin{gathered} \text{rate of change}=\frac{f(x_2)-f(x_1)^{}}{x_2-x_1} \\ \text{rate of change}=\frac{-10-0}{7-2} \\ \text{rate of change}=\frac{-10}{5} \\ \text{rate of change}=-2 \end{gathered}[/tex]Since the rate of change is a negative number, the function is decreasing over the interval [2, 7].
A researcher wants to study the effects of sleep deprivation on motor skills. Nine people volunteer for the experiment: Amanda, Brian, Christine, David, Emily, Fred,George, Heather, and Ivan. Use the second row of digits in the random number table below to select a simple random sample of three subjects (ignore zeros). Theother six subjects will go into the control group. If the subjects are numbered through 9 alphabetically, what are the numbers of the three subjects selected? List thesubjects that will go in the treatment group.Line/Column(1)(2)(3)(4)177952454778618314079264955243209744831960479733397402669224773What are the numbers of the three subjects selected?{If not an answer please an explanation, I don’t understand how to get the numbers}
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The second row has the following numbers:
64955, 24320, 97448, 26692
We are interested in numbers from 0 to 9, then we are only interested in the first digit of the numbers, which are: 6, 2, 9, 2.
Student 2 is Brian
Student 6 is Fred
student 9 is Ivan
5. A soccer ball has a circumference of 70 centimeters at widest polne. What the volume and total surface area of the soccer boll
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According to our question we have :-
[tex]\begin{gathered} 2\pi r=70 \\ r=\frac{70}{2\pi}=\frac{35}{\pi} \end{gathered}[/tex]Now volume of the ball will be:-
[tex]\begin{gathered} V=\frac{4}{3}\pi\times r^3 \\ =\frac{4}{3}\times\pi\times\frac{35}{\pi}\times\frac{35}{\pi}\times\frac{35}{\pi} \\ =\frac{4}{3}\times\frac{35}{\square}\times\frac{35\times7}{22}\times\frac{35\times7}{22} \\ =5787.5 \end{gathered}[/tex]So volume of ball ia 5787.5 cubic centimeter
Now surface area of ball will be :-
[tex]\begin{gathered} A=6\pi\times r^2^{} \\ =6\times\pi\times\frac{35}{\pi}\times\frac{35}{\pi} \\ =6\times35\times\frac{35\times7}{22} \\ =2338.6 \end{gathered}[/tex]So surface area of ball is 2338.6 centimeter square
For each question, use the following statements to write the compound statement anddetermine its truth value.P: Perpendicular lines intersect to form right angles.Q: All eagles are bald eagles.R: The capital of Texas is Houston.S: Congruent segments have equal length.Write the compound statement and determine its truth value: P V ~QPerpendicular lines intersect to form right angles or all eagles are bald eagles, falsePerpendicular lines intersect to form right angles or not all eagles are bald eagles; truePerpendicular lines intersect to form right angles or not all eagles are bald eagles; falsePerpendicular lines intersect to form right angles or all eagles are bald eagles: true
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P:Perpendicular lines intersect and perpendicular lines form right angles. True
Q:
A wing of Samuel's model airplane is in the shape of a triangle with the dimensions shownbelow. What is the value of x?A. 75B. 55C. 35D. 573.
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Given that, the triangle is a right angled triangle. Therefore,
[tex]\text{hypotenuse}^2=base^2+altitude^2[/tex]Given that, hypotenuse is 10, altitude is 5 and base is x. Thus,
[tex]\begin{gathered} 10^2=x^2+5^2 \\ x^2=100-25 \\ x^2=75 \\ x=5\sqrt[]{3} \end{gathered}[/tex]Hence, Option D.
Ben wants to put the rabbit run and hutch on his lawn.. The space for the rabbit run must .be square 350cm by 350cm. have at least 50cm space to walk around it.the space for the rabbit hutch must be rectangular 200cm by 50 cm.the rabbit hutch will be Ina corner inside the rabbit run.the grid show us the plan of the lawn
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Explanation:
We know that 1 square has 50 cm of side. The rabbit run must be a square of 350 cm by 350 cm, so we will use 7 times 7 squares on the grid, because
350/50 = 7
Additionally, it has at least 50 cm of space to walk around it, so we will let at least one square around the rabbit run.
The rabbit hutch is rectangular with measures of 200 cm by 50 cm, so it is equivalent to a rectangle of 4 squares by 1 because
200/50 = 4
50/50 = 1
Finally, the rabbit hutch will be in a corner of the rabbit run.
Answer:
Therefore, we can draw the spaces as
What equation that represents the line that passes through the two points (5, 8) and (9, 2)?
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The linear equation that passes through the two given points is:
7 = (-3/2)*x + 31/2.
What is the equation of the line?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
Here the line passes through (5, 8) and (9, 2), then the slope is:
m = (2 - 8)/(9 - 5) = -6/4 = -3/2
So we have:
y = (-3/2)*x + b
To find the value of b, we can replace the values of one of the points in the equation, I will use (5, 8)
8 = (-3/2)*5 + b
8 = -15/2 + b
8 + 15/2 = b
31/2 = b
The line is: y = (-3/2)*x + 31/2
Solve for x. The polygons in each pair are similar..*:)24302420-5+5x56910The polygons in each pair are similar. Find the scale factor of the smaller figure tothe larger figure. *2135201830O 1:7
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ANSWER
[tex]3\colon5[/tex]EXPLANATION
The polygons given are similar.
To find the scale factor of the smaller figure to the larger figure, we have to find the ratio of the side lengths of corresponding sides of the smaller triangle to the larger one.
Therefore, we have that the scale factor is:
[tex]\begin{gathered} 21\colon35 \\ \Rightarrow3\colon5 \end{gathered}[/tex]5. Find the equation of a line that is parallel to y = 2x + 8 and passes through (5, 1).
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First, let's find the slope of the given line, comparing the equation with the slope-intercept form of a linear equation (y = mx + b, where m is the slope).
Looking at the equation, we have m = 2.
Since parallel lines have the same slope, so the slope of the parallel line is also m = 2.
Then, using the point (5, 1) in the equation, we have:
[tex]\begin{gathered} y=mx+b \\ 1=2\cdot5+b \\ 1=10+b \\ b=1-10 \\ b=-9 \end{gathered}[/tex]Therefore the equation is y = 2x - 9, and the correct option is 1.
Find the measure of ZGHJ and LGIJ.68°H 31GK115angle GH) =degreesangle GIJ =degrees
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Step 1: Find arc angle GJ
The sum of the arc angles of a circle is 360°.
Therefore,
[tex]\begin{gathered}step2: Find the angle GKJ, the angle subtended by the arc GJ
The angle GKJ is the angle subtended by the arc GJ at the center of the circle
Therefore,
[tex]<\text{GKJ }=\text{ m < GJ }=146^o[/tex]Step 3: Find m < GHJ
From Circle theorem, we know that the angle at the center of a circle is twice the angle at the circumference
Therefore,
[tex]\begin{gathered} <\text{GKJ }=2\timesHence, m 73°Step 4: Find m < GIJFrom Circle theorem, the angles in the same segment are equalTherefore,[tex]<\text{GIJ }=Hence, m < GIJ = 73°Find an equation of the line that goes through the points (7,8) and (4,-8). Write your answer in the form y=mx+b .y= x+ Preview m : ; Preview b : Write your answers as integers or as reduced fractions in the form A/B.Submit QuestionQuestion 2
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For this question we will use the two points formula for the equation of a line:
[tex]y-8_{}=\frac{-8-8}{4-7}(x-7)\text{.}[/tex]Solving for y we get:
[tex]\begin{gathered} y-8=\frac{-16}{-3}(x-7), \\ y-8=\frac{16}{3}x-\frac{112}{3}, \\ y=\frac{16}{3}x-\frac{112}{3}+8, \\ y=\frac{16}{3}x-\frac{88}{3}. \end{gathered}[/tex]Answer:
[tex]y=\frac{16}{3}x-\frac{88}{3}.[/tex]Using the slope formula, find the slope of the line through the given points (2,-1) and (6,1)
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Determine the slope of line pasing through points (2,-1) and (6,1).
[tex]\begin{gathered} m=\frac{1-(-1)}{6-2} \\ =\frac{1+1}{4} \\ =\frac{2}{4} \\ =\frac{1}{2} \end{gathered}[/tex]So slope of line is 1/2.
7-18When solving a problem about the perimeter of a rectangle using the 5-DProcess, Herman built the expression below.Perimeter = x + x + 4x + 4x feeta.Draw a rectangle and label its sides based on Herman's expression.b. What is the relationship between the base and height of Herman'srectangle? How can you tell?c.If the perimeter of the rectangle is 60 feet, how long are the base and heightof Herman's rectangle? Show how you know.
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a.
A rectangle has opposite side equal to each other . Therefore, it can be drawn below
perimeter = x + x + 4x + 4x
b.
The relationship between herman rectanngle base and height can be express below
[tex]\begin{gathered} 4\text{ times the height=base} \\ \text{let } \\ \text{height}=x \\ 4\times x=base \\ \text{base}=4x \end{gathered}[/tex]c.
perimeter = 60 feet
[tex]\begin{gathered} \text{perimeter}=x+x+4x+4x \\ 60=10x \\ x=\frac{60}{10} \\ x=6 \\ \\ \text{Base}=4x=4\times6=24\text{ f}eet \\ \text{height}=x=6\text{ f}eet \end{gathered}[/tex]What is the area of a circle with a radius of 4.6Area:
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The formula for the area of a circle with radius R is;
[tex]A=\pi(R^2)[/tex]With R = 4.6 units
[tex]\begin{gathered} A=\pi\times4.6^2 \\ A=66.48\text{ square units.} \end{gathered}[/tex]Therefore the area of the circle is 66.48 square units.
An experiment consists of rolling a dice. What is the probability of rolling anumber greater than 42 Express your answer as a fraction in simplest form.(Remember a dice has 6 sides numbering 1-6)O 1/2O 2/3O 1/3O 1/6
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We have to calculate the probability of getting a number greater than 4 when rolling a six-side dice.
We can calculate this probability as the ratio between the "successes" (getting a number greater than 4) and the total possible outcomes.
In this case, the only outcomes greater than 4 are "5" and "6", so we have two successful outcomes.
The total number of outcomes is 6 (1, 2, 3, 4, 5 and 6).
Then, the probability is:
[tex]P(X>4)=\frac{\text{success}}{\text{total}}=\frac{2}{6}=\frac{1}{3}[/tex]Answer: 1/3
a graph of a linear equation passes through (-2,0) and (0,-6)1. Use 2 points to sketch the graph of the equation2. is 3x-y=-6 an equation for this graph? (Yes or no question)3. Explain your reason of how you know
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1) So we can graph the point and join the points with a line so:
2) we can rewrite the equation in the form slope intercept so:
[tex]\begin{gathered} 3x-y=-6 \\ y=3x+6 \end{gathered}[/tex]So the answer is NO
3) because the intercept with the y axis is -6 no 6 so for that reason we know that is not the function