Answer:
Rational number, whole number, and integer
Step-by-step explanation:
Exact square roots: Rational, whole and integer
Non exact square roots: Irrational
The square root of 441 is 21, since 21² = 441.
So
Rational number, whole number, and integer
I need help with this practice Having troubleIf you can, use Desmos to graph the function
In general, given a function g(x)
[tex]undefined[/tex]The graph of the function y=f(x) is given. Find the domain of f(x).Using the graph given.
Given
Graph of the function y = f(x)
Find
domain of f(x)
Explanation
As we know domain of a function is all the values of x that makes the function defined.
here in the graph , the function is defines for x values 0 to 5
since , the point 0 and 5 is in open interval , so , the graph does not include the points 0 and 5
hence , the domain is (0 , 5)
Final Answer
Therefore , the domain of the given function is (0 , 5)
I need help with 17 pls I need an answer in explanation
Step 1
2n = 70
divide both sides by 2
[tex]\begin{gathered} \frac{2n}{2}=\frac{70}{2} \\ n\text{ = 35} \end{gathered}[/tex]Step 2
Make a conclusion based on step 1
If n = 3.5
Then substituting for n = 3.5 in the equation
[tex]\begin{gathered} 2(3.5)\text{ =7} \\ 7\text{ is not equal to 70} \end{gathered}[/tex]Therefore n = 3.5 is not a solution of the equation 2n = 70
0.4(5x-15)=2.5(x+3) solution is it infinitely or no solution or one solution
There is one solution to the equation
Here, we want to check the nature of the solution to the equation
We can start this by evaluating the equation;
[tex]\begin{gathered} 0.4(5x-15)\text{ = 2.5(x+3)} \\ 2x\text{ - 6 = 2.5x + 7.5} \\ 2.5x-2x\text{ = -6-7.5} \\ 0.5x\text{ = -13.5} \\ x\text{ = }\frac{-13.5}{0.5} \\ x\text{ = -27} \end{gathered}[/tex]As we can see, only a single solution exists for the equation
What diameter must a circular piece of stock be to mill a hexagonal shape with a side length of 2.7 in.?
Given:
A circular piece of stock be to mill a hexagonal shape with a side length of 2.7 in.
Required:
We need to find the diameter of hexagon.
Explanation:
now use the sin function
[tex]\begin{gathered} sin30=\frac{1.35}{r} \\ \\ \frac{1}{2}=\frac{1.35}{r} \\ \\ r=2.7 \end{gathered}[/tex]so by r
[tex]d=2r=5.4\text{ in}[/tex]Final answer:
Diameter of hexagon is 5.4 in
the sum of the first two terms of an arit
SOLUTION:
We are told that;
[tex]\begin{gathered} a+a+d=15 \\ a+2d+a+3d=43 \end{gathered}[/tex]Rewriting, we have;
[tex]\begin{gathered} 2a+d=15 \\ 2a+5d=43 \end{gathered}[/tex]Subtracting the first and second equations, we have;
[tex]\begin{gathered} 4d=28 \\ d=7 \end{gathered}[/tex]and;
[tex]\begin{gathered} 2a+7=15 \\ 2a=8 \\ a=4 \end{gathered}[/tex]Thus, the first four terms of the sequence are;
[tex]4,11,18,25[/tex]Graph y = (1/2)|x + 2| – 1 using transformations
First let's start with the graph of y = x:
Then, let's apply the "absolute value" operator: y = |x|
Then, we have an horizontal translation of 2 units to the left: y = |x + 2|:
Then, a vertical stretch by a factor of 1/2: y = (1/2)|x + 2|:
Finally, a vertical translation of 1 unit down: y = (1/2)|x + 2| - 1:
In exercises 3 and 4 , find the values of x and y.
Trigonometry and Triangles
To solve the problem, we need to recall the following:
* The sum of the interior angles in a triangle is 180°
* The sum of two supplementary angles is 180°
* The tangent of an acute angle in a right triangle is defined as:
[tex]\tan \theta=\frac{\text{opposite side}}{adjacent\text{ side}}[/tex]We included a new variable z to help solve the problem. Details below:
Angle 59° and angle z° are supplementary because they are a linear pair, thus:
z + 59 = 180
Solving for z:
z = 121
Now we focus on the left triangle with interior angles of 45°, z°, and x°. The sum of all three must be 180°, thus:
45 + 121 + x = 180
Solving for x:
x = 180 - 45 - 121
x = 14
Now focus on the bigger triangle (the one that contains two smaller triangles).
This triangle is right (it has one interior angle of 90°) and it's also an isosceles triangle because it also has one interior angle of 45°.
Any right triangle
identify the correct graph of the circle. (x + 3)² + (y + 1) = 16I have to send the graphs in message
The general form of a equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where:
r is the radius of the circle
(h,k) are the coordinates of the center of the circle
Then, the given equation:
[tex](x+3)^2+(y+1)^2=16[/tex]The radius and the coordinates of the center are:
[tex]\begin{gathered} r=4 \\ h=-3 \\ k=-1 \\ \\ \mleft(-3,-1\mright) \end{gathered}[/tex]Then, the graph for this circle is: Photo number 2
The equation we used today to represent a line is called _______ formFor the equation y=mx+b, m is the ______For the equation y=mx+b, b is the _______
1) The equation we used today to represent a line is called :
The slope-intercept form
In this form, y=mx +b
2) For the equation y=mx+b, m is the slope
It measures how steep is the line.
3) For the equation y=mx+b, b is the line coefficient
This is the point where the line intercepts the y coordinate.
Test ContentQuestion 110 PointsA box is 36 inches long, 18 inches wide, and 6 inches deep. How many cubic feet are in the box?A 5 cubic feetB4.5 cubic feet© 3 cubic feetD2.25 cubic feet
The box is 2.25 cubic feet (option D)
Explanation:length of the box = 36 inches
width = 18 inches
depth = height = 6 inches
To get the volume of the box in cubic feet, we need to first convert the dimensions from iches to feet to make it easy to solve.
conversion from iches to ft:
12 inches = 1 ft
36 inches = 36/12
= 3 ft
18 inches = 18/12
width = 18 inches = 3/2 ft
6 inches = 6/12
height = 6 inches = 1/2 ft
The box is a rectangular prism
Volume of rectangular prism = length × width × height
[tex]\begin{gathered} \text{Volume of the rectangular prism = 3 ft }\times\text{ }\frac{3}{2}\text{ ft }\times\text{ }\frac{1}{2}\text{ ft} \\ \text{Volume of the rectangular prism = 9/4 ft}^3\text{ = }2.25ft^3 \\ \\ \\ Volume\text{ of the box = 2.25 cubic f}eet\text{ (option D)} \end{gathered}[/tex]can you please help me solve angle 1 and 2
Angle 2 is 45 degrees. because DB bisects angle ABC
Angle 1 is 90 degrees. because DB bisects
plot the point on the line with the x-coordinate x = -9
Substituting x=-9 in the given equation we get:
[tex]-4(-9)+y-38=0.[/tex]Simplifying the above result, we get:
[tex]\begin{gathered} 36+y-38=0, \\ y-2=0. \end{gathered}[/tex]Adding 2 to both sides of the equation, we get:
[tex]\begin{gathered} y-2+2=0+2, \\ y=2. \end{gathered}[/tex]Therefore, the coordinates of the point with x=-9 are:
[tex](-9,2)\text{.}[/tex]Answer:
Triangle ABC is reflected across the y-axis and then dilated by a factor of 1/2 centered at the origin. Which statement correctly describes the resulting image, triangle DEF?
There are a number of transformations that can be used to alter the size and position of a shape. These include dilation, translation, reflection, and rotation.
Dilation can be either an enlargement, which results in an image that is larger than the original figure, or a reduction, which results in an image that is smaller than the original figure. If a dilation operation is performed on a shape, we will have a change in the lengths of the shape or the area covered. However, the angles of the shape remain the same since all the sides change by the same factor.
A reflection is a transformation that preserves both size and shape of a polygon or object. All that happens in a reflection is a change in the position and orientation of the shape.
If triangle ABC is dilated and reflected, any change in the side lengths is from the dilation. The angles are preserved, however, both by dilation and reflection.
The correct option is OPTION C.
7x+2=58 it wants you to solve
7x +2=58
7x = 58-2
7x = 56
x = 56/7
x = 8
Step 2 of 2: Use the discriminant b ^ 2 - 4ac to determine the number of solutions of the given quadratic equationThen solve the quadratic equation using the tormuisx = (- b plus/minus sqrt(b ^ 2 - 4ac))/(2a)
ANSWER
The value of x is 4
EXPLANATIONS;
Given that
[tex]\text{ -x}^2\text{ = - 8x + 16}[/tex]Re-write the quadratic function
[tex]-x^2\text{ + 8x - 16 = 0}[/tex]Recall, that the general form of quadratic function is given as
[tex]\text{ ax}^2\text{ + bx + c = 0}[/tex]Relating the two functions together
a = -1
b = 8
c = - 16
Determine the number of solutions first using the discriminant
[tex]\begin{gathered} \text{ D = b}^2\text{ - 4ac} \\ \text{ D = \lparen8\rparen}^2\text{ - 4 }\times(-1\text{ }\times\text{ -16\rparen} \\ \text{ D = 64 - 4\lparen16\rparen} \\ \text{ D= 64 - 64} \\ \text{ D = 0} \end{gathered}[/tex]Since D = 0 , then , the quadratic function has one real solution
Solve the equation using the general quadratic formula
[tex]\begin{gathered} \text{ x = }\frac{-b\text{ }\pm\sqrt{b^2\text{ - 4ac}}}{2a} \\ \\ \text{ x = }\frac{-8\text{ }\pm\sqrt{8^2\text{ - 4\lparen-1 }\times\text{ -16\rparen}}}{2\times-1} \\ \\ \text{ x }=\frac{-8\text{ }\pm\sqrt{64-\text{ 4\lparen16\rparen}}}{-2} \\ \\ \text{ x = }\frac{-8\text{ }\pm\sqrt{64\text{ - 64}}}{-2} \\ \text{ x = }\frac{-8\pm\sqrt{0}}{-2} \\ \\ \text{ x = }\frac{-8\pm0}{-2\text{ }} \\ \text{ x }=\text{ }\frac{-8\text{ - 0}}{-2\text{ }}\text{ or }\frac{-8\text{ + 0 }}{-2} \\ \text{ x = 4 or 4} \end{gathered}[/tex]Hence, the value of x is 4
what two consecutive whole numbers that 12 lie between [tex] \sqrt{12} [/tex]
Simplify the number to obtain the value in decimal.
[tex]\begin{gathered} \sqrt[]{12}=\sqrt[]{2\cdot2\cdot3} \\ =2\sqrt[]{3} \\ =2\cdot1.732 \\ =3.464 \end{gathered}[/tex]The value 3.464 lies between 3 and 4, which are also consecutive whole number.
So answer is 3 and 4.
the measure of an inclined angle between two sides is 45° and the measure of the sides are 5m and 8m. find the measure of the third side.
EXPLANATION
We can represent the states in the following picture:
We can apply a Trigonometric ratio in order to get the value of the third side, assuming that it is called x:
[tex]\sin45=\frac{Opposite\text{ cathetus}}{Hypotenuse}=\frac{x}{8}[/tex]Multiplying both sides by 8:
[tex]8*\sin45=x[/tex]Switching sides:
[tex]x=8*\sin45[/tex]Multiplying terms:
[tex]x=4\sqrt{2}[/tex]In conclusion, the measure of the third side is approximately equivalent to 4√2 or 5.65
what is the distance between (-7,2) and (1,-6)
The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(1-(-7))^2+(-6-2)^2} \\ d=\sqrt[]{8^2+8^2} \\ d=\sqrt[]{64+64} \\ d=\sqrt[]{128} \\ d=11.31 \end{gathered}[/tex]The answer would be d = 11.31
What is the first step in constructing this equilateral triangle?O A. Draw two circles with radius AB.B. Draw an angle with vertex A.C. Draw an angle with vertex C.D. Draw line segment AB.SUBMIT
The first step is draw line segment AB.
Using a graphing calculator to grab the support on an approximate square viewing window
For this problem, we are given the expression for a circle and we need to determine which graph represents it.
The expression for the circle is:
[tex]x^2+y^2=49[/tex]We can rewrite it as:
[tex]x^2+y^2=7^2[/tex]This means that the radius is equal to 7. So we need to find the circle that has a center in the origin and a radius equal to 7. The correct option is the bottom right option.
tan (θ) cot (θ)=1Trig: use trigonometric identities to transform the left side of the equation into the right side
1) Let's prove this identity
Since tan (θ) = sin(θ)/cos((θ)
And cot((θ) = cos ((θ)/sin((θ)
2) Let's plug it into:
[tex]\begin{gathered} \tan \text{ (}\theta)\cot \text{ (}\theta)\text{ =1} \\ \frac{\sin (\theta)}{\cos (\theta)}\cdot\frac{\cos (\theta)}{\sin (\theta)}=1 \\ 1=1 \end{gathered}[/tex]Simplifying (dividing) sin(θ) on the numerator, with sin (θ) on the denominator and similarly cos (θ) with cos(θ) we'll get to 1 over 1 time 1 over 1 = 1
Then 1=1
Events A and B are independent. Find the indicated Probability.P(A) = 0.4P(B) =P(A and B) = 0.2
From the statement, we know that:
• P(A) = 0.4,
,• P(A and B) = 0.2.
Because A and B are independent events, the probability of A and B is the product of the individual probabilities:
[tex]P(A\text{ and }B)=P(A)*P(B)\Rightarrow P(B)=\frac{P(A\text{ and }B)}{P(A)}.[/tex]Replacing the data of the problem, we get:
[tex]P(B)=\frac{0.2}{0.4}=0.5.[/tex]AnswerP(B) = 0.5
Kevin has money into savings accounts. One rate is 7% and the other is 8%, If he has $150 more than the 8% account and the total interest is $51 how much is invested in each savings account?
Let x be the total invested in at the 7% account and y the total invested at the 8% account.
Since he has $150 more than the 8% account, it implies that x + y = y + 150 and, therefore, x = $150
Since the total interest is $51, we have:
0.07x + 0.08y = 51
0.07*150 + 0.08y = 51
10.5 + 0.08y = 51
0.08y = 40.5
y = 40.5/0.08 = $506.25
Kevin has $150 at the 7% account and 506.25 at the 8% account.
Is -13, -6, 1, 8 arithmetic?
Given the following sequence
[tex]\lbrace-13,-6,1,8,\ldots\rbrace[/tex]We want to know if this sequence is arithmetic. The general term of an arithmetic sequence is given by
[tex]a_n=a_1+(n-1)d[/tex]Where d represents the common ratio. An arithmetic sequence increases by the same value every term(this value is the common ratio). If the difference between neighbor terms is the same for all of our terms, this sequence can be written as an arithmetic sequence.
Let's calculate the difference between the terms
[tex]\begin{gathered} a_2-a_1=-6-(-13)=-6+13=7 \\ a_3-a_2=1-(-6)=1+6=7 \\ a_4-a_3=8-1=7 \end{gathered}[/tex]Since the difference is the same, this sequence is Arithmetic.
Need help on homework
Answer:
The solution of the equation is;
[tex]x=-11[/tex]Explanation:
Given the equation;
[tex]6(x-6)+4=8x-10[/tex]Applying Distributive property of multiplication, we have;
[tex]\begin{gathered} 6(x)-6(6)+4=8x-10 \\ 6x-36+4=8x-10 \\ 6x-32=8x-10 \\ \text{collect the like terms, and solve;} \\ 8x-6x=+10-32 \\ 2x=-22 \\ x=\frac{-22}{2} \\ x=-11 \end{gathered}[/tex]Therefore, the solution of the equation is;
[tex]x=-11[/tex]1 plus 1 my little sister needs help
Answer:
[tex]1+1=2[/tex]Step-by-step explanation:
If you have one apple and you buy another one, you will have 2 apples. Therefore,
[tex]1+1=2[/tex]1. A car has a 16-gallon fuel tank. When driven on a highway, it has a gasmileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency")tells us the number of miles the car can travel for a particular amount of fuel(one gallon of gasoline, in this case). After filling the gas tank, the driver got ona highway and drove for a while.
Given:
Capacity of the car's fuel tank = 16 gallons
Gas mileage of car = 30 miles per gallon
Given that the driver filled the tank and got on a highway, let's solve for the following:
• (a) How many miles has the car traveled if it has the following amounts of gas left in the tank:
Use the expression:
[tex](16-g)\times30[/tex]Where g reresents the amount of gas left.
• 15 gallons:
If the car has 15 gallons left, to calculate the distance traveled, we have:
[tex]\begin{gathered} (16-15)\times30 \\ \\ =(1)\times30 \\ \\ =30\text{ miles} \end{gathered}[/tex]If the car has 15 gallons left, it has traveled for 30 miles.
• 10 gallons:
For 10 gallons, we have:
[tex]\begin{gathered} (16-10)\times30 \\ \\ =(6)\times30 \\ \\ =180\text{ miles} \end{gathered}[/tex]If the car has 10 gallons left, it has traveled for 180 miles.
• 2.5 gallons:
[tex]\begin{gathered} (16-2.5)\times180 \\ \\ =13.5\times180 \\ \\ =405\text{ miles} \end{gathered}[/tex]If the car has 2.5 gallons left, it has traveled for 405 miles.
• Part b.
Let's write an equation that shows the relationship between the distance traveled (d), and the amount of gas left in the tank in gallons(x).
To write the equation, we have:
[tex]d=(16-x)30[/tex]• Part C.
Let's find the amount of gallons left in the tank when the car has traveled the following distances:
• 90 miles:
[tex]\begin{gathered} x=16-\frac{90}{30} \\ \\ x=16-3 \\ \\ x=13\text{ gallons} \end{gathered}[/tex]If the car has traveled 90 miles, it will have 13 gallons left in the tank.
• 246 miles:
[tex]\begin{gathered} x=16-\frac{246}{30} \\ \\ x=16-8.2 \\ \\ x=7.8\text{ gallons} \end{gathered}[/tex]If the car has traveled for 246 miles, it will have 7.8 gallons left in the tank.
• Part d.
To write the equation, we have:
[tex]x=16-\frac{d}{30}[/tex]Answer:
Step-by-step explanation:
For 90 :
90/x = 30
x=90/30
x=3 gallons
For 246 :
246/x=30
x=246/30
x=8.2 gallons
what is a equation to find interest.
The formula to find the simple interest is the following:
[tex]A=P(1+rt)[/tex]Where P is the principal amount, r is the interest rate, t is the time and A is the Future value
Robert is paid $12.00 per hour to chop firewood he chops 40% of the pile of firewood in 3/4 of an hour at this rate how much will Robert be paid to chop the entire pile of firewood?
Robert chops 40% of the pile of firewood in 3/4 of an hour.
Then, we would chop 80% of the pile of firewood in 2*(3/4)=3/2 hours.
where 3/2 = 1.5 hours
Also, he would chop the missing 20% in (3/4)/2=3/8.
The full work is for 3/8+3/2 =15/8 hours
Now, if one hour is paid $12.00, we can use the rule of three to know how much is paid for 15/8 hours:
1h-----------$12.00
15/8 h -------- $x
where x=(12.00*5/8)/1
x=22.50
Hence, Robert will be paid $22.50 to chop the entire pile of firewood.