The answer is true
the number 8 is a whole number
so
is an integer
a number that can be written without a fractional component is an integer
A natural number is an integer greater than 0
-2+{-3-[7+4(-2+5)]}-4
Answer:
- 28
Step-by-step explanation:
-2 + { -3 - [ 7 + 4·( -2 + 5 ) ] } - 4
1)
( -2 + 5 ) = 3
2)
[ 7 + 4·3 ] = [ 7 + 12 ] = 19
3)
{ -3 - 19 } = - 22
4)
- 2 + ( -22) - 4 = -2 - 22 - 4 = - 28
Luther opened a savings account and deposited $400.00. The account earns 4% interest,compounded annually. If he wants to use the money to buy a new bicycle in 2 years, howmuch will he be able to spend on the bike?nt= P(1+7)1Use the formula A = P (1 + r/n)where A is the balance (final amount), P is the principal(starting amount), r is the interest rate expressed as a decimal, n is the number of times peryear that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.
To solve this problem, we must use the formula:
[tex]A=P\cdot(1+\frac{r}{n})^{t\cdot n}\text{.}[/tex]Where:
• A = final amount = ?,
,• P = starting amount = $400.00,
,• r = interest rate in decimals = 4% = 0.04,
,• n = number of times per year that the interest is compounded = 1 (because interest is compounded annually),
,• t = time in years = 2.
Replacing the data of the problem in the equation above, we get:
[tex]A=400.00\cdot(1+0.04)^2=432.64.[/tex]Answer
After 2 years, he will be able to spend $432.64 on the bike.
Large SmallBlue 17 3Red 8 12?Find: P(Small and Blue)Remember to reduce your answer.
4) Find the area of each composite figure. 2.5 in 2.5 in 6 in in? 4.2 in А = square A trapezoid ina А figure 1/1
The figure is a combination of a square and a trapezoid;
Thus, we first look for the area of a square using the formula below;
[tex]\begin{gathered} A_{square}=length\times length \\ \text{Where the length of the square is 2.5in} \\ A_{square}=2.5\times2.5 \\ A_{square}=6.25in^2 \end{gathered}[/tex]Answer: The area of the square is 6.25 square inches.
Also, we find the area of the trapezoid using the formula below;
[tex]\begin{gathered} A_{trapezoid}=\frac{1}{2}(a+b)h \\ \text{Where a and b are the upper length and the bottom length respectively } \\ a\text{ is the length of the square = 2.5in} \\ b=\text{ 4.2in} \\ \text{h is the height = 6in} \\ A_{trapezoid}=\frac{1}{2}(2.5+4.2)6 \\ A_{trapezoid}=3(6.7) \\ A_{trapezoid}=20.1in^2 \end{gathered}[/tex]Answer: The area of the trapezoid is 20.1 square inches.
[tex]\begin{gathered} A_{figure}=A_{square}+A_{trapezoid} \\ A_{figure}=6.25in^2+20.1in^2 \\ A_{figure}=26.35in^2 \end{gathered}[/tex]Answer: The area of the figure is 26.35 square inches.
A line passes through point (2, 5) and has a slope of 3. Write an equation in Ax +By=C form for this line. Use integers for A, B, and C.
Answer:
[tex]3\, x + (-1)\, y = 1[/tex].
Step-by-step explanation:
Both the slope of this line and the coordinates of a point on this line are given. Therefore, start by finding the point-slope equation of this line: if the slope of a line in a plane is [tex]m[/tex], and this line goes through a point at [tex](x_{0},\, y_{0})[/tex], the point-slope equation of this line will be [tex](y - y_{0}) = m\, (x - x_{0})[/tex].
The slope of the line in this question is [tex]m = 3[/tex]. It is given that this line goes through the point [tex](2,\, 5)[/tex], where [tex]x_{0} = 2[/tex] and [tex]y_{0} = 5[/tex]. Substitute in these values to find the point-slope equation of this line:
[tex](y - y_{0}) = m\, (x - x_{0})[/tex].
[tex](y - 5) = 3\, (x - 2)[/tex].
Rewrite this point-slope equation in the requested format:
[tex]y - 5 = 3\, x - 6[/tex].
[tex]3\, x - 6 = y - 5[/tex].
[tex]3\, x = y + 1[/tex].
[tex]3\, x - y = 1[/tex].
[tex]3\, x + (-1)\, y = 1[/tex].
The table below shows the total number of drink sales at the football game last Saturday in the first hour: Drinks and number (45 Lemonade) (31 Fruit Punch) (47 Bottled Water) (27 Ice Tea) What percent of the drink sales came from lemonade and ice tea combined? A 42% 54% D 46%
Total number of drinks sold = 45 + 31 + 47 +27 = 150
Lemonade and ice tea = 45 +27 = 72
Divide the number of lemonades and ice tea drinks sold, by the total number of drinks sold.
72 / 150 = 0.48
Multiply by 100
0.48 x 100 = 48% (option A)
You, Newton, and Descartes walk dogs to earn spending money this summer. You spend 2 times as many minutes walking dogs as Newton. Descartes spends 3 times as many minutes walking dogs as Newton. You, Newton, and Descartes spend 3,030 minutes walking.dogs altogether. How many minutes does Newton walk dogs?
You, Newton, and Descartes walk dogs to earn spending money this summer. You spend 2 times as many minutes walking dogs as Newton. Descartes spends 3 times as many minutes walking dogs as Newton. You, Newton, and Descartes spend 3,030 minutes walking.dogs altogether. How many minutes does Newton walk dogs?
Let
x -----> minutes does Newton walk dogs
y ----> minutes does Descartes walk dogs
z ----> minutes does you walk dogs
so
z=2x ------> equation A
y=3x ------> equation B
x+y+z=3,030 ------> equation C
substitute equation A and equation B in equation C
x+(3x)+(2x)=3,030
solve for x
6x=3,030
x=505 minutes
therefore
the answer is
Newton walk dogs 505 minuteshalf of the sum of six and three then divided by seven.
Answer:
0.64285714285
Step-by-step explanation:
6+3=9
9 divided by 2= 4.5
4.5 / 7= 0.64285714285
I don't think this is what you're looking for?
1 1 A company has budgeted 5 1/3hours to complete a project, with 1/4 of the time spent on research. How much time does the company plan to spend on research? Express your answer as a mixed number.
In order to determine the time for research, calculate one quarter of the time spend in the project of the company.
Express the time for the project as a normal fraction, as follow:
5 1/3 = 5/1 + 1/3 = (15 + 1)/3 = 16/3
Next, multiply 1/4 (one quarter) by the previous fraction 16/3:
(1/4)·(16/3) = 16/12
simplify the previous fraction:
16/12 = 4/3
as a mixed number the previous result is:
4/3 = 1 1/3
consider the equation showing the distributive property 84+93=3(28+□)
We have that the distributive property states that the multiplication is done for all the terms inside the parenthesis. Then we have:
Since
3 · 28 = 84
and
3 · □ = 93
Since 3 · 31 = 93, then
□ = 31
Answer: 31Graph 8x - 4y = 16, then find its x-intercept & y-intercept.
The y-intercept of an equation is where its graph intersects the y-axis - this happens at x = 0; therefore, putting in x =0 should give us the y-intercept.
Putting in x = 0 gives
[tex]8(0)-4y=16[/tex][tex]\rightarrow-4y=16[/tex][tex]\therefore y=-4.[/tex]Hence, the y-intercept is y = -4.
The x-intercept of an equation is where its graph intersects the x-axis - this happens where y = 0; therefore, the x-intercept is found by putting in y =0:
[tex]8x-4(0)=16[/tex][tex]\rightarrow8x=16[/tex][tex]\therefore x=2.[/tex]Hence, the x-intercept is x = 2.
The graph is attached below.
Graph the line with slope of -4/5 and on the x intercept of 3
Solution
Note: Equation of a Line os given as
[tex]y=mx+c[/tex]We are given that the slope is -4/5
That is m = -4/5
[tex]y=-\frac{4}{5}x+c[/tex]It has x intercept of 3, that is the point (3, 0)
Substituting we have
[tex]\begin{gathered} y=-\frac{4}{5}x+c \\ 0=-\frac{4}{5}(3)+c \\ c=\frac{12}{5} \\ Thus,\text{ we have} \\ y=-\frac{4}{5}x+\frac{12}{5} \end{gathered}[/tex]The graph of the line is
Find the exact value and the approximate value of the area of the triangle
From the big triangle we know that:
[tex]\begin{gathered} x^2+y^2=12^2 \\ x^2+y^2=144 \end{gathered}[/tex]From the triangle on the right we also know that:
[tex]h^2+9^2=y^2[/tex]From the triangle on the left we know:
[tex]3^2+h^2=x^2[/tex]Adding the last two equations we have that:
[tex]\begin{gathered} x^2+y^2=h^2+9^2+h^2+3^2 \\ x^2+y^2=2h^2+90 \end{gathered}[/tex]Equating the last equation with the first one we have that:
[tex]\begin{gathered} 2h^2+90=144 \\ 2h^2=144-90 \\ 2h^2=54 \\ h^2=\frac{54}{2} \\ h^2=27 \\ h=\sqrt[]{27} \end{gathered}[/tex]Then, the height of the triangle is the squared root of 27.
Once we know the height we can calculate the area.
[tex]\begin{gathered} A=\frac{1}{2}bh \\ =\frac{1}{2}12\sqrt[]{27} \\ =6\sqrt[]{27} \end{gathered}[/tex]Therefore the exact value of the area is:
[tex]6\sqrt[]{27}[/tex]This can be approximated to (rounding on the hundreths):
[tex]31.18[/tex]Please help me with this math question
Answer:
145
Step-by-step explanation:
168-23 = 145
i hope this helps :)
Refer to the figure below for 12-14. 15 in. bumper sticker 3.5 in. 12. Find the perimeter of the sticker.
The perimeter of a rectangle is the sum of its 4 sides:
[tex]P=15in+15in+3.5in+3.5in=37in[/tex]Then, the perimeter of the bumper sticker is 37 inchesTrue or False? The denominator is the top number, or the part ofthe whole that is being talked about.
In a fraction, we have that the top number is the numerator and the bottom number is the denominator.
Also, in a mixed number, we have a whole number together with a fraction, but the denominator still is the bottom number of the fraction
So the statement of the question is FALSE.
The geometric mean is 10 between 25 and what number ?
EXPLANATION
A special form of average is the Geometric Mean, where we sum the numbers together and then take a square root (for two numbers), cube root (for three numbers), etc.
The geometric mean between 10 and 25 is equal to:
sqrt(10*25)= 15.81
Answer is 5*sqrt(10) or 15.81
Write the equation of the line that passes through the given point and is parallel to the given line.
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The height of the object based on the information is 1963 feet.
How to calculate the height?It should be noted that a function is important to show the relationship between the variables given in the data.
In this case, the function given for the height of the object is given as:
h = 16t² + 1899
where t = time
When the time is 2 seconds, the height will be:
h = 16t² + 1899
h = 16(2)² + 1899
h = 64 + 1899
h = 1963
The height is 1963 feet.
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write an equation that demonstrates the relationship between x and y for the points plotted on the coordinate grid
The relationship between x and y points is a linear relationship of the form:
y = mx + b
where m is the slope of the line, and b is the coordinate y for the y-intercept.
Now, by definition, we have that the slope of the line is given by:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2,Y2) are given points on the graph.
In our case, we can take
(X1, Y1) =(2,-1)
(X2,Y2) = (3,2)
then, te slope of the line would be:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}\text{ = }\frac{2-(-1)}{3-2}\text{ = }\frac{2+1}{1}=\text{ 3}[/tex]then m = 3 and the new equation for our graph would be:
y = 3x+b
Now, to find b, take any point (x,y) on the graph. In this case, for example
(x,y) = (3,2) and replace this point in the above equation:
2= 3(3) + b
solve for b:
2-9 = b
then b = -7 and we can conclude that the equation for our graph is:
y = 3x-7
Which is more, 10 meters or 100 decimeters? 10 meters 100 decimeters neither; they are equal
Answer: They are both equal
1 meter = 10 decimeter
We need to convert 100 decimeters to meters
1 meter = 10 decimeter
x meter = 100 decimeter
Cross multiply
x * 10 = 1 x 100
10x = 100
Divide both sides by 10
10x/10 = 100/10
x = 10 meters
Hence, 10 meters is equal to 100 decimeter
Answer: They are both equal
PLS HELP!! and can you also break it down for me. thx ;)
solve for x. 4x^2+3=-7x
Answer: -1 -3/4
Step-by-step explanation:
1.Move terms to the left side
4x^{2}+3=-7x
4x^{2}+3-\left( -7x\right) =0
2.Rearrange terms
4x^{2}+3+7x=0
4x^{2}+7x+3=0
3.Use the quadratic formula
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
4x^{2}+7x+3=0
4.Simplify
Evaluate the exponent
Multiply the numbers
Subtract the numbers
Evaluate the square root
Multiply the numbers
-7+1/8
5.Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x=\frac{-7+1}{8}
x=\frac{-7-1}{8}
6.Solve
Rearrange and isolate the variable to find each solution
x=-\frac{3}{4}
x=-1
Using the unit circle, what is the exact value of tang?O AA.2OB. 13C. VSO D.3
Given the function:
x^2 + 2x - 8
x^2 - 2x - 8
we are to find the zeros of the function.
To find the zero of a function, we find the root of the numerator.
That is, equsting the numerator to zero
x^2 + 2x - 8 = 0
lets get factor of the above eqaution
= x^2 - 2x + 4x + 8
x(x-2) + 4(x-2) = 0
so,
x + 4 = 0 OR x - 2 = 0
x + 4 = 0
x = -4
OR
x - 2 = 0
x = 2
so, x = -4, 2
Therefore the zeros of the function x^2 + 2x - 8 are -4, 2
x^2 - 2x - 8
So, the correct option is D which is -4, 2
The mean of 6 numbers is 7.
The numbers are in the ratio 1 : 1 : 3 : 4 : 5 : 7.
Find the range
The range of the given data set is 6.
What is the range?The gap between the largest and smallest numbers is known as the range. The average of the largest and smallest number is the midpoint. The range is the range of values, from lowest to highest. Example: The lowest value in 4, 6, 9, 3, and 7 is 3, and the highest value is 9. The range is therefore 9 3 = 6.So, the range is:
As we can observe that the ratios are already given in ascending order, then we don't need to solve the question.Instead, just subtract the lowest ratio from the highest ratio as follows:
7 - 1 = 6
Therefore, the range of the given data set is 6.
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The function P(x)=x3−2x2 is dilated by the function I(x)=P(4x).Which function rule represents I(x)?
Given
[tex]P(x)=x^3-2x^2[/tex]And
[tex]I(x)=P(4x)[/tex]To find the value of I(x).
Explanation:
It is given that,
[tex]P(x)=x^3-2x^2[/tex]Then,
[tex]\begin{gathered} I(x)=P(4x) \\ \Rightarrow I(x)=(4x)^3-2(4x)^2 \\ \Rightarrow I(x)=64x^3-2(16x^2) \\ \Rightarrow I(x)=64x^3-32x^2 \end{gathered}[/tex]Hence, the answer is I(x)=64x³-32x².
triple c, then raise to the 10th power
Given the word expression:
Triple c, then raise to the 10th power.
Here the exponent of triple c is 10.
To express the above, we have:
[tex]\begin{gathered} \text{Triple C = (3c)} \\ \\ \text{Raised to the power of 10 = (3c)}^{10} \end{gathered}[/tex]Thus, we the expression below:
[tex](3c)^{10}^{}[/tex]ANSWER:
[tex](3c)^{10}[/tex]indicate the maximum or minimum of value of f(x) whichever exists.
The given function is
[tex]f(x)=x^2-2x-5[/tex]All quadratic functions represent a parabola. If the quadratic term is positive, the parabola opens up, if the quadratic term is negative, the parabola opens down.
In this case, we observe a positive quadratic term, so the parabola opens up, which means the function has a minimum.
To find the minimum of the function, we need to find its vertex (h,k), where
[tex]h=-\frac{b}{2a}[/tex]a = 1 and b = -2.
[tex]h=-\frac{-2}{2(1)}=\frac{2}{2}=1[/tex]Then, evaluate the function to find k.
[tex]f(1)=(1)^2-2(1)-5=1-2-5=1-7=-6[/tex]The k-coordinate of the vertex refers to the minimum value.
Therefore, the answer is -6.
Find the value if n in improper fraction.
The value of n will be equal to -7/2 or [tex]-4\frac{1}{2}[/tex].
This question can be solved using the Laws of exponents. We have the expression 1/8 ÷ √2 = 2ⁿ. We can rearrange this expression as follows
1/(8×√2) = 2ⁿ
We can also write this as
1/(2³·2^1/2) = 2ⁿ
From laws of exponents if bases are same then the powers get add up that is
1/(2^7/2) = 2ⁿ
2^-7/2 = 2ⁿ
From laws of exponents, we compare that the bases are same so the powers will also be same. So, we find that n = -7/2 which can be written in improper fraction as [tex]-4\frac{1}{2}[/tex].
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There are 13 candidates for homecoming king and 14 candidates for homecoming queen. How many possible outcomes are there for homecoming king and queen ?
Answer:
welll
Step-by-step explanation:
Well we know theres only gonna be one king and one queen so the outcome can be that the other people will obviously not get to be king or queen and the other people will get jealous (im not really sure if im right sory)
Find the x-and y-intercepts.27x + 3y =-54
The x intercept of a line is where i
