The inequality that corresponds to the following expression, "A is less than 9" is:
[tex]A<9[/tex]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.
True 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.
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
half 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?
The following table shows the cost of apples. Number of 3 5 8 11 Apples (2) $2.37 Cost (y) $3.95 $6.32 $8.69 Assume the cost of apples is a linear function of the number of apples purchased. 39 www Wwwwwwwwwwwwwwww B Part A www Write a linear equation that describes the cost of apples, y, in dollars, as a linear function of the number of apples purchased, I.
We will calculate the linear equation, first we need to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
3=x1
5=x2
2.37=y1
3.95=y2
[tex]m=\frac{3.95-2.37}{5-3}=\frac{1.58}{2}=0.79[/tex]then we will substitute in the next formula
[tex]y-y_1=m(x-x_1)[/tex][tex]\begin{gathered} y-2.37=0.79(x-3) \\ y-2.37=0.79x-2.37 \\ y=0.79x \end{gathered}[/tex]the linear equation is
y=0.79x
the table displays the scores of students on a recent exam find the mean of the scores to the nearest tenth
In this case, the number of students refers to frequencies.
To find the mean, we have to use the following formula
[tex]\begin{gathered} \bar{x}=\frac{\Sigma(x\cdot f)}{N}=\frac{65\cdot4+70\cdot1+75\cdot7+80\cdot5+85\cdot8+90\cdot3+95\cdot4+100\cdot1}{33} \\ \bar{x}=\frac{260+70+525+400+680+270+380+100}{33} \\ \bar{x}=\frac{2685}{33} \\ \bar{x}\approx81.4 \end{gathered}[/tex]Hence, the mean is 81.4.Type the correct answer in the box.
Find the value of x in the figure.
Answer:
x = 35
Step-by-step explanation:
An hexagon has 6 sides, so (n-2) is 4, and the internal angles add up to 180° × 4 = 720°
so
4x - 5 + 117 + 3x - 3 + 3x + 6 + 118 + 4x - 3 = 720
14x + 230 = 720
14x = 720 - 230
14x = 490
x = 490 : 14
x = 35
Answer:
x=35
Step-by-step explanation:
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Answer:
x = -1
y = 3
Step-by-step explanation:
.............
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 minutesFind 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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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.
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
1. Which of the following expressions are monomials with degree 2?i) 2x² + 2xii) 2x²iii) x²iv) 2xa. ii and iiib. ii and ivC.iii and iv
Answer
a. ii and iii
Step-by-step explanation
A monomial is a polynomial with only one term.
A binomial is a polynomial with two terms.
The degree of a polynomial is determined by the highest exponent of the x-variable.
i) 2x² + 2x
type: binomial
degree: 2
ii) 2x²
type: monomial
degree: 2
iii) x²
type: monomial
degree: 2
iv) 2x
type: monomial
degree: 1
Then, choices ii and iii are monomials with degree 2
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
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 surface area. Leave your answers in terms of T.9 mi
Given:
The shape is
Find-:
The surface area of the cylinder
Explanation-:
The surface area of the cylinder
[tex]A=2\pi rh+2\pi r^2[/tex]Where,
[tex]\begin{gathered} r=\text{ Radius} \\ \\ h=\text{ Height} \end{gathered}[/tex]The radius and height of the cylinder
[tex]\begin{gathered} r=\frac{\text{ Diameter}}{2} \\ \\ r=\frac{12}{2} \\ \\ r=6\text{ mi} \\ \\ h=9\text{ mi} \end{gathered}[/tex]The surface area of the shape is:
[tex]\begin{gathered} A=2\pi rh+2\pi r^2 \\ \\ A=2\pi(6)(9)+2\pi(6)^2 \\ \\ A=108\pi+72\pi \\ \\ A=180\pi\text{ mi}^2 \end{gathered}[/tex]The surface area is 180π mi²
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.
Find the x-and y-intercepts.27x + 3y =-54
The x intercept of a line is where i
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].
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
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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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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.
. Ross has a spinner that is split into eight equal sections numbered 1 through 8. He spun the spinner 1120 times. Which of the following would be a good estimate of the number of times the spinner landed on number 6?
The probability of the spinner landing on number 6 is calculated as follows:
[tex]\begin{gathered} p=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ p=\frac{1}{8} \end{gathered}[/tex]Given that he spun the spinner 1120 times
√-144
Real number or not real number
Answer:
not a real number
Step-by-step explanation:
Non-real numbers are also called imaginary numbers. Imaginary numbers possess an imaginary component, which exists after taking the square root (or any even root) of a negative number
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)
Large SmallBlue 17 3Red 8 12?Find: P(Small and Blue)Remember to reduce your answer.
What is the range of the function
Answer:
[tex]\{ y\; |\; 0 \leq y < 9 \}[/tex]
Step-by-step explanation:
The range of a function is the set of all possible output values (y-values).
From inspection of the given graph:
Minimum value of y = 0Maximum value of y = 9As there is an open circle where y = 9, this means the value is not included in the range.
Therefore, the range of the function is:
[tex]\{ y\; |\; 0 \leq y < 9 \}[/tex]
Find the inverse of the function below. When typing your answer use the "^" key (shift+6) to indicate an exponent. For example, if we have x squared (x times x) we would type x^2. f(x)= \frac{5x+1}{2-5x}The numerator of f^{-1}(x) is Answer - AnswerThe denominator of f^{-1}(x) is Answer(Answer + Answer)
Answer:
[tex]\begin{gathered} \text{ The numerator of f}^{-1}(x)\text{ is 1-2x} \\ \text{ The denominator of f}^{-1}(x)\text{ is -5(x}+1) \end{gathered}[/tex]Step-by-step explanation:
To find the inverse of a function, replace f(x) by ''y'', then replace ''y'' with and x, and every x with a ''y''. Solve for y.
[tex]\begin{gathered} f(x)=\frac{5x+1}{2-5x} \\ Replace\colon\text{ f(x)}\rightarrow y \\ y=\frac{5x+1}{2-5x} \\ Replace\colon\text{ y}\rightarrow x\text{ x}\rightarrow y \\ x=\frac{5y+1}{2-5y} \\ \text{ Solve for y.} \\ x(2-5y)=5y+1 \\ 2x-5yx=5y+1 \\ -5yx=5y+1-2x \\ -5yx-5y=1-2x \\ y(-5x-5)=1-2x \\ y=-\frac{1-2x}{5x+5} \\ y=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex][tex]\begin{gathered} Replacey\colon f^{-1}(x) \\ f^{-1}(x)=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex]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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