The difference of a number x and 7 is less than or equal to the sum of the same number x and 5
The difference means subtraction.
A number is x
Less than or equal is represented with the symbol ≤
So:
The difference of a number x and 7
x-7
is less than or equal to the sum of the same number x and 5
≤ x+5
Altogether:
x-7≤ x+5
An observer stands 400 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of 300 ft/sec. Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 300 ft from the ground?
Let's draw the scenario to understand it better:
From the figure, the information given are:
[tex]\frac{dy}{d\text{t}}=\text{ 300 ft./sec}[/tex]Question:
[tex]\text{What is }\frac{dD}{dt}\text{ at y = }300\text{ ft.}[/tex]Step 1: We write a function that relates the quantities in the diagram using Pythagorean
Theorem.
[tex]\text{ 400}^2\text{ + }y^2=D^2[/tex]Step 2: Differentiate with respect to t.
[tex]2y\frac{dy}{dt}=\text{ }2D\frac{dD}{dt}[/tex]Now we wish to plug in specific numbers for every quantity in the above equation except for dD/dt. However, we notice that we don’t have a specific value for D at y = 400 ft. So first we need to find D at y = 400 ft. using the Pythagorean Theorem.
[tex]400^2\text{ + }300^2=D^2[/tex][tex]D\text{ = }\sqrt[]{400^2+300^2}[/tex][tex]D\text{ = 500 ft.}[/tex]Step 3: Finish the problem by plugging in numbers for every quantity in the equation
containing dD/dt.
[tex]2(300)(300)\text{ = 2(500)}(\frac{dD}{dt})[/tex][tex]\frac{dD}{dt}=\text{ }\frac{2(300)(300)}{2(500)}[/tex][tex]\frac{dD}{dt}=\text{ }\frac{180,000}{1000}[/tex][tex]\frac{dD}{dt}=180[/tex]Conclusion: When the rocket is 300 ft. feet from the ground, the distance between the observer and the rocket is increasing at a rate of 180 ft./sec.
Points XX and ZZ are on a number line, and point YY partitions \overline{XZ}
XZ
into two parts so that the ratio of the length of \overline{XY}
XY
to the length of \overline{YZ}
YZ
is 5:75:7.
The coordinate of XX is 1.31.3, and the coordinate of YY is 3.83.8. What is the coordinate of ZZ?
If a point divides two other points in any ratio m : n, then the coordinate of the point dividing the given two points can be known using section formula. The coordinate of the point ZZ on the number line is (4.06, 8.46).
What is section formula?Section formula is used in Coordinate geometry to find the ratio between two points on a line given one another point on the line.
Given that,
The ratio XZ : XY : YZ = 5 : 75 : 7
The coordinates of XX are (1.31, 3) and of YY are (3.83, 8).
Since YY is partitions the point XX and ZZ. In order to find the the coordinates of ZZ section formula can be used as below,
x = (m₁x₂ + m₂x₁) ÷ (m₁ + m₂) and y = (m₁y₂ + m₂y₁) ÷ (m₁ + m₂)
Here, m₁ : m₂ is equal to XY : YZ which can be known from the given ratio as,
XY : YZ = 75 : 7
=> m₁ : m₂ = 75 : 7
=> m₁ = 75 and m₂ = 7.
Suppose the coordinates of XX, YY and ZZ are (x₁, y₁), (x, y) and (x₂, y₂) respectively.
Substitute the respective values in the section formula to get,
3.83 = (75x₂ + 7 × 1.31) ÷ (75 + 7)
=> (75x₂ + 7 × 1.31) = 82 × 3.83
=> 75x₂ = 82 × 3.83 - 7 × 1.31
=> x₂ = (82 × 3.83 - 7 × 1.31) ÷ 75
=> x₂ = 4.06
And,
8 = (75y₂ + 7 × 3) ÷ (75 + 7)
=> (75y₂ + 7 × 3) = 82 × 8
=> 75y₂ = 82 × 8 - 7 × 3
=> y₂ = (82 × 8 - 7 × 3) ÷ 75
=> y₂ = 8.46
Thus, ( x₂, y₂) is equal to (4.06, 8.46).
Hence, the coordinate of ZZ is given by (4.06, 8.46).
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QuesQuestion 3 (1 point)Let sin (47) = 0.7314. Enter an angle (B), in degrees, where cos (B) = 0.7314.Answer:Blank 1:Next PageBack
Solution
Let sin (47) = 0.7314. Enter an angle (B), in degrees,
[tex]sin(47)=0.7314[/tex]where cos (B) = 0.7314 means
[tex]\begin{gathered} sin(A)=cos(90-A) \\ let\text{ A = 47} \\ sin(A)=cos(90-47) \\ sin(A)=cos43 \end{gathered}[/tex]since the vaule of sin(A) = 0.7314
Hence the cos(B) = cos43 = 0.7314
The angle of B = 43°
Which transformation produces a similar but incongruent figure?
Similar means that the figure has the same shape, but not neccesarily the same size. It is said, also, that it is incoungruent, so it definetly doesn't have the same size. A transformation that gives you a similar but incongruent figure is a dialation, rotation and/or translation. I'll do a drawing to illustrate:
Notice that I've done the three of them. I have the same figure, smaller, in another position and rotated.
Make the following conversions. Round your answers to 2 decimal places, if necessary.7 feet 6 inches toa. Inches: in.b. Feet: ft
So we need to express 7 ft 6 in in inches and in feet. For this purpose is important to remember this relation:
[tex]1ft=12in[/tex]So in a we need to express 7ft 6in in inches. This means we must convert the 7ft into inches and then add the result to 6in. If we use the rule of thre we get:
[tex]\begin{gathered} 1ft\rightarrow12in \\ 7ft\rightarrow x \\ \text{Where }x=\frac{7ft\cdot12in}{1ft}=84in \end{gathered}[/tex]Then we get:
[tex]7ft+6in=84in+6in=90in[/tex]So the answer to part a is 90in.
For part b we can take the result of part a and convert it into feet. Using the rule of three again we get:
[tex]\begin{gathered} 12in\rightarrow1ft \\ 90in\rightarrow x \\ \text{Where }x=\frac{90in\cdot1ft}{12in}=7.5ft \end{gathered}[/tex]Then the answer to part b is 7.5ft.
Donovan has 5 times as many as red fish as he does blue fish and half as many gray fish as blue fish. How many total fish (F) does Donovan have?answer optionsF = 6x + 1/2xF = 1/2x + 5 + xF = 6 + 1/2xF = 5x + 1/2x
Donavan has 6x + 1/2 x total number of fishes.
Let Donovan has x number of blue fishes.
Hence the number of red fishes = 5x
The number of gray fishes = 1/2 of x = 1/2 x
Total number of fishes = red + blue + gray = 5x + x + 1/2 x = 6 + 1/2 x
For something like an equation to have any importance, the coefficient involving at least any variable must not be 0. In actuality, the following equation would either be inconsistent (for b ≠ 0) and have no solution, or full n-tuples are solutions, as was mentioned for one variable, if any variable does actually have a zero coefficient.
A regular polynomial over such a field, from which the coefficients are drawn, can also be equalized to zero to produce a linear equation. Since linear equations typically do a good job of representing non-linear systems, they are used extensively in all branches of mathematics as well as in physics and engineering.
Therefore we can infer that Donavan has 6x + 1/2 x total number of fishes.
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How do I do pi equations?
Given:
The objective is to explain the method of solving pi equations.
The term with pi can be solved
According to one study, an average payout for slots machines is 84 cents on each dollar. What is the percent return on every dollar spent in playing slots?The percent return on every dollakspent in playing slots is %.
Given that the average payout for slots machines is 84 cents on each dollar.
We know that
[tex]100\text{ cents = 1 dollar}[/tex]The cost of return for every dollar spent is 100-84=16 cents.
The percent return on every dollar spent in playing slots is
[tex]=\frac{16}{\text{one dollar}}\times100=\frac{16}{100}\times100=16\text{ \%.}[/tex]The percent return on every dollar spent in playing slots is 16%.
how do I find the linear change
In order to find the rate of change of the given line, use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are two points of the line.
From the given graph you can select any pair of points, for example:
(x1,y1) = (2,400)
(x2,y2) = (4,1200)
replace the values of the previous coordinates in the formula for m:
[tex]m=\frac{1200-400_{}}{4-2}=\frac{800}{2}=400[/tex]Hence, the rate of change is 400
Which of the percentage of the female population is made up by the age of group 5- 9?
Given,
The data of the male and female for different age group is shown in question tab.
Required:
The percentage of the female population is made up by the age of group 5- 9.
From the given data,
It is clearly seen that the percentage of female for 5 - 9 age group is 11%.
Hence, the percentage is 11%.
hey, can someone please help me? i really need it!
Iterative rule for the sequence 7,21 , 63,189
It is a geometry sequence, it solution is going to be:
[tex]a_n=a_0*number^{n-1}[/tex]In this case
[tex]\begin{gathered} a_0=7\text{ } \\ number\text{ is going to be } \\ number=3 \end{gathered}[/tex]Sustituing:
[tex]a_n=7*(3)^{n-1}[/tex]This is the answer, so when n=1
[tex]\begin{gathered} a_1=7*(3)^{1-1}=7 \\ a_2=7(3)^{2-1}=7*3=21 \end{gathered}[/tex]Write the expression in simplest form.[tex] \sqrt{49 {x}^{5} } [/tex]
Answer:
[tex]=7x^2\sqrt[]{x}[/tex]Explanation:
Given the expression:
[tex]\sqrt{49x^5}[/tex]First, the expression can be rewritten in the form below:
[tex]\begin{gathered} =\sqrt[]{49\times x^5} \\ By\text{ multiplication of surds: }=\sqrt[]{mn}=\sqrt[]{m}\times\sqrt[]{n} \\ =\sqrt[]{49^{}}\times\sqrt[]{x^5} \end{gathered}[/tex]Next, we simplify:
[tex]\begin{gathered} =\sqrt[]{7^2}\times\sqrt[]{x^4\times x} \\ =7\times\sqrt[]{x^4}\times\sqrt[]{x} \\ =7\times x^2\times\sqrt[]{x} \end{gathered}[/tex]The simplest form of the expression is:
[tex]=7x^2\sqrt[]{x}[/tex]round to the nearest whole number. 65.73
66
1) To round it off to the nearest whole number, let's consider that:
65.73 is > 65.5 then we can round it up
2) Hence, 65.73 after rounding it up is 66 and that's the answer.
The one-to-one functions g and h are defined as follows.g(x) = 4x - 3h={(-6, 3), (-4, 7), (3, -8), (6, 4)Find the following
It is given that
[tex]g(x)=4x-3[/tex]Now to find the inverse of g
Let
[tex]\begin{gathered} y=4x-3 \\ 4x=y+3 \\ x=\frac{y+3}{4} \end{gathered}[/tex]So
[tex]g^{-1}(x)=\frac{x+3}{4}[/tex]Now we know that
[tex](g^{-1}.g)(x)=\text{ x}[/tex]So
[tex](g^{-1}.g)(2)=2[/tex]And since
[tex]h(-6)=3[/tex]So
[tex]h^{-1}(3)=-6[/tex]identify the transformation from the pre-made to the image
You can notice that each point of both images are at the same distance of the origin of coordinates. It means that the transfromation is a reflection across the line y = x
answer: reflection across y = x
what is the profit in dollar and cents that the store makes per sweater?p=26s
Given the expression:
[tex]p=26s[/tex]if 'p' represents the profit in dollar and 's' represents the number fo sweaters that the store sells, then we have that the store makes 26 dollars per sweater.
We can see this since the equation is the same as a linear function with rate of change m:
[tex]y=mx[/tex]Paul is driving his car. At the end of two hours he has driven 68 miles, then at the end of 4 hours he has driven 132 miles. What is his average rate of change?_(blank)_miles per hourType your numerical answer below.
This problem describes two points in a route of 4 hours. He went through 68 miles after the first two hours, and 132 miles after 4 hours of driving. We need to calculate the average rate of change.
The average rate of change is the division between the total distance and the time it took to travel that distance, so we have:
[tex]r=\frac{132}{4}=33\text{ miles per hour}[/tex]The average rate of change is equal to 33 miles per hour.
If LM = 14 and MN = 11, what is KM?Write your answer as a whole number or as a decimal rounded to the nearest hundredth
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
LM = 14
MN = 11
KM = ?
Step 02:
We must apply the triangle rules to find the solution.
Pythagoras Theorem
LM² = LN² + MN²
(14)² = LN² + (11)²
(14)² - (11)² = LN²
[tex]LN\text{ = }\sqrt[]{196-121}[/tex]LN = 8.66
[tex]\frac{LN}{MN}=\frac{KN}{LN}[/tex][tex]\frac{8.66}{11}=\frac{KN}{8.66}[/tex]8.66 * 8.66 = 11 * KN
6.818 = KN
KM = KN + MN
KM = 6.818 + 11 = 17.818
The answer is:
The value of KM is 17.82
i inserted a picture of the question which is question 7, i can give you the answer to the previous question which is question 6 if it helps
The first thing we have to know is that the trinomial (polynomial of three terms) is called a perfect square trinomial, the polynomial that when factorized gives us a perfect squared expression in the following way
[tex]a^2+2ab+b^2=(a+b)^2[/tex][tex]\begin{gathered} w^2-3w=350 \\ a=1 \\ 2ab=-3 \\ b=-\frac{3}{2} \\ b^2=\frac{9}{4} \end{gathered}[/tex][tex]\begin{gathered} w^2-3w-\frac{9}{4}=350-\frac{9}{4} \\ w^2-3w-\frac{9}{4}=347.75 \\ (w-\frac{3}{2})^2=347.75 \end{gathered}[/tex][tex](w-\frac{3}{2})^2-\frac{1409}{4}=0\to\text{answer}[/tex]Explain how you know and i'll mark as brainlist.
Answer: They have the same area.
Step-by-step explanation:
Here you just have to count the small squares.
In the blue shape, you can see there are 16 small squares.
And in the green shape, there is also 16 squares.
And the small squares are all equal.
So they both have the same area.
Which economic system has no government involvement in the market? a. capitalism b. communism c. socialism d. No economic system is free from government involvement.
Answer Is D
The economic system that has no government involvement in the market is d. No economic system is free from government involvement.
Why there is no economic system is free from government involvement?In reality there is no government intervention because at some point the government will comes in , this could actually be mininmal, only in the free market is where there is no government intervention.
It should be noted that in this free market, there is an unregulated system of economic exchange, where the act of taxes collection as well as quality controls, has no economic interventions which can be attributed to government .
Therefore option D is correct.
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3.Six Flags charge and entrance fee per person and a fee per every ride that you get on. When 6 teachers went to Six Flags and rode on 20 rides total, they ended up paying $350. When 15 people went to Six Flags and rode on 47 rides they paid $900. Write an expression for this situation.
Answer:
Step-by-step explanation:
Expression:
y = mx + n*b
In which m is the cost per ride and b is the entrance fee.
y is the total cost, x is the number of rides and n is the number of people.
When 6 teachers went to Six Flags and rode on 20 rides total, they ended up paying $350.
This means that:
20m + 6b = 350
When 15 people went to Six Flags and rode on 47 rides they paid $900.
This means that:
47m + 15b = 900
Solving the system:
20m + 6b = 350
47m + 15b = 900
Multiplying the first equation by -5, the second by 2.
-100m - 30b = -1750
94m + 30b = 1800
-6m = 50
The length of a rectangular rug is 4 less than twice its width. The perimeter of the rug is 34 feet. What is the area?
My first step is always to draw a picture
We are told the length is 4 less than twice the width
l = 2w-4
We are told the perimeter is 34
P =2(l+w)
Substitute the first equation in for l
P = 2( 2w-4 + w)
Combine like terms
34 = 2( 3w-4)
Distribute the 2
34 = 6w -8
Add 8 to each side
34+8 = 6w-8+8
42 = 6w
Divide by 6
42/6 = 6w/6
7 =w
Now we can find l
l = 2w-4 = 2(7) -4 = 14-4 = 10
The question asks for the area
A = l*w = 10 *7 = 70
Figure DEFG is a parallelogram.If m
Given
DEFG is a parallelogram and
Answer
Since adjacent angles of parallelogram are supplementary
D+E = 180
30 + E = 1`80
E = 180- 30 = 150
I am struggling on figuring out how to do this. Please help me
Given:-
[tex]f(x)=13x+2[/tex]To find the inverse of the function.
So now we change the value of x in the given function as y and find the value of y. so we get,
[tex]x=13y+2[/tex]Now we find the value of y. so we get,
[tex]\begin{gathered} 13y+2=x \\ 13y=x-2 \\ y=\frac{x-2}{13} \end{gathered}[/tex]So the required solution is,
[tex]y=\frac{x-2}{13}[/tex]Please help me with this problem for my son to understand thank you.Factor completely.36x^4+18x^3+40x^2Enter your answer in the box.
The expression is given to be:
[tex]36x^4+18x^3+40x^2[/tex]Rewrite the terms so that we can factorize the common terms out:
[tex]\begin{gathered} 36x^4\Rightarrow2x^2\cdot18x^2 \\ 18x^3\Rightarrow2x^2\cdot9x \\ 40x^2\Rightarrow2x^2\cdot20 \end{gathered}[/tex]Therefore, the expression can be rewritten to be:
[tex]2x^2\cdot18x^2+2x^2\cdot9x+2x^2\cdot20[/tex]Since there is a common term, 2x², we can factorize to give:
[tex]\Rightarrow2x^2(18x^2+9x+20)[/tex]The quadratic function in the parentheses cannot be factored further.
Therefore, the answer is:
[tex]2x^2(18x^2+9x+20)[/tex]What is the domain of the function shown below? f(x) = log, (x-3) O A. All real numbers greater than 0 O B. All real numbers O c. All real numbers greater than 3 D. All real numbers greater than or equal to -2
Given the function:
[tex]f(x)=\log _5(x-3)[/tex]the domain of the function is all the possible values of x that can be substituted into the function f(x)
for the log functions:
x - 3 > 0
x > 3
So, the domain of the function is all real numbers greater than 3
so, the answer will be option C
6(x-1)=3x+6+3x what is the solution?Many solution No solution or One solution
To solve this equation, we can follow the next steps:
First: we can sum similar terms like 3x + 3x.
6(x - 1) = 3x + 3x + 6
6(x - 1) = 6x + 6
Then, solve 6(x-1) using the distributive property:
6x - 6 = 6x + 6
Subtract 6x from both sides of the equation:
6x - 6x - 6 = 6x - 6x + 6
0 - 6 = 6
-6 = 6
Since the result is not congruent, we can say that this equation has no solution.
I'll send pic of equation
Given the following functions:
f(x) = 3x
g(x) = x + 4
h(x) = x^2 - 1
Before simplifying g(f(-1)), let's first determine f(-1).
f(x) = 3x
f(-1) = 3(-1)
f(-1) = -3
g(x) = x + 4
g(f(-1)) = (-3) + 4
= -3 + 4
g(f(-1)) = 1
Therefore, the answer is 1.
Which of the following is the value of y that solves the system of equations shown below?
(1) -5
(3) 6
3x + 4y = 16
(2) 8
(4) -2
x + y =16
Answer:
(4) -2
Explanation:
Given the system of equations:
[tex]\begin{gathered} 3x+4y=16 \\ x+y=6 \end{gathered}[/tex]Set x as the subject in the second equation: x=6-y
Substitute x=6-y into the first equation:
[tex]\begin{gathered} 3x+4y=16 \\ 3(6-y)+4y=16 \\ 18-3y+4y=16 \\ y=16-18 \\ y=-2 \end{gathered}[/tex]The value of y that solves the system of equations is -2.