in the figure below, two seconds are drawn to a circle from exterior point H. Suppose that HW=72, HZ=9, and HX=14.4. Find HY.
When two secants are arranged in the form of the picture the segments must obey the following rule:
[tex]HX\cdot HY=HZ\cdot HW[/tex]Applying the data from the problem we have:
[tex]\begin{gathered} 14.4\cdot HY=9\cdot72 \\ HY=\frac{9\cdot72}{14.4} \\ HY=45 \end{gathered}[/tex]The length of HY is 45.
here is the continuity checklist to use1.The function is defined at x = a; that is, f(a) equals a real number.2.The limit of the function as x approaches a exists.3.The limit of the function as x approaches a is equal to the function value at x = a.
Notice that
[tex]f(-5)=\frac{2(-5)^2+3(-5)+1}{(-5)^2+5(-5)}=\frac{50-15+1}{0}=\frac{36}{0}\rightarrow\text{ undefined}[/tex]Therefore, f(-5) is not a real number.2) Calculating the limit when x->a from the left and right,
[tex]\lim_{x\to-5^+}f(x)=\lim_{x\to-5^+}\frac{2x^2+3x+1}{x^2+5x}=\lim_{x\to-5^+}\frac{2x^2+3x+1}{x(x+5)}\approx\frac{36}{-5(\epsilon)}\approx\frac{36}{-5\epsilon}\rightarrow-\infty[/tex]Because x^2+5x=x(x+5), and approaching from the right (x+5)>0; therefore, in the limit f(x)->-infinite
ϵ is a small positive number that approaches zero as a->-5
Similarly, in the case of approaching x->-5 from the left,
[tex]\lim_{x\to-5^-}f(x)\approx\frac{36}{-5(-\epsilon)}\approx\infty[/tex]Therefore, since the limits approaching x->-5 from the left and right are not the same,
the limit of f(x) when x->-5 does not exist.The function is not continuous at x=a and, furthermore, the limit of f(x) when x->-5 does not exist.Find the slope of the line graphed below. 4- 3 3- 2-+ + 3 - 3 -5 - 2 2 4 5 -1 -27 - 3. 5
We are going to find the slope with the slope formula and the points (-2,1) and (2,4) (taken from the graph)
[tex]m=\frac{y2-y1}{x2-x1}=\frac{4-1}{2-(-2)}=\frac{3}{4}[/tex]The answer is equal to 3/4
square root of 0.0625
hello
the square root of 0.0625
[tex]\sqrt[]{0.0625}=0.25[/tex]the square root of 0.0625 is 0.25
this is square root symbol
square of a particular number is always that number multiplied by itself
for example, the square of 2 = 2 * 2 = 4
square of 3 = 3 * 3 = 9
square of 10 = 10 * 10 = 100
now to find the reverse of this, we normally use a calculator but there's a method to do this without a calculator.
step 1
separate the number into two
step 2
now we need to find an integer whose square is less or equal to the left hand side of the divided number i.e (00)
in this case the number is 0
Note: i've already explained how to find the squares of numbers for you
now
1 Expandts implify:(X+2)(-x +3X-7 +x)
Given the following expression:
[tex]\mleft(x+2\mright)(-4x^2+3x-9+x^4)[/tex]Let's simplify;
Applying the PEMDAS Rule (Parenthesis, Exponent, Multiplication, Division, Addition and Subtraction).
Step 1: Simplify first the equation within the parenthesis.
[tex](x+2)(-4x^2+3x-9+x^4)[/tex][tex](x+2)\text{ = (x + 2) ; already in simplified form}[/tex][tex](-4x^2+3x-9+x^4)\text{ = }(x^4-4x^2+3x-9)\text{ ; already in simplified form}[/tex]Step 2: Proceed with the multiplication.
[tex](x+2)(x^4-4x^2+3x-9)\text{ }[/tex][tex](x)(x^4-4x^2+3x-9)\text{ = }\mleft(x^4\mright)\mleft(x\mright)-(4x^2)(x)+(3x)(x)-(9)(x)=x^5-4x^3+3x^2\text{ - 9x}[/tex][tex](2)(x^4-4x^2+3x-9)\text{ = }(x^4)(2)-(4x^2)(2)+(3x)(2)-(9)(2)=2x^4-8x^2+6x-18[/tex]Step 3: Let's add the product of x and 2 being multiplied to -4x^2+3x-9+x^4.
[tex](x+2)(x^4-4x^2+3x-9)\text{ }[/tex][tex](x)(x^4-4x^2+3x-9)\text{ + }(2)(x^4-4x^2+3x-9)[/tex][tex](x^5-4x^3+3x^2\text{ - 9x) + }(2x^4-8x^2+6x-18)[/tex][tex]x^5-4x^3+3x^2\text{ - 9x + }2x^4-8x^2+6x-18[/tex][tex]x^5\text{+ }2x^4-4x^3+3x^2\text{ }-8x^2\text{- 9x }+6x-18[/tex][tex]x^5\text{+ }2x^4-4x^3-5x^2\text{-3x}-18[/tex]Therefore, the product of (x+2) (-4x^2+3x-9+x^4) is x^5 + 2x^4 -4x^3 -5x^2 -3x - 18.
A triangle has two sides of length 13 and 7. What is the smallest possible whole-numberlength for the third side?
ANSWER
6
EXPLANATION
We want to find the smallest possible length of the third side.
To do this, we apply the Triangle Inequality Rule.
It states that the sum of the two sides of a triangle must be greater than or equal to the length of the third side.
Let the length of the third side of the triangle be x.
This could then mean 3 things:
[tex]\begin{gathered} 13+7\ge x \\ 13+x\ge7 \\ x+7\ge13 \end{gathered}[/tex]Now, we have to solve each of them to find the least possible value of x:
[tex]\begin{gathered} \cdot20\ge x\Rightarrow x\le20 \\ \cdot x\ge7-13\Rightarrow x\ge-6 \\ \cdot x\ge13-7\Rightarrow x\ge6 \end{gathered}[/tex]The first option cannot work because then we are dealing with the greatest possible value of x as 20.
The second option cannot work because x cannot be a negative value.
The third option is valid.
Therefore, the smallest possible value of the length of the third side of the triangle is 6.
If (x, 24, 25) is a Pythagorean triple what is the value of x?
A Pythagorean triple consists of 3 positive integers a,b and c such that
[tex]a^2+b^2=c^2[/tex]Then, by substituting the given information into the last result, we get
[tex]x^2+24^2=25^2[/tex]which gives
[tex]x^2+576=625[/tex]By subtracting 576 to both sides, we obtain
[tex]x^2=49[/tex]By taking square root to both sides, we get
[tex]x=7[/tex]Therefore, the answer is: x=7
find a polynomial function of lowest degree with rational coefficients
Since -5i is a zero, then its complex conjugate +5i is also a zero of the function.
Therefore,
x + 5i, x - 5i , and x - 3 are factors of the polynomial.
Hence, the polynomial function, P(x), of the lowest degree with rational coefficients is given by
[tex]P(x)=(x+5i)(x-5i)(x-3)[/tex]Which implies that
[tex]\begin{gathered} P(x)=(x^2-(5i)^2)(x-3)=(x^2-25i^2)(x-3) \\ \text{ Since i}^2=-1,\text{ then we have} \\ P(x)=(x-3)((x^2+25)=x^3+25x-3x^2-75 \end{gathered}[/tex]Hence the polynomial is
[tex]P(x)=x^3-3x^2+25x-75[/tex]Write an expression for the volume of a rectangularprism if the length is 25 cm shorter than some given amount, x, and the width is 14 cm longer than x and the height is x cm.
The volume of a prism is given by:
[tex]V=lwh[/tex]We know that the height is x. The length is 25 shorter than x, this can be express as:
[tex]x-25[/tex]The width is 14 longer than x, this can be express as:
[tex]x+14[/tex]Plugging the expressions for the length, the width and the height we have that:
[tex]\begin{gathered} V=(x-25)(x+14)x \\ V=x(x-25)(x+14) \end{gathered}[/tex]Therefore, the volume of the prism is:
[tex]V=x(x-25)(x+14)[/tex]A fast boat to Japan travels at a constant speed of 18.95 miles per hour for 350 hours. How far was the voyage?
we have the following:
[tex]\begin{gathered} v=\frac{d}{t} \\ d=v\cdot t \end{gathered}[/tex]replacing:
[tex]\begin{gathered} d=18.95\cdot350 \\ d=6632.5 \end{gathered}[/tex]The answer is 6632.5 miles
SHOW THE EQUATION YOU SET UP10% of what number is 90?
Recall that the x% of y can be computed using the following expression:
[tex]y\cdot\frac{x}{100}\text{.}[/tex]Now, let n be the number such that its 10% is 90, then we can set the following equation:
[tex]90=n\cdot\frac{10}{100}\text{.}[/tex]Simplifying the above equation we get:
[tex]90=\frac{1}{10}n\text{.}[/tex]Multiplying the above equation by 10 we get:
[tex]\begin{gathered} 90\times10=\frac{1}{10}n\times10, \\ n=900. \end{gathered}[/tex]Answer:
Equation:
[tex]\frac{1}{10}n=90.[/tex]Number: 900.
The function h(x) = 2|x| is a transformation of the absolute value parent function, f(x) = 1 xl. Which graph shows h(x)?
Answer:
C.
Explanation:
We can answer the question if we graph some points of both functions f(x) and h(x). So, we can use the following table:
x f(x) h(x)
-1 |-1| = 1 2|-1| = 2
0 |0| = 0 2|0| = 0
1 | 1 | = 1 2 | 1 | = 2
So, we can graph both functions as:
Therefore, the answer is C.
It's A
have to get 20 characters.
The cost to rent a car is $25 plus an additional $0.15 for each mile the car is driven. How many miles was a car driven if it had a bill of $71.80?479645454312Please explain the answer.
Since the form of the linear equation is
[tex]y=mx+b[/tex]m is the rate of change
b is the initial amount
Since the cost of the rental car is $25 and $0.15 for each mile, then
The initial amount is 25 dollars
b = 25
The rate of change is 0.15 dollars per mile
m = 0.15
Then the equation is
[tex]T.C=0.15x+25[/tex]T.C is the total cost
x is the number of miles
Since the given total cost is $71.80
Then T.C = 71.8
[tex]71.8=0.15x+25[/tex]Subtract 25 from both sides
[tex]\begin{gathered} 71.8-25=0.15x+25-25 \\ \\ 46.8=0.15x \end{gathered}[/tex]Divide both sides by 0.15
[tex]\begin{gathered} \frac{46.8}{0.15}=\frac{0.15x}{0.15} \\ \\ 312=x \end{gathered}[/tex]The car was driven for 312 miles
The answer is the last option
Type the correct answer in each box. Use numerals instead of words. Consider the systems of equations below. System A System B System C I2 + y2 = 17 y = 12 - 70 + 10 = y = – 2229 - 1 2 3 - y = -65 + 5 &r - y = -17 Determine the number of real solutions for each system of equations. System A has real solutions. System B has real solutions. System C has real solutions.
A) Given:
[tex]\begin{gathered} x^2+y^2=17\ldots\ldots\ldots\text{.}(1) \\ y=-\frac{1}{2}x\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]To find: The number of real solutions
Explanation:
Substitute equation (2) in (1), we get
[tex]\begin{gathered} x^2+(-\frac{1}{2}x)^2=17 \\ x^2+\frac{x^2}{4}=17 \\ \frac{5x^2}{4}=17^{} \\ x^2=\frac{68}{5} \\ x^2-\frac{68}{5}=0\ldots\ldots.(3) \end{gathered}[/tex]Here,
[tex]a=1,b=0,\text{ and c=-}\frac{68}{5}[/tex]So, the discriminant is,
[tex]\begin{gathered} \Delta=b^2-4ac \\ =0-4(1)(-\frac{68}{5}) \\ =54.4 \\ >0 \end{gathered}[/tex]Since the discriminant is greater than zero.
Hence, it has two real solutions
Final answer:
System A has two real solutions.
Solve for y-5y> -20 PLEASE HURRY
-5y > -20
Absolute value, there are 2 solutions:
-5y>-20 and -5y< 20
-5y>-20
Divide both sides by -5
-5y/-5 < -20/-5
y< 4
-5y < 20
Divide both sides by -5
-5y/-5 > 20/-5
y > -4
how to do translate points?
Given a point (x,y) on the coordinate plane, the following are the transformation rules in translation.
Case 1
If you translate a point left by k units, we have the transformation rule:
[tex](x,y)\rightarrow(x-k,y)[/tex]Case 2
If you translate a point left by k units, we have the transformation rule:
[tex](x,y)\rightarrow(x-k,y)[/tex]Which function has a domain of {x | x > 8}? O f(x)=√x-8 + 1 x X8 O f(x) = x+8 -1 O f(x) = -1 + 8 1 +8 O f(x) = VX+1-8
Solution
- The question asks us which of the options has the domain specified below:
[tex]\mleft\lbrace x\mright|x\ge8\}[/tex]- The domain just simply refers to all the possible values of x the function can take without being undefined.
- We have been told that the domain is any x value that is greater than or equal to 8. This means that the domain contains values
[tex]8,9,10,11,12,13,\ldots[/tex]- Thus, we simply need to test each option with a number NOT in the range of numbers given above and see if the result of f(x) gives us a defined number. If it does, then, the function has a domain wider than x ≥ 8. However, if the function becomes undefined for all real numbers, then the function has a domain of exactly x ≥ 8.
- These operations are done below:
[tex]\begin{gathered} \text{ For these tests, we can use }x=0\text{ since }x=0\text{ is not in the range }x\ge8 \\ \\ \text{Option 1:} \\ f(x)=\sqrt[]{x-8}+1 \\ f(0)=\sqrt[]{0-8}+1 \\ f(0)=\sqrt[]{-8}+1 \\ \text{ Since }\sqrt[]{-8}\text{ is not a real number, this function is the correct answer} \\ \\ \\ \text{Thus,} \\ f(x)=\sqrt[]{x-8}+1\text{ is the Answer} \end{gathered}[/tex]- After testing just one value, we have been able to find an option that satisfies our condition
Final Answer
The final answer is
[tex]f(x)=\sqrt[]{x-8}+1\text{ (OPTION 1)}[/tex]Use point-slope form to write the equation of a line that passes through the point (−20,−4) with slope -4/3
→Given slope, m = -4/3
and (x;y) intercepts = (-20,-4)
we will use the following formula.
Y = mx +c
y = -4/3x +c
→We need to find the y intercep (c) , by plugging in the (x;y) = (-20;-4)
-4 = -4/3(-20) +c
-4 = (80/3) +c
-4 -(80/3) = c
therefore c = -92/3
→Finally, our equation will be :
y = -4/3x -92/3
Can you pls help me with this question thank you
r j
9 6
15 12
21 18
The correct option is C
Explanation:Given that the relationship is represented by:
r = j + 3
The only option that correlates with this relationship is:
r j
9 6
15 12
21 18
Every r is 3 more than the corresponding j
find the volume of a cylinder the length of its height is 6ft and the diameter of its base is 6ft long
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Cylinder
diameter = 6 ft
height = 6 ft
volume = ?
Step 02:
V = π * r ² * h
r = d / 2
r = 6 ft / 2 = 3 ft
V = π * (3ft)² * 6ft
V = 169.65 ft ³
The answer is:
The volume of the cylinder is 169.65 ft ³
Please help w/ logarithms and if you do not know how to solve just let me know and I'll exist the session :)
From the first table, we have;
Given that;
[tex]f(x)=b^x[/tex]But, table II gives;
Given that;
[tex]g(x)=\log _b(x)[/tex]Where b is same positive constant for both equations.
Recall from a law of logarithm that;
[tex]\text{If }\log _ba=c,\Leftrightarrow a=b^c[/tex]Thus;
[tex]\begin{gathered} g(x)=\log _b(x) \\ x=b^{g(x)} \\ \end{gathered}[/tex][tex]f(x)=7,x=1.404[/tex]Also;
from the second table;
[tex]x=10,g(x)=1.661[/tex]10. Give the formula for Area of the Rectangle below * Square Rectangle b a a a a a Perimeter = 4a b Perimeter = 2a+2b Triangle Circle а. C G b Perimeter = a+b+c Perimeter = 2tr
the formula for the area of a rectangle is multiply the basis by the height. So in this case we get
[tex]A=b\mathrm{}a[/tex]What is the quotient of 3.201 x 109 and 4.85 x 10expressed in scientific notation?
5. 47 divided by 5 =
9.4
Explanation:47 divided by 5 = 47/5
In fraction:
47/5 = 9 2/5
In decimal, 9 2/5 = 9 + 0.4
47/5 = 9.4
Solve for x
5/7(x+2)-3/7x=2/7(x+5)
Infinite
No solution
x=1
x=3
Answer:
infinite
Step-by-step explanation:
[tex]\frac{5}{7}(x+2)-\frac{3}{7}x=\frac{2}{7}(x+5) \\ \\ 5(x+2)-3x=2(x+5) \\ \\ 5x+10-3x=2x+10 \\ \\ 2x+10=2x+10[/tex]
Since we get an identity, there are infinitely many solutions.
A museum curator is hanging 9 paintings in a row for an exhibit. There are 6 Renaissance paintings and 3 Baroque paintings. From left to right, all of the Renaissance paintings will be hung first, followed by all of the Baroque paintings. How many ways are there to hang the paintings?
Answer:
4,320ways
Step-by-step explanation:
We are given the following from the questions
Number of paintings = 9
Renaissance paintings= 6
Baroque paintings = 3
Since they are hanging from left to right and we will first hang Renaissance painting before baroque painting, hence;
For Renaissance painting, this can be done in 6! ways
6! = 6*5*4*3*2*1
6! = 720ways
Similarly for Baroque painting, this can be done in 3! ways
3! = 3*2*1
3! = 6ways
The total number of ways to hang the painting = 6!*3!
The total number of ways to hang the painting = 720 * 6
The total number of ways to hang the painting = 4,320ways
Hence there are 4,320ways to hang the paintings
n the circle below, if arc AC = 60 °, and arc BD = 148 °, find the measure of < BPD.
Using the diagram below, the angles of intersecting chords theorem states that
Then,
[tex]\begin{gathered} \Rightarrow\angle1=\frac{1}{2}(\angle arc(AB)+\angle arc(CD)) \\ and \\ \angle2=\frac{1}{2}(\angle arcBC+\angle arcDA) \end{gathered}[/tex]Furthermore, since angles <1 and <3, and <2 and <4 are two pairs of vertical angles,
[tex]\begin{gathered} \angle1\cong\angle3 \\ and \\ \angle2\cong\angle4 \end{gathered}[/tex]Thus, in our case,
[tex]\angle BPD=\frac{1}{2}(\angle arcAC+\angle arcBD)=\frac{1}{2}(60+148)=104[/tex]Therefore, the answer is 104°, option d.Can you give me the answer and explain to me thank you
SOLUTION
Part 1
Even though a strong linear relationship exists between the number of churches and the number of homicides it does not suggest that building new churches increases the number of homicides.
Part 2
A strong positive linear correlation coefficient was obtained due to the presence of a lurking variable that is, a variable that is not included as an explanatory or response variable in the analysis but can affect the interpretation of relationships between variables.
A lurking variable can falsely identify a strong relationship between variables or it can hide the true relationship. For example, a research scientist studies the effect of diet and exercise on a person's blood pressure. Lurking variables that also affect blood pressure are whether a person smokes and stress levels.
In the case of the question, the lurking variable could be an increase in population in the cities. It could affect your interpretation of the relationship between the explanatory and response variables.
The ____ of 14 and 7 is 7.1. difference2. product3. sum4. Quotient
The difference between 14 and 7 is 7
The correct option is OPTION 1
Product, Sum, and Quotient donot fulfil the relationship that the 14 and 7 have in the question.
Only DIFFERENCE does.
14 - 7 = 7
So, "difference" is what the correct answer is.
Question 1. To make a quilt, a quilter is buying fabric in two colors, blue and green.The quilter needs at least 9.5 yards of fabric in total.• The blue fabric costs $9 a yard.The green fabric costs $13 a yard.The quilter can spend up to $110 on fabric.Let represent the number of blue yards of fabric purchased and let y represent the number of green yards of fabricpurchasedThe inequalities that represent the constraints in this situation arex + y ≥ 9.59x + 13y ≤ 110
1.
From the graphs we can see:
[tex]\begin{gathered} x=\frac{27}{8}=3.375 \\ y=\frac{49}{8}=6.125 \end{gathered}[/tex]So, he can purchase 3.375yd of blue fabric and 6.125yd of green fabric
2. Because the solution represents the values which satisfies the system of equations, a different value will result in an absurd answer