Answers
Answer:
x = 11
Step-by-step explanation:
Given 2 secants to a circle from an external point , then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
7(7 + x) = 6(6 + 15) ← distribute left side
49 + 7x = 6 × 21 = 126 ( subtract 49 from both sides )
7x = 77 ( divide both sides by 7 )
x = 11
Related Questions
Let n be the number of five-digit positive integers which are divisible by 36 and have their tens digit and unit digit equal. Find n/100
Answers
Answer:
1.) 10044
2.) 100.44
Step-by-step explanation:
Since n is a number of five-digit positive integers which are divisible by 36, start multiplying 36 by number. Starting from 278.
Five digits numbers start from multiplying 36 by 278. Any multiplication below 278 by 36 will give four digits numbers.
36 × 278 = 10,008
36 × 279 = 10,044
10,044 tens digit and unit digit equal. Therefore n = 10044
To find n/100, divide 10044 by 100
10044 / 100 = 100.44
6. Alex and Brian park their bikes side-by-side. Alex leaves to visit friends, and Brian leaves 30 minutes later,
headed for the same destination. Alex pedals 5 miles per hour slower than Brian. After 1 hour, Brian passes Alex. At
what speed are they each pedaling?
Answers
Answer:
See below.
Step-by-step explanation:
When Brian passes Alex they both have travelled the same distance.
Call this distance d.
Let the speed that Brian passes = x miles/hour.
Distance = speed * time so:
For Alex:
d = (x - 5) * 1.5 ( Alex cycles for 1 + 30 minutes = 1.5 hours)
For Brian:
d = x * 1
So substituting d = x in Alex's equation:
x = 1.5(x - 5)
x = 1.5x - 7.5
7.5 = 0.5x
7/5 / 0.5 = x
15 = x.
ANSWER:
Brian's speed is 15 miles/hour.
Alex's speed is 15 - 5 = 10 miles/hour.
If a wheel has a radius of 5cm
how much is one rotation of the wheel
How many rotations can the wheel do within a distance of 50km
Answers
Answer:
circumference = 2*PI*radius
circumference = 2 * PI * 5 cm
circumference = 31.4159265358979 cm
50 km = 500,000 centimeters
rotations = 500,000 / 31.4159 cm
15,915.51 rotations
Step-by-step explanation:
G is a transformation of f. What is the formula of g in terms of f?
A. [tex]-\frac{1}{2}f(x)[/tex]
B. -2f(x)
C. f ([tex]-\frac{1}{2}x[/tex])
D. f(-2x)
Answers
Answer:
C
Step-by-step explanation:
First, we can see that from f(x) to g(x), the change in x for each change in y is significantly increased. This represents a stretch in the x direction. A stretch/compression in the x direction is represented by
f(cx), with c > 1 representing a compression by c and 0 < c < 1 representing a stretch by a value of 1/c. From the vertex of each, when y changes by 1, in f(x) x changes by 2 (e.g. from x=2 to x=4), whereas in g(x) x changes by 4 (e.g. from x=-4 to x=0). Therefore, g(x) stretches x by 2, so c = 1/2, giving us
f(c(x))
= f(1/2(x))
Let's say f(a) = f(1/2(x))
Then, because the graph stretched by 2, the vertex goes from x=2 to x=4. Our vertex is at x=-4 in g(x), so to make the vertex equal to that, we can flip f(a) around the y axis. To flip this around the y axis, we can plug -a in for a, resulting in
f (-(a))
= f(-(1/2)(x))
= g(x)
Can someone helpp pls
Answers
Answer:
Step-by-step explanation:
You have to solve this as a system. We have 3 coordinates given; the first 2 are given as zeros of the quadratic, the 3rd one is given as a regular coordinate. The zeros of a quadratic are where the y values of a coordinate are 0's because the x-intercepts of a quadratic (aka zeros) exist where y = 0. We use each of those points in the standard form of a quadratic to solve for a, b, and c. First, (0, 0):
[tex]0 = a(0)^2+b(0)+c[/tex] which gives us that c = 0. We'll use that value of c as we move forward with the problem. Next we'll use (3, 0):
[tex]0=a(3)^2+b(3)+0\\0 =9a+3b[/tex]Hold that thought for a minute or 2. Next we'll use the coordinate (1, 6):
[tex]6=a(1)^2+b(1)+0\\\\6=a+b[/tex] Now we have a system that we can solve using either substitution or elimination for a and b. I used elimination:
6 = a + b
0 = 9a + 3b and multiply the top equation by -3:
-18 = -3a - 3b
0 = 9a + 3b
so
-18 = 6a and
a = -3. Now back solve for b:
6 = -3 + b so
b = 9 and our quadratic is
[tex]y=-3x^2+9x+0[/tex] or just
[tex]y=-3x^2+9x[/tex]
As part of a chemistry experiment, Barry is making a mixture of two solutions. He uses 4 cups of solution A for every 2 cups of solution B. The table below shows the numbers of cups he uses of solution A and solution B. Solution A (cups) Solution B (cups) 4 2 8 4 12 6 16 8 Using the information from the table, choose the correct statement. A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3. B. The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2. C. There are 3 cups of solution A for every 6 cups of mixture. D. For each cup of solution A, there are 2 cups of solution B.
Answers
Answer:
A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3
Step-by-step explanation:
Solution A= 4 cups
Solution B= 2 cups
Total cups of the mixture=4+2=6
A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3.
Solution A= 4 cups
Mixture=6 cups
Solution A : Mixture =4 : 6
=2:3
Option A is true
B. The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2.
Solution A= 4 cups
Mixture=6 cups
Solution A : Mixture =4 : 6
=2:3
Option B not true
C. There are 3 cups of solution A for every 6 cups of mixture.
Option C states that:
Solution A=3 cups
Mixture=6 cups
Solution A : Mixture=3:6=1:2
This is not true
D. For each cup of solution A, there are 2 cups of solution B.
Option D states:
Solution A= 1 cups
Solution B= 2 cups
This is not true
It is rather
Solution A= 2 cups
Solution B= 1 cups
Therefore, option A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3 is the correct statement
Review what you know about products and sums represented by rectangular area models. [5 points] Use algebra tiles to multiply (x-1)(3x+2).
Answers
= 3x^2 + 2x - 3x - 2
= 3x^2 - x - 2
3x^2 - x - 2
What are some ways to solve an equation?
Different ways to solve equations. We have 4 ways of solving one-step equations: Adding, Substracting, multiplication, and division. If we add the same number to both sides of an equation, both sides will remain equal.
How do you evaluate an equation?
∫ y2+y−2dy ∫ y 2 + y − 2 d y∫ 2 1 y2 +y−2dy ∫ 1 2 y 2 + y − 2 d y∫ 2 −1 y2 +y−2dy ∫ − 1 2 y 2 + y − 2 d y= (x - 1)(3x + 2)
= 3x^2 + 2x - 3x - 2
= 3x^2 - x - 2
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The equations y=x22−8 and y=2x−2 are graphed below. What are the solutions to the equation x22−8=2x−2?
A
x=−8 and x=−2
B
x=−6 and x=10
C
x=−4 and x=4
D
x=−2 and x=6
Answers
Answer:
x= -2 and x = 6
Step-by-step explanation:
The solutions are where the two graphs intersect
x=6, y= 10 is one point
x=-2 and y = -6 is the other point
The intersection points of both the equations are the solutions
From the graph the points are
(6,10)(-2,-6)Hence
x=-2 and x=6 are the solutions
Option D
Consider function f. (-412 + 6.3 + 36, 1 < -2 15, 2 < I 4 Are the statements about the graph of function ftrue or false? true false 2 false The graph crosses the y-axis at (0.–15). The graph has a point of discontinuity at I = The graph is increasing over the interval (4, co) The graph is decreasing over the interval (-12, -2). false The domain of the function is all real numbers. false
Please help
Answers
Answer:
Behold.
Step-by-step explanation
The answer to the statement is 1)false 2) false 3) true 4) true and 5) false.
Given functions,f
1) For x ≤ -2: f(x) = -12 + 6x
2) For -2 < x < 1: f(x) = 41 - 15x
3) For x ≥ 1: f(x) = 31 - 4x
1) The graph crosses the y-axis at (0, -15).
This is false because if x = 0, the function value would be -12 + 6 * 0 = -12, not -15.
2) The graph has a point of discontinuity at x = 1.
This is false because the function is defined at x = 1 there is no space, so there is no point of discontinuity at x = 1.
3) The graph is increasing over the interval (4, ∞).
This is true because the coefficient of x in the function's expression is negative, showing that it is decreasing. Therefore, as x increases, the function values decrease.
4) The graph is decreasing over the interval (-12, -2).
This is true because the coefficient of x in the first piece of the function (-12 + 6x) is positive, showing an increasing trend. Therefore, as x decreases from -12 to -2, the function values increase.
Statement 5: The domain of the function is all real numbers.
This is false because the domain of the function is limited by the intervals in its definition. The function is defined differently for different intervals of x.
So, the answer to the statement is
1) false
2) false
3) true
4) true
5) false
Learn more about functions here:
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I NEED HELP PLEASE FIRST ONE TO ANSWER THIS RIGHT GETS 5 STARS !
Answers
Answer:
The answer is 2Step-by-step explanation:
[tex] {32}^{ \frac{1}{5} } [/tex]To solve the question first write 32 in exponential form
That's
[tex]32 = {2}^{5} [/tex]Multiply the exponent by 1/5
That's
[tex] {2}^{5 \times \frac{1}{5} } [/tex]We have the final answer as
2Hope this helps you
Answer:
2
Step-by-step explanation:
32 ^ (1/5)
Rewriting 32 as 2^5
2^5 ^ 1/5
We know that a^b^c = a^ ( b*c)
2^ ( 5*1/5)
2^1
2
What is the quotient' mean?
Answers
EX: Dividing 10 by 5 gives a quotient of 2.
Answer:
When you divide, the answer is the quotient.
Step-by-step explanation:
For example:
6/3 = 2
The quotient is 2
Review the graph of function g(x).
Which point is on the graph of the inverse function g^-1(x)?
O (-3,0)
O (0,-3)
O (2,3)
O (3,4)
Answers
Answer:
A
Step-by-step explanation:
I did the wrong thing. I inverted the graph. That's not the question. The question is which one of the following is on the inverse of the graph. That means that x and y are interchanged. The answer you gave was the second best answer. The answer is (-3,0) which is A.
If f(x)= 9^x then prove that f(m+n+p) = f(m).f(n).f(p)
Answers
Answer:
f(x)=9^(x)
Plugging in m+n+p=x, we have
f(m+n+p) = 9^(m+n+p)
Using the properties of exponential a^(b+c) = a^b*a^c, we have
f(m+n+p) = 9^(m)*9^(n)*9^(p)
f(m+n+p) = f(m)*f(n)*f(p)
30 POINTS!! Quadratic function F(x) =2x^2- 4x- 6 is shown below. Which describes the domain of this function.
A. All real numbers greater than or equal to -8
B. All real number less than or equal to -8
C. All real number greater than 10
D. All real numbers
Answers
Answer:
D. All real numbers
Step-by-step explanation:
The domain is the set of values that can be used for x. There is no restriction on x, so the domain is all real numbers.
Answer:
all real numbers
Step-by-step explanation:
The domain is the possible input values
Since x can be any value, the domain is all real numbers
This is the question
Answers
For answers, please refer to the picture attached
Answer:
I can't give a full answer because I can't see the image whilst giving an answer but I'll try so....
Step-by-step explanation:
Angles in a straight line add to 180° so when you have one of two of them angles are them together and take away from 180°
Angles around a full point add to 360° so add angles together and take away from 360°
On A I think it is you have a 360° angle and have to work out 3 and you have one already done and the opposite angle is the same as that so you basically have two angles then you add them together then take from 360 then divide the answer by two and then that would be the angles for a and x
And for the last one you have been given two angles with a right angle and a right angle equals 90 so add them together and take from 180 to get the missing angle
Hope this helps :)
Which inequality is graphed on the coordinate plane shown?
A
y≥2x−6
B
y<2x−6
C
y>2x−6
D
y≤2x−6
Answers
Answer:
y ≤ 2x-6
Step-by-step explanation:
First find the equation of the line
The y intercept is -6
The slope is 2
y = 2x-6
The line graphed is solid so we know that there is an equal sign
We are graphing below the line
y ≤ 2x-6
Write an exponential function that includes the following points (2,32) and (3,64)
Answers
Answer:
y=32x-32
Step-by-step explanation:
This time no algorithm or equation was needed i saw that if the equation was y=32x there would be ordered pairs (1,32) and (2,64) so to delay it by 1 on the x side just subtract the slope from the y - intercept sorry if that doesn't make sense
Given triangle ABC is similar to triangle DEF , calculate the value of BC. Picture is below
Answers
Hello! :)
Answer:
[tex]\huge\boxed{BC = 6.4 }[/tex]
Given ΔABC ~ ΔDEF, we can set up a proportion to solve for BC, where:
[tex]\frac{AC}{DF} = \frac{BC}{EF}[/tex]
Let BC = x:
[tex]\frac{8}{15} = \frac{x}{12}[/tex]
Cross multiply:
[tex]8 * 12 = 15 * x[/tex]
[tex]96 = 15x[/tex]
[tex]x = 6.4[/tex]
Therefore, BC = 6.4 units.
Hope this helped you!
COULD A KIND SOUL PLEASE HELP ME OUT?????!!!!!!!!!!!!!!!
In the triangle shown ,AB =2x +9 and BC=5x–12. Find the value of x.
show how you go the answer so I can see if it makes sense!!!
Answers
2x +9 = 5x -12
(Now bring the x to the left, and rest to the right)
2x -5x = -12 -9
(Solve this)
-3x = -17
Then
: -3 to get x
So -17 : -3 u get 5.67
So
x = 5.67
(I think this would be the answer, if I’m wrong, I’m really sorry)
Answer:
In the given triangle, AB=BC
Now, 2x+9=5x-12
=> 5x-2x=12+9
=> 3x=21
=> x=21/3
=> x=7
Therefore, the value of x is 7.
1.
The Springfield Meteorological Center wanted to determine the accuracy of their weather forecasts. They
searched their records for those days when the forecaster had reported a 70% chance of rain. They
compared these forecasts to records of whether or not it actually rained on those particular days. The
forecast of 70% chance of rain can be considered very accurate if it rained on:
A. 95% to 100% of those days.
B. 85% to 94% of those days.
C. 75% to 84% of those days.
D. 65% to 74% of those days.
E
55% to 64% of those days.
Answers
Answer:
The correct option is;
D. 65% to 74%
Step-by-step explanation:
The accuracy of a forecast given based on a percentage or proportion or likelihood is determined by the based on the prevalence of the forecast in a similar proportion over the range of data points in which the forecast is made
Therefore, if it actually rained on 70% of those days for which the forecast was made, the forecast can be said to be very accurate.
Which is to say that the forecast of 70% chance of rain can be considered very accurate if it rained on 65 to 74% of those days which is in the range of the forecasted 70%.
#What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?
Discriminant = b2 – 4ac
–8
4
8
16
Answers
Answer:
16
Step-by-step explanation:
the quadratic equation –3 = –x2 + 2x can be changed into :
x²-2x-3= 0
a=1, b= -2 , and c = -3
so, the discriminant = (-2)²-4(1)(-3)
= 4 + 12 = 16
36. What is the solution to x+3 = -6?
HELP! answer if you can!
Answers
Answer:
x = -9
Step-by-step explanation:
subtract 3 from both sides
x = -9
Answer:
x = -9
Step-by-step explanation:
x + 3 = -6
Subtract 3 from both sides.
x + 3 - 3 = -6 - 3
x = -9
Determine what type(s) of angles are described by the following angle measures. Angle of 35 degrees.
Answers
Answer:
Acute.
Step-by-step explanation:
An angle of measure between 0 and 90 degrees is an acute angle.
find the value of a and b in each of the following diagrams.
Answers
Answer:
a=122
b=115
Step-by-step explanation:
We have a hexagon inscribed of a Circle. Let use some obvious properties to solve some of the angles.
The upper triangle that includes 112 and 30, have a missing angle. We can use triangle interior Theorem to find the missing third angle.
The missing angle is 38.
The upper trapezoid is a cyclic quadrilateral. It 4 vertices touched the circle circumference. This means the opposite angles of the trapezoids are supplementary.
The lower left angle of the upper trapezoid measure is 65. Part of that angle is 38 so the other part is
[tex]65 - 38 = 27[/tex]
Angle b forms a linear pair with the lower left angle so
[tex]b + 65 = 180[/tex]
[tex]b = 115[/tex]
Angle a is also a cyclic quadrilateral so
Angle a and 58 are supplementary
[tex]58 + a = 180[/tex]
[tex]a = 122[/tex]
whats the squareroot of 144 needs to be simplified
Answers
Answer:
12
Step-by-step explanation:
The square root of any number is basically asking "what number multiplied by itself will equal this number?"
Usually you memorize these, but there's also a quick way to do it.
We know that [tex]10\cdot10=100[/tex], so the square root must be greater than 10.
We also know that [tex]15\cdot15=225[/tex], so the square root must be less than 15.
A good mid point between these numbers is 13. Let's see what 13 squared is:
[tex]13\cdot13=169[/tex]
So it's a bit less than 13. Let's try 12.
[tex]12\cdot12=144[/tex]
So 12 is the square root of 144.
Hope this helped!
Answer:
[tex]\huge\boxed{\sqrt{144}=12}[/tex]
Step-by-step explanation:
[tex]\begin{array}{c|c}144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\144=2\cdot2\cdot2\cdot2\cdot3\cdot3=2^2\cdot2^2\cdot3^2\\\\\sqrt{144}=\sqrt{2^2\cdot2^2\cdot3^2}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{3^2}=2\cdot2\cdot3=12\\\\\text{Used}\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\sqrt{a^2}=a\\\\\text{for}\ a\ge0,\ b\geq0[/tex]
[tex] \frac{ {x}^{2} + 4x + 5 }{ {x}^{2} + 3 \sqrt{x + 4} } [/tex]
Hi
is this a rational expression or not pls reply asap
Answers
Answer:
NOT a rational expression.
Step-by-step explanation:
A rational expression is a fraction of two polynomials.
Since the denominator contains a square-root radical, it is not considered a polynomial.
Therefore the given exprssion is NOT a rational expression.
Pablo graphs a system of equations. One equation is quadratic and the other equation is linear. What is the greatest
number of possible solutions to this system?
Answers
Answer:
greatest number of solutions is 2
Step-by-step explanation:
one is a parabola, the other is a line
so it can intersect in 0, 1, 2 points
Triangle QRP is congruent to triangle YXZ. What is the perimeter of triangle YXZ?
What is the perimeter of triangle YXZ?
Answers
Answer:
Perimeter of XYZ = Perimeter of QRP
Step-by-step explanation:
Since congruent then
P of XYZ = P of QRP
plz help me this will be appreciated
Answers
Answer:
1. h
2. b
3. a
4. d
5. c
Step-by-step explanation:
all answers are straight forward. only the last (5) is phrased a bit strangely. I would have said "reflect across a horizontal line".
Find the quotient and remainder when p (x) divides with g (x) question (i) P (x) = x raise to 4 - 3 x square +4x + 5, g (x) = x square +5
Answers
Answer: [tex]x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}[/tex]
Step-by-step explanation:
P(x) = x⁴ - 3x² + 4x + 5
g(x) = x² + 5
_x²_- 8
x² + 5) x⁴ + 0x³ - 3x² + 4x + 5
-(x⁴ + 0x³ + 5x²) ↓ ↓
-8x² + 4x + 5
-(-8x² + 0x - 40)
4x + 45
[tex]\dfrac{x^4-3x^2+4x+5}{x^2+5}=\large\boxed{x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}}[/tex]