Answers
Answer:
x = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given a tangent and secant from an external point to the circle, then
The square of the tangent is equal to the product of the external part and the whole of the secant, that is
x² = 4(4 + 8) = 4 × 12 = 48 ( take the square root of both sides )
x = [tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]
Related Questions
subtract
(3x^4+7x^3-9) - (5x^2-8x+4) =
Answers
Answer:
3x^4 + 7x^3 - 5x^2 + 8x - 13
Step-by-step explanation:
(3x^4 + 7x^3 - 9) - (5x^2 - 8x + 4) =
The negative sign to the left of the second set of parentheses changes every sign inside the parentheses.
The first set of parentheses is unnecessary, so we just drop it.
= 3x^4 + 7x^3 - 9 - 5x^2 + 8x - 4
Now we combine like terms.
= 3x^4 + 7x^3 - 5x^2 + 8x - 13
According to the graph, what is the value of the constant in the equation
below?
Answers
Answer: 3.2 is the correct answer
Step-by-step explanation
If f(x) = x2 + 3x - 4, find f(4).
Answers
Answer:
f(4) = 24
Step-by-step explanation:
Plug in 4 for x in the equation:
f(x) = x² + 3x - 4
f(4) = (4)² + 3(4) - 4
Remember to follow PEMDAS. PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
and is the order of operation.
First, solve the power:
(4)² = 4 * 4 = 16
Next, multiply 3 with 4:
3 * 4 = 12
Next, combine the terms:
f(4) = 16 + 12 - 4
f(4) = (16 + 12) - 4
f(4) = 28 - 4
f(4) = 24
f(4) = 24 is your answer.
~
Answer:
24
Step-by-step explanation:
Plug x as 4.
(4)² + 3(4) - 4
16 + 12 - 4
= 24
easy question please help fast, i just want to check my answer!
Answers
Answer:
false
Step-by-step explanation:
its false I think
Here’s a graph of a linear function. Write the equation that describes that function. Express it in slope
Answers
Answer:
y = (1/3)x +4
Step-by-step explanation:
The line intercepts the y-axis at y=4. It has a "rise" of 1 unit for each "run" of 3 units, so its slope is rise/run = 1/3.
The slope-intercept form of the equation of a line is ...
y = mx + b . . . . . where m is the slope and b is the y-intercept.
When we put the proper numbers in the equation, we have ...
y = (1/3)x + 4
A person walked 50 ft. to cross
a rectangular field
diagonally. If the width of field is 30ft, its length is?
A) 40 ft
B) 30 ft
C) 100 ft
D) 6oft
Answers
Answer:
B) 40 ft
Step-by-step explanation:
Use the picture for a reference.
1. We can see the diagonal forms a triangle. Since the angles of a rectangle are right, we can use the Pythagorean Theorem to solve for x.
2. The Pythagorean Theorem
a^2 (a squared) + b^2 (b squared) = c^2 (c squared)
a = 30 ft (width)
b = x ft (unknown length)
c = 50 ft (diagonal)
3. Substitute in the values:
30^2 + x^2 = 50^2
900 + x^2 = 2500
x^2 = 1600
x = 40
The length of the field is 40 ft.
#1 Billy stacked nine pieces of wood on top of one another. If each piece was 3/4 of a foot tall, how tall was the wood pile? Round your answer to the nearest hundredth of a foot.
#2 look at the photo
please help me as soon as you can it would be greatly appreciated I’m in a hurry.
Answers
Answer:
a. 6.75 ft
b. Exponent on w is w^4
Step-by-step explanation:
a. The best thing here is to work with decimals
each piece was 3/4 foot tall which means each piece is 0.75 ft tall
Now since he staked 9, the height of the wood pile would be 9 * 0.75 = 6.75 ft
b. Firstly let’s evaluate the denominator
That becomes; 2v^-3w^8 * v^4w = 2v^(-3+4)w^(8+1) = 2vw^9
So let’s now divide this by the numerator
Since we are concerned with only the exponent on w, we place w^13 over w^9 = w^(13-9) = w^4
laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. find the probability that a randomly selected light bulb will last between 825 and 900 hours.
Answers
Answer:
0.13591
Step-by-step explanation:
What we do here is find a score of both values;
Mathematically;
z-score = (x - mean)/SD
for 825, we have (825-750)/75 = 1
For 900, we have (900-750)/75 = 150/75 = 2
So the probability we want to find is;
P(1<x<2) = P(x<2) - P(x<1)
We use the standard table for this and we arrive at;
P(1<x<2) = 0.13591
Answer:13.5
Step-by-step explanation:
Find the product h · k(x) if h(x) = 2(3x – 5) and k(x) = –2x + 1?
Answers
Answer:
The answer is option C.
Step-by-step explanation:
h(x) = 2(3x – 5) = 6x - 10
k(x) = –2x + 1
h • k (x) = (6x - 10) ( - 2x + 1)
= - 12x² + 6x + 20x - 10
The final answer is
= - 12x² + 26x - 10
Hope this helps you
Answer:
C) h · k(x) = –12x2 + 26x – 10
Step-by-step explanation:
solve the following system of linear equations using the elimination method
Answers
Answer:
x=-1, y=2, z=3
Step-by-step explanation:
First at all, you can divide these equations into two group. It is easier to you.
4x-2y+3z=1
3x+y+2z=5
x+3y-4z=-7
3x+y+2z=5
Then, you can simplify these group of equation that you divided.
So, we have to simplify these step by step.
First, we can simplify the first group of equation.
4x-2y+3z=1
3x+y+2z=5
We have to find which variable you want to eliminate. I choose y.
You can multiply the second equation of first group by 2 and eliminate them.
4x-2y+3z=1
6x+2y+4z=10
As the variable of y is same and we can eliminate y by addition.
4x-2y+3z=1
6x+2y+4z=10
become
10x+0+7z=11
10x+7z=11
10x+7z=11 as the third equation.
Next, simplify the second group of equation.
x+3y-4z=-7
3x+y+2z=5
Same way as the previous one. We need to find which variable that you want to eliminate. I choose y.
We need to balance for the first equation x+3y-4z=-7 at least one variable.
We need to multiply this equation by -3 below to get the same value of y to eliminate the above equation.
3x+y+2z=5 (multiply by -3)
-9x-3y-6z=-15
x+3y-4z= -7
-9x-3y-6z= -15
Here we go! Now these group has same value and variable to eliminate.
We can eliminate these equations by addition method.
x+3y-4z= -7
-9x-3y-6z= -15
-8x+0+10z= -22
-8x+10z= -22
Furthermore, we have to combine these equations that we have simplified from the previous groups.
10x+7z=11
-8x+10z= -22
10x+7z=11 and -8x+10z= -22 as a new group.
Finally, it is time to solve these equations!!
10x+7z=11
-8x+10z= -22
First equation of the above group, we can multiply by 10. Like this:
100x+70z=110
Second equation of the above group, we can multiply by 7. Like this:
-56x+70z=-154
So, we can see there are same value from these equation which are +70z and -70z.
Now, we can eliminate this variable by sum these equations.
100x+70z=110
-56x+70z=-154
44x= -44
x= -1
When we get x= -1 , we can use this value to any equation that you want. You can get the same answer as well.
When x= -1,
substitute into 100x+70z=110
100(-1)+70z=110
-100+70z=110
70z=110+100
70z=210
z=3
When z=3 and x= -1, we can substitute into x+3y-4z= -7
-1+3y-4(3)= -7
-1+3y-12= -7
3y=6
y=2
So, the answer is x= -1 , y=2 , z=3
I hope you will understand my solution and explanation. Bye!!
Using Cramer's Rule, what is the value of x in the solution to the system of linear equations below
X+ 3y - 16
3x + y = 8
Answers
Answer:
x = 5
Step-by-step explanation:
Here, we want to use Crammer’s rule to find the value of x
Please check attachment for complete solution
Drag the tiles to the table. The tiles can be used more than once, but not all tiles will be used.
Emma and Jackson are helping their band raise funds for a trip to New York City. They've volunteered to call every
business owner in their small town to request donations. Emma can complete the calls in 6 days if she works alone.
Jackson can complete the calls in 4 days if he works alone. To complete the task, Emma and Jackson are going to work
together for the same amount of time. Use this information to complete the table.
Answers
Answer:
Emma can complete the calls alone in 6 days, which means she can complete [tex]\frac{1}{6}[/tex] of the calls in one day. So, Emma’s rate per day is [tex]\frac{1}{6}[/tex] . Jackson can complete the calls alone in [tex]4[/tex] days, which means he can complete [tex]\frac{1}{4}[/tex] of the calls in one day. So, Jackson’s rate per day is [tex]\frac{1}{4}[/tex] . Because they’re working together, the time, [tex]x[/tex] , is the same for both.
Multiply across the table to find the part of the task each has completed. Use the equation work completed = (rate)(time) to fill in the last column cells.
Step-by-step explanation:
pls help asap it math
Answers
Answer:
2133 bricks
Step-by-step explanation:
a27=1
a4=139
a27=a4+23r
1=139+23r
23r=1-139
23r=-138
r=-138/23=-6
a4=a1+3r
139=a1-18
a1=139+18
a1=157
n=a1+......+a1+26*r=a1+a1+r+......+a1+26r=27*a1+r(1+2+...+26)
=27*157-6*26*27/2=4239-3*26*27=4239-2106=2133
Simplifying an expression. (3xy)^2 x^4 y /x^5?
Answers
Answer: 9xy3
Step-by-step explanation:
STEP
1
:
y
Simplify ——
x5
Equation at the end of step
1
:
y
(((3xy)2) • (x4)) • ——
x5
STEP
2
:
Equation at the end of step
2
:
y
(32x2y2 • x4) • ——
x5
STEP
3
:
Multiplying exponential expressions :
3.1 y2 multiplied by y1 = y(2 + 1) = y3
Dividing exponential expressions :
3.2 x6 divided by x5 = x(6 - 5) = x1 = x
Final result :
9xy3
What is the quotient of –10 and –5? the answer is : 2
Answers
Which of the following points satisfies the inequality y>1/3x-2 which side should be shaded
Answers
Answer: Hope this helps <3
Step-by-step explanation:
If 6x - y = 21 and -x + 6y = 14, what is the value of x - y?
Answers
Answer:
the value of x_y is 1.
hope u get it.....
Find lateral surface area in square units, of the following 3-
dimensional figure.
Enter just a number for your answer.
-
14 ft
7 ft
9 ft
Answers
Answer:
Lateral surface area of cuboid = 448 ft²
Step-by-step explanation:
Given:
Height of cuboid(h) = 14 ft
Length of cuboid(l) = 9 ft
width of cuboid(b) = 7 ft
Find:
Lateral surface area of cuboid
Computation:
Lateral surface area of cuboid = 2 h(l + b)
Lateral surface area of cuboid = 2(14)(9 + 7)
Lateral surface area of cuboid = 28(16)
Lateral surface area of cuboid = 448 ft²
The tens digit of a two-digit number is twice the units digits. If the digits are reversed, the new number is 18 less than the original number. Find the number.
Answers
Answer:
x=42
Step-by-step explanation:
The tens digit of a two-digit number is twice the units digits. put it in an equation:
10(2x)+x = 10x+2x+18
21x=12x+18
21x-12x=18
x=18/9=2
substitute x:
10(2x)+x = 10x+2x+18
10(2*2)+2=10(2)+2(2)+18
42=24+18
Point G is the center of the small circle. Point X is the center of the large circle. Points G, Y, and X are all on line segment GX.
Marco wants to create a new circle using GX as a radius. What will be the area of Marco’s new circle?
10Pi centimeters squared
16Pi centimeters squared
356Pi centimeters squared
676Pi centimeters squared
Answers
Answer:
GY = 10 cm
YX = 16 cm
A = πr²
A = π (26cm)²
A = 676cm² π
Step-by-step explanation:
The area of Marco's new circle is A = 676π cm²
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the radius of the circle be represented as r
Now , the value of r = 26 cm
And , area of the circle = πr²
On simplifying , we get
A = π ( 26 )²
A = 676π cm²
Hence , the area of the circle is 676π cm²
To learn more about circle click :
https://brainly.com/question/28391204
#SPJ3
The complete question is attached below :
Point G is the center of the small circle. Point X is the center of the large circle. Points G, Y, and X are all on line segment GX.
Marco wants to create a new circle using GX as a radius. What will be the area of Marco’s new circle?
10Pi centimeters squared
16Pi centimeters squared
356Pi centimeters squared
676Pi centimeters squared
13
Select the correct answer.
What is the standard form of this function?
Rx) = -(x-4)²+2
OA
Rx) = x2 + 8x-14
OB.
Ax) = x2 + 4x - 30
OC.
RX) = -x2 + 4x - 30
OD
AX) = -x2 + 8x - 14
Answers
Answer:
D. [tex]\bold{\ -x^2+8x-14\ }[/tex]Step-by-step explanation:
[tex]-(x-4)^2+2=-(x-4)(x-4)+2 = -(x^2-4x-4x+16)+2 = \\\\=-(x^2-8x+16)+2=-x^2+8x-16+2=\underline{\ -x^2+8x-14\ }[/tex]
The painting shown is by Métis artist Leah Marie Dorion from Prince Albert, Saskatchewan. It is called Hawk Woman (2006). The frame is 2 in. wide on
each side of the square painting. Write an expression to represent the dimensions and area of the painting. Multiply, and then combine like terms.
Answers
Answer:
x^2-4x-4
Step-by-step explanation:
Dimension of the painting=x
Frame=2in wide is. Each side of the square painting
Length of the painting= x-2
Area of a square=lenght^2
=(x-2)^2
Multiply
=(x-2)(x-2)
=x^2-2x-2x+4
Combine like terms
Area of the square painting=x^2-4x-4
Hey guys! I need answers really quickly. Thanks!
Answers
Answer:
30 cm²
Step-by-step explanation:
Step 1: Find the value of xy using the formula for area of triangle with 2 sides and an angle between
Area = ½*x*y*sinB
Area of ∆ABC = 30 cm²
sin B = sin 70 = 0.9397
Thus,
30 = ½*x*y*0.9397
30 = (x*y*0.9397)/2
Multiply both sides by 2
60 = xy*0.9397
Divide both sides by 0.9397
60/0.9397 = xy
xy = 63.85
Step 2: calculate the area of ∆PQR with the same formula used in step 1, and also, using the value of the product of x and y gotten in step 1
Area of ∆PQR = ½*x*y*sinQ
x*y = xy = 63.85
sin Q = sin 110 = 0.9397
Area = ½*63.85*0.9397
Area of ∆PQR ≈ 30 cm²
what is the solution to the inequality below x<5
Answers
Answer:
The correct answer is B
Answer:
0 < x < 25
Step-by-step explanation:
Which function has the smallest x-intercept value, if it exists?
O f(x) = 3x – 9
O F(x) = +4
O f(x) = Vx+1
Of(x) = x²
Answers
Answer:
The smallest x-intercept is x = -1, from equation 3.
Step-by-step explanation:
The x-intercept value of a function happens when "y", or in this case f(x), is equal to 0. Therefore we need to analyze each equation by making f(x) = 0 and finding x.
(a) [tex]f(x) = 3x - 9[/tex]
[tex]0 = 3x - 9\\3x = 9\\x = 1[/tex]
(b) [tex]f(x) = 4[/tex]
Since this is a constant function for which f(x) = 4, then there will be no x-intercept.
(c) [tex]f(x) = 3x - 9[/tex]
[tex]0 = \sqrt{x + 1}\\(0)^2 = (\sqrt{x + 1})^2\\0 = x + 1\\x = -1[/tex]
(d) [tex]f(x) = x^2\\[/tex]
[tex]0 = x^2\\x = 0[/tex]
From these options the smallest x-intercept is x = -1.
Answer:
c
Step-by-step explanation:
edge 100%
Before any dinner service, the manager confirms when the number of reservations at a restaurant is subtracted from twice the number of loaves of bread on hand must be greater than 5. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?
Answers
Answer:
Its A
Step-by-step explanation:
Answer:
its the first option
Step-by-step explanation:
A 1 km long train is travelling at 30km/h. If the train enters a tunnel that is 1 km long, how much time will it take for the train to clear the tunnel?
Answers
Answer: 240 seconds OR 4 minutes
Step-by-step explanation:
Length of the train = 1 km
Length of the tunnel = 1 km
Therefore, length of the train + length of the tunnel = (1 + 1) km = 2 km
= 2000 m
Speed of the train = 30 km/hr = 8.333 metres per second
Therefore, time taken by the train to cross the tunnel = 2000 m/ 8.333 m/sec.
= 240 seconds = 4 minutes
Check all that apply. If csc0=13/5, then:
Answers
I hope this helps you
Answer: B) sin θ = 5/13 and D) tan θ = 5/12
Step-by-step explanation:
[tex]\csc\theta=\dfrac{r}{y}=\dfrac{13}{5}[/tex]
Use Pythagorean Theorem: x² + y² = r² to calculate x = 12
[tex]\sin \theta=\dfrac{y}{r}=\dfrac{5}{13}\qquad \qquad \qquad \csc \theta=\dfrac{r}{y}=\dfrac{13}{5}\\\\\\\\\cos \theta=\dfrac{x}{r}=\dfrac{12}{13}\qquad \qquad \qquad \sec \theta=\dfrac{r}{x}=\dfrac{13}{12}\\\\\\\\\tan \theta=\dfrac{y}{x}=\dfrac{5}{12}\qquad \qquad \qquad \cot \theta=\dfrac{x}{y}=\dfrac{12}{5}[/tex]
Write an algebraic expression for the given word expression:
4.7 less than a number k
Answers
Answer:
k-4.7
Step-by-step explanation:
It is k minus 4.7 because when it says less than it means the number that is stated before the phrase is being subtracted :)
Answer:
k-4.7
Step-by-step explanation:
For writing algebraic expressions, we have translate the words to math.
4.7 less than a number k, means subtraction (notice the word- less)
Thus, we have k-4.7
Hope this helps :)
A candy company makes chocolate bars. The regular size bar has 1 oz of chocolate, while the king size bar has 2.5 oz of chocolate. The company makes batches of more than 80 bars at a time and uses less than 150 oz of chocolate for each batch. Write a system of inequalities to model this situation. Then graph it.
Answers
Answer:
They can make 70 king sized bars and 10 regular sized bars.
70*2=140 oz
140+10=150 oz