Answer:
x=4
Step-by-step explanation:
2x-3=5
Add 3 to both sides
2x=8
divide both sides by 2
x=4
[tex]2x - 3 = 5 [/tex]
[tex]2x = 5 + 3 [/tex]
[tex]2x = 8[/tex]
[tex]x = 8 \2( transposing known value to one side to get the value of x)[/tex]
[tex]x = 4(bringing it to lowest term)[/tex]
The length of the line segment containing the points (1,7) and (5,5)
is 4.47 units
A, True
B. False
Answer:
True
Step-by-step explanation:
Let A denotes the point (1,7)
Let B denotes the point (5,5)
We are supposed to find The length of the line segment containing the points
Formula : [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex](x_1,y_1)=(1,7)\\(x_2,y_2)=(5,5)\\ d = \sqrt{(5-1)^2+(5-7)^2}\\ d = \sqrt{4^2+(-2)^2}\\ d = \sqrt{4^2+(-2)^2}\\d=4.47[/tex]
So,The length of the line segment containing the points (1,7) and (5,5) is 4.47 units is true.
Hence Option A is true
What is the area of the parallelogram? A parallelogram with a base of 14 centimeters and a height of 5 centimeters.
Answer:
The answer is 70cm²Step-by-step explanation:
Area of a parallelogram = base × height
From the question
base = 14 cm
height = 5 cm
Substituting the values into the above formula we have
Area = 14 cm × 5 cm
Area = 70cm²Hope this helps you
Answer:
1,750
Step-by-step explanation:
Polygon LMNO is similar to polygon QRST and LM and QR are corresponding sides. You know the perimeter of each polygon, and you know the measure of MN. What can you find
Answer:
I can find that the measure of RS
Step-by-step explanation:
The measure of RS can be discovered as both have corresponding sides. Therefore, both are the same
Solve the equation in the image
Answer:
x = 70
Step-by-step explanation:
[tex] \sqrt{x - 6} = 8 \\ squaring \: both \: sides \\ {( \sqrt{x - 6)} }^{2} = {8}^{2} \\ x - 6 = 64 \\ x = 64 + 6 \\ \huge \red{ \boxed{ x = 70 }}\\ [/tex]
Answer:
Step-by-step explanation:
[tex]\sqrt{x-6}=8[/tex]
Take square,
[tex](\sqrt{x-6})^{2}=8^{2}\\\\x-6=64\\\\[/tex]
Add 6 to both sides,
x - 6 + 6 = 64+6
x = 70
There is a unique positive real number x such that the three numbers
log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
The number x can be written as m/n, where m and n are relatively prime positive integers.
Find m+n.
Step-by-step explanation:
If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
Let a = log82x, b = log4x and c = log2x
If a = log8 2x; 8^a = 2x... (1)
If b = log4 x; 4^b = x ... (2)
If c = log2 x; 2^c = x...(3)
Since a, b c are in GP, then b/a = c/b
Cross multiplying:
b² = ac ...(4)
From eqn 1, x = 8^a/2
x = 2^3a/2
x = 2^(3a-1)
From eqn 2; x = 4^b
x = 2^2b
From eqn 3: x = 2^c
Equating all the values of x, we have;
2^(3a-1) = 2^2b = 2^c
3a-1 = 2b = c
3a-1 = c and 2b = c
a = c+1/3 and b = c/2
Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;
(c/2)² = c+1/3×c
c²/4 = c(c+1)/3
c/4 = c+1/3
Cross multiplying;
3c = 4(c+1)
3c = 4c+4
3c-4c = 4
-c = 4
c = -4
Substituting c = -4 into equation 3 to get the value of x we have;
2^c = x
2^-4 = x
x = 1/2^4
x = 1/16
Since the number x can be written as m/n, then x = 1/16 = m/n
This shows that m = 1, n = 16
m+n = 1+16
m+n = 17
The required answer is 17.
The value of m+n in which m and n are relatively prime positive integers is 17.
What is geometric sequence?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,
[tex]\log_82 x,\log_4x, \log_2x[/tex]
The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,
[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]
Using the base rule of logarithmic function,
[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]
Using the Power rule of logarithmic function,
[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]
The number x can be written as
[tex]\dfrac{m}{n}[/tex]
Here, m and n are relatively prime positive integers. Thus, the value of m+n is,
[tex]m+n=1+16=17[/tex]
Hence, the value of m+n in which m and n are relatively prime positive integers is 17.
Learn more about the geometric sequence here;
https://brainly.com/question/1509142
i need help understanding this
Answer:
x = 6±sqrt( 31)
Step-by-step explanation:
x^2 -12x +5 =0
Subtract 5 from each side
x^2 -12x +5-5=0-5
x^2 -12x = -5
Take the coefficient of x
-12
Divide by 2
-12/2 =-6
Square it
(-6 )^2 = 36
Add this to each side
x^2 -12x +36= -5+36
(x-6)^2 = 31
Take the square root of each side
sqrt((x-6)^2) =±sqrt( 31)
x-6 =±sqrt( 31)
Add 6 to each side
x-6+6 =6±sqrt( 31)
x = 6±sqrt( 31)
A bag of marbles contains 6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble. What is the probability of
reaching into the bag and selecting a yellow marble?
1/13
2/13
1/6
2/6
Answer:
It would be B.
Step-by-step explanation:
Hope it helpssss
Mona likes to ski. One lap includes a 4 minute ride up the ski lift and 5 minutes to ski down the hill. How long will it take her to do 5 laps?
Answer:
pretty sure it is 45mins
Step-by-step explanation:
U add 4+5=9 so that is one lap
then take 9*5=45 and that would be 5 laps
Answer:
45
Step-by-step explanation: first we want to find out the time it takes to do one full lap of skiing. in order to do this you have to add 4 to 5. we do this because if we start at the bottom of the hill we have to ride 4 min up to the top then 5 min to get back to the bottom. so in all it will 9 min to do one full lap. because we want to find out how long it will take to do 5 laps we do 9x5=45
Solve the long division
Answer:
1. 158
2. 120.125
3. 148.6
4. 158.6
Step-by-step explanation:
You divide the number inside by the number outside
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
Answer:
66 ft^2
Step-by-step explanation:
the formula for the area of a triangle is b x h over 2. the base is 22 and the height is 6. 22 x 6=132. 132/2=66
area of isosceles triangle
Answer:
You find the base and height then divide by 2
Step-by-step explanation:
Answer:
height x 2 divided by 1/2
Step-by-step explanation:
An economy package of cups has 250 green cups if the green cups are 10% of the total package, how many cups are in the package?
Answer:
There are a total of 2500 cups
Step-by-step explanation:
10% of the cups are green
you can set up a equation for this
x = total cups
.10x = 250
multiply both sides by 10 to make x a whole number
x = 2500
Solve. 2(n - 1) + 4n = 2 ( 3n - 1 ) please help ASAP
Answer:
0
Step-by-step explanation:
2(n - 1) + 4n = 2 ( 3n - 1 )
2n - 2 + 4n = 6n - 2
6n - 2 = 6n - 2
6n - 6n = -2 + 2
0 = 0
A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom.
Answer:
angle of depression = -12 degrees
Step-by-step explanation:
Sin = opposite/hypotenuse
sin = -208/1000
inv sin 0.208 = -12
To solve this problem, we just need to use trigonometric ratio and use the ratio that best fits this problem. The angle of depression is equal to 76.23 degrees.
Trigonometric RatioUsing SOHCAHTOA, we can easily solve this problem, but we need to first know which ratio to use
Data;
opposite (ski run) = 1000 yardsadjacent (vertical drop) = 208 yardssince we have the value of opposite and adjacent, we can solve this using the tangent of the angle
[tex]tan\theta = \frac{opposite}{adjacent} \\tan \theta = \frac{1000}{208} \\tan\theta = 4.807\\\theta = sin^-^1 (4.0807)\\\theta = 76.23^0[/tex]
From the calculation above, the angle of depression is equal to 76.23 degrees.
Learn more on angle of depression here;
https://brainly.com/question/15580615
#SPJ2
13 POINTS!!!
In ΔABC, c = 4.2 inches, ∠C=24° and ∠A=115°. Find the area of ΔABC, to the nearest 10th of an square inch.
Answer:
12.9 [tex]in^{2}[/tex]
Step-by-step explanation:
So to find the area of this triangle, you will need to use the equation
Area = [tex]\frac{1}{2}[/tex]c*b*sin(A) = [tex]\frac{1}{2}[/tex]a*b*sin(C)
Here, we have ∠A, ∠C, and side c
We can use the fact that [tex]\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex] so solve for the other variables we do not have.
First we can find the other angle B. Since ∠A + ∠B + ∠C = 180°,
∠B = 180° - ∠A - ∠C, which is ∠B = 180° - 115° - 24° = 41°
Now that we have all three angles, we can solve for the sides
Since we only have side c, we will manipulate the equation with c and one of the others to solve for a or b. Let's solve for side b first.
Since [tex]\frac{b}{sin(B)} =\frac{c}{sin(C)}[/tex], solving for b would give us [tex]b=\frac{csin(B)}{sin(C)}[/tex]. Then plugging in our values we get [tex]\frac{4.2sin(41)}{sin(24)}[/tex]= 6.77 = b
Now we can solve for the remaining side, a, using the same method.
Since [tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex], solving for a would give us [tex]a=\frac{bsin(A)}{sin(B)}[/tex]. Then plugging on our values we get [tex]\frac{6.77sin(115)}{sin(41)}[/tex]= 9.36 = a
Now that we have all our angles and sides, we can plug in our numbers to either of our area equations ⇒
Area =[tex]\frac{1}{2}[/tex]c*b*sin(A)= [tex]\frac{1}{2}[/tex](4.2)(6.77)sin(115) = 12.9[tex]in^{2}[/tex] or [tex]\frac{1}{2}[/tex]a*b*sin(C) = [tex]\frac{1}{2}[/tex](9.36)(6.77)sin(24) = 12.9[tex]in^{2}[/tex]
The parallelogram does not have right angles. Its area is
less than ab.
equal to ab.
greater than ab.
Answer:
equal to ab
Step-by-step explanation:
The area of a parallelogram is Area = ab
therefore, the area is ab
Answer:
Less than ab
Step-by-step explanation:
i dont know how to do this if someone could show me how and what the answer is
Answer:
It is A because due to the slope it is a parallelogram.
Step-by-step explanation:
Answer:
its a
Step-by-step explanation:
HELP!!!! calculate the difference and enter it below
-1 -7
Answer:
-8
Step-by-step explanation:
-8
Answer:
6.
Step-by-step explanation:
Difference between -1 and -7.
-1-(-7) = -1 + 7 = 6
two negative signs makes it a positive sign
Cuáles de los siguientes experimentos son aleatorios. a) Número de personas que suben a un autobús en una parada. b) Aplicar el teorema de Pitágoras en un triángulo rectángulo. c) Conocer el ganador de la Liga de Campeones. D) Calcular la raíz cuadrada de un número.
Answer:
a) Número de personas que suben a un autobús en una parada.c) Conocer el ganador de la Liga de Campeones.Step-by-step explanation:
This problem is about random experiments.
Random experiments are defined as experiments where the outcome can't be predicted. To ensure that result, the subjects are selected randomly. So, in this case, the right answer must be a situation where subjects are randomly present.
People taking the bus is a random experiment, because there's no the exact subjects in a bus at any time, it happens randomly.
Also, the winner of a sport league is also a random experiment, because it happens after several games which cannot be predicted.
Therefore, the right answers are a and c.
Describe the process for calculating the volume of a cylinder.
Answer:
the formulae for the volume of a cylinder= πr²h
so we then put the figures at their respective positions. and for the pie we put either 22/7 or 3.143 or 3.14
how many solutions to x^2 =-16
Answer:
no real solutions
Step-by-step explanation:
6th question of the day
WHat is the equation for standard equation of circle?
Answer:
Where (h,k) is the center and r is the radius
Step-by-step explanation:
[tex]r^2 = (x-h)^2+ (y-k)^2[/tex]
plzzzzzzzzzzzzzaaaaaa
Answer:
C
Step-by-step explanation:
[tex]y^2+4y-32=0\\(y+8)(y-4)=0\\y=4,-8[/tex]
Therefore, the answer is C. Hope this helps!
i think of a number multiply it by 3 and subract 2 . The result is 14
Answer:
5.3
Step-by-step explanation:
Answer:
The answer is 5.3
Step-by-step explanation:
5.3x3-2= 13.9 but when you round its 14
SA police department used a radar gun to measure the speed of a sample of cars on the highway.
Assume that the distribution of speeds is approximately Normal with a mean of 71 mph and a
standard deviation of 8 mph.
Using this distribution what is the z-score of a 65-mph speed limit? *
Answer:
The z score of the 65-mph speed limit is -0.75
Step-by-step explanation:
The z score is given by the relation;
[tex]z = \frac{x- \mu}{\sigma}[/tex]
Where:
Z = Normal (Standard) or z score
x = Observed speed score
μ = Mean, expected speed
σ = Standard deviation
Where we plug in the values for x = 65-mph, σ = 8 mph and μ = 71 mph, into the z-score equation, we get;
[tex]z = \frac{65-71}{8}= \frac{-6}{8} = -\frac{3}{4}[/tex]
Hence the z score of the 65-mph speed limit =-3/4 or -0.75.
3a/4+2a/3-a/12
a. a/3
b. 4/3
c. (4a)/3
Answer: C
Step-by-step explanation:
[tex]\frac{3a}{4}+\frac{2a}{3}-\frac{a}{12}[/tex]
Find the least common denominator of 4, 3, and 12.
4-3-12 | 3
4-1-4 | 4
1-1-1 |-------- 12
The first fractions needs to be multiplied by 3, and the second fraction, by 4
[tex](\frac{(3a)*3}{(4)*3})+(\frac{(2a)*4}{(3)*4})-\frac{a}{12}[/tex]
Solve;
[tex]\frac{9a}{12}+\frac{8a}{12}-\frac{a}{12}[/tex]
Add the fractions with positive signs and subtract the one with negative sign.
[tex]\frac{(9a+8a)-a}{12}[/tex]
Solve;
[tex]\frac{17a-a}{12}=\frac{16a}{12}[/tex]
Simplify by 4;
16/4=4
12/4=3
[tex]\frac{4a}{3}[/tex]
Answer:
(4a)/3
Step-by-step explanation:
3a/4+2a/3-a/12
find L.C.M
9a+8a-1a/12=16a/12
16a/12=(4a)/3
I'll give Brainliest!!!
What is 5 1/2 divided by 5 1/3 equal?
The areas of the squares adjacent to two sides of a right triangle are 32 units^2 and 32 units^2
Answer:
64 square units.Step-by-step explanation:
In this problem, we have to find the area of an square adjacent to the third side of the right triangle.
To solve this problem, we need to use Pythagorean's Theorem, beacuse it's about a right triangle. Also, this theorem is about square areas, that's the geomtrical meaning of it.
[tex]h^{2} =32 \ u^{2} + 32 \ u^{2} = 64\ u^{2} \\h=\sqrt{64 \ u^{2} } =8u[/tex]
Therefore, the area of a square adjacent to the third side is 64 square units.
Answer:the answer is 8
Step-by-step explanation:
Tan θ =
[tex] \sqrt{13} \div \sqrt{2} [/tex]
Answer:
Step-by-step explanation:
Tan θ = [tex]\sqrt{13} \div \sqrt{2}[/tex] = 2.5495
Therefore θ = [tex]Tan^{-1}[/tex] (2.5495) =68.5832°
Answer:
Tan θ = 2.5495097...
PLZZ ANSWER CORRECTLYTHIS IS GOING TO BE GRADED!!!!
PLZ WHEN U R DOING THE PROBLEMS,PICK FROM THE CHOICES IT GIVES U!!!!!!
Answer:
That's my best answer.
Step-by-step explanation:
So for number 1 it says the total amount of wrapping paper. You should just find the surface area. I'll send a screenshot.