Answer: [tex]x=-1[/tex]
Step-by-step explanation:
By the negative exponent rule, you have that:
[tex](\frac{1}{a})^n=a^{-n}[/tex]
By the exponents properties, you know that:
[tex](m^n)^l=m^{(nl)}[/tex]
Therefore, you can rewrite the left side of the equation has following:
[tex](\frac{1}{8})^{-(2x+7)}=(\frac{1}{32})^{3x}[/tex]
Descompose 32 and 8 into its prime factors:
[tex]32=2*2*2*2*2=2^5\\8=2*2*2=2^3[/tex]
Rewrite:
[tex](\frac{1}{2^3})^{-(2x+7)}=(\frac{1}{2^5})^{3x}[/tex]
Then:
[tex](\frac{1}{2})^{-3(2x+7)}=(\frac{1}{2})^{5(3x)}[/tex]
As the base are equal, then:
[tex]-3(2x+7)=5(3x)[/tex]
Solve for x:
[tex]-6x-21=15x\\-21=15x+6x\\-21=21x\\x=-1[/tex]
Describe the solution to the inequality p>4
Answer:
P is greater than 4
Step-by-step explanation:
so P could be anything from 5 to infinity
Final answer:
The inequality p > 4 is satisfied by any real number greater than 4. The solution is represented visually by shading the number line to the right of the open circle at 4.
Explanation:
The solution to the inequality p > 4 is all real numbers greater than 4. In other words, for any number p that is greater than 4, the inequality will hold true.
To visualize this solution on a number line, you would draw an open circle at 4 and shade all numbers to the right of 4, indicating that all those numbers are part of the solution set.
This is a basic concept in algebra, focusing on understanding and solving inequalities. The solution does not include the number 4 itself because the inequality is strictly greater than (not greater than or equal to).
The students in Miss Collins class used a survey or’s measuring device to find the angle from their location to the top of a building they also measured the distance from the bottom of the building. the diagram shows the angle measure in the distance.
To the nearest foot, what is the height of the building?
A. 105ft
B. 116ft
C. 32ft
D. 54ft
(Image attached)
Answer:
A
Step-by-step explanation:
We can use trigonometric ratios to solve this.
With respect to the angle given, the building's height is the side that is "opposite".
Also, the given length of 63 feet is the "adjacent" side with respect to the angle given.
Which trigonometric ratio relates "opposite to adjacent" side?
It is TAN.
Now, let's write the ratio and solve for the height of the building (let h be height of the building). We have:
[tex]Tan(\theta)=\frac{Opposite}{Adjacent}\\Tan(59)=\frac{h}{63}\\h=Tan(59)*63\\h=104.85[/tex]
Rounding this, we get h = 105 feet, correct answer A
Answer:
The height of the building = 105 feet ⇒ answer (A)
Step-by-step explanation:
* To find the height of the building use the trigonometry functions
- Lets consider the height (h) of the building as a side of right angle triangle
and the other side is the distance from the bottom of the building
- Now we have right angle triangle one of its acute angle is 59°
- The length of one leg of the right angle = 63 feet
- We have the adjacent side of angle 59°
- we need to find the opposite side of angle (h)
∴ Lets use the function tan to find h
∵ tanФ = opposite to Ф/adjacent to Ф
∵ Ф = 59°
∵ The length of the side adjacent to Ф = 63 feet
∴ tan59 = h/63 ⇒ by using cross multiplication
∴ h = 63 × tan 59 = 104.849 ≅ 105 feet
∴ The height of the building = 105 feet answer (A)
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test. What percent of students scored below Jake? Include a step by step description of the process you used to find that percentage.
Subtract the mean from Jake's score:
520 - 500 = 20
Divide by the standard deviation:
20/60 = 0.33
Jake scored 0.33 standard deviation above the mean.
From the Z-table, 0.33 = 0.6293 = 62.93% of students scored below Jake.
Round to 63%
Answer:
z score is 0.33
( 0.6293) is the answer the next slot)
and 62.93% is last
Step-by-step explanation:
Select the measures of the angles of a triangle whose angles have measures in the ratio 6:8:10
Answer:
45, 60, 75
Step-by-step explanation:
The ratio of the angles are 6:8:10
Multiply by x to get the angle measures
6x, 8x,10x
We know the sum of the angles is 180 for a triangle
6x+8x+10x = 180
Combine like terms
24x = 180
Divide each side by 24
24x/24 = 180/24
x =7.5
Each angle is
6x = 6(7.5) =45
8x = 8(7.5) =60
10x = 10*7.5 = 75
The measures of the angles of the given triangle are 54 degrees, 72 degrees, and 90 degrees.
Explanation:To find the measures of the angles of a triangle whose angles have measures in the ratio 6:8:10, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since the ratio of the angles is 6:8:10, we can set up the equation 6x + 8x + 10x = 180, where x is a common factor. Solving this equation, we find that x = 9. Therefore, the measures of the angles are 6x = 54 degrees, 8x = 72 degrees, and 10x = 90 degrees.
50Points Plato Help!!
The number of teams who entered in a 3-on-3 charity basketbal ournament can be modeled by function T, where x is the number of years since the tournament first started. T(x)=4x+24
The entry fee paid by each team to enter the tounament can be modeled by tunction F, where x is the number of years since the tounament fist started.
F(x)=5x+45
Which function, R, best represents the total entry lees collected in the year since the tournament first started?
A.R(x)=20x^2+300x+1080
B.R(x)=20x^2+1080
C.R(x)=9x+69
D.R(x)=9x^2+29x+69
T(x) calculates the number of teams and F(x) calculates the entry fees.
To find the total entry fee, you would add the entry fee for each team together, so you need to add T(x) and F(x) together.
The answer would be C. R(x) = 9x +69
Answer:
T(x) calculates the number of teams and F(x) calculates the entry fees.
To find the total entry fee, you would add the entry fee for each team together, so you need to add T(x) and F(x) together.
The answer would be C. R(x) = 9x +69
Evaluate the log without a calculator ( Show your work )
[tex]log_{25} \frac{1}{5}[/tex]
Answer:
[tex]\log_{25}(\frac{1}{5})=-\frac{1}{2}[/tex]
Step-by-step explanation:
Let
[tex]\log_{25}(\frac{1}{5})=x[/tex]
We rewrite as an exponential equation to obtain;
[tex]\frac{1}{5}=25^x[/tex]
We rewrite both sides of the equation as an index number to base 5.
[tex]5^{-1}=5^{2x}[/tex]
Since the bases are the same, we equate the exponents to obtain;
[tex]-1=2x[/tex]
Divide both sides by 2;
[tex]x=-\frac{1}{2}[/tex]
Choose the correct answer.
If you do not pay the entire credit card bill, you are charged ____ on the unpaid part.
(1)a flat fee
(2)interest
Answer:
INTEREST just did it on odesseyStep-by-step explanation:
Answer:
If you do not pay the entire credit card bill, you are charged an interest on the unpaid part.
Step-by-step explanation:
If you do not pay the entire credit card bill, you are charged an interest on the unpaid part.
When you do not pay the entire bill or pay less than minimum or minimum amount, an interest is charged on the remaining balance.
The amount increases each month as the interest is added with the unpaid amount.
Identify the equation of the translated graph in general form x^2-y^2=9 for T(-4,2)
Answer:
B
Step-by-step explanation:
If an equation of the form [tex]x^2-y^2=a[/tex] goes through a translation T (p,q), the transformed equation has the form [tex](x-p)^2-(y-q)^2=a[/tex]
Using this, we can write the equation given as:
[tex](x-(-4))^2-(y-2)^2=9\\(x+4)^2-(y-2)^2=9\\x^2+8x+16-y^2+4y-4-9=0\\x^2-y^2+8x+4y+3=0[/tex]
So, B is the right answer.
Answer:
b. [tex]x^2-y^2+8x+4y+3=0[/tex]
Step-by-step explanation:
The given hyperbola has equation [tex]x^2-y^2=9[/tex].
This hyperbola is centered at the origin.
If this hyperbola is translated, so that its center is now at (-4,2), its equation now becomes;
[tex](x+4)^2-(y-2)^2=9[/tex]
We now expand to obtain;
[tex]x^2+8x+16-(y^2-4y+4)=9[/tex]
[tex]\Rightarrow x^2+8x+16-y^2+4y-4-9=0[/tex]
[tex]\Rightarrow x^2-y^2+8x+4y-4-9+16=0[/tex]
The correct choice is B.
[tex]\Rightarrow x^2-y^2+8x+4y+3=0[/tex]
If 2.5 is a root of the equation 2x^2+5x−q=0, what are the possible values of q?
Answer:
q = -25[tex]10 +5 = \pm \sqrt{5^2-4*2*q} \\ 225 = 25-8q \\\\8q = -200 \rightarrow q = -\frac {200}8 = -25[/tex]
Step-by-step explanation:
Grab the generic solution of the equation. [tex]\frac 52 = \frac{-5 \pm \sqrt{5^2-4*2*q}}{2*2}[/tex]. Let's isolate the radical, and square both sides.[tex]10 +5 = \pm \sqrt{5^2-4*2*q} \\ 225 = 25-8q \\\\8q = -200 \rightarrow q = -\frac {200}8 = -25[/tex]
Answer:
since we know that x1=2.5
we can just just use vieta's theorem
x1+x2=-b/a
x1*x2=c/a
What is the future value of the 10% savings from earnings of $187.45 if it earns 5% annual interest, compounded monthly for 30 years? Use the compound interest formula to estimate the present value.
Answer:
$83.75
Step-by-step explanation:
To find the future value, we first need to define our variables.
P = 187.45 x 0.10 = 18.745
r = 5% or 0.05
t = 30 years
n = 12
Now we can use the formula:
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
[tex]A=18.745(1+\dfrac{0.05}{12})^{12(30)}[/tex]
[tex]A=18.745(1+\dfrac{0.05}{12})^{360}[/tex]
[tex]A=83.75[/tex]
So the future value after 30 years is $83.75.
The future value of the 10% savings from earnings of $187.45 is $83.75.
Future valuePrincipal= 187.45 x 0.10 = 18.745
rate = 5%
time = 30 years
n = 12
Hence:
Future value=18.745 (1+0.05/12)^30×12
Future value=18.745 (1.05/12)^360
Future value=$83.75
Inconclusion the future value of the 10% savings from earnings of $187.45 is $83.75.
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What is the frequency of the function f(x)?
f(x)=3cos(5x)+2
Enter your answer, in simplest fraction form, in the box.
Answer:
The frequency = 5/2π
Step-by-step explanation:
* Lets revise some facts about the trigonometry function
- If the function is f(x) = A sin (B x + C) + D
* A is the amplitude
- The amplitude is the height from highest to lowest points and
divide the answer by 2
* The period is 2π/B
- The period is the distance from one peak to the next peak
- Period and Frequency are related where frequency = 1/period
* C is the horizontal shift
- The horizontal shift is how far the function is shifted to left
(C is positive) or to right (C is negative) from the original position.
* D is the vertical shift
- The vertical shift is how far the function is shifted vertically up
(D is positive) or down (D is negative) from the original position.
* Lets solve the problem
∵ f(x) = 3 cos (5x) + 2
∵ f(x) = A sin (B x + C) + D
∴ A = 3 , B = 5 , C = 0 , D = 2
∵ The period = 2π/B
∴ The period = 2π/5
∵ The frequency = 1/period
∴ The frequency = 1/(2π/5) ⇒ multiply up and down by 5
∴ The frequency = 5/2π
The frequency of the function f(x) = 3cos(5x) + 2 is 5/2π, represented as 5 cycles per unit interval on the x-axis.
The frequency of the function f(x) = 3cos(5x) + 2 is determined by the coefficient of x inside the cosine function. In this case, the coefficient is 5, which represents 5 cycles per unit interval on the x-axis. The standard form for a cosine function's frequency is given when the function is written as cos(2πft), with f representing the frequency. To match this form, we can rewrite the function as cos(2π(5/2π)x), making it clear that f = 5/2π cycles per unit interval, which is the frequency.
In simplest fraction form, the frequency of the function f(x) is 5/2π.
Using the linear equation 3x+2y=6, express y in terms of x
Answer: any number
Step-by-step explanation: 3x+2y=6, 2y=6-3x, we want y by itself, so divide by 2 from both sides, y=3-1.5x, then we plug it into the equation,3x+2(3-1.5)=6, then solve. 3x+6-3x=6, 3x-3x=0,so 6=6, y could be any possible answer
The expression for y in terms of x is y = 3 - (3/2)x the linear equation 3x+2y=6 .
To express y in terms of x using the linear equation 3x + 2y = 6, we need to isolate y on one side of the equation.
Step 1: Move the 3x term to the other side of the equation.
Subtract 3x from both sides:
3x + 2y - 3x = 6 - 3x
2y = 6 - 3x
Step 2: Now, to solve for y, divide both sides by 2:
y = (6 - 3x) / 2
Step 3: We can further simplify the equation:
y = 6/2 - (3x/2)
y = 3 - (3/2)x
So, the expression for y in terms of x is y = 3 - (3/2)x.
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A circle is divided into 20 equal parts. What is the angle measure of three of those left parts?
Answer:
54
Step-by-step explanation:
A circle is 360 degrees
We divide it into 20 parts
360/20 = 18
Each part is 18 degrees
We want the angle means of 3 of the parts
3*18 = 54
Three of the parts measures 54 degrees
Measure the length of the top of your desk in centimeters. Describe how you found the length
Answer:
55 centimeters
Step-by-step explanation:
Ok buddy, just say like 55 centimeters, and say you used a measuring tape.
2. What's the area of a circle with radius 18 units? A. 36? units2 B. 324? units2 C. 18? units2 D. 9? units2
c. 18 is the answer you get
Answer:
1017.87602
Step-by-step explanation:
A = π R squared = π · 18 squared ≈ 1017.87602
An equal number of men and women were randomly selected and asked how many hours per week they spend exercising
Answer:
1. Greater than
2 less than
3. More
Step-by-step explanation:
Please help me out!!!!!
Answer:
[tex]\frac{c}{a+b}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = A(0, 0) and (x₂, y₂ ) = C(a +b, c)
m = [tex]\frac{c-0}{a+b-0}[/tex] = [tex]\frac{c}{a+b}[/tex]
Answer:
[tex]\large\boxed{\dfrac{c}{a+b}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points A(0, 0) and C(a + b, c). Substitute:
[tex]m=\dfrac{c-0}{a+b-0}=\dfrac{c}{a+b}[/tex]
Bryan is cooking cupcakes for a bake sale at his club. The recipe calls for 12 cups of flour. He has already put 3 cups of flour in the mixing bowl. How many more cups does he need to put in? Write an equation to represent this problem. Then solve.
Answer:
9 cups
Step-by-step explanation:
12-3 = 9
Answer:
Bryan needs 9 cups more.
Step-by-step explanation:
Bryan is cooking cupcakes for a bake sale at his club. The recipe calls for 12 cups of flour.
Number of cups of flour, he already has = 3
Lets say he needs x cups more.
So, equation forms = [tex]12=x+3[/tex]
=> [tex]12-3=x[/tex]
x = 9
Hence, Bryan needs 9 cups more.
Simplify the equation √8^17
The answer is 8^8 * /8
Pl help me
WILL GIVE BRAINLIEST
Answer:
up
Step-by-step explanation:
Since this is written as y = function of x, it will open up or down
y = 3x^2 -5x -10
The coefficient of x^2 is positive so it will open up
The radius of a circle is ________ to the tangent where the radius intersects the circle.
A. supplementary
B. perpendicular
C. parallel
D. congruent
Olympic volleyball player Bev Oden averaged 3.42 "kills" (spikes that end a rally) per game. Predict her number of kills in a 5 game match.
Answer: 17.1
Step-by-step explanation:
If she averages 3.42 kills per game, she should average that for each of the 5 games. You need to multiply 3.42 times 5 for the total of 5 games.
3.42 x 5 = 17,1
Bev Oden, achieve approximately 17 kills in a 5 game match .
To predict the number of kills Bev Oden will achieve in a 5 game match, we can use her average kills per game to make the calculation.
Given that Bev Oden averages 3.42 kills per game, we simply multiply her average by the number of games in the match.
Step-by-step calculation:
Average kills per game: 3.42Number of games: 5Total kills = 3.42 kills/game x 5 games = 17.1 killsTherefore, Bev Oden is predicted to achieve approximately 17 kills in a 5 game match.
You work for a dress maker and your boss sends you to the fabric store to buy blue fabric. She tells you to buy the best deal. What is the best deal on fabric? A) 20 yards for $30.00 B) 40 yards for $45.00 C) 50 yards for $70.00 D) 65 yards for $85.00
Answer:
B 40 yards for $45 is the best deal at $1.13 per yard
Step-by-step explanation:
Break it down by finding the unit price per yard (divide cost by yardage)
A. 30/20 = $1.50 per yard
B. 45/40 = $1.125 per yard
C. 70/50 = $1.40 per yard
D. 85/65 = $1.30 per yard
Answer:a
Step-by-step explanation:
What's is 5x2/3
A. 3 1/3
B 3 2/5
C 5 2/3
D 10/15
Answer:
The answer is A. 3 1/3
Step-by-step explanation:
Simplify:
10/3
Then, convert to a mixed fraction:
3 1/3
Hope this helped.
The mathematical expression 5x2/3 = 15/3 x 2/3 = 30/9 = 5 2/3.
Option C is correct.
How do we calculate?an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Step 1: Simplify 5x2/3
5x2/3 = (5 x 2)/3
5x2/3 = 10/3
Step 2: Simplify 10/3
10/3 = 3 + 2/3
10/3 = 5 2/3
An expression in math can also be described as a statement having minimum of two numbers, or variables, or both and an operator connecting them.
Therefore, the correct answer is C.
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Solve the system using elimination. Write the solution as an ordered pair. (1 point) SHOW YOUR WORK FOR FULL CREDIT! (2 points)
13x + y = 15
-9x - 3y = -15
Answer: (1,2)
Step-by-step explanation:
You must:
- Multiply the first equation by 3.
- Add both equations.
- Solve for the variable left. In this case will be x.
Then:
[tex]\left \{ {{39x +3y = 45} \atop {-9x - 3y = -15}} \right.\\------\\ 30x=30\\x=1[/tex]
Substitute x=1 into any of the original equtions and solve for y:
[tex]13(1)+y=15\\y=2[/tex]
The solution is: (1,2)
Answer:
The solution of the system of equation is (1 , 2)
Step-by-step explanation:
The system of equation is:
* 13x + y = 15 ⇒ (1)
* -9x - 3y = -15 ⇒ (2)
- By using elimination ⇒ we must make on of the
two variables in the two equations has the same value
with different sign
- So we will multiply equation (1) by 3 to eliminate y
∴ 3(13x) + 3(y) = 3(15)
∴ 39x + 3y = 45 ⇒ (3)
- Now add (2) and (3)
∴ 39x + -9x = 45 + -15
∴ 30x = 30 ⇒ ÷ 30 both sides
∴ x = 1
- Substitute the value of x in equation (1) or (2)
- Lets use (1)
∴ 13(1) + y = 15
∴ 13 + y = 15 ⇒ subtract 13 from both sides
∴ y = 15 - 13
∴ y = 2
∴ The solution of the system of equation is (1 , 2)
A figure is translated horizontally 4 units. Which drawing shows a correct translation? A B C D
Answer:
The Answer is C!! (With two L's pointing right)
Step-by-step explanation:
Answer:
Give the other person brainliest they deserve it!
Step-by-step explanation:
Which transformation shows a translation of 3 units to the right?
A) B) C) D)
Five friends buy a shirt that costs x dollars and a pair of shoes that cost $24.00.
How many parameters are needed to fully describe any normal distribution?
Answer:
There are only two parameters needed to define any normal distribution curve.
Step-by-step explanation:
The two parameters are mean and standard deviation. This will allow us to see how far from the mean the curve exists and where the center is.
Parallel lines e and f are cut by transversal b.
e=(2x+10)
f=(3x-15)
What is the value of x?
1
5
25
37
Answer:
25
Step-by-step explanation:
Answer:
the answer is 25. hope this helps