Answer:
J would be the answer, my friend.
log2 (24/3) = log5 (x)
log(8)/log(2) = log(x)/log(5)
log(x) = [log(5)][3]
log(x) = log(5^3)
x = 5^3 = 125
Step-by-step explanation:
Answer:
x = 125
Step-by-step explanation:
[tex] \log_2 24 - \log_2 3 = \log_5 x [/tex]
Use the rule of subtracting logs:
[tex] \log_b x - \log_b y = \log_b \dfrac{x}{y} [/tex]
[tex] \log_2 \dfrac{24}{3} = \log_5 x [/tex]
[tex] \log_2 8 = \log_5 x [/tex]
[tex] 3 = \log_5 x [/tex]
Use the definition of log:
[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]
[tex] x = 5^3 [/tex]
[tex] x = 125 [/tex]
I need to write an equation for y = mx + b, The numbers i have are 20-80 and 1-4
Answer:
y = 20x
m = 20 and b = 0
Step-by-step explanation:
For input values of x = 1, output value of y = 20 and for x = 4, y = 80.
Therefore, the equation of this relation can be written as
[tex]\frac{y - 80}{80 - 20} = \frac{x - 4}{4 - 1}[/tex]
⇒ 3(y - 80) = 60(x - 4)
⇒ 3y - 240 = 60x - 240
⇒ y = 20x
Now, y = mx + b is the equation and hence, m = 20 and b = 0 and the actual equation is y = 20x. (Answer)
the formula d = 26t + 32.5 can be used to find the distance (d) between two cars after traveling (t) hours in opposite directions. How many hours will it take for the cars to be 117 miles apart?
A: 0.5
B: 2.05
C: 3.25
D: 4.5
Answer:
C
Step-by-step explanation:
The formula given is:
[tex]d=26t+32.5[/tex]
Where
d is the distance between two cars
and
t is the time it takes
We want the time it takes (so we need t) for the cars to be 117 miles apart (this is the distance). Thus, it means:
d = 117
t = ???
We plug in 117 into d and solve the equation for t. Shown below:
[tex]d=26t+32.5\\117=26t+32.5\\117-32.5=26t\\84.5=26t\\t=\frac{84.5}{26}\\t=3.25[/tex]
So, it takes 3.25 hours
Correct answer is C
Final answer:
Using the formula d = 26t + 32.5 and setting d to 117 miles, we solve for t to find that it takes approximately 3.25 hours for the two cars to be 117 miles apart. The correct answer is C: 3.25.
Explanation:
To find out how many hours it will take for two cars to be 117 miles apart if they travel in opposite directions using the formula d = 26t + 32.5, we need to set d equal to 117 miles and solve for t.
First, we substitute 117 for d in the equation:
117 = 26t + 32.5
Next, we subtract 32.5 from both sides to isolate the term with t:
117 - 32.5 = 26t => 84.5 = 26t
Then we divide both sides by 26 to solve for t:
t = 84.5 / 26 => t ≈ 3.25
Hence, it will take approximately 3.25 hours for the cars to be 117 miles apart.
Thus, the correct answer is C: 3.25.
If an account is increasing at a rate of 3.3% compounded semiannually, what is the exact value of in the following present value
ordinary annuity formula?
PV-P1-(1+1)*
a) 3.3
b) 0.033/100
c) 0.033/2
d) 0.33/2
Answer:
The correct answer is C. 0.033/2
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Annual interest rate = 3.3% compounded semiannually
2. Let's find the exact value of the rate:
Number of periods (n) = n/2, given that periods are semesters and not years
Annual interest rate (r) = 3.3% = 3.3/ 100 = 0.033
For using the correct value in the present value annuity formula, we also have to divide the annual interest rate because the interest is compounded semiannually or every six months, what it means:
0.033/2
The correct answer is C. 0.033/2
c. [tex]\frac{0.033}{2}[/tex]
on edgen
Explain the difference between (-10) To the second power. And -10 To the second power.
Answer:
Basically when you use parantheses it protects that number from becoming negative...
-10^2 is -100 but with paranthesis is 100
Answer:
without the parenthesis it would just be 100 but with it, it would be -100 :)
The senior classes at High school A and High school B planned separate trips to New York city. The senior class at high school A rented and filled 1 van and 6 buses with 372 students, High school B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. how many students can a van carry? How many students can a bus carry?
Each van carried 18 students and each bus carried 59 students.
Step-by-step explanation:
Let,
students carried by one van = x
students carried by one bus = y
According to given statement;
x+6y=372 Eqn 1
4x+12y=780 Eqn 2
Multiplying Eqn 1 by 4
[tex]4(x+6y=372)\\4x+24y=1488\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](4x+24y)-(4x+12y)=1488-780\\4x+24y-4x-12y=708\\12y=708[/tex]
Dividing both sides by 12
[tex]\frac{12y}{12}=\frac{708}{12}\\y=59[/tex]
Putting y=59 in Eqn 1
[tex]x+6(59)=372\\x+354=372\\x=372-354\\x=18[/tex]
Each van carried 18 students and each bus carried 59 students.
Keywords: Linear equations, subtraction
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Each van carried 18 students and each bus carried 59 students.
Step-by-step explanation:
Let,
students carried by one van = x
students carried by one bus = y
According to given statement;
x+6y=372 Eqn 1
4x+12y=780 Eqn 2
Multiplying Eqn 1 by 4
Subtracting Eqn 2 from Eqn 3
Dividing both sides by 12
Putting y=59 in Eqn 1
Mia ordered five DVDs, all at the same price, from an online retailer. There was a shipping charge of $14.50 for the complete order but no sales tax. If Mia’s total charge for her order was $79.45, what was the price of each DVD?
Answer:
$12.99
Step-by-step explanation:
you take $79.45 and subtract it by $14.59 that equals $64.95. Then you take 64.95 and divide it by 5 and your total of each DVD is 12.99
The price of each DVD from online retailer is, $12.99
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
There was a shipping charge of $14.50 for the complete order but no sales tax.
And, Mia’s total charge for her order was $79.45.
Now, The cost of 5 DVD = $79.45 - $14.50
= $64.95
Hence, The price of each DVD from online retailer is,
⇒ $64.95 / 5
⇒ $12.99
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what is the solution to the linear equation - 12 + 3B -1 = -5 - b
Step-by-step explanation:
3B+b=_5+12+1
4Bb=8
4Bb/4=8/4
Bb=2
Answer:
B = 2
Step-by-step explanation:
To solve the linear equation;
- 12 + 3B -1 = -5 - B
we will first collect like-term that is; we will make all the B variables to be on the left-hand side of the equation and all the constant to be on the right-hand side of the equation
( when -B cross over to the left-hand side of the equation, B becomes positive, when -12 and -1 cross over to the right-hand side of the equation, they become positive 12 and 1)
3B + B = -5 + 12 + 1
4B = 8
Divide both-side of the equation by 4 to get the value of B
4B/4 = 8/4
(on the left-hand side of the equation ,4 will cancel out 4 leaving us with B and 8 will be divided by 4 to give us 2)
B = 2
Therefore the solution to the linear of the equation is B = 2
Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft. from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.
will give 5 stars and mark brainliest.
Answer:
6.67 feet
Step-by-step explanation:
The situation is as shown in the figure.
ON is the normal to the mirror at the point of incidence O
⇒ ∠BON = ∠DON = 90°
By the laws of reflection: angle of incidence = angle of reflection :
∠AON = ∠CON
⇒ ∠AOB = ∠COD
⇒tan(∠AOB) = tan(∠COD)
⇒[tex]\frac{AB}{OB}[/tex] = [tex]\frac{CD}{OD}[/tex]
⇒[tex]\frac{6}{4}[/tex] = [tex]\frac{10}{x}[/tex]
⇒x = [tex]\frac{40}{6}[/tex] = [tex]\frac{20}{3}[/tex] = 6.67 ft
∴ Distance of the mirror from basketball goal is 6.67 ft
Final answer:
Using the principles of similar triangles, we determine that the mirror is 6 feet from the basketball goal by setting up a proportion between the heights and distances of the triangles formed by the goal and Mumford's line of sight. The mirror is 6 feet from the basketball goal.
Explanation:
To determine how far the mirror is from the basketball goal, we can use the principles of similar triangles. Basketball star Mumford is a six-foot-tall senior forward, meaning he is 6 feet above the ground. The basketball goal is 10 feet tall. If he walks backward four feet, and then he is able to see the top of the basketball goal, we can set up a proportion because the angles of incidence and reflection are equal.
Let's let x be the distance from the base of the basketball goal to the mirror. We then have two similar triangles to work with:
The large triangle with the height of the goal (10 feet) and the base x + 4 feet (distance from the goal to Mumford's eyes).
The smaller triangle with the height from Mumford's eyes to the ground (which is 6 feet because he's a six-foot-tall person) and the base x (distance from the goal to the mirror).
The proportion we set up is:
(Height of basketball goal) / (Distance from goal to Mumford's eyes) = (Height of Mumford's eyes from the ground) / (Distance from goal to the mirror)
10 / (x + 4) = 6 / x
Solving for x gives us the distance from the mirror to the basketball goal:
10x = 6(x + 4)
10x = 6x + 24
4x =24
x = 6
Therefore, the mirror is 6 feet from the basketball goal.
4. A home purchased for $120,000 in 2012 is sold for $156,000 in 2015. What is the percent
change in the price?
2x - (4x - 4) = 16 - 8
What is the answer
Answer:
X=-2
Step-by-step explanation:
PLUG IT IN HTE EQUATION BRAINLIEST PLZZZ
Answer:
x = - 2
Step-by-step explanation:
Given
2x - (4x - 4) = 16 - 8 = 8 ← distribute parenthesis and simplify left side
2x - 4x + 4 = 8
- 2x + 4 = 8 ( subtract 4 from both sides )
- 2x = 4 ( divide both sides by - 2 )
x = - 2
5a(-3b)(-2a^2b^3)
what is the answer to this question?
Answer:
(3•5•2a3b4)
Step-by-step explanation:
Step by step solution :
Step 1 :
Equation at the end of step 1 :
-15ab • (0 - (2a2 • b3))
Step 2 :
Multiplying exponential expressions :
2.1 a1 multiplied by a2 = a(1 + 2) = a3
Multiplying exponential expressions :
2.2 b1 multiplied by b3 = b(1 + 3) = b4
A company donated money to valley high school. The principal decided to evenly split the funds between the fifteen classes to spend on supplies. If $3,840 was donated, how much did each class get
Answer:
$256
Step-by-step explanation:
Each class got $256. I know this because I did 3,840 divided by 15 which got me the CORRECT answer of $256
Answer:
$256
Step-by-step explanation:
if there was $3840 donated and theres 15 classes that need to get an even amount so you would do 3840÷15 to see how many times 15 can go in to 3840 to find the even amount of money each class should recieve which is $256
. The function s(l) = 1.34 √l models the maximum speed s in knots for a sailboat with length l in feet at the waterline. a. Use the model to find the length of a sailboat with a maximum speed of 12 knots. Round to the nearest foot.
Answer:
The length of the sailboat is 80 feet.
Step-by-step explanation:
The function
[tex]s(l) = 1.34 \sqrt{l}[/tex] ................ (1)
models the maximum speed s in knots for a sailboat with length l in feet at the waterline.
So, using this model we have to find the length of a sailboat with a maximum speed of 12 knots.
Now, from equation (1) we get
[tex]12 = 1.34 \sqrt{l}[/tex]
⇒ [tex]\sqrt{l} = 8.955[/tex]
⇒ [tex]l = (8.955)^{2} = 80[/tex] feet (Answer)
{The value is round to the nearest foot}
Paula used these steps to solve an equation:
Step 1: -4(7 + 8) - 21 = 25
Step 2: -4r – 32 - 2x = 25
Step 3: -61 – 32 = 25
Step 4: -6x = 57
Step 5: x = -95
Between which two steps did Paula use the division property of equality?
Answer:
Between step 4 and step 5
Step-by-step explanation:
The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.
That is, if a, b, and c are real numbers such that a = b and c ≠0, then
[tex]\frac{a}{c} = \frac{b}{c}[/tex]
At step 4: The equation was -6x = 57
To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below
[tex]-6x = 57[/tex] ---- Divide both sides by -6 (Step 4)
[tex]\frac{-6x}{-6} = \frac{57}{-6}[/tex] ---- (Intermediary between step 4 and 5)
[tex]x = -9.5[/tex] ----- Step 5
Hence, we can conclude that the division property of equality was done between step 4 and step 5
1. What is the definition of a function in algebra?
2. which one of the sets below is a function? Explain why.
(3,3) (4,4) (5,5) (6,6) (1,6) (2,6) (3,4) (2,8)
3. What is slope-intercept form?
4. In the equation y = -2x + 6 identify the slope and y-intercept
5. what is the slope and equation of a horizontal line and a vertical line?
1. The definition of a function is based on the concept of a mapping from one set to another, where each element in the domain has a unique image in the range. This is a fundamental concept in mathematics and is used to describe relationships that are deterministic in nature.
2. To determine if a set of ordered pairs is a function, one must ensure that no two ordered pairs have the same first component (x-value) and different second components (y-values). This is known as the vertical line test. If a vertical line can be drawn that intersects the graph of the relation at more than one point, then the relation is not a function.
3. The slope-intercept form is a standard form for linear equations that is particularly useful for graphing lines and for understanding the slope and y-intercept of the line. It is derived from the general form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
4. In the given equation y = -2x + 6, the coefficient of x represents the slope, which is -2, indicating that for every 1 unit increase in x, y decreases by 2 units. The constant term, 6, represents the y-intercept, which is the value of y when x = 0.
5. A horizontal line has a slope of zero because there is no change in the y-value as the x-value changes. Thus, the slope, which is the ratio of the change in y to the change in x, is zero. The equation of a horizontal line is simply y = b, where b is the y-value of every point on the line.
A vertical line has an undefined slope because the change in x is zero (since x does not change), and division by zero is undefined in mathematics. The equation of a vertical line is x = a, where a is the constant x-value for every point on the line.
10 students per teacher. Write two ratios to represent this information
x/5 +8=3 what would x be
Answer: x= -25
Step-by-step explanation:
Answer:
x=-25
Step-by-step explanation:
x/5 = 8 = 3 you would multiply both sides by 5
youd end up with x+40=15 then you would move the constan to the right
x=15-40 you would subtract 40 from 15
x=-25
i will give brainliest
Which expression represents the sequence below?
16, 24, 32, 40.....
an=4n+1 an=8n+8 an=8n+16
Answer:
[tex]a_n = 8n+8[/tex] represent the sequence 16,24,32,40...
Step-by-step explanation:
The sequence given is
16,24,32,40.
And the options given are
an=4n+1
an=8n+8
an=8n+16
We will check for all so as to find the correct expression.
In the given sequence the first term is 16,
i.e a1 = 16
1). We will check for an = 4n+1 whether the first term is 16 or not.
We will put the value of n as 1;
[tex]a_1= 4\times1+1= 4+1=5[/tex]
With this option we get the first term as 5 but in the given sequence first term is 16.
Hence this option is Incorrect.
2). We will check for an = 8n+8 whether the first term is 16 or not.
We will put the value of n as 1;
[tex]a_1= 8\times1+8= 8+8=16[/tex]
With this option we get the first term as 16 and in the given sequence also first term is 16.
Hence this option is correct.
3). We will check for an = 8n+16 whether the first term is 16 or not.
We will put the value of n as 1;
[tex]a_1= 8\times1+16= 8+16=24[/tex]
With this option we get the first term as 24 but in the given sequence first term is 16.
Hence this option is Incorrect.
Hence we can say that an = 8n+8 represent the sequence 16,24,32,40...
Through:(5,1), parallel to y =1/5x-4
If the line is parallel to y=1/5x-4, the line must have the same slope.
So, the slope of your line is 1/5.
Now we need to find the y intercept. We should use the point given.
y=mx+b
1=1/5(5)+b
b=0
Equation: y=1/5x
Answer:
y = (1/5)x
Step-by-step explanation:
y = mx+b
m= slope would be the same i.e. 1/5 , since it's parallel to the given equation.
y= 1
x= 5
Hence, let's look for the equation of this line of which the coordinate is provided!
1 = (1/5)(5) + b
1 = 1 +b
1-1 = b
b = 0
Hence the equation of this line is:
y = 1/5(x)
Hope this helps!
Mark brainliest of you think I helped! Would really appreciate!
801,504 round to the nearest thousand
Answer:
802,000
Step-by-step explanation:
The number in the thousands place is 1, and the number to the right of it is 5. And if the number to the right is greater than or equal to 5 the place value that you are rounding goes up by one.
5,069 round to the nearest tenth
Answer:
5,070
Step-by-step explanation:
Answer:
5069.0
Step-by-step explanation:
The tenth value is the value directly after the decimal point. In this case, the number given is a whole number, and so to find the tenth place value, add a decimal point and a 0 to the back.
~
please solve much appreciated
Answer:
i) C; x=y= 80°, ii) B; x= 58°, iii) D; x= 62° and y= 56°, iv) D; none of these are correct.
Step-by-step explanation:
i) Full angle around is 360°
As given one angle is 100°,which means vertically opposite angles are equal to 100°
Now, remaining angle is equal to [tex]360-200= 160°[/tex]
∵ x and y are vertically opposite angle, which means they are equal.
∴x=y= 80°
ii) As we know straight angle is equal 180°
As given one of the angle is 32° and other says, it is a right angle which is equal to 90°.
∴ ∠x= [tex]180-(90+32)= 58°[/tex]
∴∠x= 58°
iii) Full angle = 360°
2∠x = 124° (∵ Vertically opposite angle are equal )
⇒∠x= [tex]\frac{124}{2}[/tex]
∴∠x= 62°
∠x+∠x+∠y= 180° (∵ it is a straight angle)
2∠x+∠y= 180°
⇒[tex]124+ y= 180[/tex]
Subtracting both side by 124
⇒∠y= [tex]180-124= 56°[/tex]
∴∠y= 56°
iv) Full angle= 360°
∴ ∠x+22°+32°+51°= 360°
Subtracting both side by 105
∠x= [tex]360-105= 255°[/tex]
∴∠x= 255°
Which means none of the given option are correct.
What is the equation of a circle with center (1, -4) and radius 2?
A. (x-1)^2 + (y+4)^2 = 4
B. (x-1)^2 - (y+4)^2 = 4
C. (x-1)^2 + (y+4)^2 = 2
D. (x+1)^2 + (y-4)^2 = 4
Answer:
A) (x-1)^2+(y+4)^2=4
Step-by-step explanation:
Here's the equation of a circle with center and radius:
(x-h)^2+(y-k)^2=r^2 with the center being at the point (h, k)
and the radius being r.
(x-1)^2+(y-(-4))^2=2^2
(x-1)^2+(y+4)^2=4
The equation of a circle with center (1, -4) and radius 2 is (x-1)²+(y+4)²=4
The correct option is (A).
What is equation of circle?The equation of circle represents the locus of point whose distance from a fixed point is a constant value. This fixed point is called the center of the circle and the constant value is the radius of the circle.
The standard equation of circle with center at (x1,y1) and radius r is (x−x1)²+(y−y1)²=r².
We know equation of circle,
(x-a)²+(y-b)²=r²
Here, a=1, b=-4 and r=2
So,
(x-1)²+(y-(-4))²= 2²
(x-1)²+(y+4)²=4
Hence, the equation of circle is: (x-1)²+(y+4)²=4
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Given 1+ cos x/ sin x + sin x/1+ cos x= 4, find a numerical value of one trigonometric function of x.
Answer:
The numerical value of the trigonometric function is 30 °
Step-by-step explanation:
Given trigonometric function as :
[tex]\frac{1 + cos x}{sin x}[/tex] + [tex]\frac{sin x}{1 + cos x}[/tex] = 4
or, Taking LCM we get
[tex]\frac{(1+cosx)^{2}+sin^{2}x}{(sinx)\times (1+cosx)}[/tex] = 4
Or, ( 1 + cos x )² + sin² x = 4 × ( sin x ) × ( 1 + cos x )
1 + cos² x + 2 cox + sin² x = 4 sin x + 4 sin x × cos x
or, ( cos² x + sin² x ) + ( 1 + 2 cos x ) = 4 sin x ( 1 + cos x )
∵ cos² x + sin² x = 1
or, 1 + 1 + 2 cos x = 4 sin x ( 1 + cos x )
or, 2 + 2 cos x = 4 sin x ( 1 + cos x )
or, 2 ( 1 + cos x ) = 4 sin x ( 1 + cos x )
Or, [tex]\frac{2 ( 1+ cos x )}{4 ( 1 + cos x )}[/tex] = sin x
Or, sin x = [tex]\frac{1}{2}[/tex]
∴ x = [tex]sin^{-1}\frac{1}{2}[/tex]
∵ sin 30 ° = [tex]\frac{1}{2}[/tex]
I.e x = 30 °
Hence The numerical value of the trigonometric function is 30 ° answer
Answer: D. sin x= 1/2
Step-by-step explanation:
Edg 2020
What is the y intercept of the equation y=4x+1
Answer:
+1
Step-by-step explanation:
The y-intercept is +1.
Please help!!!!!!!! The question is in the picture!
Answer:
D
Step-by-step explanation:
multiply out the top to get 6x - 4 + 2x - 2 = 8x - 6
next look at the 4 choices.
when we multiply out and combine only for the x term, only the bottom two give us 8x.
3/4 * 4x + 5 * x = 8x
3/4 * 4x + 1/6 * 30x = 8x
next we look at the bottom two for which one will give us -6, in this case only D will.
3/4 * -8 + 5 * 15 = 69
3/4 * -12 + 1/6 * 18 = -6
What is the following product? Square root y^3 * square root x^3
The product of two square roots is equal to the square root of the product, so the product of √y3 and √y3 is y3.
The equation is asking you to multiply the square root of y cubed by itself.
Based on the properties of square roots, if you multiply the square root of a number by itself, you get the original number.
This is because multiplication is the inverse operation for square roots. Meaning, it undoes the square root.
So, in this scenario, you are multiplying [tex]\sqrt{y^{3} }[/tex] * [tex]\sqrt{y^{3} }[/tex]which results in y^3.
Thus, the product of [tex]\sqrt{y^{3} }[/tex] and [tex]\sqrt{y^{3} }[/tex]is y^3, assuming y≥0.
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You find a car that costs $18,500. If the interest rate on a 5-year loan is 6.25% and you make monthly payments on the car, what is the total amount of interest that you will pay over the life of the loan?
i need help with 7-10 plz help
Answer:
bro in Ur pictures there is no 7-10
Step-by-step explanation:
10-7 is 3 right so 7-10 is -3 it simple . but show me questions again because there is no 7-10 . Thank for ur asking me !
Evaluate the expression when y = 4. 5 + y + 8
a.13
b.17
c.21
d.72
Answer:
17 is the simplified answer.
Step-by-step answer:
Given that:
y = 4.
We have to evaluate:
=5 + y + 8
By putting value of y that is y =4 in above equation:
=5 +4 +8
=9 +8
=17
So 17 is simplified answer for this question.
I hope it will help you!