ANSWER: 27 because the less people there is the more longer it takes
2 logx 2 + logx 6 = 2
I really need this answer on properties of logarithms: practice
Answer:
Step-by-step explanation:
Simplify the expressionApply the logarithm power identityApply the logarithm product identitySimplify the expression2Exponentiate both sides
log10(4x8)=2log10(48)=2
48=102
x=258=258√
Wally Martin purchased an office chair for $167.87. He received a $19.95 rebate from the manufacturer and a $8.95 rebate from the store. What is the final price?
what are the x- and y- coordinates of point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B? x= [m/m+n](x2 -x1) +x1 y = [m/m+n](y2 - y1) +y1
The coordinates of the point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B are (-1, 2).
How to obtain the coordinates of point P?The coordinates of point P are obtained applying the proportions in the context of the problem.
P is 2/3 the length of the line segment from A to B, hence the equation is given as follows:
P - A = 2/3(B - A)
Then the x-coordinate of P is obtained considering the x-coordinates of A and B as follows:
x - 9 = 2/3(-6 - 9)
x - 9 = -10
x = -1.
The y-coordinate of P is obtained considering the y-coordinates of A and B as follows:
y + 8 = 2/3(7 + 8)
y + 8 = 10
y = 2.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Find the equation of the line containing the point
P(−2, 3)
and perpendicular to the graph of
3x + 9y = −2.
Answer:
Step-by-step explanation:
y = 3x + 9
Find the volume of the composite figure.
Answer:
volume = 290m
Step-by-step explanation:
box 1
[tex]vol= lwh\\=3*5*6\\=90m[/tex]
box 2
[tex]vol=lwh\\=8*5*5\\=200m[/tex]
total volume = 90+200 =290m
Out of 144 children who have school dinners, 1/3 chose pasta, 1/4 chose jacket potatoes and the rest chose curry. How many chose curry?
Answer:
A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us
Step-by-step explanation:
i may be wrong but I tried
7.2 Puzzle Time
Where Did Columbus Land when He Found America
The answer to the puzzle is (3)O (7)N which makes word ON, (4)T (10)H (1)E which makes word THE, (6)B (8)E (2)A (9)C (5)H which makes the word BEACH
What is a quadrilateral?
A quadrilateral is a 4 sided polygon. On the basis of its properties quadrilaterals are classified as Trapezium,Kite, Parallelogram, Rectangle, Rhombus and square.
Complete the sentence:
1.Parallelogram-(E)
2.Quadrilateral-(A)
3.Supplementary-(O)
4.Bisect-(T)
5.Congruent-(H)
Using the diagram:
6.Given that KG=17 units, KJ=14 units.
As we know from the figure, GH is congruent to KJ and HJ is congruent to side KG.
Therefore, GH=KJ=14units- (B)
7.∠GKJ=86° and ∠GHJ=(x+6)°
We know that ∠GKJ is congruent to ∠GHJ
Therefore, x+6 = 86
x=86-6
x=80-(N)
8.Given KH=20 & KF= KH÷2 {diagonal pf parallelogram bisect}
=20 ÷ 2
=10 units-(E)
9.Given ∠HJK=82° & We know ∠HJK+∠GKJ=180° {consecutive angles}
∠GKJ=180-∠HJK
=180-82
=98°-(C)
10.Give that, ∠HJK=82° & we know ∠HGK=∠HJK {opposite angles of parallelogram}
∠HGK=82°-(H)
To know more about quadrilaterals, visit:
https://brainly.com/question/29635320
#SPJ1
SOLVE THIS BUT I DON'T WANT ANSWER I WANT SOLVING AND ANSWER
50PTS
WILL MARK AS BRAINLIEST
50/1.428
Answer:
Alright
Step-by-step explanation:
50/1.428
Multiply the numerator by the denominator to get 50000/1428
Set equation up in long division format
Divide 50000 by 1428 to get 3
Divide 7160 by 1428 to get 5
Divide 200 by 1428 to get 0
Divide 2000 by 1428 to get 1
Divide 5720 by 1428 to get 4
Divide 80 by 1428 to get 0
Divide 800 by 1428 to get 0
35.014
Adrian eats 2/3's of a pack of gum each
day. How many packs of gum will he
have eaten after 7 days?
10 points given!!
A study found that the mean amount of time cars spent in drive-throughs of a certain fast-food restaurant was 137.5 seconds. Assuming drive-through times are normally distributed with a standard deviation of 27 seconds, complete parts below:
why is ÷ by five a step, there did this 5 come from if its not in the inequality?
Answer:
You divide by five because it's the common factor of 5 and 15 in the 4th line of work and the goal is to solve for x. The only way to get x alone in the inequality 5x>15 is to divide each side by 5. This would give you x and 3, hence the answer: x > 3
[tex]\frac{5x}{5} =x\\\\\frac{15}{5} =3[/tex]
the sum of
44+45+46+47+...+131
Answer:313:)
Step-by-step explanation:
PLEASE HELP???!!!!!!!
The quadratic equation on the graph can be written as:
y = x² + 6x + 8
Which function is represented byy the graph?Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:
y = a*(x - h)² + k
Here we can see that the vertex is at (-3, -1), replacing that we will get:
y = a*(x + 3)² - 1
Now we can also see that it passes through the point (-2, 0), replacing these values we will get:
0 = a*(-2 + 3)² - 1
0 = a - 1
1 = a
Then the quadratic is:
y = (x + 3)² - 1
Expanding that we get:
y = x² + 6x + 9 - 1
y = x² + 6x + 8
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
Please help
Find the surface area (show work)
Answer:
148 cm²
Step-by-step explanation:
You want the surface area of a cuboid with edge lengths 4 cm, 5 cm, and 6 cm.
AreaThe formula is shown in your problem statement.
It can be made easier to compute using a little rearranging:
SA = 2LW +2LH +2WH
SA = 2(LW +LH +WH)
SA = 2(LW +H(L +W))
The choice of dimensions for L, W, and H doesn't matter.
SA = 2(4·6 +5(4+6)) = 2(24 +5(10)) = 2(74) = 148 . . . . cm²
The surface area is 148 cm².
A superintendent of a school district awarded a total of $5000 in bonuses to the most productive teachers that helped impact student achievement this pat year. The bonuses were awarded in the amount of $500 or $1000. If at least one $500 bonus and at least one $1000 bonus were awarded, what is a total possible number of $500 bonuses awarded?
A total possible number of bonuses awarded is given as follows:
6 bonuses.
How to obtain the total number of bonuses awarded?The total number of bonuses awarded is obtained applying the proportions in the context of the problem.
The total amount of bonuses is of $5,000, and at least one $500 bonus and at least one $1000 bonus were awarded, hence the remaining amount to be awarded is of:
5000 - (500 + 1000) = $3,500.
For an amount of $3,500, a possible division of the bonuses is given as follows:
One bonus of $500.Three bonuses of $1000.Hence a possible number of bonuses is given as follows:
2 + 1 + 3 = 6 bonuses.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Marisol draws a rectangle with a length of 12 inches and a width of 6 inches
Area of the rectangle is 72 square inches and the perimeter of the same rectangle is 36 inches by using this parameters Marisol can draw a rectangle.
What is a rectangle?A quadrilateral or four-sided polygon with four right angles (90° angles) and opposite sides that are parallel and the same length is referred to as a rectangle. It is a two-dimensional shape with four vertices and two pairs of parallel sides.
Given that,
the length is 12 inches and width is 6 inches,
So, The Area of rectangle = (Length × Width)
= 12 inches × 6 inches
= 72 square inches
So the area of the rectangle is 72 square inches.
The perimeter of a rectangle is given by adding up the lengths of all four sides.
The Perimeter of rectangle = (2 × length) + (2 × width)
= 2 × 12 inches + 2 × 6 inches
= 24 inches + 12 inches
= 36 inches
So the perimeter of the rectangle is 36 inches.
To know more about rectangle, visit:
https://brainly.com/question/2607596
#SPJ1
In summary, Marisol's rectangle has a length of 12 inches, a width of 6 inches, an area of 72 square inches, and a perimeter of 36 inches.
Sure, I'd be happy to help you with your question! Marisol has drawn a rectangle that has a length of 12 inches and a width of 6 inches. The rectangle is a two-dimensional shape that has four straight sides and four right angles. To calculate the area of the rectangle, we can use the formula:Area = Length x Width.
In this case, the area of the rectangle is 12 inches x 6 inches = 72 square inches. The perimeter of the rectangle is the distance around the outside of the shape, which is calculated by adding the lengths of all four sides. In this case, the perimeter of the rectangle is 2 x (length + width) = 2 x (12 inches + 6 inches) = 2 x 18 inches = 36 inches.
It's important to note that the length and width of the rectangle can be interchanged and the area and perimeter will remain the same.In conclusion, Marisol's rectangle measures 12 inches long, 6 inches wide, 72 square inches in size, and has a circumference of 36 inches.
To learn more about : Marisol's
https://brainly.com/question/6686394
#SPJ11
21 20 18 15 11 ? WHAT COMES NEXT
Answer: 6
Step-by-step explanation:
21 - 1 = 20
20 - 2 = 18
18 - 3 = 15
15 - 4 = 11
11 - 5 = 6
stal Find the Product (X+3÷x)²
the product of (x + 3/x)² is x² + 6 + 9/x².
Why it is and what is Algebra?
To find the product of (x + 3/x)², we can use the formula for squaring a binomial:
(a + b)² = a² + 2ab + b²
In this case, we have a = x and b = 3/x, so we can substitute these values into the formula and simplify:
(x + 3/x)² = x² + 2(x)(3/x) + (3/x)²
= x² + 6 + 9/x²
Therefore, the product of (x + 3/x)² is x² + 6 + 9/x².
Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols. It involves the use of letters and symbols to represent numbers and quantities in equations and expressions. The primary goal of algebra is to solve mathematical problems and equations using various operations such as addition, subtraction, multiplication, and division.
Algebraic concepts can be applied to a wide range of mathematical and real-world problems, including geometry, physics, engineering, economics, and statistics.
To know more about Algebra related questions visit:
https://brainly.com/question/24875240
#SPJ1
Complete question:
Find the product of (x + 3/x)²2.
Steps for solving t|u prove mt=mu
We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.
How to solve the problem?Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.
To get mt = m, substitute u = tk into mt = mu (tk).
Rewrite m(tk) as (mt)k using the associative property of multiplication.
To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.
Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.
Since 1 Equals k, we get u = tk = t(1) = t.
We get mt = mt by substituting u = t into the original equation mt = mu.
As a result, we have demonstrated that mt = mu when t | u.
To know more about equation visit:
brainly.com/question/649785
#SPJ1
Investing $1,000 at a 5% annual interest rate for 6 years, compounded every two months,
yields $1,348.18. Without doing any calculations, rank these four possible changes in order
of the increase in the interest they would yield from the greatest increase to the least
increase:
• Increase the starting amount by $100.
• Increase the interest rate by 1%.
• Let the account increase for one more year.
• Compound the interest every month instead of every two months.
Once you have made your predictions, calculate the value of each option to see if your
ranking was correct.
Answer:
Step-by-step explanation:
Ranking:
Compound the interest every month instead of every two months.
Increase the interest rate by 1%.
Let the account increase for one more year.
Increase the starting amount by $100.
Calculations:
If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.
If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.
If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.
If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.
Prove the Converse of the Pythagorean Theorem
The Converse of the Pythagorean Theorem is proved below.
What is Pythagoras Theorem ?
Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The converse of the Pythagorean theorem states that if a triangle has sides of length a, b, and c, where c is the longest side, and a² + b² = c², then the triangle is a right triangle.
To prove the converse of the Pythagorean theorem, we can use the fact that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is, if a triangle has sides of length a, b, and c, where c is the longest side and c² = a² + b², then the triangle is a right triangle.
Proof:
Suppose we have a triangle ABC, with sides of length a, b, and c, where c is the longest side. Assume that a² + b² = c². We want to show that triangle ABC is a right triangle.
We will use the Law of Cosines to show that angle C is a right angle. The Law of Cosines states that for any triangle ABC with sides of length a, b, and c opposite angles A, B, and C, respectively:
c² = a² + b² - 2ab cos(C)
Substituting a² + b² = c² into this equation, we get:
c² = c² - 2ab cos(C)
2ab cos(C) = 0
cos(C) = 0
Since 0 is the cosine of 90 degrees, this implies that angle C is a right angle. Therefore, triangle ABC is a right triangle.
Thus, this completes the proof of the converse of the Pythagorean theorem.
To know more about Pythagoras theorem visit:
https://brainly.com/question/343682
#SPJ1
Which point on the graph tells you the amount of sugar you'll
use if you don't make any pies?
Total Cups of Sugar
The point on the graph that tells you the amount of sugar you'll use if you don't make any pies is (0, 0).
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
y represent the amount of sugar.x represent the number of pies.k is the constant of proportionality.In order to have a proportional relationship, the variables representing the amount of sugar and time must have the same constant of proportionality:
Constant of proportionality, k = y/x
Constant of proportionality, k = 4/3
Constant of proportionality, k = 12.
Therefore, the required equation is given by:
y = kx
y = 4x/3
When x = 0, the value of y is given by:
y = 4(0)/3
y = 0 pies.
Read more on proportional relationship here: brainly.com/question/28350476
#SPJ1
dose 2+2=4?.............................
Answer:
[tex]yeah \: 2 + 2 = 4[/tex]
find the area of this shape (4.5 ft 3 ft 3ft)
Answer:assuming its a rectangle its 13.5
Step-by-step explanation: L x H = Area
What is the mode of Region A?
The mode for the region A is 2.6.
What exactly is mode?
In statistics, the mode is the value that has highest frequency in a data set. It is one of the three measures of central tendency, along with the mean and median.
To find the mode of a data set, you simply identify the value that appears most often. If no value is repeated, the data set has no mode.
The mode is particularly useful when dealing with categorical data or data that can be easily grouped into categories, such as colors, types of fruit, or letter grades. In such cases, the mode can provide insight into which category is most common or prevalent.
Now,
As given Values for Region A are
2.3 2.5 2.6 2.6 2.6 2.7 2.7 2.8
Here 2.6 comes most times or frequency of 2.6 is highest of all.
Hence,
The mode for the region A is 2.6.
To know more about Mode visit the link
https://brainly.com/question/30891252
#SPJ1
Provide a trigonometric equation. Considering only the space between = 0 and 2π the equation must only have solutions at x = 1 and x = 2. Explain your thought process and the work you did to create the equation. You may round decimal values to 3 places.
Therefore , the solution of the given problem of equation comes out to be f(x) = sin(/2 x) (when x = 1 or 2).
What is an equation?Variable words are commonly used in complex algorithms to show consistency between two statements that are not compatible. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization yields b + 7 as opposed to a single formula the fact that split 12 into two parts, which can be used with data collected from y + 7.
Here,
The goal is to construct a trigonometric equation with only answers at
x = 1 and x = 2.
f(x) = A sin(Bx+C+D)
=> B + C + D + A = 0 (equation 1)
=> Equation 2: A sin(2B + C + D) = 0
=> B + C sin A = 0 (equation 3)
=> Sin(2B+C) = A = 0 (equation 4)
Since sin(x) = 0 when x is a multiple of, formulae 3 and 4 can be rewritten as follows:
=> B + C = nπ (equation 5)
=> 2B + C = mπ (equation 6)
with numbers n and m. When we simultaneously solve equations 5 and 6 for B and C, we obtain:
=> B = (m - n)π/2 (equation 7)
=> C = nπ - B (equation 8)
=> When x = 1, C = /2 - /2 = 0.
=> When x = 2, C = − /2 = 3/2.
Thus, the result is as follows:
when f(x) = sin(/2 x) (when x = 1 or 2)
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
which of these animals can travel at the greatest distance from sea level?
Answer:
Dragonflies
Step-by-step explanation:
They can fly on top of the water, but also, they have the fastest turns per second for their wings.
PLEASE HELP ASAP ITS DUE IN AN HOUR
Answer:
[tex]3^2-5[/tex]
Step-by-step explanation:
Given equation:
( 3 - 2^2) + 5
3 - 4 + 5 (Simplify exponent)
-1 + 5 (Solve 3 - 4)
4 (Simplified)
Evaluation
2^2 + 5
4 + 5
9 (not the answer)
3^2 - 5
9-5
4 (answer)
What is the length of side x?
Given:-
A right angled triangle with two angles 60° and 30° is given to us.Length of two shorter sides is x and √10 .To find:-
The value of x .Answer:-
Here since the given triangle is a right angled triangle, we may use the trigonometric ratios . We can see that perpendicular and base are involved in this question whose measures are "x" and "√10" respectively with respect to 60° angle. So here we may use the ratio of tangent as , in any right angled triangle,
[tex]\implies\tan\theta =\dfrac{p}{b} \\[/tex]
and here p = x , and b = √10 . So on substituting the respective values, we have;
[tex]\implies \tan\theta = \dfrac{x}{\sqrt{10}} \\[/tex]
Also the angle here is 60° , so that;
[tex]\implies\tan60^o =\dfrac{x}{\sqrt10} \\[/tex]
The value tan60° is √3 , so we have;
[tex]\implies \sqrt3 =\dfrac{x}{\sqrt10}\\[/tex]
[tex]\implies x =\sqrt{10}\cdot \sqrt{3}\\[/tex]
[tex]\implies x =\sqrt{10\cdot 3} \\[/tex]
[tex]\implies x =\sqrt{30} \\[/tex]
The value of √30 is approximately 5.48 , so that;
[tex]\implies \underline{\underline{\red{\quad x = 5.48\quad }}} \\[/tex]
Therefore the value of x is approximately 5.48 .
Answer:
The length of side x in simplest radical form is [tex]\sqrt{30}[/tex].
Step-by-step explanation:
From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.
A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:
b is the shortest side opposite the 30° angle.b√3 is the side opposite the 60° angle.2b is the longest side (hypotenuse) opposite the right angle.We have been given the side opposite the 30° angle, so:
[tex]\implies b=\sqrt{10}[/tex]
The side labelled "x" is the side opposite the 60° angle, so:
[tex]\implies x=b\sqrt{3}[/tex]
Substitute the found value of b into the equation for x:
[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]
[tex]\implies x=\sqrt{10 \cdot3}[/tex]
[tex]\implies x=\sqrt{30}[/tex]
Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].
[tex]\hrulefill[/tex]
We can also calculate the length of side x using the tangent trigonometric ratio:
[tex]\boxed{\tan \theta=\sf \dfrac{O}{A}}[/tex]
where:
θ is the angle.O is the side opposite the angle.A is the side adjacent the angle.From inspection of the given right triangle:
θ = 30°O = √(10)A = xSubstitute these values into the formula:
[tex]\implies \tan 30^{\circ}=\dfrac{\sqrt{10}}{x}[/tex]
[tex]\implies \dfrac{\sqrt{3}}{3}=\dfrac{\sqrt{10}}{x}[/tex]
[tex]\implies x\sqrt{3}=3\sqrt{10}[/tex]
[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}[/tex]
Rationalise the denominator by multiplying the numerator and denominator by √3:
[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}\cdot \dfrac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac{3\sqrt{10}\sqrt{3}}{3}[/tex]
[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]
[tex]\implies x=\sqrt{10\cdot3}[/tex]
[tex]\implies x=\sqrt{30}[/tex]
Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].
15 points! please help pleasee!
Step-by-step explanation:
the perimeter is the sum of the lengths of all outside sides.
at the top is a triangle.
at the bottom is a rectangle.
the triangle looks like an isoceles triangle (both legs are equal), but the given measurement tells us otherwise.
if it were isoceles, the height would split the baseline into 2 equal halves (20/2 = 10ft).
per Pythagoras the 12 ft Hypotenuse would be
Hypotenuse² = 10² + 10² = 100 + 100 = 200
Hypotenuse = sqrt(200) = 14.14213562... and NOT 12 ft.
so, we need to calculate the actual part of the 20ft baseline (again Pythagoras) :
12² = 10² + part²
144 = 100 + part²
44 = part²
part = sqrt(44) = 6.633249581... ft
that means the 2nd part of the baseline is
20 - 6.633249581... = 13.36675042... ft
and we get the second leg of the large triangle again via Pythagoras :
leg² = 10² + 13.36675042...² = 100 + 178.6700168...
leg² = 278.6700168...
leg = sqrt(278.6700168...) = 16.69341238... ft
we need to sum up both legs of the triangle, 2 widths and one length of the rectangle, as the triangle base line and the second length of the rectangle cover each other up, and are not visible to the outside of the combined object.
P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈
≈ 64.69 ft