For this case we must complete squares:
[tex]x ^ 2 + 10x = 15[/tex]
We add the square of half the coefficient of the term "x",
[tex](\frac {b} {2a}) ^ 2[/tex] on both sides of the equation:
[tex]x^2+10x+(\frac {10} {2 (1)}) ^ 2 = 25 + 15\\x ^ 2 + 10x + 5 ^ 2 = 25 + 15[/tex]
According to the perfect square trinomial we have:
[tex](a + b) ^ 2 = a ^2 + 2ab + b ^ 2[/tex]
Rewriting the expression we have:
[tex]a = x\\b = 5\\(x + 5) ^ 2 = 25 + 15\\(x + 5) ^ 2 = 40[/tex]
ANswer:
[tex](x + 5) ^ 2 = 40[/tex]
i need help REAL fast
Answer:7.25
Step-by-step explanation: when you multiply 7.25 both sides the 7.25 on the left will cancel out the 7.25x leaving x = 29
two lines intersecting at a right angle
Answer:
Perpendicular Lines
Answer:
Step-by-step explanation:
Perpendicular Lines
solve the equation for y
0.6y + 1.2 = 0.3y - 0.9 + 0.8y
Answer:
y= 1.67
Step-by-step explanation:
0.6y + 1.2 = 0.3y + 0.9 + 0.8y
0.3 = 0.5y
1.67 = y
Answer:
0.6y+1.2=0.3y-0.9+0.8y
+0.9= +0.9
0.6y+2.1=1.1y
-0.6y=-0.6y
2.1=0.5
y=4.2
Step-by-step explanation:
First you want to isolate the variable to one side which is exactly why I added 0.9 to both sides. Then you want to combine like terms. By combining like terms you can now distribute the variable by the value remaining, which led to me getting y=4.2
A bicyclist covered 5/7 of his route and an additional 40 miles. He has yet to cover 118 miles less than 0.75 of his route. How long is his route in miles?
Answer:
6 miles
Step-by-step explanation:
Let the route length be r. The distance the cyclist has already covered is then (5/7)r + 40. This plus 0.75r - 118 must = r, the length of the entire route.
Then:
(5/7)r + 40 + (3/4)r - 118 = r
The LCD of the fractions 5/7 and 3/4 is 28. We thus have:
(20/28)r + 40 + (21/28)r - 118 = r, or
(41/28)r - 78 = (28/28)r
Combining the r terms, we get 13r = 78, and so r = 78/13 = 6.
The cyclist's bike route is 6 miles long.
Answer:
168 miles
Step-by-step explanation:
three vertices of a square are (-1, 2), (-1, 8), and (5,2) what is the fourth vertex of the square
A. (-5, 2)
B. (5, 8)
C. (2, 8)
D. (2, -5)
Answer:
The correct answer option is B. (5, 8).
Step-by-step explanation:
We are given the following coordinates of the vertices of a square and we are to find the coordinates of its fourth vertex:
[tex] ( - 1 , 2 ) , ( - 1 , 8 ) , ( 5 , 2 ) [/tex]
We know that all four sides of the square are equal so the vertices are equidistant from each other.
So the fourth vertex will be (5, 8).
The answer is b. (5,8)
Please help me answer this!
Answer:
option B
[tex]\frac{280}{\sqrt{L}\sqrt[3]{P}}[/tex]
Step-by-step explanation:
Step 1
S varies inversely of the cube root of P
s [tex]\alpha[/tex][tex]\frac{1}{\sqrt[3]{P} }[/tex]
s = [tex]\frac{k}{\sqrt[3]{P} }[/tex]
Step 2
S varies inversely with square root of L
s[tex]\alpha\frac{1}{\sqrt{L} }[/tex]
s = [tex]\frac{k}{\sqrt{L} }[/tex]
Step 3
Jointly
s = [tex]\frac{k}{\sqrt{L} \sqrt[3]{P} }[/tex]
Step 4
Plug values given in the question to find constant of proportionality
7 = [tex]\frac{k}{\sqrt{100}\sqrt[3]{64}}[/tex]
7 = k /(10)(4)
7 = k/40
k = 280
Step 5
General formula will be
s = [tex]\frac{280}{\sqrt{L}\sqrt[3]{P}}[/tex]
Explain why the definitions of each rigid-motion transformation needs to be more precise than just referring to them as slides, flips and turns.
Answer:
Step-by-step explanation:
The definitions of rigid-motion transformations need to be precise as they entail more than physical descriptions of motions. They have unique mathematical definitions and are important for understanding and interpreting real-world movements and physical phenomena.
Explanation:The definitions of each rigid-motion transformation, namely slides (translations), flips (reflections), and turns (rotations), need to be more precise because they are not solely about the physical manifestation of the motion. These transformations have distinct mathematical underpinnings. For instance, a translation involves moving the figure along a specified direction and distance in a straight line, without changing the orientation of the figure. A reflection involves 'flipping' the figure over a line of reflection, altering its orientation but not its shape or size. A rotation involves turning the figure around a specified point for a given angle.
Moreover, in both rotational and translational motion - two forms of rigid-body motion, there are accurate variables such as displacement, velocity, and acceleration related to translational motion and the corresponding angular variables in rotational motion. These specific definitions are crucial for the mathematics behind movement and interpreting the world around us. Understanding such concepts can also aid in studying physical phenomena as diverse as a spinning ballet dancer or a rotating planet.
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What is the arc length if 0=6pi/5 and the radius is 2cm?
Answer:
s=12pi/5
Step-by-step explanation:
S=theta*r
s=6pi/5(2)
s=12pi/5
what is the center and radius for the circle with equation 2x^2-8x+2y^2+12y+14=0
Answer:
Center : (2,-3)
Radius : sqrt(6)
Step-by-step explanation:
Rewrite this is standard form to find the center and radius.
(x-2)^2 + (y+3)^2 = 6
From this, we can determine that the center is (2,-3) and the radius is sqrt(6)
Answer:
center is (2,-3)
Radius =[tex]\sqrt{6}[/tex]
Step-by-step explanation:
[tex]2x^2-8x+2y^2+12y+14=0[/tex]
To find out the center and radius we write the given equation in
(x-h)^2 +(y-k)^2 = r^2 form
Apply completing the square method
[tex]2x^2-8x+2y^2+12y+14=0[/tex]
[tex](2x^2-8x)+(2y^2+12y)+14=0[/tex]
factor out 2 from each group
[tex]2(x^2-4x)+2(y^2+6y)+14=0[/tex]
Take half of coefficient of middle term of each group and square it
add and subtract the numbers
4/2= 2, 2^2 = 4
6/2= 3, 3^2 = 9
[tex]2(x^2-4x+4-4)+2(y^2+6y+9-9)+14=0[/tex]
now multiply -4 and -9 with 2 to take out from parenthesis
[tex]2(x^2-4x+4)+2(y^2+6y+9)+14-8-18=0[/tex]
[tex]2(x-2)^2 +2(y+3)^2 -12=0[/tex]
Divide whole equation by 2
[tex](x-2)^2 +(y+3)^2 -6=0[/tex]
Add 6 on both sides
[tex](x-2)^2 +(y+3)^2 -6=0[/tex]
now compare with equation
(x-h)^2 + (y-k)^2 = r^2
center is (h,k) and radius is r
center is (2,-3)
r^2 = 6
Radius =[tex]\sqrt{6}[/tex]
Choose the equation below that represents the line passing through the point (2, −5) with a slope of −3
For this case we have that the point-slope equation of a line is given by:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
Where:
m: It's the slope
[tex](x_ {0}, y_ {0}):[/tex]It is a point
We have to:
[tex]m = -3\\(x_ {0}, y_ {0}): (2, -5)[/tex]
Substituting:[tex]y - (- 5) = - 3 (x-2)\\y + 5 = -3 (x-2)\\y + 5 = -3x + 6\\y = -3x+1[/tex]
ANswer:
[tex]y + 5 = -3 (x-2)\\y = -3x+1[/tex]
ANSWER
[tex]y = - 3x + 1[/tex]
or
[tex]3x + y = 1[/tex]
EXPLANATION
The equation is calculated using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
where m=-3 is the slope and
[tex](x_1,y_1) = (2, - 5)[/tex]
We substitute the the values to get:
[tex]y- - 5= - 3(x-2)[/tex]
Expand
[tex]y + 5= - 3x + 6[/tex]
[tex]y = - 3x + 6 - 5[/tex]
[tex]y = - 3x + 1[/tex]
This is the slope-intercept form.
Or in standard form;
[tex]3x + y = 1[/tex]
you are dealt one card from a standard 52 card deck. find the probability of being dealt a card greater than 2 and less than 8
The given range is comprised of cards with a value between 3 and 7, inclusive, and there are 4 of each from the available suits. So there are 20 cards that fit the bill.
The probability of drawing 1 such card is
[tex]\dfrac{\binom{20}1}{\binom{52}1}=\dfrac{20}{52}=\dfrac5{13}[/tex]
In a standard 52 card deck, there are 20 cards that are greater than 2 and less than 8. As such, the probability of being dealt one of these cards is 20/52, which is approximately 0.385 or 38.5%.
Explanation:In a standard deck of 52 cards, there are four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.
In order to find the probability of being dealt a card greater than 2 and less than 8, we need to determine the total number of cards in that range. In each suit, this would be the cards numbered 3, 4, 5, 6, and 7, a total of 5 cards per suit. Therefore, across all four suits, there are 5x4=20 relevant cards. In this case, the favourable outcomes are the 20 relevant cards, and the total outcomes are the 52 cards in the deck. Therefore, the probability of being dealt a card greater than 2 and less than 8 is 20/52, which simplifies to approximately 0.385 or 38.5%.Learn more about Probability here:https://brainly.com/question/22962752
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solve the equation
y=2x-4, 3x+y=11
Answer:
(3, 2)
Step-by-step explanation:
Given the 2 equations
y = 2x - 4 → (1)
3x + y = 11 → (2)
Substitute y = 2x - 4 into (2)
3x + 2x - 4 = 11
5x - 4 = 11 ( add 4 to both sides )
5x = 15 ( divide both sides by 5 )
x = 3
Substitute x = 3 into (1) for corresponding value of y
y = (2 × 3) - 4 = 6 - 4 = 2
Solution is (3, 2)
Answer:
Step-by-step explanation:
this system not equation :
y=2x-4 ....(1)
3x+y=11....(2)
put the value of y by (1) in to (2) :
3x+2x-4 = 11
add4 : 3x+2x =15
5x=15
x=15/5 = 3
but: y = 2x-4
so : y = 2(3) -4
y = 6-4=2
How many times does 12 go into 32
Answer: the answer is 2
Step-by-step explanation:
12 x 2 is 24
12 x 3 is 36
so it goes into 32, 2 times.
Final answer:
12 goes into 32 a total of 2 full times with a remainder of 8, which can also be expressed as 2 and 2/3 times. The calculation is done using long division.
Explanation:
The question asks how many times does 12 go into 32. This is a division problem where you need to divide 32 by 12. To calculate this, you can use long division. Dividing 32 by 12 gives you 2 with a remainder of 8, since 12 times 2 is 24 and 32 minus 24 leaves 8. Therefore, 12 goes into 32 2 full times with 8 left over, or 2 remainder 8.
Another way to express this is in terms of decimal or fractions. Since 8 is 2/3 of 12, you can also say that 12 goes into 32 2 and 2/3 times. However, if you are strictly looking for how many full times 12 can divide into 32 without considering fractions, the answer is simply 2.
For what natural values of n:
is the difference (2−2n)−(5n−27) positive?
The expression (2−2n)−(5n−27) is not positive for any natural values of n, because when simplified, the inequality n < −(25/7) suggests n would need to be a negative value, which is not possible for natural numbers.
To determine for which natural values of n the expression (2−2n)−(5n−27) is positive, we must solve for the values of n that make the expression greater than zero. Simplifying, we get:
2 − 2n − 5n − 27 > 0
−7n − 25 > 0
Since we have a negative coefficient for n, as n increases, the value of the left side of the inequality decreases. To find the values of n that satisfy the inequality, we isolate n:
−7n > 25
n < −(25/7)
Considering n must be a natural number (positive integer), there are no natural values of n that satisfy the inequality, as natural numbers are always non-negative, and our inequality requires n to be less than a negative number.
A salesperson earns a salary of $700 per month plus 2% of the sales. Which inequality correctly represents the total sales if the salesperson is to have a monthly income of at least $1800?
Answer:
55000
Step-by-step explanation:
1800 - 700 = 1100
1100 / 0.02 = 55000
Omar makes a total of $51.75 selling brownies and muffins at a bake sale if he sells 16 brownies for $2.25 each how many muffins does he sell at $1.75 each?
Answer:
He can make 9 Muffins
Step-by-step explanation:
16*2.25=36
51.75 - 36=15.75 Subtract the total number of selling he made by how much he made with the brownies
15.75/1.75=9 Divide the number you got after subtracting by by how many he is going to sell each of then
Omar made $36 from selling brownies. He made $15.75 from selling muffins, and since each muffin cost $1.75, he therefore sold 9 muffins at the bake sale.
Explanation:To solve this problem, we must first find the total money Omar made from selling brownies. We do this by multiplying the price of each brownie ($2.25) by the number of brownies sold (16), which gives $36. Then we subtract this total from the total money Omar made ($51.75) to find out how much money he made from selling muffins, which is $51.75 - $36 = $15.75.
Next, we divide this amount by the price of each muffin ($1.75) to find out the number of muffins sold, as follows: $15.75 ÷ $1.75 = 9.
So, Omar sold 9 muffins at the bake sale.
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please answer the question in the screenshot below
Answer:
x = 20
∠B = 92
∠C = 40
Step-by-step explanation:
im pretty sure
Answer:
x = 20. ∠B = 92° and ∠C = 40°
Step-by-step explanation:
Angles of a triangle are ∠A = 48°, ∠B = (6x - 28)° and ∠C = (2x)°
Since sum of all the angles of the triangle is 180°
So ∠A + ∠B + ∠C = 180°
48° + (6x - 28)° + (2x)° = 180°
48 + 6x - 28 + 2x = 180
8x + 20 = 180
8x = 180 - 20
8x = 160
x = [tex]\frac{160}{8}=20[/tex]
Now ∠B = (6x - 28) = 6×20 - 28
∠B = 120 - 28 = 92°
And ∠C = 2x° = 2×20 = 40°
Therefore, x = 20. ∠B = 92° and ∠C = 40° is the answer.
If the period of a sinusoidal function is equal to 18 what is it’s period
Final answer:
The period of a sinusoidal function is the amount of time it takes for the function to complete one full cycle.
Explanation:
The period of a sinusoidal function is the amount of time it takes for the function to complete one full cycle. In this case, if the period of the sinusoidal function is 18, then the function will complete one full cycle every 18 units of time. This means that after 18 units of time, the function will have returned to its starting point.
For example, if we have a sinusoidal function f(x) = sin(x), then the period of this function is 2π, because it takes 2π units of time for the function to complete one full cycle. In general, the period of a sinusoidal function can be calculated using the formula T = 2π/ω, where T is the period and ω is the angular frequency.
The ratio of the height of two similar pyramids is 4:7. The volume of the smaller pyramid is 1,331cm, to the nearest whole number, what is the volume of the larger pyramid ?
Answer:
The volume of the larger pyramid is equal to [tex]7,133\ cm^{3}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z----> the scale factor
In this problem, the ratio of the height is equal to the scale factor
[tex]z=\frac{4}{7}[/tex]
step 2
Find the volume of the larger pyramid
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z----> the scale factor
x----> volume of the smaller pyramid
y----> volume of the larger pyramid
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{4}{7}[/tex]
[tex]x=1,331\ cm^{3}[/tex]
substitute
[tex](\frac{4}{7})^{3}=\frac{1,331}{y}\\ \\(\frac{64}{343})=\frac{1,331}{y}\\ \\y=343*1,331/64\\ \\y=7,133\ cm^{3}[/tex]
Please help me with this problem i don’t understand it
“What is the distance between (13,15) and (7,-2)
Answer:
13
Step-by-step explanation:
the answer is 13.
Answer is 18.03
See attached photo
6 What is the answer to this problem
The answer I believe it’s A if not try C
How much is 3788 plus 83762
Answer:
87550
Step-by-step explanation:
Answer:
3788 + 83762 = 87,550
15' 3" − 5' 6"
(iT'S nOT eAsY
Answer:
It's easier than you think
15' 3" = 14 ' 15" so the problem is:
14' 15" - 5' 6" =
9' 9"
Step-by-step explanation:
Pretty sure the answer is 9’9”
What is the expression equivalent to? Screenshots attached. Please help, ASAP! Important.
Answer:
Choice C is the correct solution
Step-by-step explanation:
We can split up the terms under the cube root sign to obtain;
[tex]\sqrt[3]{32}*\sqrt[3]{x^{8} }*\sqrt[3]{y^{10} }\\\\\sqrt[3]{32}=\sqrt[3]{8*4}=\sqrt[3]{8}*\sqrt[3]{4}=2\sqrt[3]{4}\\\\\sqrt[3]{x^{8} }=\sqrt[3]{x^{6}*x^{2}}=\sqrt[3]{x^{6} }*\sqrt[3]{x^{2} }=x^{2}*\sqrt[3]{x^{2} }\\\\\sqrt[3]{y^{10} }=\sqrt[3]{y^{9}*y }=\sqrt[3]{y^{9} }*\sqrt[3]{y}=y^{3}*\sqrt[3]{y}[/tex]
The final step is to combine these terms;
[tex]2\sqrt[3]{4}*x^{2}*\sqrt[3]{x^{2} }*y^{3}*\sqrt[3]{y}\\\\2x^{2}y^{3}\sqrt[3]{4x^{2}y }[/tex]
Use substitution method for y=10x-9 and y=x+18
Answer:
x=3
y=21
Step-by-step explanation:
To use substitution method, first we need to decide which variable solve first, either x or y.
Here we decide to start by 'y' using equation y=x+18, which is already solved for 'y'
That same equation is then substitute into the first equation:
x+18= 10x-9
From here, we isolate 'x' variable and grouping terms, we have this:
27=9x
Resulting x=3
Now, we can use the above result in the second equation (y=x+18)
Leading to y=3+18=21.
Please help me answer these
Answer:
1 is 27
Step-by-step explanation:
What is the distance between the points (7, −10) and (−8, −10)?
Answer:
15
Step-by-step explanation:
Using the distance formula
Answer:
15
hope this helps please make mine the brainliest
Select all the equations where d=4 is a solution
A. 2d+3=11
B.11d+15
C.5d+7=27
D.9+2d=16
E.3d=7
A. 2 • 4 = 8 + 3 = 11 (select)
B. 11 • 4 = 44 +15 = 59 (select only if the solution is 59; the answer was not included)
C. 5 • 4 = 20 + 7 = 27 (select)
D. 2 • 4 = 8 + 9 = 17 (do not select)
E. 3 • 4 = 12 (do not select)
A) 2d + 3 = 11 → 2d = 8 → d = 4, this is right
B) 11d + 15 → this is an expression, so no
C) 5d + 7 = 27 → 5d = 20 → d = 4, this is right
D) 9 + 2d = 16 → 2d = 7 → d = 3.5, this isn't right
E) 3d = 7 → d = 2.3, this isn't right
That means the answers are A and C
Hope this helps!!
Three people each select a letter of the alphabet. What is the probability that they select the same letter?
Final answer:
The probability that three people independently select the same letter of the alphabet is 1/676.
Explanation:
The question asks about the probability that three people select the same letter of the alphabet independently. Since there are 26 letters in the alphabet, the first person can pick any letter with a probability of 1 (they are sure to pick some letters). The second person must pick the same letter as the first, which has a probability of 1/26. Similarly, the third person also has a probability of 1/26 to pick the same letter as the first two. To find the combined probability for all three events happening in sequence (all three picking the same letter), we multiply the individual probabilities: 1 * (1/26) * (1/26) = 1/676.
The cost to manufacture x pairs of sunglasses can be represented by a function, C(x). If it cost 398 to manufacture 4 pairs of sunglasses, which of the following is true
a) c(4)=99.50
b) c(398)=4
c) c(4)=398
d) c(99.50)=1
can someone solve it and show steps please
The correct answer is c) C(4) = 398, which appropriately links the cost of manufacturing 4 pairs of sunglasses ($398) with the function C(x).
Explanation:The function C(x) represents the cost to manufacture x pairs of sunglasses.
Given that it costs $398 to manufacture 4 pairs, we can substitute these values into the function to find which statement is accurate.
The logic behind this is simple: C(x) is typically understood to be the cost associated with producing x units.
Therefore, when x is the number of units produced, C(x) is the total cost to produce those units.
Substituting 4 into the function C(x) would give us the total cost for 4 pairs of sunglasses.
Thus, we can say C(4) = 398. This matches response option c), which states that C(4) = 398, and is therefore true.
Response options a), b), and d) all incorrectly mix up the inputs and outputs of the cost function and therefore can be disregarded.