Answer:
1/6
Step-by-step explanation:
The three numbers, a, b, c, satisfy the equations ...
a +b +c = 1a -b -c = 0a +b -5c = 0Subtracting the last equation from the first gives ...
(a +b +c) -(a +b -5c) = (1) -(0)
6c = 1
c = 1/6
Now, we know the sum of the first two numbers is 5/6 (five times the last), and the difference of the first two numbers is 1/6 (equal to the last). Then the least of the first two numbers is ...
(5/6 -1/6)/2 = 1/3
and the third number, 1/6, is shown to be the smallest.
The smallest of these numbers is 1/6.
____
In order, the numbers are 1/2, 1/3, 1/6.
____
Comment on finding the second-smallest number
For ...
a +b = 5/6 . . . . . sum of the two numbersa -b = 1/6 . . . . . . difference of the two numbersWe can find b by subtracting the second equation from the first:
(a +b) -(a -b) = (5/6) -(1/6)
2b = 4/6 = 2/3 . . . . . simplify
b = 1/3 . . . . . . . . . . . . divide by 2
Please note that half the difference of the sum and difference is the generic solution to finding the smallest in a "sum and difference" problem.
a box shaped like a rectangular prism has a height of 17 in and a volume of 2720 in^3. the length is 4 inches greater than twice the width. what is the width of the box
Answer:
8 inches
Step-by-step explanation:
You want to find the width (w) in inches such that ...
V = LWH
2720 = (2w+4)·w·17 . . . . . . . . . . fill in the given values
80 = (w+2)(w) = w^2 + 2w . . . . . divide by 34
81 = (w +1)^2 . . . . . . . . . . . . . . . . complete the square
9 = w+1 . . . . . . square root (we only care about the positive solution)
8 = w . . . . . . . . subtract 1
The width of the box is 8 inches.
Answer:
8 inches
Step-by-step explanation:
Loliidewkwkwkwkkdjieejwjwm
Answer:
1234567890
Step-by-step explanation:
1234567890-zxhjk
What is the simplified form of the expression? 5c2-4c+3D-3+2c2d-3c+d-7
The simplified form of the expression is [tex]7c^2d - 7c + 4d - 10[/tex].
To simplify the expression, we first combine like terms:
[tex]5c^2d - 4c + 3d - 3 + 2c^2d - 3c + d - 7[/tex]
Grouping similar terms:
[tex](5c^2d + 2c^2d) + (-4c - 3c) + (3d + d) + (-3 - 7)[/tex]
Simplifying each group:
[tex]7c^2d - 7c + 4d - 10[/tex]
Thus, the simplified form of the expression is [tex]7c^2d - 7c + 4d - 10[/tex]. This result arises from combining the coefficients of like terms. The coefficients of [tex]c^2d[/tex] add up to 7, those of c add up to -7, those of d add up to 4, and the constants add up to -10.
Complete Question:
What is the simplified form of the expression?
[tex]$$5 c^2 d-4 c+3 d-3+2 c^2 d-3 c+d-7$$[/tex]
[tex]a. 3 c^2 d-7 c+2 d-10\\\\b. 3 c^2 d-7 c+4 d-10\\\\c. 7 c^2 d-7 c+2 d-10\\\\d. 7 c^2 d-7 c+4 d-10[/tex]
The solids are similar. Find the volume V of the red solid.
Answer:
196 mm³
Step-by-step explanation:
The ratio of volumes the the cube of the ratio of linear dimensions. Hence the volume of the red solid is ...
(7/21)³×(5292 mm³) = 196 mm³
I will rate brainliest help
Answer:
The correct answer is A) x does not equal 8
Step-by-step explanation:
In order to find gaps in the domain, we look for two things. The first we look for is negatives under square roots (which are not an issue here since there are none) and then we look for 0, denominators. So to find the gap, we set the denominator equal to 0 and see what the x value cannot be.
x - 8 = 0
x = 8
I need help with 1.12 and 1.13
Answer:
1.12 B. sin(s) = cos(u)
1.13 C. showing similar triangles
Step-by-step explanation:
1.12 First of all, it is useful to identify the complementary angles. These are the two acute angles in the same right triangle: (s, u) or (t, v), or the adjacent angles that together make a right ange: (s, t) or (u, v).
Only choices B and D involve complementary angles. Only choice B shows the right relationship between trig functions of those angles.
___
1.13 It helps if you've seen the short, cute proof of the Pythagorean theorem using similar triangles. One of the early steps in the proof is to show the triangles are similar: choice C.
Even if you've never seen that proof, you can still make a good guess as to the correct choice. Choices A and D are just plain incorrect. Choice B might be the end result of the proof of the Pythagorean theorem, but won't be a step in that proof. In any event, the point of the proof is to show AC^2 + BC^2 = AB^2, not the equation of choice B.
That leaves choice C, which is both correct and likely to be a step in the proof.
HELP Find the number of non-degenerate triangles whose vertices are three of the points on this six-point star.
Answer:
20
Step-by-step explanation:
The number of combinations of 6 points taken 3 at a time is ...
6!/(3!·(6-3)!) = 6·5·4/(3·2·1) = 5·4 = 20
___
If you number the points 1–6, the points of the 20 triangles will be ...
123 124 125 126 134
135 136 145 146 156
234 235 236 245 246
256 345 346 356 456
a point is chosen at random in a large square what percent of the time will the point be in the shaded region
Answer:
84.5%
Step-by-step explanation:
The area of the smaller square is ...
smaller square = (5.98 cm)^2 = 35.7604 cm^2
The area of the larger square is ...
larger square = (15.2 cm)^2 = 231.04 cm^2
So, the shaded area is ...
larger square - smaller square = (231.04 -35.7604) cm^2 = 195.2796 cm^2
Then a randomly chosen point will be in the shaded region this fraction of the time:
(shaded area)/(larger square area) = 195.2796/231.04 ≈ 0.84522 ≈ 84.5%
What linear function represents the line given by the point slope equation y+7= 2/3(x+6)?
Answer:
The graph of the line in the attached figure
Step-by-step explanation:
we have
[tex]y+7=\frac{2}{3}(x+6)[/tex]
This is the equation of a line into point slope form
The slope is [tex]m=\frac{2}{3}[/tex]
The line pass through the point (-6,-7)
To graph the line find the y-intercept
Remember that
The y-intercept of the line is the value of y when the value of x is equal to zero
so
For x=0
[tex]y+7=\frac{2}{3}(0+6)[/tex]
[tex]y+7=\frac{2}{3}(6)[/tex]
[tex]y+7=4[/tex]
[tex]y=4-7=-3[/tex]
The y-intercept is the point (0,-3)
with the point (-6,-7) and (0,-3) plot the line
see the attached figure
emilio writes the inequality 17(f+2) + 45.99<200 to better represent the situation, using the variable f to represent the number of friends. solve the inequality, then write the maximum nymber of friens attende the birthday party.
Expand the left hand side:
[tex]17f+34+45.99<200[/tex]
Simplify the left hand side:
[tex]17f+79.99<200[/tex]
Subtract 79.99 from both side:
[tex]17f<120.01[/tex]
Divide both sides by 17:
[tex]f<\dfrac{120.01}{17} \approx 7.06[/tex]
So, he must invite less than 7 friend to the party.
Final answer:
To solve the inequality, distribute 17 to f and 2, combine like terms, subtract 79.99 from both sides, and divide both sides by 17. The maximum number of friends that can attend the birthday party is 7.
Explanation:
To solve the inequality 17(f+2) + 45.99 < 200, we first distribute 17 to f and 2: 17f + 34 + 45.99 < 200. Combine like terms: 17f + 79.99 < 200. Next, subtract 79.99 from both sides of the inequality: 17f < 120.01. Finally, divide both sides of the inequality by 17: f < 7.06. So the maximum number of friends that can attend the birthday party is 7.
If for all real values of x, (x + c)(x + 4) = x2 + 8x + 4c, then c = ?
A. 2
B. 4
C. 6
D. 8
E. 10
Answer:
B. 4
Step-by-step explanation:
When you perform the multiplication, you get ...
(x +c)(x +4) = x² + (c+4)x +4c = x² + 8x +4c
Then ...
c + 4 = 8 . . . . coefficients of x must match
c = 4 . . . . . matches choice B
Hector needs to buy a window shade in his house. He measured the width of the window as 37 inches. The actual measurement is 40 inches. What is the percent error
Answer:
3/40 = 7.5%
Step-by-step explanation:
3/40 percent error.
3/40 = 7.5%
List parallelograms, polygons, quadrilaterals, and rectangles in order from the least specific group to the most specific one.
A) parallelograms, polygons, quadrilaterals, rectangles
Answer:
(B)
Step-by-step explanation:
Option (B) is in correct order when talking about the specific ones.
Polygon is the least specific as it can be of many sides.
example: A polygon with 3 sides is a triangle. and the polygon with 4 sides is a quadrilateral.
Hence, quadrilateral is on the second number in least specific group.
Quadrilaterals with 2 sides parallel and equal are known as parallelogram.
Therefore, they are on the 3rd number in specific group.
Parallelograms with opposite sides parallel and equal and all the vertex angles at right angles are known as rectangles.
Therefore, rectangles are the most specific one in the group. The list is given by (option (B):
1) polygons
2) quadrilaterals
3) parallelograms
4) rectangles.
mark brainliest :)
Answer:
The answer is B!!!!
Step-by-step explanation:
I not that good at explain but i'll try to explain :).Ummmmmmm....I took the same test so thats how I know
A: Line n was translated up 8 units.
B: Line m was translated down 4 units.
C: Line l was translated down 8 units.
D: Line m was translated up 4 units.
Answer:
4
Step-by-step explanation:
move up a units then take a line and move that down 4 units then down four more then back up 8 and you get your answer of
Solve the quadratic equation. (x + 1)^2 = 16
A) x = 3 or -5 B) x = -3 or 5 C) x = ±5 D) x = ±1
If the square of a certain quantity must be 16, that quantity must be either 4 or -4.
In fact, in both cases we have [tex]4^2=(-4)^2=16[/tex]
So, we have two possible solutions:
[tex]x+1=4 \iff x=3[/tex]
[tex]x+1=-4 \iff x=-5[/tex]
Answer:
A. x= 3 or -5
Step-by-step explanation:
The solution is x = 3 or -5. The steps for solving the equation are shown.
(x + 1)2 = 16
(x + 1)2
= ±
16
x + 1 = ± 4
x + 1 = 4 or x + 1 = -4
x = 3 or -5
Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle.
a = 240
b = 127
c = 281
Answer:
area of the triangle is about 15,183.766
Step-by-step explanation:
The sum of the two shortest sides is 367, which is greater than the longest side, hence these side lengths can form a triangle.*
The perimeter is ...
p = 240 +127 +281 = 648
so the semi-perimeter is ...
s = p/2 = 648/2 = 324
Heron's formula tells you the area is ...
A = √(s(s -a)(s -b)(s -c)) = √(324·84·197·43) = √230,546,736
A ≈ 15,183.766
The area of the triangle is about 15,183.766 square units.
_____
* The terms s-a, s-b, and s-c are all positive, which is further evidence the side lengths will form a triangle. If one or more of those factors is negative, the side lengths will not form a triangle.
What is a perfect square? 20,21,24,25
Which of the following measurements could be the side lengths of a right triangle?
A.
54 in, 72 in, 108 in
B.
54 in, 81 in, 90 in
C.
45 in, 72 in, 90 in
D.
54 in, 72 in, 90 in
Answer:
Step-by-step explanation:
To determine the side lengths of a right triangle, use the converse of the Pythagorean Theorem, where c is the longest side, as shown below.
If c2 < a2 + b2, the triangle is acute.
If c2 = a2 + b2, the triangle is right.
If c2 > a2 + b2, the triangle is obtuse.
Check each answer choice, according to the rules above.
This is an acute triangle.
This is an obtuse triangle.
This is an obtuse triangle.
This is a right triangle.
Therefore, 54 in, 72 in, and 90 in are the side lengths of a right triangle.
Correct option is (D) 54 in, 72 in, 90 in
Using the converse of the Pythagorean Theorem, we can determine whether the given sides form a right angled triangle or not
Thus if '[tex]c^2 < a^2 + b^2[/tex]' then the triangle is acute angled triangle
Similarly if ' [tex]c^2 = a^2 + b^2[/tex] ' then the triangle is right angled triangle
Similarly if ' [tex]c^2 > a^2 + b^2[/tex] ' then the triangle is obtuse angled triangle
Thus we would be checking for each options
Option(A) :
Given that the sides are 54 in, 72 in, 108 in
[tex]108^{2} =11664[/tex]
[tex]54^2+72^2=2916+5184\\54^2+72^2=8100[/tex]
Thus it can be seen that
[tex]108^2 > 54^2 + 72^2[/tex]
We can say that the given sides form an acute angled triangle
Option(B) :
Given that the sides are 54 in, 81 in, 90 in
[tex]90^{2} =8100[/tex]
[tex]54^2+81^2=2916+6561\\54^2+81^2=9,477[/tex]
Thus it can be seen that,
[tex]90^2 > 54^2 + 81^2[/tex]
We can say that the given sides form an obtuse angled triangle
Option(C) :
Given that the sides are 45 in, 72 in, 90 in
[tex]90^{2} =8100\\45^2+72^2=2025+5184\\45^2+72^2=7209[/tex]
Thus it can be seen that,
[tex]90^2 > 45^2 + 72^2[/tex]
We can say that the given sides form an obtuse angled triangle
Option(D) :
Given that the sides are 54 in, 72 in, 90 in
[tex]90^{2} =8100\\54^2+72^2=2916+5184\\54^2+72^2=8100[/tex]
Thus it can be seen that,
[tex]90^2 =54^2 + 72^2[/tex]
We can say that the given sides form an right angled triangle
Thus, 54 in, 72 in, and 90 in are the side lengths of a right triangle.
Given two functions j(x)=−3x+2 and k(x)=3+4x , what is the function rule for (kj) (x) ?
Answer:
(k·j)(x) = -12x^2 -x +6
Step-by-step explanation:
(k·j)(x) = k(x)·j(x) = (4x+3)(-3x+2) . . . . . substitute function definitions
= 4·(-3)x^2 +(4·2+3(-3))x +3·2 . . . . . multiply using the distributive property
= -12x^2 -x +6
PLEASE HELP!!!!!!!!!!!!!!!!!!
Answer:
it is d
Step-by-step explanation:
Answer:
b. secants
Step-by-step explanation:
A line that intersects a circle in two places is called a "secant."
___
It is a tangent line if it intersects the circle in one point.
It is a diameter if it is a chord that goes through the center of the circle.
It is a chord if it is a line segment with each endpoint being on the circle. (BE and CD are chords.)
"Cosecant" is the name of the trigonometric function that is the ratio of the hypotenuse of a right triangle to the side opposite the angle of interest.
What is rotation?
A translation that leaves the origin fixed while not losing the shape of the curves
A translation that changes the origin while not losing the shape of the curves
A translation that leaves the origin fixed while changing the shape of the curves
A translation that changes the origin while also changing the shape of the curves
The right choice is (C) A translation that leaves the origin fixed while changing the shape of the curve
Step-by-step explanation:A transformation in which the center of rotation is fixed and everything else on the plane rotates about that point by a given angle is called rotation. A rotation is described by the centre of rotation, the angle of rotation, and the direction of the turn. The centre of rotation is the point that a shape rotates around. Each point in the shape must stay an equal distance from the centre of rotation.
Answer: a translation that leaves the origin fixed while not losing the shapes of the curves
Step-by-step explanation:
what is the equation of the line through (5,1) with a slope of -3?
a. y+1 = 3(x+5)
b. y-1 = 3(x-5)
c. y-1 = -3(x-5)
d. y+1 = -3(x-5)
Answer:
C
Step-by-step explanation:
The equation of a line is given by the formula [tex]y-y_1=m(x-x_1)[/tex]
Where [tex]x_1[/tex] is the x-coordinate (it is given as 5)
[tex]y_1[/tex] is the y-coordinate (it is given as 1), and
m is the slope (it is given as -3)
Plugging in all the info into the formula we have:
[tex]y-y_1=m(x-x_1)\\y-1=-3(x-5)[/tex]
From the answer choices, we see that C is the correct answer.
Answer:
c.y-1 = -3(x-5)
Step-by-step explanation:
We have given slope of a line and the point that is passing through the line.
slope = -3 and (x₁,y₁) = (5,1)
We have to find the equation of line.
y-y₁ = m(x-x₁) is point-slope form of the equation of line where m is slope.
Putting given values in above formula, we have
y-(1) = -3(x-(5))
y-1 = -3(x-5) is the equation of the line through (5,1) with a slope of -3.
A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points
A(−7,2)
B(3,2)
, and
D(−7,−2)
Point C is the fourth vertex of the rectangle.
What is the distance from point B to point C?
Enter your answer in the box.
Answer:
4
Step-by-step explanation:
The distance from B to C is the same as the distance from A to D. Points B and C will both have the same x-value, as do points A and D. Points B and C will have the same difference in y-values (2 -(-2) = 4) that points A and D have.
The distance from B to C is 4 units.
What is the slope of the line?
A. 0
B. 1
C. Undefined
D. Infinity
A. 0
The slope of a horizontal line is always 0.
An electronics store reduced the price of a TV from $800 to $728. What was the percent of decrease?
Answer:
9%
Step-by-step explanation:
✯Hello✯
↪ We can formulate an equation to help us solve this
↪ 800(x%) = 728 in this case x=91
↪ We do 100-91 meaning that this is a 9% decrease on price
↪ To check that this is correct we can work out 9% of 800 which is 72
When subtracting 72 from 800 it is confirmed that 728 is the right amount
❤Gianna❤
Final answer:
To find the percent of decrease in the TV's price, calculate the difference between the original and the new price, divide by the original price, and multiply by 100, which results in a 9% decrease.
Explanation:
To calculate the percent of decrease when the price of a TV is reduced from $800 to $728, you subtract the new price from the original price and then divide by the original price. Next, you multiply the result by 100 to get the percentage.
Step-by-step calculation:
Find the difference in price: $800 - $728 = $72.
Divide the difference by the original price: $72 ÷ $800 = 0.09.
Multiply by 100 to get the percentage: 0.09 x 100 = 9%.
So, the percent of decrease in the price of the TV is 9%.
Given: circle k(O), m∠P=95°, m∠J=110°, m∠LK=125°
Find: m∠PJ
Answer:
The measure of the arc PJ is [tex]75\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle L
we know that
In a inscribed quadrilateral opposite angles are supplementary
so
[tex]m<L+m<J=180\°[/tex]
we have
[tex]m<J=110\°[/tex]
substitute
[tex]m<L+110\°=180\°[/tex]
[tex]m<L=70\°[/tex]
step 2
Find the measure of arc KJ
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<P=\frac{1}{2}(arc\ LK+arc\ KJ)[/tex]
substitute the values
[tex]95\°=\frac{1}{2}(125\°+arc\ KJ)[/tex]
[tex]190\°=(125\°+arc\ KJ)[/tex]
[tex]arc\ KJ=190\°-125\°=65\°[/tex]
step 3
Find the measure of arc PJ
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<L=\frac{1}{2}(arc\ PJ+arc\ KJ)[/tex]
substitute the values
[tex]70\°=\frac{1}{2}(65\°+arc\ PJ)[/tex]
[tex]140\°=(65\°+arc\ PJ)[/tex]
[tex]arc\ PJ=140\°-65\°=75\°[/tex]
Find the average rate of change for f(x) = x2 + 7x + 10 from x = −20 to x = −15. A) −28 B) −36 C) 28 D) 36
Answer:
Step-by-step explanation:
Answer:
The average rate of change of [tex]f(x)=x^2 + 7x + 10[/tex] over the interval [tex]-20\leq x\leq -15[/tex] is -28.
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by this expression:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
It is a measure of how much the function changed per unit, on average, over that interval.
To find the average rate of change of [tex]f(x)=x^2 + 7x + 10[/tex] over the interval [tex]-20\leq x\leq -15[/tex] you must:
Evaluate x = -15 and x = -20 into the function f(x)
[tex]f(-15)=(-15)^2 + 7(-15) + 10=130\\f(-20)=(-20)^2 + 7(-20) + 10=270[/tex]
Applying the expression for the average rate of change we get
[tex]\frac{f(-15)-f(-20)}{-15+20} \\\\\frac{130-270}{-15+20} \\\\\frac{-140}{5}\\\\-28[/tex]
HELP help me find the arc of the semicircle found in the picture
Shouldn’t it be 180 because that half of a circle (360)
I think this should be it!
Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Antoine threw it, is modeled by: h(x)=-2x^2+4x+16. How many seconds after being thrown will the ball hit the ground?
Answer:
Step-by-step explanation:
H(x)=0
-2x^2 +4x+16=0
X^2 - 2x - 8 = 0
(X + 2) (x-4) = 0
X + 2 = 0 or x -4 = 0
X= -2 or x=4
Since -2 doesn’t make sense use 4
The ball will hit ground in 4 seconds
Answer:
4 seconds
Step-by-step explanation:
Given : The ball's height (in meters above the ground), x seconds after Antoine threw it, is modeled by: [tex]h(x)=-2x^2+4x+16.[/tex]
To Find: How many seconds after being thrown will the ball hit the ground?
Solution:
We are supposed to find after how much time the ball hits the ground.
So, we are required to substitute h = 0 because when ball hits the ground the height will be 0
So, [tex]0=-2x^2+4x+16[/tex]
[tex]2x^2-4x-16=0[/tex]
[tex]x^2-2x-8=0[/tex]
[tex]x^2-4x+2x-8=0[/tex]
[tex]x(x-4)+2(x-4)=0[/tex]
[tex](x-4)(x+2)=0[/tex]
[tex]x=4,-2[/tex]
Since time cannot be negative .So, neglect -2
Hence A ball will take 4 seconds to hit the ground after being thrown.
How much would $500 invested at 9% interest compounded continuously be worth after 4 years? Round your answer to the nearest cent.
Answer:
=705.79
Step-by-step explanation:
F=P(1+i)n where F is the Future amount P is the Present amount/Capital i is the interest rate n is the number of periods.
In this case you have the given as follows:
P = $500 i = 9% n = 4 years
Substituting the values to the formula you'll have:
F=500(1+0.09)^4
=705.79