Answer:
190 percentage of the weight limit is 114 pounds.
Step-by-step explanation:
Given: A rocking horse has a weight limit of 60 pounds.
We have to find what percentage of the weight limit is 114 pounds.
x percentage of the weight limit is 114 pounds.
⇒ x% of 60 = 114
[tex]\frac{x}{100} \times 60 = 114[/tex]
Solve for x;
[tex]\frac{6x}{10} = 114[/tex]
Multiply both sides by 10 we get;
[tex]\frac{6x}{10} \times 10 = 114 \times 10[/tex]
[tex]6x = 1140[/tex]
Divide both sides by 6 we get;
[tex]x = \frac{1140}{6}[/tex]
Simplify:
x = 190%
Therefore, 190 percentage of the weight limit is 114 pounds.
To find the percentage, divide the given weight by the weight limit and multiply by 100. 114 pounds is 190% of the weight limit of 60 pounds.
To find the percentage of the weight limit, we need to divide the given weight (114 pounds) by the weight limit (60 pounds) and then multiply the result by 100. So, the calculation would be:
Percentage = (114 pounds / 60 pounds) * 100
Simplifying this equation, we get:
Percentage = 190%
Therefore, 114 pounds is 190% of the weight limit of 60 pounds.
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Write a linear function that passes through the points (-5, -6) and (2, 8).
The point-slope form of line:
[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-5, -6) and (2, 8). Substitute:
[tex]m=\dfrac{8-(-6)}{2-(-5)}=\dfrac{8+6}{2+5}=\dfrac{14}{7}=2\\\\y-(-6)=2(x-(-5))\\\\\boxed{y+6=2(x+5)}[/tex]
The thousand islands are located along the border between New York and Canada the adventure club wants to place a stone marker on all 1,000 of the islands the club has placed stones on 680 islands so far how many islands remain for the adventure club to visit
Answer:
320.
Step-by-step explanation:
1,000 - the 680 that have been completed gives you 320.
What is the remainder R when the polynomial p(x) is divided by (x - 2)? Is (x - 2) a factor of p(x)? P(x) = -4x4 + 6x3 + 8x2 - 6x - 4 A) R = 0, no B) R = 0, yes C) R = -72, no D) R = -72, yes
Answer:
B
(x-2) is a factor since remainder is 0.
Step-by-step explanation:
We divide (x-2) into the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] through long division or synthetic. We choose long division and look for what will multiply with (x-2) to make the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] .
[tex](x-2)(-4x^3)=-4x^4+8x^3[/tex]
We subtract this from the original [tex]-4x^4-(-4x^4)+6x^3-(8x^3)+8x^2-6x-4[/tex].
This leaves [tex]-2x^3+8x^2-6x-4[/tex]. We repeat the step above.
[tex](x-2)(-2x^2)=-2x^3+4x^2[/tex].
We subtract this from [tex]-2x^3-(-2x^3)+8x^2-(4x^2)-6x-4=4x^2-6x-4[/tex]. We repeat the step above.
[tex](x-2)(4x)=4x^2-8x[/tex].
We subtract this from [tex]4x^2-(4x^2)-6x-(-8x)-4=2x-4[/tex]. We repeat the step above.
[tex](x-2)(2)=2x-4[/tex].
We subtract this from [tex]2x-(2x)-4-(4)=0[/tex]. There is no remainder. This means (x-2) is a factor.
The remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2) is 0, indicating that (x - 2) is indeed a factor of p(x).
Explanation:To find the remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial p(x) by a linear term (x - a) is equal to p(a). Therefore, to find R, simply calculate p(2).
p(2) = -4(2)4 + 6(2)3 + 8(2)2 - 6(2) - 4
p(2) = -4(16) + 6(8) + 8(4) - 12 - 4
p(2) = -64 + 48 + 32 - 12 - 4
p(2) = 0
Since the remainder is 0, this means that (x - 2) is a factor of p(x).
The correct answer is therefore R = 0, and yes, (x - 2) is a factor of p(x).
800,000,000,000 + 20,000,000,000 + 3,000,000,000 + 50,000,000 + 4,000,000 + 600,000 + 50,000 + 8,000 + 700 + 80 + 6
What is the GCF of the following expression:
5y^5+35y^4+15y^3
Answer:
5y^3
Step-by-step explanation:
Find what is common to all the terms
5y^5 = 5 * y*y*y*y*y
35y^4 = 5*7*y*y*y*y
15y^3 = 3*5*y*y*y
The all have 5*y*y*y
So the GCF is 5 y*y*y or 5y^3
What is the distance between the points (21, 16) and (9, 11)?
Answer: 13 units
The x value goes from x = 21 to x = 9, which is an x distance of 12 units (21-9 = 12)
The y distance is 5 units (16-11 = 5)
We have a right triangle with legs of 12 and 5. The hypotenuse is x
Use the pythagorean theorem to find x
a^2 + b^2 = c^2
5^2 + 12^2 = x^2
25 + 144 = x^2
169 = x^2
x^2 = 169
x = sqrt(169)
x = 13
The hypotenuse of this right triangle is 13 units, so this is the distance between the two points.
Find the ratio of the volume of one sphere to the volume of the right cylinder
Answer:
B
Step-by-step explanation:
Let [tex]r[/tex] be the radius of one sphere.
Volume of sphere is [tex]V=\frac{4}{3}\pi r^3[/tex]Since radius is r, the height of the cylinder will be [tex]4r[/tex]
Also, the cylinder has the same radius as the sphere: [tex]r[/tex]
Plugging in the values we get: [tex]V=\pi (r)^{2}(4r)=4\pi r^3[/tex]
Ratio of volume of 1 sphere to volume of cylinder is:
[tex]\frac{\frac{4}{3}\pi r^3}{4\pi r^3}=\frac{\frac{4}{3}}{4}=\frac{4}{3}*\frac{1}{4}=\frac{1}{3}[/tex]
The ratio is 1:3
Answer choice B is right.
Hannah buys 2/3 pound of roast beef.She uses 1/4 pound to make a sandwich for lunch. How many roast beef does she have left
Answer:
2/3 - 1/4
=> taking L.C.M of the denominators we get,
=> 8/12-3/12
=> 5/12 is left with her,, ;)
HOPE THIS HELPS YOU...;)
Charles is going camping with his family 3 /4 miles away they walked at a steady speed of 2/1/4 per hour how many minutes will it take them to get to campsite
Isabelle wants to buy a bicycle. She has saved $9.76.Her mom tells her she needs 8 times more than amount. How much money does she need to buy a bicycle.
Answer:
$68.32
Step-by-step explanation:
Is 9.76 = x
And the value needed is 8 * this amount, then it can be shown with 8x
8x = 9.76 * 8
8x = 78.08
So the total price is $78.08
To find the money needed, simply subtract the saved money from this amount:
78.08 - 9.76 = 68.32
So she needs $68.32!
Isabelle needs $78.08 to buy the bicycle, which is 8 times her current savings of $9.76.
Explanation:Isabelle's current savings stands at $9.76. But she needs to have 8 times this amount in order to buy the bicycle. Mathematically speaking, you find how much she needs by multiplying her current savings by 8. So, $9.76 x 8 equals $78.08. Therefore, Isabelle needs a total sum of $78.08 to buy the bicycle.
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How do you recognize if a binomial is a difference of perfect squares and how is the pattern used to factor the binomial?
Answer:
A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
Step-by-step explanation:
A binomial is an expression with only terms where at least one is a term with a variable. When we can factor for difference of squares, we can have two variable terms or just one with a constant.
A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
Thomas earns 15 per hour if he recurved a 10% per hour pay increase how much does Thomas now make per hour
Answer:
He will make 16.50 per hour after his raise.
Step-by-step explanation:
15 x .10 = 1.50
15.00 + 1.50 = 16.50
in 1950, the U.S. federal budget was $39.4 billion, in 2000, the federal budget was $2025.2 billion. The exponential function is f=39.4Be^0.0787932i. Use your function to estimate the budget in 2010
Answer:
The budget in 2010 is $4453.10915 billion
Step-by-step explanation:
We are given exponential function as
[tex]f(t)=39.4e^{0.0787932t}[/tex]
where t is the time in years since 1950
now, we can find time in 2010
t=2010-1950=60
now, we can plug t=60
and we get
[tex]f(60)=39.4e^{0.0787932\times 60}[/tex]
we get
[tex]f(60)=4453.10915[/tex]
So, the budget in 2010 is $4453.10915 billion
Suppose the length and the width of the sandbox are doubled.
The length of the sandbox is 10 and the width is 6.
a.Find the percent of change in the perimeter.
b. Find the percent of change in the area.
Rectangle is the closed shaped polygon with 4 sides. Opposite sides of the rectangle are equal. when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.
Given-
The length of the sandbox is 10.
The width of the sandbox is 6.
a) The percent of change in the perimeter.
Perimeter of the rectangleThe perimeter of the rectangle is the twice of the sum of its side.The perimeter P of the sandbox is,
[tex]P =2\times (10+6)[/tex]
[tex]P =2\times (16)[/tex]
[tex]P=32[/tex]
When the length and the width of the sandbox are doubled the perimeter [tex]P_d[/tex] of the box is,
[tex]P_d=2\times(20+12)[/tex]
[tex]P_d=2\times(32)[/tex]
[tex]P_d=64[/tex]
Percentage [tex]\DeltaP[/tex][tex]\Delta P[/tex] change in the perimeter,
[tex]\Delta P=\dfrac{64-32}{32}\times 100[/tex]
[tex]\Delta P=100[/tex]
b) The percent of change in the area.
Area of the rectangleThe area of the rectangle is the product of its side.The area A of the sandbox is,
[tex]A = (10\times6)[/tex]
[tex]A=60[/tex]
When the length and the width of the sandbox are doubled the area [tex]A_d[/tex] of the box is,
[tex]A_d=20\times12[/tex]
[tex]P_d=240[/tex]
Percentage [tex]\DeltaP[/tex][tex]\Delta A[/tex] change in the area,
[tex]\Delta A=\dfrac{240-60}{60}\times 100[/tex]
[tex]\Delta P=300[/tex]
Thus when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.
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which pair of angles is a pair of corresponding angles?
Answer:
2 and 6
Step-by-step explanation:
Corresponding angles are the angles that occupy the same relative position at each intersection.
1 and 5
2 and 6
4 and 8
3 and 7
Explain how to solve 7 + x > 12 .Tell what property of inequality you would use
Answer:
x > 5
Step-by-step explanation:
isolate x by subtracting 7 from both sides
x > 12 - 7
x > 5
A population of bacteria is growing according to the exponential model P = 100e(.70)t, where P is the number of colonies and t is measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]
A) 0.7
B) 1.6
C) 5.7
D) 7.2
Divide the following polynomial, then place the answer in the proper location on the grid. Write your answer in order of descending powers of x.
(a^2n - a^n - 6) ÷ (a^n + 8)
The correct answer for dividing [tex](a^{2n} - a^n - 6) by (a^n + 8)[/tex] is indeed:
[tex](a^n - 9) + (-78)/(a^n + 8).[/tex]
Let's divide the given polynomials:
[tex]\frac{a^{2n -a^n -6}}{a^n +8}[/tex]
Here's the breakdown of the solution:
Factoring: We can factor the numerator [tex](a^{2n} - a^n - 6)[/tex] using difference of squares:
[tex](a^{2n} - a^n - 6) = (a^n)^2 - (a^n) - 6 = (a^n + 2)(a^n - 3)[/tex]
Division: Now, we can divide the factored numerator by the denominator:
[tex][(a^n + 2)(a^n - 3)] / (a^n + 8) = (a^n + 2) - [(a^n + 8) * (a^n - 3)] / (a^n + 8) = (a^n + 2) - (a^n - 3) = a^n - 9[/tex]
Remainder: Since the degree of the numerator is less than the degree of the denominator, we get a non-zero remainder.
This remainder is obtained by dividing the constant term (-6) in the numerator by the constant term (8) in the denominator, resulting in [tex]-78/(a^n + 8).[/tex]
Therefore, the final answer is [tex](a^n - 9) + (-78)/(a^n + 8)[/tex], with a quotient of [tex](a^n - 9)[/tex] and a non-zero remainder of [tex](-78)/(a^n + 8).[/tex]
MATH HELP PLEASE!!
find the area of the shaded region.
use the formula A= pi r^2 to find the area of the circle.
a. 8pi x + 24pi
b. 8pi x - 24pi
c. x^2 + 8pi x + 24pi
d. x^2 +8pi x - 24pi
Answer:
b
Step-by-step explanation:
B// 8pi x-24pi
The line with equation a+2b=0 coincides with the terminal side of an angle 0 in standard position and cos 0 < 0. What is the value of sin0?
Question:
line x + 2y = 0 is end side of angle θ
and cos θ < 0
Answer: sin θ = √5/5
Step-by-step explanation:
cos θ < 0 means x < 0
Line is y = -x/2, slope -1/2
Line intersects unit circle when x^2+y^2=1
x^2 + (-x/2)^2 = 1
x^2 + x^2/4 = 1
5x^2/4 = 1
x = -√(4/5) = -2√(1/5) = -2√5/5
y = √5/5
x^2 = 4/5, y^2 = 1/5
sin θ is y value at intersection of line and unit circle, √5/5
In this exercise we have to use the given equation and thus calculate the intersection value:
[tex]sin (\theta) = \sqrt{5/5}[/tex]
So knowing that you were informed:
Line x + 2y = 0 is end side of angle θ and cos θ < 0 means x < 0. Line is y = -x/2, slope -1/2 and the Line intersects unit circle when :
[tex]x^2+y^2=1\\x^2 + (-x/2)^2 = 1\\x^2 + x^2/4 = 1\\5x^2/4 = 1\\x = -\sqrt{4/5} = -2\sqrt{1/5} = -2\sqrt{5/5}\\y = \sqrt{5/5}\\x^2 = 4/5, y^2 = 1/5[/tex]
[tex]sin(\theta)[/tex] is y value at intersection of line and unit circle, [tex]\sqrt{5/5}[/tex]
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BRAINLIEST AND 50 POINTS
1.) A jar contains 4 red, 5 white, and 3 blue marbles. A marble is drawn from the jar. What is the probability that the marble is
Blue?______ White?_____ Red?_____ Not red?_____
Answer:
P ( blue ) = 1/4
P ( white ) = 5/12
P ( red ) = 1/3
P ( not red ) = 2/3
Step-by-step explanation:
To find the probability of a marble being chosen, it is the number of that color over the total
We need to find the total number of marbles
4 red+ 5 white+3 blue = 12 marbles
P ( blue ) = 3 blue / 12 total = 3/12 = 1/4
P ( white ) = 5 white / 12 total = 5/12
P ( red ) = 4 red/ 12 total = 4/12 = 1/3
How man marbles are not red
total marbles - red marbles = 12-4 = 8
8 marbles are not red
P ( not red ) = 8 not red / 12 total = 8/12 = 2/3
Ivanna is saving money to buy a game. So far she has saved $24, which is three-fourths of the total cost of the game. How much does the game cost ?
Answer:
The game costs 32 dollars total, we know this because if you divid 32 by 4 its 8 and . if you multiply 8 times 3 its 24
Step-by-step explanation:
The total cost of the game is $32, calculated using the concept of fractions in mathematics where the given $24 was considered as three-fourths of the total game cost.
Explanation:The subject of the question involves the concept of fractions in mathematics. Here the information provided states that $24, which Ivanna has saved, represents three-fourths (or 3/4) of the total cost of the game. To find out the total cost of the game, we will consider the $24 as three parts, and we need to find out the value of one part (or one-fourth). So, we divide $24 by 3, which gives us $8. This $8 is one-fourth of the total game cost. Now, to get the total cost, we will multiply this one-fourth value ($8) by 4. So, the total cost of the game is $8 * 4 = $32.
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The measure of an exterior angle of a triangle is equal to the *blank* of the measures of the two *blank* interior angles.
(a). Difference; remote
(b). Product; alternate
(c). Sum; remote
(d). Sum; alternate
(e). Difference; adjacent
Answer:
C
Step-by-step explanation:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
The measure of an exterior angle of a triangle is equal to the sum of the measure of the two opposite interior angles.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the sum of all the interior angles in a triangle is 180°.
We also know that the measure of an exterior angle of a triangle is the sum of the measure of two opposite interior angles.
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4. A bracelet that normally sells for $30.00 is on sale for $25.50. What is the percent discount?
Answer:
It is 15% off
Step-by-step explanation:
30.00-(15%×30.00)= 25.5
CE and BD are angle bisectors of △ABC which intersect at point F. If ∠BFC=110°, find the measure of ∠A.
Answer:
∠A=40°
Step-by-step explanation:
Equation 1: ∠A+∠B+∠C=180°
Equation 2: ∠B/2+∠C/2+110°=180°
2(Equation 2): ∠B+∠C+220°=360°
∠B+∠C=140°
Equation 1 - 2(Equation 2): ∠A=40°
Therefore, ∠A=40°
Can someone help me with this problem
Answer:
12
Step-by-step explanation:
There are 6 for tails. Each is 2. 6 x 2 =12
Can someone help me with 7-9
Answer:
Warning:
I think that these are correct, but don't make this your official source :)
7. B
8. D
9. B
I hope this helps :)
Write the equation of the line containing the point (3, –2) and having a slope of 2 in slope-intercept form.
Slope-intercept form:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))
You know m = 2, so you can plug it into the equation
y = 2x + b
To find "b", plug in the point (3, -2) into the equation
y = 2x + b
-2 = 2(3) + b
-2 = 6 + b
-8 = b
y = 2x - 8
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope m = 2 and the point (3, -2) → x = 3 and y = -2.
Substitute:
[tex]-2=(2)(3)+b[/tex]
[tex]-2=6+b[/tex] subtract 6 from both sides
[tex]-8=b\to b=-8[/tex]
Substitute to the equation y = mx + b:
Answer: y = 2x - 8when you multiply a function by -1, what is the effect on its graph?
a) the graph flips over the x-axis
b) the graph flips over the line y=x
c) the graph flips over the y-axis
Answer:
A. the graph flip over the x - axis...
Option b) the graph flips over the line y=x
When you multiply two function together, you will get a third function as the result, and that third function as the result, and that third function will be the product of the two original functions . when we multiply the function by -1 ,it becomes y=-f(x) . Then the coordinates becomes (x, -f(x))
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Help pleasee? Same ones
Since we are given that ABC is congruent to JKL, then AB has to be equal to JK
therefore --- [tex]14x+7=5x+34[/tex]
Subtract 7 from both sides
[tex]14x=5x+27[/tex]
Subtract 5x from each side
[tex]9x=27[/tex]
Divide 9 on each side
[tex]x=3[/tex]
Since, We are asked to find the length of AB and JK
plug in 3 for x
[tex]5(3)+34=15+34=49[/tex]