Final answer:
Using the Pythagorean theorem with the given lengths of the sides a=8 and b=15, the hypotenuse c is found to be 17 units.
Explanation:
The question involves finding the length of the hypotenuse c in a right triangle using the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Given that a = 8 and b = 15, we can apply the theorem:
c² = a² + b²
c² = 8² + 15²
c² = 64 + 225
c² = 289
c = √289
c = 17
Therefore, the length of the hypotenuse c is 17 units.
Write the fraction as a whole or mixed number.
Hong Kong reported approximately 1,500 cellular phones per 1,000 people. Express the number of phones per person as a whole or mixed number.
Answer:
[tex]1\frac{1}{2}[/tex]
Step-by-step explanation:
If there is 1500 cellular phones per 1000 people, then the number of phones per person is:
[tex]\frac{1500}{1000} = \frac{15}{10} = \frac{3}{2}[/tex]
Now we know that [tex]\frac{3}{2} = 1 + \frac{1}{2} = 1\frac{1}{2}[/tex]
Susan is planting marigolds and impatiens in her garden. Each marigold costs $9, and each impatien costs $7. Susan wants the number of marigolds to be more than twice the number of impatiens. She has a maximum of $125 to spend on the plants. This situation can be modeled by the following system of inequalities.
Which statement describes the system of inequalities?
A.
The system represents the minimum amount that Susan can spend on impatiens, x, and marigolds, y, and the relationship between the number of impatiens and marigolds.
B.
The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.
C.
The system represents the minimum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.
D.
The system represents the maximum amount that Susan can spend on impatiens, x, and marigolds, y, and the relationship between the number of marigolds and impatiens.
Answer:
B.
The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.
Answer:
B.
The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.
What is the factored form of the polynomial?
x2 - 12x + 27?
(x + 4)(x+3)
(x - 4)(x + 3)
(x + 9)(x + 3)
(x-9)(x - 3)
Answer:
The answer is option D.
Step-by-step explanation:
Answer:
D: Answer:(x-9)(x-3)
Step-by-step explanation:
iiiiiiiiytffhjhffjdjhdhdhdhdhhdhdd
Answer:
x = 30
Step-by-step explanation:
The sum of the 3 interior angles of a triangle = 180°, hence
x + x + 10 + 3x + 20 = 180
5x + 30 = 180 ( subtract 30 from both sides )
5x = 150 ( divide both sides by 5 )
x = 30
Please look at attachment. Has all info needed. Need help
Step-by-step explanation:
When the object hits the ground, h = 0.
0 = -21.962x + 114.655
x = 5.2
From the table, the object landed at x = 4.6 seconds. So the line of best fit predicts a time 0.6 seconds greater than actual.
The original height is when x = 0.
h = -21.962(0) + 114.655
h = 114.7
So the line of best fit predicts the object was dropped from a height of 114.7 meters. This is higher than the actual 100 meters.
At x = 3.5:
h = -21.962(3.5) + 114.655
h = 37.8
So the line of best fit estimates the object reached a height of 37.8 meters after 3.5 seconds.
We know that at x = 0, h = 114.7. This is more than 4 meters from the actual initial height of 100 m.
Therefore, the answer must be A.
Answer:
A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
Step-by-step explanation:
What is the area of the kite? Height of 6ft base of 14ft. 21 square feet 40 square feet 42 square feet 84 square feet
Answer:area is 84
Step-by-step explanation:
6*14
Answer:
its c 42 square feet
Step-by-step explanation:
-2x + 3 < 5
solve and show steps please
Answer:
x < -1
Step-by-step explanation:
5 - 3 = 2
-2x < 2
x < -1
Answer:
Answer is x > -1
Step-by-step explanation:
Because -2x + 3 < 5
-3 -3 minus 3 on both sides
Then: -2x < 5
-2 -2 divide negative 2 on both sides
And get x > -1, Because if you divide by negative numbers the sign always flips.
Sorry i had to reedit it's -1 because you divide my bad.
Hope my answer has helped you and if not i'm sorry.
Write the following equation in standard form : 8/7x^3 + x^4 + 6x +1
Answer:
x^4 +8/7x^3 + 6x +1
Step-by-step explanation:
8/7x^3 + x^4 + 6x +1
Standard from is from the largest power to the smallest power
x^4 +8/7x^3 + 6x +1
Please explain your answer
Answer: Blueberry = $6, Pumpkin = $17
Step-by-step explanation:
Let B represent blueberry pie and P represent pumpkin pie.
Kim: 12B + 8P = 208
- Krystal: 10B + 8P = 196
2B = 12
B = 6
Input B = 6 into either of the equations to solve for P
10B + 8P = 196
10(6) + 8P = 196
60 + 8P = 196
8P = 136
P = 17
find the slope and y-intercept of each line y=4x+1
Answer:
Step-by-step explanation:
the slope is 4
y int is 1
the graph of y= sqrtx is translated 4 units left and 1 unit up to create the function h(x). the graph of h(x) is shown on the coordinate grid. what is the range of h(x)?
Answer:
C. [tex]\{y|y\ge 1\}.[/tex]
Step-by-step explanation:
Consider the parent function [tex]f(x)=\sqrt{x}.[/tex]
The domain of this function is [tex]x\ge 0;[/tex]The range of this function is [tex]y\ge 0.[/tex]Now consider given function [tex]h(x)=\sqrt{x+4}+1[/tex] (translated 4 units left and 1 unit up.)
The domain of this function is [tex]x\ge -4;[/tex]The range of this function is [tex]y\ge 1.[/tex]Answer:
The range of the function h(x) is [tex]R=\{y|y\geq 1\}[/tex]
Step-by-step explanation:
Given : The graph of [tex]y=\sqrt{x}[/tex] is translated 4 units left and 1 unit up to create the function h(x).
To find : What is the range of h(x)?
Solution :
When the graph f(x) is translated then
1) f(x)+b shifts the function b units upward.
2) f(x + b) shifts the function b units to the left.
The graph of [tex]y=\sqrt{x}[/tex] is translated 4 units left.
i.e. [tex]y=\sqrt{x+4}[/tex]
The graph of [tex]y=\sqrt{x}[/tex] is translated 1 unit up.
i.e. [tex]y=\sqrt{x+4}+1[/tex]
So, The required function h(x) is [tex]h(x)=\sqrt{x+4}+1[/tex]
The range of a function is set of output values produce by a function.
In the given graph, y value is always greater than and equal to 1.
So, The range of the function h(x) is [tex]R=\{y|y\geq 1\}[/tex]
I need help here been stuck here ?!
Answer:
Step-by-step explanation:
Angle 9 = 85 degrees
Angle 9 and < 11 are vertical angles
Vertical angles are equal
<11 = 85 degrees
simplify
(18-9.(-4/3)+10×2)
Answer:
what is the period after the 9?
Answer:
50
Step-by-step explanation:
Evaluate the products before addition
18 - (9 × - [tex]\frac{4}{3}[/tex] ) + (10 × 2)
= 18 - (- 12) + 20
= 18 + 12 + 20
= 50
what is the area of the polygon given below?
Answer:
C 340 square units
Step-by-step explanation:
Divide it into smallest pieces.
I see two rectangles that I'm going to do.
The long rectangle reading the paper from bottom to top is a 4 by (4+11+4) rectangle.
The wide rectangle reading the paper from left to right is a 24 by 11 rectangle.
We need to find the area of both of these rectangles and then just add them together to get the total area.
So first rectangle has area 4(19)=76 and the second rectangle has area 264. The sum of these two numbers are 340 square units.
Hello There!
The answer would be 340 square units
First, let's find the area of our small rectangle located to the left. The formula for a rectangle is width*height so we would multiply19 because we know that on our right rectangle the height is 11 and we would add 4 to that and add another 4 to that to get our length of our rectangle on the left.
Next, we multiply 24 by 11 because we are using our same formula for the rectangle on the right and once we multiply, we get a product of 264.
Finally, we add 264 and our area of the rectangle on the right together and get a sum of 340 square units.
Have A Great Day!
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to
$(6)-1
276)+1
(6)
2(6) + 1
36-1
26+1
(6)-1
(6)+1
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to (r/s)(6) is: A. [tex]\frac{3(6) - 1}{2(6)+1}[/tex]
In Mathematics, an algebraic expression is a type of mathematical equation which is typically used for showing the relationship existing between two (2) or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.
Based on the information provided, the quotient of the two expressions can be computed as follows;
[tex]\frac{r(x)}{s(x)} =\frac{3x - 1}{2x+1} \\\\[/tex]
When the value of x is 6, the output value of the expression
[tex]\frac{r}{s}(6) =\frac{3(6) - 1}{2(6)+1}[/tex]
Complete Question;
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to (r/s)(6)?
Nick borrowed $1250, to be repaid after 5 years at annual simple interest rate of 7.25%. how much interest will be due after 5 years? how much will nick have to repay.
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1250\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ t=years\dotfill &5 \end{cases} \\\\\\ I=(1250)(0.0725)(5)\implies 453.125 \\\\\\ \stackrel{\textit{he'll have to repay}}{1250+453.125}\implies 1703.125[/tex]
Find a1, for the given geometric series. Round to the nearest hundredth if necessary. Sn= 44,240, r= 3.8, n= 9
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=9\\ r=3.8\\ \stackrel{S_n}{S_9}=44240 \end{cases}[/tex]
[tex]\bf 44240=a_1\left( \cfrac{1-3.8^9}{1-3.8} \right)\implies 44240\approx a_1\left( \cfrac{-165215.101}{-2.8} \right) \\\\\\ 44240\approx a_1(59005.393)\implies \cfrac{44240}{59005.393}\approx a_1\implies \stackrel{\textit{rounded up}}{0.75=a_1}[/tex]
When all the terms of a geometric sequence are added, then that expression is called geometric series. The first term of the given geometric series is 0.75.
What is a geometric series?When all the terms of a geometric sequence are added, then that expression is called geometric series.
What is the sum of terms of a geometric sequence?Let's suppose its initial term is, the multiplication factor is r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
Given the sum of the geometric series is 44,240, while the number of terms is 9. Also, the common ratio of the series is 3.8. Thus, we can write,
Sₙ = a(rⁿ-1)/(r-1)
44240 = a(3.8⁹ - 1)/(3.8 - 1)
44240 = a 59005.3933
a = 0.75
Hence, the first term of the given geometric series is 0.75.
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Select the correct answer.
Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has oil and the test predicts it?
A.
0.09
B.
0.11
C.
0.36
D.
0.44
Reset Next
Answer:
C. 0.36
Step-by-step explanation:
There is already a 45% chance of having oil on the land.
The oil kit has an 80% accuracy rate.
Therefore the kit has an 80% chance, of that 45% chance, of detecting oil. (Assume the owners in the area are correct in their 45% assumption)
This can be expressed as 80%*40% or 0.8*0.45
= 0.36 or 36%
Hope this helps!
Answer:
C. 0.36
Step-by-step explanation:
Which is a factor of x2 + 5x – 24?
O
(x-6)
(x + 6)
(X-8)
(X + 8)
Answer:
the answer would be d
Step-by-step explanation:
About 60% of the normal human
being's body weight is composed of
water. How much of a 125 pound
person is water weight?
F 72 pounds H 76 pounds
G 75 pounds I 80 pounds
The water weight of a 125lb person is 75lbs.
The graphs of f(x) =2/3x and g(x) =2/3x-2 are shown below.
Y1=2/3x , Y2=2/3x-2
those are the graph of the functions
The volume of a cylinder with a base of radius ris the area of the base times
the length of its height (h). Which of the following is the formula for the
volume of a cylinder?
f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)?
[tex]f(n+1)=f(n)-8\\f(1)=100\\\\f(2)=100-8=92\\f(3)=92-8=84\\f(4)=84-8=76\\f(5)=76-8=68\\f(6)=68-8=60[/tex]
What is the perimeter of an equilateral triangle if each side is (x+3)?
Answer:
all work is shown and pictured
what is the differnce between (-4)-6
Answer:
24
Step-by-step explanation:
(-4) -6? well it equals 24 because a negative plus a negative equals a positive.
Hope my answer has helped you! If not i'm sorry.
Answer:
The correct answer is -10. 24 isn't correct ^^^^.
Step-by-step explanation:
Linear Equation
Which line represents the linear equation
-3y = 15 - 4x?
The equation -3y = 15 - 4x rewritten in slope-intercept
form is
The y-intercept is and the slope of the line is
Line
v is the graph of the line -3y = 15 - 4x.
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{We have the equation:}\\\\-3y=15-4x\\\\-3y=-4x+15\qquad\text{ivide both sides by (-3)}\\\\\boxed{y=\dfrac{4}{3}x-5}\\\\\boxed{slope=\dfrac{4}{3}}\\\boxed{y-intercept=-5}[/tex]
[tex]\text{To draw a graph we need only two points.}\\\text{We choose any value of x, put it to the equation of the line}\\\text{and calculate the value of y:}\\\\for\ x=0\\\\y=\dfrac{4}{3}(0)-5=0-5=-5\to(0,\ -5)\\\\for\ x=3\\\\y=\dfrac{4}{3}(3)-5=4-5=-1\to(3,\ -1)\\\\\text{The graph is in attachment}.[/tex]
Answer:
answer in picture
Step-by-step explanation:
5. Which equation is of a circle that has a center at
(3,-2) and a radius of 9?
A (x + 3)2 + (y - 2)2 = 9
B (x + 3)2 + (y - 2)2 = 81
C (x - 3)2 + (y + 2)2 = 9
D (x - 3)2 + (y + 2)2 = 81
Answer:
[tex]\large\boxed{D.\ (x-3)^2+(y+2)^2=81}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center at (3, -2) and the radius r = 9. Substitute:
[tex](x-3)^2+(y-(-2))^2=9^2\\\\(x-3)^2+(y+2)^2=81[/tex]
What is the value of y in the solution to the system of equations?
*x+3y=1
2x – 3y = -30
Answer:
[tex]\large\boxed{y=\dfrac{32}{9}}[/tex]
Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}x+3y=1\\2x-3y=-30\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=-29\qquad\text{divide both sides by 3}\\.\qquad x=-\dfrac{29}{3}\\\\\text{put the value of x to the first equation}\\\\-\dfrac{29}{3}+3y=1\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\left(-\dfrac{29}{3\!\!\!\!\diagup_1}\right)+(3)(3y)=(3)(1)\\\\-29+9y=3\qquad\text{add 29 to both sides}\\\\9y=32\qquad\text{divide both sides by 9}\\\\y=\dfrac{32}{9}[/tex]
By adding the system of equations and solving for x, then substantifying back into the first equation, we find that y in this system of equations is approximately 3.5556.
Explanation:To find the value of y in the given system of equations, you can add the two equations together. The first equation is x+3y=1 and the second equation is 2x – 3y = -30. Here are the steps:
Add the two equations: (x + 3y) + (2x - 3y).The y terms cancel out and you end up with 3x = -29.Divide both sides by 3 to solve for x: x = -29/3 which is about -9.6667.Substitute x = -9.6667 into the first equation: -9.6667 + 3y = 1.Isolate y by adding 9.6667 to both sides and then divide both sides by 3: y = (1 + 9.6667)/3. You will find that y = 3.5556 approx.
This value, 3.5556, is the value of y in the solution for the system of equations.
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Which of the following is the maximum value of the equation y=-x^2+2x+5
a. 5
b. 6
c. 2.
d. 1
Answer: b. 6
Step-by-step explanation:
The maximum value is the y-value of the vertex.
Step 1: Find the x-value (aka Axis Of Symmetry) using the formula: [tex]x=\dfrac{-b}{2a}[/tex]
[tex]x=\dfrac{-(2)}{2(-1)}=\dfrac{-2}{-2}=1[/tex]
Step 2: input the x-value (above) into the given equation to solve for y:
[tex]y=-x^2+2x+5\\y=-(1)^2+2(1)+5\\y=-1 + 2 + 5\\y = 6[/tex]
Explain how to find the missing exponent given the base and the value
Answer:
To find the value of missing exponent, we have to split the number which is in other side of equal sign (which is not having power) as the multiple of base of the missing exponent.
On both sides, powers have the same base, so their exponents must be equal.
Step-by-step explanation:
Problem 1:Write the missing exponent:
25=5^x
Let x be the missing exponent.
To find the value missing exponent, we have to split the number which is in the left side as the multiple of the base of the missing exponent.
That is,
25=5*5 or 5^2
Now,
5^2=5^x
Powers have the same base so their exponent must be equal.
Hence the missing exponent is 2