Answer:
-10
Step-by-step explanation:
Phythagorean theorem HELPPPP PLSSSSS ASAPPP
Answer:
5
Step-by-step explanation:
We know that we can use the Pythagorean theorem
a^2 + b^2 =c^2
where a and b are the legs and c is the hypotenuse
one of the legs is 12 and the hypotenuse (diagonal) is 15
a^2 + 12^2 = 15^2
a^2 +144 = 169
a^2 +144-144 =169-144
a^2 = 25
Taking the square root of each side
sqrt(a^2) = sqrt(25)
a = 5
Answer:
l = 9 cm
Step-by-step explanation:
Using Pythagoras' identity in one of the right triangles with legs width w, length l and hypotenuse h , then
l² + w² = h²
l² + 12² = 15²
l² + 144 = 225 ( subtract 144 from both sides )
l² = 81 ( take the square root of both sides )
l = [tex]\sqrt{81}[/tex] = 9
Help plzzzz!!!!!!! thank you .
Answer:
120°
Step-by-step explanation:
<U + <T = 180
or, 6x-6+9x+21=180
or, 15x=165
or, x=11
so, <T = 9×11+21 = 120
First you to find the worksheet and download it
plase I need help
Answer:
a) The horizontal asymptote is y = 0
The y-intercept is (0, 9)
b) The horizontal asymptote is y = 0
The y-intercept is (0, 5)
c) The horizontal asymptote is y = 3
The y-intercept is (0, 4)
d) The horizontal asymptote is y = 3
The y-intercept is (0, 4)
e) The horizontal asymptote is y = -1
The y-intercept is (0, 7)
The x-intercept is (-3, 0)
f) The asymptote is y = 2
The y-intercept is (0, 6)
Step-by-step explanation:
a) f(x) = [tex]3^{x + 2}[/tex]
The asymptote is given as x → -∞, f(x) = [tex]3^{x + 2}[/tex] → 0
∴ The horizontal asymptote is f(x) = y = 0
The y-intercept is given when x = 0, we get;
f(x) = [tex]3^{0 + 2}[/tex] = 9
The y-intercept is f(x) = (0, 9)
b) f(x) = [tex]5^{1 - x}[/tex]
The asymptote is fx) = 0 as x → ∞
The asymptote is y = 0
Similar to question (1) above, the y-intercept is f(x) = [tex]5^{1 - 0}[/tex] = 5
The y-intercept is (0, 5)
c) f(x) = 3ˣ + 3
The asymptote is 3ˣ → 0 and f(x) → 3 as x → ∞
The asymptote is y = 3
The y-intercept is f(x) = 3⁰ + 3= 4
The y-intercept is (0, 4)
d) f(x) = 6⁻ˣ + 3
The asymptote is 6⁻ˣ → 0 and f(x) → 3 as x → ∞
The horizontal asymptote is y = 3
The y-intercept is f(x) = 6⁻⁰ + 3 = 4
The y-intercept is (0, 4)
e) f(x) = [tex]2^{x + 3}[/tex] - 1
The asymptote is [tex]2^{x + 3}[/tex] → 0 and f(x) → -1 as x → -∞
The horizontal asymptote is y = -1
The y-intercept is f(x) = [tex]2^{0 + 3}[/tex] - 1 = 7
The y-intercept is (0, 7)
When f(x) = 0, [tex]2^{x + 3}[/tex] - 1 = 0
[tex]2^{x + 3}[/tex] = 1
x + 3 = 0, x = -3
The x-intercept is (-3, 0)
f) [tex]f(x) = \left (\dfrac{1}{2} \right)^{x - 2} + 2[/tex]
The asymptote is [tex]\left (\dfrac{1}{2} \right)^{x - 2}[/tex] → 0 and f(x) → 2 as x → ∞
The asymptote is y = 2
The y-intercept is f(x) = [tex]f(0) = \left (\dfrac{1}{2} \right)^{0 - 2} + 2 = 6[/tex]
The y-intercept is (0, 6)
The speed of a car as a function of time is shown in the figure(attached up) . Find the distance travelled by the car in 8 seconds and its acceleration .
______________________________
[tex]\sf\bold{The\:above\:graph\:says:}[/tex]
$\sf\bold\red{a=slope\:of\:v-t\:graph}$$\space$
$\sf\bold{here:}$
$\sf\bold\red{a=acceleration}$$\space$
$\sf\bold{Find\:acceleration\:by\:v-t\:graph:}$
$\mapsto$ $\sf\small{TanØ =}$ $\sf\dfrac{slope\:of\:y}{slope\:of\:x}$= $\sf\dfrac{20}{8}$ $\sf{m/s^2}$
$\space$
$\mapsto$ [tex]\sf\underline\bold\purple{a=2.5m/s^2}[/tex]$\space$
$\sf\bold{Now,calculate\:the\:distance:}$
$\sf\bold{By\:equation\:of\:motion.}$$\sf{s=}$ $\sf{ut+}$ $\sf\dfrac{1}{2}$ $\sf{at^2}$$\space$
$\sf\bold{Given\:parameters:}$
$\sf\bold{u=0}$$\sf\bold{a=5/8}$$\sf\bold{t=8}$$\space$
$\sf\bold{Substituting \: the\:values:}$
$\mapsto$ $\sf\small{s=0+}$ $\sf\dfrac{1}{2}$ $\times$ $\sf\dfrac{5}{8}$ $\sf\small{8^2}$
$\space$
$\longmapsto$ $\sf\underline\bold\purple{S=80m}$
$\space$
❍Therefore , the acceleration is $\sf\bold{2.5m/s^2}$ and the distance traveled by car is $\sf\bold{80m.}$
_______________________________
80 m is distance ! Please mark as brainliest
A student graphed function f(x) =( x+2)² - 5. How would the new function be written if it is translated 3 units to the right, shifted 2 units down and vertically stretched by a factor of 2?
Answer:
f(x)=2(x-3)-2
Step-by-step explanation:
when you hear if it translate to the right, it mean subtract " - "
so translate 3 unit right, it mean minus 3.
and same if translate left, it mean add, "+"
But if it mean shift down, it mean minus -
and if it mean shift up, it mean add +
so shift down 2 unit, mean -2
stretch factor of 2, mean multiply by 2
I hope this help! Im gonna explain further more if you have any question☺
The transformation of a function involves changing the features of the original function to another.
The new function is: [tex]f"(x) = 2(x- 1)^2 - 14[/tex]
The function is given as:
[tex]f(x) = (x + 2)^2 - 5[/tex]
When translated right, the rule is:
[tex](x,y) \to (x - h, y)[/tex]
In this case;
[tex]h= 3[/tex] --- i.e. 3 units right
So, the function becomes
[tex]f'(x) = (x + 2 - 3)^2 - 5[/tex]
[tex]f'(x) = (x - 1)^2 - 5[/tex]
When shifted down, the rule is:
[tex](x,y) \to (x, y - b)[/tex]
In this case;
[tex]b =2[/tex] --- i.e. 2 units down
So, the function becomes
[tex]f'(x) = (x- 1)^2 - 5-2[/tex]
[tex]f'(x) = (x- 1)^2 - 7[/tex]
When vertically stretched, the rule is:
[tex](x,y) \to (x, ay)[/tex]
In this case;
[tex]a =2[/tex] --- i.e. factor of 2
So, the function becomes
[tex]f"(x) = 2*[(x- 1)^2 - 7][/tex]
[tex]f"(x) = 2(x- 1)^2 - 14[/tex]
Hence, the new function is: [tex]f"(x) = 2(x- 1)^2 - 14[/tex]
Read more about function transformations at:
brainly.com/question/24326503
SHOW YOUR STEPS PLEASE. SOMEONE PLEASE HELP ME I NEED THE ANSWER ASAP!!!
The cost, c(x), in dollars per hour of running a certain steamboat is modelled by the function c(x)=1.7x^2-13.6+166.4, where x is the speed in kilometres per hour. At what approximate speed should the boat travel to achieve minimum cost? what is the minimum cost?
Answer:
x = 4
139.2
Step-by-step explanation:
Given the Cost function :
C(x) = 1.7x² - 13.6x + 166.4
To achieve minimum cost ;
dc/dx = 0
dc/dx = 2(1.7)x - 13.6
3.4x - 13.6 = 0
3.4x = 13.6
x = 13.6 / 3.4
x = 4
To achieve minimum cost, speed = 4 ;
Minimum cost will be :
C(x) = 1.7x² - 13.6x + 166.4
Put x = 4
C(4) = 1.7(4)² - 13.6(4) + 166.4
C(4) = 27.2 - 54.4 + 166.4 = 139.2
Minimum cost = 139.2
Instructions: Find the missing side. Round your answer to the nearest
tenth.
19
х
66°
X =
Step-by-step explanation:
the missing side is the adjacent side of the angle 66..which also has an opposite side of 19, therefore you use tan
tan66=19/x
tan66x/tan66=19/tan66
x=8.5
I hope this helps
Measure of base of the triangle, value of x is 8.46 unit.
What is trigonometric ratio?Trigonometric ratios can be calculated by taking the ratio of any two sides of a right triangle. Given the scale of the other two sides, we can evaluate the third side using the Pythagorean theorem. We can compare the length of any two sides and the angle of the base using trigonometric ratio. The angle θ is an acute angle (θ < 90°) and is usually measured counterclockwise with respect to the positive x-axis. The basic formula for trigonometric ratios is:
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
sec θ = Hypotenuse/Base
cosec θ = Hypotenuse/Perpendicular
cot θ = Base/Perpendicular
Given,
In right triangle,
Base of the triangle is x
Measure of angle = 66°
Perpendicular = 19 unit
tanθ = Perpendicular/base
tan66° = 19/x
2.246 = 19/x
x = 19/2.246
x = 8.46 unit
Hence, 8.46 unit is measure of base of the triangle, that is value of x.
Learn more about trigonometric ratio here:
https://brainly.com/question/25122825
#SPJ7
Can someone help me with this question pls
Answer:
D
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = - 94 and d = a₂ - a₁ = - 112 - (- 94) = - 112 + 94 = - 18 , then
S₁₀ = [tex]\frac{10}{2}[/tex] [ (2 × - 94) + (9 × - 18) ]
= 5(- 188 - 162)
= 5 × - 350
= - 1750
Please help explanation need it
Answer:
56 + 77 + 88 + 99 = 320km²
Step-by-step explanation:
A triangular prism has 5 sides. We can start with the top and bottom, which have a base of 7 km and a height of 8km, making each of their areas equal to 7 * 8/2 = 28. Adding those up, we get 28+28 = 56 km² as the surface area of the top and bottom portions.
Next, we have the face that has 7 as the base and 11 as the height. The area of that is 7 * 11 = 77km²
After that, we have the face with 8 as the base and 11 as the height, making the area of that 8 * 11 = 88km²
Finally, we have the face with 9 as the base and 11 as the height, making that area 9 * 11 = 99km²
Adding these all up, the total surface area is
56 + 77 + 88 + 99 = 320km²
Consider the quadratic expression 13x^2 + nx - 17. For certain values of n, it may be factored into a product of two linear polynomials, both of which have integer coefficients. What are all such values of n?
Answer:
n = 220, 4, -4, -220
Step-by-step explanation:
factors of 17: 17, 1, -1, -17
13 is prime number: 13 x 1 = 13
(ax+b)(cx+d) = axcx+axd+bcx+bd
(x + 17)(13x - 1) = 13x^2 + 220x - 17, n = 220
(x - 17)(13x + 1) = 13x^2 - 220x - 17, n = -220
(x + 1)(13x - 17) = 13x^2 - 4x - 17, n = -4
(x - 1)(13x + 17) = 13x^2 + 4x - 17, n = 4
Please explain, thank you
Answer:
C. 2.
Step-by-step explanation:
The graph descends from the left so the coefficient of the leading term is negative. It is also a cubic equation with zeros of -20, about 6.5 and about 13. so we can write the equation as below. The last 2 values can only be guessed because the x axis only shows values which are multiples of 5.
f(x) = a(x + 20)(x - 6.5)(x - 13) where a is a negative constant.
(This is only an approximation).
By the Remainder theorem, when the expression is divided by (x + 10):
f(-10) = -20 so we have
-20 = a (-10 + 20)(-10-6.5)(-10 - 13)
(10)(-16.5)(-23)a = -20
a = -20 / (10)(-16.5)(-23)
a = -0.0053
When the equation is divided by (x - 10) then f(10) is the remainder so substituting we have as the remainder:
-0.0053(10+20)(10-6.5)(10 -13)
-0.0053 * 30 * 3.5 * -3
= 1.7 approximately.
Looks like the answer is 2.
HELP PLS WITH PYTHAGOREAN THEOREM
Answer:
100 ft
Step-by-step explanation:
We need to find the diagonal ( or hypotenuse)
We can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
80^2 + 60^2 = c^2
6400+3600 = c^2
10000 = c^2
Taking the square root of each side
sqrt(10000) = sqrt(c^2)
100 = c
Evaluate the function for x = 3a.
f(x) = 2x^2 – 3x +4
A. 9а
B. 6a^2- 9a + 4
C. 18a^2 - 9a +4
D. 12a^2 - 6a+4
Answer:
C
Step-by-step explanation:
We are given the function:
[tex]f(x) = 2x^2 -3x+4[/tex]
And we want to evaluate it for x = 3a.
Substitute:
[tex]f(3a) = 2(3a)^2-3(3a)+4[/tex]
Square:
[tex]f(3a) = 2(9a^2)-3(3a)+4[/tex]
Simplify:
[tex]f(3a) = 18a^2-9a+4[/tex]
Hence, our answer is C.
Triangle ABC is translated right 8 units and down 15 units to triangle XYZ. Triangle ABC
has these angle measures:
m∠A=45∘
m∠B=53∘
m∠C=82∘
What is the measure of angle Y?
9514 1404 393
Answer:
53°
Step-by-step explanation:
The names of the triangles indicate that angle B corresponds to angle Y. Translation does not affect side lengths or angle measures, so angle Y is the same measure as angle B.
m∠Y = 53°
Answer: 53
Step-by-step explanation:
can someone give me a little assistance and an explanation ?
9514 1404 393
Answer:
when the number of persons is less than 10
Step-by-step explanation:
The red line indicates the charges for Mount Joy Pool. It is below the blue line for "number of people" less than 10. That means Mount Joy Pool charges less than Woodbridge Pool for fewer than 10 people.
Assuming Arthur is interested in paying as little rent as necessary, he should select Mount Joy Pool when he is renting for less than 10 people.
__
Additional comment
The rent for 10 people is the same at either location, so there is nothing to favor Mount Joy Pool for 10 people. For more than 10 people, Woodbridge Pool charges less rent.
The function f(c)=95c+32 is used to convert temperatures from Celsius, c, to Fahrenheit, f(c). What is the temperature in Fahrenheit when it is 22° Celsius? Round your answer to the nearest integer. A 40° B 54° C 72° D 97°
C 72°
Answer:
we have
f(c)=9/5C+32
now
22°C to °F
°C=22°
we have
f(c)=9/5C+32
f(c)=9/5*22+32=71.6≈72
answer is
22°C=72°F
Answer: [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boldsymbol{72^\circ F}[/tex]
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol{} f(c)=\frac{9}{5} c+32 \ \ in \ \ our \ \ case \\\\\\\\f(22)=\frac{9\cdot 22}{5} +32=39,6+32=7\underline1,6\approx72^\circ F[/tex]
Center (-1,5); passes through (-4,-6)
Answer:
what is the question
Step-by-step explanation:
The two-way table shows the number of boys and girls in the school band and choir. Is there a greater percentage of girls in the school band or in the choir? Explain.
Answer:
the school band
Step-by-step explanation:
the band, the band has a percentage of 53.85...,which is (14/26)x100, and the choir has 35.71% which is (5/14)x100
anyone can help me with this
Answer:
4x-7=-5x²
or, 5x²+4x-7=0
so the standard form of the equation is,
5x²+4x-7=0
or, f(x) = 5x²+4x-7
Answered by GAUTHMATH
find the value of x.
Answer: x=35
Step-by-step explanation:
To find the value of x, we can use the Pythegorean Theorem because this is a right triangle.
Pythagorean Theorem: a²+b²=c²
[tex]12^2+x^2=(x+2)^2[/tex] [exponent and distribute]
[tex]144+x^2=x^2+4x+4[/tex] [subtract both sides by 144]
[tex]x^2=x^2+4x-140[/tex] [subtract both sides by x²+4x]
[tex]-4x=-140[/tex] [divide both sides by -4]
[tex]x=35[/tex]
Now, we know that x=35.
COULD SOMEONE PLEASE HELP ME (PICTURE) ITS URGENT MARKING BRAINLIEST 15 POINTS
Please help I will give brainliest to whoever helps
Answer:
A = x + 15
B = 1 + 2
Step-by-step explanation:
x 2 + 17x + 30
x2 + 15 x + 2x + 30
1 ( x + 15 ) + 2 ( x + 15 )
( x + 15 ) ( 1 + 2 )
Hope this answer helps you :)
Have a great day
Mark brainliest
write the equation of the graph below
Answer:
Step-by-step explanation:
This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:
[tex]y=a(x-h)^2+k[/tex] and this will allow us to solve for the value of a:
[tex]6=a(6-4)^2+5[/tex] and
[tex]6=a(2)^2+5[/tex] and
6 = 4a + 5 and
1 = 4a so
[tex]a=\frac{1}{4}[/tex] and the equation is
[tex]y=\frac{1}{4}(x-4)^2+5[/tex]
(2x-7)²-6(2x-7)(x-3)=0
Answer:
-8x² - 106x + 175 = 0
Step-by-step explanation:
Given:
(2x - 7)²- 6(2x - 7)(x-3) = 0
Find:
Solution of the following explanation
Computation:
(2x - 7)²- 6(2x - 7)(x-3) = 0
[(2x)² + (7)² - (2)(2x)(7)] - (12x - 42)(x-3) = 0
[4x² + 49 - 28x] - [12x² - 36x - 42x + 126] = 0
[4x² + 49 - 28x] - [12x² - 78x + 126] = 0
-8x² - 106x + 175 = 0
What is the factor of
[tex] {x}^{4} - x[/tex]
Plz
The battery standby duration (in hours) of a new model of cell phone is known to be normally distributed. Ten pieces of such new model of cell phone supplied from the manufacturer are randomly chosen and the actual standby durations are recorded as below:
48.2 47.8 45.6 47.2 49.3
51.2 44.2 45.4 49.2 43.6
The manufacturer claimed that this new model of cell phone has the mean battery standby duration of longer than 46.5 hours. Test at 1% significance level if this claim is true.
x = number of hours
want to find probability (P) x >= 13
x is N(14,1) transform to N(0,1) using z = (x - mean) / standard deviation so can look up probability using standard normal probability table.
P(x >= 13) = P( z > (13 - 14)/1) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413
To convert that to percentage, multiply 100, to get 84.13%
Please mark me brainliest
subtract these polynomials
Answer:
option (D) is the answer
Answer:
[tex]-4x^{2} + 6x + 4[/tex]
Answer choice D
Step-by-step explanation:
not sure how to solve
How does the graph of g(x) = 1/x-5 +2 compare to the graph of the parent function f(x)= 1/x?
Answer: Its 5 units to the right and 2 units up.
When do you use the Distributive Property?
Answer:
when you have items outside a parentheses that needs to be multiplied by the items inside
a(b+c) = ab + ac
Step-by-step explanation:
