Answer:
The missing side is 8 ft long
Step-by-step explanation:
According to Pythagoras theorem "It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides"
mathematically it is stated as
[tex]c^2= a^2+b^2\\\\c=\sqrt{a^2+b^2}[/tex]
Given that
c, hypotenuse= 17 ft
a = 15 ft
b= ?
Applying the Pythagoras theorem formula by inserting our given parameters and solving for b we have
[tex]17^2= 15^2+b^2[/tex]
Making b subject of formula we have
[tex]b^2= 17^2-15^2\\\\b^2= 289-225\\\\b^2= 64\\\\[/tex]
Square root both sides we have
[tex]b= \sqrt{64} \\\\b= 8[/tex]
Hence the missing side is 8 ft long
Evaluate the function. f(x) = -x2 - 6x + 12 Find f(4)
Answer:
f( 4 ) = - 28Step-by-step explanation:
f(x) = - x² - 6x + 12
To find f(4) substitute the value of x that's 4 into the expression above and solve.
That's
f( 4) = - (4)² - 6(4) + 12
= - 16 - 24 + 12
= - 40 + 12
We have the final answer as
f(4) = - 28Hope this helps you
The function y = (x - 4)2 + 3 is a transformation of the function y = x?. How is the function's vertex affected by the
transformation?
The vertex of the graph of y = x? is shifted to the left 4 units and down 3 units.
The vertex of the graph of y = x? is shifted to the left 3 units and down 4 units.
The vertex of the graph of y = x is shifted to the right 3 units and up 4 units.
The vertex of the graph of y = x?is shifted to the right 4 units and up 3 units.
Answer: The vertex of the graph of y = x^2 is shifted to the right 4 units and up 3 units
Step-by-step explanation:
Option (D) the vertex of the graph of y = x^2 is shifted to the right 4 units and up 3 units is the correct answer.
What is graph of a function?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The function y = (x - 4^)2 + 3
Plot the graph on substituting the function [tex]y=x^{2}[/tex] as shown in the graph below.
On comparing the two functions, the transformation of the vertex of the graph of y = x^2 is shifted to the right 4 units and up 3 units.
Thus the function y = (x - 4)^2 + 3 is a transformation of the function y = x^2.
Hence we can conclude that option (D) the vertex of the graph of y = x^2 is shifted to the right 4 units and up 3 units is the correct answer.
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What is the equation of the quadratic function represented by this graph
Answer:
f(x) = - x² + 2x + 8or f(x) = - (x - 1)² + 9 or f(x) = - (x + 2)(x - 4)Step-by-step explanation:
f(0) = 8 {y-axis intercept = (0, 8)}
Vertex = (1, 9)
f(x) = a(x - 1)² + 9
8 = a(0-1)² + 9
8 = a + 9
a = -1
f(x) = - (x - 1)² + 9
f(x) = - (x² - 2x + 1) + 9
f(x) = - x² + 2x - 1 + 9
f(x) = - x² + 2x + 8
x₁ = -2 and x₂ = 4, so also:
f(x) = -(x + 2)(x - 4)
Answer:
g(x) = -1 (x + 2)(x − 4)
Step-by-step explanation:
To write the equation of the function in factored form, g(x) = a(x − r1)(x − r2), find the values of r1, r2, and a.
The function has x-intercepts of -2 and 4, so (x − (-2)), or (x + 2), and (x − 4) are factors of the equation.
To find a, look at how the value of y changes for 1 unit to the right of the vertex. The y-value goes down 1 unit for a point 1 unit to the right of the vertex, so a = -1.
The equation of this quadratic function is g(x) = -(x + 2)(x − 4).
Thank me later ᵇⁱᵗᶜʰᵉˢ
Evaluate each expression if a =2, b = -3 and c = -1 and d =4. 2cd+3ab
Step-by-step explanation:
Given
a = 1
b = -3
c = -1
d = 4
Everything is given to us ,we have to replace variable by numbers and solve the equation
put the values of variables in th given equation we get our answer
[tex]2( - 1)(4) + 3(2)( - 3)[/tex]
[tex] - 8 - 18[/tex]
[tex] - 26[/tex]
-26 is ur answer
Hope it helps u mate
If a =2, b = -3 and c = -1 and d =4. 2cd+3ab is - 26.
What is a variable ?As name suggests variables can have different values.We put a certain values to a variable according to our desired results also can be thought as inputs that determines output.
According to the given question we have to evaluate an expression with variables and the values of the variables are given so we will just substitute their values and obtain our result.
Given a =2, b = -3 and c = -1 and d =4.
∴ 2cd+3ab
= 2(-1)(4) + 3(2)(-3)
= 2(-4) + 6(-3)
= - 8 - 18
= - 26.
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Find the area of the triangle.
A.54
B.18
C.36
D.27
Answer:
B. 18
Step-by-step explanation:
Base: 3-(-6)=9
Height: 6-2=4
Area =1/2bh = 1/2(9)(4)= 18 square units
Sally begins hiking at an elevation of 224 feet. Then, she descends 131 feet
and climbs 67 feet higher than her current position. She then descends
163 feet. Write an addition sentence to describe the situation. Then determine
and interpret the sum.
Answer:
-3 feets
Step-by-step explanation:
Given the following :
Starting point = 224 feets
Then descends 131 feets
Then climbs 67 feets higher than her current position
Then descends 163 feets
Addition sentence to describe the situation :
224feets + (-131)feets + 67feets + (-163)feets
Negative (-) points represents descent
224feets - 131feets + 67feets - 163feets = - 3feets
This means Sally is - 3 feets below her initial position.
Find the circumference if the area of the circle is 64π m2.
Answer:
C = 50.27 m
Step-by-step explanation:
A = πr²
64π = πr²
64 = r²
r = ±8
r = 8
C = 2πr
C = 2π(8)
C = 50.27 m
Two distinct lines, l and m, are each perpendicular to the same line n. Select all the true statements. Lines l and m are perpendicular Lines l and n are perpendicular Line m and n are perpendicular Lines l and m are parallel Lines l and n are parallel Line m and n are parallel
Answer:
The correct options are;
Lines l and n are perpendicular
Lines m and n are perpendicular
Step-by-step explanation:
Where two lines l an m are said to be perpendicular to a given line n, then we have;
1) When l and m are in different planes,
a) l and m can be parallel lines to each other or
b) l and m can be perpendicular to each other or
c) l and m can be at an angle x, to each other
2) When l and m intersect with the line n at a point p, then, we have;
l and m must be in the same plane with each other.
Describe and correct the error a student made when solving the equation 7=-4(x+7)-3+2x. What is the correct solution?
Answer:
7=-4(x+7)-3+2x
BODMAS
7=-4x-28-3+2x
7=-2x-31
7+31=-2x
x=38/2
x= -19
what transformation(s) is taking place
Answer:
Dilation is the transformation
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x ≥ −5 and x < 4
Step-by-step explanation:
-4x + 1 ≤ 21 and 5x + 2 < 22
5x + 2 < 22 = x < 4
We can plug it in: 5 x 3 + 2 < 22 = 17 < 22
-4x + 1 ≤ 21 = x= -5 and lower
Plug it in: -4 x -5 + 1 ≤ 21 = 21 ≤ 21 = x ≥−5
So both answers would be:
x ≥−5 for -4x + 1 ≥ 21
x < 4 for 5x + 2 < 22
cos x° = sin(3x+10°) find tan x°
Answer:
Step-by-step explanation:
we can write sin(3x+10)= cos{90-(3x+10)}
now
cosx= cos{90-(3x+10)}
eliminating cos from both sides we get
x=90-3x-10
4x=80
x=20
tan 20=0.364
it can be 40 also if we take the sin part
It takes Zina 1 hours to build a model skyscraper and Rachel 3 hours to do the
same job. It will take hours to build a model skyscraper working
together?
(ignore this answer, i cant delete it srry..)
Answer:
It takes them 45 minutes
Step-by-step explanation:
Let's say that x is the amount of work in one hour that zina does
so the amount of work that rachel does in the same hour is 1/3x, because 3 times slower
so we have
x+1/3x=100%
what does that mean?
it means the amount of hours taken to complete a skycraper
so we solve for x
x=75%
so we need to figure out how much hours does zina takes to complete 75% of the skycraper
1 hour ----- 100%
x hours ---- 75%
1 hour *75%/100%=x hours
1 hour (3/4)=x hours
60 minutes (3/4)= x minutes
x=45 minutes
What is the y-intercept of the polynomial f(x)f(x) f(x) defined below? Write the y-value only. f(x)=−4x2+x5+10x3+5x+8x4f(x)=-4x^2+x^5+10x^3+5x+8x^4 f(x)=−4x 2 +x 5 +10x 3 +5x+8x 4
Answer:
y = 0
Step-by-step explanation:
Given
f(x) = 4x² +x⁵ +10x³ +5x+8x⁴
Required
Determine the y intercept
The y intercept of a function is a point where x = 0
So, we have to substitute 0 for x in the above function
f(x) = 4x² +x⁵ +10x³ +5x+8x⁴ becomes
f(0) = 4(0)² +(0)⁵ +10(0)³ +5(0)+8(0)⁴
f(0) = 4 * 0 + 0 + 10 * 0 + 5 * 0 + 8 * 0
f(0) = 0 + 0 + 0 + 0 + 0
f(0) = 0
Substitute y for f(0)
y = 0
Hence, the y intercept is 0
3 2/3 + 2.3 (the three is repeating) and the answer choices are
a) 5
b) 5 2/3
c) 6
d) 6 1/3
i need help please :/
Answer: C) 6
================================================
Explanation:
2.33333... where the 3s go on forever is the same as 2 + 1/3 or 2 & 1/3
So we really have 3 & 2/3 added onto 2 & 1/3
The fractional portions add to 2/3 + 1/3 = 3/3 = 1, which will carry over.
The whole number portions add to 3+2 = 5, and we add on the carry of 1 to get 5+1 = 6
--------------
Using your calculator
3 & 2/3 = 3 + 2/3 = 3 + 0.667 = 3.667 approximately
adding this onto 2.333 leads to
3.667 + 2.333 = 6
Technically the 6's go on forever in the decimal form of 3 & 2/3, but rounding wont have an effect on the answer when we add
The sum of the given fraction is 6. Therefore, option C is the correct answer.
Given that, 3 2/3 + 2.3333....
We need to find the sum of the given fractions.
How to find the sum of fractions?To add fractions follow these steps:
Step 1: Make sure the bottom numbers (the denominators) are the same.
Step 2: Add the top numbers (the numerators), and put that answer over the denominator.
Step 3: Simplify the fraction (if possible).
Now, 2.3333.... can be written as
x=2.333.... ------(1)
10x=23.333.... ------(2)(Multiply by 10 to both sides of the equation)
Subtract equation (1) from (2)
That is, 10x-x=23.333.....-2.333......
⇒9x=21
⇒x=21/9
⇒x=7/3
⇒x=2 1/3
Now, 3 2/3 + 2 1/3
=(3+2) 2/3 + 1/3
=5 3/3
=5+1=6
The sum of the given fraction is 6. Therefore, option C is the correct answer.
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a carpenter works one third as long after lunch as he worked before lunch if he worked 8 hours total how long did he work before lunch
Answer:
6 hours before lunch
Step-by-step explanation:
Let x = hours before lunch
after lunch = 1/3x
Total time worked = 8 hours
x+1/3 x = 8
Combine like terms
4/3x = 8
Multiply each side by 3/4
3/4 * 4/3x = 8 * 3/4
x = 6
6 hours before lunch
Answer:
The carpenter worked 3x, or 6 hrs, before lunch.
Step-by-step explanation:
Represent the time worked before lunch as 3x and the time worked after lunch as x. Then 3x + x = 8 hrs, and so:
4x = 8 hrs, and
x = 2 hrs
The carpenter worked 3x, or 6 hrs, before lunch.
Name four points in the diagram.
B
B
S
С
A
E
D
point A
to
point B
С BC
point D
DE
point E
points
point T
Answer: Point A ,Point E , Point B, Point D
Step-by-step explanation:
In the given figure we have two planes named as S and T that are join by a line .
There is one line on each of them .
On plane S points are B and C.
On plane T points are D, and E.
On the intersection of planes, we have point A.
Now from the given options, the four points are:
Point A ,Point E , Point B, Point D
Imagine that you stop at a nearby coffee chain and purchase a $5 coffee every morning on your way to work. You do this 5 days a week for 50 weeks out of the year. While it may seem like a small expense each day, this habit can add up and affect your personal finances. How much would this habit cost you over the next five years
Answer:
$6250
Step-by-step explanation:
Hello!
First, we find out how much you spend a week.
Since you buy a $5 coffee 5 days a week we multiply the price for a coffee by 5.
5 * 5 = 25.
Next, we find out how much you spend a year.
Since you do it 50 weeks a year we multiply the amount you spend a week by 50
25 * 50 = 1250
Then, we find out how much you spend in 5 years.
We multiply the cost a year by the amount of years
1250 * 5 = 6250
The answer is $6250
Hope this helps!
Answer:
$6250 Just took a quiz
Step-by-step explanation:
please help me out
Answer:
(i) F = 25 N
(ii) F = 35.36 N
(iii) F = 43.3 N
Step-by-step explanation:
We note that the component of force acting along the incline surface is given by the relation
Force, acting parallel to the incline plane, [tex]F_p[/tex] = M×g×sin(θ)
Given that the weight of the body is given as 50 N, we have;
M×g = 50 N
Therefore we have;
(i) For the plane with angle of elevation = 30°
[tex]F_p[/tex] = M×g×sin(θ) = 50 × sin(30°) = 25 N
The force [tex]F_p[/tex] = F = 25 N
F = 25 N
(ii) For the plane with angle of elevation = 45°
[tex]F_p[/tex] = M×g×sin(θ) = 50 × sin(45°) = 50 × (√2)/2 = 25·√2 N
[tex]F_p[/tex] = F = 25×√2 N = 35.36 N
F = 35.36 N
(iii) For the plane with angle of elevation = 60°
[tex]F_p[/tex] = M×g×sin(θ) = 50 × sin(60°) = 50 × (√3)/2 = 25·√3 N
[tex]F_p[/tex] = F = 25×√3 N = 43.3 N
F = 43.3 N.
Use braces and digits to designate the set of natural numbers.
Answer:
[tex]N = \{1,2,3,4,5,6,.....\}[/tex]
Step-by-step explanation:
Required
Determine the sets of natural number
Represent this set with letter N
From definition of natural numbers, they are integer numbers starting from 1;
In other words: 1,2,3,4,5, and so on.
To represent this as a set of N, we have
[tex]N = \{1,2,3,4,5,6,.....\}[/tex]
The ..... means that the counting still continues
Which line segment shows the height that corresponds to the given base of the triangle btw it isnt high school
Answer:
B
Step-by-step explanation:
The height has to be perpendicular ( 90 degrees) to the base
B is the height to the base
Find the slope and then write the slope as a simplified fraction
A) (-6,3) (9,7)
B)(4,-10)(-2,-6)
Answer:
slope: (y² - y¹) / (x² - x¹)
(-6, 3) (9, 7)
(7 - 3) / (9 + 6) = 4 / 15
y = 4/15x + b
slope: (4/15)x
(4, -10) (-2, -6)
(-6 + 10) / (-2 - 4) = 4 / -6 = 2 / -3
y = (-2/3)x + b
slope: (-2/3)x
One spring day, Dylan noted the time of day and the temperature, in degrees
Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 56° F. For the
next 2 hours, the temperature rose 3° per hour. For the next 3 hours, it rose 4º per
hour. The temperature then stayed steady until 6 p.m. For the next 4 hours, the
temperature dropped 3° per hour. The temperature then dropped steadily until the
temperature was 61° at midnight. On the set of axes below, graph Dylan's data.
Helppppp pleaseeee I’m terrible with graphing
Answer:
Please find attached the required graph for the temperature time relationship
Step-by-step explanation:
The parameters given are arranged in a tabular form as follows;
At
Time [tex]{}[/tex] Temperature
6 a. m. [tex]{}[/tex] 56° F
7 a. m. [tex]{}[/tex] 59° F
8 a. m. [tex]{}[/tex] 62° F
9 a. m. [tex]{}[/tex] 66° F
10 a. m. [tex]{}[/tex] 70° F
11 a. m. [tex]{}[/tex] 74° F
12 p. m. [tex]{}[/tex] 74°F
1 p. m. [tex]{}[/tex] 74°F
2 p. m. [tex]{}[/tex] 74°F
3 p. m. [tex]{}[/tex] 74°F
4 p. m. [tex]{}[/tex] 74°F
5 p. m. [tex]{}[/tex] 74°F
6 p. m. [tex]{}[/tex] 74°F
7 p. m. [tex]{}[/tex] 71°F
8 p. m. [tex]{}[/tex] 68°F
9 p. m. [tex]{}[/tex] 65°F
10 p. m. [tex]{}[/tex] 62°F
11 p. m. [tex]{}[/tex] 61.5°F
12 a. m. [tex]{}[/tex] 61°F
With the above table as the data points, the graph can be drawn
From Excel, The Mean temperature is approximately 68.1°F
The standard deviation is 6.079 °F
Since Dylan noted the time of day and the temperature, in degrees Fahrenheit, and his findings are as follows: At 6 am, the temperature was 56 ° F, for the next 2 hours, the temperature rose 3 ° per hour, for the next 3 hours, it rose 4º per hour, and the temperature then stayed steady until 6 pm, while for the next 4 hours, the temperature dropped 3 ° per hour, and the temperature then dropped steadily until the temperature was 61 ° at midnight , to determine the average temperatures, the following tables must be made:
6 AM = 56
7 AM = 59
8 AM = 62
9 AM = 66
10 AM = 70
11 AM = 74
6 PM = 74
7 PM = 71
8 PM = 68
9 PM = 65
10 PM = 62
11 PM = 61.5
12 AM = 61
Thus, the average daily temperature was 68°F.
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Solve the inequality and enter your solution as an inequality in the box below, using "" for if necessary. 8 >4-x>6
Answer:
-4 < x < -2
Step-by-step explanation:
8 > 4 - x > 6
4 > -x > 2
-4 < x < -2 (flip the sign when multiplying / dividing by a negative number)
The total money earned if Lee sold four scarves at twenty dollars each.
Answer:
$80
Step-by-step explanation:
If we have four scarves, and each costs $20, we can multiply these two numbers to find the total profit made.
[tex]20\cdot4[/tex]
2 times 4 is 8, and adding a 0 to that is 80.
Hope this helped!
Which of the following does not describe a control group? O A. a group of patients given a new drug B. a group of patients given a placebo O C. a group of trees not given a new growth hormone O D. a group of students not given a new software package
Answer:
the answer = C (may be but not sure)
Answer:
The answer has to be A
Step-by-step explanation:
The trees have nothing changed about them, so they can be considered to be the control. In additon, placebo is given as a control in medical trials, so it cannot be correct. And, the students have nothing changed in D, so the answer to this question has to be A, where the patients are given a new drug.
289 and y more is 206
Answer:
Equation translates to 289 + y = 206
it solves to y = -83
====================================================
Explanation:
The "and y more" means we are adding y onto 289 to get the expression 289+y. This is set equal to 206 because of the term "is" in the original statement.
Therefore, "289 and y more is 206" translates fully to the equation 289+y = 206
This is the same as saying y+289 = 206
To isolate y, we undo what is happening to it. We are adding 289 to it, so we must subtract 289 from both sides
y+289 = 206
y+289-289 = 206-289
y = -83
So we are adding -83 to 289 to get 206
5,
5,
6,
8,
11,
What is the next number
3 is what my answer was
============================================
Explanation:
From 5 to 5, we add 0
From 5 to 6, we add 1
From 6 to 8, we add 2
From 8 to 11, we add 3
Assuming this pattern keeps up, the next term is found by adding 4.
So 11+4 = 15 is the next term.
Given xy = 4 and x2 + y2 = a, which expression is equal to (x + y)2?
a + 6
a + 8
a + 4
Answer:
a + 8
Step-by-step explanation:
Note that
(x + y)² = x² + 2xy + y²
= x² + y² + 2xy
= a + 2(4) = a + 8
Here, we are required to determine an expression equal to (x + y)²
The correct answer is therefore (a + 8)
First, x² + y² = a can be rewritten completing the square method as;
(x+y) (x+y) = a + 2xy
when we expand the expression above; we have;
x² + 2xy + y² = a + 2xy
since, 2xy is present on both sides of the equation;
we still get the expression; x² + y² = a
Therefore, (x+y)² = a + 2xy
we can then substitute the value 4 for xy in the equation above;
Thus, since xy = 4, therefore 2xy = 8
Consequently, (x+y)² = a + 8
The correct answer is therefore (a + 8)
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PLZ HELP ME ASAP!!!!
Answer:
33.05°
Step-by-step explanation:
The diagram above is a right angled triangle.
To solve for this question, we would be making use of the trigonometric function of Sine
sin θ = Opposite side/Hypotenuse
From the above diagram,
Opposite side = 162.5 yards
Hypotenuse = 298 yards
θ = unknown
sin θ = 162.5 yards/298 yards
sin θ = 0.5453020134
θ = arc sin(0.5453020134)
θ = 33.045304587°
Approximately
θ = 33.05°