The perimeter of the triangle is 13 inches. What is the length of the shortest side?
Answer:
3 in
Step-by-step explanation:
Sum of all sides of ∆ = perimeter
Given that it has a perimeter of 13 in, and the following sides: (x - 5) in, x/2 in, and 6 in, therefore:
[tex] x - 5 + \frac{x}{2} + 6 = 13 [/tex]
Solve to find the value of x
[tex] \frac{2x - 10 + x + 12}{2} = 13 [/tex]
[tex] \frac{3x + 2}{2} = 13 [/tex]
Multiply both sides by 2
[tex] \frac{3x + 2}{2}*2 = 13*2 [/tex]
[tex] 3x + 2 = 26 [/tex]
Subtract 2 from both sides
[tex] 3x + 2 - 2 = 26 - 2 [/tex]
[tex] 3x = 24 [/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{24}{3} [/tex]
[tex] x = 8 [/tex]
The shortest side = (x - 5) in
Plug in the value of x
= (8 - 5) in
= 3 in
Solve for x -4x + 3x = 2
Answer:
No Solution
Step-by-step explanation:
x-4x+3x=2
0x=2
0=2 or x=2/0
Either way, no solution
A garden table and a bench cost $755 combined. The garden table costs $95 less than the bench. What is the cost of the bench?
Answer:
The bench costs $425
Step-by-step explanation:
First lets define our variables:
t = garden table
b = bench
Next, we have to use the information to create two formulas. One formula is for the cost of a garden table and a bench. The second is for the cost of the garden table.
t + b = 755
t = b - 95
For the next step, we can solve for be by using the second formula we created and replacing (t) in the first formula:
b - 95 + b = 755
2b - 95 = 755
2b = 850
bench = 425
To find out how much the cost of the cost of the table is, you can plug in the cost of the bench (b) back into the second equation:
t = b - 95
t = 425 - 95
table = 330
I hope this helps!
-TheBusinessMan
y is inversely proportional to the cube of x. It is given that for a certain value of x, the value of y is 7. Find the new value of y when x is doubled.
Inversely proportional means as one variable increases the other variable decreases.
In this problem, x is doubled which means it's increased, therefore, y is decreased.
7 / 2 = 3.5
The new value of y is 3.5
Please help me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1. true
2. true
3. false
4. false
5. true
6. false
7. fase
8. true
3. Multiply
(5 points)
O
33
-6
40
O
mo
O
Answer: -7920
Step-by-step explanation: 33x-6x40= -7920
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial.
Then classify the polynomial by the number of terms.
4w11 - w12
standard form
degree
leading coefficient
Answer:
Standard Form:-w^12+4w^11
Degree: 12 degree
Leading Coefficient: -1
Step-by-step explanation:
Standard Form: Order the exponents from greatest to least.
Degree: The largest exponent is the degree; the exponent in the first term, IF it is in standard form.
Leading Coefficient: The coefficient of the first term in standard form. There is and understood 1 before the w in the first term.
The required answers are given below,
Standard Form:-w¹²+4w¹¹
Degree: 12 degree
Leading Coefficient: -1
What are polynomials?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Standard Form: Order the exponents from greatest to least. The largest exponent is the degree; the exponent in the first term, IF it is in standard form.
Leading Coefficient: The coefficient of the first term in standard form. There is an understood 1 before the w in the first term.
The answers are given as below,
Standard Form:-w¹²+4w¹¹
Degree: 12 degree
Leading Coefficient: -1
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how do I isolate V1 in this equation
[tex]\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }[/tex]
Let's start off by multiplying each side by [tex]T_{1}[/tex]
[tex]P_{1}V_{1} } = \frac{P_{2}V_{2} T_{1} }{T_{2} }[/tex]
Divide each side by [tex]P_{1}[/tex]
[tex]V_{1} = \frac{P_{2}V_{2} T_{1} }{T_{2}P_{1} }[/tex]
A golf ball is hit with a club from the ground on a flat surface. The height of the ball, h(t), in feet, t seconds after it was hit can be modeled by the function h(t)=40t-16t^2.
Move the number to the blanks to describe the path of the ball.
When the ball is hit at 0 seconds, it has a height of _____ feet. The ball's height increases until it reaches its maximum height of _____ feet after ____ seconds. The ball's height then decreases until it reaches the ground _____ seconds after it was hit.
Fill in the blanks with these numbers: 0, 0.4, 1.25, 2, 2.5, 4, 16, 25, 40
Answer:
The correct numbers are;
1) 0
2) 25
3) 1.25
4) 2.5
When the ball is hit at 0 seconds, it has a height of 0 feet. The ball's height increases until it reaches its maximum height of 25 feet after 1.25 seconds. The ball's height then decreases until it reaches the ground 2.5 seconds after it was hit
Step-by-step explanation:
The given equation for the height of the ball, h(t), in feet, is given as follows
h(t) = 40·t - 16·t²
Therefore;
1) When the ball is hit at 0 seconds, it has a height of h(0) = 40×0 - 16×0² = 0 feet
2) The time to reach maximum height by the ball is found by taking the derivative (slope) of the function for the height of the ball and noting that at maximum height, the derivative (slope) = 0
Therefore;
h'(t) = 40 - 2 × 16·t = 0
40 - 32·t = 0
t = 40/32 = 5/4 seconds = 1.25 seconds
3) The maximum height is then found from the value of the function at t = 5/4 seconds as follows;
h(5/4) = 40×5/4 - 16×(5/4)² = 50 - 25 = 25 feet
4) The time in which the ball reaches the ground where h(t) = 0 is given from the formula for the height of the gulf ball as follows;
h(t) = 0 = 40·t - 16·t²
40·t - 16·t² = 0
(40 - 16·t)·t = 0
Therefore;
t = 0 seconds or t = 40/16 = 2.5 seconds
(40 - 16·t) = 0/t = 0
t = 40/16 = 2.5 seconds
Therefore, the filling the blanks with the correct numbers gives;
When the ball is hit at 0 seconds, it has a height of 0 feet. The ball's height increases until it reaches its maximum height of 25 feet after 1.25 seconds. The ball's height then decreases until it reaches the ground 2.5 seconds after it was hit
hello I have a question to ask.
A man's age today is three years less than four times the age of his oldest daughter. Let a represent the daughter's age. Write an expression to represent the man's age.
Evaluate each expression.
6! =
3! - 2! =
6!/3!=
Answer:
I hope it will help you :)
Answer:
6! = 720
3! - 2! = 12
6!/3!= 120
Step-by-step explanation:
just finished the assignment.
How do you work out the gradient of a line?
Step-by-step explanation:
The gradient of the line = (change in y-coordinate)/(change in x-coordinate) . We can, of course, use this to find the equation of the line. Since the line crosses the y-axis when y = 3, the equation of this graph is y = ½x + 3 . To find the gradient of a curve, you must draw an accurate sketch of the curve.
solve for y. 3[y-13]=12
Answer:
y = 17
Step-by-step explanation:
3(y-13)=13
3y-39=12
3y=51
y=17
Answer:
y = 17
Step-by-step explanation:
3[y-13] = 12
3*y + 3*-13 = 12
3y - 39 = 12
3y = 12 + 39
3y = 51
y = 51/3
y = 17
Check:
3[17-13] = 12
3*4 = 12
Solve for f.
Round your answer to 2 decimals.
9f = {(12f – 2)
Answer:
f=0.67
Step-by-step explanation:
Let's solve your equation step-by-step by isolating f.
9f=12f−2
Step 1: Subtract 12f from both sides.
9f−12f=12f−2−12f
You get:
−3f=−2
Step 2: Divide both sides by -3.
−3f/−3 = −2/−3
You get:
f= 2/3, or f= 0.67
Hope this helps! :)
What is the value of x? 2/7(x+4)=−6 Answers: x=−35 x=−25 x = 25 x =35
Answer:
2/7(x+4)=−6
or x+4 = -(6*7)/2
or x+4 = -21
0r x= -25
Find a and d for the function f(x) = a cos(x) + d such that the graph off matches the figure.
a = amplitude
d = shift
Just from looking at the graph, I can tell that d = -3.5
The amplitude = 1/2
We want to find the coefficients of a given function such that the graph of the function matches the given graph.
We will get:
a = -0.5
d = -3
------------------------
We start with the general function:
f(x) = a*cos(x) + d.
Let's analyze the graph
In the figure, we can see that the graph passes through the point (0, -3.5)
This means that our function evaluated in x = 0 is equal to -3.5, then we can write:
f(0) = a*cos(0) + d = -3.5
a + d = -3.5
We also can see that the distance between a peak and a through is 1 unit, and a, the amplitude, must be (in absolute value) half of that. Also note that when x = 0 we have a local minimum, while for the normal cosine we have a local maximum at x = 0, then a must be a negative number.
Then we have that:
a = - (1/2) = -0.5
Now that we know the value of a we can replace it in the other equation to get:
a + d = -3.5
-0.5 + d = -3.5
d = -3.5 + 0.5 = -3
Then the values of a and d are:
a = -0.5
d = -3
The function is:
f(x) = -0.5*cos(x) - 3
And the graph of this can be seen at the end of the answer, where it does not match exactly because the x-scale in the image is in units of pi, while in my graph is in integers.
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At a certain company, the monthly salary of project managers can be modeled by the function f(x) = x4 – 10x 2 + 10,000, where x is the number of years of employment. After how many years would a project manager be eligible for a $20,000 monthly salary? after working for exactly 10 years after working for at least 10 1/4 years after working for exactly 12 years after working for at least 12 1/4 years
Answer:
after working for at least 10 1/4 years
Step-by-step explanation:
After working for at least 10 1/4 years a project manager would be eligible for a $20,000 monthly salary.
What is the formula to solve quadratic equation?A quadratic equation, [tex]ax^{2} +bx+c=0[/tex] is solved by
[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2}[/tex]
Given function [tex]f(x)=x^4-10x^2+10000[/tex]
Function that has monthly salary $20,000 will be [tex]x^4-10x^2+10000=20000[/tex]
[tex]x^4-10x^2+10000-20000=0[/tex]
[tex]x^4-10x^2-10000=0[/tex]
Now using the formula [tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2}[/tex]
[tex]x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}[/tex]
[tex]x^2=\frac{10 \pm \sqrt{40100} }{2}[/tex]
[tex]x^2=\frac{10 \pm 200.2}{2}[/tex]
[tex]x^2=5 \pm 100.1[/tex]
[tex]x^2=105.1[/tex]
[tex]x=\sqrt{105.1}[/tex]
[tex]x=10.25[/tex]
Hence, after working for at least 10 1/4 years a project manager would be eligible for a $20,000 monthly salary.
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Please help!
No wrong/spam answers!
Answer:
c) 25
Step-by-step explanation:
[tex] \because \: l \parallel m \\ \therefore \: 3x \degree = (2x + 25) \degree ..(alternate \: \angle 's)\\ 3x = 2x + 25 \\ 3x - 2x = 25 \\ \huge \orange{ \boxed{x = 25}}[/tex]
Answer:
Spam answer
Step-by-step explanation:
c) 25
what is the square root of 30? round to the nearest tenth
Answer:
5.5
Step-by-step explanation:
5.477
Rounded to the nearest tenth it will be
5.5
Answer:Square Root of 30 to the nearest tenth, means to calculate the square root of 30 where the answer should only have one number after the decimal point.
Here are step-by-step instructions for how to get the square root of 30 to the nearest tenth:
Step 1: Calculate
We calculate the square root of 30 to be:
√30 = 5.47722557505166
Step 2: Reduce
Reduce the tail of the answer above to two numbers after the decimal point:
5.47
Step 3: Round
Round 5.47 so you only have one digit after the decimal point to get the answer:
5.5
To check that the answer is correct, use your calculator to confirm that 5.52 is about 30.
Step-by-step explanation: I HOPE I HELPS
The first two numbers in a sequence h are h(1) = 2 and h(2) = 6.
1. If h is an arithmetic sequence, write a definition for the nth term of h. Explain
or show your reasoning.
2. If h is a geometric sequence, write down a definition for the nth term of h. Show reasoning
Answer:
Step-by-step explanation:
Given the first two numbers of a sequence as 2, 6...
If it is an arithmetic difference, the common difference will be d = 6-2 = 4
Formula for calculating nth term of an ARITHMETIC sequence Tn = a+(n-1)d
a is the first term = 2
d is the common difference = 4
n is the number if terms
Substituting the given values in the formula.
Nth term Tn = 2+(n-1)4
Tn = 2+4n-4
Tn = 4n-4+2
Tn = 4n-2
2) If the sequence us a geometric sequence
Nth term of the sequence Tn = ar^(n-1)
r is the common ratio
r is gotten by the ratio of the terms I.e
r = T2/T1
r = 6/2
r = 3
Since a = 2
Tn = 2(3)^(n-1)
Hence the nth term of the geometric sequence is Tn = 2(3)^(n-1)
Help needed ASAP will give BRAINLIEST
a speck of dust is 1.2 x 10^-6m wide. Which of the following is the best way to rewrite this quantity, using more appropriate units? I will Make you brainiest to the first one who answers it. A. 1.2 x 10^-4 b.1.2 x 10^-6 c.1.2 x 10^-3 d 1.2 x 10^-9
Answer:C 1.2x 10^-6
Step-by-step explanation:
Find the area of a rectangle with base 4 ft and helght 4 in.
Answer:
16in ^2
Step-by-step explanation:
4*4
Answer:
Area of rectangle is 16
Step-by-step explanation:
Area of rectangle = base, 4, times the height, 4
Area of rectangle = 4 times 4
Area of rectangle = 16
What is the sum of the measures of the interior angles of an octagon? Enter your answer in the box.
The sum of interior angles of an octagon will be 1080°.
We have a Octagon.
We have to find the sum of the measures of the interior angles of a pentagon.
What is Octagon ?In geometry, a Octagon is a eight - sided polygon.
According to the question, we have - A Octagon.
The formula for finding sum of the measures of the interior angles of a polygon is = ( n - 2) x 180°. The number of triangles in each polygon is two less than the number of sides.
The formula for calculating the sum of interior angles is:
For a Octagon - n = 8.
Therefore - the sum of interior angles of an octagon will be -
(8 - 2) x 180
180 x 6
1080°
Hence, the sum of interior angles of an octagon will be 1080°.
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The perimeter of a rectangle is 50 inches.if the width of the rectangle is 5 inches smaller then twice the length,find the AREA of the rectangle in square inches
Identify ALL of the constants & coefficients of the following equation:
1/2b-16= -4
Answer:
1/2b=-4+16
1/2b= 12
b=12×2
b=24
Answer:
constants = -16 and -4
coefficients are 1/2
Step-by-step explanation:
a constant is a number not attached to a variable. a coefficient is a number attached to a variable
What is the scientific notation for 6.782 x 10-4
Answer:
that is already in scientific notation
Step-by-step explanation:
if you are asking for what's the actual number, then it's 0.000678
ASAP HELPPP !!!!Which of the following statements best describes a linear pair? A linear pair consists of complementary angles. A linear pair consists of supplementary angles. A linear pair consists of nonadjacent angles. A linear pair consists of vertical angles.
Answer:
A linear pair consists of supplementary angles
Step-by-step explanation:
Because a linear pair is 2 lines that form an 180 degree angle.
The statement that best describes a linear pair is that A linear pair consists of supplementary angles. The correct option is B.
What is Supplementary Angle?When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.
for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.
If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two angles are two pairs of linear angles. That means, that if linear angles are aligned adjacent to each other, their exterior sides will make a straight line.
Further, since the angle at any side of a line is 180°. Therefore, the sum of these two angles will be equal to 180°.
Hence, the statement that best describes a linear pair is that A linear pair consists of supplementary angles.
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So um what’s the answer to this. -7(2+k)=7
Answer:
k = -3
Step-by-step explanation:
-7(2 + k) = 7
Divide both sides by (-7)
2 + k = 7/-7
2 + k = -1
Subtract 2 form both sides
k = -1 - 2
k = -3
Answer:
k = -3
Step-by-step explanation:
[tex]-7(2+k)=7\\\\-14-7k=7\\\\-14+14-7k=7+14\\\\-7k=21\\\\\frac{-7k=21}{7}\\\\\boxed{k=-3}[/tex]
Hope this helps.
9in, BC = 5x , and AD = 53 in
Answer:
none of them are correct
Step-by-step explanation: