Find the length of the missing side of a rectangle if the diagonal is 13 cm and the shortest side is 5cm
And please show the steps and explain
Answers
Answer:
12 cm
Step-by-step explanation:
I drew a picture of a rectangle with a diagonal measurement of 13 units and what appear to be the shortest side to be 5 units. (This picture was not drawn to scale.) We were has to find the longest side which I said was b. Notice the diagonal cuts the rectangle into right triangles.
We will need to use Pythagorean Theorem to find the length of the longer side of the rectangle.
[tex]5^2+b^2=13^2[/tex]
[tex]25+b^2=169[/tex]
Subtract 25 on both sides:
[tex]b^2=144[/tex]
Take square root of both sides:
[tex]b=\sqrt{144}[/tex] (I did not worry about the negative answer to this because we are dealing with lengths.)
[tex]b=12[/tex]
Related Questions
Paul wants to write equations in the form y=mx + b for the lines passing through
point D that are parallel and perpendicular to line h. First he finds the slopes of these
two lines. What could he do next to find the y-intercepts?
Answers
Answer:
Substitute the slope and the coordinates of point D in the equation of the line y=mx+b and then solve for b in each equation
Step-by-step explanation:
we know that
The first step is calculate the slopes of these two lines. Remember that if two lines are parallel then the slopes are the same (m1=m2) and if two lines are perpendicular then the slopes is equal to m1*m2=-1
The second step is substitute the slope m2 and the coordinates of point D in the equation of the line in slope-intercept form y=mx+b and then solve for b in each equation
how do you workout 7x-19<16
Answers
Answer:
To work this problem out you would do it as if it were just a simple equation
7x-19<16 (you would first have to add 19 to both sides)
7x<35 (then you would divide by 7 to get the variable by itself)
x<5 ( you answer would then be 5)
Step-by-step explanation:
davis bought some candy for $35. this was seven dollars less than four times what he bought at the movie store. how much did he spend at the movie store
Answers
The amount spent at the movie store is $ 10.5
Solution:Given that Davis bought some candy for $ 35
This was seven dollars less than four times what he bought at the movie store
Which means that $ 35 is equal to seven dollars less than four times what he bought at the movie store
Let "m" be the amount spent at the movie store
$ 35 = seven dollars less than four times what he bought at the movie store
35 = 4m - 7
35 + 7 = 4m
42 = 4m
m = 10.5Thus the amount spent at the movie store is $ 10.5
Solve 13 - 2x > 21
x>-4
x > -17
x< -17
x<-4
Answers
Answer:
x>-4
Step-by-step explanation:
13-2x > 21
-13 -13
-2x >8
(-2x)/(-2) >(8)/(-2)
x>-4
7.
What is the solution to the equation shown below?
2/3x+5=1
Answers
[tex] \frac{2}{3} x + 5 = 1[/tex]
[tex] \frac{2}{3} x = 1 - 5[/tex]
[tex] \frac{2}{3} x = ( - 4)[/tex]
[tex]x = ( - 4) \div \frac{2}{3} [/tex]
[tex]x = ( - 4) \times \frac{3}{2} [/tex]
[tex]x = \frac{ - 12}{ \: \: \: 2} [/tex]
[tex]x = ( - 6)[/tex]
[tex]∴ \frac{2}{3} \times ( - 6) + 5 = 1[/tex]
A clothing factory makes 7,200 t shirts in one week on average there are 45 employees at the factory if each employee makes the same number of t shirts how many t shirts does each employee make in one week
Answers
Answer:
160Step-by-step explanation:
Divide 7,200 by 45
The number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
A clothing factory makes 7,200 t-shirts in one week on average there are 45 employees at the factory.
Let x be the number of t-shirts each employee make in one week
The value of x can be calculated as follows:
x = 7,200/45
x = 160
Thus, the number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
Find each unit cost rounded to the nearest cent. Then determine the better buy.
3 cans of corn for $1.68; 5 cans of corn for $2.45
Answers:
$5.04 per can; $12.25 per can; 3 cans for $1.68
$5.04 per can; $12.25 per can; 5 cans for $2.45
$.56 per can; $.49 per can; 3 cans for $1.68
$.56 per can; $.49 per can; 5 cans for $2.45
Answers
Answer:
$.56 per can; $.49 per can; 5 cans for $2.45
Step-by-step explanation:
If it were a dollar for two cans, it's pretty easy to figure out each can is 50 cents. So you use the same idea. if you have x cans for y dollars, if you divide both numbers by x you get the price of 1 can.
3 cans for 1.68 is 1 can for 1.68/3 = .56 so 56 cents
5 cans for 2.45 is 1 can for 2.45/5 = .49 so 49 cents.
You could use this trick dividing by the price and find how many cans you need to but to pay 1 dollar.
3 cans for 1.68 is 3/1.68 for 1 dollar or 1.786 cans for 1 dollar. Doesn't make a lot of sense since you can't but part of a can, but I wanted to show you how you could use the logic for other things.
A Six Flags theme park charges $30 for adults and $15 for kids. How many adult tickets and kid tickets were sold, if a total of 1,644 tickets were sold for a total of $11,250?
Answers
Answer:
The number of adult tickets sold is 894 and the number of kid tickets is 750.
Step-by-step explanation:
Given:
A Six Flags theme park charges $30 for adults and $15 for kids.
Total of 1,644 tickets were sold.
Total amount of tickets $11,250.
Now, to find the number of adult tickets and kid tickets.
Let the number of kid tickets be [tex]x.[/tex]
And the number of adult tickets be [tex]y.[/tex]
So, the total number of tickets:
[tex]x+y=1644.[/tex].....(1)
Solving the equation we get the value of [tex]x[/tex]:
[tex]x=1644-y.[/tex]
Now, the total amount of tickets of adult and kids:
[tex]15x+30y=11250.[/tex]
So, by putting the value of [tex]x[/tex] we get:
[tex]15(1644-y)+30y=11250[/tex]
[tex]24660-15y+30y=11250[/tex]
[tex]24660+15y=11250[/tex]
Subtracting both sides by 24660 we get:
[tex]15y=-13410[/tex]
Dividing both sides by -15 we get:
[tex]y=894[/tex]
Thus number of adult tickets = 894.
Now, putting the value of [tex]y[/tex] in equation (1):
[tex]x+894=1644[/tex]
On solving we get:
[tex]x=1644-894[/tex]
[tex]x=750.[/tex]
So. the number of kid tickets = 750.
Therefore, the number of adult tickets sold is 894 and the number of kid tickets is 750.
Answer: 750
Step-by-step explanation:
i do not get this i'm so dumb
Answers
Answer:
The answer is B. 6 and 8.
Answer:
B) 6 and 8
Step-by-step explanation:
[tex]3 \times 8 = 24[/tex]
[tex]4 \times 6 = 24[/tex]
[tex]2 \times 12 = 24[/tex]
Solve /x-5/=3
A. x=2, x=8
B. x=-8, x=8
C. x=-2, x=2
D. x=-8, x=-2
Answers
Answer:
A) x=2, 8
Step-by-step explanation:
abs(x-5)=3
x-5=3, x-5=-3
x=3+5=8,
x=-3+5=2
Final answer:
option A. x=2, x=8
Explanation:
To solve the equation |x-5|=3, we need to consider both cases regarding the absolute value function. The absolute value of an expression is equal to 3 if the expression itself is 3 or -3. Therefore, we have two equations to solve:
x - 5 = 3x - 5 = -3Solving the first equation:
x = 3 + 5x = 8Solving the second equation:
x = -3 + 5x = 2Thus, the solutions for the equation |x-5|=3 are x=2 and x=8, which corresponds to option A.
Solve for w, x, y, z
x + 2y - z = 3
2x - y + z - w = -3
y + 2z - w = -7
x + 3y + 2z + 2w = 3
Answers
Answer:
x= 1; y= 0; z= -2 and w= 3.
Step-by-step explanation:
Given that,
1) x + 2y - z = 3
2) 2x - y + z - w = -3
3) y + 2z - w = -7
4) x + 3y + 2z + 2w = 3
now, from 1) z = x + 2y -3 →→(5)
from 2) w = 2x -y + z +3
⇒w = 2x -y + x + 2y -3 +3 (from (5))
w = 3x + y →→(6)
Now substitute (5) and (6) in 3), we get
y +2(x + 2y -3) - (3x + y) = -7
⇒ 4y - x = -1 →→→(7)
Now substitute (5) and (6) in 4), we get
x + 3y + 2(x + 2y -3) + 2(3x + y) = 3
⇒ 9x +9y = 9
⇒ x + y =1 →→→(8)
⇒ x= 1-y , substituting this in (7) gives 5y -1 = -1
⇒ y = 0 and x = 1
substituting these values in
(5) and (6) gives, z = -2 and w = 3
⇒ x= 1; y= 0; z= -2 and w= 3.
a store buys hirts for $18 and marks them up by 49% for retail sale. What is the retail price of each shirt.
Answers
Answer:
26.82
Step-by-step explanation:
Answer:
$26.82
Step-by-step explanation:
Product Cost: $18
Markup: 49%
Selling Price = (49% / 100% * $18) + $18 = $8.82 + $18 = $26.82
This gives you a price markup of $26.82.
this is my first answer and it could very well be wrong, sorry ;(
Inequalities and variables
Answers
Answer:
[tex]a - 6 \leqslant 15 + 8a[/tex]
[tex] - 7a \leqslant 21[/tex]
[tex]a \geqslant - 3[/tex]
Given the function f(x) = 4(x − 11) − 9, determine the value of x such that f(x) = -13.
Answers
Answer:
For x = 10, the value of the given function f(x)= 4(x − 11) − 9 is -13.
Step-by-step explanation:
Here, the given expression is:
f(x) = 4(x − 11) − 9
Now, given: f(x) = -13
⇒ -13 = 4(x − 11) − 9
Now, solving for the value of x, we get:
-13 = 4(x-11) -9
⇒ -13 = 4 x - 44 - 9
or, -13 + 44 + 9 = 4x
or, 4 x = 40
or, x = 40/4 = 10
or, x = 10
Hence, for x = 10, the value of the given function f(x)= 4(x − 11) − 9 is -13.
A cube has a volume of 343 cubic cm. What is the area of the base
Answers
Answer:
49 cm²
Step-by-step explanation:
The volume (V) of a cube is calculated as
V = s³ ← s is the length of the side, thus
s³ = 343 ( take the cube root of both sides )
s = [tex]\sqrt[3]{343}[/tex] = 7, thus
area of base = s² = 7² = 49 cm²
What is the equation of the line in the slope-interception form that passes through (3,-1) and (-1,5)
Answers
Answer:
y+1=-3/2(x-3)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-(-1))/(-1-3)
m=(5+1)/-4
m=6/-4
simplify
m=-3/2
y-y1=m(x-x1)
y-(-1)=-3/2(x-3)
y+1=-3/2(x-3)
given the following formula solve for a
s = a+b+c/2
Answers
Answer:
[tex]a=2s-b-c[/tex]
Step-by-step explanation:
Given formula:
[tex]s=\frac{a+b+c}{2}[/tex]
To solve for [tex]a[/tex]
In order to solve for [tex]a[/tex] we will try to isolate [tex]a[/tex] on one side of the equation.
Steps to isolate [tex]a[/tex].
1) Multiplying both sides by [tex]2[/tex] to remove fractions.
[tex]2\times s=2\times \frac{a+b+c}{2}[/tex]
[tex]2s=a+b+c[/tex]
2) Subtracting both sides by [tex]b[/tex]
[tex]2s-b=a+b-b+c[/tex]
[tex]2s-b=a+c[/tex]
3) Subtracting both sides by [tex]c[/tex]
[tex]2s-b-c=a+c-c[/tex]
[tex]2s-b-c=a[/tex]
Thus, we successfully isolated [tex]a[/tex] on one side. The formula for [tex]a[/tex] can be given as:
∴ [tex]a=2s-b-c[/tex]
What does calculus mean
Answers
Answer:the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus.
Step-by-step explanation:
Final answer:
Calculus is the mathematics of change, encompassing derivatives and integrals, which are fundamental for solving rates of change and accumulation problems in various fields, including engineering and economics.
Explanation:
Calculus is a branch of mathematics that focuses on the study of change. It is divided into two major areas: differential calculus and integral calculus. Differential calculus deals with the concept of a derivative, which measures how a function changes as its input changes. This can be visualized as the slope of the tangent line to a curve at a given point. Integral calculus, on the other hand, involves the calculation of an integral, which can be thought of as the area under a curve or the accumulation of quantities. Together, these concepts allow us to solve complex problems involving rates of change and accumulation.
Calculus is essential in many fields such as engineering, physics, economics, and even biology. For example, in engineering, calculus is used to model and solve problems related to motion, forces, and energy.
It's important to note that students who do not take calculus in high school can still pursue engineering by taking calculus in their first year of college. The understanding of dimensions and units within calculus also applies to physical quantities, exemplifying the principle that dimensions obey the rules of algebra.
If a student is planning to major in economics, a strong recommendation is to learn at least a little calculus. This math competency greatly facilitates the understanding of advanced economics and helps speed up the learning process, especially in constructing and analyzing algebraic models used to describe economic relationships and functions.
Bryson drove 42 miles on Monday. On Tuesday, he drove 12 miles less than he did on Monday. Find the ratio of miles driven on Tuesday to the total Miles driven on Monday and Tuesday
Answers
Answer:
Tuesday : Total = 30 : 72 = 5 : 12
Step-by-step explanation:
Monday: 42 miles
Tuesday: 42 - 12 = 30 miles
Monday + Tuesday: 42 + 30 = 72 miles
Tuesday : Total = 30 : 72 = 5 : 12
Evaluate the expression 9 P 4
Answers
Answer:
The answer is 3024
Step-by-step explanation:
you do 9!/(9-4)! which comes out to 3024
A sports shop has 84 employees. 25% of the employees work part-time. How many part-time employees does the sports shop have?
Answers
Answer:
The sports shop has 21 part-time employees.
Step-by-step explanation:
Solution:
What is 25% of 84?
.Y is 25% of 84
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 25% * 84
Converting percent to decimal:
p = 25%/100 = 0.25
Y = 0.25 * 84
Y = 21
Or another quicker way....
50% is half of the whole, and 25 is half of 50.
84/2/2
equals 21 too, I don't recommend to use it as row form.
The sports shop has 21 part-time employees, found by calculating 25% of 84.
The question asks how many part-time employees a sports shop with 84 employees has if 25% of them work part-time. To find the answer, we need to calculate 25% of 84 employees. The calculation is done as follows:
First, convert the percentage to a decimal by dividing it by 100: 25% = 0.25.
Then, multiply the total number of employees by this decimal: 84 times 0.25 = 21.
Therefore, the sports shop has 21 part-time employees.
The legs of an iscosceles triangle have lengths 3x-1 and -x +27. The base has length 5x+1. What is the length of the base
Answers
Answer: 36
Step-by-step explanation:
The legs are given to be :
3x - 1 and -x + 27
The base = 5x + 1
One of the properties of an isosceles triangle is that two sides are equal , that is the two legs are equal. This means that
3x - 1 = - x + 27
3x + x = 27 + 1
4x = 28
x = 7
To calculate the length of the base, substitute x = 7 into the length of the base given , that is
Length of the base = 5(7) + 1
L = 35 + 1
L = 36
How do you rewrite an equation in slope-intercept form
Answers
Answer:
y = mx + b
Step-by-step explanation:
m is slope
b is y-intercept
Write 3 7/9 as an improper fraction.
Answers
Answer:
34/9
Step-by-step explanation:
3 7/9 = 9*3+7 =34
34/9
Answer:34/9
Step-by-step explanation:
9*3 = 27
27+7= 34 then add the denominator
Find
HCF of
(726, 255).
Answers
Good evening ,
Answer:
3Step-by-step explanation:
255 = 3×5×17
726 = 2×3×11^2
Then HCF(255,726) = 3.
:)
Find the missing side length
CAN SOMEONE PLEASE HELP ME?
PLEASEEEEE!!!
Answers
Answer:
13.31803792
Step-by-step explanation:
Law of Cosines
a= 8
b= 18
c= ?
[tex]c^2=a^2b^2-2ab*cos(c)[/tex]
[tex]c^2=8^2-18^2-2*8*18*cos(43)[/tex]
c = 64 + 324 - 2 * 8 * 18 * cos(43)
cos(43) = 0.7313537016
Order of Operations
64 + 324 - 2 * 8 * 18 * 0.7313537016 = 177.3701339
Square Root the answer
[tex]\sqrt{177.3701339}[/tex] = 13.31803792
If Log x (1 / 8) = - 3 / 2, then x is equal to.
A. - 4
B. 4
C. 1 / 4
D: 0
Answers
[tex]log_{x}(1/8)=-3/2[/tex]
This is equal to...
[tex]x^{-3/2}=1/8[/tex]
We want "x" so we need to isolate it using laws of exponents...
[tex]x^{(-1)(3/2)}=1/8[/tex]
[tex]x^{3/2}=8[/tex] because [tex]x^{-a}=1/x^{a}[/tex]
[tex]x=\sqrt[3]{8^{2}}[/tex] because [tex]x^{a/b}=\sqrt[b]{x^{a}}[/tex]
x = 4
answer: B
7<-(-k-3)+2 solve inequality
Answers
Answer:
7<k+3+2
7<k+5
2<k
which is same as k>2
Which of the following exponential functions goes through the points (1, 12) and (2, 36)?
a
f(x) = 4(3)−x
b
f(x) = 3(4)−x
c
f(x) = 3(4)x
d
f(x) = 4(3)x
Answers
Answer:
The function through which given point passes is f(x) = 24 x - 12 .
Step-by-step explanation:
Given as :
The points are
[tex]x_1[/tex] , [tex]y_1[/tex] = 1 , 12
[tex]x_2[/tex] , [tex]y_2[/tex] = 2 , 36
now, slope of the line
Let The slope of line = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Or, m = [tex]\frac{36 - 12}{2-1}[/tex]
Or, m = 24
So The slope of line = m = 24
Now, equation of line in point-slope form
y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex] )
Or, y - 12 = 24 × (x - 1 )
or, y - 12 = 24 x - 24
or, y = 24 x - 24 + 12
or, y = 24 x - 12
or , f(x) = 24 x - 12
So, The function through which given point passes is f(x) = 24 x - 12 . Answer
Solve for x and y in the given the 45° - 45° - 90° triangle shown above. When applicable, simplify all radicals and show your work.
Answers
Answer:
Therefore,
[tex]x=y= 4\sqrt{2}=5.6568\ units[/tex]
Step-by-step explanation:
Given:
Consider In Right Angle Triangle ABC
∠B = 90°
∠C = ∠A = 45°
AB = y
BC = x = adjacent side
AC = 8 = hypotenuse
To Find:
x = ?
y = ?
Solution:
In Right Angle Triangle ABC by Cosine Identity we have
[tex]\cos C = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}\\[/tex]
substituting the above given values we get
[tex]\cos 45 = \dfrac{BC}{AC}=\dfrac{x}{8}[/tex]
[tex]\dfrac{1}{\sqrt{2} } =\dfrac{x}{8}\\\therefore x=\dfrac{8}{\sqrt{2} } \\Rationalizing\ we\ get\\\therefore x=\dfrac{8}{\sqrt{2}}\times \dfrac{\sqrt{2} }{\sqrt{2}}}\\\therefore x=4\sqrt{2}=4\times 1.4142=5.6568\ units[/tex]
As The triangle is 45 - 45 - 90
It is an Isosceles Right triangle
[tex]x=y[/tex]..... Isosceles Triangle property
[tex]\therefore y=4\sqrt{2}=4\times 1.4142=5.6568\ units[/tex]
Therefore,
[tex]x=y= 4\sqrt{2}=5.6568\ units[/tex]