Answer:
4 inches long each i think im not completely sure
Step-by-step explanation:
Rectangle has its adjacent sides perpendicular to each other. The lengths of the sides of the considered rectangle are: 5 inches and 12 inches.
What is perimeter?Its the sum of length of the sides used to made the given figure.
For a rectangle, as the rectangle has two of its sides equal to its length, and rest two are equal to its width, thus,
perimeter of rectangle = twice of (width + length)
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB.
In a rectangle, its adjacent sides are perpendicular to each other(making 90 degrees with each other), thus, when its diagonal is drawn, we can use Pythagoras theorem to relate its length, width and length of the diagonals (both of diagonals of a rectangle are of same length).
Thus, using Pythagoras theorem, we get:
[tex](|Diagonal|)^2 = |Length|^2 + |Width|^2[/tex]
Suppose its length and width are L and W, then we get two equations:
Perimeter = 2(L + W) = 34 inches
Diagonal² = 13² = 169 = L² + W²
From the first equation, getting L in terms of W, we get:
[tex]L = 17 - W[/tex]
Putting this value in second equation, we get:
[tex]L^2 + W^2 = 169\\(17-W)^2 + W^2 = 169\\289 + W^2 + W^2 -34W = 169\\2W^2 -34W + 120 = 0\\W^2 - 17W + 60 = 0\\W^2 -12W - 5W + 60 = 0 \\W(W - 12) - 5(W - 12) = 0\\\\(W-5)(W-12) = 0\\W = 5, 12[/tex](in inches)
Thus, we get L= 17-W = 12 or 5,
Thus, dimensions of the considered rectangle are 5 inches and 12 inches.
Learn more about solutions of quadratic equations here:
https://brainly.com/question/3358603
The point slope form of the eqaution of the line that passes through (-5,-1) and (10, -7) is y+7= -2/5 (x - 10) what is the standard form of the equation for this line 2x-5y=-15 2x-5y= -17 2x+5y=-15 2x+5y=-17
Answer:
2x + 5y = -15Step-by-step explanation:
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
We have the equation in point-slope form:
[tex]y+7=-\dfrac{2}{5}(x-10)[/tex]
Convert it to the standard form:
[tex]y+7=-\dfrac{2}{5}(x-10)[/tex] multiply both sides by 5
[tex]5y+35=-2(x-10)[/tex] use the distributive property a(b + c) = ab + ac
[tex]5y+35=(-2)(x)+(-2)(-10)[/tex]
[tex]5y+35=-2x+20[/tex] subtract 35 from both sides
[tex]5y=-2x-15[/tex] add 2x to both sides
[tex]2x+5y=-15[/tex]
Help me solve plz. Use substitution to check. y - 4 = 36
Answer:
y = 40
Step-by-step explanation:
Isolate the variable (y). Note the equal sign, what you do to one side, you do to the other. Add 4 to both sides.
y - 4 = 36
y - 4 (+4) = 36 (+4)
y = 36 + 4
y = 40
Check. Substitute 40 for y.
Plug in 40 for y.
y - 4 = 36
(40) - 4 = 36
36 = 36 (True).
~
Eli claims that the product of and is . Which explains whether Eli is correct?
Answer: last option.
Step-by-step explanation:
According to the Product of powers property, you have:
[tex]a^n*a^m=a^{(n+m)}[/tex]
As you can see, when you can add the exponents when you have powers with equal base.
Then, [tex]6^5[/tex] and [tex]5^{-3}[/tex] do not have the same base, therefore, the exponents can't be added.
Therefore, Eli is incorrect, because he added the exponents even though the bases are not the same.
Answer:
d
Step-by-step explanation:
please mark brainliest
Evaluate cos^2 (n/12)
Answer:
[tex]\frac{2+\sqrt{3} }{4}[/tex]
Step-by-step explanation:
We can use the identity [tex]Cos^2(x)=\frac{1}{2}+\frac{1}{2}Cos(2x)[/tex] to write it as:
[tex]Cos^2(\frac{\pi}{12})=\frac{1}{2}+\frac{1}{2}Cos(2(\frac{\pi}{12}))\\=\frac{1}{2}+\frac{1}{2}Cos(\frac{\pi}{6})\\=\frac{1}{2}+\frac{1}{2}(\frac{\sqrt{3} }{2})\\=\frac{1}{2}+\frac{\sqrt{3} }{4}\\=\frac{2+\sqrt{3} }{4}[/tex]
Note: The value of [tex]Cos(\frac{\pi}{6})[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex]
The answer is the 2nd one, [tex]\frac{2+\sqrt{3} }{4}[/tex]
Giraffes are herbivores,or plant eaters. A giraffe can eat up to 75 pounds of leaves each day. Write and evaluate an expression to find how many pounds of leaves 5 giraffes can eat in a week.
Answer: 2625
Let’s say you multiply 5 giraffes by 75 pounds = 375lbs 5 giraffes eat a day multiply the 5 giraffes and they answer should be 2625lbs
the First one witch for me is six (6)
what is an equation of the line that is perpendicular to y-3 =-4(x+2)
Answer:
[tex]y - 3 = \frac{1}{4}(x+2)[/tex] or choose any line with slope 1/4
Step-by-step explanation:
The slope of this line is -4. The slope of the line perpendicular to this line will be the negative reciprocal or 1/4.
Write the equation using the slope m=1/4 and the point slope form.
[tex]y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x+2)[/tex]
This is the equation of the line that is perpendicular and passes through the same point (-2,3) as the equation listed.
Answer:
[tex]y=\frac{1}{4} x+c[/tex] where [tex]c[/tex] can be any number.
Step-by-step explanation:
First we need to clear for y:
[tex]y-3 =-4(x+2)\\y=-4(x+2)+3\\y=-4x-8+3\\y=-4x-5[/tex]
and now we have an equation of the form:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
in this case [tex]m=-4[/tex] and [tex]b=-5[/tex]
to find and equation perpendicular to this line, the following must be true:[tex]m*m_{1}=-1[/tex]
where m is the slope of the original line that i just mentioned, and [tex]m_{1}[/tex] is the slope of the new line. Substituting [tex]m=-4[/tex]
[tex]-4*m_{1}=-1[/tex]
clearing for [tex]m_{1}[/tex]
[tex]m_{1}=\frac{-1}{-4} \\m_{1}=\frac{1}{4}[/tex]
thus, the new perpendicular line must have the form:
[tex]y=m_{1}x+c\\y=\frac{1}{4}x+c[/tex]
where the y-intecept [tex]c[/tex] can be any number, some examples are:
[tex]y=\frac{1}{4}x+3\\y=\frac{1}{4}x-8[/tex]
and so on, the important thing to be a perpendicular line is that the slopes are related to the equation [tex]m*m_{1}=-1[/tex].
Line jk passes through points j(-4,-5) and k(-6,3). What is the value of b
Answer:
b = -21Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
b - y-intercept → (0, b)
We have the points J(-4, -5) and K(-6, 3).
The points J, K and y-intercept A(0, b) are collinear. Therefore the slope of JA and KA are the same.
We have the equation:
[tex]\dfrac{b-(-5)}{0-(-4)}=\dfrac{b-3}{0-(-6)}\\\\\dfrac{b+5}{4}=\dfrac{b-3}{6}\qquad\text{cross multiply}\\\\6(b+5)=4(b-3)\qquad\text{use the distributive property}\\\\6b+30=4b-12\qquad\text{subtract 30 from both sides}\\\\6b=4b-42\qquad\text{subtract 4b from both sides}\\\\2b=-42\qquad\text{divide both sides by 2}\\\\b=-21[/tex]
The equation for the circle below is x^2+y^2=64 what is the length of the circle’s radius
Answer:
r = 8Step-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 equation:
[tex]x^2+y^2=64\\\\(x-0)^2+(y-0)^2=8^2[/tex]
Therefore the center is (0, 0) and the radius r = 8
Answer:
The circles radius is 8
Step-by-step explanation:
It is 8 because that's what they say it is
Convert 6 pounds, 4 oz. to ounces.
64 oz.
76 oz.
95 oz.
100 oz.
Answer:
The answer is 100 oz
Step-by-step explanation:
HOPE THIS HELPS YOU
A group of volunteers has been collecting toys to deliver to a local charity. Over the last 6 days, The volunteers have collected 492 toys. What has been their collection rate, in toys per day?
Answer:
82 toys per day
Step-by-step explanation:
492 divided by 6 = 82 (toys)
6 divided by 6 = 1 (days)
492/6 = 82/1
Answer:
a
Step-by-step explanation:
Which two numbers does 65/10 lie between?
Answer:
6 and 7
Step-by-step explanation:
because 65/10 equals 6.5
Answer:
It lies between 6 and 7
what decimal is equivalent to -7 / 8
That decimal would be -.875
Hey there!
In order to find the decimal divide the numerator (top number) from the denominator (bottom number)
~ -7 ÷ 8 = 0.875 (as a decimal)
~ Thus your answer will most likely be, -0.875
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
What is x+8y=-15 7x+8y=-19
Answer:
x = − 15 − 8 y
y=-7/8x-19/8
Step-by-step explanation:
If you are trying to solve for x the answer for first problems is
x = − 15 − 8 y
second problem the slope intercept form is:
y=-7/8x-19/8
I'm not sure exactly what you are looking for but I hope that is it.
The town swimming pool is d feet deep. The width of the pool is 5 feet greater than 5 times its depth. The length of the pool is 50 feet greater than 5 times its depth. Enter a simplified expression to represent the volume of the pool.
Answer:
[tex]V = 25d ^ 3 + 275d ^ 2 + 250d[/tex]
Step-by-step explanation:
If the pool has a rectangular shape then its volume can be written as:
V = Width * Length * Depth
Let's call:
w = width
l = length
d = depth.
So we know from the statement of the problem that:
[tex]d = d[/tex]
[tex]w = 5 + 5d[/tex] (5 feet more than 5 times the depth)
[tex]l = 50 + 5d[/tex] (50 feet more than 5 times the depth)
Then, the volume can be written according to the depth as:
[tex]V = d(5 + 5d)(50 + 5d)[/tex]
[tex]V = d[250 + 25d + 250d + 25d ^ 2][/tex]
[tex]V = 25d ^ 3 + 275d ^ 2 + 250d[/tex]
The volume of the swimming pool is represented by the expression V = (5d + 50)(5d + 5)(d), where d is the depth of the pool.
The student is asked to find a simplified expression to represent the volume of the swimming pool, with the pool's depth given as d feet. To calculate the volume, we need to find the dimensions for the width and length of the pool. The width is described as 5 feet greater than 5 times its depth, which translates to
5d + 5 feet.
The length is 50 feet greater than 5 times its depth, so it will be
5d + 50 feet. The volume (V) of a rectangular solid is given by the product of its length (L), width (W), and depth (D), so the volume of this swimming pool is
V = LWD = (5d + 50)(5d + 5)(d).
Plz help me i need it
Answer: [tex]a)\quad f^{-1}(x)=\sqrt[3]{\dfrac{x+5}{3}}[/tex]
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y. Note: f(x) is y
[tex]y=3x^3-5\\\\\text{Swap the x's and y's:}\\x=3y^3-5\\\\\text{Add 5 to both sides:}\\x+5=3y^3\\\\\text{Divide both sides by 3:}\\\dfrac{x+5}{3}=y^3\\\\\\\text{Take cubed root of both sides:}\\\sqrt[3]{\dfrac{x+5}{3}}=y[/tex]
Please solve this question ASAP.
Answer:
m∠QPR = 80°Step-by-step explanation:
Look at the picture.
We know: the sum of the measures of the angles of the triangle is equal to 180 °.
Therefore
In ΔTQR we have the equation:
[tex]\alpha+\beta+130^o=180^o[/tex] subtract 130° from both sides
[tex]\alpha+\beta=50^o[/tex]
In ΔPQR we have the equation:
[tex]2\alpha+2\beta+m\angle QPR=180^o[/tex]
[tex]2(\alpha+\beta)+m\angle QPR=180^o[/tex]
Substitute from the first equation
[tex]\alpha+\beta=50^o[/tex]
[tex]2(50^o)+m\angle QPR=180^o[/tex]
[tex]100^o+m\angle QPR=180^o[/tex] subtract 100° from both sides
[tex]m\angle QPR=80^o[/tex]
Bob is thinking about leasing a car the lease comes with an interest rate of 8% determine the money factor that will be used to calculate bonus payment
Answer:
0.00333
Hope that helps.
according to the rational root theorem, what are all the potential rational roots of f(x)=5x^3-7x+11
Answer:
[tex]\pm11,\pm1,\pm\frac{11}{5},\pm\frac{1}{5}[/tex]
Step-by-step explanation:
The given polynomial function is
[tex]f(x)=5x^3-7x+11[/tex]
According to the Rational Roots Theorem, the ratio of all factors of the constant term expressed over the factors of the leading coefficient.
The potential rational roots are
[tex]\pm\frac{11}{1}=\pm11[/tex]
[tex]\pm\frac{1}{1}=\pm1[/tex]
[tex]\pm\frac{11}{5}[/tex]
[tex]\pm\frac{1}{5}[/tex]
-5/2 x 5/7
help me i bad at math
Answer:
Step-by-step explanation:
assuming that the X is a multiplication symbol and not a variable, because the multiplication symbol is * not x, 5*5/2*7=25/14=1 and 11/14
A die is rolled 3 times. What is the probability of getting 1’s on each roll?
Answer: The answer is around 16.66%
Answer:
Step-by-step explanation
The first step you have to get it into this form
a[tex]x^{2}[/tex] + bx + c
So that would be
3x[tex]x^{2}[/tex] + 1x + c
we do not know what c is
we have to get x by it self from 3x[tex]x^{2}[/tex] so first you have to square it now we are at 9x
9x divided by 9 that would leave us with x
so our finished product is x + 1x + c
we have to get x by itself from 1x so we do exactly what we just did 1x divided by 1x would leave us with x
x + x=[tex]x^{2}[/tex] + x
[tex]x^{2}[/tex] + c is the finished product which is your answer
What is the surface area of this cylinder to the nearest integer?
57 in2
75 in2
132 in2
250 in2
Answer:
131.95in^2
Step-by-step explanation:
The formula for surface area in a cylinder is A = 2pi*r*h + 2pi*r^2
The radius in this cylinder is half the diameter in the cylinder which is 6, so the radius is 3.
The height is 4 since it is given.
Then we just plug the values into the equation and we get a surface area around 131.95in^2
Answer:
The answer is C. 132 [tex]in^{2}[/tex]
Step-by-step explanation:
Remember: If the answer is not there, check your work or round up! :)
Patrick 8
Jeffery 12
Robin 7
Sally 15
Manuel 4
Ming 10
Jesse 12
Mark 17
Jenna 16
The owner of a car dealership keeps track of the monthly car sales for the salespeople at the dealership. What is the range for the number of cars sold?
My Answer:
The range is from 4 to 17.
When you are identifying a range you need to identify the highest and lowest number. This is your range because all of the other numbers are between the identified two.
Answer:
Step-by-step explanation:
4 to 17.. that is the answer to ur question love.
A plate lunch costs $1.35. Bought separately, the items cost: sandwich, $0.95; milk, $0.35; and fruit, $0.20. Which is the less expensive way to buy the items?
Plz explain
Add 0.95 0.35 and 0.20 and if it’s less than 1.35 it’s ur answer but if 1.35 is less, than that’s ur answer
Answer:
Step-by-step explanation:
Cost of items =$0.95+$0.35+$0.20=$1.50
Plate cost=$1.35
Plate is less expensive way to buy items
picking a blue shirt from a drawer with 8 blue shirts and 2 white shirts
Answer:
you have 10 shirts in all to choose from
Step-by-step explanation:
if ur picking a shirt then you will have 10 all together.
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷The answer is 8/10, 4/5, or 80%.
Since there are 8 blue shirts out of 10 shirts, you have a 8/10 chance to pick a blue shirt. Since this is probability, it is best to show it in percent and decimal form too.
8/10=80%=0.8 chance
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
18........................
Answer:
D
Step-by-step explanation:
We will use the radical property [tex]\sqrt{a*b} =\sqrt{a} \sqrt{b}[/tex] to simplify this.
The problem is [tex]\sqrt{169*x^5}[/tex]
We can simplify this as:
[tex]\sqrt{169*x^5} \\=\sqrt{169} \sqrt{x^5}[/tex]
Now we can use the property of radicals, [tex]\sqrt[n]{x^a} =x^{\frac{a}{n}}[/tex] , to write as:
[tex]\sqrt{169} \sqrt{x^5} \\13*x^{\frac{5}{2}}[/tex]
D is right answer.
Answer:
d. [tex]13x^{\frac{5}{2}}[/tex]
Step-by-step explanation:
The given expression is
[tex]\sqrt{169x^5}[/tex]
We can rewrite this as
[tex]\sqrt{169}\times \sqrt{x^5}[/tex]
We rewrite as a rational exponent to obtain;
[tex](13^2)^{\frac{1}{2}}\times (x^5)^{\frac{1}{2}}[/tex]
Recall that;
[tex](a^m)^n=a^{mn}[/tex]
[tex]13^{(2\times \frac{1}{2})}\times (x)^{5\times \frac{1}{2}}[/tex]
[tex]13^1 (x)^{\frac{5}{2}}[/tex]
The correct choice is D
[tex]13x^{\frac{5}{2}}[/tex]
please graph this.
x + y ≤ 6
x ≤ 4
Answer:
The graph attached
y ≤ 6 - x
x ≤ 4
Step-by-step explanation:
∵ x + y ≤ 6
∴ y ≤ 6 - x
* Lets draw the line y = 6 - x
* Assume that:
· x = -1 ⇒ y = 7 ⇒ (-1 , 7)
· x = 0 ⇒ y = 6 ⇒ (0 , 6)
· x = 1 ⇒ y = 5 ⇒ (1 , 5)
· x = 2 ⇒ y = 4 ⇒ (2 , 4)
* Plot the points on the graph and make the line sold ( ≤ )
* Shade all the region under the line
∵ x ≤ 4
* Lets draw the line x = 4
* All the points on this line have x-coordinate = 4 (vertical line)
* Draw a vertical line on x = 4 the line is sold (≤)
* Shade all the region left to the line
* The solutions of this system of equations will be on the
common shaded
parts of the two lines (red and blue together)
How many 2/3 's make up 4 1/5
Answer:
6³/₁₀
Step-by-step explanation:
Number of bits = Total amount/Size of each bit
= (4⅕)/(⅔)
Convert the mixed number to an improper fraction
No. = (²¹/₅)/(⅔)
Invert the denominator and change division to multiplication
No. = ²¹/₅ × ³/₂
Multiply numerators and denominators.
No. = ⁶³/₁₀
Convert the improper fraction to a mixed number.
No. = 6³/₁₀
It takes 6³/₁₀ ⅔s to make up 4⅕.
How many flowers, spaced every 3 in., are needed to surround a circular garden with a 150-ft radius? Use 3.14 for pi.
Final answer:
To surround a circular garden with a 150-ft radius every 3 inches with flowers, calculate the garden's circumference using the formula C = 2πr, convert it to inches and divide by the spacing. You'd need approximately 3,768 flowers.
Explanation:
To calculate the number of flowers needed to surround a circular garden with a 150-ft radius spaced every 3 inches, you have to find the circumference of the garden and then determine how many 3-inch spaces fit along that circumference.
First, find the circumference (C) of the garden using the formula C = 2πr, where π (pi) is approximately 3.14 and r is the radius. In this case:
C = 2 × 3.14 × 150 ftC = 2 × 3.14 × 150 ft = 942 ftConvert 942 ft into inches because the spacing is in inches:
C = 942 ft × 12 in/ft = 11,304 inNow, divide the circumference in inches by the spacing to get the number of flowers:
Number of flowers = 11,304 in / 3 in per flowerNumber of flowers = 3,768Therefore, you would need 3,768 flowers to surround the garden spaced every 3 inches.
What is the mean of the mean of the data set below?
12, 15, 10 ,11
Answer:
12
Step-by-step explanation:
12+15+10+11=48
48/4=12
Sum of all the data which is 12+15+10+11=48 then divide by how many data point which is 4
48/4 =12
Use the slope formula to find the missing coordinate. m = -7/2 , T(13, 2), W(_, -5)
A. -11
B. 11
C. 15
Answer:
Option C. [tex]15[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]T(13,2)\ W(x2,-5)[/tex]
[tex]m=-\frac{7}{2}[/tex]
Substitute the values and solve for x2
[tex]-\frac{7}{2}=\frac{-5-2}{x2-13}[/tex]
[tex]-\frac{7}{2}=\frac{-7}{x2-13}[/tex]
equate the denominators
[tex]x2-13=2\\x2=2+13\\ x2=15[/tex]
Answer:
The answer is C-15