Answer:
14z + 16 is your perimeter
Step-by-step explanation:
To solve the perimeter, add all sides together. Note that in a rectangle, the opposite sides are congruent and parallel to each other.
Let Perimter = p
p = 2(4z + 3) + 2(3z + 5)
Simplify. Distribute the numbers.
2(4z + 3) = 8z + 6
2(3z + 5) = 6z + 10
Simplify. Combine like terms
p = 8z + 6 + 6z + 10
p = 14z + 16
14z + 16 is your perimeter
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the rhombus, m<1 = 168. what are m<2 and m<3?
Answer:
∠2 = 168°
∠3 = 6°
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so ∠2≅∠1 = 168°.
∠3 is the base angle of the isosceles triangle with an apex angle of 168°. Hence it will be (180° -168°)/2 = 6°.
I am a rectangle. One of my sides is 8 centimeters long. Another side is 6 centimeters long. What is my area?
Answer:
48
Step-by-step explanation:
To get the area of a rectangle or square, its only one step, really.
The formula for a rectangle is A=x*y, where x and y are the two side lengths of the rectangle.
Answer:
48
Step-by-step explanation:
8*6=48
90 POINTS MATH
Find the range of possible values for the variable. Show work.
Final Answer
_______ < y < ________
1.25 < y < 8.32124...
Step-by-step explanation:The least y can be is the value that makes the angle in the smaller triangle be zero. (This condition will exist when the difference of side lengths is 4.)
... 4y -5 = 0
... y = 5/4 . . . . . add 5, divide by 4.
_____
The greatest y can be is the value obtained when the triangle is isosceles. For the larger triangle, that makes the side lengths (s) be ...
... 3/s = sin(43°/2)
... s = 3/sin(21.5°)
Then for the smaller triangle, that makes the angle be ...
... 4y -5 = arcsin(2/s) = arcsin(2/3·sin(21.5°))
... y = 1.25 + arcsin(2/3·sin(21.5°))/4
... y ≈ 8.32124
Answer:
1.25 < y <= 8.32124
Step-by-step explanation:
We use the law of cosines for two triangles:
[tex]c^2 = a^2 + b^2 - 2 a b \cos(\gamma) \\ d^2 = a^2 + b^2 - 2 a b \cos(\delta)[/tex]
This answer shows how to use the Reduce and Exists functions of Mathematica to solve either this problem, or the general problem of a pair of triangles with two sides of one triangle equal to two sides of the other triangle. That answer (with [tex]c,\, d,\, \gamma,\, \text{and}\ \delta[/tex] as independent variables which must be given ranges) has 11 cases, and would be a terrible waste of time to find by hand.
The law of cosines is used twice, with the same values for a and b, but different values for c and γ . Here I use the constants [tex]c = 6\,\ \gamma = 43°\, \ d = 4[/tex]. The following equations and inequalities are supplied to Reduce, with an Extential quantifier specifying that Reduce should discover the range of values for [tex]\cos(\gamma)[/tex].
[tex]\text{problem}=\exists _{\{a,b\}}\left(\begin{array}{ccc}36=a^2+b^2-2 a b \cos (43 {}^{\circ})\ \ \land\\16=a^2+b^2-2 a b \cos (\delta )\,\,\land\\ 0<a\land 0<b\land -1<\cos (\delta )<1\end{array}\right)\\ \\ \text{variables}=\{a,b,\cos (\delta )\}\\ \\ \text{red}=\text{Reduce}[\text{problem},\text{variables},\mathbb{R}]\,\,\,\,\,\text{gives}\,\,\,\,\,\frac{1}{9} (4 \cos (43 {}^{\circ})+5)\leq \cos (\delta )<1\\\\\text{N}[\text{red}]\,\,\,\text{gives}\,\,\,0.880602\leq \cos (\delta )<1.[/tex]
This proves (since we used Reduce, not Solve, which is less reliable) that
a triangle exists that has angle 43°, two adjacent sides of length a and b and opposite side of length 6, and thata second triangle exists with unknown angle, adjacent sides a and b equal to the corresponding sides of the first triangle, and opposite side length 4.There is only one range of angles which satisfy the requirements.[tex]\text{mincos}=\text{First}[\text{red}]\ \ \text{gives}\ \ \frac{1}{9} (4 \cos (43 {}^{\circ})+5)\\\text{maxcos}=\text{Last}[\text{red}]\ \ \text{gives}\ \ 1\\\\\text{Solve}[4 y-5=\delta,y ]\ \ \ \text{gives}\ \ \ \left\{\left\{y\to \frac{\delta }{4}+\frac{5}{4}\right\}\right\}\\ \\\\\ \frac{5}{4}<y\leq \frac{1}{4} \left(\frac{\cos ^{-1}}{{{}^{\circ}}}\left(\frac{1}{9} (4 \cos (43 {}^{\circ})+5)\right)}+5\right)[/tex]
The perpendicular bisectors of two sides of a triangle meet at point that belongs to the third side. Prove that this is a right triangle.
The point of intersection of the perpendicular bisectors of a triangle is the circumcenter, the center of the circle that contains the three triangle vertices.
If that center is on one side, that side must be a diameter of the circle. The diameter cuts the circle into two arcs, each of which measures 180°.
The third vertex of the triangle and its two legs form an inscribed angle that subtends an arc of 180°. The measure of that angle is half the measure of the arc, so the angle measures 90° and is a right angle.
A triangle with a right angle is a right triangle. QED
a model is made of a car. please help.
Answer:
10.8 : 1
Step-by-step explanation:
In raw terms the ratio of car length to model length is ...
... 9 ft : 10 in
As a pure number this will be ...
... 108 in : 10 in = 10.8 : 1
How would the expression x3 - 64 be rewritten using difference of cubes? A. (x + 4)(x2 - 4x - 16) B. (x - 4)(x2 + 4x + 16) C. (x + 4)(x2 - 4x + 16) D. (x - 4)(x2 + 16x + 4)
Answer:
B. (x - 4)(x2 + 4x + 16)
Step-by-step explanation:
a3 – b3 = (a – b)(a2 + ab + b2)
substitute a=x n b=4 (cuz 64=4x4x4)
x3 - 64 = (x-4)(x2+4x+4x4)
= (x - 4)(x2 + 4x + 16)
The expression rewritten using difference of cubes as (x - 4)(x^2 + 4x + 16). Option b is correct.
Expansion of x^3 - 64 to be determine.
Difference of cube = [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Here,
[tex]=x^3 - 64 \\=x^3-4^3[/tex]
a =x ; b = 4, put a and b in below equation,
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
[tex]x^3-4^3=(x-4)(x^2+4x+16)[/tex]
Thus, the expression rewritten using difference of cubes as (x - 4)(x^2 + 4x + 16).
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Max delivers 8520 pieces of mail in one year. If he delivers the same number of pieces of mail each month, about how many pieces of mail does he deliver in two months? Explain your steps
Answer:
1420 pieces of mail he delivered in 2 months.
Step-by-step explanation:
If he delivered the same amount each month, you would divide 8520 by 12 (number of months in a year). Then once you divide it, the number you get is 710 now multiply 710 by 2 (because they ask how many he delivered in 2 months). And the answer would be 1420
Answer:
Max delivers 1420 in two Months because 8520 divided by 12 is 710 and thats just one month so 710 x 2 = 1420.
Step-by-step explanation:
The expression 700(1.005644)4x shows the quarterly interest rate Letrice earns after x years. Which expression shows the x isolated in the exponent in an equivalent form?
Answer:
[tex]700(1.022768)^x[/tex]
Step-by-step explanation:
We have been give an expression [tex]700(1.005644)^{4x}[/tex] that shows the quarterly interest rate Letrice earns after x years.
We can find an equivalent expression with x isolated by using exponent properties.
Since power rule of exponents states that an exponent raised to another exponent can be simplified by multiplying the exponents
So using power rule of exponents we can write our expression as:
[tex]700((1.005644)^4)^x[/tex]
Now let us simplify our expression.
[tex]700(1.0227678485832441)^x[/tex]
Upon rounding to 6 decimal places we will get,
[tex]700(1.022768)^x[/tex]
Therefore, the expression [tex]700(1.022768)^x[/tex] shows the x isolated in the exponent in an equivalent form.
When Arjun makes hot cocoa, he adds 20\text{ mL}20 mL20, space, m, L of chocolate syrup for every 333 ounces of hot water. Arjun's brother, Eli, adds 45\text{ mL}45 mL45, space, m, L of chocolate syrup for every 666 ounces of hot water.
Which hot cocoa is more chocolatey?
Answer:
Eli's
Step-by-step explanation:
If Arjun were to double his recipe, he would use 40 mL of syrup for every 666 ounces of hot water. Eli uses more syrup (45 mL) for that amount of water, so ...
... Eli's hot cocoa is more chocolatey.
The person whose hot cocoa is more chocolaty is:
Eli
Step-by-step explanation:When Arjun makes hot cocoa, he adds 20 mL of chocolate syrup for every 3 ounces of hot water.This means that if he double this quantity.
Then there will be:
40 ml of chocolate syrup for every 6 ounces of hot water.
Also, Eli, adds 45 mL of chocolate syrup for every 6 ounces of hot water.This means that Eli's cocoa will be more chocolaty.
( Since, 45>40)
Write an equation for the line
y = 1/9x + 3 5/9
Step-by-step explanation:The slope between the two marked points is ...
... m = (change in y)/(change in x)
... = (4 -3)/(4 -(-5))
... m = 1/9
Then the point-slope equation for the line with slope m through point (h, k) can be written as ...
... y = m(x -h) +k
... y = 1/9(x -(-5)) +3 . . . . . m = 1/9, (h, k) = (-5, 3)
... y = 1/9x + 3 5/9 . . . . . . simplify
are theese rational
11/12 times 9/22
x + (-2x)
Answer:
11/12 times 9/22 - rational
x + (-2x) unknown
Step-by-step explanation:
11/12 is a rational number (the ratio of integers)
9/22 is a rational number (the ratio of integers)
11/12 * 9/22 is a rational number
The product of 2 rational numbers is rational
x+-2x = x but we do not know if x is rational or irrational , so we cannot say if it is rational or not. If x is rational, the sum is rational. If r is irrational, the sum is irrational.
Determine the slope of the line that is perpendicular to the line y = -7x - 12.
Select one:
A. 17
B. −3
C. −7
D. −12
Answer:
1/7th
Step-by-step explanation:
To find the perpendicular slope find the negative reciprocal
e.i. 1/3 would be -3/1 or -3
The slope of the line perpendicular to y = -7x - 12 is 1/7.
Explanation:The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The given line has a slope of -7, so the slope of the line perpendicular to it would be the negative reciprocal of -7, which is 1/7.
Therefore, the slope of the line that is perpendicular to the line y = -7x - 12 is 1/7.
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Solve the inequality for b.
Answer:
-2 ≥ b
Step-by-step explanation:
10 ≤ -2 ( 9 + 12b ) / 3
10 ≤ -2 ( 3 + 4b )
-10 ≥ 2 ( 3 + 4b )
-10 ≥ 6 + 8b
-16 ≥ 8b
-2 ≥ b
Hunter wants to draw an obtuse equilateral triangle, but hes's having trouble drawing it. Is sush a triangle possible to draw? Explain your reasoning.
let's recall that the sum of all interior angles in a triangle is 180°.
an equi-lateral, equal sides, triangle has all sides that are equal.
sides that are equal will yield an equal opposite angle.
so if all sides are equal, all angles are equal, for a sum of 180°, that's only possible with 60°, 60° and 60° angles, and all of them are acute, none obtuse.
Select all radical expressions that are equivalent to 5 2/3
Answer:
1 and 3
Step-by-step explanation:
(5^(1/3))^2 = 5^(2/3)(5^2)^(1/2) = 5^(2/2) = 5(5^2)^(1/3) = 5^(2/3)(5·3)^(1/2) = 5^(1/2)·3^(1/2)(5^(1/2))^3 = 5^(3/2)(5·2)^(1/3) = 5^(1/3)·2^(1/3)___
Applicable rules are ...
[tex]\sqrt[n]{x^{m}}=x^{\frac{m}{n}}\\\\(x^{b})^{c}=x^{bc}\\\\(ab)^{c}=a^c\cdot b^c[/tex]
What adds to 5 minus negative 2 gives you the result 6?
-1
Step-by-step explanation:You apparently want to find the value of x such that ...
... x + 5 -(-2) = 6 . . . . . . the problem statement
... x + 5 + 2 = 6 . . . . . . . simplify signs
... x +7 = 6 . . . . . . . . . . . perform the addition
... x = 6 -7 = -1 . . . . . . . subtract 7 from both sides of the equation, evaluate
-1 adds to 5 - (-2) to give the result 6.
Together, Kyle and Tyler traveled 425 miles to the beach. If Kyle traveled 240 miles, how far did Tyler travel? A) 2x = 425 B) x + 240 = 425 C) x − 240 = 425 D) x − 425 = 240
Answer:
the answer is x=185
Step-by-step explanation:
x+240=425
-240 -240
x= 185
Answer:
B) x + 240 = 425
Step-by-step explanation:
Kyle and Tyler travelled 425 miles to the beach. This means that:
Kyle's distance + Tyler's distance = 425 miles
Kyle travelled 240 miles:
240 miles + Tyler's distance = 425 miles
We want to discover how far Tyler travelled:
240 miles + x = 425miles or x + 240 miles = 425 miles
This also means that:
425 miles - 240 miles = x
x = 185 miles
or
185 miles + 240 miles = 425 miles
il give brainliest thanks
Answer:
D) a = 14, b = 6√2
Step-by-step explanation:
The given figure is trapezoid.
When we draw perpendicular to base "a", we get h = 6
From 45, 45, 90 degrees triangle, the ratio of sides 1:1:√2
since h = 6, b = 6√2
a = 8 + 6
a= 14
Therefore, a = 14 and b = 6√2
Thank you.
Find the value of x that makes the equation true.
x/9 = -6
A. -54
B. -48
C. 54
D. 48
x/9 = -6
Solve for X by multiplying both sides by 9:
x = -6 * 9
x = -54
Brenda has 5/6 of a pie to divide evenly among 4 people. How much pie will each person get?
Brenda has 5/6 of a pie to divide evenly among 4 people. The poundage each person will get is computed by dividing 5/6 by 4, resulting in 5/24 of the pie per person.
Explanation:To find out how much pie each person will get, we need to divide Brenda's portion of the pie by the number of people. Brenda has 5/6 of a pie, and there are 4 people. So, if we divide 5/6 by 4, we'll get the amount of pie per person.
This can be represented by the following math equation: 5/6 ÷ 4 = x, where x is the amount of pie each person gets. You do this by performing the division as if it were a multiplication but flipping the second fraction, so it turns into
5/6 * 1/4 = 5/24. Therefore, each person will get 5/24 of the pie.
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PLEASE HELP ASAP: highest amount of points
for my career development
you are paid a salary of $23,000 annually, you pay 12% in taxes. What is your net pay biweekly?
Answer:
$778.46 is the bi-weekly net pay
Step-by-step explanation:
Net pay is the gross pay minus taxes
Net pay = gross pay - gross pay * tax rate
Simplifying this equation by factoring out gross pay
Net pay = gross pay (1- tax rate)
Substituting this in
Net pay = gross pay (1- tax rate)
We know the
hours worked = 23000
tax rate = .12
Net pay = 23000 (1- .12)
Net pay = 23000 (.88)
Net pay = 20240
But this is per year, and we want it bi weekly
There are 52 weeks in a year, divide by 2 (bi weekly)= 26
So divide 20240 by 26, so you get paid every 2 weeks.
$20240/26 = 778.46 (we round to the nearest cent)
Please help with this question:)
Answer:
x=1
Step-by-step explanation (this way is not the shortest one):
if 2x-3>0, then the equation 2x-3=2x-1 has no roots.
if 2x-3<0 (x<1,5), then the equation 3-2x=2x-1 has one root, x=1
PLEASE HELP, will give brainliest if you answer consider the function represented by the equation 16b = 4r - 12. write the equation in function notation, where b is the independent variable. Must show work for full credit
Answer:b=1/4r-3/4
Step-by-step explanation:
What is the effect on the graph of the function f(x)=x when f(x) is replaced with -1/2f(x)?
Answer:
For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression
Step-by-step explanation:
Parent function is f(x)= x
We need to find the effect of the graph when f(x) is replaced with -1/2f(x)
When negative sign is multiplied outside f(x) like -f(x), then there will be a reflection over x-axis
When negative sign is multiplied inside f(x) like f(-x) then there will be a reflection over y-axis
When a number is multiplied outside f(x) then there will be a vertical stretch or compression
Here 1/2 is multiplied outside f(x). [tex]\frac{1}{2}[/tex] is less than 1 so there will be a vertical compression
For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression
PLZ help on 1 and 2 ASAP have to turn in homework now.
How many years will it take you to double your money if; Round off your answers to one decimal place. 1) Your ROI or rate of return is 4%? years. 2) Your ROI is 10%? years. 3) Your ROI is 13%? years.
Assuming the return is compounded annually, the multiplier each year for rate "r" is (1+r). Then the multiplier for "t" years is (1+r)^t. We want this to be 2.
... 2 = (1+r)^t
... log(2) - t·log(1+r)
... log(2)/log(1+r) = t
The attachment shows the rounded calculator result for r={4%, 10%, 13%}.
You can calculate the years it would take to double your investment using the 'Rule of 72', by dividing 72 by your rate of return. Thus, with an ROI of 4%, 10%, and 13%, it would take roughly 18.0, 7.2, and 5.5 years respectively to double your investment.
Explanation:The time it takes to double your money can be calculated using the 'Rule of 72'. This rule states that if you divide 72 by the rate of return, you get the number of years it will take to double your money. So, for your situation:
1) With an ROI of 4%, it will take 18.0 years (72 divided by 4).
2) With an ROI of 10%, it will take 7.2 years (72 divided by 10).
3) With an ROI of 13%, it will take 5.5 years (72 divided by 13). Remember, this is an approximation and actual results may vary due to compounding frequency and timing of deposits and withdrawals. This rule is a simple way to estimate the effects of compound interest.
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Please help. Accuplacer question.
Answer:
D. 6
Step-by-step explanation:
The system can be solved by subtracting double the second equation from the first:
... (4x +3y) -2(2x +y) = (20) -2(7)
... y = 6 . . . . . . . . . for solution (x, y) = (a, b), this tells you b=6.
Putting this into the second equation gives ...
... 2x +6 = 7
... 2x = 1
... x = 1/2
The solution is (x, y) = (a, b) = (1/2, 6). b = 6.
Given: The coordinates of triangle PQR are P(0, 0), Q(2a, 0), and R(2b, 2c). Prove: The line containing the midpoints of two sides of a triangle is parallel to the third side. As part of the proof, find the midpoint of PQ
To find the midpoint of PQ in the given triangle PQR, we use the midpoint formula, which states that the coordinates of the midpoint are the average of the x-coordinates and the average of the y-coordinates of the given points.
Explanation:To prove that the line containing the midpoints of two sides of a triangle is parallel to the third side, we need to show that the slope of the line is equal to the slope of the third side. Let's find the midpoint of PQ first.
The coordinates of P and Q are P(0, 0) and Q(2a, 0). The midpoint formula is given by:
Midpoint of PQ = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
Substituting the values, we get Midpoint of PQ = ( (0 + 2a) / 2 , (0 + 0) / 2 ) = (a , 0)
Therefore, the midpoint of PQ is (a , 0).
please help me with these!!!
Answer:
7. 5/2 . . . (scale factor and ratio of perimeters are the same)
9. 19"
Step-by-step explanation:
7. The ratio of areas is the square of the scale factor, so ...
scale factor = √((75 m^2)/(12 m^2)) = √(25/4) = 5/2
The ratio of perimeters is the same as the scale factor.
The scale factor and ratio of perimeters is 5/2.
___
9. The difference in distances is the difference in wheel circumferences. The circumference is π times the diameter, so you want
difference = (31π) -(25π) = π(31 -25) = 6π ≈ 18.8 . . . . inches
The truck travels about 19 inches farther on each revolution of the wheel.
Which one is the right symbol ?
Answer:
the greater or less then pointing to the normal three 3 to the right is correct because 3 is a larger number then negative three (-3). It should look like this (-3) < 3
Step-by-step explanation:
Here is a scale to help you with these problems -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, < 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Which ever way the greater or less than < is open is greater than the other side. The end that is closed points to the numbers that are less than the other side.