The measure of each angle of this isosceles triangle is equal to 27°, 27°, and 126°.
What is an isosceles triangle?An isosceles triangle can be defined as a type of triangle that has two (2) of its sides equal in length and two (2) equal angles. This ultimately implies that, an isosceles triangle comprises two (2) angles that have the same measure or are equal in magnitude.
Let the variable x represent the angles that have the same measure or are equal in magnitude. Therefore, the sum of the measures of the angles of this isosceles triangle is given by this mathematical expression:
x + x + (45° + 3x) = 180°.
5x + 45° = 180°.
5x = 180° - 45°
5x = 135°
x = 135°/5
x = 27°
Therefore, the measure of each angle of the isosceles triangle is given by:
First angle = 27°.
Second angle = 27°.
Third angle = 45° + 3(27) = 126°.
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Find the missing exponent. 2 =32
Answer:
5
Step-by-step explanation:
The only way I know how to go about this is to multiply 2 until it becomes 32
2x2=4
4x2=8
8x2=16
16x2=32
Now just count how many 2 I used and I used 5 so the missing exponent is 5
Hopes this helps please mark brainliest
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The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.
In the given question,
The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;
C(x) = 3x^2-1500x+199,000
(a) In the given question we have to find the number of bicyles that must be manufactured to minimize the cost.
The given function is
C(x) = 3x^2-1500x+199,000
To find the maximum or minimum value we firstly find the value of f'(x).
C'(x) = 6x-1500
Now put f'(x)=0
6x-1500=0
Add 1500 on both side, we get
6x=1500
Divide by 6 on both side we get
x=250
Hence, the number of bicycles that must be manufactured to minimize the cost of 250.
(b) Now finding the value of function at x=250
C(250) = 3(250)^2-1500*250+199,000
C(250) = 3*62,500-375,000+199,000
C(250) = 187,500-375,000+199,000
C(250) = 11,500
The minimum cost is $11,500.
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[tex]x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} \\[/tex]
Answer: [tex]x^{26}[/tex]
Step-by-step explanation:
The [tex]x^2[/tex] appears 13 times. Using the exponent rule [tex]x^a x^b=x^{a+b}[/tex], we get that:
[tex]x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2=x^{2(13)}=x^{26}[/tex]
What is the quotient (x2 − 9x + 20) ÷ (x − 4)? (1 point) x − 5 x − 4 x + 4 x + 5
Answer:
The guy under me is correct
Step-by-step explanation:
Answer:
x - 5
Step-by-step explanation:
Factor the expressions that are not already factored
(x^2 - 9x + 20) / (x - 4)
Cancel out x - 4 in both numerator and denominator
[tex]\frac{(x-5)(x-4)}{x-4}[/tex]
x - 5
prove that cos A - sin A +1 / cos A + sin A-1 = cosec A+ cot A
(Pls help, urgently needed)
We have to prove (cosA−sinA+1)/(cosA-sinA-) = cotA+cosecA using Trigonometric Functions
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
L.H.S=(cosA−sinA+1)/(cosA-sinA-)
dividing by sinA
=cotA+1−cosecA/cotA−1+cosecA
=(cotA−1+cosecA)(cotA+1+cosecA)/(cotA+1)²-cosec²A
=(cotA+cosec)²-1/2cotA
=cotA+cosecA(R.H.S)
Hence the above trigonometric function is proved.
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Kaela wants to purchase a pair of shoes at Macy’s that cost $80. If Macy’s charges a
6% sales tax, how much will Kaela pay for the shoes, including tax?
Answer: $84.80
Step-by-step explanation:
The actual sales tax was 4.80 because 6% of 80 is 4.80
Then add the 4.80 to the 80 to get your total
Hope this helped :)
In the image below, the measure of angle 3 is equal to the sum of the measures of angle 6 and what other angle?
For the given figure, angle 3 will be equal to angle 2.
According to the question,
We have the following information:
We have a figure where some angles are marked in form of numbers and the measure of angle 3 is equal to the sum of the measures of angle 6.
Now, we know that vertically opposite angles are equal and angle 1 and angle 4 are vertically opposite angles like angle 2 and angle 3.
(More to know: the sum of three angles of a triangle is equal to 180°.)
Hence, for the given figure, angle 3 will be equal to angle 2.
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ZABC is bisected by ray BD. m2 ABC = 80°. What is mZ ABD?
OA. 50⁰
OB. 40°
O C. 100⁰
OD. 75⁰
The require angle, angle ABD = 40 degrees
What do you mean by angle bisector ?A bisector has two primary characteristics:
Any point along an angle's bisector is equally - spaced from the angle's sides.
The angle bisector divides the other side of a triangle in proportion to the other two sides.
Given : ∠ ABC is bisected by a ray BD
∠ ABC = 80°
Since the angle ABC is being bisected this means that the angles are equal
Let the bisected angle be x
thus we can write it mathematically as
x + x = 80
2x = 80
dividing both the sides as 2 we would get
x = 40 degrees
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Which algebraic expression represents “the apples were divided equally into seven boxes”?
Answer:
Step-by-step explanation:
a=apples
a/7
Could someone help quick
The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
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The value of constant proportionality is 2.5. The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
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everyone can someone help me here please (complete solution and graph)
Answer:
1: x^2+y^2-6x-4y-3=0
2: x^2+y^2-10x+4y=0
3: x^2+y^2-10x+2y+1=0
a fair coin is tossed 28 times. what is the probability that at most 25 tails occur? a) 0.99998628 b) 0.00000152 c) 0.99999848 d) 0.00001220 e) 0.01001372 f) none of the above.
The probability that at most 25 tails occur is 0.99999848.
We know that,
P(x = x) = ⁿCₓ × pˣ × [tex]q^{n-x}[/tex]
p = probability of success = 0.5
n = number of trials = 28
q = 1 - p = 0.5
The probability of the tail occurring at most 25 times can be written as
P(X ≤ 25) = P (X = 0) + P(X = 1) + ..... + P(X = 25)
Using a binomial probability calculator,
P(X ≤ 25) = 0.99999848
Therefore the probability that at most 25 tails occur is 0.99999848
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¿Cuál será el monto que se pagará por un préstamo de $200,000 a una tasa de interés del 36% si se negocia pagarlo en 2 años? C = $200,00
El interés junto con el préstamo de $ 200,000 tiene un monto de $ 8,080.
¿Cuánto debe pagar el usuario por un préstamo tras un plazo de dos años?En este problema tenemos el caso de una persona que pide prestado $ 200,000 a una tasa de interés anual de 36 %, cuyo pago se realiza tras un plazo de dos años de realizarse el préstamo. Asumimos, que la deuda se genera por interés compuesto, esto es, un interés acumulativo. El interés compuesto es descrito mediante la siguiente fórmula:
I = C' · [(1 + r / 100)ⁿ - 1]
Donde:
C' - Dinero prestado, en unidad monetaria.I - Intereses a pagar, en unidad monetaria.r - Tasa de interés, en porcentaje.n - Número de plazos, en años.Si sabemos que C' = 200,000, r = 36 y n = 2, entonces el interés a pagar al final del plazo es:
I = 200,000 · [(1 + 2 / 100)² - 1]
I = 8080
El interés a pagar es $ 8080, además del préstamo de $ 200,000.
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how do i solve 8x-8=4x
The solution to the algebraic equation 8x - 8 = 4x is x = 2
How to solve algebraic equation?Algebra: This is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
8x - 8 = 4x
Collect like terms8x - 4x = 8
4x = 8
divide both sides by 4x = 8/4
x = 2
Check:
8x - 8 = 4x
substitute x = 2 into the equation
8(2) - 8 = 4(2)
16 - 8 = 8
8 = 8
Other examples of algebraic equation
3x + 5 = 11
substract 5 from both sides
3x = 11 - 5
3x = 6
divide both sides by 3
x = 6/3
x = 2
Therefore, the value of x from the equation is given by 2
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lin rode he skateboard 3 miles in 9 minutes. she rode at a constant speed. how far did she go if she only went for 1 minute?
First, break down the problem.
Someone can skate 3 miles in 9 minutes.
What is their speed? How far would they go if they did that speed for 1 minute?
To find speed given time and distance, divide distance by time.
3/9 = 1/3
Speed is 1/3 mile per minute
if they travel one minute, they will travel 1/3 of a mile
hope this helps :)
Find the product. (a2)(2a3)(a2 â€"" 8a 9) 2a7 â€"" 16a6 18a5 2a7 â€"" 16a6 â€"" 18a5 2a8 â€"" 16a7 18a6 2a12 â€"" 16a7 18a6
The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle.
Solve the equation for the variable w
When you have done that
state the value of 'w' if the perimeter of the rectangle is equal to 37 feet and the length is equal to 4 feet.
hurrryyyy pls
Answer:
14.5 feet
Step-by-step explanation:
To make subject as 'w' and solving:To make the subject as 'w', isolate w.
To isolate 'w', subtract 2L from both sides .2L + 2W =P
2W = P - 2L
Now, divide both sides by 2.[tex]\sf W = \dfrac{P-2L}{2}\\\\W =\dfrac{P}{2}-\dfrac{2L}{2}\\\\ \boxed{W = \dfrac{P}{2}-L}[/tex]
P = 37 feet
L = 4 feet
[tex]\sf W =\dfrac{37}{2}-4\\\\[/tex]
= 18.5 - 4
W = 14.5 feet
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4)?
The required expression of the reflection of the point is (-x, y).
Given that,
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4) is to be determined.
The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
A line segment has endpoints at (–4, –6) and (–6, 4) and an image with endpoints at (4, –6) and (6, 4) is produced the equation of the reflection is given as,
(x, y) ----> (-x, y)
Thus, the required expression of the reflection of the point is (-x, y).
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Select the correct answer.
What is the domain of function f?
Answer:
D
Step-by-step explanation:
The domain of this function is all real numbers because you can see that there are no endpoints on the graph. The function is going off of the graph, which means it is continuing aka never-ending.
(-∞,∞) aka all real numbers
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The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3[tex]x^{2}[/tex]+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3*[tex]3^2[/tex] + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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The sum of the two numbers is -34 and their difference is 5. Find the numbers.
Answer:
y = -19.5, x = -14.5
Step-by-step explanation:
We can form equations from this statement:
x + y = -34
x - y = 5
If we rearrange the second equation, we get:
x - y = 5
x = 5 + y
Then, we substitute this value into the other equation to get the answer.
x + y = -34
5 + y + y = -34
Then solve:
2y + 5 = -34
2y = -39
so, y = -19.5
now we can find x with y:
-19.5 + x = -34
-34 + 19.5 = x
x = - 14.5
Here is a parallelogram.
Work out the value of x.
x cm
Area = 12 cm²
2.5 cm
The value of x for the given parallelogram is 4.8 cm.
According to the question,
We have the following information:
We have a parallelogram with base x cm, height 2.5 cm and area 12 square centimeters.
(More to know: in a parallelogram, the opposite sides are equal and parallel to each other. Opposite angles of parallelogram are equal and the sum of consecutive angles is 180°.)
We know that the following formula is used to find the area of the parallelogram:
Area of parallelogram = Base*height
x*2.5 = 12
x = 12/2.5
x = 4.8 cm
Hence, the value of x is 4.8 cm.
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Mrs. Shelly paid $3 for 6 muffins and Mrs. Kloske paid $9 for 18 muffins. How much did
Mrs. Smith pay for 30 muffins?
Explain your answer
a) $3
b) $10
c) $15
d) $30
Select all correct answers. which values are part of the solution set based on the result of the inequality? -4x + 24 < -2x + 2 9.5 -10 11.5 15 10 -3
11.5 and 15 are the values that are part of the solution set of the inequality.
Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.
To determine the solution set of the given inequality, isolate the variable to one side and simplify.
-4x + 24 < -2x + 2
-4x + 2x < -24 + 2
-2x < -22
22 < 2x
11 < x
Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.
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The demand function for a certain make of replacement cartridges for a water purifier is given by the equation p=−0. 01x2−0. 1x+21 where p is the unit price in dollars and xis the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $9/cartridge. (Round your answer to two decimal places. )
The demand function for a certain is given by the equation p=−0. 01x2−0. 1x+21 then the determined values will be −50.905557, −0.427737,41.333295.
From the given values,
R=px
9 = (−0. 01x2−0. 1x+21) x
0.01x3+0.1x2−21x−9=0
By reducing the equation,
X = −50.905557, −0.427737,41.333295.
Therefore, the determined values will be −50.905557, −0.427737,41.333295.
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a survey of 500 high school students was taken to determine their favorite chocolate candy. of the 500 students surveyed, 118 like snickers, 185 like twix, 179 like reese's peanut butter cups, 60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups, and 17 like all three kinds of chocolate candy. how many students like snickers, but not twix or reese's peanut butter cups? a) 118 b) 101 c) 100 d) 18 e) 83 f) none of the above.
There are 18 students who like snickers but not twix or reese's peanut butter cups.
Given, that 500 high school students was taken to determine their favorite chocolate candy.
118 like snickers, 185 like twix, 179 like reese's peanut butter cups,
60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups,
and 17 like all three kinds of chocolate candy.
Let A = Set of students like snickers
B = Set of students like twix
C = Set of students like reese's peanut butter cups
Now, we have to find the number of students like snickers but not twix or reese's peanut butter cups i.e. A - A∩B - A∩C + A∩B∩C
A - A∩B - A∩C + A∩B∩C = 118 - 60 - 57 + 17
A - A∩B - A∩C + A∩B∩C = 135 - 117
A - A∩B - A∩C + A∩B∩C = 18
Hence, there are 18 students who like snickers but not twix or reese's peanut butter cups.
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If y=8 when x=4, write the direct variation equation and find y when x=5
HELPP
(Help!)
#8 The tables represent some points on the graphs of lines m and n. Which system of equations is represented by lines m and n?
(A) −6x − y = 8 −3x + 2y = 9
(B)6x + y = −8 3x − 2y = 9
(C) 6x − y = −8 −3x − 2y = 9
(D) 6x − y = 8 3x + 2y = 9
#9 A produce company sells crates filled with a mixture of apples and oranges during the holiday season to grocery stores. Each crate contains a total of 72 pieces of fruit. Suppose that a crate has 8 more apples than oranges.
Which system of linear equations can be used to determine the number of pieces of each kind of fruit in the crate?
(A) a + o = 72 o = a + 8
(B) 8a + o = 72 a + o = 8
(C) a + o = 72 a = o + 8
(D) a + 8o = 72 a + o = 8
#10 The tables represent some points on the graphs of lines r and s. Which system of equations is represented by lines r and s?
(A) −4x + 3y = 12 2x − 5y = −10
(B) −4x − 3y = −12 −2x + 5y = 10
(C) 4x + 3y = −12 2x − 5y = 10
(D) 4x − 3y = −12 −2x − 5y = 10
The linear functions representing the systems of equations in each case are given as follows:
8. (D) 6x − y = 8 3x + 2y = 9
9. (C) a + o = 72 a = o + 8.
10. (C) 4x + 3y = −12 2x − 5y = 10.
What is a linear function?The slope-intercept representation of a linear function is presented by the rule as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.b is the y-intercept of the function, being the numeric value of the function when the input variable x assumes a value of 0.For the line m, we have that when x increases by 6, y increases by 36, hence the slope is:
m = 36/6 = 6.
Considering the positive slope of 6, at x = 0, the numeric value is 12 less than the numeric value at x = 2, hence the intercept is:
b = 4 - 2 x 6 = -8.
Hence the equation is:
y = 6x - 8.
6x - y - 8.
Thus option d is correct.
For item 9, we use the variables a and o. The total is of 72, hence:
a + o = 72.
Suppose that a crate has 8 more apples than oranges, hence:
a = o + 8.
Thus option c is correct.
For line r in item 10, when x increases by 3, y decays by 4, hence the slope is:
m = -4/3.
When x = 0, y = -4, hence the intercept is:
b = -4.
Thus the equation is:
y = -4x/3 - 4
3y = -4x - 4.
4x + 3y = -12.
Meaning that option c is correct.
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what is the distance between point P (-5,7) and point Q (6,7) ?
Answer:
11
Step-by-step explanation:
Distance formula is square root of (x2-x1)^2+(y2-y1)^2
square root of (6-(-5))^2+(7-7)^2
square root of (11)^2+(0)^2
square root of 121+0
square root of 121
11
distance is 11