The measure of the base angles is 39° respectively.
An Isosceles triangle is a triangle that has two equal sides.
Note: The base angle of an isosceles triangle is equal.
From the question,
The sum of the angle in a triangle is 180°.
⇒ a+b+c = 180°............... Equation 1
Given:a = 102°b = c = x = base angle of the isosceles triangle.Substitute these values into the equation.
102+x+x = 180102+2x=180Solve for x.
2x = 180-1022x = 78x = 78/2x = 39°Hence, the measure of the base angles is 39° respectively.
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A computer can sort x objects in t seconds, as modeled by the function below: t=0.007x^2+0.003x. How long, in seconds, will it take the computer to sort 15 objects? Round your answer to the nearest hundredth of a second.
As modeled by the function below: t=0.007x^2+0.003x. The time it will take the computer to sort 15 objects is 1.62sec
What is Time?
Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.
Given:
t = 0.007x^2+0.003x
x = 15
Substituting the value in the equation we get,
t = 0.007(15)^2+0.003(15)
t = 0.007(225) + 0.045
t = 1.575 + 0.045
t = 1.62sec
Hence, It will take 1.65sec to sort 15 objects
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if 45 grams of a drug are contained in 200 mL how many grams are contained in 80 ml
Polygon ABCDE rotates 52º about the origin to create polygon A′B′C′D′E′. If measure of angle BCD equal 31 º , what is the measure of angle B'C'D' ?
sorry cant give answers not a multiple choice question
Answer:
Answer is 31,
Step-by-step explanation:
PLATO Confirmed
A pizza parlor has 8 different toppings and 3 different cheeses to choose from on the menu. How many pizza combinations are possible if each pizza has 1 topping and 1 cheese
Final answer:
To find the number of pizza combinations available using 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, one multiplies the number of topping choices by the number of cheese choices, giving 8 x 3 = 24 possible combinations.
Explanation:
Calculating Pizza Combinations
When calculating the number of possible pizza combinations with 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, we use basic counting principles. Each pizza can be thought of as a combination of one topping and one cheese. Since these choices are independent, we multiply the number of options for toppings by the number of options for cheeses to find the total combination possibilities. This results in 8 toppings multiplied by 3 cheeses, giving 24 possible combinations.
The formula used is straightforward: Number of combinations = Number of toppings × Number of cheeses.
Pizza Combination Calculation Example
For instance, if you were at a pizza parlor where you could choose from pepperoni, mushrooms, onions, and 5 other toppings, along with mozzarella, cheddar, and one other cheese, you could create 24 unique pizzas. Just pick one topping and one cheese, and that's your combination.
Suppose that one worker can produce 15 cookies, two workers can produce 35 cookies together, and three workers can produce 60 cookies together. what is the average product of the first two workers?
Sue traveled 96 miles in 12 hours. A unit rate to describe Sue's travel is 8 miles per hour. What is another unit rate in this situation? (1 point) 1/8 mile per hour, 1/8 hour per mile, 1 mile per hour, 8 hours per mile
Answer:
I believe the answer is 1/8 hour per mile
Step-by-step:
I don't know. I just believe that that is the most reasonable answer to this question and I have this question as well, it might seem hard it's really not.
How many radians are contained in a central angle that is 2/3 of a circle?
The radians that are contained in a central angle that is 2/3 of a circle will be 4π / 3 radians.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The central angle that is 2/3 of a circle will be given as,
⇒ 2π × (2 / 3)
Simplify the expression, then we have
⇒ 2π × (2 / 3)
⇒ 4π / 3 radian
The radians that are contained in a central angle that is 2/3 of a circle will be 4π / 3 radians.
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Ms. Winter makes homemade bath soaps and bottles of lotion. In her inventory, she had 48 bath soaps and 64 bottles of lotion. She wants to use all of her inventory to make as many gift baskets as she can use using the same number of bath soaps and the same number of lotion bottles in each gift basket. She will be able to make at most ? gift baskets. Each basket will contain ? bath soaps and ? bottles of lotion.
What is the remainder obtained by dividing x7 x5 1 by the generator polynomial x3 1?
The remainder obtained by dividing on [tex]{x^7} + {x^5} + 1[/tex] the generator polynomial [tex]{x^3} + 1[/tex] is [tex]\boxed{{-x^2} + {x} +1}[/tex]
Given:
The generator polynomial is [tex]{x^3} + 1.[/tex]
The polynomial is [tex]{x^7} + {x^5} + 1[/tex]
Explanation:
There are two methods of dividing the two polynomials.
(1). Synthetic division
(2). Long division method
The fraction can be expressed as,
[tex]{\text{Fraction}}= \dfrac{{{x^7} + {x^5} + 1}}{{{x^3} + 1}}[/tex]
The denominator of the fraction is [tex]{x^3} + 1[/tex] and the numerator of the fraction is [tex]{x^7} + {x^5} + 1.[/tex]
Divide [tex]{x^7} + {x^5} + 1[/tex] by [tex]{x^3} + 1[/tex] to obtain the remainder and the quotient of the polynomial.
The remainder obtained by dividing on [tex]{x^7} + {x^5} + 1[/tex] the generator polynomial [tex]{x^3} + 1[/tex] is [tex]\boxed{{-x^2} + {x} +1}[/tex]
Kindly refer the image attached below.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Long division method
Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree, cubic polynomial, quadratic equation.
Final answer:
To find the remainder of the polynomial division of x^7 + x^5 + 1 by x^3 + 1, one would perform polynomial long division or synthetic division, continuing until the degree of the remainder is less than the divisor.
Explanation:
The student is asking how to find the remainder of a polynomial division. Specifically, they want to know the remainder when dividing x^7 + x^5 + 1 by the polynomial x^3 + 1. To solve this, one would typically use long division of polynomials or synthetic division. The process is similar to long division with numbers. We would start by looking at the highest degree terms of both polynomials and divide them, then multiply the divisor by the result and subtract from the dividend. Repeat this process until the degree of the remainder is less than the degree of the divisor. Since finding the remainder requires us to consider terms up to x^2, we are essentially looking for the result of division that does not perfectly divide, similar to how 7 divided by 3 leaves a remainder.
Find 14/15−1/3 . Write your answer as a fraction in simplest form.
An animal park has 120 gazelles. If the population increase 5% in on year, how many gazelles will the park have next year?
The number of gazelles will the park have next year will be 126 if An animal park has 120 gazelles. If the population increase 5% in on year.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
An animal park has 120 gazelles. If the population increase 5% in on year,
= 5% of 120
= 6
= 6 + 120
= 126
Thus, the number of gazelles will the park have next year will be 126 if An animal park has 120 gazelles. If the population increase 5% in on year.
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Scott bought three bags of candy with 75 pieces in each one. He plans to divide all the candy evenly among seven friends. How many pieces of candy will Scott have left for himself?
Answer:
The answer is only one piece of candy
Step-by-step explanation:
Firstly, we have to determine the total amount of pieces of candy:
There are three bags with 75 pieces in each one, so the total is:
[tex]75+75+75=225[/tex]
Then, in order to determine the amount of pieces of candy for every friend,
we have to divide the total amount by 7, where the remainder of the division is the answer.
[tex]\frac{225}{7}=32*7+1[/tex]
Remainder=1
Finally, every friend of Scott receive 32 pieces of candy evenly and Scott is left with only one piece of candy.
Lulu buys a dress for $67, a hat for $35, and shoes for $49. How much did Lulu spend?
Jackson earned $60 and put 1 5 of those earnings into his savings account. How much did he put into his savings account?
Answer:
12
Step-by-step explanation:
=1x60
5x1
=60
5
12
Sam gets $1000 dollars per month. She has to spend $20 a day on transportation, she also needs to buy groceries each week and have $30 extra spending money per week. How much money should be spent on food per day?
If y =18 and x=60 what is the constant of proportionality
Final answer:
The constant of proportionality when y = 18 and x = 60 is calculated by dividing y by x, which results in a constant of 0.3.
Explanation:
To find the constant of proportionality when y = 18 and x = 60, we must assume that the relationship between y and x is directly proportional. This means that as x increases, y increases at a constant rate, and vice versa. If the relationship is directly proportional, we can write y = kx, where k is the constant of proportionality.
To calculate k, we simply divide y by x. So we have:
k = y / x
k = 18 / 60
k = 0.3
Therefore, the constant of proportionality is 0.3.
Find the maximum and minimum values of f(x,y,z)=3x+3y+3zf(x,y,z)=3x+3y+3z on the sphere x2+y2+z2=1x2+y2+z2=1.
You purchased xyz common shares for $45 per share one year ago. one year later aftering receiving $4 dividend per share, you sold your stock at $48 per share. what is your total return for the one year period?
a. 14.58%
b. 8.89%
c. 15.56%
d. 6.67%
A machine laying underground cable can place 125 meters of cable in 5 minutes
The machine lays cable at a rate of 25 meters per minute. This is calculated by dividing 125 meters by 5 minutes.
To determine how quickly the machine can lay underground cable, we need to calculate the rate of cable it places per minute. We start by noting that the machine can lay 125 meters of cable in 5 minutes.
We calculate the rate as follows:
Divide the total length of cable by the total time: 125 meters / 5 minutes = 25 meters per minute.This means the machine lays cable at a rate of 25 meters per minute.
Complete Question: A machine laying underground cable can place 125 meters of cable in 5 minutes. What is the rate per minute?
Prove that if b is a square matrix then b+b^t is symmetric
Line M passes through the points (–5, 9) and (–1, 9).
Each box holds 10 cartons of milk.there are 300 cartons of milk.how many boxes are there?
If $850 is deducted each month for 12 months from your checking account to pay your mortgage, what impact will it have on your checking account balance?
A) $10,200
B) $850
C) -$10,200
D) -$850
A cube has a volume of 512 mm^3. If all sides of the cube are divided by 4, what will the resulting volume be?
A) 8 mm^3
B) 27 mm^3
C) 7.2 mm^3
D) 12 mm^3
In his bookstore Toby places 21 books on shelves with 7 books on each shelf how many shelves does Toby need
Which of the following is an example of a proper fraction?
A. 7⁄6
B. 4⁄3
C. 3⁄4
D. 4⁄4
Last year Mr. Henderson paid a total of $98.40 for phone service and $79.20 for garbage pick up what was his average cost per month for phone service and garbage pick up?
determine whether each equation is a linear equation. write yes or no. if yes, write the equation in standard form. if the answer is no, circle the part that makes it no
1. y = 4 - 2x
The given equation y = 4 - 2x is a linear equation, however, it is not in standard form. The standard form is 2x + y = 4.
Explanation:The equation y = 4 - 2x is indeed a linear equation. A linear equation is an equation that represents a straight line when graphed. It generally has the form 'y = mx + b' where 'm' represents the slope of the line, and 'b' represents the y-intercept. Here, 'm' is -2 and 'b' is 4.
However, it is not currently in standard form. The standard form of a linear equation is 'Ax + By = C', where A, B, and C are integers, and A and B are not both zero. To write the equation in standard form, we can re-arrange it as 2x + y = 4.
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What is another way to write 46
Final answer:
The number 46 can be written as 'forty-six', 'XLVI' in Roman numerals, '101110' in binary, '56' in octal, '2E' in hexadecimal, a sum or product of other numbers, or in scientific notation as 4.6 x 10ⁱ.
Explanation:
There are several ways to write the number 46 in mathematics. One alternative way to express the number is by using words, such as 'forty-six'. Another method is to use Roman numerals, which would be 'XLVI'. Additionally, 46 can be represented in other numerical bases; for example, in binary, it is '101110', in octal, it is '56', and in hexadecimal, it is '2E'. If we dive into mathematics, 46 can also be written as a sum of other numbers, such as 23 + 23, or a product of primes, which for 46 is 2 x 23. Lastly, 46 can be expressed in scientific notation as 4.6 x 10±, though this form is more commonly used for very large or very small numbers.
Which fraction is equivalent to 4 over negative 9?
A.) -4 over 9
B) 4 over 9
C) -4 over -9
D) 9 over 4
Answer:
A) -4 over 9
Step-by-step explanation:
We have the fraction [tex]\frac{4}{-9}[/tex] the equivalent of this fraction is [tex]\frac{-4}{9}[/tex]
[tex]\frac{4}{-9}= \frac{-4}{9} =-\frac{4}{9}[/tex]
Both fractions are the same and equivalent, the negative sign makes the whole fraction negative regardless of whether it is in the numerator or denominator.