The equation to solve when the three angles of a triangle measure x,y and 39 is x + y + 39 = 180°.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
It is important to note that the total angles in a triangle is 180°.
Therefore, in this case, the angles will be illustrated thus:
x + y + 39 = 180. This illustrates the equation.
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one number is 10 more than another. their product is -25
Answer: resource - trust me bro
Step-by-step explanation: Let x = the smaller numberLet 2x + 10 = the larger numberx(2x + 10) = 1002x^2 + 10x - 100 = 0Divide both sides of the equation by 2.x^2 + 5x - 50 = 0(x - 5)(x + 10) = 0x - 5 = 0 or x + 10 = 0x = 5 or x = -10, not a positive number2x + 10 = 2(5) + 10 = 20
Last year, Dan had $ 10,000 into invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account?
The amount invested in the account that yields 10% simple interest is $1,000.
The amount invested in the account that yields 7% simple interest is $9,000.
How much was invested in each account?The first step is to form a system of equations using the information provided in the question:
a + b = $10,000 equation 1
0.1a + 0.07b = 730 equation 2
Where:
a = amount invested in the account that yields 10% simple interest
b = amount invested in the account that yields 7% simple interest
The elimination method would be used to solve the equations
Multiply equation 1 by 0.1
0.1a + 0.1b = 1000 equation 3
Subtract equation 2 from equation 3
0.03b = $270
Divide both sides of the equation by 0.03
b = $270 / 0.03
b = 9,000
Substitute for b in equation 1
a + 9,000 = 10,000
a = 10,000 - 9,000
a = 1000
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Replace the _ with the symbol that makes a true sentence 2/15_0.83
Answer:
See below
Step-by-step explanation:
2 /1 5 = .1333
so 2/15 < .83
Using front-end estimation, find a reasonable estimate of: 719x26=?
The estimation of 719 x 26 is 14,000
What is rounding off?Making a number simpler so that its value stays near to its original state is known as rounding. Although less exact, the outcome of rounding off a number is simpler to utilise.
Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
Estimation of 719 x 26
Now, Round off nearest hundred for 719 which is 700
i.e., Round 719 = 700
Now, Round off nearest hundred for 26 which is 20
i.e., Round 26 = 20
Hence, the estimation is 700 x 20 = 14,000.
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What is 8370dividedby62
Question 4
Simplify the expression: (7x + 2)²
A 49x² + 4
B 49x² + 28x + 4
C 49x² - 4
D 25x² + 9
Answer:
B
Step-by-step explanation:
(7x+2)(7x+2)
7x×7x=49
7x×2+2×7x=28x
2x2=4
Here's a brain teaser.
(I already know the answer)
1=5
2=10
3=15
4=20
5=?
Answer:
5 = 1
or
5 = 25
Step-by-step explanation:
I've seen two answers to this.
1. Since we are told 1 = 5, then 5 = 1.
One answer is 1 = 5
2. Since each number on the right is 5 times the number on the left, then 25 corresponds to 5, and 5 = 25.
Answer: 5=1 (The correct answer) 5=25 (The answer that makes sense but is not correct).
Step-by-step explanation:
Explanation for answer 1: It say's that 1 = 5.
Explanation for answer 2: If we follow the pattern of adding 5 each time we go up a number then 5 would equal 25.
Dr. Ortega gave Austin, one of her patients, 180 micrograms of medication. Based on Austin's height and weight, she expects that there will be about 162 micrograms remaining in his body after one hour. Dr. Ortega knows that the amount of medication remaining in Austin's body will continue to decrease each hour.
Write an exponential equation in the form y=a(b)x that can model the amount of medication in Austin's body, y, x hours after the medicine was administered.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
To the nearest microgram, how much of the medication can Dr. Ortega expect to remain in Austin's body after 6 hours?
micrograms
The exponential function that can model the amount of medication in Austin's body, y, x hours is of: [tex]y = 180(0.9)^x[/tex]
What is the exponential function?The definition of the exponential function is presented as follows:
[tex]y = a(b)^x[/tex]
The parameters a and b are listed as follows:
a is the amount when x = 0.
b is the rate of change.
Given that the initial dose was of 180 micrograms, hence the parameter a is;
a = 180.
After one hour, the concentration was of 162 micrograms, hence the parameter b is;
b = 162/180 = 0.9.
Hence the equation is:
[tex]y = 180(0.9)^x[/tex]
After six hours, the concentration is given as;
[tex]y = 180(0.9)^6[/tex]= 96 micrograms.
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A car dealership decreased the price of a certain car by 5%. The original price was $47,200.
What is the new value and the original value?
Answer:
New: $44,840 Original: 47,200
Step-by-step explanation:
You have to multiply 47,200 by 95% or 0.95
In a photo contest, two judges are giving scores to each photo. Each judge gives a score for impact (worth 40%), composition (worth 30%), lighting (worth 20%), and color balance (worth 10%). Lester entered a photo in the contest and received the following scores: Impact: 8 and 9 Composition: 7 and 7 Lighting: 8 and 7 Color balance: 5 and 7 Enter a number in each box to create an expression that represents Lester's final score.
Lester's final score from the two Judges is 7.6
How to calculate Lester's final scoreThe scores of the judges are in percentage and this will be converted to decimal by dividing by 100
impact (worth 40%) = 0.4
composition (worth 30%) = 0.3
lighting (worth 20%) = 0.2
color balance (worth 10%) = 0.1
Average score from the Judges will be used to multiply the percentages
Impact: 8 and 9
= 8.5 * 0.4 = 3.4
Composition: 7 and 7
= 7 * 0.3 = 2.1
Lighting: 8 and 7
= 7.5 * 0.2 = 1.5
Color balance: 5 and 7
= 6 * 0.1 = 0.6
sum of the scores gives Lester's final score as 7.6
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Question 5 (1 point), You are making your friend a triangular fabric decoration for their home. It has ripped so you need to go buy new fabric. The fabric you are buying is $3 per square foot. Using the dimensions below, how much money do you need to buy enough fabric?
Answer:
1). True
2). x = 16.4 m^2
3). A = 24, h = 4
4). A = 18.39
5). 162
Step-by-step explanation:
I took this quiz on K12 and got everything correct! Brainliest welcome! :)
A Starbucks gift card has a balance of $75. Assume that the person who owns the gift card only uses it to purchase Frappuccino drinks that cost $4.65 apiece.
Hi can someone please help me? Thank you!
Can someone please help me , thank you :)!
Answer:
a )
[tex]6 ( ? ) = 27[/tex]
b )
? = The amount of rice in each container.
So, 1 container = ( ? ) ounce.
6 containers have = 6 x ( ? ) ounces.
We know that 6 containers have 27 ounces so...
[tex]6 ( ? ) = 27[/tex]
[tex]? = \frac{27}{6}[/tex]
[tex]? = 4.5[/tex]
Final Answer: 4.5 ounces in each container
Hope this helps! :)
it costs a paper company 4x+185 dollars to produce x notebooks. how many notebooks can they produce for $285
The paper company can produce 25 notebooks for $285
How to determine the number of notebooks?From the question, the equation of the total cost is given as
Equation = 4x + 185
Rewrite as
Cost = 4x + 185
Express the equation as a cost function
So, we have the following representations
C(x) = 4x + 185
When the total cost is $285, we have
C(x) = 285
This gives
4x + 185 = 285
Subtract 185 from both sides
4x = 100
Divide by 4
x = 25
Hence, the number of notebooks is 25
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This is the kinetic energy of a 64 kg object travelling at 12 m/s.
11.2kj
4.6kj
960j
Kinetic energy of a 64 kg object travelling at 12 m/s is 4.6kj.
Kinetic energy = KE = [tex]\frac{1}{2}mv^{2}[/tex]
Mass = m = 64 kg
Velocity = v = 12 m/s
KE = [tex]\frac{1}{2}*64*(12)^{2}[/tex]
= 4608 J
1000 j = 1 kj
1 j = 1/1000 kj
4608 j = 4608/1000 kj
= 4.608 kj
Hence, kinetic energy is 4.6 kj.
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Differentiate the function with respect to x.
Differentiation of f(x) is [tex]-8x^{3} sinx^{4}[/tex].
Given,
f(x) = [tex]cos2x^{4}[/tex]
Now, we will differentiate f(x) with respect to x,
[tex]\frac{d}{dx}cos2x^{4} = (\frac{d}{dx}cos2x^{4})(\frac{d}{dx}2x^{4} )[/tex]
[tex]= (-sin2x^{4})(2*4x^{3})[/tex]
[tex]= -8x^{3}sin2x^{4}[/tex]
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Solve the system of equations by the substitution method.
x+y=8
y=-3x
Using the substitution method, the solution to the system of equations is: x = -4 and y = 12.
How to Solve a System of Equations by Substitution?To solve a system of equations using the substitution method, find the value of one of the variables in one equation, then substitute it in the second equation and solve to find the value of the second variable.
Given the equations:
x + y = 8 --> eqn. 1
y = -3x --> eqn. 2
Substitute -3x for y into equation 1:
x + (-3x) = 8
x - 3x = 8
-2x = 8
-2x/-2 = 8/-2
x = -4
Substitute x = -4 into equation 2:
y = -3(-4)
y = 12
The solution is, x = -4 and y = 12.
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3f + -4 = 0 solve for f
Answer:
f = 4/3
f = 1.3
f = 1 1/3
Step-by-step explanation:
Move all terms that don't contain f to the right side and solve.
Write the prime factorization of 48
The prime factorization of 48 is 2⁴ × 3.
What are prime numbers?Those greater than one are known as prime numbers. They simply have two variables: the number itself and factor 1. This indicates that these numbers cannot be divided without leaving a remainder by any number other than 1 and the number itself.
Given:
The number is 48,
Factorize 48 we get 2 × 2 × 2 × 2 × 3
= 2⁴ × 3
Therefore, the prime factorization of 48 is 2⁴ × 3.
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How many hour is 4:30 until 6:00
Answer: 1 hour and 30 minutes or 1.5 hours
Answer:
1 hour and 30 minutes
Step-by-step explanation:
Which describes the graph of y=-(x - 3)² + 2?
O A. Vertex at (-3,2)
OB. Vertex at (3,-2)
OC. Vertex at (-3, -2)
OD. Vertex at (3, 2)
x-3=0
so x = 3
-(y-2)=0
so y = 2
vertex = (3,2)
There are 3 trees in your neighbor's yard. Each tree in the yard has 2 birdhouses and each birdhouse has 4 birds. How many birds are
there in all?
Dave's science class is competing to see who can build the tallest tower. Each group of students gets 10 newspapers and 2 yards of tape. Dave's group decides to roll up each of their newspapers. Then, they tape each roll with 4 inches of tape. How many inches of tape do they have left?
32 inches more of tape students need.
Given that,
Students in Dave's science class are trying to build the tallest structure. Ten newspapers and two yards of tape are given to each group of kids. The decision is made by Dave's group to roll up each newspaper. Then, they use 4 inches of tape to seal each roll.
We have to find how many more inches of tape are there.
We know that,
1 yard is 36 inches.
So,
2 yards is 2 times 36 is 72 inches.
The inches of the tape they need is 10 times 4 is 40.
So,
72-40 is 32 inches
Therefore, 32 inches more of tape students need.
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Can anyone help me in this question? pls.........
Answer: A
Step-by-step explanation :
HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )
What is the value of x?
The required value of x is 3 in the given equilateral triangle.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The triangle given in the figure is an equilateral triangle.
We know that all sides are equal in the equilateral triangle.
As per the given figure,
side AB = side AC
6x - 3 = 3x + 6
6x - 3x = 6 + 3
Apply the arithmetic operation,
3x = 9
x = 9/3
x = 3
Therefore, the required value of x is 3 in the given equilateral triangle.
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An ice cream factory has 4 machines that make the same type of ice cream. The rate of production for each machine is shown in the table. Based on the date given, which machine works atthe fastest rate?
Using division operations and based on the rates of production, given, Machine D works the fastest.
How is the rate of production determined?The rate of production can be computed using the division operation, which divides the dividend by the divisor, to obtain the quotient (rate).
The rate of production is the number of goods that can be produced during a given period of time.
The rate of production or production rate also refers to the time consumed in the production of a unit of goods or services.
There are, therefore, two ways of determining production rate. Firstly, we can divide the total production by the hours consumed.
Secondly, the production rate can be computed by dividing the total production time by the number of goods produced.
Units Production Rate of
Produced Hours Production
Machine A 10,000 15 667 cups per hour
Machine B 25,000 20 1,250 cups per hour
Machine C 30,000 30 1,000 cups per hour
Machine D 15,000 10 1,500 cups per hour
Thus, using division operation, Machine D produces at the fastest rate than the other three machines.
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Question Completion:Units Production
Produced Hours
Machine A 10,000 15
Machine B 25,000 20
Machine C 30,000 30
Machine D 15,000 10
How many solutions does the equation a+b+c+d=15 have?
The equation a+b+c+d=15 has infinite many solutions
How to determine the number of solutions?From the question, the equation is given as
a+b+c+d = 15
From the above representation of the equation, we can see that:
The equation is a linear equationAlso, the equation has 4 variablesWhen a linear equation that has more than one variable is given, the number of solutions cannot be quantified i.e. infinite number of solutions
Hence, the equation has infinite number of solutions
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Which triangle congruence postulate would be used to prove the following triangles congruent?
1. AAS
2. SSS
3. SAS
4. HL
The velocity function of a car is given by v(t) = -3t2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop.
A.
a = -6.46 m/s²
B.
a = -2.76 m/s²
C.
a = -0.46 m/s²
D.
a = 2.76 m/s²
Answer: In photo below
You're Welcome :)
The acceleration of the car three seconds before it comes to a stop is -2.76 m/s² (Letter B).
Derivative
Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.
In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.
For derivating an equation, you should apply the rule: [tex](\frac{d}{dx} ) (x^n ) = nx^{n-1}[/tex]. Example: x²= 2x
The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you should solve this quadratic function:
Δ=b²-4ac=[tex]18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432[/tex]
[tex]t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}[/tex]
[tex]t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}[/tex]
[tex]t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}[/tex]
Like t is a positive number, you should use [tex]t_2[/tex]. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is [tex]2\sqrt{3}[/tex].
The acceleration can be found from the derivative of the velocity function. See below.
a(t)= -6t+18 , for t=[tex]2\sqrt{3}[/tex]
a(t)= -6*[tex]2\sqrt{3}[/tex]t+18
a(t)= [tex]-12\sqrt{3}[/tex]t+18
a(t)=-2.76
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