Answer:
largest angle = 90°
Step-by-step explanation:
let the smallest angle be x then and other 2 angles are 3x and x + 30
the sum of the 3 angles in the triangle sum to 180° , that is
x + 3x + x + 30 = 180
5x + 30 = 180 ( subtract 30 from both sides )
5x = 150 ( divide both sides by 5 )
x = 30
3x = 3 × 30 = 90
x + 30 = 30 + 30 = 60
the 3 angles are 30° , 60° , 90°
with 90° being the largest
The curve above is the graph of a sinusoidal function. It goes through the points (- 4, 0) and (2, 0) Find a sinusoidal function that matches the given graph If needed, you can enter pi = 3.1416 as in your answer, otherwise use at least 3 decimal digits
A sinusoidal function that matches the given graph is y=cosπx/3+2.
From the given question, the curve is the graph of a sinusoidal function.
It goes through the points (- 4, 0) and (2, 0).
We have to find the sinusoidal function that matches the given graph.
For this problem, we can use either of these general equations :
y = Asin(Bx + C) + D or y = Acos(Bx + C) + D.
A = amplitude = distance on Y-axis from centre of graph to highest or lowest point.
So from the given graph
A = 1
T = period = distance on X-axis over one complete cycle
So from the given graph
T = 6.
So B=2π/6 =π/3
D = distance that graph has been moved up or down on the Y-axis
D = 0
C= horizontal shift (left side if positive)
From the given Graph
C = 2
So, equtaion is
y = Acos(Bx + C) + D
Putting the each variable value
Using π =3.1416.
y = 1*cos(π/3 x + 2) + 0
y = cosπx/3 + 2
Hence, a sinusoidal function that matches the given graph is y=cosπx/3+2.
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The table shows the temperature (v) at different altitudes (x). This is a linear relationship. Find the y-intercept for this relationship. 0 Altitude (ft), X Temperature (°F). 2,000 61 4,000 53 6,000 45 8,000 10,000 12,000 37 29 21 69 They-Intercept for this relationship is b =
HELP plsss i dont know how to do this problem
b) -2
Step-by-step explanation:Hey! Let's help you with out with this question!
Alright! So! We're trying to figure out the slope of the table. And how do we do that? Well, there is actually a formula that can help us here! And that is using the slope between two points.
What is the formula for the slope between two points?The formula is as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
It allows us to figure out the slope by taking two coordinate points and sub them into the formula to find m, which in this case is the slope!
Let's use this equation twice, we do this to make sure that the slope is consistent throughout the table.
Using the formula for the first two points:The first two points are:
(3, 36)(6, 30)Now, we apply the formula as such:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{30-36}{6-3}[/tex]
[tex]m=\frac{-6}{3}[/tex]
[tex]m=-2[/tex]
Alright, so we have a slope [tex]m=-2[/tex] for the first two points! Let's check if the last two points have the exact same slope as well!
Using the formula for the last two points:The last two points are:
(9, 24)(12, 18)We apply the formula again!
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{18-24}{12-9}[/tex]
[tex]m=\frac{-6}{3}[/tex]
[tex]m=-2[/tex]
Conclusion:Well, what do you know? Given our application of the slope between two points, we get a common answer [tex]m=-2[/tex]. So, therefore, it would be b) [tex]m=-2[/tex]
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evaluate the expression (7-4)/(8÷2)
Start simplifying both numerator and denominator,
[tex]\begin{gathered} 7-4=3 \\ 8\div2=4 \end{gathered}[/tex]rewrite the expression
[tex]\frac{(7-4)}{8\div2}=\frac{3}{4}[/tex]Maria used a number line to find 12 ÷ 4.
Explain how she can use the number line to model the division.
Maria can draw a number line connecting the points 0 and 12, then divide the distance between them into four equal parts. The division operation produces the location of the point closest to zero.
What is number line ?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in elementary mathematics. Every point on a number line is assumed to be a real number, and every real number is assumed to be a point.
Integers are frequently represented as specially marked points evenly spaced on a line. Despite the fact that the image only shows the integers from -3 to 3, the line includes all real numbers, which continue indefinitely in each direction, as well as numbers that are between the integers. It is frequently used to help teach simple addition and subtraction, particularly with negative numbers.
The number line is also known as a real line or real number line in advanced mathematics. It is formally defined as the set R of all real numbers viewed as a geometric space, namely the Euclidean space of dimension one. It's also known as a vector space, metric space, topological space, measure space, or linear continuum.
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Given two circles on a coordinate plane, use transformations to prove that both circles are similar
The two circles are said to be similar because they undergo a rigid transformation that does not change its shape.
How to prove similarity using transformation?A similarity transformation is defined as one or more rigid transformations (reflection, rotation, translation) followed by a dilation. Now, when a figure is transformed using a similarity transformation, an image is created that is similar to the original figure. This means that, two figures are similar if a similarity transformation will map the first figure to the second figure.
By definition of similarity transformation, looking at the given diagram, both shapes are circles and as such it is obvious that one circle has been dilated by a scale factor to get the other circle.
Thus, they have the same shape and are similar circles.
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On the radio one morning, a weather reporter stated that the temperature was two degrees below zero, but the temperature would continue to rise throughout the day. Which inequality could be used to represent all the temperature readings, T, that day?
the inequality for this situation is
T >= -2
[tex]T\ge-2[/tex]Find the domain and function of the graph
The Domain of the function is given as 2, 6 and 3 ≤ x ≤ 5.
Given that,
A graph of the function is shown, we have to determine the domain of the graph,
The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
here,
The function is defined on the values of x, as 2, 6 and from 3 to 5,
So the domain of the function is said to be as 2, 6 and 3 ≤ x ≤ 5.
Thus, the Domain of the function is given as 2, 6 and 3 ≤ x ≤ 5.
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Please help right now!
What is the answer for this equation 3X+y=5
The equation
[tex]3x+y=5[/tex]has two variables: x and y.
And since we have only one equation, the variables have infinite possible values, which are related to that equation.
Another way of seeing that is by calling x the independent variable, and then y will be the dependent variable (its value depends on the value of x).
So, we can isolate y on the left side of the equation, to obtain:
[tex]\begin{gathered} 3x+y=5 \\ \\ 3x+y-3x=5-3x \\ \\ y=-3x+5 \end{gathered}[/tex]Now, we see that the above equation represents a line (an infinite set of points), that has a slope -3 and a y-intercept 5.
Therefore, all the points on that line are solutions to the given equation.
If we graph that set of solutions on a xy-plane, we obtain the line below:
write an equation in slope intercept form for the line with the slope 1/5 and y - intercept 6
Given data:
The given slope of the line is m=1/5 .
The given y-intercept is c=6.
The expression for the equation of the line in slope intercept form is,
[tex]y=mx+c[/tex]Subbstitute the given values in the above expression.
[tex]y=\frac{1}{5}x+6[/tex]Thus, the equation of the line in slope intercept form is y=(1/5)x+6.
PLEASE HELP ASAP!!! 30 POINTS IF YOU HEL ME!!! I WILL MARK BRAINLIEST!
Answer:
.
Step-by-step explanation:
5. Complete the table to fill in the points that satisfy the equation: y = 1/3 x + 5?
Answer:
Step-by-step explanation: For this question, we need to make a table first.
For which we'll assume values of x and y.
Let the value of x be 0 then y will be 5
if value of x=3 then y=6
hence, we arrive at two points that are satisfying the equation.
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graph the circle which is centered at (-5,1) and which has a point (-2,-3) on it
We can start by placing the center at (-5,1).
The radius of the circle will be the distance between the center and the point (-2,-3).
If we graph this two points, we can use an angle protractor to draw the circle passing through point P(-2,-3) and centered at (C(-5,1):
Braelyn is writing an equation to represent the perimeter of a rectangle with the width equal to half the length. she knows that the perimeter is equal to 18 units and needs to find the length and width of the rectangle. which equations represent this relationship? select the four correct answers. x one-half x = 18 2 x x = 18 2 (x) 2 (2 x) = 18 x one-half x x one-half x = 18 2 (x one-half x) = 18 2 x one-half x = 18
The correct options are 2,3,4,5, according to given question.
What do you mean by equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to data in the given question,
We have the given information:
P = 18
w= l/2
Perimeter of a rectangle equals to twice the sum of length and width:
P= 2(l+w)
If we assume width = x, then:
l = 2x
2(x+2x) = 18 or
2x + 4x = 18
If we assume length = x, then:
w = 1/2x
2(x + 1/2x) = 18 or
2x + x = 18
Therefore, the correct options are below:
x + one-half x = 18 === incorrect
2 x + x = 18 === correct
2 (x) + 2 (2 x) = 18 === correct
x + one-half x + x + one-half x = 18 === correct, same as second option
2 (x + one-half x) = 18 === correct, same as second option
2 x + one-half x = 18 === incorrect
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A heptagon has angles measure of 105°, 141°, 132°, 109°, 143° and 131°. What is the measure of the seventh angle?
so I am doing Eureka math and 7th grade kinda need help....rewrite the expression by using distributive property and collecting like terms. 2 4/5v - 2/3(4v+1 1/6)
Answer:
2/15v + 7/9
Step-by-step explanation:
We take our base equation, then we will make every mixed number into an improper fraction. This will give us 14/5v - 2/3(4v+ 7/6). Then we will open the parentheses. This gives us: 14/5v - 8/3v+ 14/18. We will bring both the v's to a common denominator, giving us 42/15v - 40/15v+ 14/18. Then we can subtract and simplify. 2/15v + 7/9.
An amusement park charges $35.50 for admission. On Saturday 6789 people visited the park. About how much money did the park earn from admission that day?
ESTIMATE PLEASE!!
Write a quadratic equation in standard form whose graph passes through the given points (1,2) (2,-1) (3,-6)
we have
Write a quadratic equation in standard form whose graph passes through the given points (1,2) (2,-1) (3,-6)
A quadratic equation in standard form is equal to
y=Ax^2+Bx+C
substitute the given values
(1,2)
2=A(1^2)+B(1)+C
2=A+B+C ------> equation 1
(2,-1)
-1=A(2^2)+B(2)+C
-1=4A+2B+C -------> equation 2
(3,-6)
-6=A(3^2)+B(3)+C
-6=9A+3B+C -------> equation 3
step 1
In the equation 1 isolate the variable A
A=2-B-C -------> equation 4
step 2
substitute equation 4 in equation 2 and 3
-1=4(2-B-C)+2B+C
-1=8-4B-4C+2B+C
-1=8-2B-3C
2B+3C=
Robert is standing on a bridge that spans a canyon. He drops a pebble from the bridge, and records how long the pebble takes to reach the water below. If the pebble takes 5.49 seconds to reach the water, what is the height of the bridge?
"Height of the bridge is 148 m"
Given :
time = 5.49 s
Since pebble is dropped from a height it will have acceleration due to gravity (g = 9.8 m/s²) ∴ a = 9.8 m/s²
Let us assume that Initial velocity (v) is 0 m/s² (pebble is not moving)
we have to find distance d = ?
Now according to formula
d = vt + 1/2 at²
Now putting the values in the formula
d = 0 × 5.49 + 1/2 × 9.8 × (5.49)²
d = 0 + 147.68
d = 147.68 ≈ 148 m
Therefore the height of the bridge is 148 m.
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help meeeeeeeeeeeeeee pleaseeeeeee help meeeeeeeeeeeeeee pleaseeeeeee
Answer:
Width = 4.7 m, Length = 6.7 m
Step-by-step explanation:
Let the width be [tex]w[/tex]. Then, the length is [tex]w+2[/tex].
[tex]w(w+2)=32 \\ \\ w^2+2w-32=0 \\ \\ w=\frac{-2 \pm \sqrt{2^2-4(1)(-32)}}{2(1)} \\ \\ w \approx 4.7 (w>0) \\ \\ w+2 \approx 6.7[/tex]
A fruit juice owner has three types of juices. 320 liters of the first kind, 350 liters of the second kind, 400 liters of the third kind. How many bags with the amount of each juice will he be able to do?
Three types of juice means 3!
that is ., 3*2*1 =6
He will be able to fill 6 bags with the specified amount of each juice.
In mathematics, the term "factorial" refers to the sum of all positive integers that are less than or equal to a certain positive integer, which is followed by an exclamation point.
What is a factorial problem?In a factorial, you multiply the supplied integer by all of the positive whole numbers that are less than it. To put it another way, = n (n 1) ... 2 1.The mathematical operation known as a factorial, denoted by the symbol (! ), multiplies a number (n) by each number that comes before it. The factorial function instructs you to multiply all the whole numbers starting at the selected number and going all the way down to one. In further mathematical terms, a number's factorial (n!) equals n (n-1).When a group of variables are independent happenings, a factorial distribution occurs. In other words, there is no interaction between the variables; for two events, x and y, the probability of x remains constant when y is taken into account. Therefore,To learn more about factorial refer to:
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An artist is making a scale model of a statue. On the model 2 inches represents 1 foot on the actual statue. Which graph best represents this relationship?
The graph best represents this relationship of the scale model of a statue is B.
What is meant as the scale factor?A scale factor is described as the ratio of the scale of a provided original object to the scale of a new object that is its depiction but of a various sizes (bigger or smaller). It is necessary to specify how much the shape has already been enlarged when describing enlargement. Scale factor 3 signifies that the new shape is three times the size of the original shape.The shape will be smaller if the scale factor is a fraction. This is known as reduction.For the given question;
On the model 2 inches represents 1 foot on the actual statue.
Thus, model 4 inches represents 2 foot on the actual statue.
This is given by graph B.
Thus, the graph best represents this relationship of the scale model of a statue is B.
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m∠1 =?
m∠2 = ?
m∠3 = ?
Answer:
1= 31 degrees
2= 121 degrees
3= 47 degrees
Step-by-step explanation:
IMPORTANT: SUM OF ALL THREE ANGLES OF A TRIANGLE EQUAL 180
For angle 1 we add 59+90 since those are the 2 known angles
90+59=149
Now subtract by 180
180-149=31
Angle 1 is equal to 31
Now for angle 2 we subtract 59 from 180 since it is on a flat surface the sum of those angles will equal 180 degrees
180-59=121
Angle 2 is 121 degrees
Now for angle 3 we add 121 and 12 since we know those 2 angles
121+12=133
Now subtract from 180
180-133= 47
Angles 3 is 47 degrees
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Raymond invested $4, 000 in a new company. The value of his investment has been growing at a rate of 6% per year for the last 5 vears. Write a function to represent the growth of his investment of $4,000, where A is the total value of his investment and t is the time invested in years. What is the total value of his investment after 5 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000\left(1+\frac{0.06}{1}\right)^{1\cdot 5} \implies A=4000(1.06)^5\implies A \approx 5352.90[/tex]
now, we're assuming is a 6% growth of the current amount per year, namely compounded, as opposed to simple interest.
b = (2a)²
Work out the value of b when a = 5
Answer:
100
Step-by-step explanation:
Kelly opened a simple interest account with deposit of $2200. At the end of 4 years, the balance of the account was $2200. What is the annual interest rate on the account.
The simple interest formula is:
I = P R T, where I is the interest earned, P is the principal, R is the insterst per year and T is the time in years
If the initial deposit is $2,200 and after 4 years the balance is still $2,200, then the interest rate is zero
Tell me how I can eliminate the y-terms in this system! ASAP!
4x-8y=20
3x+4y=5
Multiply by what number on both sides
Answer:
2?
Step-by-step explanation:
I couldn't find an answer but 2 was the most appropriate so try that, and sorry I wasn't much of a help
Answer:
2
Step-by-step explanation:
combine like terms: 3(x - 6) + 4x
7x - 18
Explanations:The given expression is:
3 (x - 6) + 4x
Open the brackets by expanding the expression
3x - 18 + 4x
Combine like terms
3x + 4x - 18
7x - 18
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer: 2 =
27⁰
111°
answer x=
The measure of angle of a triangle x is 42°.
According to the question,
We have the following information:
In a triangle, the measurements of two of its angles are 27° and 111°.
We know that the sum of three angles of a triangle is 180°.
So, we have the following expression to find the value of x:
27+111+x = 180
Adding the numbers on the left hand side:
(Note that the variable can not be added to any integer. It can only be added to the same variable.)
138+x = 180
Subtracting 138 from both the sides:
x = 180-138
x = 42°
Hence, the value of x for the given triangle is 42°.
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