Answer:
3(-2x+1)
Step-by-step explanation:
John’s golf score was 4 less than 2/3rds of Sam’s. If the sum of their score was 100, find Sam’s score
Answer:
62.4
Step-by-step explanation:
Sam's score= x
John's score= 2/3x-4
john's score + sam's score=100
x+2/3x-4=100
5/3x-4=100
5/3x=104
5x=312
x=62.4
Sam's score is 62.4
John's score is 37.6
Find the exact values of cos^-1(1/2) on the unit circle
The value of cos⁻¹(1/2) on the unit circle is 60°.
What is unit circle?A circle with a radius of one unit is referred to as a unit circle. In the Cartesian coordinate plane, the unit circle is typically depicted. The second-degree equation with the variables x and y is used to algebraically represent the unit circle.
Given:
cos⁻¹(1/2)
As we know that for the unit circle, the value of the radius is 1,
Calculate the value of cos x as shown below,
cos x = radius of the circle / √(r² + p²)
cos x = 1 / √(1² + 1²)
cos x = 1 / √2
x = cos⁻ (1 / √2)
x = 45°
Thus, cos⁻¹(1/2) = 60°
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Analysts at the Milk Company calculated the average price of a gallon of its milk over 10 years. The following table shows the years since 2010 and the average price of a gallon of milk at that time.
Years (since 2010) 0 1 2 3 4 5 6 7 8 9
Price (in dollars) 3.16 3.43 3.37 3.36 3.42 3.21 3.24 3.01 2.85 3.05
Which of the following representations is most appropriate for showing how the price changed each year?
The representation that is the most appropriate for showing how the price changed each year is given by:
The second graph.
How to choose the correct graph?There are two steps to identify the correct graph, as follows:
Obtain the input and the output variable.Classify the input variable as discrete or continuous.The input and the output variables are given as follows:
Input variable: Number of years since 2010.Output variable: Price of the gallon of milk.As the input variable is graphed on the horizontal axis, while the output variable is graphed on the vertical axis, the first and the fourth graphs are incorrect, as they have each variable on the wrong axis.
The price keeps changing throughout the years, that is, the price does not remain constant throughout the year, meaning that the domain is continuous, and thus the graph is composed by a solid line.
This means that the second graph is the correct graph in this problem. (the solid, approximately horizontal line).
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HELP ME WITH GEOMETRY PELASE
Answer:
4
Step-by-step explanation:
This is a right triangle.
We can find the value of the missing side, hypotenuse, using Pythagoras theorem:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
The sum of square value of both legs is equal to the square value of hypotenuse.[tex] {2}^{2} + ({2 \sqrt{3} )}^{2} = {c}^{2} [/tex]
Find the square value of each expression[tex]4 + 12 = {c}^{2} [/tex]
Find the sum[tex]16 = {c}^{2} [/tex]
Find the root of both sides4 = c
Graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin
Use the polygon tool to graph the triangle.
Polygon
+Move
-10-9-745
*
O
-3-2
9
9
8
7-
6
5
4
3
2
1-
29
NY
Undo
1
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4
Redo
5
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x Reset
4
a
9
HELP
The image of the triangle after the dilation with a scale factor of 2 is graphed on the image shown at the end of the answer.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
Hence, to graph the image of triangle ABC on this problem, we have to:
Identify the coordinates of the vertex.Multiply each coordinate of each vertex by the scale factor.The coordinates of the vertices of the original triangle are given as follows:
(0,0), (-4,-2), (-4,4).
The scale factor for the dilation is is given as follows:
k = 2.
Then the coordinates of the vertices of the image of the triangle after the dilation are given as follows:
(0,0), (-8,-4), (-8,8).
The triangle with these three vertices is graphed on the image presented at the end of the answer.
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How do you find the 6th angle of a hexagon?
If the measure of the five angles are 140° each , then the measure of sixth angle of hexagon is 20° .
What is a Hexagon ?
The hexagon is defined as the two dimensional closed polygon that have six sides, 6 vertices and 6 angles .
the measure of the 5 angles of hexagon is = 140° each ;
which means that the sum of measure of 5 angles is = [tex]5 \times 140[/tex] = 700° ;
and we know that the sum of all 6 angles of the hexagon is 720° ;
let the measure of the sixth angle be = x ;
So , [tex]700 + x = 720[/tex] ;
⇒ [tex]x = 720-700 = 20[/tex] .
Therefore , the measure of sixth angle is 20° .
The given question is incomplete , the complete question is
A hexagon has five angles that measure 140° each. What is the measure of the sixth angle ?
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Can you help me with this
Answer:
[tex]y=\frac{1}{2}x+1[/tex]
Step-by-step explanation:
The points [tex](-2,0)[/tex] and [tex](0,1)[/tex] lie on the line.
The slope of the line is [tex]m=\frac{1-0}{0-(-2)}=\frac{1}{2}[/tex].
Since the [tex]y[/tex]-intercept is [tex](0,1)[/tex], the equation is [tex]y=\frac{1}{2}x+1[/tex].
What is 1 + 1
hurry im doing a very important test pls
Answer:
Step-by-step explanation:
1+1=2 hope this helps
need help I can help with Spanish hw (I speak fluent Spanish)
Answer:
Step-by-step explanation:
So how you answer this question is the 3rd one
WILL GIVE BRAINLIEST!!
Sarah is working in her parent's candy shop making chocolate covered strawberries. She gets paid $50 a week, in addition to $2 for every chocolate covered strawberry she makes. She made $225 this week. Write an equation to show how many strawberries Sarah made this week.
A.50 - 2x = 225
B.50x - 2 = 225
C.50 + 2x = 225
D.50x + 2 = 225
Answer:
a
Step-by-step explanation:
a
In a baseball series, teams A and B play until one team has won 4 games. If team A has probability 2/3 of winning against B in a single game, what is the probability that the series will end only after 7games are played
The probability that the series will end only after 7 games are played is 1.77
Here we have given that teams A and B play until one team has won 4 games.
And here we also know that the probability of winning for Team A is 2/3,
Then the probability of winning Team B is calculated as,
=> 1 - 2/3
=> 1/3
Then the probability that the series will end only after 7 games are played is calculated as,
=> P(X = 3) + P(X = 4)
When we apply the values on it, then we get
=> 4C3(2/3)(1/3) + 4C4(2/3)(1/3)
When we simplify this one then we get,
=> 1.77
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How to graph quadratic equation
Answer:
Below
Step-by-step explanation:
Pick a bunch of values of 'x' .....calculate the corresponding 'y' values then plot the ordered pairs and connect the dots with a smooth curved line ...
A certain principal has been invested into a savings account at the specified interest rate and interest type. An equation can be created to model that savings account. Which of the following statement is true?
A. An investment of $300 gaining simple interest at a rate of 2% can be modeled by the equation B = 300 + 2t.
B. An investment of $300 gaining compound interest at a rate of 4% can be modeled by the equation B = 300 x 1.04^t
C. An investment of $300 gaining simple interest at a rate of 6% can be modeled by the equation B = 300 + 60t
D. B. An investment of $300 gaining compound interest at a rate of 4% can be modeled by the equation B = 300 x 1.6^t
The solution is Option B.
An investment of $300 gaining compound interest at a rate of 4% can be modeled by the equation B = 300 x ( 1.04 )ⁿ , where n = t
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount to be invested be represented as P
The value of P = $ 300
Let the final amount be represented as A
Let the time period be = n = t
Let the rate of interest be represented as r = 4 %
r = 4/100
The value of r = 0.04
Now , the compound interest is calculated by the equation ,
A = P ( 1 + r/n )ⁿᵇ
Substituting the values in the equation , we get
A = 300 ( 1 + 0.04 )ⁿ
On simplifying the equation , we get
A = 300 ( 1.04 )ⁿ
where n = t = number of years
Hence , the equation is 300 x 1.04^t
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I need help in solving these problems please and thank you
The possible value of x is 17 and the degree measure of each angle is m∠P = 57°, m∠Q = 110°, and m∠R = 17°.
What are the degree measures of the three angles in triangle?
The angle sum of a triangle will always be equal to 180°. The angle sum of a quadrilateral is equal to 360°, and a triangle can be created by slicing a quadrilateral in half from corner to corner. Since a triangle is essentially half of a quadrilateral, its angle measures should be half as well. Half of 360° is 180°.
We have given,
The triangle PQR,
m∠P=(4x - 9), m∠Q=(6x+2), and m∠R=x. (a) Write an equation to find x.
a)
In a triangle, the sum of the degree measures of the three angles must be 180 degrees.
So for the triangle with angles P, Q, and R, we can use this rule to write the following equation:
m∠P + m∠Q + m∠R = 180
(4x - 9) + (6x + 2) + x = 180
11x - 7 = 180
11x = 187
x = 17
This equation shows that x = 17 is the only possible value of x that satisfies the triangle inequality rule for the given triangle.
b) To find the degree measure of each angle:
m∠P = 4x - 9 = 4(17) - 9 = 57°
m∠Q = 6x + 2 = 6(17) + 2 = 110°
m∠R = x = 17°
Hence, the possible value of x is 17 and the degree measure of each angle is m∠P = 57°, m∠Q = 110°, and m∠R = 17°.
.
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How are rays and angles related? a ray , and an angle is two . the measure of an angle related to the length of its sides. so, the measure of an angle the same at all distances from its vertex.
Rays and angles are related because when two rays share a common endpoint, they form an angle
What is an angle?An angle's measure serves as its definition; it is independent of the angle's side lengths. A ray is a segment of a line where one point is fixed and the other has no end.
The combination of two rays with the same endpoint is called an angle. The vertex of the angle is the common endpoint of the rays, which are referred to as the sides of the angle. The distance between the rays is how an angle is measured.
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Complete question
How are rays and angles related?
An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function C (x) = 0,5x2-180x + 35,646. What is the minimum unit cost? Do not round your answer. Unit cost :50 x 5 ?
The minimum unit of cost is 19446.
The function C (x) = [tex]0.5x^{2}-180x+35646[/tex].
Minimum point: The minimum point of a function can be defined as the point at which a function takes its lowest value. This point is found by equating the derivative of the function to zero and solving.
For a quadratic equation of the form
f(x)= [tex]ax^{2}+bx+c[/tex]
The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients.Minimum occur when a is positive and it occurs at x=[tex]\frac{-b}{2a}[/tex]
Here cost function quadratic with a= 0.5 , b= -180
So minimum is at
[tex]x=\frac{--180}{2*0.5}[/tex]
=180
So minimum cost is when x=180. So find C(180) to get minimum unit cost .
C(180)=[tex](0.5)*(180)^{2}-180*180+35646[/tex]
=19446
Therefore, the minimum unit of cost is 19446.
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For two acute angles ∠E and ∠F, cos(E)=sin(F). Let m∠E=(8x–12)° and m∠F=(6x–10)°. What is m∠F, in degrees?
Answer:
If cos(E) = sin(F), then we know that m∠E + m∠F = 90 degrees (since E and F are acute angles).
We are given that m∠E = (8x - 12) degrees, and we want to find m∠F.
We can substitute the given value of m∠E into the equation m∠E + m∠F = 90 degrees, and solve for m∠F:
(8x - 12) + m∠F = 90
m∠F = 78 - 8x
So the measure of angle F is 78 - 8x degrees.
We are also given that m∠F = (6x - 10) degrees. So we can substitute this value into the equation we just found:
m∠F = (6x - 10) = 78 - 8x
We can now solve this equation for x:
6x - 10 = 78 - 8x
14x = 88
x = 6
So we know that x = 6.
Now we can substitute this value back into the equation m∠F = (6x - 10) to find the measure of angle F:
m∠F = (6x - 10) = (6 * 6) - 10 = 24 degrees
So the measure of angle F is 24 degrees.
Calculate 324•17 and give your answer in standard form, correct to 3 significant figures
Answer:
6,340
Step-by-step explanation:
Follow the steps in the image.
-Hope this helped
i need help........
One vertex of a triangle is at point P(3, 2) . The triangle is dilated by a scale factor of 4 . The center of dilation is the origin. Which statement is true? Responses The new triangle is both similar to and congruent to the original triangle. The new triangle is both similar to and congruent to the original triangle. The new triangle is congruent to the original triangle but not similar. The new triangle is congruent to the original triangle but not similar. The new triangle is neither similar to nor congruent to the original triangle. The new triangle is neither similar to nor congruent to the original triangle. The new triangle is similar to the original triangle but not congruent.equation y=3x where x is the number of days, and y is the total number of hats made. Julia also knits scarves at the rate shown in the graph. How many more days will it take Julia to knit 24 hats than it will take her to knit 10 scarves?
The correct statement regarding the dilation is given as follows:
The new triangle is similar to the original triangle but not congruent.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The definitions for similar and congruent triangles are given as follows:
Similar triangles: same angle measures.Congruent triangles: same side lengths.For the dilation, due to the multiplication of the side lengths by the scale factor, the side lengths are modified, meaning that the original triangle and the dilated triangle are not congruent.
The angle measures, conversely, remain constant, meaning that the original triangle and the dilated triangle are similar.
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Write a rule for the pattern below. Draw the next figure in the pattern. How many circles will the next figure in the pattern have?
Answer:
15 circles
The pattern is 1,3,6,10....... which is increasing One digit for each pattern
Melissa Josh and Pablo have a total of $66 in their wallet Pablo has three times which Josh has Josh has nine more dollars than Melissa how much do they have in their wallets 
Let M be the amount of money Melissa has, J be the amount of money Josh has, and P be the amount of money Pablo has. We can set up the following equation:
M + J + P = $66
P = 3J
J = M + $9
Substituting the second equation into the third equation, we get:
J = M + $9
3J = 3(M + $9)
3M + 3*$9 = 3J
3M + 3*$9 = 3(M + $9)
3M + 3*$9 = 3M + $27
$27 - $27 = 3M - 3M
0 = 0
Since 0 = 0, the equation holds true for any values of M, J, and P as long as they add up to $66. Therefore, there is not enough information to determine how much money Melissa, Josh, and Pablo have in their wallets.
Please solve 8 I can’t figure this out
Answer:
x = 15
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{MP}{XZ}[/tex] = [tex]\frac{NP}{YZ}[/tex] ( substitute values )
[tex]\frac{x+5}{30}[/tex] = [tex]\frac{4x-10}{75}[/tex] ( cross- multiply )
30(4x - 10) = 75(x + 5) ← distribute parenthesis on both sides
120x - 300 = 75x + 375 ( subtract 75x from both sides )
45x - 300 = 375 ( add 300 to both sides )
45x = 675 ( divide both sides by 45 )
x = 15
Helpp
Nolen was standing near the Washington Monument in Washington DC. The line to go up inside was quite
long. He was bored and decide to have fun and find out how many feet he was away from the door. In the
tourism guide it says the monument is 550 feet tall. He took out his cellphone app and measured an angle
of 75° to the top of the monument. His eye height was 5.7 ft. How far away was he from the door?
Nolen was standing
feet away from the door.
**Round to nearest tenth.
Nolen was 145.8 feet far away from the door.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms.
Given, In Washington, DC, Nolen was standing close to the Washington Monument. There was a sizable line to enter. He decided to have some fun and see how far he was from the entrance because he was bored. The monument is described as being 550 feet tall in the tourism brochure. He pulled out his phone and used the software to measure the monument's top at a 75° angle. He had 5.7 feet of eye height.
The accompanying image will assist us in better comprehending this situation.
Let's make the triangle from the eyes of the Nolen.
We will get the height of the triangle = 544.3feet
and the angle is 75
Thus, the Base of the triangle = height / tan∅
the Base of the triangle = 544.3 / tan 75
the Base of the triangle = 145.844 feet
Therefore, The distance between Nolen and the door of the monument is 145.8 feet.
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Engineers are analyzing the performance of windshield wiper blades. At the end of one swipe, the tip of a blade is at (-5, 7) when represented graphically. What is the sine value of this function?
The sine value of the function will be 7 times square root of 74 over 74.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Firstly, we need to get for the value for r. This will be
r² = (−5)² + 7²
r² = 74
r = square root of 74
After, formulate the equation of a sine. This will be:
sin x = 7/r
sin x = 7/✓74
sin x = (7×✓74)/74
Therefore, the sine value of the function will be sin x = (7×✓74)/74.
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"Your question is incomplete, probably the complete question/missing part is:"
Engineers are analyzing the performance of windshield wiper blades. At the end of one swipe, the tip of a blade is at (−5, 7) when represented graphically. What is the sine value of this function?
Negative 7 square root 74 divided by 74 7 times square root of 74 over 74 square root 74 negative 5 times square root of 74 over 74
The Valley High Marching Band is selling candy bars for a fundraiser. Sierra sold some candy bars. Breanna sold twice as many candy bars as Sierra. Together Sierra and Breanna sold no less than 45 candy bars. Write an inequality to represent this situation. Give three possible solutions for how many candy bars Sierra sold.
Answer:
S ≥ 15
Step-by-step explanation:
Let S be the number of candy bars Sierra sold and B be the number of candy bars Breanna sold.
We know that S + B ≥ 45 and B = 2S.
Substituting the second equation into the first equation, we get:
S + 2S ≥ 45
3S ≥ 45
S ≥ 15
Three possible solutions for how many candy bars Sierra sold are:
Sierra sold 15 candy bars
Sierra sold 16 candy bars
Sierra sold 17 candy bars
15 points, Complete the statement based on the following information.
Can you please re-post a clear image to get the correct and instant answer?
Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 14)(0,14) and (6, 896)(6,896).
The exponential function in the form y=ab^xy=ab^x is [tex]y=14^{(2)}^{x}[/tex]
An exponential function is defined as a mathematical function of the following form:
f(x) = a^x. where x is a variable, and a is a constant and is also called the base of the function.
where a> 0 and a≠ 1.
first, we have to find a and b values, to find a and b values we have to substitute the points into the given equation.
y=ab^xy=ab^x we can rewrite it as y=ab^x
using (0, 14 ), then the equation becomes:
14=ab^0 [b^0 =1 ], then
14 = a × 1
⇒ a = 14
y = 14b^x
Now, use the second point: (6, 896 )
896 = 14 b^6 ( divide both sides by 14 )
64 = b^6 ( take the sixth root of both sides )
[tex]b=\sqrt[6]{64}[/tex]
b=2
substitute a and b values in the equation, and we get:
Hence, y = 14^(2)^x is the exponential function.
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Consider the relation below
Is the relation a function?
Is the relation a one to one function ?
Is the inverse of the relation below itself a function?
The statements that complete the blanks are underlined as follows
Is the relation a function? YesIs the relation a one to one function ? NoIs the inverse of the relation below itself a function? NoIs the relation a function?From the question, we have the following parameters that can be used in our computation:
The graph
The given graph is a quadratic graph
All quadratic graphs are functions
So, the relation is a function
Is the relation a one to one function ?This statement is false,
This is so because one y value points to two different x values, as evident on the graph
Is the inverse of the relation below itself a function?As a general rule, the inverse of a quadratic function is not a function
This means that the inverse of the given relation is not a function
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9
Ten less than the quotient of a number and 4 is 6.
Which equation models the sentence?
©10=8+4=6
Activity Details
OFT
3
6 67
8
The correct equation which models the sentence will be;
⇒ x/4 - 10 = 6
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''Ten less than the quotient of a number and 4 is 6.''
Now,
Since, The algebraic expression is,
''Ten less than the quotient of a number and 4 is 6.''
Let a number = x
Hence, The mathematical expression is,
⇒ x/4 - 10 = 6
Solve for x as;
⇒ x/4 = 10 + 6
⇒ x/4 = 16
⇒ x = 16 × 4
⇒ x = 64
Thus, The value of number = 64.
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evaluate the iterated integral. π 0 1 0 √1 − z2 0 z sin(x) dy dz dx
We can evaluate the given iterated integral to be -πcos2(x) (z - 0 ).
We start with the innermost integral: 0 √1 − z2 0 z sin(x) dy. We can simplify this expression to 0 sin(x) ( √1 − z2 - 0 ). We then integrate this expression with respect to y, yielding sin2(x).
Next, we move on to the middle integral, which is sin2(x) dz. We can easily integrate this expression with respect to z and get sin2(x) (z - 0 ).
Finally, we take the outermost integral, which is sin2(x) (z - 0 ) dx. We can integrate this expression with respect to x and get -cos2(x) (z - 0 ).
Putting everything together, we can evaluate the given iterated integral to be -πcos2(x) (z - 0 ).
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