-4x + 10 = 50 plz help
Answers
\(\huge\text{Hey there!}\)
\(\large\text{-4x + 10 = 50}\)
\(\large\text{SUBTRACT by 10 to BOTH SIDES}\)
\(\large\text{-4x + 10 - 10 = 50 - 10}\)
\(\large\text{Cancel out: 10 - 10 because that gives you 0}\)
\(\large\text{Keep: 50 - 10 because it helps us solve for your x value}\)
\(\large\text{50 - 10 = 40}\)
\(\large\text{New equation: -4x = 40}\)
\(\large\text{DIVIDE by -4 to BOTH SIDES}\)
\(\mathsf{\dfrac{-4x}{4}=\dfrac{40}{-4}}\)
\(\large\text{Cancel out: }\mathsf{\dfrac{-4}{-4}}\large\text{ because that gives you 1}\)
\(\large\text{Keep: }\mathsf{\dfrac{-40}{4}}\large\text{ because it helps find x}\)
\(\mathsf{\dfrac{-40}{4}= -40\div4 \rightarrow \bf -10}\)
\(\boxed{\boxed{\large\text{Answer: \bf x = -10}}}\huge\checkmark\)
\(\text{Good luck on your assignment and enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
Related Questions
The recipe for a signature pizza uses `3` cups of cheese, `\frac{3}{4}` cup of olives, and `1\frac{1}{2}` cups of ham. How much cheese, olives, and ham is needed to make `10` signature pizzas?
Answers
You would need 30 cups of cheese, 7.5 cups of olives, and 15 cups of ham to make 10 signature pizzas.
To determine the amount of cheese, olives, and ham needed to make 10 signature pizzas, we need to multiply the amounts given in the recipe by the number of pizzas.
1. Cheese:
The recipe calls for 3 cups of cheese per pizza. To find the total amount of cheese needed for 10 pizzas, we multiply the amount per pizza by the number of pizzas:
3 cups/pizza * 10 pizzas = 30 cups of cheese
So, you would need 30 cups of cheese to make 10 signature pizzas.
2. Olives:
The recipe requires 3/4 cup of olives per pizza. To find the total amount of olives needed for 10 pizzas, we multiply the amount per pizza by the number of pizzas:
3/4 cup/pizza * 10 pizzas = 7.5 cups of olives
So, you would need 7.5 cups of olives to make 10 signature pizzas.
3. Ham:
The recipe specifies 1 1/2 cups of ham per pizza. To find the total amount of ham needed for 10 pizzas, we multiply the amount per pizza by the number of pizzas:
1 1/2 cups/pizza * 10 pizzas = 15 cups of ham
So, you would need 15 cups of ham to make 10 signature pizzas.
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no jk drtyguhiytr5tyguhigyft fyguhijk
Answers
Answer:
1232
Step-by-step explanation:
13/91= 176/x
1/7=176/x
x= 176*7
x= 1232 bass
Given the polynomial function P(x) = 2x3 – 3x
2 – 23x + 12 (You may use a short bond paper for this part of the
evaluation or use the back page of this paper.)
a. Use the Leading Coefficient Test to determine the graph’s end behavior.
b. Determine the zeros of the function.
c. State whether the graph crosses the x- axis or touches the x- axis and turns around, at each xintercept.
d. Find the y-intercept.
e. Determine number of turning points
f. If necessary, find a few additional points and graph the function.
e. Graph the function.
Answers
The characteristics of the graph depends on the leading coefficient and
the degree of the polynomial.
Responses:
a. From the positive leading polynomial of the odd degree polynomial;
The right end of the graph points upwards, and the left end of the graph will points downwardsb. x = 4, x = 0.5, and x = -3
c. Yes the graph crosses the x-axis
d. The y-intercept is the point y = 12
e. 2 turning points
f. Additional points of the graph are(1, -12), (3, -30) and (5, 72)
g. Please find attached the graph of the function.
Which properties determines the behavior of a polynomial?The given function is; P(x) = 2·x³ - 3·x² - 23·x + 12
a. Given that the leading coefficient is positive and the degree is odd, we have;
The direction in which the right end of the graph will point will be upwards, and the direction in which the left end of the graph will point is downwardb. The zeros of the function are found as follows;
P(x) = 2·x³ - 3·x² - 23·x + 12
At the zeros, 2·x³ - 3·x² - 23·x + 12 = 0
By factorization, using an online tool, we have;
2·x³ - 3·x² - 23·x + 12 = (x - 4)·(2·x² + 5·x - 3) = (x - 4)·(2·x - 1)·(x + 3) = 0
Alternatively, we have;
By trial and error, we have, at x = 4, 2·4³ - 3·4² - 23·4 + 12 = 0
Therefore;
(x - 4) is a factor
(2·x³ - 3·x² - 23·x + 12) ÷ (x - 4) = (2·x² + 5·x - 3)
(2·x² + 5·x - 3) = 2·x² + 6·x - x - 3 = 2·x·(x + 3) - 1(x + 3) = 0
(2·x² + 5·x - 3) = 2·x·(x + 3) - 1(x + 3) = (2·x - 1)·(x + 3)
Which gives;
2·x³ - 3·x² - 23·x + 12 = (x - 4)·(2·x - 1)·(x + 3)
Therefore, the zeros are;
x = 4, x = \(\frac{1}{2}\) = 0.5, and x = -3
c. The maximum number of turning points in a cubic function are 2
Given that the graph has three zeros at x = -3, x = 0.5, and x = 4, the
graph crosses the x-axis to get three zeros from the two turning points.
d. The y-intercept is given by the point at which the graph crosses the y-axis, which is the point, x = 0 which is found as follows;
f(0) = 2·0³ - 3·0² - 23·0 + 12 = 12
The y-intercept is the point on the graph with y = 12Which gives the point (0, 12)
e. The number of turning points of a polynomial of degree n is n - 1
Therefore;
The number of turning point of the polynomial 2·x³ - 3·x² - 23·x + 12 having 3 zeros are 2 turning points.f. Additional points of the graph are;
f(1) = 2·1³ - 3·1² - 23·1 + 12 = -12
f(3) = 2·3³ - 3·3² - 23·3 + 12 = -30
f(5) = 2·5³ - 3·5² - 23·5 + 12 = 72
Therefore;
The points, (1, -12), (3, -30) and (5, 72) are points on the graph
g. Please find attached the graph of the function created with MS Excel
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How do you think the area of the polygon compare to the area of the circle
Answers
Answer:
It is split open, therefore creating a new polygon
Step-by-step explanation:
Given a triangle with coordinates at A(2, 3), B(8, 3), and
C(5, 6) classify the triangle as obtuse/acute/right and
scalene/isosceles/equilateral.
Use the sketch to show your thinking.
(Select all that apply.
Right
Acute
Obtuse
Isoceles
Equilateral
Answers
The triangle is Isosceles and Acute.
From the given data, the coordinates of the three points of the triangle are, A(2, 3), B(8, 3), and C(5, 6).
applying the distance formula, D = √((x2-x1)²+(y2-y1)²) the distance AC and BC are obtained as 3√2 and the distance AB as 2√3.
From this, it can be concluded that AC=BC≠AB.
thus since two of the sides, AC and BC are equal and the third side AB is not equal to AC and BC hence the given triangle is an isosceles triangle.
To check whether the given triangle is right, acute.
A right triangle is a triangle with one of its angles equal to 90 degrees.
An acute triangle is a triangle with all three of its angles less than 90 degrees.
An obtuse triangle is a triangle with at least one of its angles greater than 90 degrees.
To check whether the given triangle is right, acute, or obtuse we use the law of cosines.
To find the angle of a triangle given 3 of its sides, let the angle between the sides AB and AC be A then,
cos(A) = (AC² + AB² − BC²)÷(2×AB×AC).
cos(A) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6
\(cos^{-1}\)(2÷√6) = 39.182.
Let the angle between the sides AB and BC be B then,
cos(B) = (BC² + AB² − AC²)÷(2×AB×BC).
cos(B) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6
\(cos^{-1}\)(2÷√6) = 39.182.
Let the angle between the sides AC and BC be then,
cos(C) = (AC² + BC² − AB²)÷(2×AC×BC).
cos(C) = (3√2² + 3√2² - 2√3²)÷(2×3√2×3√2) =2÷3
\(cos^{-1}\)(2÷3) = 53.544.
Since all the angles A, B, and C is less than 90 degrees the triangle is acute.
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Let theta be an acute angle of a right triangle. Find the values of the other five trigonometric functions of theta.
Answers
The exact values of the remaining trigonometric functions are listed below:
Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4
Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11
Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3
Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2
How to find the exact values of trigonometric functions
In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:
sin θ = y / √(x² + y²)
cos θ = x / √(x² + y²)
tan θ = y / x
cot θ = x / y
sec θ = √(x² + y²) / x
csc θ = √(x² + y²) / y
Now we proceed to determine the exact values of the trigonometric functions:
Case 3: y = 4, √(x² + y²) = 5
x = √(5² - 4²)
x = 3
cos θ = 3 / 5
tan θ = 4 / 3
cot θ = 3 / 4
sec θ = 5 / 3
csc θ = 5 / 4
Case 4: x = 5, √(x² + y²) = 6
y = √(6² - 5²)
y = √11
sin θ = √11 / 6
tan θ = √11 / 5
cot θ = 5√11 / 5
sec θ = 6 / 5
csc θ = 6√11 / 11
Case 5: x = 8, √(x² + y²) = √73
y = √(73 - 8²)
y = 3
cos θ = 8√73 / 73
sin θ = 3√73 / 73
tan θ = 3 / 8
cot θ = 8 / 3
csc θ = √73 / 3
Case 6: x = √3, y = 1
sin θ = 1 / 2
cos θ = √3 / 2
tan θ = √3 / 3
sec θ = 2√3 / 3
csc θ = 2
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PLEASE help me, im really struggling on this.
Answers
The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let x represent the number of pounds of bananas sold and y represent the grapes sold, hence:
x + y = 52 (1)
Also:
x + 2.25y = 72 (2)
The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72
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A marriage counselor is interested in the proportion of clients she counsels who stay married. Define the following in terms of the study. Give examples where appropriate. Part (a) The population A. The population is a group of clients of this counselor. B. The population is all of the clients of this counselor. C. The population is all of the clients of this counselor who stay married. D. The population is all couples in marriage counseling.
Answers
Depending on how many couples in marriage counseling exist outside of this counselor's practice.
A. The population is a group of clients of this counselor - this would include all of the clients of the counselor, regardless of whether or not they stayed married.
B. The population is all of the clients of this counselor - this would include all of the clients of the counselor, regardless of whether or not they stayed married.
C. The population is all of the clients of this counselor who stay married - this would include only the clients of the counselor who stayed married.
D. The population is all couples in marriage counseling - this would include all couples, regardless of whether they were clients of this counselor or not.
For example, if the counselor had 100 clients and 50 of them stayed married, the population of part (a) would be 100, the population of part (b) would be 100, the population of part (c) would be 50, and the population of part (d) could be larger or smaller than the other parts, depending on how many couples in marriage counseling exist outside of this counselor's practice.
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An automaker has introduced a new midsize model and wishes to estimate the mean EPA combined city and highway mileage, u. that would be obtained by all cars of this type. In order to estimate the u, the automaker has conducted EPA mileage tests on a random sample of 35 of its new midsize cars and has obtained the sample of mileages. 71 = 35 x = 24 population = 1.2 Calculate the 70% confidence interval. (round to the second decimal point) Lower bound of 70% confidence interval= Upper bound of 70% confidence interval=
Answers
To estimate the mean EPA combined city and highway mileage, the automaker conducted EPA mileage tests on a random sample of 35 midsize cars. The sample mean is 24, and the population standard deviation is 1.2. The task is to calculate the 70% confidence interval for the population mean.
To calculate the confidence interval, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))
First, we need to determine the critical value associated with a 70% confidence level. The critical value can be found using a standard normal distribution or a t-distribution, depending on the sample size and whether the population standard deviation is known.
Since the sample size is relatively large (n = 35), we can use the standard normal distribution. The critical value for a 70% confidence level corresponds to a z-score of ±1.036.
Next, we calculate the margin of error:
Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size)) = 1.036 * (1.2 / √35) ≈ 0.380
Finally, we can calculate the lower and upper bounds of the confidence interval:
Lower Bound = Sample Mean - Margin of Error = 24 - 0.380 ≈ 23.62
Upper Bound = Sample Mean + Margin of Error = 24 + 0.380 ≈ 24.38
Therefore, the 70% confidence interval for the mean EPA combined city and highway mileage is approximately 23.62 to 24.38.
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PLSSSS HELP!!!!
ILL MARK BRAINLIEST!!!!
The dashed triangle is a dilation image of the solid triangle with the center at the origin. Is the dilation an
enlargement or a reduction? Find the scale factor of the dilation.
Answers
Answer:
-2/-6 = 1/3 = 3
Step-by-step explanation:
The solid triangle has the points A(-6,0) B(6,5) and C(6,-6).
The dashed triangle has the points A1(-2,0) B1(2,1) and C1(2,-2)
The dilation of the dashed triangle is an enlargement because the scale factor is a whole number which is: 3.
Recall:
Dilation reduces or enlarges a figure/shapeThe image of a dilation is the original image before reduction or enlargement occurred.The scale copy is the new image formed after reduction or enlargement as the case may be.Scale factor = any side length of the new image / corresponding side length of the old imageIf the scale factor is a fraction, the dilation it's a reduction. If the scale factor is a whole number, the dilation is an enlargement.Thus:
Find the distance between the points (2, -2) and (0, -2) for the dashed triangle.
Distance between (2, -2) and (0, -2) = 2 unitsFind the corresponding distance for the solid triangle using points (6, -6) and (0, -6):
Distance between (6, -6) and (0, -6) = 6 unitsScale factor = \(\mathbf{\frac{6}{2} = 3}\)
The scale factor is a whole number, so, the dilation is an enlargement.
In summary, the dilation of the dashed triangle is an enlargement because the scale factor is a whole number which is: 3.
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Write a story about temperatures that this expression could represent:
27 + (-11)
Answers
Answer:
Liliana has 27 candies from her teacher. But her mother didn't want her to eat too much candy, so she took 11 of Liliana's candies.
Step-by-step explanation:
Hope it help, and please give me Brainlest!
If sinA=root3 cosA,find the value of sinA and cosA
Answers
The value trigonometric rations of sinA = √5/2 and cosA = 1/2.
Given that,
SinA = √3 cosA
Divide both side by cos A
⇒ SinA/cosA = √3
Since we know that,
Tan A = SinA/cosA
Therefore,
SinA/cosA = √3
⇒ tan A = √3
Squaring both sides, we get
⇒ tan² A = 3
⇒ sec²A - 1 = 3
⇒ sec²A = 4
Taking square root both sides, we get
⇒ secA = 2
⇒ 1/cosA = 2
⇒ cosA = 1/2
Now again squaring both sides we get
⇒ cos²A = 1/4
⇒ sin²A - 1 = 1/4
⇒ sin²A = 1/4 + 1
⇒ sin²A = 5/4
Taking square root both sides, we get
⇒ sinA = √5/2
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I will give a brainliest
b) Find the equation of the trend line (line of best fit). Show your work. (2 points)
Answers
Answer:
Step 1:
Draw a graph - Put Customers on the x-axis and Tips on the y-axis
Equation of a line = mx + c
Then look for where the line crosses the x-axis (this is "c")
Choose two points and find the gradient using this formula:
Change in y/change in x
The number you just got is your "m"
Put it all together and you have y = Mx + C
Hope this helps please mark as brainliest :P
Step-by-step explanation:
Answer:
y = 1.86211x + 4.42878Step-by-step explanation:
Given data in the table added to scatter plot and line of best fit calculated using a graphing calculator.
See the attached graph.
The line of best fit is:
y = 1.86211x + 4.42878
Linda made a block of scented soap which weighed 1/2 of a pound. She divided the soap into 3 equal pieces. How much did each piece of soap weigh?
Answers
Answer:
Each piece of soap weighs about 0.16 pounds.
Step-by-step explanation:
We Know
Linda made a block of scented soap, which weighed 1/2 of a pound.
1/2 = 0.5
She divided the soap into 3 equal pieces.
How much did each piece of soap weigh?
We Take
0.5 ÷ 3 ≈ 0.16 pound
So, each piece of soap weighs about 0.16 pounds.
A SCUBA diver went down to 550 feet below sea level. The entire descent took 10 minutes. What is his
average number of feet each minute? Think about which number is negative and why, then write an integer
equation and solve
Answers
Okay so 550/10 is 55. So he went down 55 feet per minute. Or in otherwords, -55 (negative 55). Its negative because your going down.
Heart if it did help!
Answer:
Step-by-step explanation:
Average number of feet = Entire descent ÷ total time taken
= 550 ÷ 10 = 55 per minute
= -55
Negative sign denotes he is descending.
The picture up above
Answers
Answer:
its being reflected over the y-axis
Step-by-step explanation:
What's the value of
\( \sqrt{21 \times 21 \times 2 \times 2} \)
Answers
Answer:
42
Step-by-step explanation:
as there two equal numbers of both 21 and 2 then the outcome will be just 21×2=42
Answer:
Hey!
Your answer after multiplying would be\(\sqrt{1764}\) which equals 42.So, the answer is:-42!Hope this helps you!
:)
PLEASE HELP ME ASAP !! Manny has $12,000 and is
saving for a used car that
costs $15,000. He is able to
save $300.00 per month
toward his car. Write and
solve an inequality for this
situation if m represents the
number of months that
Manny must save to buy the car.
Answers
Answer:
12,000+300m >= 15,000
300m >= 3,000
m>= 10
Step-by-step explanation:
This is basically the inequality that represents the problem and is solved algebratically.
Answer:
Inequality: 12,000 + 300m > 15,000
m = 10
It will take Manny 10 months to get the money for his car.
Step-by-step explanation:
The inequality is 12,000 + 300m > 15,000 ($12,000 + 300 dollars per month > $15,000)
Here is an image of how to solve the inequality:
please help!
Find x so that a || b
Answers
For number 2 do the same thing as number 1
96 + (6x -30) = 180 degrees
for number 3: (6x - 30) = 84
for number 4: (7x + 5) = 33 degrees
Find AC
Round to the nearest tenth.
BC=5
B=108°
A=31°
Answers
B/sin(b)=a/sin(a)
b=a sin(b)/sin(a)
B=5 sin(108)/sin(31)
b=9.2
The total area of the two triangles is _____ square inches.Numerical Answers Expected!Answer for Blank 1:
Answers
The total area of the two triangles is 28 square inches.
Step 1: Calculate the area of the first triangle.
The first triangle is a right triangle with a base of 4 inches and a height of 3 inches.
Area of a triangle = (1/2) * Base * Height
Area of the first triangle = (1/2) * 4 * 3 = 6 square inches.
Step 2: Calculate the area of the second triangle.
The second triangle is an isosceles triangle with a base of 4 inches and a height of 4 inches.
Area of a triangle = (1/2) * Base * Height
Area of the second triangle = (1/2) * 4 * 4 = 8 square inches.
Step 3: Add the areas of the two triangles.
Total area = 6 + 8 = 14 square inches.
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2. Given that (ab - c) + d = e
Solve for a
Answers
Ab=e-d+c
A=e-d+c/b
Write the equation in point-slope form of a line that passes through the point (-13,71) and has the slope of m = -11 / 17
Answers
Answer:
y - 71 = -11/17 (x +13)
Step-by-step explanation:
The formula for point slope form is: y - y1 = m (x - x1). You plug in the x and y coordinate into x1 and y1 of the equation, and plug in the slope for m.
suppose f is a function with f ( 20 ) = 17 and f ' ( 20 ) = 1 . using the local linearization l ( x ) at x = 20 , estimate the following values of f .
Answers
By using the local linearization at x = 20, we can estimate the values of f(21) and f(19) to be 18 and 16, respectively.
To estimate the values of f using local linearization at x = 20, we'll use the formula:
l(x) = f(a) + f'(a) * (x - a)
Where l(x) is the local linearization function, f(a) is the value of the function at the point a, f'(a) is the derivative of the function at the point a, and (x - a) is the difference between the given x and the point a.
Using the given information, where a = 20, f(a) = 17, and f'(a) = 1, we can estimate the following values of f:
To estimate f(21):
l(21) = f(20) + f'(20) * (21 - 20)
= 17 + 1 * (21 - 20)
= 17 + 1
= 18
So, the estimated value of f(21) is 18.
To estimate f(19):
l(19) = f(20) + f'(20) * (19 - 20)
= 17 + 1 * (19 - 20)
= 17 - 1
= 16
So, the estimated value of f(19) is 16.
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Consider the following rational equation: + a) List the set of non-permissible values of the variable x. b) Solve the equation and write a solution set. 3x -2 x+1 x+2 x+3(x+1)(x+2)(x+3) c) Are all the potential solutions valid?
Answers
a) To determine the set of non-permissible values of x, we need to identify any values of x that would make the denominator zero. In this case, the denominator is (x + 1)(x + 2)(x + 3). Therefore, the non-permissible values of x occur when the denominator is equal to zero.
Setting the denominator equal to zero:
(x + 1)(x + 2)(x + 3) = 0
From this equation, we can see that the non-permissible values of x are -1, -2, and -3, since they would make the denominator zero.
Therefore, the set of non-permissible values of x is {-1, -2, -3}.
b) To solve the equation, we set the rational expression equal to zero:
3x - 2 = 0
Solving for x:
3x = 2
x = 2/3
Therefore, the solution to the equation is x = 2/3.
The solution set is {2/3}.
c) Since the non-permissible values of x are -1, -2, and -3, we need to check if any of these values are solutions to the equation.
For x = -1:
3(-1) - 2 = -3 - 2 = -5 ≠ 0
For x = -2:
3(-2) - 2 = -6 - 2 = -8 ≠ 0
For x = -3:
3(-3) - 2 = -9 - 2 = -11 ≠ 0
Since none of the non-permissible values of x result in a zero denominator, all the potential solutions in this case are valid.
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x +3–3=. x +3 0=. x +3+3
Answers
The solution of the equation based on the information given is x = 0.
How to calculate the equationCombine the like terms on both sides of the equation.
X + 3 - 3 = 2x + 3 => X = 2x + 3 - 3
Simplify the expression on the right side by combining the like terms.
X = 2x
Subtract "2x" from both sides of the equation to isolate the variable "x" on one side.
X - 2x = 0
Simplify the expression on the left side by combining the like terms.
-x = 0
x = 0
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X +3–3= 2x +3
A teaspoon of salt has a mass of 6 grams. What is its mass in milligrams?0) 600 milligrams60 milligrams0) 6.000 milligrams60.000 milligrams Ten points if you get this pls
Answers
1 milligram = 0.001 gram
x milligrams = 6 grams
By crossmultiplying, it becomes
0.001 * x = 6 * 1
0.001x = 6
x = 6/0.001
x = 6000
The mass in milligrams is 6000 milligrams
There are 40 tudent in the math club and 35 percent of them are ixth grader how many tudent in the math club are not ixth grader
Answers
Answer: 14
Step-by-step explanation: just trust me i can do this very well :)
Directions:
Sarah is going to the movies and she has $10 to spend on snacks. Smoothies are $3
and candy bars are $1 each. She will be spending all of the $10.
Budget: $10
Smoothies: $3
Candy bars: $1
Draw a line graph that represents the budget constraints and possible purchasing
options that Sarah has with her $10.
Answers
The attached graph represents the graph of the equation 3x + y = 10
How to determine the line graph?The given parameters are:
Budget: $10Smoothies: $3Candy bars: $1Represent the number of smoothies with x and the number of candy bears with y.
So, the equation is:
3x + 1y = 10
This gives
3x + y = 10
Next, we plot the graph of the above equation
See attachment for the graph of 3x + y = 10
Read more about linear equations at:
https://brainly.com/question/14323743
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The line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
Sarah is going to the movies, and she has $10 to spend on snacks. Smoothies are $3 and candy bars are $1 each. She will be spending all of the $10.
Let's suppose the number of smoothies is x and the number of candy bars is y:
Then, we can frame a linear equation in one variable:
3x + y = 10
Drawing the above the line on the coordinate plane:
Thus, the line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ1
Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval (0,2x)Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution."- sec(-x) = 5sec(x) + 1
Answers
For this problem, we are provided with the following expression:
\(-\sec (-x)=5\sec (x)+1\)We need to solve it for x over the interval [0, 2pi).
We have:
\(\sec (-x)=\sec (x)\)Therefore, we can replace the left side of the equation as shown:
\(\begin{gathered} -\sec (x)=5\sec (x)+1 \\ \end{gathered}\)Now we need to isolate the sec(x) on the left side.
\(\begin{gathered} -5\sec (x)-\sec (x)=1 \\ -6\sec (x)=1 \\ \sec (x)=-\frac{1}{6} \\ \frac{1}{\cos (x)}=-\frac{1}{6} \\ \cos (x)=-6 \end{gathered}\)Now we can apply the arc cosine to determine the value of x.
\(\begin{gathered} \arccos (\cos (x))=\arccos (-6) \\ x=\arccos (-6) \end{gathered}\)There are no real values for x that have a cosine equal to -6. Therefore, this problem has no real solution.