The inequality is represented by y < 5/3(x+1)
Use the information about the straight line and find the equation of the line.
Given coordinates (-3,-4) and (0,1), we can find the slope
Slope,
Change in y = y2 – y1 = 1-(-4) = 5
Change in x = x2 – x1 = 0-(-3) = 3
Therefore, Slope (m) = Change in y / Change in x = 5/3
Equation of line using m = 5/3 and points (0,1) and (x, y) in form of y = mx + c
Y – 1/ X – 0 =5/3
3(Y-1) = 5(X)
3Y -3 = 5X
3Y = 5X + 3
Y = 5X + 3/3
Y = 5/3(X + 1)
To find the inequality take a point in the shaded region and check it in the above equation.
Given Options
a. y < Five-thirds x – 2
b. y < Negative five-thirds x + 1
c. y > Five-thirds x + 2
d. y > Negative five-thirds x + 2
Let’s take points (-3,-4) for verification
Option a: y < 5/3 (x-2)
-4 < 5/3(-3-2)
--4 < -3.33
-4 is less than -3.33
Thus option a is in the shaded region
Option b: y < -5/3 (x+1)
-4 < -5/3(-3+1)
--4 < 3.33
-4 is less than 3.33
Thus option a is in the shaded region
Option c: y > 5/3 (x+2)
-4 > 5/3(-3+2)
--4 > -1.67
-4 is NOT GREATER than -1.67
Thus option c is NOT in the shaded region
Option d: y > -5/3 (x+2)
-4 > - 5/3(-3+2)
--4 > 1.67
-4 is NOT GREATER than 1.67
Thus option d is NOT in the shaded region
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Answer:
y > Five-thirdsx + 2
Step-by-step explanation:
The square of the difference between a number and 7 is 81 . Find the number(s).
Answer:
16 or -2
Step-by-step explanation:
Let the number be x.
Difference between the number and 7
= x -7 or 7-x
The square of the difference between x and 7
= (x -7)²
(x -7)²= 81
Square root both sides:
[tex]x - 7= \pm \sqrt{81} [/tex]
[tex]x - 7 = \pm9[/tex]
Add 7 to both sides:
[tex]x = 7\pm9[/tex]
x= 16 or x= -2
Thus, the number could either be 16 or -2.
Solve the linear programming problem.
Minimize and maximize
P = 10x + 5y
Subject to
2x+3y 230
2x+y ≤ 26
-2x+3y ≤ 30
x, y 20
The minimized value is 50 and the maximized value is 130
How to minimize and maximize the function?The objective function is:
P = 10x + 5y
Subject to
2x+3y ≤30
2x+y ≤ 26
-2x+3y ≤ 30
x, y >0
Next, we plot the graph of the constraints (see attachment)
From the graph, the vertices of the feasible regions are:
(0, 10),(12, 2) and (6,14)
Substitute these values in P = 10x + 5y
P = 10(0) + 5(10) = 50
P = 10(12) + 5(2) = 130
P = 10(6) + 5(14) = 130
Hence, the minimized value is 50 and the maximized value is 130
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PLEASE HELP
True or false
False
Step-by-step explanation:
Answer:
true.
Step-by-step explanation:
[tex]b^t=\frac{n}{a}; \ = > \ t=log_b\frac{n}{a}; \ = > \ t=\frac{log\frac{n}{a}}{logb}.[/tex]
HELP ASAP!!!
At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply. x = -8 x = 4 x = 3 x = -3 x = 8 x = -4
Answer:
A,E
Step-by-step explanation:
Answer:
x = 3
x = -8
Step-by-step explanation:
Write and solve an inequality that means a number plus four is greater than or equal to twelve.
Answer:
[tex]x+4\geq 12[/tex]
Step-by-step explanation:
x - a number
x+4 - a number plus 4
x+4[tex]\geq[/tex] - a number plus 4 is greater than or equal to
x+4[tex]\geq[/tex]12 - a number plus 4 is greater than or equal to twelve
Answer:
Inequality: x + 4 ≥ 12
Solution: x ≥ 8
Step-by-step explanation:
Plus: "+" → to add something to something else
Greater than or equal to: "≥" → the expression on the left side of the inequality sign is greater than the expression on the right side of the sign.
Let x be the unknown number.
A number plus four is greater than or equal to twelve:
x + 4 ≥ 12
To solve the found inequality, subtract 4 from both sides:
⇒ x + 4 - 4 ≥ 12 - 4
⇒ x ≥ 8
Therefore, the solution to the inequality is x ≥ 8. The unknown number x can be any real number equal to or greater than 8.
Jim takes a piece of plywood that is 45 centimeters long and uses a table saw to make a 53-
centimeter cut from corner to opposite corner. What was the width of the piece of plywood?
centimeters
Answer:
28 cm
Step-by-step explanation:
The corner to corner cut is a hypotenuse. We know one leg, 45cm. So use Pythagorean theorem to solve for the other leg. See image.
On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the timeframe allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The conditions for inference are met. What are the appropriate test statistic and P-value? Find the t-table here. t = –1.85; the P-value is 0.9678. t = –1.85; the P-value is between 0.025 and 0.05. t = 1.85; the P-value is 0.9678. t = 1.85; the P-value is between 0.025 and 0.05.
Using the t-distribution, the correct option regarding the test statistic and the p-value is given as follows:
t = –1.85; the P-value is between 0.025 and 0.05.
What are the hypothesis tested?
The null hypothesis is:
[tex]H_0: \mu = 25[/tex]
The alternative hypothesis is:
[tex]H_1: \mu < 25[/tex]
What are the test statistic and the p-value?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In this problem, the values of the parameters are given as follows:
[tex]\overline{x} = 23.5, \mu = 25, s = 4.8, n = 35[/tex]
Hence the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{23.5 - 25}{\frac{4.8}{\sqrt{35}}}[/tex]
t = -1.85.
Using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.
Hence the correct statement is:
t = –1.85; the P-value is between 0.025 and 0.05.
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50/22 as a decimal rounded to the nearest hundreth
Step-by-step explanation:
the answer is 2.27. hope this helps
Factor the following expression. x² - 10x +9 2 Factor the following expression . x² - 10x +9 2
Answer:
x² - 10x + 9 = (x-9)(x-1)
the factored expression would be (x-9)(x-1)
2, 9, 11, 18, 20, 27,
the next 3 numbers.
Answer:
29, 36, 38
Step-by-step explanation:
The pattern is add 7 then 2, then 7, then 2, then 7, then 2. You should get the hang of it. All you have to do is just do the same thing for the next three numbers.
If x=3 y=4 z=6 then 4x+8yz+3y equals
Answer:
216
Step-by-step explanation:
4x+8yz+3y
Let x=3 y=4 z=6
Substitute the values into the expression
4(3)+8(4)(6)+3(4)
Multiply first
12+192+12
Then add
216
Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13%, percent monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck?
Thank you for asking this question. Here is your answer:
We will consider the price of the truck to be $x
And the amount of tax in the percentage would be 13%
13/100
= $ 0.13x (this is the actual amount of the tax)
Now we will calculate the total price of the truck =
$x + $ 0.13x
= $ x(1 + 0.13)
If there is any confusion please leave a comment below.
Given the coordinate T(8, -4), find the location of T after a dilation using a scale factor of 0.4.
The new coordinate will be T'(3.2 , -1.6) .
What is the meaning of Dilation ?Dilation is the transformation that changes the size of the object without changing its shape .
If a coordinate point is (x,y) and a dilation of scale factor f is applied then the new coordinates will be (fx ,fy)
The coordinate given in the question is T(8, -4)
The scale factor is 0.4
The new coordinate is
T'( 0.4 * 8 , 0.4 * (-4))
T'(3.2 , -1.6)
Therefore the new coordinate will be T'(3.2 , -1.6)
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3y + 9x = 21 Graph A On a coordinate plane, a line goes through (negative 3, negative 2) and (0, 7). Graph B On a coordinate plane, a line goes through (0, negative 7) and (3, 2). Graph C On a coordinate plane, a line goes through (0, 7) and (3, negative 2). Graph D On a coordinate plane, a line goes through (negative 3, 2) and (0, negative 7). a. Graph A c. Graph C b. Graph B d. Graph D Please select the best answer from the choices provided
Answer:
Graph C
Step-by-step explanation:
Graph A (-3, -2) (0, 7)
3(7) + 9(0) = 21
21 = 21 ✓
3(-2) + 9(-3) = 21
-6 - 27 = 21
-33 = 21 ✖
Graph B (0, -7) (3,2)
We know from above that (0, 7) is a point on the line 3y + 9x = 21, therefore point (0, -7) cannot be on that line.
3(2) + 9(3) = 21
6 + 27 = 21
33 = 21 ✖
Graph C (0, 7) (3, -2)
We know from above that (0, 7) is a solution.
3(-2) + 9(3) = 21
-6 + 27 = 21
21 = 21 ✓
Since both points on graph C is a solution to the equation of the line given, it is the answer (looking at graph D is not necessary unless you want to double check your answer).
sin theta = 1/4, tan theta > 0
Find cos theta/2
Answer:
Step-by-step explanation:
sin θ=1/4,tan θ>0
so θ lies in first quadrant.
cos θ=√(1-sin²θ)=√(1-(1/4)²)=√(1-1/16)=√(15/16)=√15/4
[tex]2cos^2 \frac{\theta}{2} =1+cos \theta[/tex]
[tex]2~cos^2\frac{\theta}{2} =1+\frac{\sqrt{15} }{4} =\frac{4+\sqrt{15}}{4} \\cos~\frac{\theta}{2} =\sqrt{\frac{4+\sqrt{15} }{4 \times 2} } \\cos\frac{\theta}{2} =\frac{\sqrt{8+2\sqrt{15}} }{4}[/tex]
5
The recursive formula for a geometric sequence is given below. What is the third term in the sequence?
f(1) = 2
f(n) = 3f(n − 1)
-
OA. 18
OB. 54
OC. 162
OD. 12
Reset
Submit
[tex]\Large{ \boxed{ \tt{ \blue{A}}}}\Large{ \boxed{ \tt{ \pink{N}}}}\Large{ \boxed{ \tt{ \green{S}}}}\Large{ \boxed{ \tt{ \purple{W}}}}\Large{ \boxed{ \tt{ \red{E}}}}\Large{ \boxed{ \tt{ \pink{R}}}}[/tex]
[tex] \: \: [/tex]
A. 18[tex] \: \: [/tex]
[tex]\Large{ \boxed{ \tt{ \blue{S}}}}\Large{ \boxed{ \tt{ \pink{O}}}}\Large{ \boxed{ \tt{ \green{L}}}}\Large{ \boxed{ \tt{ \purple{U}}}}\Large{ \boxed{ \tt{ \red{T}}}}\Large{ \boxed{ \tt{ \pink{I}}}}\Large{ \boxed{ \tt{ \blue{O}}}}\Large{ \boxed{ \tt{ \pink{N}}}}[/tex]
[tex] \: \: [/tex]
[tex] \mathtt{f(1) = 2}[/tex][tex] \tt{f(2) \: = \: 3f \: (1) \: = \: 3(2) \: = \: 6}[/tex][tex] \tt{f(3) \: = \: 3f(2) \: = \: 3(6) \: = \: 18}[/tex][tex]\color{pink}─────────────────────────────────────[/tex]
keep learning
Jacob spends 13/4 dollars to paint 9/3 square feet. Find the cost to paint a
square feet per dollar.
The cost to paint a is 12/13 square feet per dollar.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Jacob spends 13/4 dollars to paint 9/3 square feet.
[tex]\dfrac{\dfrac{9}{3}}{ \dfrac{ 13}{4}} = \dfrac{9}{3} \times \dfrac{ 4}{13}\\\\= \dfrac{ 36}{39}\\\\= \dfrac{ 12}{13}[/tex]
Hence, the cost to paint a is 12/13 square feet per dollar.
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again help me pease
Answer:
See below ~
Step-by-step explanation:
1) a) 50 km / 2 h
⇒ 25 km/h
b) 540 kg / 3 days
⇒ 180 kg/day
c) 125 m / 5 min.
⇒ 25 m/min.
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate…
a) 50km/2h
=> 25 kilometers per hour
b) 540kg/3d
=> 180 kilogram per day
c) 125m/5min
=> 25 meter per minute
2) Sarah takes a small business loan for
$25,000. The term for repayment is 60
months and the interest rate is 5.75%.
formula,
Use the loan amortization
what is the estimated monthly
payment?
Using it's formula, it is found that the estimate monthly payment is of $480.42.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.The parameters are given as follows:
P = 25000, n = 60, r = 0.0575.
Hence:
r/12 = 0.0575/12 = 0.00479167.
Hence the payment will be of:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 25000(0.00479167)\frac{(1+0.00479167)^{60}}{(1+0.00479167)^{60}-1}[/tex]
A = 480.42.
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The system of equations y = one-fourth x minus 1 and y = negative one-half x minus one-fourth is shown on the graph below.
On a coordinate plane, 2 lines intersect at (1, negative three-fourths).
The solution of the system of equations is (1, -3/4)
How to solve the system of equations?
Here we have the system of equations:
y = (1/4)*x - 1
y = -(1/2)*x - 1/4
To solve it, we use the fact that the variable "y" is the same in both equations, then we can write:
(1/4)*x - 1 = -(1/2)*x - 1/4
Now we can solve that for x:
(1/4)*x - 1 = -(1/2)*x - 1/4
(1/4)*x + (1/2)*x = 1 - 1/4
(1/4)*x + (2/4)*x = 1 - 1/4
(3/4)*x = 3/4
x = 1
To get the y-value of the solution, we just evaluate x = 1 in any of the two given lines, using the first one:
y = (1/4)*(1) - 1 = -3/4
So the solution is (1, -3/4)
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HELP! ASAP!
A box without a top is to be made from a rectangular piece of cardboard, with dimensions 4 in. by 8 in., by cutting out square corners with side length x and folding up the sides.
(a) Write an equation for the volume V of the box in terms of x.
(b) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Step-by-step explanation:
Part A:
So the height is going to be x when you fold the sides up. So that's one part of the volume but for the width it was going to be 4 but since two corners were cut out with the length x the new width is going to be (4-2x). The same thing applies for the length which should be 8 inches but since two corners were removed with the length x it's now (8-2x)
v = x(4-2x)(8-2x)
Part B:
The volume can be graphed although there must be a domain restriction since the height, width, or length cannot be negative. So let's look at each part of the equation
so for the x in front it must be greater than 0 to make sense
for the (4-2x), the x must be less than 2 or else the width is negative.
for the (8-2x) the x must be less than 4 or else the length is negative
so the domain is going to be restricted to 0 < x < 2 so all the dimensions are greater than 0
By using a graphing calculator you can see the maximum of the given equation with the domain restrictions is 0.845 which gives a volume of 12.317
3. The function represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period.
(a) During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
(b) Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
(c) When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.
Answer:
a
Step-by-step explanation:
Hassan put 437.2 grams of brown sugar into a canister. Then he carefully measured out 430.43 grams of it to use in a recipe for cookies. How much brown sugar is left in the canister?
Find the product write your answer in exponential form 7^-1•7^-7
Answer:
1/5764801
Step-by-step explanation:
7^-1 × 7^-7
= 1/7(7^-7)
= 1/7(1/823543)
= 1/5764801
Gianna is constructing a circle that passes through all three vertices of the triangle shown.
Where will the center of the circle be located?
OA. on a vertex of the triangle
OB. inside the triangle
OC. on a side of the triangle
OD. outside the triangle
B
Based on the definition of a circumcircle, the center of the circle as shown in the image below is located: B. inside the triangle.
What is a Circumcircle?A circumcircle, as shown in the diagram attached below, is a circle that is drawn so that all the vertices of a triangle touches the circumference of the circle.
Thus, as shown in the image attached below, the center of the circle is located: B. inside the triangle.
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Answer: OUTSIDE THE TRIANGLE
Step-by-step explanation: ANSWER ON EDMENTUM/PUTO
What is the range of the function g(x) = –3sec(2x + 4) – 1?
(–∞, –2] ∪ [0, ∞)
(–∞, –4] ∪ [0, ∞)
(–∞, –4] ∪ [2, ∞)
(–∞, –5] ∪ [1, ∞)
The range of the function g(x) will be (–∞, –4] ∪ [2, ∞). Option C is correct.
What is the difference between domain and range?The domain denotes all potential x values, while the range denotes all possible y values.
When we plot the graph of the given function we will get the maximum and the minimum value till we get the function plot. The difference in the value of those coordinates is the range of the function.
The range of the function g(x) will be (–∞, –4] ∪ [2, ∞).
Hence option C is correct.
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The vertex of the graph of y = -4(x + 3)² + 2 is
DONE
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The vertex of the parabola will lie at (-3,2).
What is the Equation of a parabola?A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in the form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Comparing the given equation with the equation of a parabola, we will get,
y = a(x -h)² + k
y = -4(x+3)² + 2
Hence, the vertex of the parabola will lie at (-3,2).
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Question 13 of 50
Choose two statements (the original conditional statement and its converse)
that could form the biconditional "The object weighs a ton if and only if the
scale reads 2000 pounds."
A. If the object weighs a ton, then the scale reads 2000 pounds.
B. If the scale does not read 2000 pounds, then the object does not
weigh 2000 pounds.
C. If the scale reads 2000 pounds, then the object weighs a ton.
D. The scale reads 2000 pounds if and only if the object weighs a
ton.
it can be more then one answer too
Conditional statements are ones that begin with a hypothesis and end with a conclusion. The correct option is A and C.
What are conditional Statements?Conditional statements are ones that begin with a hypothesis and end with a conclusion. It is sometimes referred to as a "If-then" statement. If the hypothesis is correct but the conclusion is incorrect, the conditional statement is incorrect.
The two statements that among which one is original and the other one is its converse is If the object weighs a ton, then the scale reads 2000 pounds, and If the scale reads 2000 pounds, then the object weighs a ton.
Hence, the correct option is A and C.
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The graph of a function is shown on the coordinate plane below.
Between which two values of x is the function nonlinear and increasing?
A -5 and -3
B -3 and 1
C 1 and 4
D 4 and 6
The answer to this question is choice B
What are the solutions to the quadratic equation below?
x²-2x-168 =0
Answer:
x= 14, –12
Step-by-step explanation:
The given question might make you believe that it's difficult due to it's frightening digit (168) but in fact in you use the following methods, it's going to be a pieces of cake.
the delta formula:
Δ=b²–4ac===> (–2)²–4(1)(–168)=676
[tex]x 1 = \frac{ - ( - 2) + \sqrt{676} }{2} = 14 [/tex]
[tex]x2 = \frac{ - ( - 2) - \sqrt{676} }{2} = - 12[/tex]
well this can be on of the methods and the other one is
The full square formula:
[tex]x ^{2} - 2x - 168 = 0 \\ {x}^{2} - 2x = 168[/tex]
[/tex]
now what you need to do is to put this on both side of the equation (½b)²=1
[tex] {x}^{2} - 2x + 1 = 168 + 1 \\ {(x - 1)}^{2} = 169 \\ x - 1 = 13 = = > x = 14 \\ x - 1 = - 13 = = = > x = - 12[/tex]
