Final answer:
To make the inequality 43 < y - 30 true, add 30 to both sides to get 73 < y. Any number greater than 73, such as 74, 80, or 90, will satisfy the inequality.
Explanation:
To find values that make the inequality 43 < y - 30 true, you simply need to add 30 to both sides of the inequality. This gives you:
73 < y
This means that any value greater than 73 will make the inequality true. Here are three examples:
y = 74 (since 74 is greater than 73)y = 80 (since 80 is greater than 73)y = 90 (since 90 is greater than 73)You can choose any three numbers greater than 73, and they will satisfy the inequality 43 < y - 30.
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Exponential Growth/Decay Function
The value of a car is $21,500. It loses 12% of its value every year.
(a) Write a function that represents the value y (in dollars) of the car after x years. (b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
Which ordered pair represents the x-intercept for the linear equation, 3y + 4x = 8?
Final answer:
To find the x-intercept for the equation 3y + 4x = 8, set y to 0 and solve for x, which results in x = 2. Thus, the ordered pair for the x-intercept is (2, 0).
Explanation:
The question is asking to determine the x-intercept of the linear equation 3y + 4x = 8. The x-intercept occurs where the graph of the equation crosses the x-axis, which is when y is equal to 0. To find the x-intercept, you set y to 0 and solve for x:
3(0) + 4x = 8
4x = 8
x = 8/4
x = 2
Therefore, the ordered pair that represents the x-intercept is (2, 0). This is the point on the graph where the line crosses the x-axis.
Find the points on the surface 4 x^2 + 4 y^2 + 1 z^2 = 1 at which the tangent plane is parallel to the plane -4 x - 4 y + 4 z = -8.
Joan and Ernie are earning money for summer camp. Joan receives a $7 weekly allowance plus $6 for each hour she helps her father paint. Ernie writes the equation y = 5x + 7 to represent the relationship between the number of hours he helps his father with yard work and his weekly allowance. Which statement best describes the graphs of their earnings for one week?
The Correct statement are:
Joan has more money in 10 weeks
Their y-intercepts are the same
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Joan:
Joan receives a $7 weekly allowance plus $6 for each hour
so, the Equation for Joan Earning, y= 6x+ 7
Ernie Earning y = 5x + 7
So, the slope for Joan is 7 and Ernie's slope is 7.
Then, the Correct statement is:
Joan has more money in 10 weeks
Their y-intercepts are the same
Learn more about slope here:
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Find the general solution of the differential equation y'' +4y = 3sin2t
A theater company charges $9.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets an a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets?
Question
A theater company charges $9.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets an a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets?
Answer:
10.50c + a
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A sandwich shop has 30 stores and 60% of the stores are in California. The rest of the stores are in Nevada. How many stores are in California amd bow many are in Nevada?
Answer:
18
Step-by-step explanation:
Call a household prosperous if its income exceeds $100,000. call the household educated if the householder completed college. select an american household at random, and let a be the event that the selected household is prosperous and b the event that it is educated. according to a survey, p(a) = 0.132, p(b) = 0.227, and the probability that a household is both prosperous and educated is p(a and
b.= 0.082. what is the conditional probability that a household is prosperous, given that it is educated? (round your answer to four decimal places.) .3612 explain why your result shows that events a and b are not independent. if a and b were independent, then p(a|b) would equal p(a), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(a), and p(a and
b.would equal the sum p(a) + p(b). if a and b were independent, then p(a|b) would equal p(a and b), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and
b.would equal the sum p(a) + p(b). submit answer save progress
0.5x+78.2=287 whats the value of x
What is the slope of the line that goes through (2, 5) and (-6, -2) ?
Richard goes to the electronics store. He buys 2 memory cards that cost $8.99 each and 3 packages of batteries that are on sale for $7.47 each. He also buys a case for his cell phone for $2.99 and a wireless headset for $29.99. What is the total cost of Richard’s items, before sales tax?
which collection of three side lengths will not form a triangle
6, 10 18
10, 12 ,15
10, 15, 6
10, 18 ,12 please tell me how you figured it out.
To determine if a collection of three side lengths will form a triangle, we use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By applying this theorem to each collection of side lengths given, we can determine which ones will form a triangle.
Explanation:A triangle is a three-sided figure lying on a plane with three angles adding up to 180 degrees. To determine if a collection of three side lengths will form a triangle, we use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For the collection 6, 10, 18, the sum of the two smaller sides (6 + 10) is less than the largest side (18), so this collection will not form a triangle.For the collection 10, 12, 15, the sum of the two smaller sides (10 + 12) is greater than the largest side (15), so this collection will form a triangle.For the collection 10, 15, 6, the sum of the two smaller sides (6 + 10) is greater than the largest side (15), so this collection will form a triangle.For the collection 10, 18, 12, the sum of the two smaller sides (10 + 12) is greater than the largest side (18), so this collection will form a triangle.Find the value of x so that line m is parallel to line n.
A. 57
B. 51
C. 50
D. 49
Answer:
,C) x =50
Step-by-step explanation:
Given : Parallel line m and n in figure.
To find : Find the value of x
Solution : We have given
Two parallel line with traversal line
Alternate interior angle property : The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles are equal.
3x + 11 and angle 161 are alternate angle .
3x + 11 =161.
On subtracting both sides by 11
3x = 161 -11
3x = 150
On dividng both sides by 3
x =50
Therefore,C) x =50
Ms. Romero is buying a scrapbook and sheets of designer paper. She has $30 and needs at least $15.75 to buy the scrapbook. Each sheet of paper costs $0.29. 30−0.29x≥15.75 to find the number of sheets of paper, x, she can buy. How many sheets of paper can she buy?
Ms. Romero can buy up to 49 sheets of paper.
To determine the number of sheets of paper \( x \) that Ms. Romero can buy, we start with the inequality:
[tex]\[ 30 - 0.29x \geq 15.75 \][/tex]
First, isolate the term involving \( x \) by subtracting 15.75 from both sides:
[tex]\[ 30 - 15.75 \geq 0.29x \][/tex]
Simplify the left side:
[tex]\[ 14.25 \geq 0.29x \][/tex]
Next, solve for \( x \) by dividing both sides by 0.29:
[tex]\[ \frac{14.25}{0.29} \geq x \][/tex]
Calculate the value:
[tex]\[ x \leq \frac{14.25}{0.29} \]\[ x \leq 49.13793103448276 \][/tex]
Since \( x \) must be a whole number, we take the greatest integer less than or equal to 49.13793103448276, which is 49. Therefore, the maximum number of sheets of paper she can buy is:
[tex]\[ x = 49 \][/tex]
Thus, Ms. Romero can buy up to 49 sheets of paper.
Which is a true statement about the diagram? m∠5 + m∠6 = m∠1 m∠3 + m∠4 + m∠5 = 180° m∠1 + m∠2 = 180° m∠2 + m∠3 = m∠5
m<1 +m<2 = 180° is the answer
Answer:
Third option is the right choice.
Step by step explanation:
We have been given an diagram and we are asked to choose the true statement about the diagram.
Let us see our all choices one by one.
1. [tex]m\angle5+m\angle6=m\angle1[/tex]
We can see that [tex]\angle5[/tex] and [tex]\angle6[/tex] are supplementary and there measure should be equal to 180 degrees. [tex]\angle1[/tex] is exterior angle of our triangle and its measure must be equal to sum of measures of [tex]\angle5[/tex] and [tex]\angle3[/tex].
Therefore, 1st option is incorrect.
2. [tex]m\angle3+m\angle4+m\angle5=180^{o}[/tex]
We can see that [tex]\angle3[/tex] and [tex]\angle4[/tex] are supplementary and they must be equal to 180 degrees. Therefore, 2nd option is also incorrect.
3. [tex]m\angle1+m\angle2=180^{o}[/tex]
We can see from our diagram that [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary. Therefore, 3rd option is the correct choice.
4. [tex]m\angle2+m\angle3=m\angle5[/tex]
We can see that [tex]\angle2[/tex], [tex]\angle3[/tex] and [tex]\angle5[/tex] are interior angles of our triangle and their measure should be equal to 180 degrees. By exterior angle theorem sum of measures of [tex]\angle2[/tex] and [tex]\angle3[/tex] will be equal to measure of [tex]\angle6[/tex] instead of [tex]\angle5[/tex].
Therefore, our 4th option is also incorrect.
Solve this derivative using the quotient rule
Write equations for the horizontal and vertical lines passing through the point (5, -6)
Horizontal line:
Vertical line:
A right triangle has one leg that is 17 centimeters shorter then the other. If the hypotenuse is 25 what is the length of the two legs
what does x=? I know it is vertical
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
A; an = 2 • 3n - 1
B; an = 2 • (-3)n - 1
C; an = 2 • 3n
D; an = 2 • (-3)n + 1
The answer is B, I have just confirmed it.
Giving brainiest+points need explanation on this one my answer is 25 is it right?
Multiply x^2-8x+15/3x * 8x/x-3
Jake needs to put gas in the delivery van. Regular gasoline is $3.20 per gallon. He only had a $ 20 bill on him. How many gallons can he buy
Expand the log as a sun or difference
Nolan bought 26 yards of rope, the rope costs 2 dollars per foot, how much did Nolan play for the rope?
For the number -5/8 name the opposite, reciprocal and absolute value
opposite:
Reciprocal:
Absolute value:
The bookstore marked some notepads down from ???$ 3.00 but still kept the price over ???$ 2.00. It sold all of them. The total amount of money from the sale of the pads was ???$ 27.95. How many notepads were??? sold? What was the price of each??? notepad?
the city is planning to build a new park by enlarging the current park by a scale factor of 4. The current park has an area of 37,625 yd squared. what is the area of the new park
how to we get radius
Use the information below to find EF such that triangle ABC is congruent to triangle DEF
AB=36 BC=24 DE=48 m<B=110 m<E=110 EF=?