You learned from your science teacher that water expands when you freeze it. The next time you freeze your water bottle, you leave room for the water to expand, avoiding the cracking of the bottle.
What kind of reasoning did you use?
Question 6 options:
deductive
geometric reasoning
inductive
There are two positive numbers. four times the small number plus 3 times the big number is 41. two times the small number plus the big number is 15. what is 10 times the big number minus 6 times the small number;
Final answer:
To find the value of 10 times the big number minus 6 times the small number, we need to solve a system of equations. The solution to the system is x = 2 and y = 11, so the value of 10y - 6x is 98.
Explanation:
To find the value of 10 times the big number minus 6 times the small number, we need to solve the system of equations:
4x + 3y = 41 (equation 1)
2x + y = 15 (equation 2)
We can first solve equation 2 for y by subtracting 2x from both sides: y = 15 - 2x. Now we can substitute this value of y into equation 1:
4x + 3(15 - 2x) = 41
Simplifying, we get: 4x + 45 - 6x = 41
Combining like terms, we have: -2x + 45 = 41
Subtracting 45 from both sides, we get: -2x = -4
Dividing both sides by -2, we get: x = 2
Now we can substitute this value of x back into equation 2 to solve for y:
2(2) + y = 15
Simplifying, we get: 4 + y = 15
Subtracting 4 from both sides, we get: y = 11
Finally, we can calculate 10 times the big number minus 6 times the small number:
10y - 6x = 10(11) - 6(2) = 110 - 12 = 98
Is 7/35 and 35/70 proportional?
Find the sum of the first 17 terms of the arithmetic sequence 10, 14, 18, 22, 26...
Line p passes through A(-2, -4) and has a slope of 1/2 What is the standard form of the equation for line p?
A professional baseball team won 84 games.The team won 14 more games than it lost.There were no ties.How many games did the team lose?How many did it play?
convert the Dimensional Analysis Problem Convert 12 days into seconds Will GIVE BRAINIEST!
12 days
12X24= 288 HRS
288X60=17280 MINS
17280X60=1036800 SECONDS
Lisa earns $8.10 an hour and worked 40 hours. Jamie earns $10.80 an hour. How many hours would Jamie need to work to equal Lisa’s earnings over 40 hours
Answer:
it takes 30 hours for Jamie to equal Lisa's earnings
Step-by-step explanation:
Lisa earns $8.10 an hour and worked 40 hours.
Total amount Lisa earns = rate times hours
Total amount Lisa earns =[tex]8.10 \cdot 40=324[/tex]
Jamie earns $10.80 an hour
LEt 'n' be the number of hours Jamie works
Total amount Jamie earns =[tex]10.80 \cdot n=10.80n[/tex]
we need to find out 'n' when Jamie earnings is equal to Lisa earnings
[tex]10.80n= 324[/tex]
Divide by 10.80 on both sides
n= 30
So it takes 30 hours for Jamie to equal Lisa's earnings
What is one point on a graph for the equation y=-3x-1 and how do we substitute it?
use the slope intercept equation to find the slope and the y intercept
y = mx-b
m = slope
b = y intercept
m is the number before the x so -3 is the slope
and -1 is the y intercept
so a point on the graph would be the y intercept at (0,-1)
How do you find the width of a rectangle when the perimeter is given?
Gail lives in Kentucky and pays 6% in sales tax. She just bought $165 in groceries, but $80 worth of those groceries were nontaxable. What is the total amount that Gail paid for the groceries, including sales tax?
A.$165.99
B.$170.10
C.$165.51
D.$174.90
HELPPPPPP ME
Answer:
Option B. $170.10
Step-by-step explanation:
Gail bought groceries worth = $165.00
She gets rebate of taxes on the amount = $80.00
She has to pay tax on = 165 - 80 = $85.00
In her state sales tax are = 6%
So her tax on groceries = 6% of 85 = 0.06 × 85 = $5.10
Now she paid total amount = 165 + 5.10 = $170.10
Gail paid $170.10 for the groceries, including sale tax
Option B. $170.10
What is the value of x?
enter your answer in the box
x = [ ]
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
We have been given an image of two right triangles and we asked to find the value of x.
First of all , we will find the length of segment RT using sine.
[tex]\text{Sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{Sin}(60^{\circ})=\frac{2\sqrt{3}}{RT}[/tex]
[tex]RT=\frac{2\sqrt{3}}{\text{Sin}(60^{\circ})}[/tex]
[tex]RT=\frac{2\sqrt{3}}{\frac{\sqrt{3}}{2}}[/tex]
[tex]RT=\frac{2\sqrt{3}}{\sqrt{3}}\times 2[/tex]
[tex]RT=2\times 2[/tex]
[tex]RT=4[/tex]
Now we know that length of segment RT and angle QRT of triangle QRT, so we will use tangent to find the length of segment QR (x) as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(45^{\circ})=\frac{x}{4}[/tex]
Multiplying both sides of our equation by 4 we will get,
[tex]\text{tan}(45^{\circ})*4=\frac{x}{4}*4[/tex]
[tex]\text{tan}(45^{\circ})*4=x[/tex]
Substituting [tex]\text{tan}(45^{\circ})=1[/tex] we will get,
[tex]1*4=x[/tex]
[tex]4=x[/tex]
Therefore, the value of x is 4 units.
Pam buys a shirt that costs $11.99 , pants that cost $23.98 , and a belt that costs $9.95 she has a coupon for 20% off the entire purchase. about how much will the three items cost ?
Can Anyone Help Me
Real-world problems that have more than one answer can be described by relations.
A. True
B. False
What value of c makes x2 − 12x + c a perfect square trinomial? −36 −24 24 36
Answer: The value of c must be 36 to make it perfect square trinomial.
Explanation:
A standard perfect square trinomial is [tex]x^2+2ax+a^2=(x+a)^2[/tex] where [tex]a^2[/tex] is the constant term.
Given trinomial [tex]x^2-12x+c=x^2+2(-6)a+c[/tex]
On comparing with standard perfect square trinomial we get a=-6
Therefore the constant term c=[tex]a^2=(-6)^2=36[/tex]
Such that the trinomial becomes [tex]x^2-12x+36=x^2+2(-6)x+(-6)^2=(x-6)^2[/tex] a perfect square trinomial.
Hence the value of c for the given trinomial must be 36 to make it perfect square trinomial.
Please answer this question will mark as brainliest and 15 points
690-6 = 684
690+6 = 696
the answer is A
Can someone please help. Will you graph the functions and approximate an x-value in which the exponential function surpasses the polynomial function. In your final answer, include a copy of the graph.
y = 2x^2 + 7
y = 5^(x-4)
Answer:
paying a price to keep Mowgli alive would b ur answer
Step-by-step explanation:
when adding 3 and -9, how do you know that the sun is negative?
Translate the following word phrase into an algebraic expression.
" The product of 8 and a number increased by 2"
A. 8x-2
B. 8(x+2)
C. 8x+2
D. x÷8+2
From a team of five students, you choose two students at random without replacement. Calculate the probability that the first student selected is the team leader and the second is the assistant team leader. Please show all work!!
Answer:
1/20
Step-by-step explanation:
1/4*1/5=1/20
Solve each equation. Leave the answer as an improper fraction. 16x2 = 49
Answer:
[tex]x= +-\frac{7}{4}[/tex]
Step-by-step explanation:
[tex]16x^2= 49[/tex]
Solve the equation for x
To solve the equation , we need to isolate x
To get x alone , we need to remove the numbers attached with x
To remove 16 we divide both sides by 16
[tex]x^2 = \frac{49}{16}[/tex]
Now to remove square from x we take square root on both sides
[tex]\sqrt{x^2} = \sqrt{\frac{49}{16}}[/tex]
square root (49) = 7
square root (16)= 4
So , [tex]x= +-\frac{7}{4}[/tex]
When we take square root we include +-
A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Check all that apply.
(–2, 0) and (2, 5)
(–4, 5) and (4, –5)
(–3, 4) and (2, 0)
(1, –1) and (6, –5)
(2, –1) and (10, 9)
Answer:
Options A and Option E.
Step-by-step explanation:
A line has a slope of -4/5. Now a line perpendicular to this line will have the slope as [tex]m_{1}.m_{2}=-1[/tex]
Therefore [tex]m_{2}=-\frac{1}{m_{1}}=\frac{1}{\frac{4}{5} }=\frac{5}{4}[/tex]
Now we will find the slope with the help of points given in the options if they lie on the perpendicular line.
A). [tex]m=\frac{5-0}{2+2}=\frac{5}{4}[/tex]
B). [tex]m=\frac{-5-5}{4+4}=\frac{-10}{8}=-\frac{5}{4}[/tex]
C). [tex]m=\frac{0-4}{2+3}=-\frac{4}{5}[/tex]
D). [tex]m=\frac{-5+1}{6-1}=\frac{-4}{5}=-\frac{4}{5}[/tex]
E). [tex]m=\frac{9+1}{10-2}=\frac{10}{8}=\frac{5}{4}[/tex]
Options A and E are the correct options.
One linear function, t(x), can be modeled by the values in the table below. A second linear function can be modeled by the equation 4x − y + 4 = 0. When comparing the x-intercepts of these lines, which function has the largest x-intercept and what is this value?
x t(x)
−3 0
0 −4
3 −8
6 −12
9 −16
t(x) has the largest x-intercept: −4.
4x − y + 4 = 0 has the largest x-intercept: −1.
t(x) has the largest x-intercept: −3.
4x − y + 4 = 0 has the largest x-intercept: 4.
Answer:
a
Step-by-step explanation:
Which property is x ( y + z) = xy + xz
What is the equation of a line that is parallel to 2x+3y=3 and passes through the point (3, −4) ? Enter your answer in the box.
Final answer:
The equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4) is y = −(2/3)x − 2. We found this by first converting the given line into slope-intercept form to find the slope, and then using the point-slope form with the given point.
Explanation:
To find the equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4), we first need to determine the slope of the given line. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope. We can rewrite the given equation in slope-intercept form by isolating y:
2x + 3y = 3
3y = −2x + 3
y = −(2/3)x + 1
This shows that the slope (m) of the given line is −(2/3). Since parallel lines have the same slope, the slope of the new line will also be −(2/3). Now we use the point-slope form of a line which is y − y1 = m(x − x1), where (x1,y1) is a point on the line. Plugging in the given point (3, −4) and the slope −(2/3), we get:
y − (−4) = −(2/3)(x − 3)
Distributing the slope on the right side and moving −4 to the other side gives us the final equation:
y = −(2/3)x + 2 + −4
y = −(2/3)x − 2
This is the equation of the line that is parallel to 2x+3y=3 and passes through the point (3, −4).
While hiking, Emily recorded that she climbed 125 feet, descended 31 feet to find a new trail and then went 145 feet further up the mountain to end her hike. How far up the mountain was Emily when she stopped climbing for the day
what is the approximate circumference of the circle shown below
The correct option is [tex]\boxed{\bf option A}[/tex] i.e, [tex]\boxed{\bf 129\text{ cm}}[/tex].
Further explanation:
A circle is the set of all points on a plane whose distance from a fixed point is constant.
There are infinite points on the circle and distance of these points from the center of circle is always constant.
The distance from the center of the circle to any point on the circle is called as radius of the circle.
The circumference is the length of the circle and the formula of the circumference [tex]C[/tex] for the circle is as follows:
[tex]\boxed{C=2\pi r}[/tex] …… (1)
Here, [tex]r[/tex] is the radius of the circle and the value of [tex]\pi[/tex] is approximately equal to [tex]3.14[/tex].
The formula of the circumference for circle is terms of diameter is as follows:
[tex]\boxed{C=d\pi}[/tex]
Here, [tex]d[/tex] is the diameter of the circle.
The relationship between diameter and the radius is as follows:
[tex]\boxed{d=2r}[/tex].
From attached Figure 1 it is observed that the radius of the circle is [tex]20.5\text{ cm}[/tex].
Substitute [tex]r=20.5[/tex] in the equation (1) to obtain the value of circumference [tex]C[/tex] as follows:
[tex]\begin{aligned}C&=2\pi r\\&=2\cdot 3.14 \cdot 20.5\\&=128.74\\ &\approx129\end{aligned}[/tex]
Therefore, the circumference of the circle is [tex]\boxed{\bf 129\text{\bf cm}}[/tex].
Thus, the correct option is [tex]\boxed{\bf option A}[/tex].
Learn more:
1. Learn more about circle https://brainly.com/question/1952668
2. Learn more about radius of circle https://brainly.com/question/1506955
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Circle
Keywords: Circle, radius of a circle, point, distance, diameter, circumference, d=2r, C=2pir, 129. centimeter, locus of circle, approximate, value, shown below.
i need help solving this problem. i have been stuck on it for hours. please help
Solve each system by elimination:
9a-3d=3
-3a+d=-1
Scott earns 16.85 per hour at his job. He works 7 hour per day , 4 days per week. What Scott's gross income in 4 weeks
Scott's gross income in 4 weeks, rounded to the nearest cent, is $1887.20.
Calculate Scott's daily earnings:
Scott earns $16.85 per hour, and he works for 7 hours per day.
Daily earnings = $16.85/hour × 7 hours = $117.95
Calculate Scott's weekly earnings:
Scott works 4 days per week.
Weekly earnings = Daily earnings × Number of days worked per week
= $117.95/day × 4 days/week
= $471.80
Calculate Scott's gross income for 4 weeks:
Scott works for 4 weeks.
Gross income for 4 weeks = Weekly earnings × Number of weeks
= $471.80/week × 4 weeks
= $1887.20
However, we need to ensure the precision of the final answer. As currency involves cents, it's important to round appropriately.
Since we're dealing with money, we'll round to the nearest cent.
After rounding, the gross income for 4 weeks is $1887.20.
what is the slope of the line