Answer: To find the point of intersection of two lines without using graph paper, we can use the method of solving a system of equations.
First, we need to find the slope-intercept form of each line. The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of Line A, we can use the slope formula: m = (y2 - y1)/(x2 - x1). Plugging in the given points, we get: m = (-1 - 3)/(-2 - (-4)) = -4/2 = -2.
Therefore, Line A can be written as y = -2x + b. To find the y-intercept, b, we can plug in one of the points, such as (-4,3) and solve for b: 3 = -2(-4) + b, so b = 11.
So, the slope-intercept form of Line A is y = -2x + 11
We can use the same process to find the slope-intercept form of Line B: m = (7 - 4)/(-5 - (-4)) = 3/1 = 3. So Line B can be written as y = 3x + b. Plugging in one of the points, (-4,4), we get 4 = 3(-4) + b, so b = 16.
So, the slope-intercept form of Line B is y = 3x + 16
Now we have two equations: y = -2x + 11 and y = 3x + 16. To find the point of intersection, we need to find the values of x and y that make both equations true. To do this, we can set the two equations equal to each other:
-2x + 11 = 3x + 16
Subtracting 3x from both sides:
-5x = 5
Dividing both sides by -5:
x = -1
Now we can substitute this value of x back into either equation to find the corresponding value of y. Using y = -2x + 11:
y = -2(-1) + 11 = -2 + 11 = 9
So the point of intersection of Line A and Line
Step-by-step explanation:
if she needs to allocate her waking time of 15 hours between these two activities, how much studying is she going to do per day?
She would be doing 9 hours of studying per day and 6 hours of other activities. This is because 15 hours divided by 9 hours of studying and 6 hours of other activities would equal the same amount of time allocated to each activity.
The amount of studying she is going to do per day is 9 hours, and the amount of other activities she is going to do per day is 6 hours. This means that she will be dedicating roughly 60% of her waking hours to studying and 40% to other activities. This is a good balance between the two activities, and it will ensure that she is able to adequately focus on both her studies and other activities.
This balance will also help her to stay motivated and not become overwhelmed by her studies. Having a set amount of time for both activities will also help her to organize her day and stay on track. It will give her a sense of structure and allow her to plan her day accordingly.
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How do you isolate the variable in x + 5 = 12?
does anyone know how to read this I don’t know what it says
Jasmine's average speed was 33 3/4 miles per hour.
How far did she travel if it took her 3 1/5 hours?
A. 79 1/2 miles
B. 89 1/2 miles
C. 98 miles
D. 108 miles
The distance travelled by Jasmine in 3 1/5 hours is 108 miles.
What is the distance travelled by Jasmine in the given time?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Speed = 33 3/4 miles per hourElapsed Time = 3 1/5 hoursDistance = ?Plug in given values into the above equation and solve for distance.
Speed = Distance / time
Distance = Speed × Time
Distance = 33 3/4 × 3 1/5
Convert to improper fraction
Distance = (33 × 4 + 3)/4 × ( 3 × 5 + 1)/5
Distance = 135/4 × 16/5
Distance = 2160 / 20
Distance = 108 miles
Therefore, the distance covered is 108 miles.
Option D) 108 miles is the correct answer.
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Help me please and thank you !!!!
The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]
What is a positive exponent?A positive exponent indicates that the base should be multiplied by that many.
An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite. Negative exponents like xn can be rewritten as 1 / rs. As an illustration, qr^-4 s^6 q ^-8 s^6 q^-1 rs^6
The Power Rule for Exponents is a further exponent rule that follows from this. You multiply the exponents while keeping the base constant to simplify a power of a power. As an illustration, b for any positive s^6 q ^-8 s^6 q^-1 rs^6 number x and integers q and s.
⇒ qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹
⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹
⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹
⇒ qr⁻⁸ × r⁻⁴ × s⁹
[tex]$ \Rightarrow \frac{1}{q^8} \times \frac{1}{r^4} \times s^9[/tex]
[tex]$ \Rightarrow \frac{s^9}{q^8r^4}[/tex]
Thus , The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]
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Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
PLSSSSS HELPPP!!!!!
The surface area of the rectangular prism is 112 square metes.
What is surface area?The sum of all area of each surface that make up an object is referred to as its surface area.
So that in the given question,
Area of a rectangle = length x width
i. area of its base = length x width
= 8 x 2
= 16 sq. m
ii. area of its front surface = length x width
= 4 x 8
= 32 sq. m
iii. area of it one of its sides = length x width
= 4 x 2
= 8 sq. m
Therefore,
surface area of the rectangular prism = (2 x 16) + (2 x 32) + (2 x 8)
= 32 + 64 + 16
= 112
The surface area of the rectangular prism is 112 square meters.
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11. A C Best Buy is selling a 62" TV for $1,250. The TV is on sale for 15% off and there is a 6% sales tax. What is the final cost of the TV? $998.75 $1126.25 B D $198.75 $1523.75
Answer:
$1,684.25
Step-by-step explanation:
(.85 x 1250) = 1062.50 If we take off 15% we leave on 85% which as a decimal is .85
Now add the tax
1062.50 + .06(1062.50)
1620.50 + 63.75
1684.25
Suppose you roll the number cube 199 more times would you expect the experimental probability of rolling a 3 or 4 the same as your answer in exercise 5
30 5.109 ÷ 100 in decimal
The result of the division of the number by 100 gives 3.05109 in decimal.
Define the term decimal number?A decimal is really a number that is divided into two parts: another whole and a fraction.
Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.Then, there are two parts to a decimal number: a whole number portion and a fractional portion. The whole component of something like a decimal number has the same decimal point value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.For the given number.
= 305.109 ÷ 100
Then point will shift to 2 decimals towards left.
= 3.05109
Thus, the result of the division of the number by 100 gives 3.05109 in decimal.
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Which function has a range limited to only negative numbers?
Answer:
F(x)=-x^2
Step-by-step explanation:
The one example of function with range of only negative number is:
F(x)=-x^2
Why this? We know for every x, x^2 is positive. So -x^2 will be negative.
a tin box of 1 m length, 85cm width and 60cm depth is to be made. if the box is without top, find the area of the tin required to make the box and the cost of tin at the rate of 0.50 Rupees per sq. cm
The area of the tin box without the top is 39100 square cm.
The cost of making this tin box is Rs. 19550.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, A tin box of 1 m in length, 85cm in width, and 60cm in depth is to be made.
We know the total surface area of a cuboid is 2(lw + wh + wl).
Therefore, The surface area of the cuboid without the top would be,
= 2(lw + wh + wl) - (l×w).
= 2(100×85 + 85×60 + 85×100) - (85×60).
= 2(22100) - 5100.
= 44200 - 5100.
= 39100 square cm.
The cost of making this tin box is Rs.(39100×0.50).
= Rs. 19550.
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A plane is on its approach to land on the runway. The jet’s height above the ground is given in feet as a function of the time in seconds. The following table tracks the plane as it lands:
t (in seconds)
h (in feet)
0
4000
5
3500
10
3000
15
2500
20
2000
25
1500
Is this function linear? If it is, what is the slope? Use the formula m = StartFraction delta h Over delta t EndFraction.
a.
No, this is not a linear function.
b.
Yes, this function is linear; the slope is 500 feet/second.
c.
Yes, this function is linear; the slope is 100 feet/second.
d.
Yes, this function is linear; the slope is -100 feet/second.
Answer:
d. Yes, this function is linear; the slope is -100 feet/second.
Step-by-step explanation:
Find the difference in height at two different time periods.
If
Δh = difference in height values
Δt = difference in seconds
then
[tex]\mathrm{slope = \dfrac{\Delta h}{\Delta y}}[/tex]
Take the difference in heights at t = 0 and t = 5
The height drops from 4000 to 3500 feet so Δh = 3500 - 400 = -500
Δt = 5- 0 = 5 seconds
slope = -500/5 = -100
If you compute the slope between any pair of heights and time difference you will get the same value
So slope is constant indicating a linear function
You can graph the solutions of an inequality on a number line. How can you show the solutions of the inequality 3x +2 ≥ 1/2 ( x + 5 )
A graph of the solutions of this inequality 3x + 2 ≥ 1/2(x + 5) is shown on the number line attached below.
How to graph the solutions of the inequality?In this exercise, we would solve the given inequality by making x the subject of formula as follows;
3x + 2 ≥ 1/2(x + 5)
By multiplying both sides of the inequality by 2, we have the following:
(3x + 2) × 2 ≥ 1/2(x + 5) × 2
6x + 4 ≥ x + 5
By rearranging and collecting like terms, we have the following:
6x - x ≥ 5 - 4
5x ≥ 1
x ≥ 1/5
Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle on the number line (graph) is closed because of the greater than or equal to (≤) symbol.
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4(2x – 5) = 4
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work.
The equation has one solution
The solution to the equation is x = 3
How to solve the equation4(2x – 5) = 4
To solve this, we would first have to open the bracket.
4 * 2x - 4*5 = 4
8x - 20 = 4
We would want to have the variable x stand on its own
so we take like terms
8x = 4 + 20
8x = 24
To get the value of x divide through the equation by 8
x = 24 / 8
x = 3
The solution is just one at x = 3
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use zero product property to determine x ints of y= x^2 +4x-20 exact and approximate
By cancelative property, the roots of quadratic equation x² + 4 · x - 20 are: Exact: - 2 + 2√6, - 2 - 2√6, Approximate: 2.899, -6.899.
How to find the roots of a polynomial by cancelative property
In this problem we must factorize a quadratic equation and use an algebraic property known as cancelative property, defined as:
If a · b = 0, then a = 0 or b = 0.
In addition, we can apply the following factorization rule:
x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)
First, factorize the quadratic equation:
x² - (- 2 + 2√6 - 2 - 2√6) · x + (- 2 + 2√6) · (- 2 - 2√6)
(x + 2 - 2√6) · (x + 2 + 2√6)
Second, apply cancelative property:
x + 2 - 2√6 = 0
x = - 2 + 2√6
x + 2 + 2√6 = 0
x = - 2 - 2√6
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Please help me this is driving me crazy
Answer:
24 days = 1500 tables
25 days = Fewer than 1500 tables
Step-by-step explanation:
So we have the inequality of < which is fewer than. Let's start by labeling all the numbers given.
What we want to find is how many days, so we'll make days = x
2100 is the initial and they sell 25 a day... 25 a x.
Combining them all we get a basic inequality of:
2100 - 25x < 1500
Let's get X alone.
Subtracting 2100 from both sides gives you
-25x < -600.
We have negatives on both sides. For me, if I see that, I make both of them positive;
25x < 600
Last step is to divide the 25 out of the X which means you'll divide 25 by 600 also
X = 24
Which means day 24 will be exactly 1500. We wanted fewer though, so adding a day gives you an answer of 25 days.
$37 dinner; 15% tip what can I do to get the answer
Answer: $5.55
Step-by-step explanation: 15% = 0.15
37 / 0.15 = 5.55
if an integer is randomly selected from all positive 2-digit integers, what is the probability that the integer chosen has (a) a 4 in the tens place? (b) at least one 4 in the tens place or the units place? (c) no 4 in either place?
The probability of 4 in the tens place is [tex]\frac{1}{9}[/tex], the probability of at least one 4 in the tens place or the units place is [tex]\frac{1}{5}[/tex], the probability no 4 in either place is [tex]\frac{4}{5}[/tex].
(a) total number of 2-digit terms =(99 - 10) + 1 = 90
n(s) = 90
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%
number of 2 digits that have 4 in tens place = 40, 41, 42 ......49
n(a) = 10
P(A) =[tex]\frac{ n(a)}{n(s)}[/tex]
Substituting the values
P(A) = [tex]\frac{10}{90}[/tex]
P(A) = [tex]\frac{1}{9}[/tex]
Therefore, P(A) = [tex]\frac{1}{9}[/tex]
(b) From the previous one, we know the P(A) = [tex]\frac{1}{9}[/tex]
Number of 4's in units place = 14, 24, 34.....94 = 9
n(b) = 9
P(B) = [tex]\frac{ n(b)}{n(s)}[/tex]
Substituting the values
P(B) = [tex]\frac{9}{90}[/tex]
P(B) =[tex]\frac{1}{10}[/tex]
P(A and B) = [tex]\frac{1}{10}[/tex]
Using OR probability, we have
P(A or B) = P(A) + P(B) - P(A and B)
P([tex]\frac{1}{9}[/tex] or [tex]\frac{1}{10}[/tex]) = [tex]\frac{1}{9}[/tex] + [tex]\frac{1}{10}[/tex] - [tex]\frac{1}{90}[/tex]
P([tex]\frac{1}{9}[/tex]or [tex]\frac{1}{10}[/tex]) = [tex]\frac{1}{5}[/tex]
Therefore, P([tex]\frac{1}{9}[/tex]or [tex]\frac{1}{10}[/tex]) = [tex]\frac{1}{5}[/tex]
(c) Probability of no 4 in either place = 1 - ( probability of 4 in either place)
= 1 - [tex]\frac{1}{5}[/tex] = [tex]\frac{4}{5}[/tex]
Therefore, probability of no 4 in either place = [tex]\frac{4}{5}[/tex]
Therefore, the probability that the integer chosen has a 4 in the tens place is [tex]\frac{1}{9}[/tex], P([tex]\frac{1}{9}[/tex] or [tex]\frac{1}{10}[/tex]) = [tex]\frac{1}{5}[/tex], and probability of no 4 in either place = [tex]\frac{4}{5}[/tex].
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Given the function h(x)=3x, which statement is true about h(x)?
O The function is decreasing on the interval (-∞, 0).
O The function is increasing on the interval (-∞, 0).
O The function is decreasing on the interval (0, ∞).
O The function is increasing on the interval (0, ∞).
Answer:
Two statement are true.
O The function is increasing on the interval (-∞, 0).
O The function is increasing on the interval (0, ∞).
Step-by-step explanation:
The function h(x) = 3x is a linear function (straight line) with a slope of 3, and a y-intercept of 0. The constant, positive slope means that h(x) will increase over the interval (-∞, ∞).
See the attached graph.
A coffee shop has a group of seats at the counter and t individual tables, where each
table has the same number of seats. If 2t + 8 represents the total number of seats in the
restaurant, what does 8 represent?
a)the number of seats at each table
b) the number of seats at the counter
c) the total number of customers in the coffee shop
d) the total number of tables in the coffee shop
In the expression 2t+8, 8 represents the number of seats at each table.
What is Expression?An expression is combination of variables, numbers and operators.
Given that A coffee shop has a group of seats at the counter and t individual tables.
where each able has the same number of seats.
2t + 8 represents the total number of seats in the restaurant.
8 represents the number of seats at each table and 2t is the number of individual seats.
Hence, in the expression 2t+8, 8 represents the number of seats at each table.
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+
At a sale this week, a sofa is being sold for $173.60. This is a 72% discount from the original price.
What is the original price?
The original price of the sofa before the discount is $241.11.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Let the original price of the sofa be x.
Given that 72% of the original price is $173.60, this can be written mathematically as follows:
72/100 × x = 173.60
72x = 17360
x = 241.11
Hence, the original price of the sofa before the discount is $241.11.
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This is for geometry I need to know step by step appreciate it
For the given similar triangles, the value of x = 5.
What are similar triangles used for?Similar triangles share the same associated angle measurements and proportional side lengths.
Due to their similar shapes, two figures that are not always the same size can appear comparable. We might claim, for instance, that all circles are equivalent. Squares and equilateral triangles share similar characteristics. Although similar figures need not be congruent in order to be comparable, congruent figures are always comparable.
Despite having the same shape, similar triangles have different diameters. In identical triangles, corresponding angles are equal. In analogous triangles, the ratio of the corresponding sides is the same. Any pair of equivalent sides' squares and any comparable triangle's area have the same ratio.
As the given triangles are similar,
the sides are in same ratio,
⇒ 56 / 8x - 5 = 24 / 15
⇒ 8x - 5 = 35
⇒ 8x = 40
⇒ x = 5
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suppose you went on a vacation in a different country and returning to your school. is the variable 'time to destination' quantitative or qualitative?
The variable 'time to destination' quantitative.
Quantitative variables are those whose values are obtained through measurement or counting. A qualitative variable, also referred to as a category variable, is a non-numerical variable. It describes information that can be categorized. Examples like Eye colors, States, Dog breeds etc.
Any variable that isn't numerical is referred to as a qualitative variable or a category variable. It describes information that falls into a category. Generally speaking, a variable is considered to be quantitative if it can be used mathematically (such as addition). Otherwise, it's top-notch. You cannot, for instance, add blue and green.
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The equation of the line is ____?
Answer:
Step-by-step explanation: using the y-intercept form, I see the y-intercept is 40 , at the point (0,40)
and we have a point (4,160), so
slope = (160-40)/(4-0) = 30
equqtion: y = 30x + 40 or 30x - y = -40
Please help I need the answers ASAP.
Question 6:
The relationship between ∠2 and ∠7 is that they are corresponding angles.
Question 8:
Since ∠1 and ∠2 are alternate exterior angles, m∠2=m∠1 so 180°
Question 9:
Options A, C, and D are correct.
*Note*
For option B the angles are supplementary.
For option E the angles are vertical angles.
Question 10:
∠1 and ∠2 lie in the interior of the parallel lines and are on opposite sides of the transversal. So, ∠1 and ∠2 are equal.
simplify the expression
the quotient of y and 4 is at most 19
The inequality of the statement is y/4 ≤ 19
How to determine the inequalityFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement represented as
the quotient of y and 4 is at most 19
The variable in the above statement is y
This means that the quotient of y and 4 cannot exceed 19
The term cannot exceed implies less than or equal to
So, we have the following representation
y/4 ≤ 19
Hence, the statement is
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Find the equation for the circle with a diameter whose endpoints are (2,−5​) and (-3,1).
Write the standard equation for the circle.
(Use integers or fractions for any numbers in the equation.)
The equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1) is (x - 1)^2 + (y - 1)^2 = 13.
The endpoints are (2, -5) and (-3,1).
The standard form equation for a circle is known as
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where (a, b) are the center's coordinates and (r) is the radius.
Taking into account the stated endpoints of the diameter. The center will then be at the midpoint, and the radius will be the distance between the center and either of the two endpoints.
Calculating the midpoint is as follows:
[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
where, [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points.
Now putting the values
[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{-2+4}{2}, \frac{3-1}{2}\right)[/tex]
[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{2}{2}, \frac{2}{2}\right)[/tex]
[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(2, 1)[/tex]
Now we determine the equation of circle.
The center (2, 1) and the terminal are the two points (-2, 3).
r = [tex]\sqrt{(-2-1)^2+(3-1)^2}[/tex]
r =[tex]\sqrt{(-3)^2+(2)^2}[/tex]
r = [tex]\sqrt{9+4}[/tex]
r = √13
Now we can write the equation of circle as:
(x - 1)^2 + (y - 1)^2 = (√13)^2
(x - 1)^2 + (y - 1)^2 = 13
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The complete question is:
Find the equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1).
Write the standard equation for the circle.
Can someone write an equivalent expression to 8(y - 7)?
Answer: 8y-56
Step-by-step explanation: the equivalent expression is 8y-56
Answer: 8y - 56
Step-by-step explanation: Hello! Here are the steps to solve this:
8(y - 7) Use the distributive property, distribute 8 to y and 8 to -7
8y - 56 8 x y = 8y, 8 x -7 = -56
8y - 56 is an equivalent expression to 8(y - 7) because it is simplified. I hope this helps!
what is the answer to this
The matching of the inequality with the statement will be 1-B, 2-D, 3-A, and 4-C.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The matching of inequality with the statement is given as,
The inequality t < 28 represents that Tia ran the race in under 28 seconds.The inequality t > 28 represents that the temperature is warmer than 28°F.The inequality t < 29 represents that Tony is younger than 29 years old.The inequality t > 29 represents that the table is heavier than 29 kilograms.The matching of the inequality with the statement will be 1-B, 2-D, 3-A, and 4-C.
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