Solution
The equation of two curves are
[tex]y_{1}=y=2 \times (5 x+3)\\\\y_{2}=y=x^2-15[/tex]
Equating the two curves that is y values, to find their point of Intersection
→ 2 × (5 x+3)=x²-15
→10 x +6=x²-15⇒⇒Used distributive property of multiplication with respect to addition
→x² -10 x -15 -6=0
→x² -10 x-21=0
For a Quadratic equation of the type
[tex]\rightarrow ax^2+b x +c=0\\\\x=\frac{-b \pm \sqrt{D}}{2 a}\\\\D=b^2-4ac[/tex]
Using discriminant method to solve the problem
[tex]x=\frac{-(-10)\pm\sqrt{(-10)^2-4 \times 1 \times (-21)}}{2 \times 1}\\\\x=\frac{10 \pm \sqrt{100+84}}{2}\\\\x=\frac{10 \pm \sqrt{184}}{2}\\\\x=5 \pm \sqrt{46}\\\\x_{1}=5+6.78\\\\x_{1}=11.78\\\\x_{2}=5-6.78\\\\x_{2}=-1.78[/tex]
The x coordinate of point of intersection are, 11.78 and -1.78.
Find the sum of the solutions of this equation 20x^2-39x-80=0
Help? Sampling
A toy bin has twenty toys in it, five of each type. Storm wants to know which type of toy he would pick if he pulled out one.
Which of the following would be the most appropriate sampling technique?
A. He could use a spinner with four equal-sized sections, one for each toy.
B. He could make a chart to show all of the toys that other people pulled out. <<?
C. He could use a spinner with five equal-sized sections, one for each toy.
D. He could use a random number generator with the total number of toys as the top number.
Answer:
Option (C) is correct choice.
Explanation:
The most appropriate sampling technique for Storm to determine which type of toy he would pick from the bin is option C. He could use a spinner with five equal-sized sections, one for each type of toy.
Option A (using a spinner with four equal-sized sections) does not accurately represent the distribution of toys in the bin, as there are five types of toys.
Option B (making a chart of toys that other people pulled out) relies on the data from others and does not involve Storm directly selecting a toy.
Option D (using a random number generator) is not as straightforward and intuitive as directly selecting a toy from the bin.
Therefore, option C provides Storm with a fair and simple method to randomly select one type of toy from the bin.
Wendy wanted to understand whether students at her school were in favor of an extended school day. She surveyed some students and displayed the results in the table below:
In favor Opposed Undecided
Grade 9 4 7 7
Grade 10 9 11 5
Grade 11 12 13 5
Grade 12 10 5 12
If the principal randomly selects a student in grade 12 from this survey, what is the probability that the student is in favor of extending the school day?
Answers:
0.37
0.27
0.49
0.52
Answer:
0.37
Step-by-step explanation:
Eric plans to rent a Beach House for a week. He has a coupon for 20% off the daily base rate of $200. He will also have to pay an additional $20 a day for utilities. Which expression represents the situation. (d represents the number of days)
Answer: 180 d is the required expression.
Step-by-step explanation:
Since, He has a coupon for 20% off the daily base rate of $200.
Therefore, His daily base cost = 80 % of 200 = [tex]\frac{20\times 80}{100}[/tex] = $ 160
Additional cost he pay in a day = $20
Therefore, his total cost of one day = 160 + 20 = 180
Thus, his total cost in d days = 180 d
Which is the required expression.
Answer:
180d C)
Step-by-step explanation:
40 is 20 percent of 200, if you remove 40 from 200 you get 160. then add 20 and you have 180.
Find the circumference of a pizza if the diameter is 10 inches.
0.314 in.
3.14 in.
3.04 in.
31.4 in.
Answer: 31.4 in.
Step-by-step explanation:
We know that the circumference of the circle is given by :-
[tex]C=\pi d[/tex], where d is the diameter of the circle.
Given : The diameter of the pizza = 10 inches
Then the circumference of the pizza will be :-
[tex]C=\pi (10)[/tex]
We put the value of [tex]\pi =3.14[/tex], we get
[tex]C=3.14 (10)=31.4[/tex]
Hence, the circumference of a pizza is 31.4 in.
Find the area of the quadrilateral in the figure
In the given figure the area of quadrilateral is 19.64 square units.
Option (C) is correct.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180.
In the given figure,
A quadrilateral is shown.
The quadrilateral can be seen as two triangles,
One triangle whose sides are 6, 6 and 5
And second triangle whose sides are 3, 4, and 5.
In first triangle, use Heron's formula to find the area,
The area of triangle = √ S.(S- a).(S -b).(S-c)
The semi perimeter of triangle = 6 + 6 +5 / 2 = 17 / 2 = 8.5
Area = √ 8.5 x (8.5 - 6) x (8.5 - 6) x (8.5 - 5)
= √8.5 x 2.5 x 2.5 x 3.5
= 13.635
The second triangle whose side are 3, 4 and 5, makes a right angle.
The area of second triangle = 1/2 x base x height = 1/2 x 4 x 3 = 6
Total area = 13.635 6 + 6 = 19.635
The required area of quadrilateral is 19.635 square units.
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Best explained and correct answer gets brainliest.
value = 45 x (1+0.015)^15
45 x 1.015^15=
45 * 1.25 = 56.26
answer is B $56.26
The diagonals of a parallelogram are 12 meters and 20 meters and intersect at an angle of 60°. find the length of the longer side.
Final answer:
To find the length of the longer side of the parallelogram, you can use the law of cosines.
Explanation:
To find the length of the longer side of the parallelogram, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those two sides and the cosine of the included angle.
In this case, one of the diagonals is 12 meters and the other is 20 meters. The included angle is 60°.
Letting 'a' be the length of the longer side, we can set up the equation:
a^2 = 12^2 + 20^2 - 2(12)(20)cos(60°)= 304
a=17.43
A certain forest covers an area of 3900 km2 . suppose that each year this area decreases by 8% . what will the area be after 10 years? use the calculator provided and round your answer to the nearest square kilometer.
A = P(1-r)^t
A = 3900(1-0.08)^10
A = 3900(0.92)^10
A = 3900(0.434388454)
A = 1694.11
1694 square km
What is the area of the rectangle shown on the coordinate plane?
Take a look at the table of possible outcomes when a pair of fair dice is rolled. What is the probability that the sum of the numbers rolled is either even or a multiple of 5?
Answer:
He is correct
Step-by-step explanation:
A positive integer is 47 more than 9 times another. their product is 18601860. find the two integers.
What is the surface area of a cone with a diameter of 28 cm. and height 22 cm in terms of Ï.
196Ï cm2
365Ï cm2
561.1Ï cm2
2202.8Ï cm2
To find the surface area of a cone, use this formula.
pi (r) (r + [square root of h^2 plus r^2] ) substitute
h = height = 22 r = radius = 28/2 = 14 [ ] = sq. root
pi (14) (14 + [ 22^2 + 14^2 ]) solve exponents
pi (14) (14 + [484 + 196]) add
pi (14) (14 + [680]) solve square root
pi (14) (14 + 2[170]) add
pi (14) (40.0768) multiply
pi (561.075) is about 561.1 rounded to nearest tenth
So the answer is C. 561.1pi cm^2
Round to the nearest hundredth.
Every day, about 140,000,000 plastic water bottles are bought in the United States. Each bottle is about 0.25 meters long, and the equator of the Earth is about 40,000,000 meters around.
How many times can the Earth's equator be circled by a line of plastic bottles used in the United States every day?
Answer:
0.875 times Earth's equator is circled by plastic bottles every day.
Step-by-step explanation:
Given: No of plastic water bottles every day = 140,000,000
Length of a bottle = 0.25 m
length of equator of earth = 40,000,000 m
To find: no times Earth's equator is circled by line of bottles every day
No of plastic water bottles every day = 140,000,000
Length of 1 plastic water bottle = 0.25m
⇒ Length of 140,000,000 plastic bottles = 0.25 × 140000000
= 35000000 m
No. of times Earth's Equator is circled by bottles = [tex]\frac{35000000}{400000000}[/tex]
= 0.875
Therefore, 0.875 times Earth's equator is circled by plastic bottles every day.
Answer:
0.875
Step-by-step explanation:
what is the surface area of a square pyramid with a base of 12cm and a slanted height of 8cm?
Cylindrical coordinates? Hi,
I am having problems with a homework question,
I am asked to sketch the solid by the given inequalities.
0 <= theta <= pi/2 and r <= z <= 2
How do I find r?
If possible please guide me to the answer instead of giving it to me. I need to know this stuff.
Thanks in advance for any help.
Chelsea made 15 of the 28 recipes she downloaded from the Internet. What percent of the recipes did she make?
Final answer:
Chelsea made 15 out of 28 recipes she downloaded from the Internet, which translates to approximately 54% of the recipes when calculated using the percentage formula: (Part/Total) × 100.
Explanation:
To find out what percent of the recipes Chelsea made, we will use the formula for calculating the percentage:
Percentage = (Part/Total) × 100
Here, the part is the number of recipes she made, and the total is the number of recipes she downloaded. Chelsea made 15 recipes out of 28. So we set it up like this:
Percentage = (15/28) × 100
Solution:
Percentage = (15/28) × 100
Percentage = 0.5357... x 100
Percentage = 53.57...
When you round to the nearest whole number, Chelsea made approximately 54% of the recipes.
Chelsea made approximately 53.57% of the recipes from the Internet, totaling 15 out of 28 recipes.
To find the percentage of recipes Chelsea made, follow these steps:
Step 1: Calculate the fraction of recipes she made.
Fraction made = (Number of recipes made) / (Total number of recipes)
= 15 / 28
Step 2: Convert the fraction to a percentage.
Percentage = Fraction * 100
= (15 / 28) * 100
Step 3: Perform the calculation.
Percentage = (15 / 28) * 100
≈ 53.57%
So, Chelsea made approximately 53.57% of the recipes.
Which equation represents the vertical asymptote of the graph?
In this question, with the help of the graph we have to find the vertical asymptote .
First let's check out what is vertical asymptote .
Vertical asymptotes are straight lines of the equation , toward which a function f(x) approaches infinitesimally closely, but never reaches the line.
And in the graph, the function approaches to 12 but never touches it .
So the vertical asymptote is x=12 .
The equation which represents the vertical asymptote of the graph given is; x =12.
The Vertical Asymptote of a graphThe vertical asymptote of a graph is simply a vertical line on the x-axis to which the graph of a function approaches but never touches.
By observation, the line x=12 separates the curves and both curves do not touch the line.
Ultimately, the line x=12 is the vertical asymptote of the given graph.Read more on vertical asymptote;
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AB=diameter of the circle O. OC=radius. Arc AXB is an arc of the circle with centre C. Prove areas of the shaded region are =
a rectangle has an area of 12m and a width of 400cm. what is the length?
By how much does a^3 - 2a exceed a^2 + a - 6?
Answer
a³ - a² - 3a + 6
Explanation
The equation requires you to subtract the two expressions.
(a³ - 2a) - (a² + a - 6)
In such an expression we subtract the like term only.
(a³ - 2a) - (a² + a - 6) = a³ - 2a - a² - a + 6
= a³ - a² -2a - a + 6
= a³ - a² - 3a + 6
If f(x) = ∣(x2 − 8)∣, how many numbers in the interval 0 ≤ x ≤ 2.5 satisfy the conclusion of the mean value theorem?
First let us find the slope of the straight line formed when x1 = 0 to x2 = 2.5.
y = x^2 – 8
y1 = 0^2 – 8 = - 8
y2 = 2.5^2 – 8 = -1.75
The formula for finding the slope is:
m = (y2 – y1) / (x2 – x1)
m = (-1.75- (- 8)) / (2.5 – 0)
m = 2.5
The mean value theorem states that the slope must be 2.5 at least once between x1 = 0 to x2 = 2.5.
Taking the 1st derivative (slope) of the equation:
dy / dx = 2x
Since dy / dx = m = 2.5
2x = 2.5
x = 1.25
Therefore the answer is: One number at x = 1.25
Factor k 2 + 13k + 12.
Answer:
The factors of the given polynomial are : (k + 1)(k + 12)
Step-by-step explanation:
The quadratic equation which is needed to be factorized is given as :
k² + 13k + 12
In order to factorize this, arrange 13k in such a way that the product of its factors equals to 12k² ⇒ 13k = 12k + k
⇒ k² + 13k + 12
⇒ k² + k + 12k + 12
⇒ k(k + 1) + 12(k + 1)
⇒ (k + 1)(k + 12)
Hence, The factors of the given polynomial are : (k + 1)(k + 12)
A video game that costs $30 is on sale for 25% off. What is the sale price?
$37.50
$5
$27.50
$22.50
A city’s population, P (in thousands), can be modeled by the equation P = 130( 1.03)^x where x is the number of years after January 1, 2000. For what value of x does the model predict that the population of the city will be approximately 170,000?
To find the value of x for which the model predicts a population of approximately 170,000, solve the equation P = 130(1.03)^x. Divide both sides by 130, take the logarithm of both sides, and solve for x. The approximate value of x is 9.855.
Explanation:To find the value of x for which the model predicts a population of approximately 170,000, we need to solve the equation:
170 = 130(1.03)x
To solve for x, we can start by dividing both sides of the equation by 130:
170/130 = (1.03)x
1.3077 = (1.03)x
Next, take the logarithm of both sides of the equation:
log(1.3077) = x * log(1.03)
Using a calculator, we can find that x is approximately 9.855.
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Firstly, we need to clarify that the population given in the question, 170,000, is represented in 'thousands' in the modelling equation. Therefore, for simplicity, it is referred to as '170' in the equation.
We know from the problem that the population model is:
P = 130 * (1.03 ^ x),
where P is the population (in thousands) and x is the number of years since the start point (January 1, 2000). Given that we're looking for the point in time where the population is approximately 170,000 (or '170' in the terms of the equation), we can set P = 170 and solve for x:
170 = 130 * (1.03 ^ x)
Solving an equation in terms of x with an exponent can be handled neatly with logarithms. You can isolate the variable by taking the natural log (ln) of both sides. So we can transform our equation like this:
ln(170 / 130) = ln(1.03 ^ x)
Next, we use the property of logarithms that says the log of a number raised to an exponent is equal to the exponent times the log of the number:
ln(170 / 130) = x * ln(1.03)
Solving for x gives:
x = ln(170 / 130) / ln(1.03)
Calculating the value gives x ≈ 9.075604092564975. However, since the population is generally reported on an annual basis, we round the value of x up to the nearest whole number. That gives us:
x_rounded ≈ 10 years.
So, according to the model, the city's population will reach approximately 170,000 around 10 years after January 1, 2000.
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Select the postulate or theorem that you can use to conclude that triangles are similar.
Answer:
AA similarity postulate.
Step-by-step explanation:
Two triangles which are of same shape are called similar triangles.
In the given triangles two angles are marked 90 degrees and another pair of angles are marked the same that is equal.
In the given figure:
m∠P==m∠L=90°
m∠J=m∠M.
Two angles are equal .
The AA similarity postulate states: if two pairs of corresponding angles are congruent, then the triangles are similar .
Answer :AA similarity postulate.
Answer:
AA
Step-by-step explanation:
9.1 ÷ 3576 long division
Answer: the answer is 0.00254474272
goooood luck
In an isosceles triangle the base angles are congruent. True False
The formula for the volume of a pyramid is V=13BhV=13Bh, where B is the area of the base and h is the height. Rearrange the formula to solve for the height (h).
h=B3Vh=B3V
h=V3Bh=V3B
h=3VBh=3VB
h=3BV
To solve for the height h in the volume formula V = 1/3Bh for a pyramid, the formula needs to be rearranged to h = 3V/B by first multiplying both sides by 3 and then dividing by B.
The formula for the volume of a pyramid is V = 1/3Bh, where B is the area of the base and h is the height. To solve for the height, h, we need to rearrange the formula.
Starting with V = 1/3Bh, we want to isolate h:
Multiply both sides of the equation by 3 to cancel out the fraction: 3V = Bh.
Next, divide both sides by B to solve for h: h = 3V/B.
The correct formula to solve for height is h = 3V/B.