Final answer:
To determine the nature of the roots of the function f(x)=7x²+5x-1, we calculate the discriminant, which is 53. Since it's positive, the equation has two distinct real roots.
Explanation:
The nature of the roots of the quadratic function f(x)=7x²+5x-1 can be determined by calculating the discriminant, which is part of the quadratic formula. The discriminant is given by b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. For the given function, a = 7, b = 5, and c = -1. Therefore, the discriminant equals:
D = b² - 4ac
D = (5)² - 4(7)(-1)
D = 25 + 28
D = 53
Since the discriminant is positive (D > 0), the quadratic function has two distinct real roots.
Which transformations will produce similar, but not congruent, figures?
Triangle PQR is reflected across the x-axis and then rotated 90° clockwise to form triangle P"Q"R" .
Triangle PQR is reflected across the y-axis and then dilated by a scale factor of 6 to form triangle P"Q"R" .
Triangle PQR is rotated 180° counterclockwise and then translated 11 units left to form triangle P"Q"R" .
Triangle PQR is rotated 90° clockwise and then reflected across the y-axis to form triangle P"Q"R" .
Find the area and perimeter of each composite figure use 3.14 for pi round your answer to the nearest 10th
Find the surface area and volume of each figure use 3.14 for pi round your answer to nearest 10th
I have examples if needed
1. Perimeter is 3 + 3 +3 +4 +5 = 18 feet
Area = 3*3 = 9, 1/2*3*4 = 6, 9 + 6 =15 square feet
2. perimeter = 2.5 +2.5+ 2.5+2.5+0.5+0.5 = 11 meters
Area = 3*.5 = 1.5, 3*2=6, 6+1.5 = 7.5 square meters
3. perimeter = 3.14*2*3 = 18.84 +8 = 26.8 inches
Area = 6*4 = 24 + 3.14*3^2 = 28.26 = 28.26 +24 = 52.3 inches
4. surface area = 2*π*6*20+2*π*6^2= 980.2 yards
Volume = π*6^2*20 = 2261.9 cubic yards
5.surface area = 2*(9*7+2*2+2*9) = 190 cm
Volume = 2*7*9 = 126 cubic cm
6. surface area = 2*(11*11+11*11+11*11) = 726 mm
Volume = 11 *11*11 = 1331 cubic cm
1. Area = 15 square feet
2. Area = 5.5 square meters
3. Area = 52.26 square inches
4. Surface area = 312π square yards, Volume = 720π cubic yards
5. Surface area = 127 square cm, Volume = 126 cubic cm
6. Surface area = 726 square mm, Volume = 1331 cubic mm
let's go through each problem step by step with proper calculations:
**Problem 1:**
Given:
Perimeter = 3 + 3 + 3 + 4 + 5 = 18 feet
Area calculations:
- For the triangle: Area = 1/2 × base × height = 1/2 × 3 × 4 = 6 square feet
- For the rectangle: Area = length × width = 3 × 3 = 9 square feet
Total Area = 6 + 9 = 15 square feet
**Problem 2:**
Given:
Perimeter = 2.5 + 2.5 + 2.5 + 2.5 + 0.5 + 0.5 = 11 meters
Area calculations:
- For the triangle: Area = 1/2 × base × height = 1/2 × 0.5 × 2 = 0.5 square meters
- For the rectangle: Area = length × width = 2.5 × 2 = 5 square meters
Total Area = 0.5 + 5 = 5.5 square meters
**Problem 3:**
Given:
Perimeter = 3.14 × 2 × 3 + 8 = 18.84 + 8 = 26.84 inches
Area calculations:
- For the rectangle: Area = length × width = 6 × 4 = 24 square inches
- For the circle: Area = π × radius² = 3.14 × 3² = 28.26 square inches
Total Area = 24 + 28.26 = 52.26 square inches
**Problem 4:**
Given:
Surface area calculations:
- For the cylinder:
- Lateral Surface Area = 2 × π × radius × height = 2 × π × 6 × 20 = 240π square yards
- Top and bottom circles: Area = 2 × π × 6² = 72π square yards
Total Surface Area = 240π + 72π = 312π square yards
Volume calculations:
- Volume = π × radius² × height = π × 6² × 20 = 720π cubic yards
**Problem 5:**
Given:
Surface area calculations:
- For the rectangular box:
- Front and back: 9 × 7 = 63 square cm
- Sides: 2 × (2 × 9) = 36 square cm
- Top and bottom: 2 × (2 × 7) = 28 square cm
Total Surface Area = 63 + 36 + 28 = 127 square cm
Volume calculations:
- Volume = length × width × height = 9 × 7 × 2 = 126 cubic cm
**Problem 6:**
Given:
Surface area calculations:
- For the cube:
- All faces are identical: 6 × (11 × 11) = 726 square mm
Volume calculations:
- Volume = side³ = 11³ = 1331 cubic mm
Help me with the first one please
Please answer this question!
Set up a proportion and use cross multiplication to solve. 100 is 250% of?
Answer:
[tex]40[/tex]
Step-by-step explanation:
Let
x-------> the number
[tex]\frac{x}{100\%}=\frac{100}{250\%}[/tex]
[tex]x*250\%=100*100\%\\ \\x=10,000/250\\ \\x= 40[/tex]
Which shows the correct word and expanded forms for the decimal? 3.28
a. three and twenty-eight thousandths 3 + 0.2 + 0.08
b. three and twenty-eight thousandths 3 + 0.02 + 0.008
c. three and twenty-eight hundredths 3 + 0.2 + 0.8
d. three and twenty-eight hundredths 3 + 0.2 + 0.08?
Bill ate 1/4 pound of trail mix on his first break during a hiking trip. On his second break, he ate 1/6 pound. How many pounds of trail mix did he eat during both breaks? Explain.
What is the solution for 2(4r+6)=2/3(12r+18)
A quadrilateral whose opposite sides are parallel and congruent and whose opposite angles are congruent is a ____. a. trapezoid c. kite b. heptagon d. parallelogram.
PLZ ANSWER ASAP!!
If you randomly choose a letter in the word "mathematics", find the probability that you choose an "a".
ABCD is a rectangle. The length of BD is 8 units and m
What is the length of AC and m
what type of triangle has two angles at 70 degrees and one at 40 degrees
I've forgotten how to work out these kind of problems...could someone explain please? Will give brainiest. (Picture attached)
For items 14 and 15 use the following functions
f(x)=5x+1
g(x)=3x-4
14. Evaluate f(2), g(2), (f o g) (2), and (g o f)(2).
15. Write the composite functions h(x)=g(f (x)) and k(x)=f(g(x)).
Nick’s house is 4.28 miles from school. if nick’s average stride length is 3.1 feet, how many strides will it take him to walk to school?
a cone with a mass of 6 g has a radius measuring 5 cm and a height of 2 cm . what is its density?
HELP PLEASE!!! 15pts!!
Dominic is a landscape architect and is designing a garden with an area of up to 500 square feet. He will use two types of plants: zinnias and petunias. Each zinnia plant requires 1.6 square feet of ground and each petunia plant requires 1.8 square feet of ground. Each zinnia plant costs $4 and each petunia plant costs $3, and the architect must spend no more than $600.
Let z represent the number of zinnia plants and p represent the number of petunia plants.
Three of the constraints for this situation are z≥0 , p≥0 , and 1.6z+1.8p≤500 .
What is the other constraint for this situation?
Enter your answer in the boxes.
__ z + __ p ≤ __
The third constraint was based on the total area that the garden can only take. Now the last constraint must be based on the total cost that should be spend in order to make a 500 square feet of garden, that is:
4 z + 3 p ≤ 600
What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ?
Enter your answer in the box. Do not round any side lengths.
___ units²
Introduction to addition or subtraction of fractions with different denominator 3/5+1/3
The diagonals of rhombus fghj intersect at point k. if side gh is equal to 3x - 10 and side jh is equal to 6x - 19, find x
the square root of a number is -18. what is the other square root?
Determine whether the ordered pair (1,4)is a solution of the linear inequality y-4x<0.
If you vertically compress the absolute value parent function, f(x) = |x|, by a factor of 3, what is the equation of the new function?
A. g(x) = |x – 3|
B. g(x) = |3x|
C. g(x) = 1/3 |x|
D. g(x) = 3|x|
That is correct. On APEX its C. g(x)= 1/3 |x|
You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over
determine if x+2 is a factor of p(x) = x4 + 3x3 +4x2 -8
A cylinder has a height of 6 meters and a diameter that is 6 times the measure of the height
A circle with center (3,5) intersects the y-axis are(0,1). find the radius of the circle, find the coordinates of the other point of intersection with the y-axis. what are the coordinates of the point of intersection of the circle and the x-axis
The coordinates of the other point of intersection with the y-axis will be (0, 9). And the x-intercept is at (3, 0).
What is the equation of circle?Let r be the radius of the circle and the location of the center of the circle be (h, k).
Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
A circle with center (3,5).
Then the equation of the circle will be
(x - 3)² + (y - 5)² = r²
The circle intersects the y-axis at (0,1).
Then the radius of the circle will be
(0- 3)² + (1 - 5)² = r²
9 + 16 = r²
r² = 25
r = 5
Then the equation of the circle will be
(x - 3)² + (y - 5)² = 5²
Then the other y-intercept of the circle (0, a) will be
(0 - 3)² + (a - 5)² = 5²
9 + (a - 5)² = 25
(a - 5)² = 16
a - 5 = 4
a = 9
The intersection of the circle with x-axis at (b, 0) will be
(b - 3)² + (0 - 5)² = 5²
25 + (b - 3)² = 25
(b - 3)² = 0
b - 3 = 0
b = 3
Thus, the coordinates of the other point of intersection with the y-axis will be (0, 9). And the x-intercept is at (3, 0).
The graph is given below.
More about the equation of circle link is given below.
https://brainly.com/question/10618691
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Mitch refuses to dine at a certain restaurant because he recalls reading two or three negative reviews of its service on a popular website. Mitch is falling prey to:
In this situation, we can actually see that Mitch was simply basing her taste on the information that is readily available to her. She does not even consider whether those reviews are legit or reliable. Mitch is falling into what we call as:
“the availability heuristic”
Mitch is falling prey to the bandwagon effect, where he avoids dining at a restaurant based on a few negative reviews he read online. The bandwagon effect is a cognitive bias that leads us to adopt beliefs or behaviors because we think everyone else is doing the same.
Explanation:Mitch is falling prey to the bandwagon effect. The bandwagon effect is when someone adopts a certain belief or behavior because they believe that everyone else is doing it too. In this case, Mitch refuses to dine at a certain restaurant because of negative reviews he read on a popular website, assuming that those reviews reflect the majority opinion.
The bandwagon effect is a cognitive bias that can influence our decision-making process. It is important to be aware of this bias and make decisions based on objective information rather than simply following the crowd.
Learn more about Bandwagon Effect here:https://brainly.com/question/34612602
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Round $0.6848 to the nearest cent.
A rectangular park, with dimensions of 1500ft x 2000ft has a diagonal walking path that goes from corner to corner. How long is the walking path?