x1,x2(-1, 7/3)
to slove this you need the formula
from equation a=3 b=-4 c=7;
x=(-b±√b²-4ac)/2a
x=(4±√-4²-4×3×7)/2×3
x=(4±√100)/6
x=(4±10)/6
x1=4-10/6 x2=4+10/6
x1=-6/6 x2=14/6
x1=-1 x2=7/3
The sum of roots is 4/3, and the product of roots is -7/3 for the quadratic equation [tex]3x^2[/tex] - 4x - 7 = 0.
To find the sum and product of the roots of the quadratic equation [tex]\(3x^2 - 4x - 7 = 0\)[/tex], we can use Vieta's formulas.
Vieta's formulas state that for a quadratic equation of the form [tex]\(ax^2 + bx + c = 0\),[/tex] the sum of the roots [tex](\(r_1\) and \(r_2\))[/tex] is given by [tex]\(-\frac{b}{a}\),[/tex] and the product of the roots is given by [tex]\(\frac{c}{a}\).[/tex]
In your equation, [tex]\(a = 3\), \(b = -4\), and \(c = -7\).[/tex]
So, the sum of the roots [tex](\(r_1\) and \(r_2\)) is:[/tex]
[tex]\[r_1 + r_2 = -\frac{b}{a} = -\frac{-4}{3} = \frac{4}{3}\][/tex]
And the product of the roots [tex](\(r_1\) and \(r_2\)) is:[/tex]
[tex]\[r_1 \cdot r_2 = \frac{c}{a} = \frac{-7}{3}\][/tex]
So, the sum of the roots is [tex]\(\frac{4}{3}\)[/tex], and the product of the roots is [tex]\(\frac{-7}{3}\).[/tex]
A touch tank has a height of 3 feet. Its length is three
times the width. The volume of the tank is 270 cubic feet.
Find the length and width of the tank,
3 ft
Answer:
5.5 cu ft vol = L*w*h* w=x L= 3x h=3
270= 3[3x*x]
Final answer:
To find the length and width of the touch tank, we need to use the formula for the volume of a rectangular tank. By substituting the given values and solving the equation, we can find the width and length.
Explanation:
Let's assume that the width of the touch tank is x feet. So, the length of the tank would be 3x feet.
The volume of a rectangular tank is given by the formula volume = length × width × height. We can substitute the given values into this formula.
270 = (3x) * x * 3
Simplifying the equation, we get:
270 = 9x^2
Dividing both sides of the equation by 9:
x^2 = 30
Taking the square root of both sides of the equation:
x = √30 ≈ 5.48
Therefore, the width of the touch tank is approximately 5.48 feet. Since the length is three times the width, the length would be approximately 3 × 5.48 = 16.44 feet.
A trapezoid with bases of 18 feet and 12 feet, height of 4 feet, and side length of 5 feet. What statements are true? Check all that apply. The height of the new trapezoid will be 1 ft. The height of the new trapezoid will be 16 ft. The area of the new trapezoid is One-fourth times the area of the original trapezoid. The area of the new trapezoid is StartFraction 1 Over 16 EndFraction times the area of the original trapezoid. The area of the new trapezoid is 4 times the area of the original trapezoid.
Answer:
A and D
Step-by-step explanation:
Got it right :)
Final answer:
The true statement about the new trapezoid is that the area of the new trapezoid is \(1/16\) times the area of the original trapezoid, assuming that all dimensions are scaled down by the same factor.
Explanation:
The area of a trapezoid is given by the formula: [tex]Area = \((base_1 + base_2) / 2\) * height[/tex]. For the original trapezoid with bases of 18 feet and 12 feet and a height of 4 feet, the area is [tex]\((18 + 12) / 2\) * 4 = 60[/tex] square feet. If the dimensions of the trapezoid are scaled down or up, the new height and area can be determined by using the same proportionality principle that applies to triangles. If the height is reduced by a factor of 4, which means the new height is 1 foot, then the area will also be reduced by the same factor squared (since area is a two-dimensional measure). Therefore, the new area will be 1/16 times the original area, which equals 60 / 16 = 3.75 square feet.
is 1.6 rational or irrational
Rose lives 3/4 of a mile from her cousin. One day she rode her bike to her cousin's house. When she got 2/5 of the way there, her bike chain broke and she had to walk the rest of the way. What part of a mile did Rose go on her bike before it broke?
Answer: 3/10 of a mile
Step-by-step explanation:
Hi, to answer this question we simply have to multiply the 2/5 of the way that she travelled on her bike before it broke by the total distance (3/4 of a mile)
2/5 x 3/4 = 3/10 of a mile
She travelled 3/10 of a mile on her bike before it broke
Feel free to ask for more if needed or if you did not understand something.
Rose traveled [tex]\( \frac{3}{10} \)[/tex] of a mile on her bike before it broke, found by multiplying 2/5 by 3/4. Equation: Distance on bike = (2/5) × (3/4).
To find out what fraction of a mile Rose traveled on her bike before it broke, we need to find 2/5 of 3/4 mile.
[tex]\[ \text{Distance traveled on bike} = \left(\frac{2}{5}\right) \times \left(\frac{3}{4}\right) \][/tex]
[tex]\[ = \frac{2}{5} \times \frac{3}{4} \][/tex]
[tex]\[ = \frac{2 \times 3}{5 \times 4} \][/tex]
[tex]\[ = \frac{6}{20} \][/tex]
[tex]\[ = \frac{3}{10} \][/tex]
So, Rose traveled [tex]\( \frac{3}{10} \)[/tex] of a mile on her bike before it broke.
The equation for this would be:
[tex]\[ \text{Distance on bike} = \left(\frac{2}{5}\right) \times \left(\frac{3}{4}\right) \][/tex]
Complete Question:
Rose lives 3/4 of a mile from her cousin. One day she rode her bike to her cousin's house. When she got 2/5 of the way there, her bike chain broke and she had to walk the rest of the way. What part of a mile did Rose go on her bike before it broke? Show your work and write an EQUATION in the box to the right.
A piece of copper has a mass of 58kg and displaces 5918ml. What is its density?
Answer:
8.96 g/cm2
Step-by-step explanation:
Bree made 48 cookies. She used 1,104 chocolate chips for all of the cookies. How many chocolate chips were in each cookie?
Answer:
23
Step-by-step explanation:
its 23 beacuase 1104 divided by 48 is 23 so its 23 chips
Answer: 23
Step-by-step explanation: 1,104 divided by 48 = 23
What do the three red tiles in the model of the equation below represent?
2 long x tiles and 3 square 1 tiles = 3 negative x tiles
–3
3
–3x
3x
Answer:
the answer is c
Step-by-step explanation:
Answer:
The answer is -3x because the red tiles represent -x so since there are 3 -x tiles the answer would be -3x
can someone help me with this equation plsss i really need it
3(6x–5)–7(3x+10)=0
Answer:
-28 1/3
Step-by-step explanation:
is the expression 4 - x the same as x – 4? Explain
Answer:
Yes
Step-by-step explanation:
The order of the factors does not alter the product
Yes because of your property’s
Steve bought a triangular mat to cover a corner of his room. How much area of the floor will this mat cover?
A. 60 square feet
B. 80 square feet
C. 48 square feet
D. 24 square feet
Please help worth 40 points!
Answer:
i believe is c
Step-by-step explanation:
because you addd 10 plus 8 times 6.
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The area of the floor that will be covered by the Matt is 24 sq. ft.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.
The area of the floor covering will be equal to the area of the triangular carpet. Therefore, using the Heron's formula we can write,
s = (10+8+6)/2 = 12
Area of the triangle = √[12(12-10)(12-8)(12-6)] = √(12×2×4×6) = 24 sq ft.
Hence, the area of the floor that will be covered by the Matt is 24 sq. ft.
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On a exam you get two points for each question answered correctly,zero points for each question left blank,and lose one point for each question answered incorrectly.what is your total score on the exam if you answer 22 questions correctly,leave 7 questions blank,and answer 5 questions incorrectly? P.S simplify expression
Answer:
Total score = 39 points
Step-by-step explanation:
For each correct question, you get 2 points, and there are 22 correct questions, so:
22 * 2 = 44 points.
For each question left blank, you get 0 points, and there are 7 questions left blank, so:
7 * 0 = 0 points
For each incorrect question, you get -1 point, and there are 5 incorrect questions, so:
5 * (-1) = -5 points.
The total number of points is:
Score = 22*2 + 7*0 + 5*(-1) = 44 + 0 - 5 = 39 points
40.40
What is the area of the base of the cone below? Round the answer to the nearest tenth if necessary.
V = 52 in 3
14.7 in2
Please hurry 29 points
17.3 in2
18 5 in 2
19.5in 2
Answer:
D) 19.5 in^2
Step-by-step explanation:
Volume is 1/3base * height
52in^3 = 1/3x*8
multiply by 3
156in^3 = x*8
divide by 8
19.5 = x
x = 19.5
Answer:
D
Step-by-step explanation:
Trapezoid $RSTU$ is a cross section of a lampshade. The diagonals of $RSTU$ are congruent, and the measure of $\angle S$ is $112\degree$ . What is the measure of $\angle U$ ?
The sum of the angle ∠T and angle ∠U will be a 180°. Then the angle ∠U will be 68°.
What is a trapezium?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.
Trapezoid RSTU is a cross-section of a lampshade.
The diagonals of RSTU are congruent, and the measure of angle S is 112 degrees.
Then the measure of angle U will be
Angle S and angle T are equal.
∠S = ∠T = 112°
And the sum of the angle ∠T and angle ∠U will be a 180°.
Then we have
∠T + ∠U = 180°
112° + ∠U = 180°
∠U = 68°
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The measure of angle U in the trapezoid RSTU with congruent diagonals and angle S measuring 112 degrees is 68 degrees, using the properties of an isosceles trapezoid.
To find the measure of in the trapezoid RSTU, with diagonals congruent and the measure of angle S being 112 degrees, we need to use the properties of a trapezoid and the fact that the diagonals are congruent. In an isosceles trapezoid, the base angles are congruent, meaning angles S and U are congruent because diagonals are congruent. Since the sum of angles in a quadrilateral is 360 degrees, we can set up an equation: 2(112) + 2(angle U) = 360.
Solving for angle U, we get:
224 + 2(angle U) = 3602(angle U) = 136angle U = 68 degreesHence, the measure of angle U in the trapezoid RSTU is 68 degrees.
What is the midpoint between (7 - 3i) and ( 3 + 2i).
Answer:
Step-by-step explanation:
5-0.5i
The Lumberjack Hardware store found that 5 out of every 10 paint sprayers they recently received were not properly assembled. If they received 385 paint sprayers, about how many paint sprayers can they expect to be faulty?
Answer: 193 faulty paint sprayers
Step-by-step explanation: 5/10 is = to 1/2 so half of them are faulty
next divide 365 by 2 to get 192.5 remember if the decimal is 5 or greater you can round up since you cannot have half a paint sprayer you have to round up to 193 paint sprayers
hope this helps mark me brainliest if it helped
Find the area of the polygon.
_12 cm
| 19 cm
12 cm
The area of the polygon is |
square centimeters.
Answer:
[tex]A = 1172.965\,cm^{2}[/tex]
Step-by-step explanation:
Let be a side of 12 cm (l) and an apothem of 19 cm (p). First, the number of sides has to be determined:
[tex]n =\frac{360^{\textdegree}}{2\cdot \tan^{-1}\left(\frac{6\,cm}{19\,cm} \right)}[/tex]
[tex]n = 10.271[/tex]
The polygon has ten sides and the side length shall be re-adjusted:
[tex]\theta = \frac{360^{\textdegree}}{10}[/tex]
[tex]\theta = 36^{\textdegree}[/tex]
The side length is:
[tex]l = 2\cdot (19\,cm)\cdot \tan 18^{\textdegree}[/tex]
[tex]l = 12.347\,cm[/tex]
The area of the polygon is:
[tex]A = \frac{n\cdot l \cdot p}{2}[/tex]
[tex]A = \frac{(10)\cdot (12.347\,cm)\cdot (19\,cm)}{2}[/tex]
[tex]A = 1172.965\,cm^{2}[/tex]
if the volume of a cube is 1,000 cubic feet what is the surface area
Here,
volume(v)=1000 ft^3
also,
v=l^3
or,1000=l^3
therefore,
l=10ft
Now,
Surface area(A)=6l^2
=6×10^2
=600 ft^2
Hope it helps!!!!!
If the volume of a cube is 1,000 cubic feet then the Surface area(A) of a cube of side 10 feet would be 600 ft^2.
What is a cube?A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.
The volume of a cube can be calculated as the cube of the sides of a given figure.
The volume of a cube = side ^3
Given ; if the volume of a cube is 1,000 cubic feet
The volume(v) = 1000 ft^3
also, The volume(v) = l^3
or,1000 = l^3
therefore, l = 10ft
The side of the given cube is 10 feet.
Now,
The Surface area(A) of a cube = 6l^2
= 6 × 10^2
= 600 ft^2
Hence, if the volume of a cube is 1,000 cubic feet then the Surface area(A) of a cube of side 10 feet would be 600 ft^2.
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this is asking using the completing the square method
Answer:
first box [
4
]
second box [
7
____
2
]
third box[
0
]
Step-by-step explanation:
Which of the following triangle lengths form right triangles? Select all that apply
(7, 11, 13)
(10,24,26)
(12, 16, 20)
(12, 35, 37)
(13, 15, 19)
Answer:
B,C,D
Step-by-step explanation:
The correct option is (10,24,26) , (12, 16, 20) and (12, 35, 37).
What are the three sides of a right triangle?In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. We use special words to describe the sides of right triangles.
What is considered a right triangle?A right triangle is a triangle with one right angle (one angle equal to 90°). The side opposite the right angle (the longest side) is called the hypotenuse. The remaining two sides (the sides that intersect to determine the right angle) are called the legs of the right triangle.
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0.00005026 as a scientific notation
Answer:
5026*10^-5
Step-by-step explanation:
Answer:
5.026 x 10-5
Step-by-step explanation:
I will comment the other answer choices but help me please
Do I choose A or B?
If so: B
Which table shows a positive correlation? A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 5, 5, 5, 5, 5. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 10, 18, 31, 37, 52. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 24, 25, 13, 9, 6. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 9, 12, 17, 21, 22.
Answer: The Answer is B
Step-by-step explanation:
The first box has all 5's so it's just going to be a straight line.
The third box is a negative correlation because the number are going down in the right column
The fourth column doesn't make any sense because the X column has all 8's
So the answer is B.
Hope this helps : )
The table shows a positive correlation in B; The first column is labeled x with entries 1, 2, 3, 4, and 5. The second column is labeled y with entries 10, 18, 31, 37, and 52. A 2-column table with 5 rows.
What is correlation?The correlation of two pairs of data values tells about the degree of movement that can occur in one of the data when another data value is increased or decreased respectively.
Since it is called that the Correlation coefficient is a measure of how similar two datasets are acting.
The first box has all 5s =hence, it's just going to be a straight line.
The third box is a negative correlation due to the number is going down in the right column
The fourth column, the X column has all 8's
Hence, the answer is B.
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The cost to enter a waterpark increases from $56 per person to $73 per person. What percent of the entry fee increase
Final answer:
The percent increase of the waterpark's entry fee is approximately 30.36%, which is calculated by finding the difference between the new and original cost, dividing by the original cost, and then converting that number to a percentage.
Explanation:
To calculate the percent increase of the entry fee to the waterpark, we need to follow these steps:
Find the amount of the increase by subtracting the original cost from the new cost.Divide the amount of the increase by the original cost.Multiply the result by 100 to convert it to a percentage.Step 1: The increase in cost is $73 - $56 = $17 per person.
Step 2: The increase divided by the original cost is $17 ÷ $56 ≈ 0.30357.
Step 3: To find the percent increase, we multiply the result from step 2 by 100: 0.30357 × 100 ≈ 30.36%.
Therefore, the percent increase of the entry fee is approximately 30.36%.
To find the percent increase in the entry fee, subtract the old fee from the new fee, divide by the old fee, and multiply by 100. The entry fee increase is approximately 30.36%.
Explanation:To find the percent increase in the entry fee, you need to calculate the difference between the new fee and the old fee, and then divide that difference by the old fee. Finally, multiply the result by 100 to get the percentage.
Find the difference in the fees: $73 - $56 = $17Divide the difference by the old fee: $17 ÷ $56 ≈ 0.3036Multiply the result by 100 to get the percentage: 0.3036 × 100 ≈ 30.36%The entry fee increase is approximately 30.36%.
Solve the following systems: 3x+4y=0 2x+3y=1
Answer:
Answer is x= -4 and y= 3
Step-by-step explanation:
[tex]given \: equations \: are \\ 3x + 4y = 0 \: \: and \: 2x + 3y = 1 \\ multiply \: by \: 2 \: in \: first \: equation \\ 6x + 8y = 0 \\ multiply \: by \: 3 \: in \: second \: equation \\ 6x + 9y = 3 \\ subtracting \: the \: above \: mentioned \: equation \: \\ we \: get \: - y = - 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 3 \\ substitute \: y = 3 \: in \: first \: equation \\ 3x + 4(3) = 0 \\ 3x = - 12 \\ x = - 4[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
a) Write down 375 as the product of prime factors.
Give your answer in index form.
b) Work out the highest common factor of 375 and 150.
Answer:
a) 3x5³
b) 75
Step-by-step explanation:
a) find the Prime factors of 375 by dividing your number by prime numbers (you answers must be whole) use a factor tree to help you
a) do the same to 150
one you have you answers in this case we have
375- 3x5x5x5
150 - 2x3x5x5
you collect all the like terms, this will be 3x5x5 then you just simply multiply it And it gives you 75
375 as a product of prime factors is 3x5^3 and the highest common factor of 375 and 150 is 25.
Explanation:To express 375 as the product of prime factors, you must first determine the prime numbers that when multiplied together will equal 375. The prime factors of 375 are 3 and 5. So, 375 can be written as 3x5^3.
Next, to find the highest common factor of 375 and 150, you need to first find the prime factors of both numbers. As shown above, the prime factors of 375 are 3 and 5. The prime factors of 150 are 2, 3 and 5.
The highest common factor is identified by locating the largest number that can divide both numbers without leaving a remainder. The highest common factor of 375 and 150 is hence, 25 because it's the greatest factor that both numbers have in common.
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It costs $8.50 to park a vehicle at the Wild Rapids Water Park. The admission price to the park is $27.50 per person. If a group in one vehicle spends $228.50 to park and enter the park, how many people attended? Write an equation, and then solve.
Answer:
8 people
Step-by-step explanation:
step1:move 8.50 to the other side
228.50=8.50+27.50x
220=27.50x
step 2:find x by dividing
220=27.50x
x=8
hope this helps,mark me brainliest.
There are 8 people who attended the park.
To solve the problem, let's define the variables and write an equation. Let x be the number of people who attended. The total cost is the sum of the parking fee plus the admission fees.
The parking fee is $8.50, and the admission fee per person is $27.50. Therefore, the total cost can be expressed as:
Total Cost = Parking Fee + (Admission Fee per Person * Number of People)
This simplifies to:
$228.50 = $8.50 + $27.50 * x
First, subtract the parking fee from the total cost:
$228.50 - $8.50 = $27.50 * x
$220 = $27.50 * x
Now, divide both sides by the admission fee per person to find x:
x = $220 / $27.50
x = 8
Thus, 8 people attended the park.
Peter ran 4 ⅔ miles on Tuesday. On Wednesday, he ran ⅘ of this distance. How far did he run?
Answer:
3.73333
Step-by-step explanation:
Answer:
Step-by-step explanation:
Distance = 4/5 of 4 2/3
[tex]=\frac{4}{5}*\frac{14}{3}\\\\=\frac{4*14}{5*3}[/tex]
= 56/15
= 3 11/15 miles
Finish the phrase "Lack of planning on your part doesn't require..." (use all lowercase letter and put spaces between each word).
Help me please !
Its another lock
Answer:
"Lack of planning on your part doesn't require an emergency on my part."
Step-by-step explanation:
Doesnt it say it in the photo?
Which sphere has a volume of approximately 113.1 cubic inches?
A.Glass ball: r = 3 inches
B.Soccer ball: r = 4 inches
C.Lamp: d = 10 inches
Answer:
it's a glass ball r = 3 inches
Step-by-step explanation:
edgenutiy
Answer:
glass ball 3 inches ( ; ( :
Step-by-step explanation:
Which sphere has a volume of approximately 113.1 cubic inches?
Glass ball: r = 3 inches
A glass ball.
Soccer ball: r = 4 inches
A soccer ball.
Lamp: d = 10 inches
A round lamp.
Create a rational function with a non-constant denominator) that has NO vertical
asymptotes.
Answer:
[tex]y = \frac{3\cdot (x+1)}{x+1}[/tex]
Step-by-step explanation:
A rational function with no vertical asymptotes contains an avoidable discontinuity, an example is presented hereafter:
[tex]y = 3[/tex]
[tex]y = 3\cdot 1[/tex]
[tex]y = 3\cdot \frac{x+1}{x+1}[/tex]
[tex]y = \frac{3\cdot (x+1)}{x+1}[/tex]