Using the vertex of the quadratic equation, it is found that the value of b is of -9.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
The axis of symmetry is [tex]x = x_v = -\frac{b}{2a}[/tex].
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, we have that the function is defined as follows:
[tex]f(x) = 3x^2 + bx + 4[/tex]
We have that [tex]a = 3, x_v = \frac{3}{2}[/tex], hence the value of b is found as follows:
[tex]x = -\frac{b}{2a}[/tex]
[tex]\frac{3}{2} = -\frac{b}{6}[/tex]
b = -6 x 3/2
b = -9.
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math question on picture
Answer:
28 cm
Step-by-step explanation:
let the unknown side be x , then
using Pythagoras' identity in the right triangle
x² + 21² = 35²
x² + 441 = 1225 ( subtract 441 from both sides )
x² = 784 ( take square root of both sides )
x = [tex]\sqrt{784}[/tex] = 28
Answer:
the unknown side is 28
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2} \\c = 35\\a = 21\\21^{2} + b^{2} = 35^{2}\\441 + b^{2} = 1225\\b^{2} = 1225 - 441\\b^{2} = 784\\b = \sqrt{784} \\b = 28[/tex]
find the product 12 times 2/3
simplify. Your answer completely
Answer:
2/3 X 12 =8
Step-by-step explanation:
2.
-----. X 12 =2 x 12= 24 Which is 24/3 =8
3
5/You spin the spinner
AND flip a coin. Find the
probability of the
compound events. Write
as a fraction and percent.
a) P(1 and tails) =
b) P(even and heads) = (The spinner is 1-5)
Answer:
a) P(1 and tails) = 1/10 = .1
b) P(even and heads) = 1/5 = .2
Step-by-step explanation:
The spinner has 5 outcomes: 1-5.
The coin has 2 outcomes: Heads or Tails.
We want to find the probability of P(1 ∩ T) and P(2,4 ∩ H).
a) P(1 and tails)Spinning the spinner and flipping the coin are independent events; therefore, getting one outcome has no effect on the outcome of another.
For independent events, the multiplication rule is:
P(A and B) = P(A) * P(B)If we use this formula for A, we get that:
P(1 and tails) = P(1) * P(tails)The probability of getting a 1 on the spinner is P(1) = 1/5.
The probability of getting tails on the coin toss is P(tails) = 1/2.
We can now multiply these probabilities together:
P(1 and tails) = 1/5 * 1/2 = 1/10The probability of getting a 1 on the spinner and tails on the coin toss is P(1 and tails) = 1/10 or .1.
b) P(even and heads)There are two even numbers between 1 and 5: 2 and 4.
The probability of getting an even number on the spinner is 2/5.
The probability of getting heads on the coin toss is 1/2.
We can multiply these probabilities together:
P(even and heads) = 2/5 * 1/2 = 2/10 = 1/5The probability of getting an even number on the spinner and heads on the coin toss is P(even and heads) = 1/5 or .2.
Select all the rational numbers.
Answer:
A, C and D
Step-by-step explanation:
Work out the volume for this prism
[tex]area = 24 \: {cm}^{2} [/tex]
[tex]height = 8 \: cm[/tex]
to find:the volume of the given prism.
solution:[tex]v = area \: of \: cross \: section \times height[/tex]
[tex]v = 24 \times 8[/tex]
[tex]v = 192 \: {cm}^{3} [/tex]
hence, the volume of the prism is 192 cubic centimeters.
There are two cubes, one smaller than the other. The two cubes combined has a volume of 118.125in. Find the side length of each cube if the smaller cube is 2/3 the length of the larger cube.
Step-by-step explanation:
let the big cube side be b
small cube side be s
s = 2/3 * b
bv + sv = 118.125
b^3 + 8/9 b^3= 118.125
17 b^3/8 = 118.125
b^3 = 55.58
b = 3.816in
s = 2.544in
PLEASE HELP ME!!!!!!!!!!!!!!
Answer:
[tex]|-a| =a[/tex]
Step-by-step explanation:
Fill in the table using this function rule.
-
y=-6x-2
Answer:
(x,y)
(-5,28)
(-1,4)
(0,-2)
(1,-8)
Step-by-step explanation:
You just have to plug in the values of x into the function rule to get all the values. Hope this helps!
please help its a math problem
An iPhone costs $1400 loses 3/8 of its value each year. What is the value of the iPhone after 3 years?
Question 6 options:
$341.80
$546.88
$1398.86
$73.83
Answer:
$341.80
Step-by-step explanation:
Value after 1 year :
1400 x (1 - 3/8)1400 x 5/825 x 7 x 5125 x 7$875Value after 2 years :
875 x 5/84375/8$546.88Value after 3 years :
546.88 x 5/82734.40/8$341.80A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes. What is the volume of the roof to the nearest tenth of a foot? What is the volume of the entire house, including the roof?
The volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.
How to find the volume of the composite figures?To find the volume of the composite figures, follow the steps listed below:,
Separate the figure.Calculate the volume of each figure by which the composite figure is made of.Add the volume of all the individual figures to get the total volume of composite figures.A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes. The volume of the roof is:
[tex]V=\dfrac{1}{3}(\text{length x width x height})\\V=\dfrac{1}{3}40\times40\times20\\V\approx10667\rm\; ft^3[/tex]
The volume of the room is:
V=length x width x height
V=40 x 40 x 30
V=48000 ft³
The volume of the entire house, including the roof, is,
V=10667+48000
V=58667 ft³
Thus, the volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.
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“which sport do you prefer soccer or basketball is”that biased or unbiased question
Answer: both
Step-by-step explanation:
Write the equation of the line that is parallel to x = 3 and passes through the
point (4, -3)
The equation of the line that is parallel to x = 3 and goes through (4, -3) is: x = 4).
What is the Slope of Parallel Lines?The slopes or parallel lines are always the same.
Given the equation of a vertical line, x = 3, the slope is undefined. So also, the slope of the line that is parallel to x = 3 is undefined.
If the line passes through the point (4, -3), it means it intercepts the x-axis at x = 4.
Therefore, the equation of the line that passes through (4, -3) and is parallel to x = 3 is: x = 4.
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Pleeaaaaase help!!!!!!!!!!
Answer:
Step-by-step explanation:
A triangular pyramid has 6 edges, 4 vertices, and 1 base
I can get the mean and the mode but I forgot how to get the mode
Answer:
median = 535
mode = 540
mean = 538.75
Step-by-step explanation:
To find the median, place the scores in order from smallest to largest, then find the middle score:
390, 460, 480, 480, 500, 510, 520, 530, 540, 540, 540, 580, 620, 630, 650, 650
As there is an even number of scores (16), the median is the average (mean) of the two middle scores (highlighed above).
Therefore, the median is 535
The mode is the number that appears the most.
Therefore, the mode is 540.
The mean is the total of the scores divided by how many scores there are.
Mean = (390 + 460 + 480 + 480 + 500 + 510 + 520 + 530 + 540 + 540 + 540 + 580 + 620 + 630 + 650 + 650) ÷ 16
⇒ Mean is 538.75
Find the area of each figure. If necessary, use 3.14 for and round to the nearest hundred.
Answer:
132 m²
Step-by-step explanation:
Split the figure into 2 parts :
Area of TriangleArea of RectangleArea (Triangle)
A = 1/2bhA = 1/2 x (20 - 8 - 6) x (10 - 6)A = 1/2 x 6 x 4A = 3 x 4A = 12 m²Area (Rectangle)
A = bhA = 20 x 6A = 120 m²Area (Figure)
12 + 120132 m²A model of a sailing boat is made to the scale
1 : 50, i.e a length of 1 cm on the model
represents 50 centimetres on the real yacht.
If one of the sails on the real yacht has an area
of 5 m² what will be the area of the same sail
on the model?
Answer:
[tex]20cm^2[/tex]
Step-by-step explanation:
We are talking of a linear scale ie 1 cm = 50 cm
So if the real yacht length is 10 meters(10,000 cm), then the model length will be 10000/50 = 200 cm
However, when talking about areas, the scale factor is different. We cannot simply divide 5m by 50
Let's say the sail height is 1 meter and the sail width is 5 meters which will give a sail area of 5 sqm.
The scaled height would be 100/50 = 2cm and scaled width will be 500/50 = 10 cm
So the area of the sail on the model will be 2 x 10 =200 square cm
In short, area of sail on model = (area of sail on real yacht( ÷ (50 x 50)
Since there are 10,000 square cm to 1 square meter we get the answer as 5 x 10000/2500 = 20 square cm
Jennifer has more than $960 in her bank account. She wants to gift her brother a laptop worth $540. If she withdraws 60 weekly for her expenses, what is the maximum number of withdrawals she can make to ensure there is enough money in her account to buy the laptop?
Answer:
It would take 10 weeks to buy the laptop so she could cover the price of the laptop and tax.
Step-by-step explanation:
Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. Find the volume v of this solid. V =
The solid was obtained by rotating the region bounded by x² = 27y, x = 0, and y = 1 about the y-axis is 42.411 cubic units.
What is integration?It is the reverse of differentiation.
Consider the solid obtained by rotating the region bounded by the given curves about the y-axis.
[tex]\rm x = 3\sqrt{3y} \ or \ x^2 = 27y[/tex]
x = 0, and y = 1
Then the volume of the solid will be
[tex]\rm Volume = \int _{0}^{1} \pi x^2 dy\\\\Volume = \int _{0}^{1} \pi 27y dy\\\\Volume = 27\pi \int _{0}^{1} \ ydy\\\\Volume = 27 \pi [\dfrac{y^2}{2}] _{0}^{1}\\\\[/tex]
[tex]\rm Volume = 13.5 \times \pi \times [y^2] _{0}^{1}\\\\Volume = 13.5 \times \pi \times (1^2 - 0^2)\\\\Volume = 42.411 \ cubic \ units[/tex]
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A soccer team is having a car wash. The team spent $55 on supplies. They earned $330, including tips. The team's profit is the amount the team made after paying for supplies. Use a sum of integers to find the team's profit.
the original purchase price of a car is 12,000. Each year, its value depreciates (loses value) by 5%. Three years after its purchase, what is the value of the car?
Answer:
10,200
Step-by-step explanation:
P(1-r)^n
r = decimal form of the interest rate percent
n = amount of years
principal times (1 - decimal form of the interest rate percent) to the (amount of years) power
12000 (1-.05)^3
use PEMDAS
12000 times (.95)^3
12000 times .857375 =
ANSWER:
10288.5
Which of the following are polynomials?
The equations in options B and D are the polynomials other equations are not polynomial.
What is polynomial?Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
The exponent of the polynomial should be always a whole number like {0,1,2,3,4,5,6,.........}
Here in the option, only two equations are polynomials that are
(2/3)x²+x+1 and x³+2x+√2
Hence the equations in options B and D are the polynomials other equations are not polynomial.
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Solve the following system of inequality
x < 3y - 18
Step-by-step explanation:
If you are solving for y :
[tex] \: [/tex]
[tex]x < 3y - 18[/tex]
[tex]x + 18 < 3y[/tex]
[tex] \frac{x + 18}{3} < \frac{3y}{3} [/tex]
[tex]y > \frac{3}{x} + 6[/tex]
what’s the answer to this problem , figure out the area and perimeter of this triangle
Answer:
area: 5×27÷2
perimeter:8+27+34
. Calculate the area and perimeter of a circle with radius
6cm.
Calculate the length of the diameter in a circle whose
Answer:
113.1cm2
Step-by-step explanation:
looked it up
A bags 4 red marbles, 5 green and 9 blue. What is the probability of picking a red marble?
2/9
1/18
1/4
2/18
Answer:
1/4
Step-by-step explanation:
(I think ) sorry it it's wrong
Select the fraction that is equivalent to 1/3. (2 points)
a
2/6
b
4/6
c
3/4
d
2/3
Answer:
A 2/6
Step-by-step explanation:
1/3
x 2/2
2/6
Question 13
2 Points
A farmer has two types of milk, one that is 20% milkfat and one that is 12% milkfat. How much of each is needed to get 20 gallons of 15%
milkfat
An equation is formed of two equal expressions. The amount of 20% milk and 12% milk that is needed to be mixed is 7.5 gallons and 12.5 gallons, respectively.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the amount of 20%milk mixed be represented by x, while the amount of 12% milk mixed is represented by y. Therefore, the two-equation can be written as,
x+y=20 gallons
0.20x + 0.12y = (0.15×20)
Solve the first equation for x, therefore,
x = 20 - y
substitute the value of x in the second equation,
0.20(20-y) + 0.12y = 3
4 - 0.2y +0.12y = 3
-0.08y = -1
y = 12.5 gallons
substitute the value of y in the first equation,
x + 12.5 = 20
x = 7.5 gallons
Hence, the amount of 20% milk and 12% milk that is needed to be mixed is 7.5 gallons and 12.5 gallons, respectively.
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What do you know to be true about the values of a and b?
60%
759
A. a
B. a = b
C. a>b
D. Can't be determined
Answer:
I don't think there is a way the values can be determined...
If a and b are in different triangles then the true option is that values of a and b can't be determined.
What is triangle?A triangle is a two dimensional figure having three sides and three angles.
Sum of angles of a triangle is equal to 180° whether it is a right angled or not.
How to find angle?In first triangle one angle is x°, second is 75° and third one is a° and in second triangle one angle is 60°, second is y°, third one is b°.
Sum of angles in first triangle is x+75+a=180
Sum of angles in second triangle is y+60+b=180
because any relationship between x and y is not given in the questions so values of a and b cannot be determined.
Hence the correct option is D which is that values of a and b cannot be determined.
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Find the surface area of a square pyramid with side length 6 cm and slant height 5
cm.
The surface area of the square pyramid is 96 sq. mi.
Given:
side length (s) = 6 mi
slant height (l) = 5 mi
*image of a typical square pyramid is shown in the attachment below.
Recall:
Formula for surface area of square pyramid (SA) = [tex]A+\frac{1}{2}Pl[/tex]
Where,
[tex]A=[/tex] area of the base = [tex]s^2=6^2=36[/tex] sq mi
[tex]P=[/tex] perimeter of the base = [tex]4(s)=4*6=24[/tex] mi
[tex]l=[/tex] slant height = 5 mi
Plug in the values
[tex]SA=36+\frac{1}{2} *24*5[/tex]
[tex]SA=36+60[/tex]
[tex]SA=96[/tex]
The surface area(SA) of the square pyramid is 96 sq. mi
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(geometry)
a trapezoid has an area of 10 square units what scale factor would be required to dilate the trapezoid to have an area of 90 square units
. 9
.6
.3
.1/3
A trapezoid has an area of 10 square units. The scale factor would be 3 to dilate the trapezoid to have an area of 90 square units.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor.
Let the linear scale factor be k.
The area scale factor is [tex]k^2[/tex]
We'll multiply the old area (10) by the area scale factor ([tex]k^2[/tex] ) to get the area of 90 square units
[tex]10 \times k^2 = 90\\\\k^2 = \frac{90}{10} \\\\k^2 = 9\\\\k = \sqrt{9} \\\\k = 3[/tex]approximately
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