Answer:
11t² + 7t + 3
Step-by-step explanation:
⇒ (5t² + 4) - (6t² - 7t + 1)
⇒ 5t² + 4 - 6t² + 7t - 1
⇒ 11t² + 7t + 3
Answer: [tex]-t^2 + 7t + 3\\\\[/tex]
Work Shown:
[tex](5t^2 + 4) - (6t^2 - 7t + 1)\\\\5t^2 + 4 - 6t^2 + 7t - 1\\\\(5t^2 - 6t^2) + 7t + (4-1)\\\\-t^2 + 7t + 3\\\\[/tex]
Directions: Identify the binomial factors of the following trinomials.
1. x2 + 14x + 13
2. x2 + 7x + 12
3. x2 + 8x + 15
4. x2 + 8x + 12
5. x2 + 7x + 10
6. x2 + 5x + 6
7. x2 + 5x + 4
8. x2 + 10x + 21
9. x2 + 10x + 16
10. x2 + 6x + 9
11. x2 + 9x + 20
12. x2 + 9x + 14
13. x2 + 13x + 42
14. x2 + 9x + 18
15. x2 + 17x + 70
(Remember, the factors of the last term that equal the addends of the second term.)
Answer:
1. x= -1 & x= -13
2. x= -3 & x= -4
3. x= -3 & x= -5
4. x= -6 & x= -2
5. x= -5 & x= -2
8. x= -7 & x= -3
9. x= -8 & x= -2
10. x= -3 & x= -3
11. x= -5 & x= -4
12. x= -2 & x= -2
13. x= -6 & x= -7
14. x= -6 & x= -3
15. x= -10 & x= -7
CL 1-146. Solve for the variable(s) in each triangle below. a. 15,20, and 15.
The variable(s) in each triangle below 9, 12 and 16.
What is Area of Triangle?The basic formula to find the area of a triangle is, area of triangle = 1/2 (b × h); where 'b' is the base and 'h' is the height of the triangle.
Let the base of the triangle be 15.
So, the area is:
Area= 1/2*b*h
= 1/2*15*20
= 150.
Let the base of the triangle be 25.
So, the area is:
Area= 1/2*b*h
150= 1/2*25*h
= 300/25
h =12
Now, using Pythagoras Theorem
15²= h²+x²
15²=12²+x²
225-144= x²
x²= 81
x=±9
Now, x+y=25
y=16
Thus , values are 9,12 and 16.
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f(x) = ax³ + 2x² + bx + c. Given that f(0) = f, f(1) = 4 and f(-2) = 8, find the value of a, b and c.
Answer:
a = -1/6
b = 7/6
c = 1
Step-by-step explanation:
[tex]f(x)=ax^3+2x^2+bx+c\\\\f(0)=a(0)^3+2(0)^2+b(0)+c\\\\1=c[/tex]
[tex]f(1)=a(1)^3+2(1)^2+b(1)+1\\\\4=a+2+b+1\\\\4=a+b+3\\\\1=a+b\\\\1-b=a[/tex]
[tex]f(-2)=(1-b)(-2)^3+2(-2)^2+b(-2)+1\\\\8=-8+8b+8-2b+1\\\\8=6b+1\\\\7=6b\\\\\frac{7}{6}=b[/tex]
[tex]1-b=a\\\\1-\frac{7}{6}=a\\ \\-\frac{1}{6}=a[/tex]
So, the true equation would be [tex]f(x)=-\frac{1}{6}x^3+2x^2+\frac{7}{6}x+1[/tex] if you substitute the coefficients and the constant.
2. Find the coordinate of A(-4, 6) after it has been rotated 90 degrees counterclockwise, reflected over the x-axis, and dilated by a scale factor of 2.
The new coordinates of A is (-12,8)
What is Dilation ?To dilate something in the coordinate plane, multiply each coordinate by the scale factor. This is called mapping.
For any dilation the mapping will be (x,y) → (kx,ky).
Convert the point (x, y) to (-y, x) in order to rotate 90 degrees counter clockwise.
The given point is A(-4 ,6) ,after it has been rotated the new coordinates are A(-6,-4)
After reflecting it over x axis the new coordinated will be (-6,4)
Then dilating it with a scale factor of 2
The new coordinates of A is (-12,8)
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Zoe is decorating the outside of a box in the shape of a triangular prism. The figure
below shows a net for the box.
15 ft
12 ft
12 ft
17 ft
13.89 ft
13.89 ft
What is the surface area of the box, in square feet, that Zoe
decorates?
The surface area of the box, in square feet, that Zoe decorates is 430.35 square feet
The surface area of the boxTo determine the surface area from the net of the box, we simply calculate the area of each shape.
From the given figure, we have the following shapes and dimensions:
Rectangles: 15 ft by 12 ft and 13.89 ft by 15 ftTriangle: Base = 12 ft and Height= 7 ftThe area is then calculated using:
Area = Areas of the rectangle + Area of the triangle
So, we have:
Area = 15 * 12 + 13.89 * 15 + 0.5 * 12 * 7
Evaluate the sum of products
Area = 430.35
Hence, the surface area of the box, in square feet, that Zoe decorates is 430.35 square feet
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Answer:577.35 square feet
Step-by-step explanation:
♀️
a cylindrical pipe is 36 ft long and has a volume of 100ft. find its approximate diameter to the nearest hundredth of a foot
Answer:
0.940
Step-by-step explanation:
100 = 36 x pi x r^2
now divide both sides by 36pi
r^2 = 0.88419412...
then square root both sides
r = 0.94031597...
I need help with this
Answer:
(a) = 37π/180 radians
(b) = 37°
Step-by-step explanation:
Converting km/h ⇒ m/s :
⇒ 54 km/h x 5/18
⇒ 3 x 5
⇒ 15 m/s
===============================================================
Formula to calculate the angle :
⇒ tanθ = v/r
⇒ tanθ = (15 m/s)/(20 m)
⇒ θ = tan⁻¹ (0.75)
⇒ θ = 37°
=============================================================
Converting to radians :
⇒ Radian measure = Angle measure × π/180°
⇒ Radian measure = 37° × π/180°
⇒ Radian measure = 37π/180 radians
=============================================================
Solutions :
(a) = 37π/180 radians
(b) = 37°
45 POINTS & BRAINLIST -- PLEASE HELP
Convert the following functions.
A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.
B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit**
Answer:
45 POINTS & BRAINLIST -- PLEASE HELP
Convert the following functions.
A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.
B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit
Step-by-step explanation:
45 POINTS & BRAINLIST -- PLEASE HELP
Convert the following functions.
A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.
B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit
Find the value of the trigonometric function 2sin 30 degree/cos 30 degree. Round your answer to four decimal places. 2 sin 30 degree/cos 30 degree=
Answer:
Step-by-step explanation:
The value of the given trigonometric function is 1.1547.
Trigonometric RatiosThe main trigonometric ratios are: sinβ, cosβ and tg β. From these ratios, you can calculate other trigonometric ratios such as sec β, cossec β and cotg β.
These ratios help you find the angles and the sides of a rectangle triangle.
The question asks [tex]\frac{2 *sin(30)}{cos (30}[/tex], for the angle 30° you have sin=1/2 and cos= [tex]\frac{\sqrt{3} }{2}[/tex].
Thus,
[tex]\frac{2 *sin(30)}{cos (30}=\frac{2 *\frac{1}{2} }{\frac{\sqrt{3} }{2} }=\frac{1}{\frac{\sqrt{3} }{2} }= \frac{2}{\sqrt{3} } =\frac{2\sqrt{3} }{3}=1.1547[/tex]
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Two parallel wires are separated by 0. 06 m, each carrying 3 a of current in the same direction. What is the magnitude of the force per unit length between the wires?
The magnitude of the force per unit length between the wires is [tex]3 \times 10^{-5} N/m[/tex].
What is the magnitude of the force?In a wire carrying a current I 2, the force that each wire feels due to the presence of the other depends on the distance between them and the magnitude of the currents.
Force per unit length = magnetic permeability * (current 1) * (current 2) / (2 π distance between the wires).
The below expression for the force per unit length.
Moreover, before using the below formula we have to change the unit centimeter into a meter. So, we just divide the centimeter by 100.
[tex]\rm \dfrac{Force}{length}=\dfrac{u_0 \times i _1 \times i_2}{2\pi d}\\\\\dfrac{Force}{length}=\dfrac{u_0 \times i _1 \times i_2}{2\pi d}\\\\Where; \ \mu_0 = 4\pi \times 10^{-7} , i_13 . \ i_2 = 3 \ d=0.06[/tex]
Substitute all the values in the formula
[tex]\rm\dfrac{Force}{length}=\dfrac{u_0 \times i _1 \times i_2}{2\pi d}\\\\Where; \ \mu_0 = 4\pi \times 10^{-7} , i_13 . \ i_2 = 3 \ d=0.06\\\\ \dfrac{Force}{length}=\dfrac{4\pi \times 10^{-7} \times 3 \times3}{2\pi \times 0.06}\\\\ \dfrac{Force}{length}= 3 \times 10^{-5} N/m[/tex]
Hence, the magnitude of the force per unit length between the wires is [tex]3 \times 10^{-5} N/m[/tex].
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1/4×___=5
fill in the blank.
Answer:
20
Step-by-step explanation:
5x4=20 5 is one quarter of 20
Answer:
[tex] \frac{1}{4} \times 20 = 5 \\ [/tex]
The children at Farmfield School are collecting money for charity.
Their target is to collect £360
So far they have collected £57.73
How much more money do they need to reach their target?
The Wilson family purchased a home for $140,000. The housing market has increased in value by 6.2% every year. Determine an equation that would represent what the house would be valued at in the next six years.
(9-5+X)+ (39+211)
whats the Solution?
Answer:
254 + xStep-by-step explanation:
(9-5+X)+ (39+211)
whats the Solution?
(9 - 5 + x) + (39 + 211) =
4 + x + 39 + 211 =
254 + x
Answer:
254 + x
Step-by-step explanation:
(9 - 5 + x) + (39 + 211) =
4 + x + 39 + 211 =
254 + x
Hope this helps
:)
Doctors can use radioactive chemicals to treat some forms of cancer. The half life of a certain chemical is 5 days. A patient receives a treatment of 28 millicuries of the chemical. (A millicurie is a unit of radioactivity.) How much of the chemical remains in the patient 10 days later?
Answer:
7 millicuries
Step-by-step explanation:
A period of 10 days is 2 times the half-life of 5 days.
In the first 5 days, the amount of the chemical decayed by half from 28 millicuries to 14 millicuries. In the next 5 days, it decayed by half again, from 14 millicuries to 7 millicuries.
10 days later, 7 millicuries of the chemical remains.
How do I Factorise X^2 - 25
To Factorize Something:
⇒ means to put it into the simplest terms that when multiplied
together transforms into the original form
Let's Solve:
[tex]x^2-25=(x+5)(x-5)[/tex]
Let's Check:
[tex](x+5)(x-5)=x*x+(-5)x+5x-25=x^2-5x+5x-25=x^2-25[/tex]
Answer: (x+5)(x-5)
Hope that helps!
Answer:
(x + 5)(x - 5)
Step-by-step explanation:
[tex]x^2-25[/tex]
[tex]=x^2-5^2[/tex]
[tex]x^2-5^2=\left(x+5\right)\left(x-5\right)[/tex]
[tex]=\left(x+5\right)\left(x-5\right)[/tex]
Can someone explain me the answer and how to solve it
Answer:
The radius is 8.
Step-by-step explanation:
Because OA is a radius and AB is a tangent, Angle A is a right angle. So you can use Pythagorean theorem (shortcut Pythagorean triple)
OA^2 + 15^2 = 17^2
OA^2 + 225 = 289
OA^2 = 64
OA = 8
OA is a radius, the radius = 8
Giving Brainlist please help! Calculate the area of the figure.
Answer:
A. 120 cm²
Step-by-step explanation:
Area of figure :
1/2 x base x height1/2 x 24 x 1012 x 10120 cm²What type of event is composed of two or more separate events?
Answer:
A compound event
Step-by-step explanation:
compound event is more complex than a simple event, as it involves the probability of more than one outcome. Another way to view compound events is as a combination of two or more simple events
How many hours and minutes is 125 minutes
Answer:
2 hours and 5 minutes.
Step-by-step explanation:
2 hours is 60mins+60mins which is equal to 120mins and then the extra 5mins
Hilary studied for a total of 2 hours and 5 minutes this week.
If Hilary studied for 25 minutes each day for five days this week, we can calculate the total study time by multiplying the number of minutes studied per day (25) by the number of days (5):
25 minutes/day × 5 days = 125 minutes
To convert this to hours and minutes, we need to divide the total minutes by 60 (since there are 60 minutes in an hour) to get the number of hours and find the remainder as minutes.
125 minutes ÷ 60 = 2 hours and 5 minutes
Therefore, Hilary studied for a total of 2 hours and 5 minutes this week.
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The rectangular prism below has a base area of 44.3 units2 and a volume of 221.5
a
units. Find its height.
[tex]base \: area = 44.3 \: {units}^{2} [/tex]
[tex]volume = 221.5 \: {units}^{3} [/tex]
To find:the height of the given rectangular prism.
Solution:[tex]volume= base \: area \times height[/tex]
[tex]height = \frac{volume}{base \: area} [/tex]
[tex]height = \frac{221.5}{44.3} [/tex]
[tex]height = 5 \: units[/tex]
Therefore, the height of the given rectangular prism is 5 units.
The value of height of rectangular prism is,
⇒ h = 5 units
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The rectangular prism below has a base area of 44.3 units² and a volume of 221.5 units³.
Since, The volume of rectangular prism is,
⇒ V = Base area x height
⇒ 221.5 = 44.3 × h
⇒ h = 221.5 / 44.3
⇒ h = 5 units
Thus, The value of height of rectangular prism is,
⇒ h = 5 units
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A motorist travels 122 km before his first stop. If he had 10% of his journey to complete at this point, how long was the total ride
Answer:
233km
Step-by-step explanation:
If the area of a circle is 4(pi), what is
its radius?
Answer:
radius=2cm
because area =πr²
π2²=4π
hope this helps
please give me brainliest
Please help!!!!!!!!!
Answer:
option d -1 is the answer
Answer:
I think C (19) might be wrong though
An ordered pair that makes a linear equation true is called a?
Answer:
the solution of the equation.
Step-by-step explanation:
Can someone try to help?
Answer:
Step-by-step explanation:
What is the value of x in the parallelogram below
Answer:
x=7
Step-by-step explanation:
We know that in a parallelogram diagonals bisect each other
Therefore
x=7
PLease HELP ASAP!!! READ THE QUESTION CAREFULLY
Answer:
1/3
Step-by-step explanation:
Which decimal is equivalent to -3 1/8? *20 points*
a. -3.18
b. -3. 125
c. -3. 1205
d. -3.12
Answer: -3.125
Step-by-step explanation: -1 divided by 8 = .125
2. Two painting companies were hired to paint two different buildings. The amount of area
left to paint on both buildings is related to the amount of time that the painters spend
on painting each of them. This relationship is shown in the two graphs below:
a. what are the linear functions modelling the two relationships in the graphs above?
b. which painting company is painting their building at a faster rate? how much faster?
c. which painting company had less area to paint when they began painting their building?
d. how many hours will it take each painting company to completely finish painting their building?
pls help its due today and its 100 points
#a
#1
(0,2100)(7,2000)Slope:-
m=2000-2100/7=-100/7Equation in point slope form
y-2100=-100/7(x)y=-100/7x+2100Slope=-100/7
#2
(0,1800)(8,1700)Slope
m=1700-1800/8=-100/8Y intercept=1800
Equation
y=-100/8+1800Slope=-100/8
#b
First company is painting faster
-100/7 ÷-100/88/7 times faster#c
Comapny B
as their y intercept is 1800 which is less than 2100#d
for #1
-100/7x+2100=0100/7x=2100x=21(7)=147hours#2
100/8x=1800x=18(8)x=144hours