Answer:
x = -8
Step-by-step explanation:
6x - 3 = -51
Add 3 to each side
6x - 3+3 = -51+3
6x = -48
Divide each side by 6
6x/6 = -48/6
x = -8
Answer:
x = -8
Step-by-step explanation:
[tex]6x - 3 = -51?\\To - find-x- collect-like-terms.\\6x=-51+3\\6x =-48\\Divide-both-sides-of-the-equation-by-6\\\frac{6x}{6} = \frac{-48}{6} \\x = -8[/tex]
David is throwing a stone in the air at an angle from the ground with an initial velocity of 30 feet per second. The equation gives the height of the stone thrown. Find the maximum height of the stone.
(SHOW WORK)
Answer:
42 feet.
Step-by-step explanation:
h=-10t² + 40t +2
The vertex of the quadratic function described by the equation is located at
t = -(40)/(2(-10)) = 2
Next is to find the value of height at t=2 will be
h = -10(2²) +40(2) +2 = -40 +80 +2 = 42feet
The maximum height is 42 feet.
Tamir wants to build a square wooden stage. His original pin for a stage x
feet long and x feet wide had to be made smaller to fit the space. The stage
needs to be 5 feet narrower and 3 feet shorter than his original plan. Which
multiplication problem represents this situation? What is the area of the
smaller stage?
Answer:
b .
Area=(x-5) (x-3)
Area = x^2 -8x+15
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Area of a rectangle = width x length
The original length and width was x, so if the stage needs to be 5 feet narrower and 3 feet shorter.
x-5
x-5
The formula is:
A=(x-5) (x-3)
Solving:
A = (x.x) + (x.-3) + (-5.x)+ (-5.-3)
A = x^2 -3x -5x+15
A = x^2 -8x+15
Caitlin bought 6 cookies for a total of $10. At this rate, what is the cost of 9 cookies?
Answer:
15$
Step-by-step explanation:
cost of 1 cookie = 10/6
cost of 9 cookies = 9* 10/6 = $15
Answer:
15 dollars
Step-by-step explanation:
6 cookies for 10 dollars
3 cookies for 5 dollars.
6+3 cookies for 10+5 dollars
Given f(x) = 2x5 + 12, what is the value of (f-1 o f)(2)?
Answer:
2
Step-by-step explanation:
You are trying to find (f' o f)(2). This means that you need to put f(x) into f'(x) and solve for 2.
First, find f'(x). To do this, take the original function and switch the x and y values.
y = 2x⁵ + 12
x = 2y⁵ + 12
x - 12 = 2y⁵
(x - 12)/(2) = y⁵
y = ⁵√(x - 12)/(2)
Now, you need to put f(x) into the inverse function through the x-value. Simplify completely.
y = ⁵√((2x⁵ + 12) - 12)/(2)
y = ⁵√((2x⁵)/(2)
y = ⁵√x⁵
y = x
Now plug in the value given to you.
(f⁻¹ o f)(2) = 2
The answer is 2.
The perimeter of a rectangle is 16.6km, and its area is 13.42km2. Find its length and width. length : km width : km
Answer:
l=5.12 & w=2.62
Step by step explanation:
A=l×w
13.42=lw
w=13.42/l
[tex]p = 2(l + w) \\ 16.6 = 2(l + \frac{13.42}{l} ) \\ 16.6 = 2( \frac{ {l}^{2} + 13.42}{l}) \\ 16.6 = 2(l + 13.42) \\ 16.6 = 2l + 26.84 \\ 2l = 26.84 - 16.6 \\ 2l = 10.24 \\ l = \frac{10.24}{2} \\ l = 5.12km[/tex]
Since you have found the value of the length you can find the value.of the width.
[tex]w = \frac{13.42}{l} \\ w = \frac{13.42}{5.12} \\ w = 2.62km[/tex]
Find the sum of the first 18 terms of the arithmetic sequence whose nth term is an = 3n - 1.
Answer:
495
Step-by-step explanation:
In order to find the sum of the first 18 terms you have to find the 18th term and the first term using the equation given.
a1=3(1)-1 a1=2
a18=3(18)-1 a18= 53
Then plug in 53 for an, 18 for n, and 2 in for a1 in the sum equation: Sn=n/2(a1+an)
Sn=18/2(2+53) Solve for sn= 495
The parallelogram shown below has an area of 30 units^2
2
squared.
Find the missing height.
h = units
Answer:
6
Step-by-step explanation:
The measure of the missing side of the given parallelogram with an area of 30 unit² will be 6 units.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram.
There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.
The area of a parallelogram is given as (1/2) × (sum of parallel sides) × (distance between parallel sides).
Area = (1/2) × (5 + 5) × h
30 = 10h/2
5h = 30
h = 6 units.
Hence "The measure of the missing side of the given parallelogram with an area of 30 unit² will be 6 units".
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Given the question missing the figure attached below,
Please help! Correct answer only, please! I need to finish this assignment this week. Determine the value of the following if it is possible. If it is not possible, explain.
Answer:
Option D is the correct answer
Step-by-step explanation:
Since, dimensions of both the matrices are different. Hence we can't add them.
A man 2 m high observes the angle of elevation to the top of a building to be 71° and the angle of depression to the bottom of the building to be 26°. How tall is the building?
Answer:
The building is 13.91 m tall
Step-by-step explanation:
The parameters given are;
Angle of elevation to the top of the building = 71°
Angle of depression to the bottom of the building = 26°
Height of the man = 2 m
Therefore, the sight of the man, the man's height, and the distance of the man from the building forms a triangle where:
The hypotenuse side = The sight of the man to the bottom of the building
Hence;
In ΔABC, A being at the eye level or head level of the man, B at the foot and C at the bottom of the building
∴ ∠A + Angle of depression to the bottom of the building = 90°
∠A = 90° - 26° = 64°
∠B = 90° and ∠C = 26° (Sum of angles in a triangle)
[tex]Tan(C) = \frac{AB}{BC}[/tex]
Distance of the man from the building = BC
[tex]Tan(26) = \frac{2}{BC}[/tex]
[tex]BC= \frac{2}{ Tan(26) } = 4.1 \, m[/tex]
Given that the angle of elevation to the top of the building = 71°, we have;
ΔAET
Where:
A is at the head level of the man,
E is the point on the building directing facing the man and
T is the top of the building
Hence AE = BC and ∡TAE = 71°
TE + AB= The height of the building
[tex]Tan(TAE) = \dfrac{TE}{AE}\\\\Tan(71) = \dfrac{TE}{4.1}[/tex]
∴ TE = tan(71°) × 4.1 = 11.91 m
Hence the height of the building = 11.91 + 2 = 13.91 m.
Ashley's car used 10 gallons of gas to drive 478 miles. At what rate does her car use gas in miles per gallon? Express your answer in simplest form.
Answer:
47.8
_____
1
Step-by-step explanation:
Answer:
she got it by breaking up the problem step by step for
Step-by-step explanation:
she has done this putting the form like so
10 - 478
I hope this
Find the volume of a pyramid with a square base, where the perimeter of the
base is 12.8 m and the height of the pyramid is 12.5 m. Round your answer
to the nearest tenth of a cubic meter.
Answer:
m3
Submit Answer
Answer:
[tex]42.7\,\,cubic\,\, meters[/tex]
Step-by-step explanation:
Given: Perimeter of base of a pyramid = 12.8 m
Height of the pyramid = 12.5 m
To find: volume of a pyramid
Solution:
Perimeter of base of a pyramid = 12.8 m
As base of the pyramid is a square,
12.8 = [tex]4(side\,\,of\,\,a\,\,square)[/tex]
side of a square = [tex]\frac{12.8}{4}=3.2\,\,m[/tex]
Area of a square (A) = [tex](side\,\,of\,\,a\,\,square)^2=(3.2)^2=10.24\,\,m^2[/tex]
Height of the pyramid (h) = 12.5 m
Volume of the pyramid = [tex]\frac{Ah}{3}=\frac{1}{3}(10.24)(12.5)=42.7\,\,cubic \,\,meters[/tex]
Someone pls help me it would be amazing thank u a lot
Answer:
36.87°
Step-by-step explanation:
With reference angle C
perpendicular (p) = 27
base(b) = 36
Now
Tan C = p/b
Tan C = 27/36
C = tan ^-1( 27/36)
= 36.87°
Hope it helps
:)
Answer:
36.87
Step-by-step explanation:
May i have some help please?
Answer:
1/5 = 0.2
0.3 = 1/3
1/2 = 0.5
Answer:
1/5 =0.2
3/10 = 0.3
1/2 =0.5
PLEASE HELP 20 POINTS!
This pattern follows the rule add 2. What is another feature of this pattern?
An image of a pattern. Term one has one dot, term two has three dots, term three has five dots, term four has seven dots.
A. The terms appear even, odd, even, odd.
B. All the terms are even.
C. Two terms are even, then two terms are odd.
D. All the terms are odd.
Answer:
Option D
Step-by-step explanation:
According to the image description provided:
Term one starts with one dot. One is an odd number.
If you add two to an odd number, the sum would be another odd number. This is what's happening with the pattern.
For example:
[tex]3+2 =5[/tex]
Three is an odd number. If you add two to it, you would get five, which is another odd number.
Term two has 3 dots, term three has 5 dots, term four has 7 dots.
So, all terms should be odd.
Option D should be the correct answer.
Please give an accurate answer and show work.
Answer:
3.06
Step-by-step explanation:
[tex]\log_{5}(\dfrac{2}{3}x-2)+2=0\\\\\log_{5}(\dfrac{2}{3}x-2)=-2\\\\[/tex]
This means that 5 to the power of -2 is [tex](\dfrac{2}{3}x-2)[/tex], meaning that:
[tex]\dfrac{2}{3}x-2=5^{-2}=\dfrac{1}{25} \\\\\dfrac{2}{3}x=\dfrac{51}{25} \\\\2x=\dfrac{153}{25} \\\\x=\dfrac{153}{50}=3.06[/tex]
Hope this helps!
Which expression is equivalent to the expression 5b+16?
36-6+2b+ 22
50-6+b+22
26+4+2+12
75+ 3-2b+9
Answer:
None are equivalent
Step-by-step explanation:
PLEASE HELP!!!!!!!! IMAGE ATTACHED!!!!
Answer:
Step-by-step explanation:
4) (-2,3) ; (-1,-2)
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-2-3}{-1-[-2]}\\\\=\frac{-5}{-1+2}\\\\=\frac{-5}{1}\\\\=-5[/tex]
5) line is parallel to x-axis. So, slope= 0
6) (1,1) ; (-2, -1)
[tex]Slope=\frac{-1-1}{-2-1}\\\\=\frac{-2}{-3}\\\\=\frac{2}{3}[/tex]
Brainliest question please please help me please
Answer: C outside of the circle
Step-by-step explanation:
The answer is c because
point 4, -1 falls outside of the
circle.
Hope this helps :)
Answer:
Its on the circle
Step-by-step explanation:
Ellen has $14,000 in a savings account, has a $500 outstanding credit card
bill, owes $2400 on her car payment, and has $18,000 left on her student
loans. What is the total of her liabilities?
Answer:
It'd be $4,700
Step-by-step explanation:$500 + $2,400 + $1,800 = $4,700. Minus that amount from her savings account total and that's how much money she has left.
what is the circumference of a circle with radius 20cm
Answer:125.66cm
Step-by-step explanation:
Circumference formula is C=2pi (r)
So C=2(pi or 3.14) (20)
Just plug the 20 (radius for the r) and you have the answer.
What is an equation of the line that passes through the point (− 2, 5) and is parallel to the line 3x + 4y = 12 ?
Answer: [tex]y=-\frac{3}{4} x+3.5[/tex] or [tex]y=-\frac{3}{4}x+\frac{7}{2}[/tex]
Step-by-step explanation:
A parallel line has the same slope and different y-intercepts.
Let's change our equation to slope-intercept.
[tex]3x+4y=12[/tex]
[tex]4y=12-3x[/tex]
[tex]y=\frac{12-3x}{4} =3-\frac{3}{4}x[/tex]
[tex]y=3-\frac{3}{4} x[/tex]
Now that we know our slope is -3/4, we know the equation will have -3/4 as the slope. Let's leave b blank so that we can find the y-intercept of the parallel line.
[tex]5=-\frac{3}{4}(-2)+b[/tex]
[tex]5=\frac{3}{2} +b[/tex]
[tex]3.5=b[/tex]
Our parallel equation is [tex]y=-\frac{3}{4}x+3.5[/tex] or [tex]y=-\frac{3}{4} x+\frac{7}{2}[/tex]
About 180,000 people live in a 5-mile radius of a city's town hall. Find the population density in people per square mile. Round your answer to the nearest whole number.
Answer:
2291
Step-by-step explanation:
Given: Radius of a city's town hall is equal to 5-mile and about 180,000 people live in a city's town hall
To find: population density per square mile
Solution:
Population density refers to the number of people per unit of area.
Let r denotes radius of the town hall = 5 miles
Area of the town hall = [tex]\pi r^2=\pi (5)^2=25\,\pi[/tex] square miles
Population density per square mile = Population of a city's town hall/area of the town hall = 2290.9 [tex]\approx 2291[/tex]
Q6.
2
(8 + 2 x 6)2 =
the two at the end of the brackets is squared it a small two
Answer: 1600
Step-by-step explanation:
2(8+2x6)
2(8+12)
2(20)
40
[tex]40^{2}[/tex]
1600
Mark me as the brainiest answer.
Pia used 2/3of her sugar to make 3/4of a batch of cookies. How much of her sugar would she need to make the whole batch? Write the expression you would use and then solve it.
Please answer
Answer:
Equation;
(3/4)x = 2/3
Solving;
x = 8/9
she would need 8/9 of her sugar to make a full batch.
Step-by-step explanation:
Let x represent the amount of sugar that would be needed to make the whole batch.
Given that;
Pia used 2/3 of her sugar to make 3/4 of a batch of cookies.
Since 2/3 of her sugar is needed to make 3/4 of a batch of cookies, then;
(3/4)x = 2/3
Solving the equation, dividing both sides by 3/4;
(3/4)x ÷ 3/4 = 2/3 ÷ 3/4
x = 2/3 × 4/3
x = 8/9
Therefore she would need 8/9 of her sugar to make a full batch.
please can you help for this questiong
what is the solution to the graph below?
Answer:
1,5
Step-by-step explanation:
1,5 is located within the shaded region.
If f(x) = 3x^2 +1 and g(x) = 1-x, what is the value of (f-g)(2)
Answer:
14
Step-by-step explanation:
Let's find (f-g)(x)
[tex]3x^{2} + 1 - (1-x)\\3x^{2} + 1 -1 + x\\3x^{2} + x[/tex]
Now let's plug in x=2, so to find (f-g)(2)
[tex]3(2)^{2} + 2\\12 + 2 = 14[/tex]
Which shows the image of RST after the rotation (x, y) (y, -x)
Answer:
Option A shows the image of RST after the rotation
Step-by-step explanation:
Coordinates of S=(1,3)
Coordinates of R = (-2,1)
Coordinates of T = (-1,7)
We are given that after rotation(x,y)→(y,-x)
So, The new coordinates after rotation will be :
Coordinates of S'=(3,-1)
Coordinates of R'= (1,2)
Coordinates of T'= (7,1)
These are the coordinates of triangle of Option A
So, Option A is true .
Hence Option A shows the image of RST after the rotation
A. shows the image of RST after the rotation.
In the geometry, an equilateral triangle is the triangle in which have all 3 sides have same length. an equilateral triangle is also equiangular; that is, all 3 internal angles are also congruent to each other and are each 60 degrees It is also a regular polygon, so it is also referred to as the regular triangle.
Which plane does the triangle RST belong to?
The XY-coordinate plane or triangle RST are equilateral. Points R or In the x y -coordinate plane, triangle R S T is equilateral. Points R and T had coordinates ( 0, 2) and ( 1, 0), respectively.
Coordinates of S=(1,3)
Coordinates of R = (-2,1)
Coordinates of T = (-1,7)
We are given that after rotation(x,y)→(y, -x)
So, The new coordinates after the rotation will be :
Coordinates of S'=(3,-1)
Coordinates of R'= (1,2)
Coordinates of T'= (7,1)
These are the coordinates of the triangle of Option A
So, Option A is true.
Hence Option A shows the image of RST after the rotation.
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What is the volume of this rectangular prism?
2 cm
3 cm
7
cm
4
Answer:
4 cm and 2cm
Step-by-step explanation:
Volume of the rectangular prism is 10.5 cm³.
What is Rectangular Prism?Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.
Given three dimensions of a rectangular prism as given below in the image.
Length = 3 cm
Width = 7/4 cm
Height = 2 cm
Volume of a rectangular prism = Length × Width × Height
= 3 × 7/4 × 2
= 3 × 7/2
= 10.5 cm³
Hence the volume of the rectangular prism is 10.5 cm³.
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Which equation represents a circle with a center at (2,8) and a radius of 11?
(x – 3)2 + (y + 2)2 = 11
(x-2)2 + (y + 8y2 = 121
(x + 2)2 + (y - 3)2 = 11
(x + 3)2 + (y – 2y = 121
Answer:
[tex](x-2)^2+(y-8)^2=121[/tex]
Step-by-step explanation:
This is because if you can see that the, x is being subtracted by 2, making the x-coordinate +2. and the y is being subtracted by 8, making the y coordinate +8.
(2, 8) = Coordinates
And the reason it has a radius of 11 is because the 121 on the other is the product of 11 times 11.