Answer:
x = 10Step-by-step explanation:
2x + 1 = 4x - 19
Solve for x
2x + 1 = 4x - 19
2x - 4x = -19 - 1
-2x = -20
x = 20 : 2
x = 10
----------------
check
2 * 10 + 1 = 4 * 10 - 19
21 = 21
the answer is good
Answer: [tex]\Large\boxed{x=10}[/tex]
Step-by-step explanation:
2x + 1 = 4x - 19
Add 19 on both sides
2x + 1 +19 = 4x - 19 + 19
2x + 20 = 4x
Subtract 2x on both sides
2x + 20 - 2x = 4x - 2x
20 = 2x
Divide 2 on both sides
20 / 2 = 2x / 2
[tex]\Large\boxed{x=10}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Rearrange the formula to highlight the radius
[tex]\displaystyle\\Answer:\ r=\sqrt{\frac{3V}{\pi h} } .[/tex]
Step-by-step explanation:
[tex]\displaystyle\\V=\frac{1}{3} \pi r^2h.\\[/tex]
Multiply both sides of the equation by 3:
[tex]3V=\pi r^2h.[/tex]
Divide both sides of the equation by πh:
[tex]\displaystyle\\\frac{3V}{\pi h} =\frac{\pi r^2h}{\pi h} \\\frac{3V}{\pi h}=r^2\\ r^2=\frac{3V}{\pi h} .\\r*r=\sqrt\frac{3V}{\pi h} *\sqrt{\frac{3V}{\pi h} } \\r=\sqrt{\frac{3V}{\pi h} } .\\[/tex]
HELPPP There are 30 pencils in a box (15 pairs). 2 pair(s) are yellow,
3 pairs are brown, and the rest are tan. What is the probability of
pulling out a brown pencil on the first draw?
Write your answer as a reduced fraction.
Answer:
1/10
Step-by-step explanation:
Probability= number of brown pencil/number of pencil in the box
3/30
=1/10
Answer: 1/5
Step-by-step explanation:
30/15 pairs is 2 pencils per pair. That means there are 4 yellow pencils, 6 brown pencils, and the rest are tan.
30-10=20. There are 20 tan pencils.
6/30 is the probability of a brown pencil being pulled out.
This simplifies to 1/5.
The angle between the generator and the central axis of a double-napped cone is 60°. a plane intersecting the cone makes an angle of 50° with the central axis. which conic section is formed?
The right option is (c).
As a result of the plane intersecting the cone here at an angle of 50° being less than the angle between the generator and central axis at an angle of 50°, a conic section is created.
What is Hyperbola?A smooth curve in a plane known as a hyperbola is one whose geometric characteristics or equations for which it is the solution set characterize it. Two parts of a hyperbola, known as connected components or branches, are mirror reflections of one another and resemble two infinite bows.
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I understand that the question you are looking for is:
"The angle between the generator and the central axis of a double-napped cone is 60°. A plane intersecting the cone makes an angle of 50° with the central axis. Which conic section is formed?"
(a)circle
(b)ellipse
(c)hyperbola
(d)parabola
2. If P = √2+1 √2-1 and Q = √2-1 √2+1 Find P2 + Q2 + PQ 1
The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
How to find the value of a expression including elimination of radical in denominators
Herein we have two irrational terms whose denominators are radical expressions, which can be treated by algebraic handling and properties for radical expressions:
P = (√2 + 1) / (√2 - 1)
P = [(√2 + 1) / (√2 - 1)] · [(√2 + 1) / (√2 + 1)]
P = (√2 + 1)² / (2 - 1)
P = (√2 + 1)²
P = 2 + 2√2 + 1
P = 3 + 2√2
Q = (√2 - 1) / (√2 + 1)
Q = [(√2 - 1) / (√2 + 1)] · [(√2 - 1) / (√2 - 1)]
Q = (√2 - 1)²
Q = 2 - 2√2 + 1
Q = 3 - 2√2
Then, the value of P² + Q² + P · Q is:
M = (3 + 2√2)² + (3 - 2√2)² + (3 + 2√2) · (3 - 2√2)
M = 9 + 12√2 + 8 + 9 - 12√2 - 8 + 3 - 8
M = 9 + 8 + 9 - 8 + 3 - 8
M = 21 - 8
M = 13
The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
RemarkThe statement is poorly formatted and reports typing mistakes, correct form is presented below:
If P = (√2 + 1) / (√2 - 1) and Q = (√2 - 1) / (√2 + 1), then find P² + Q² + P · Q.
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The marked price of an article is rs 10000 . If he discounted rate and VAT rate are equal and the price with VAT is 9900 find the vat rate .
The rate of VAT is 10%.
In the question, we are asked to find the VAT rate, given that the market price of an article is Rs. 10000, the rate of discount and the rate of VAT are equal, and the price after VAT is Rs. 9900.
We assume the rate of discount and the rate of VAT to be r%.
Thus, discount = r% of Rs. 10000 = Rs. r/100 * 10000 = Rs. 100r.
Thus, the price after discount = Rs. 10000 - 100r = Rs. 100(100 - r)
Then, VAT = r% of (Rs. 100(100 - r)) = Rs. r/100 * 100(100 - r) = Rs. r(100 - r).
Thus, the price after VAT = Rs. 100(100 - r) + Rs. r(100 - r) = Rs. (100 + r)(100 - r).
The price after VAT is given to be Rs. 9900.
Thus, (100 + r)(100 - r) = 9900,
or, 100² - r² = 9900,
or, r² = 100² - 9900,
or, r² = 10000 - 9900 = 100,
or, r = ±√100 = ±10.
Since r is the rate of VAT, it cannot be negative, making r = 10.
Thus, the rate of VAT is 10%.
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How long does it take for millions of dollars worth of emerald transactions to occur in bogota? a year three months a day a week
Answer: It will be A Day
Step-by-step explanation:
PLS HELP PLS
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
The scale factor from Figure A to Figure B is 4
How to determine the scale factor from Figure A to Figure B?From the question, we have the following statement:
Figure B is a scaled copy of Figure A.
The corresponding side lengths of figure A and figure B are:
Figure A = 10
Figure B = 40
The scale factor from Figure A to Figure B is then calculated as:
Scale factor = Figure B/Figure A
Substitute the known values in the above equation
Scale factor = 40/10
Evaluate the quotient
Scale factor = 4
Hence, the scale factor from Figure A to Figure B is 4
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What number is represented by the question mark?
111= 0, 3213=0, 7756= 1,7662= 2, 6855= 3, 8096= 5,6666=4 . 8193= 3,9313= 1,8639= 4,1234=0, 2581 = 2,7186= 3, 2679=?
Based on the sequence of numbers given, the number that is represented by the question mark is 2679 = 2.
What is the sequence given?The sequence requires that you count the number of circles that a group of number has. For instance 9 has one circle and 8 has two circles because of the way they are drawn.
The numbers 111, 3213, and 1234 will therefore be equal to 0 because there is no number that has a circle in it.
The number 8096 however, will be equal to 5 because there are 5 circles. Two in 8. 1 in 0. 1 in 9. 1 in 6.
This means that the last number of 2679 will therefore be equal to 2 because there are two circles. One circle is in 6, and the other circle is in 9.
In conclusion, the number represented by the question mark is 2.
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Using addition rules, show how to add the two real numbers. 7 + (-14)
Answer:
- 7
Step-by-step explanation:
note that
+ (- ) = - ( adding a negative is equivalent to subtraction )
- (- ) = + ( subtracting a negative is equivalent to addition )
then
7 + (- 14) = 7 - 14 = - 7
Using the online tool, find two different combinations of radius and height that produce two cylinders with nearly the same volume. Record the
dimensions and volumes of the two cylinders below.
The radii and the heights of the two cylinders are
Cylinder 1: Height = 6 and Radius = 5Cylinder 2: Height = 10 and Radius = 3.87How to determine the combinations of radius and height?The volume of a cylinder is
V = πr²h
When the volumes of two cylinders are almost equal, then it means that:
V1 ≈ V2
This gives
πr²h ≈ πR²H
Divide both sides by π
r²h ≈ R²H
Assume that r = 5 and h = 6
So, we have:
5² * 6 ≈ R²H
Evaluate the product
150 ≈ R²H
Assume H = 10
So, we have:
150 ≈ R² * 10
Divide by 10
R² ≈ 15
Take the square root of both sides
R ≈ 3.87
Hence, the radii and the heights of the two cylinders are
Cylinder 1
Height = 6 and Radius = 5
Cylinder 2
Height = 10 and Radius = 3.87
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Answer:
These radius and height values will produce the same volume:
radius = 6 units and height = 18 units
radius = 9 units and height = 8 units
Simplify the expression. h4(h3)–6
Answer:
[tex]h^7-6[/tex]
Step-by-step explanation:
1) Regroup terms.
[tex]h^4h^3-6[/tex]
2) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]h^{4+3}-6[/tex]
3) Simplify 4 + 3 to 7.
[tex]h^7-6[/tex]
M angle JKL=
Help me please thank u so much
Answer:
22°
Step-by-step explanation:
Since IJ is a diameter, arc LJ measures 68 degrees.
Therefore, the measure of angle JKL is (112-68)/2=22°
A. Undefined b. Zero c.negative b. Positive
I believe the slope is negative. If it was positive then it would have been " / "
Answer:
C
Step-by-step explanation:
• A vertical line has an undefined slope
• A horizontal line has a slope of zero
• A line sloping downwards from left to right has a negative slope
• A line sloping upwards from left to right has a positive slope
-------------------------------------------------------------------
the line here slopes downwards from left to right and has a negative slope
A rectangular prism with a square base is cut from the center of a triangular prism. each side of the square base measures 1.7 units.what is the volume of the shaded solid? round to the nearest tenth of a cubic unit.11.6 units345.4 units357.0 units368.6 units3
Rounding to the closest tenth of a cubic unit, the shaded solid's volume is 45.4 cubic units.
What is rectangular prism?The 3D shape of a rectangular prism has six rectangular faces. Multiply a rectangular prism's three dimensions—length, width, and height—to determine its volume. Cubic units are used to measure volume.
According to the given information:The following formula can be used to determine a rectangular prism's volume:
Vr = Height * Width * Length
Triangular prism volume Vt is determined by its base area and height.
concerning the rectangular prism;
Vr = 1.7 × 1.7 × 4
Vr = 11.56 units in 3
Regarding the triangular prism
Vt = 0.5 × 5.7 × 5 × 4
Vt = 57 unit3
Volume of the solid shaded by Vt - Vr
The solid's shaded volume is equal to 57 - 11.56.
The colored solid's volume is 45.44 cubic units.
Due to this, the shaded solid's volume, when rounded to the nearest tenth of a cubic unit, is 45.4 cubic units.
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How does the mean absolute deviation (mad) of the data in set 1 compare to the mean absolute deviation of the data in set 2? set 1: 12, 8, 10, 50 set 2: 13, 9, 8 the mad of set 1 is 13 less than the mad of set 2. the mad of set 1 is 13 more than the mad of set 2. the mad of set 1 is 2 more than the mad of set 2. the mad of set 1 is 2 less than the mad of set 2.
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
How to estimate the Mean Absolute Deviation from the given data?Set 1: 12, 8, 10, 50
Set 2: 13, 9,8
To determine the mean for each set
Mean = totality of elements/number of elements
Mean of Set 1:
[tex]$=\frac{12+8+10+50}{4}[/tex]
[tex]$=\frac{80}{4}=20$[/tex]
Mean of Set 2:
[tex]$=\frac{13+9+8}{3}[/tex]
[tex]$=\frac{30}{3}=10$[/tex]
To determine the mean absolute deviation (MAD) of the data in each set.
M.A.D of Set 1:
[tex]$=\frac{|12-20|+|8-20|+|10-20|+|50-20|}{4}[/tex]
[tex]$=\frac{8+12+10+30}{4}=\frac{60}{4}=15$$[/tex]
M.A.D of Set 2:
[tex]$=\frac{|13-10|+|9-10|+|8-10|}{3}[/tex]
[tex]$=\frac{3+1+2}{3}=\frac{6}{3}=2$[/tex]
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
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Select the correct answer.
Consider this expression.
x-4
2(x+4)
For which product or quotient is this expression the simplest form?
O A.
B.
O C.
O D.
2x+8
x²16
x²16
2x+8
2x+8
x²16
x²16
2x+8
÷
÷
.
.
x² + 8x + 16
x +4
x +4
x² + 8x + 16
x² + 8x + 16
x + 4
x+4
x² + 8x + 16
The rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
Multiplying rational expressionsRational expressions are written in the form a/b where a and b are integers.
According to the question, we need to determine the expression that is equal to x-4/2(x+4)
From the fourth option;
x²-16/2x+8 * x+4/x²+8x+16
Factorize the quadratic part to have;
x²-16/2x+8 * x²+8x+16/x+4
(x+4)(x-4)/2(x+4) * x+4/(x+4)^2
Cancel out the common expression to have;
x-4 * 1/2(x+4)
x-4/2(x+4)
Hence the rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Last one
Because if we simplify
(4x³y-6xy³)/2xy(2xy(2x²-3y²))/2xy2x²-3y²Verified
Answer:
D is the correct Answer.
Step-by-step explanation:
4x^3+-6xy^3
2xy
When dividing exponents you will subtract. Leaving you with 2x^3-3y^2.
Therefore your answer is D.
5. Mr. Griffin asked the students to form the number eighty-four million, five
hundred thirty thousand, two hundred sixteen. Ben still had the number card
with the 3. In what place was Ben standing? Show your work in the space
below. Remember to check your solution
Answer:
Ben was standing in the
Step-by-step explanation:
84 000 000
+ 00 530 000
+ 00 000 216
_________________
84 530 216
From this u can see that the 3 is in the ten thousands place
Find the slope when y2=9, y1=13, x2=4, and x1=0.
Answer:
Formula=√(x2-x1)²+(y2-y1)² =√(4-0)²+(9-13)2 =√16+16 =√32
Answer: slope=-1
Step-by-step explanation:
9-13 -4
------ --------- -4/4=-1
4-0 4
Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.
The volume of the figure is 1, 005. 4 mi³
Volume of a cylinderNote that the figure is a cylinder
The formula for volume of a cylinder is given as;
Volume = πr²h
Where
h = height = 5 mi
r = radius = 8mi
Substitute into the volume
Volume = 3. 142 × 8 × 8 × 5
Volume = 1,005. 4 mi³
Thus, the volume of the figure is 1, 005. 4 mi³
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A lampshade made from a piece of sheet plastic has a radius of the inner circle to be 7cm and that of the outer circle is 28cm. if its arc subtends an angle of 315 degree at the center, what is the area of the plastic used to form the lampshade
The area of the plastic used to form the lampshade is 2021.25 square centimeters
How to determine the area of the plastic used to form the lampshade?The given parameters in the question are:
Outer radius, R = 28 cm
Inner radius, r = 7 cm
Angle, ∅ = 315
The area of the plastic used to form the lampshade is calculated using the following area of sector formula
A = ∅/360 * π(R² - r²)
Substitute the known values in the above equation
A = 315/360 * 22/7 * (28² - 7²)
Evaluate the exponents
A = 315/360 * 22/7 * (784 - 49)
Evaluate the difference
A = 315/360 * 22/7 * 735
Evaluate the product
A = 2021.25
Hence, the area of the plastic used to form the lampshade is 2021.25 square centimeters
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A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm. a regular hexagon has an apothem with length 14 centimeters and a perimeter of 96 centimeters. what is the approximate area of the hexagon?
The approximate area of the hexagon = 672 cm²
What is hexagon ?
In geometry, hexagon is a polygon with 6 sides. If the lengths of all the sides and the measurement of all the angles are equal, such hexagon is called a regular hexagon. In other words, sides of a regular hexagon are congruent.apothem of the hexagon = 14 cm
perimeter of the hexagon = 96 cm
Area of the hexagon = [(3√3) / 2] a² ; where a is the measure of the side
hexagon has 6 sides.
Perimeter = 6a
96 cm = 6a
96 cm / 6 = a
16 = a
There are 6 triangles in the hexagon .
Area of a triangle = (height * base) / 2
A = (14 cm * 16 cm) / 2
A = 224 / 2
A = 112 cm²
The approximate area of the hexagon = 112 cm² * 6 triangles = 672 cm²
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Answer: D). 672 cm2
Step-by-step explanation:
You decide that you want to purchase a Tesla SUV. You borrow \$95,000 for the purchase. You agree to repay the loan by paying equal monthly payments of \$1,200 until the balance is paid off. If you're being charged 6\% per year, compounded monthly, how long will it take you to pay off the loan?
Using compound interest and a graphing calculator, it is found that it will take about 15 years for the loan to be paid off.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For this problem, the parameters are given as follows:
A(0) = 95000, r = 0.06, n = 12.
Hence the value of the loan after t years is:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 95000\left(1 + \frac{0.06}{12}\right)^{12t}[/tex]
[tex]A(t) = 95000(1.005)^{12t}[/tex]
You have monthly payments of $1,200, hence the amount paid after t years is:
P(t) = 12 x 1,200t = 14400t
Then we have to solve for:
A(t) = P(t)
[tex]14400t = 95000(1.005)^{12t}[/tex]
Which is solved in the graph below, meaning that it will take about 15 years for the loan to be paid off.
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A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid.
A solid right pyramid has a square base. The base edge length is 2 centimeters longer than the height of the pyramid. The height of the pyramid is 6 centimeters.
If the height is 6 cm, what is the volume of the pyramid?
24 cm3
48 cm3
128 cm3
144 cm3
Answer: it’s 128 (also what you did on my question was not cool, do better)
Step-by-step explanation:
We know the height is 6 and the length is 2 more than the height then the length is 8 (6+2=8) and then you solve for volume and get 128
The correct answer for the volume of the pyramid is [tex]128[/tex] cm³.
Given:
Square base edge lenght 2 cm than the height of the pyramid.
Height of the pyramid is 6 cm.
Square base edge length = Height of pyramid + 2cm
= 8 cm.
Base area:
Area of the square is calculated as side².
Area of square = 8*8
= 64 cm²
Volume of pyramid is calculated as [tex]\dfrac{1}{3} *basearea*height[/tex]
[tex]\dfrac{1}{3}*64*6\\\\ =128[/tex]
The volume of the pyramid is [tex]128[/tex] cm³.
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Kwame must earn more than 16 1616 stars per day to get a prize from the classroom treasure box. Write an inequality that describes S SS, the number of stars Kwame must earn per day to get a prize from the classroom treasure box.
The inequality that describes the number of stars S that Kwame must earn per day to get a prize from the classroom treasure box is: S > 16.
What is the inequality that models this situation?The number of stars that he earns is represented by the variable S. He must earn more than 16 stars to earn a prize from the classroom treasure box, hence the inequality that represents the desired amount is given as follows:
S > 16.
Which is read as:
S is greater than 16, which is derived from the Fact that Kwame must earn more than 16 stars per day to get a prize, as stated in the problem.
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How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 9 members?
Answer:
3024
Step-by-step explanation:
Each chosen member (out of 9 members) will occupy a different position
out of these four (president , vice-president , secretary , treasurer).
So, here we have to calculate the Number of Permutations of 9 members Taken 4 at a Time :
= 9P4
= 9 × 8 × 7 × 6
= 3024
What is the volume of this rectangular prism? 1cm,6cm,2cm
Step-by-step explanation:
The result is 12 cm³ because to get the volume of a figure you have to multiply all the characters
Simplify 7 + (−3)
A: -10
B: -4
C: 4
D: 10
Answer: 4
Step-by-step explanation:
[tex]7+(-3)\\=7-3\\=\boxed{4}[/tex]
Suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally adjacent seat. How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?
688,747,536 ways in which the people can take the seats.
How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?There is a 2 by 10 rectangular greed of seats with people. so there are 2 rows of 10 seats.
When the whistle blows, each person needs to change to an orthogonally adjacent seat.
(This means that the person can go to the seat in front, or the seats in the sides).
This means that, unless for the 4 ends that will have only two options, all the other people (the remaining 16) have 3 options to choose where to sit.
Now, if we take the options that each seat has, and we take the product, we will get:
P = (2)^4*(3)^16 = 688,747,536 ways in which the people can take the seats.
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Find the value of x if a, b, and c are collinear points and b is between a and c. ab=x 6,bc=3x−5,ac=36−x
The value of x if a, b, and c are collinear points and b is between a and c : 7
What is collinear points?Collinear points are those that are situated on the same line of sight or within a single line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either close to or far from one another.
According to the given information:
if A, B, and C are col-linear points and B is between A and C
then
AB+BC=AC
AB=x+6
BC=3x-5
AC=36-x
substituting value:(x+6)+(3x-5)=36-x
(x+3x)+(6-5)=36-x
4x+1=36-x
4x+x=36-1
5x=35
x=35/5
x=7
The value of x is 7
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