The equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
A line is parallel to y=-2x-5 and intersects the point (-1,3)The equation of the new line will be:-
y - y₁ = m ( x - x₁ )
Since the line is parallel to the line y = -2x - 5 so slope will be same m = -2 now the coordinates are ( -1, 3).
y - ( 3) = -2 [( x - (-1) ]
y - 3 = -2x - 2
y = -2x + 3 -2
Y = -2x + 1
Therefore the equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.
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-9x²(x²+2x²y - 3y²)
Simplify
−9x^4−18x^4y+27x^2y^2
HAVE A NICE DAY!Answer:
=−18x^4y−9x^4+27x^2y^2
Step-by-step explanation:
(−9x^2)(x^2+2x^2y−3y^2)
=(−9x^2)(x^2+2x^2y+−3y^2)
=(−9x^2)(x^2)+(−9x^2)(2x^2y)+(−9x^2)(−3y^2)
=−9x^4−18x^4y+27x^2y^2
=−18x^4y−9x^4+27x^2y^2
---
Hope I helped! Have a great day :)
A triangular prism has an equilateral base with side length x inches. The height of the prism is four times as long as the side length.
What is the lateral area of the prism?
12x square inches
12x2 square inches
36x square inches
36x2 square inches
The area of the prism is 12x² inches². Thus, the correct option is B.
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
For a prism, the lateral sides of a prism are made up of rectangles which consist of the height and the length of the base. Therefore, a triangular prism has an equilateral base with a side length x inches. The height of the prism is four times as long as the side length. The lateral area will be,
Lateral Area = 3(x×4x) = 12x² inches²
Hence, the area of the prism is 12x² inches². Thus, the correct option is B.
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the graph of the function 10/x
The function will have a vertical asymptotes of x = 0 and horizontal asymptotes of y = 0.
What are rational functions?Rational function are functions that are written as a ratio. For instance a/b can be expressed as rational function.
According to the question, we are to plot the graph of the function 10/x
The function will have a vertical asymptotes of x = 0 and horizontal asymptotes of y = 0.
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find X if X is equal to 9x=6
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
[tex]\textsc{heya!}[/tex]
[tex]\square\!\!\!\!\checkmark[/tex]what we need to do:
find x if 9x=6[tex]\square\!\!\!\!\!\checkmark[/tex] what we are provided with:
9x=6[tex]\textsc{solution:}[/tex]
[tex]\bold{x=\frac{2}{3}}[/tex][tex]\textsc{explanation:}[/tex]
divide both sides by 9; after performing this operation, we obtain:
[tex]\bold{x=\frac{6}{9}}[/tex]
divide top & bottom by 3; we obtain the solution
[tex]\bold{x=\frac{2}{3}}[/tex]
[tex]\textsc{hopefully\;helpful!}[/tex]
by: [tex]^da_n^cIn_g}[/tex]
have a great rest of your day ahead ~ = )
~
Jamal puts $2300 into an account that does not earn any interest.
Every month after that, he deposits the same amount of money.
This sequence
represents his account balance for the first few months:
$2300, $2500, $2700, ...
What is the explicit formula for the amount of money in his account at the beginning of month n?
A. a(n) = 2300 + (n − 1)200
B. a(n) = 200-2300"-1
C. a(n) = 2300 200-1
D. a(n) = 200+ (n − 1)2300
The explicit formula for the amount of money in his account at the beginning of month n is a(n) = 2300 + (n − 1)200.
What is the explicit formula?The explicit formula would be a linear function. A linear function is a function that has a single variable raised to the power of 1.The rate of increase in the account is a constant amount : $200
Amount of money at the beginning of the month = beginning balance + (number of months - 1) x rate of increase
a(n) = 2300 + (n − 1)200
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If you apply the below transformations to the square root parent function,
F(x)=√x, what is the equation of the new function?
• Shift eight units left.
. Shift two units down.
O A. G(x) = VX- 2 - 8
B. G(x)=√x-8-2
C. G(x)=√x+8 - 2
OD. G(x)=√x-2 +8
Answer:
C. g(x) = sqrt(x+8)-2
Step-by-step explanation:
"Shift two units down" is easier to see in the equation because an up or down shift is just tacked right on to the end of the equation. So "shift DOWN 2" is a minus two on the end of the equation. This means that A and D are both NOT the answer.
Left and right shifts are the opposite of what you might expect. Left shift is a "+ anumber" and Right shift is
"- anumber" This is tucked in very close to the x, because a left or right shift is a change in the x-direction. Again left shift is "+ anumber", so in your question, "shift eight units left" shows in the equation as the plus8 beside the x.
So B is wrong and C is the answer.
Help! Select the correct answer from each drop-down menu.
Consider right triangle ABC.
(file is attached below!)
The value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The values of the angels will be calculated by using the trigonometry property.
Sin A = Perpendicular / Hypotenuse
Sin A = 9 /41
Cos A = Base / Hypotenuse
Cos A = 40 / 41
Therefore the value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).
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What is the equivalent decimal to this fraction? 10/45 0.2 0.222222222... 0.232323232323... 0.181818181818...
Factorize the numerator and denominator, then simplify:
10/45 = (2×5)/(9×5) = 2/9
Now,
1/9 = 1/10 + 1/90
1/90 = 1/10 × 1/9 = 1/10 × (1/10 + 1/90) = 1/100 + 1/900
1/900 = 1/100 × 1/9 = 1/100 × (1/10 + 1/90) = 1/1000 + 1/9000
and so on, which is to say
1/9 = 1/10 + 1/100 + 1/1000 + …
or
1/9 = 0.111…
so that multiplying both sides by 2 gives
2/9 = 0.222…
x – y = 2 2x = 3y in elimination method
Answer:
x=6, y=4
Step-by-step explanation:
x - y = 2
2x = 3y => 2x - 3y = 0
x - y = 2 | ×(-2) => -2x + 2y = -4
2x - 3y = 0
-2x + 2y = -4
2x - 3y = 0
___________
0 - y = - 4 | ×(-1)
y = 4
Substitution in x - y = 2:
x - 4 = 2 | +4
x = 2+4 = 6
Situation:
A 8 gram sample of a substance that's a
by-product of fireworks has a k-value of
0.1001.
N = Noe-kt
No = initial mass (at time t = 0)
N = mass at time t
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
The half life of the substance is 6.92 days.
What is the Half life ?Half life can be defined as the time required to reduce the concentration to half of its initial value.
Here the equation given is
[tex]\rm N = N_o e^{-kt}[/tex]
The concentration will reduce to half therefore
[tex]\rm N= \dfrac{N_o}{2}[/tex]
so,
[tex]\rm 39/2 = 39 e^{- 0.1001 * t_{1/2}}[/tex]
ln 0.5 = - 0.1001 * t(1/2)
-0.693 = -.1001 * t(1/2)
t(1/2) = 6.92 days.
Therefore the half life of the substance is 6.92 days.
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Two six-sided dice are rolled. Using the sample space for rolling two dice shown in the figure below, find the probability that the sum of the dice is either 4 or 7. Give your answer as a reduced fraction.
Answer:
Step-by-step explanation:
There are 36 ways 2 dice can be thrown. Sometimes colors are used to tell the difference between the dice.
36 comes from 6*6
Suppose you have 2 dice 1 blue and the other white
Blue White
1 1
2
3
4
5
6
There's 6 ways that have been thrown. Then you go to the blue dice being 2. You get six more. Then 3 gives you six more 4 gives you another six. and so on. The whole procedure adds to 36
you can throw a four 3 ways
Blue white
1 3
3 1
2 2
You can throw 7 six ways
Blue white
1 6
6 1
2 5
5 2
3 4
4 3
So of the 36 ways to throw the dice 9 will successful. (6 + 3)
Answer: 9/36 = 1/4 times you will be successful
100 POINTS
Give explanation also pls or reported
AB is a common tangent of circles C, D, E and F.
Suppose that AC = 12, DB = 9 and AE = BF = 3.
If the midpoint of EF is the center of a circle that is tangent to both circles E and F, what are the possible values for its radius?
Answer:
6√3 ±3 ≈ {7.392, 13.392}
Step-by-step explanation:
The length of AB is the long side of a right triangle with hypotenuse CD and short side (AC -BD). The desired radius values will be half the length of EF, with AE added or subtracted.
__
length of ABRadii AC and BD are perpendicular to the points of tangency at A and B. They differ in length by AC -BD = 12 -9 = 3 units.
A right triangle can be drawn as in the attached figure, where it is shaded and labeled with vertices A, B, C. Its long leg (AB in the attachment) is the long leg of the right triangle with hypotenuse 21 and short leg 3. The length of that leg is found from the Pythagorean theorem to be ...
AB = √(21² -3²) = √432 = 12√3
tangent circle radiiThis is the same as the distance EF. Half this length, 6√3, is the distance from the midpoint of EF to E or F. The radii of the tangent circles to circles E and F will be (EF/2 ±3). Those values are ...
6√3 ±3 ≈ {7.392, 13.392}
Answer:
6√3 ± 3
Step-by-step explanation:
AC is the radius of Circle C ⇒ radius = 12
DB is the radius of Circle D ⇒ radius = 9
Therefore, CD = AC + DB = 12 + 9 = 21
AE is the radius of Circle E ⇒ radius = 3
BF is the radius of Circle F ⇒ radius = 3
If AB is the common tangent of Circles C, D, E and F, then:
∠CAB =∠AEF = ∠DBA = ∠BFE = 90°
(as the tangent to a circle is always perpendicular its the radius).
Also AB = EF
To find the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F, we first need to find the length of EF (marked by x on the attached diagram).
CD is the hypotenuse of a right triangle with base equal to EF and a smaller leg of the difference between the radii of Circles C and D.
(Refer to the green shaded triangle on attachment 1)
Therefore, to find EF (x), use Pythagoras' Theorem a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ a² + b² = c²
⇒ 3² + x² = CD²
⇒ 3² + x² = (12 + 9)²
⇒ 9 + x² = 441
⇒ x² = 432
⇒ x = √432
⇒ x = 12√3
⇒ EF = 12√3
As the radius of Circles E and F is 3, the possible diameter of the circle with its center as the midpoint of EF is 6 less or 6 more than the length of EF.
⇒ diameter = EF ± 6
= 12√3 ± 6
As the radius is half of the diameter, the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F is:
⇒ radius = diameter ÷ 2
= (12√3 ± 6) ÷ 2
= 6√3 ± 3
(see attachments 2 and 3 → the possible circles are shown in orange)
Mr.khatiwada. is a unmarried secondary level mathematics teacher in a community school.His monthly salary is Rs 39990with Rs 2000 allowance and gets one months basic salary as festival expense.if 10%and next 13%of his basic salary is deposited in his provident fund and civil investment trust respectively,how much income tax should he pay in this year.
The income tax that will be paid for the year will be RS 4199.
How to calculate the tax?The total income that the ma gets will be:
= 39990 + 2000
= 41990
The tax rate is given as 10%. Therefore, the income tax that will be paid this year will be:
= 10% × 41990
= 4199
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5. Se hizo una encuesta a estudiantes, de una carrera de un total de 6000 estudiantes encuestados el 75% le gusta leer. ¿Cuántos estudiantes les gusta leer?
La encuesta indica que de entre todos los estudiantes de una carrera, 4500 les gusta leer.
PercentageThe percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the example: [tex]\frac{30}{100} =\frac{3}{10}=0.3*100=30 \%[/tex].
The question gives:
6000 students75% of students like to readThen, you will have:
[tex]6000\cdot \frac{75}{100}\\ \\ 6000\cdot \frac{3}{4}\\ \\ \frac{18000}{4} =4500[/tex]
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Describe how the product of 0.4 x 2 would look on a ten-square grid.
The product would have____
squares shaded out of 10.
Explanation:
Draw out a 10 squares.
Shade in 4 of them to represent 4/10 = 0.40 = 0.4
Then use another color to shade another 4 squares. You should have 4+4 = 8 squares shaded, out of 10 total, giving 8/10 = 0.80 = 0.8
This is one visual way to see how 0.4 x 2 = 0.8
In other words, 0.4 x 2 means we have two copies of 0.4 added together. You could write it as 0.4 x 2 = 0.4 + 0.4 = 0.8 if you wanted.
See the diagram below.
make mathematical expression and simplify. The sum of 4 and 5 is subtracted form one-third of the difference of 40 and 4.
Answer:
X= -3
Step-by-step explanation:
(4+5)-1/3(40-4)=X
X=9- 1/3(36)
X=9-12
Suppose a square pyramid has a height of 5 meters and a base whose area is 36 square meters.
Explain how to determine the slant height of the pyramid.
The slant height can be found using Pythagoras theorem, the slant height is the hypotenuse side of the pyramid. Therefore, slant height = √34 meters
How to find the slant height of a pyramid?The base of the pyramid is a square.
Therefore,
area of a square = l²
where
l = side lengthhence,
area of the base = l
36 = l²
l = √36
l = 6 meters
Therefore, using Pythagoras theorem,
l² = 5² + 3²
l² = 25 + 9
l² = 34
l = √34 meters
slant height = √34 meters
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Math need help please
Answer:
none
Step-by-step explanation:
4x - 6 = 2(2x + 3)
4x - 6 = 4x + 6
Everything cancels out meaning there are no real solutions
What is the measure of AC?
Answer:
The measure of a minor arc is less than 180° , and equal to the measure of the arc's central angle . A major arc is the longer arc connecting two endpoints on a circle. The measure of a major arc is greater than 180° , and equal to 360° minus the measure of the minor arc with the same endpoints.
please help me I'm almost done
Answer:
[tex]\mathsf {SA = 112 in.^{2} }[/tex]
Step-by-step explanation:
[tex]\textsf {Formula used :}\\\implies \textsf {SA = 2(length * width + width * height + length * height) }[/tex]
[tex]\textsf {Given :}\\\textsf {Length = 5 in.}\\\textsf {Width = 4 in.}\\\textsf {Height = 4 in.}[/tex]
[tex]\textsf {Solving :}[/tex]
[tex]\implies \mathsf {SA = 2 (5 * 4 + 4 * 4 + 5 * 4)}[/tex]
[tex]\implies \mathsf {SA = 2 (20 + 16 + 20)}[/tex]
[tex]\implies \mathsf {SA = 2 (56)}[/tex]
[tex]\implies \mathsf {SA = 112 in.^{2} }[/tex]
Find the slope please
Pls help me I need answers in summer school teachers won’t help!!
Answer:
21. x = 18.1
22. x =28.7
Step-by-step explanation:
SOH = sin(theta) = opp/hyp
CAH = cos(theta) = adj/hyp
TOA = sin(theta) = opp/adj
21. You would be using tangent.
tan(theta) = Opp/Adj
tan(32°) = x/29
x = 29 * tan(32°)
x = 18.1
22. You would be using cosine
cos(theta) = Adj/Hyp
cos(43°) = 21/x
x * cos(43°) = 21
x = 21 / cos(43°)
x = 28.7
Use a Calculator to help you solve for those side lengths or degrees.
If you were to search of SOHCAHTOA online and find an image you would be able to see their example problem done using
SOHCAHTOAI am not sure if I am allowed to use an online example image since I got warned for some reason without explanation to the warning.
An automobile manufacturer produces production parts with 98% accuracy. What is the probability that in a production run of 25 parts, at most 2 are found to be defective?
An automobile manufacturer produces production parts with 98% accuracy. the probability is mathematically given as
P(X\leq2) = 0.9868
What is the probability that in a production run of 25 parts, at most 2 are found to be defective?Generally, the equation for the probability is mathematically given as
[tex]P(X\leq2) = P(X=0) + P(X=1) + P(X=2)[/tex]
Therefore
[tex]P(X=0)=\binom{25}{0}* 0.98^{25}* 0.02^{0}=1* 0.6035* 1\\\\P(X=0)=0.6035[/tex]
Hence
P(X=1)=0.3079
P(X=0)=0.07554
In conclusion, bringing the equation into view
[tex]P(X\leq2) = P(X=0) + P(X=1) + P(X=2)[/tex]
[tex]P(X\leq2) = 0.6035 +0.3079 + 0.07554[/tex]
P(X\leq2) = 0.9868
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An arithmetic sequence starts
-10, -13, -16,
Find the sum of its first 35 terms.
Answer:
-10,-13,-16 and importance of being in a good night friends ni pta nhi hai to you
What slope would make the lines parallel
Answer:
3
Step-by-step explanation:
Parallel lines are a fixed distance apart and will never meet, no matter how long they are extended. Lines that are parallel have the same gradient . The equations above, y = 3x -2 and y = ? x +3 have the same gradient of 3 if they are to be parallel
Hope you understood and this helped and have a good day
If you help me you get a lot of points
Answer:
Step-by-step explanation:
#a
pattern 0 will include 4 reds in square
Because it's independent of pattern no
#b
Figure 1 has 4+4=8
Figure 2=4+8+2=14
Figure 3=4+12+3=19
The pattern n rule is
n²+3n+4So for 13th n
13²+3(13)+4169+39+4212squares#c
attached
y=x²+3x+4#d
Already given in c
Find the volume of a right circular cone that has a height of 4.5 ft and a base with a diameter of 19 ft. Round your answer to the nearest tenth of a cubic foot.
if it's diameter is 19, then its radius must be half that, or 9.5.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=9.5\\ h=4.5 \end{cases}\implies V=\pi (9.5)^2(4.5)\implies V\approx 1275.9~ft^3[/tex]
If the value of a home is assessed at $110,000, and the homeowner pays property tax at a rate of 25 mills, how much would the homeowner have to pay in property tax each year?
$2,500
$3,125
$1,100
$2,750
Using proportions, it is found that the homeowner would have to pay $2,750 in property tax each year.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The tax at a rate of 25 mills means that for each $1,000 in value of the home, he pays $25 in taxes. Hence, for a home of value of $110,000, the amount he pays in taxes is given by:
A = 110 x 25 = $2,750.
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Two trains, Train A and Train B, weigh a total of 526 tons. Train A is heavier than Train B. The difference of their weights is 466 tons. What is the weight of each train?
Answer:
Train A = 466
Train B = 60
Step-by-step explanation:
What's the least common
denominator of ¾,
⅘, and ⅔?
O A. 15
O B. 12
O c.20
O D. 60
Answer:
D. 60
Step-by-step explanation:
60 is the only number that 3 and 4 and 5 all go into.
4 does not go into 15, so not answer A.
5 does not go into 12, so not answer B
3 does not go into 20, so not answer C
D is correct. 4 and 5 and 3 all go into 60.