Answer:
[tex]3x - y = -4[/tex]
Step-by-step explanation:
To make things easier, let's first find the equation in slope-intercept form ([tex]y = mx + b[/tex] where m is the slope and b is the y-intercept.
1. Find the slope:
[tex]\frac{7 - 1}{1 - (-1)} = \frac{6}{2} = 3[/tex]
2. Find the y-intercept by plugging in (-1,1) into the equation [tex]y = 3x + b[/tex]
[tex]1 = 3(-1) + b[/tex]
so [tex]b[/tex] = 4
3. Therefore the equation of the line in slope-intercept form is [tex]y = 3x + 4[/tex]
4. To convert slope-intercept form into standard form, let's move the 3x over to the other side and divide by -1 to get rid of the negative.
Our result is [tex]3x - y = -4[/tex].
Hope this helps :)
A 30-foot ramp is used to move product to a loading dock. The ramp makes a 24° angle with the horizontal. The ramp is to be replaced with a ramp that is 50 feet long. What angle does this replacement ramp make with the horizontal? Round your answer to the nearest tenth of a degree.
Check the picture below.
[tex]sin(\theta )=\cfrac{\stackrel{opposite}{30\cdot sin(24^o)}}{\underset{hypotenuse}{50}}\implies sin^{-1}[sin(\theta )]=sin^{-1}\left[ \cfrac{30\cdot sin(24^o)}{50} \right] \\\\\\ \theta =sin^{-1}\left[ \cfrac{30\cdot sin(24^o)}{50} \right]\implies \theta \approx 14.1^o[/tex]
The value of angle does this replacement ramp make with the horizontal is,
⇒ θ = 14.1°
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
A 30-foot ramp is used to move product to a loading dock.
The ramp makes a 24° angle with the horizontal.
And, The ramp is to be replaced with a ramp that is 50 feet long.
Hence, By given figure;
We have;
⇒ sin θ = 30 × sin 24° / 50
⇒ θ = sin ⁻¹ (30 × sin 24° / 50)
⇒ θ = 14.1°
Thus, The value of angle does this replacement ramp make with the horizontal is,
⇒ θ = 14.1°
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Hey:This is super easy!!
3x+4=10
Answer:
x = 2
Step-by-step explanation:
We can find this by doing the short (and wildly incorrect way, according to teachers) way and input two in. The way the teachers want you to do it is this way:
3x + 4 = 10
3x + 4 (-4) = 10 (-4)
3x = 6
3x = 6/3
x = 2
2 is your answer.
HELP PLEASE 100 POINTS!!!
Given that triangle PHT is a right triangle and Line HY is an altitude, what is the missing justification in the proof that (PH)^2 + (HT)^2 = (PT)^2?
The missing reason is reflexive property.
Therefore, the correct option is D.
What is a triangle?A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle.
Given that a triangle PHT is a right triangle and Line HY is an altitude.
According to the reflexive property, a side or an angle is congruent to itself.
If A is an angle of a triangle, then using reflexive property.
∠A ≅ ∠A
∠PHT ≅ ∠HYT (Both are right angles)
∠T ≅ ∠T (Reflexive property)
ΔPHT ~ ΔHYT (AA rule of similarity)
Other statements and reasons are already in the table.
Hence the correct option is D.
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This figure represents an arrow painted on a walkway 12 times.
What is the area of the walkway that is painted with the 12 arrows?
70 cm²
90 cm²
840 cm²
1080 cm²
The area of the walkway that is painted with the 12 arrows will be 840 cm². Then the correct option is C.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
This figure represents an arrow painted on a walkway 12 times.
The figure is given below.
The figure is the combination of a triangle and a rectangle. Then the area of the figure will be
Area = 1/2 x 8 x 5 + 10 x 5
Area = 20 + 50
Area = 70 cm²
Then the area of the walkway that is painted with the 12 arrows will be
Area of the walkway = 70 x 12
Area of the walkway = 840 cm²
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How many days would it take to breathe one billion times if you were
breathing at a rate of 12 times per minute?
Answer:
I think it would be 1,000,000.
Step-by-step explanation:
Let's begin with a correction: the verb in question is TO BREATHE; one instance of doing so is the noun BREATH.
12 times per minute; 60 minutes per hour; 24 hours per day; multiplying all of these gives some number of breaths per day. I'm going to call it B (you can calculate it).
Answer:
Step-by-step explanation:
12 / min
720 / hr
17,280 / day
6,307,200 / yr
Now divide 1,000,000,000 by 6,307,200 and you get 158 years
If P is directly proportional to Q. And Q = 30 when P = 40. Find Q when P = 70
Answer:
Q = 52.5
Step-by-step explanation:
given P is directly proportional to Q then the equation relating them is
P = kQ ← k is the constant of proportion
to find k use the condition Q = 30 when P = 40 , then
40 = 30k ( divide both sides by 30 )
[tex]\frac{40}{30}[/tex] = [tex]\frac{4}{3}[/tex] = k
P = [tex]\frac{4}{3}[/tex] Q ← equation of proportion
when P = 70 , then
70 = [tex]\frac{4}{3}[/tex] Q ( multiply both sides by 3 to clear the fraction )
210 = 4Q ( divide both sides by 4 )
52.5 = Q
Is this function linear or exponential?
x y
0
–
5
1
–
10
2
–
20
3
–
40
4
–
80
The function represented by the table of values is an exponential function
How to determine the function type?The table is given as:
x 0 1 2 3 4
y 5 10 20 40 80
On the table, we have the following highlights:
As x increases by 1y multiplies by 2This means that the function has a common ratio
Only exponential functions have a common ratio
Hence, the function is an exponential function
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In a particular region, for families with a combined income of $80,000 or more, 20% have no children, 30% have one child, 40% have two children, and 10% have three children. Use this information to construct the probability distribution for X, where x represents the number of children per family for this income group. Arrange x in increasing order and write the probabilities P(x) as decimals.
The probability distribution for x will be given below.
x 0 1 2 3
P(x) 0.20 0.30 0.40 0.10
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
In a particular region, for families with a combined income of $80,000 or more, 20% have no children, 30% have one child, 40% have two children, and 10% have three children.
Let x be the number of children per family.
We have to construct a probability distribution for x from the given information.
x = 0, 1, 2, 3
For x = 0, the probability will be
P(x) = 20 / 100 = 0.20
For x = 1, the probability will be
P(x) = 30 / 100 = 0.30
For x = 2, the probability will be
P(x) = 40 / 100 = 0.40
For x = 2, the probability will be
P(x) = 10 / 100 = 0.10
Then the probability distribution for x will be given as
x 0 1 2 3
P(x) 0.20 0.30 0.40 0.10
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What is the radius of a cone that has a lateral area of 70TT and a total surface area of 120TT?
A)50 units
B)50TT units
C)7.1 units
D)7.117 units
Step-by-step explanation:
the lateral area of the cone is, well, the lateral area.
the total surface area of the cone is the lateral area plus the area of base circle.
so, the difference between both is the area of the base circle :
120pi - 70pi = 50pi
the area of a circle is
pi×radius²
and that is in our case
pi×radius² = 50pi
radius² = 50
radius = sqrt(50) = 7.071067812... ≈ 7.1 units
therefore, C is the right answer.
How many solution that following equation has? 2x +4= 2x-5 0 1 02 O infinitely many
Answer:
NO SOLUTIONStep-by-step explanation:
2x +4 = 2x - 5
4 + 5 = 2x - 2x
9 = 0
NO SOLUTION
The figure shows a planter Mrs Washington uses for flowers please help fast
Answer:
67.5 ft^3
Step-by-step explanation:
7.5 * 2 * 3.5 + 3 * 2.5 *2 = 67.5 ft^3
What is the radius of oT?
Answer Here
+
21
20
R
The length of the half chord is given as 21. The length of the perpendicular drawn from the center to the chord is 20. The radius would be 29 units.
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).
The length of the half chord is given as 21.
The length of the perpendicular drawn from the center to the chord is 20.
By Pythagoras' Theorem
[tex]|r|^2 = |21|^2 + |20|^2\\\\|r|^2 = 441 + 400\\\\|r|^2 = 841\\\\|r| = \sqrt{841} \\\\r = 29[/tex]
The radius of the circle would be 29 units.
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Find the sum or difference
(X-2)+(x+6)
The sum of the expression (x - 2) and (x+6) is 2x + 8
How to find sum of an expression?The sum of numbers simply means to add up the numbers.
Therefore,
(x -2) + (x + 6)
Hence,
(x - 2) + (x + 6)
open the brackets
Therefore,
x - 2 + x + 6
combine like terms
x + x + 2 + 6
add or subtract the like terms
2x + 8
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Which of the following is not a type of electromagnetic radiation that telescopes can detect?
A. Microwave
B. Ultraviolet
C. Infrared
D. Heliocentric
Answer:
B I just got that question it was B
URGENT AND IMPORTANT. WILL GIVE BRAINLIEST TO FASTEST CORRECT ANSWER. PLEASE ANSWER ASAP. PHOTO ATTACHED OF PROBLEM.
Answer:
A
B
C
and
D
Step-by-step explanation:
A
B
C
and
D
od
2
(
2 7 1-3
1 3 1-2
6:1-6
b =
d =
IDONE
Answer:
[tex] a = \boxed{1},\: b=\boxed{0}\\\\c=\boxed{0},\: d=\boxed{1}[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix} 2 & 7\\\\1 & 3\end{bmatrix}\:\begin{bmatrix} -3 & 7\\\\1 & -2\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex]Multiply both the matrices on left side, we find:[tex]\begin{bmatrix} 2(-3)+7(1) & 2(7)+7(-2)\\\\1(-3)+3(1) & 1(7)+3(-2)\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex][tex]\rightarrow\begin{bmatrix} -6+7 & 14-14\\\\-3+3 & 7-6\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex][tex]\rightarrow\begin{bmatrix} 1 & 0\\\\0 & 1\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex]Comparing the corresponding elements of both the matrices on both sides, we find:[tex] a = \boxed{1},\: b=\boxed{0},\:c=\boxed{0},\: d=\boxed{1}[/tex]The parabola y = -(x − 3)² + 6 has its focus at (3,1). Determine and state the equation 20 of the directrix.
well, tis noteworthy that the equation of the parabola above is already in vertex form, which means its vertex is at (3 , 6) and its focus point is at (3 , 1).
now, the focus point is below the vertex, meaning is a vertical parabola opening downwards, like a hump.
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]y=-\cfrac{1}{20}(x-3)^2+6\implies y-6=-\cfrac{1}{20}(x-3)^2\implies \stackrel{4p}{-20}(y-\stackrel{k}{6})=(x-\stackrel{h}{3})^2 \\\\\\ 4p=-20\implies p=-\cfrac{20}{4}\implies p=-5[/tex]
the focus point must be a negative distance since the parabola is opening downwards, and the directrix is across the vertex at "p" distance, Check the picture below.
Jacob learns that the mass of a new planet found in the solar system is 2,330,000,000,000,000,000,000,000 kilograms. What is the mass represented in scientific notation? A. 2.33 × 1024 kilograms B. 2.33 × 10-24 kilograms C. 2.33 × 1023 kilograms D. 23.3 × 1023 kilograms
Answer:
2.33 x 10^24 kilograms
Step-by-step explanation:
hope this helps!!
=2.33 × [tex]10{^{21}[/tex]
scientific notation
= 2.33e21
scientific e notation
= 2.33 × [tex]10{^{21}[/tex]
engineering notation
= 2.33 × [tex]10{^{21}[/tex]
21
Order of Magnitude
for scientific and standard forms
two setillion three hundred thirty quintillion
Solve for x in the first equation, then solve the system using substitution. Write your answer as (x, y).
2x-6y=14
4x - y = 9
Answer:
( 18.4, 4.6 )
Step-by-step explanation:
2x - 6y = 14
Add 6y to both sides
2x = 6y + 14
divide both sides by 2
x = (3y + 7)
Substitute this ^ for x in the othe equation
4 (3y + y) - y = 9
distribute the 4
12y + 4y - y = 9
combine like terms
15y = 9
divide both sides by 15
y = 4.6
Now substitute this value for y in the equation we previously substituted .to find the value of x
x = 3 (4.6) + 4.6
x = 13.8 + 4.6
x = 18.4
Hope this makes sense and was helpful!
A flag pole is 35 feet high. The sun shines a shadow of the flag pole to the ground. The shadow,
going out from the base of the flag pole is 12 feet long. What is the distance from the top of the
flag pole to the tip of the shadow?
Which equation is true when r = 7 ?
Answer:
7 = 49 ÷ r
Step-by-step explanation:
To find the equation that is true when r = 7, we need to find a number after the equals sign that is a multiple of 7.
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77...
Therefore, the only answer option in which the number after the equals sign is a multiple of 7 is:
7 = 49 ÷ r
To prove this, input r = 7 into each of the equations:
6 = 30 ÷ r
⇒ 6 = 30 ÷ 7
⇒ 6 ≠ 4.285... ← incorrect!
7 = 54 ÷ r
⇒ 7 = 54 ÷ 7
⇒ 7 ≠ 7.714... ← incorrect!
7 = 49 ÷ r
⇒ 7 = 49 ÷ 7
⇒ 7 = 7 ← correct!
9 = 72 ÷ r
⇒ 9 = 72 ÷ 7
⇒ 9 ≠ 10.285... ← incorrect!
Factor completely.
128-32x + 2x² =
Answer:
[tex]\mathrm {(x - 8)(x + 8)}[/tex]
had to be corrected. sorry for the inconvenience.
Answer:
(x - 8)(x + 8) will be your answer.
Step-by-step explanation:
Lets do this step by step.
1) Find the GCF of the expression.
2x^2 - 32x - 128 --> 2(x^2 - 16x - 64)
2) Use the X-method to factor.
It gives us the expression 2(x^2 - 8x)(-8x -64).
3) Factor for x.
(x^2 - 8x) --> x(x - 8)
(-8x - 64) --> -8(x + 8)
Our answer is (x - 8)(x + 8)
Caroline, Colin & Sarah share some money.
Caroline gets
1
9
of the money.
Colin and Sarah share the rest in the ratio 1:3.
What proportion does Colin get?
Caroline, Colin & Sarah share some money.Caroline will get [tex]\dfrac{2}{3}[/tex] when Caroline, Colin & Sarah share some money.
What is the ratio?The ratio defined as the sharing of the two or three things or it represent that one thing or number is how many times to the other.
One part is excluded in the problem. That part is:
"Caroline gets [tex]\dfrac{1}{9}[/tex] of the money."
If Caroline gets 1/9th, then remaining is:
[tex]1-\dfrac{1}{9}=\dfrac{8}{9}[/tex]
Colin and Sarah share in ratio 3 is to 1, that means 3 + 1 = 4 parts...
8/9th in 4 parts means, each part is:
[tex]\dfrac{\dfrac{8}{9}}{4}=\dfrac{2}{9}[/tex]
We know Colin gets "3" parts of the total, each part is (2/9)th, so 3 parts would be:
[tex]3\times \dfrac{2}{9}=\dfrac{6}{9}=\dfrac{2}{3}[/tex]
Colin gets [tex]\dfrac{2}{3}[/tex] money when three of them share money.
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How do I use the standard altherigm?
Answer:
Step-by-step explanation:
The standard algorithm is a way of doing multiplication by using partial products or multiplying in parts. What you do with this algorithm is multiply the top number by the bottom number one digit at a time, working your way from right to left.
Convert -4x+2y=16 to slope intercept form simplify your answer
[tex]\text{Slope-intercept form is y=mx+c, where m is the slope and c is the y-intercept.}\\ \\~~~~~-4x+2y = 16\\\\\implies 2y = 16+4x\\\\\implies y = \dfrac 12(16+4x)\\\\\implies y = 8 + 2x\\\\\implies y=2x +8\\\\\text{It is now in the slope-intercept form.}[/tex]
colleen is searching online for airline tickets. Two weeks ago, the cost to fly from boston to hartford was $200. now its cost $340. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answer:
A) 70%
B) 95%
Step-by-step explanation:
A) $200 to $340
Increase = $340 - $200 = $140
Percentage of increase = $140/$200 * 100% = 70%
B) Additional $50
Increase = $140 + $50 = $190
Percentage of increase = $190/$200 * 100% = 95%
Kara’s car used 1/16 gallons of gas to drive 1/8 of a mile at this rate how many miles can Kara’s car drive using one gallon of gas
Hi!
I am not quite sure the formula I am supposed to use for this or where each piece of information belongs. How would I solve this question?
Jeff Krause purchased 1,000 shares of a speculative stock in January for $1.89 per share. Six months later, he sold them for $9.26 per share. He uses an online broker that charges him $10.00 per trade. What was Jeff's annualized HPR on this investment?
Thanks!
Based on the price he purchased the stock and the amount he sold them for, Jeff's annualized HPR on the investment is 2,395%.
How much is Jeff's annualized HPR?First find the net profit:
= (1,000 x 9.26) - (1,000 x 1.89) - 10
= $7,360
The HPR is:
= 7,360 / (1,000 x 1.89)
= 389.4%
The annualized HPR is:
= (1 + 389.4%)² - 1
= 2,395%
Note: Taken to the power of 2 because there are two six-month periods in a year.
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Find the area of the Wrangle
The area of the triangle in square units 8 units 10 units
Answer:
The area is 40 units
Step-by-step explanation:
The five number summary of a dataset was found to be:
45, 52, 56, 61, 69
Step-by-step explanation:
Given the five summary of a data set:
45 - min
52 - Q1
56 - Median
61 - Q3
69- Max
Thus, any number less than Q1-(1.5×IQR)
, or any number that is greater than
Q3+ (1.5 × IQR) would be considered an outlier.
The IQR of the data set = Q3 - Q1 = 61-
52 = 9
Thus,
Q1- (1.5 × IQR) =52- (1.5* 9) = 52 - 13.5=38.5
Therefore, an observation is considered
an outlier if it is below: 38.5
Q3 + (1.5 * 1QR) = 61 + (1.5 * 9) =61+13.5 =74.5
Therefore, an observation is considered
an outlier if it is above: 74.5
