Answer:
[tex]\frac{ -b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Step-by-step explanation:
1) the equation listed above is the quadratic formula! you can solve ANY quadratic equation with it
quadratic equations in the form of:
ax^2+bx+c
just substitute a,b,and c for the numbers in the quadratic equation!
2)factoring:
my 2nd favorite method:
your equation will be in the form of:
ax^2+bx+c
where you need to find:
what*what=c
and
what+what=b
once you find those two things out then substitute those numbers in place of "b"
for example:
x^2+7x+10
factors of 10: 5,2 10,1 -2,-5 -10,-1
factors of 10 that=7
5,2
so
x^2+5x+2x+10
now group this equation:
group a) x^2+5x
group b) 2x+10
gcf of group a) x
so
x(x+5)
group b) gcf:2
so
2(x+5)
combine the numbers outside the parantheses:
(x+2)(x+5)=0
x+2=0
x=-2
x+5=0
x=-5
hence x=-2,-5
hope this helps!
Dan was thinking of a number. Dan halves the number and gets an answer of 18.8. Form an
equation with 2 from the information.
Answer: the equation is x/2=18.8
Step-by-step explanation: you start with x because that’s the number and you divide it by 2 because that’s the same as halving then you write =18.8.
Final answer:
To form the equation based on the information provided, use the fact that Dan halves the number and gets 18.8. Solve by applying basic algebra to find the original number Dan was thinking of.
Explanation:
Equation: Let the original number that Dan was thinking of be represented by x. Given that Dan halves the number and gets 18.8, we can form the equation:
x / 2 = 18.8
Solving for x: Multiply both sides by 2 to find that the original number Dan was thinking of is x = 18.8 x 2 = 37.6.
You have 4 reindeer, Bloopin, Balthazar, Gloopin, and Prancer, and you want to have 3 fly your sleigh. You always have your reindeer fly in a single-file line
Answer:
P43=4!(4–3)!=241=24 24 possible choices
Step-by-step explanation:
There are four choices you can make for the lead reindeer. For each possible choice, there are then three remaining you can choose to fly second, making 4×3=12 choices for the lead pair. For each possible choice there are two remaining reindeer to take up the back position, making 12×2=24 choices for the team of three.
This type of problem is called a permutation problem, and we write Pnr for the number of ways of choosing r items from n possibilities when the order of the items matters. In this case we are choosing 3 reindeer from 4 possibilities, and the order they appear in the flying line does matter, so the answer we want is P43. The general formula is Pnr=n!(n−r)!. For the answer we are looking for we therefore have:
P43=4!(4–3)!=241=24
Brainliest?
Assignment
Active
Applying Properties of Congruent Prisms
The volume of one prism is known, along with the height For the two prisms to be congruent, what must the area
of another prism. The values are shown below.
of the base be, given that the triangular bases are
congruent?
3 in 2
6 in?
12 in 2
15 in 2
15 in
V = 90 in.
Intro
Done
Answer: 6 in ^2
Step-by-step explanation:
The shapes are congruent, so all the given values have to apply to both shapes. Keeping this in mind, the only answer that works is 6in^2.
A hypothetical square grows so that the length of its diagonals are increasing at a rate of 8m/min. How fast is the area of the square increasing when the sides are 8m each.
Answer: The area of the square is increasing at a rate of 90.4 m2/min (square meters/minute)
Step-by-step explanation: Please see the attachments below
Answer:
The area of the square is increasing at 90.51m^2/min
Step by step explanation:
Given;
Change in diagonal length ∆d = 8m/min
Length l = 8m
When l = 8m
d^2 = 2l^2 = 2×8^2 = 128
d = √128
Area of a square = l^2 = (d^2)/2
d = diagonal
Change in area = ∆A = dA/dd
∆A = 2 × d/2 × ∆d = d×∆d
∆A = √128 × 8 = 90.51m^2/min
what is the midpoint of the segment shown below -1 5 -6 -2
The midpoint of the segment with endpoints (-1, 5) and (-6, -2) is calculated using the midpoint formula and is (-3.5, 1.5).
The question seems to be asking for the midpoint of a segment with given endpoints. However, the numbers provided (-1, 5, -6, -2) do not clearly define a specific segment in a conventional two-dimensional coordinate system. Typically, a line segment in two-dimensional space is represented by the coordinates of its endpoints, such as (x₁, y₁) and (x₂, y₂).
If we assume the numbers are pairs of coordinates, we could interpret them as the endpoints (-1, 5) and (-6, -2). To find the midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂), you use the midpoint formula: Midpoint M = [tex](\frac{x_1 + x_2}{ 2}, \frac{y_1 + y_2}{2})[/tex]
Applying this to the given points: M = [tex](\frac{-1 + (-6)}{ 2}, \frac{5 + (-2)}{ 2} = (\frac{-7}{ 2}, \frac{3 }{ 2})[/tex] = (-3.5, 1.5).
The midpoint of the segment with endpoints (-1, 5) and (-6, -2) is (-3.5, 1.5).
---
what is the perimeter of triangle SOW
Answer:
2322
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
PLEASE HELP !!!! Solve the system using either substitution or elimination: 3x+6y=6 x-5y=23
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: ( 8 , − 3 ) Equation Form: x = 8 , y = − 3
Follow me on instagram at officialholydrip
Help me answer this please
Answer:
x=115 y=65
Step-by-step explanation:
You get 115 for X because angle x is vertical to 115 degrees.
You get 65 because y is supplementary to x, and 180-65=115.
Answer:
x = 115 degree and y = 65 degree
Step-by-step explanation:
Here we can see
x = 115 ( being vertically opposite angles )
So Now
x + y = 180 ( being linear pair )
115 + y = 180
y = 180 - 115
Therefore y = 65
Hope this helps
You use a garden hose to fill a wading pool. If the water level rises 17 centimeters every 6 minutes and you record the data point of (12,y), what is the value of y? Use slope to justify your answer.
Answer:
try 45
Step-by-step explanation:
The water level rises at a rate of approximately 2.83 cm per minute. Therefore, the water level would be approximately 34 cm after 12 minutes.
Explanation:This problem involves the concept of linear relationships and slopes in mathematics. Given that the water level rises by 17 cm every 6 minutes, we can find the rate of increase per minute by dividing 17 cm by 6 minutes. This value, approximately 2.83 cm/minute, is the slope of the linear relationship.
This means each additional minute increases the water level by about 2.83 cm. If we denote the time as x and the water level as y, the linear equation expressing this relationship can be written as y = 2.83x.
To find the value of y when x (time) is 12 minutes, we substitute x = 12 into this equation. So, y = 2.83 * 12 = 33.96 cm. Therefore, the water level would be close to 34 cm after 12 minutes.
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Write each equation in logarithmic form.
Answer:
B) [tex]log_3 81=4[/tex]
Step-by-step explanation:
The definition of logarithm is the following:
The logarithm of a certain number x with respect to a certain base b is the exponent by which b should be raised in order to give x. Mathematically, given the equation
[tex]b^y = x[/tex] (1)
The logarithm of x to base b is defined as
[tex]y=log_b x[/tex] (2)
In this problem, we have the following equation:
[tex]3^4=81[/tex]
By comparing it with equation (1), we notice that:
b = 3
y = 4
x = 81
Therefore, by re-arranging the variables using equation (2), we can rewrite it as:
[tex]4=log_3 81[/tex]
Which corresponds to option B.
Is 0.424242424242 a rational or irrational number?
Answer:
Rational, 0.424242... = 42/99
Step-by-step explanation:
let x = 0.4242424242....
We can convert this to a fraction
100x = 42.424242....
100x - x = 42
99x = 42
x = 42/99 a rational number
Answer: 0.424242424242 is a rational number
Step-by-step explanation:
D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. Find (a) the equilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point. D(x)=(x-7)^2, S(x)=x^2+4x+31
(a) Equilibrium point: x = 1
(b) Consumer surplus at equilibrium: 0
(c) Producer surplus at equilibrium: 0
We have,
To find the equilibrium point, we need to set the demand (D(x)) equal to the supply (S(x)):
D(x) = S(x)
Given:
D(x) = (x - 7)^2
S(x) = x^2 + 4x + 31
(a) Equilibrium point:
Setting D(x) equal to S(x):
(x - 7)^2 = x^2 + 4x + 31
Expanding and rearranging the equation:
x^2 - 14x + 49 = x^2 + 4x + 31
Simplifying and rearranging further:
-14x - 4x = 31 - 49
-18x = -18
x = 1
Therefore, the equilibrium point is x = 1.
(b) Consumer surplus at the equilibrium point:
Consumer surplus represents the difference between the price consumers are willing to pay and the price they actually pay.
At the equilibrium point, the price consumers are willing to pay (D(x)) is equal to the price they actually pay (S(x)).
Substituting x = 1 into the demand function D(x):
D(1) = (1 - 7)^2
D(1) = (-6)^2
D(1) = 36
Consumer surplus at the equilibrium point is the difference between what consumers are willing to pay and what they actually pay:
Consumer surplus = D(x) - S(x)
Consumer surplus = 36 - S(1)
Consumer surplus = 36 - (1^2 + 4(1) + 31)
Consumer surplus = 36 - (1 + 4 + 31)
Consumer surplus = 36 - 36
Consumer surplus = 0
Therefore, at the equilibrium point, the consumer surplus is 0.
(c) Producer surplus at the equilibrium point:
Producer surplus represents the difference between the price producers are willing to accept and the price they actually receive.
At the equilibrium point, the price producers are willing to accept (S(x)) is equal to the price they actually receive (D(x)).
Substituting x = 1 into the supply function S(x):
S(1) = 1^2 + 4(1) + 31
S(1) = 1 + 4 + 31
S(1) = 36
Producer surplus at the equilibrium point is the difference between what producers are willing to accept and what they actually receive:
Producer surplus = S(x) - D(x)
Producer surplus = 36 - D(1)
Producer surplus = 36 - (1 - 7)^2
Producer surplus = 36 - (-6)^2
Producer surplus = 36 - 36
Producer surplus = 0
Therefore, at the equilibrium point, the producer surplus is also 0.
Thus,
(a) Equilibrium point: x = 1
(b) Consumer surplus at equilibrium: 0
(c) Producer surplus at equilibrium: 0
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The equilibrium point in the market occurs when the demand and supply are equal, which can be found by solving the given function equations. Consumer surplus and producer surplus at the equilibrium point are computed as the area between the demand/supply curves and the equilibrium price.
Explanation:The equilibrium point is when the demand and supply are equal, this happens i.e., D(x) = S(x). Therefore, we first equate (x-7)^2 = x^2 + 4x + 31. Solving this equation gives us the equilibrium quantity, x.
The consumer surplus is the area between the demand curve and the consumer's actual payment, i.e., the area under D(x) above the equilibrium price. This equals to the integral from 0 to x of D(x) minus the equilibrium price. The producer surplus is the area between the supply curve and the consumer's payment, i.e., the area under S(x) below the equilibrium price. This equals to the integral from 0 to x of the equilibrium price minus S(x).
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Give the approximate: square root 48
Final answer:
The approximate square root of 48 is found by locating it between the perfect squares of 36 (6²) and 49 (7²), leading to a closer estimation of about 6.9 when considering 48 as 16 * 3 and simplifying.
Explanation:
The question asks to find the approximate square root of 48. To do this, we first recognize that the exact square root of 48 is not a whole number, and therefore, we need to find two perfect squares between which 48 lies. The perfect squares closest to 48 are 49 (7²) and 36 (6²). Since 48 is closer to 49, we can estimate that the square root of 48 is slightly less than 7. A more refined method involves thinking of 48 as 16 * 3, which then gives us √16 * √3 = 4√3. Knowing that √3 is approximately 1.732, we can multiply this by 4 to get an approximation of 6.928. Therefore, a good approximation for the square root of 48 is approximately 6.9.
What is the equation of the axis of symmetry?
Answer:
For a quadratic function in standard form, y=ax2+bx+c
the axis of symmetry is a vertical line x=−b2a .
Step-by-step explanation:
Hope this helps !
ayla is buying fence for two triangular sections of her garden. How much fence would she need for ΔDFG?
a. 80 ft
b. 82 ft
c. 85 ft
d. 83 ft
Answer:
80 ft
Step-by-step explanation:
Answer:
A. 80 ft.
Step-by-step explanation:
Triangle ABC is similar to Triangle DFG so they are proportional. 20/4=5; 25/5=5; so 7*5=35.
20+25+35=80
Two cards are drawn with replacement, one after the other, and the outcomes recorded. What is the probability that at least one of the two cards is a face card (Jack, Queen, or King)? (Give the answer as a decimal rounded to three decimal places.)
The probability of drawing at least one face card when drawing two cards with replacement from a standard deck is approximately 0.407.
Explanation:The student is asking for the probability of drawing at least one face card (Jack, Queen, or King) when drawing two cards with replacement from a standard deck of 52 cards. To find this, we can use the complement rule: subtract the probability of not drawing a face card in both draws from 1. There are 12 face cards in a deck of 52 cards, so the probability of drawing a non-face card (event N) on one draw is 40/52 (since there are 40 non-face cards).
Using the complement rule:
Calculate the probability of drawing a non-face card both times: P(NN) = (40/52) * (40/52).Subtract the above probability from 1 to get the probability of at least one face card: P(at least one F) = 1 - P(NN).Now perform the calculations:
P(NN) = (40/52) * (40/52) = 0.5929 (approximately).
P(at least one F) = 1 - 0.5929 = 0.4071 (rounded to three decimal places).
Therefore, the probability of drawing at least one face card in two draws with replacement is approximately 0.407.
How many centimeters are in x meters??
Answer:
Multiply by 100
Step-by-step explanation:
There are 100 centimeters in a meter, so multiply your value for meters by 100
100 i learned this before so if you have 2 meters there are 200 centimeters
A pilot flew his single-engine airplane 6060 miles with the wind from City A to above City B. He then turned around and flew back to City A against the wind. If the wind was a constant 3030 miles per hour, and the total time going and returning was 1.31.3 hours, find the speed of the plane in still air.
Answer: the speed of the plane in still air is 101.2 mph
Step-by-step explanation:
Let x represent the speed of the plane in still air.
The pilot flew his single-engine airplane 60 miles with the wind from City A to above City B. If the wind was a constant 30 miles per hour, it means that the total speed at which he flew the plane while going is (x + 30) mph.
Time = distance/speed
Time spent while going is
60/(x + 30)
He then turned around and flew back to City A against the wind. it means that the total speed at which he flew the plane while returning is (x - 30) mph.
Time spent while returning is
60/(x - 30)
If the total time going and returning was 1.31.3 hours, it means that
60/(x + 30) + 60/(x - 30) = 1.3
Cross multiplying, it becomes
60(x - 30) + 60(x + 30) = 1.3(x - 30)(x + 30)
60x - 1800 + 60x + 1800 = 1.3(x² + 30x - 30x - 900)
120x = 1.3x² - 1170
1.3x² - 120x - 1170 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 1.3
b = - 120
c = - 1170
Therefore,
x = [- - 120 ± √(- 120² - 4 × 1.3 × - 1170)]/2 × 1.3
x = [120 ± √(14400 + 6080)]/2.6
x = [120 ± √20480]/2.6
x = (120 + 143.1)/2.6 or x = (120 - 143.1)/2.6
x = 101.2 or x = - 8.9
Since the speed cannot be negative, then x = 101.2 mph
Which ratio completes the probability distribution table?
Answer:
16/48
Step-by-step explanation:
When you look for a pattern from frequency to probability, it is clear that the frequency will become the numerator for the probability and the denominator will remain 48. This appears to be the rule of the probability distribution table, so using this established rule, we can use 16 as the numerator for the probability, and then remember that 48 is always the numerator, which gives you 16/48 in result.
An object is translated from A (-6, -4) to A' (-18, -8). What is the translation rule?
Answer:
The translation rule is (x , y) → (x - 12 , y - 4)
Step-by-step explanation:
Let us revise the translation of a point
If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y) ⇒ T (x , y) → (x + h , y)If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y) ⇒ T (x , y) → (x - h , y)If the point (x , y) translated vertically up by k units then its image is (x , y + k)→ (x + h , y) ⇒ T (x , y) → (x , y + k)If the point (x , y) translated vertically down by k units then its image is (x , y - k) ⇒ T (x , y) → (x , y - k)An object is translated from A (-6, -4) to A' (-18, -8)
∵ A is (-6 , -4)
∵ A' is (-18 , -8)
∴ x-coordinate = -6
∴ x'-coordinate = -18
- By using the translation rule above
∵ x' = x + h
∴ -18 = -6 + h
- Add 6 to both sides
∴ -12 = h
∴ h = -12
∵ h is a negative value
- That means A translated to the left 12 units
∴ The rule is (x , y) → (x - 12 , y)
∵ y-coordinate = -4
∴ y'-coordinate = -8
∵ y' = y + k
∴ -8 = -4 + k
- Add 4 to both sides
∴ -4 = k
∴ k = -4
∵ k is a negative value
- That means A down 4 units
∴ The rule is (x , y) → (x , y - 4)
The translation rule is (x , y) → (x - 12 , y - 4)
At a concession stand, five hot dogs and two hamburgers cost $9.25; two hot dogs and five hamburgers cost $10.00. Find the cost of one hot dog and the cost of one hamburger.
Answer:
hot dogs- $1.25
hamburgers- $1.50
Step-by-step explanation:
let hot dogs be x and hamburgers be y∀
five hot dogs and two hamburgers cost $9.25
5x + 2y = $9.25 (eq. 1)
5x=9.25-2y
divide both sides by 5x
x= 1.85-0.4 (insert this in eq. 2)
two hotdogs and five hamburgers cost $10.00
2x + 5y = $10.00 (eq. 2)
2×(1.85-0.4) +5y=10.00
3.7 - 0.8 + 5y = 10.00
-0.8+5y=10.00-3.7
4.2y=6.3
divide both sides by 4.2 to evaluate the variable
6.3 divided by 4.2
y=1.50
now find x
x=1.85-0.4×1.5
x=1.85-0.6
x= 1.25
Eli has saved $8 more than 1/3 of Angela's savings.If they each save $10 more Eli will have saved &4 more than Angela's savings.How much has Eli saved?
Answer:
Eli has saved $10
Step-by-step explanation:
Let us use the first letters of their names to represent them.
A for Angela and E for ELi
So, from the first statement, we can write out an equation: E = [tex]\frac{1}{3}[/tex]A + 8, that is, one-third of Angela's savings + $8 will give us Eli's savings
From the second statement, we can write out: E + 10 = (A + 10) + 4 which means that if $10 is added to both their savings, Eli will still have $4 more than Angela.
So, we can solve both equations;
Equation 1: E = [tex]\frac{1}{3}[/tex]A + 8
Equation 2: E + 10 = (A + 10) + 4; which can be rewritten as E + 10 = A + 14
and then E = A + 4
The two equations (in bold), can then be solved simultaneously.
Let us carry out this operation to eliminate the E: Subtract equation 1 from equation 2, so that;
A + 4 - ( [tex]\frac{1}{3}[/tex]A + 8) = E - E
[tex]\frac{2}{3}[/tex]A - 4 = 0
[tex]\frac{2}{3}[/tex]A = 4
A = 4 × [tex]\frac{3}{2}[/tex] = 6
So, if A is 6, and E = A + 4 (from equation 2, that means that E = 6 + 4 = 10
So, Eli has saved $10, while Angela has saved $6.
If we check what was said in the question about their savings, which is what we have represented using the equations, the answers can be confirmed.
Answer:
Eli has saved $10
Step-by-step explanation:
Let us denote Angela's saving by "x".
If Eli's saving is $8 more than one-third of Angela's saving, then Eli's saving is:
[(1/3 × x) + 8 = x/3 + 8]
We will make x/3 + 8 to have a common denominator:
x/3 + 8 = (x+24)/3
If Eli and Angela each saved $10 more, then their respective savings would have been:
(x+24)/3 + 10 for Eli
x+10 for Angela.
At this savings, Eli would have been $4 richer than Angela.
i.e [((x + 24)/3) + 10] - (x+10) = $4
We will make [(x+24)/3] + 10 to have common denominator.
(x + 24 + 30)/3
= (x + 54)/3
Then:
[(x+54)/3] - [(x+10)/1] = 4
[x+54-(3x+30)]/3 = 4/1
(-2x + 24)/3 = 4
cross multiply
-2x + 24 = 12
-2x = -12
x = -12/-2
x = 6
Since Eli's saving = x/3 + 8
Then his actual saving
= 6/3 + 8
= 2 + 8
= $10
13. You are at the top of a lighthouse that is 400 ft. Tall. You look down towards the ocean and see a whale located 700 ft. From the shore. What is the angle of depression from your position?
Answer:
29.7°
Step-by-step explanation:
In a right triangle representing the geometry of the problem, the side opposite the angle is the height of your observation (400 ft). The side adjacent to the angle is the distance from shore (700 ft).
You know the tangent ratio is ...
Tan = Opposite/Adjacent
so your angle of depression satisfies ...
tan(angle of depression) = (400 ft)/(700 ft)
Using the inverse function, we find ...
angle of depression = arctan(4/7) ≈ 29.745°
The angle of depression is about 29.7°.
6. Ruth is having hardwood floors installed in her living room. The cost for the material is $2840 plus an installation charge of $1.90 per square foot. If the total cost for the material plus installation is $5120, determine the area of her living room. 7. Sean is deciding whether to select a satellite receiver or cable for his television programming. The satellite receiver costs $298.90 and the monthly charge is $68.70. With cable, there is no initial cost to purchase equipment, but the monthly charge for comparable channels is $74.80. After how many months will the total cost of the two systems be equal
Answer:
(6) 1200 square feet
(7) 49 months
Step-by-step explanation:
Let the area of the living room be x square feet. Since the material cost is fixed as $2840 and cost ler square feet provided as $1.9 while and the total cost is given as $5120 then the the problem can be represented as
1.9x+$2840=$5120
Putting like terms together then
1.9x=$5120-$2840=$2280
Making x the subject of the above, by dividing both sides by 1.9 then
X=2280/1.9=1200 square feet.
Therefore, area is 1200 square feet.
(7)
Let the number of months when cost are similar be y.
For satelite option, since fixed cost of $298.9 is charged then monthly rate is $68.7 it means after y months, the expenditure for this plan will be 68.7y+$298.9
For cable option, since it only charges monthly fee of $74.80 then after y months, the expenditure amounts to 74.80y
Since after y months the expenses are same, then we equate both options to be equal. Therefore,
74.80y=68.70y+298.90
Putting like terms together then
74.80y-68.70y=298.90
6.1y=298.90
Dividing both sides by 6.1 to make y the subject then
Y=298.9/6.1=49 months
Trina makes 3 retanglular quilts for her grandchildren. The first measures 70 inches by 90 inches. She enlarges these dimensions by a scale factor of 1.2 to make a second quilt. Then she enlarges the dimensions by a scale factor of 1.5 to make the third quilt. What are the dimensions of the third quilt?
Answer:
8.2, 105.00
Step-by-step explanation:
Take the first measures and add the enlargements to get the dimensions of the third quilt. This probably is wrong I just had to answer a question
What is the area of the parallelogram?
Answer:
a=bh
Step-by-step explanation:
the answer is 70
im sorry if thats not right
Answer:
The answer to your question is Area = 70 cm²
Step-by-step explanation:
Data
height = 5 cm
base = 14 cm
side = 13 cm
To solve this problem just look for the formula and substitute the values. It is not necessary the length of the short side.
Formula
Area = base x height
-Substitution
Area = 14 x 5
-Result
Area = 70 cm²
Check whether (5,12,13) forms a pythagorean triplet.
what is 10/15 in simplest form?
Answer:
2/3
Step-by-step explanation:
Answer: 2/3
Step-by-Step:
divide 10 by 5 = 2, then divide 15 by 5 =3, so 2/3
1) y varies directly with x. If y = -4 when x = 2, find y when x = -6.
Answer:
-12
Step-by-step explanation:
2 - -4 = 6 --> y + 6 = x
x = -6, so subtract 6 from x to find y
-6 - 6 = -12
y = -12
Does that help?
To find y when x = -6, given that y varies directly with x and y = -4 when x = 2, we first calculate the proportionality constant k, and then use it to find the new value of y.
Explanation:If y varies directly with x, this means that y can be expressed as y = kx, where k is the proportionality constant. Given that y = -4 when x = 2, we can first find the value of k by substituting these values into the direct variation equation:
-4 = k(2)
From this, we can solve for k:
k = -2
Now, to find y when x = -6, we substitute -6 for x in the original direct variation equation y = kx, using our found value of k:
y = (-2)(-6)
y = 12
Therefore, when x = -6, y will be 12.
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The measure of angle 1 is 130°. 2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 4, 3, 2. Which other angle must also measure 130°? angle
The angle that must also measure 130° is angle 4.
Angle 4 must also measure 130°. When two lines intersect, the vertically opposite angles are congruent, meaning angle 1 and angle 4 are equal. Therefore, if angle 1 measures 130°, angle 4 must also measure 130°.
If angle 1 measures 130°, angle 3 must also measure 130°.
When two lines intersect, they form pairs of angles known as vertical angles or vertically opposite angles. These angles are congruent, meaning they have the same measure. The key property of vertical angles is that they are formed by opposite rays.
In the given scenario:
Angle 1 and angle 3 are vertically opposite angles because they are formed by the intersecting lines and share the same vertex.
Since angle 1 measures 130°, according to the properties of vertical angles, angle 3 must have the same measure.
This is a fundamental property of vertical angles: they are always congruent. Therefore, if angle 1 measures 130°, angle 3 must also measure 130°.
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