The standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.
The standard form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
We are given a point (3,3) and a slope of -1/2, we can use the point-slope form to write the equation of the line as follows -
y - 3 = -1/2(x - 3)
To convert this equation to standard form, we can simplify the equation as follows -
y - 3 = -1/2x + 3/2
y = -1/2x + 3 + 3/2
y = -1/2x + 9/2
Hence, the standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.
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find the size of x
write your answer in degrees
Size of x = 102°
What is angle ?In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.
Given,
In triangle ABC
Sum of interior angles is 180°
∠CAB + ∠ABC + ∠BCA = 180°
87° + ∠ABC + 36° = 180°
123° + ∠ABC = 180°
∠ABC = 180° - 123°
∠ABC = 57°
In triangle DBG
Exterior angle is equal to sum of two opposite interior angles.
DGF = GDB + DBG
DGF = GDB + ABC
DGF = 45° + 57°
DGF = 102°
DGF and EFC are alternate angles made by EF and DG on BC
∴ EFC = DGF
x = 102°
Hence, 102° is size of x.
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The numbers 528 and 540, written as the products
of their prime factors, are 528 = 24 x 3 × 11 and
540=22 x 3³ x 5. Hence, find
(i) the smallest non-zero whole number h for
which 528h is a multiple of 540,
(ii) the smallest whole number k for which
a factor of 540
Answer: To find the smallest non-zero whole number h for which 528h is a multiple of 540, we need to find the smallest positive whole number h such that 528h is divisible by 540.
First, we can simplify the prime factorization of 540:
540 = 22 x 3³ x 5
To make 528h a multiple of 540, we need to ensure that the prime factors of 528h are the same as the prime factors of 540.
528 = 24 x 3 x 11
So, 528h = (24 x 3 x 11)h = 24h x 3h x 11h
We can see that 24h and 11h are not factors of 540.
So, the only way to make 528h a multiple of 540 is to make 3h a factor of 3³.
3h = 3³ = 27
So, h = 27/3 = 9
So, the smallest non-zero whole number h for which 528h is a multiple of 540 is 9.
For (ii)
The smallest whole number k for which a factor of 540
540 = 22 x 3³ x 5
The smallest whole number k that is a factor of 540 is 5.
Step-by-step explanation:
Shaquana went shopping for a new phone. The sales tax where she lives is 3.5%. If the price of the phone is pp dollars and cents, which expression represents the total price plus tax?
After applying the sales tax, the expression for the total price of the phone is 1.03p.
What is sales tax?
The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a standard sales tax is imposed, collected by the shop, and paid to the government.
The amount for phone is represented as - p dollars and cents
The sales tax percentage is - 3% = 0.03
The sales tax applied on the phone is - 0.03p
The total price of the phone is denoted by the expression -
Total Price = Price of phone + Sales Tax
Total Price = p + 0.03p
Total Price = 1.03p
Therefore, the total price is obtained as 1.03p.
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PLEASE HURRY TEST QUESTION LIMITED TIME!!
Question-The signals of a radio station can be received up to 80 miles away. Your house is 50 miles east and 20 miles south of the station. Can you receive the radio signals? Show all work using the equation editor to justify your answer.
Yes I can receive the radio signals.
A function f(x) increases by a factor of 10 over every unit interval in x and f(0)=1.
Which could be a function rule for f(x)?
Answer: A function that increases by a factor of 10 over every unit interval in x and starts at f(0)=1 could be represented by the function rule f(x) = 10^x.
This function starts at f(0) = 10^0 = 1 and for every increase of 1 in the input x, the output f(x) increases by a factor of 10. For example:
f(1) = 10^1 = 10
f(2) = 10^2 = 100
f(3) = 10^3 = 1000
and so on.
Another possible function rule could be f(x) = 10x +1 it starts at f(0) = 1 and for every increase of 1 in the input x, the output f(x) increases by a factor of 10. for example:
f(1) = 101 +1 = 11
f(2) = 102 +1 = 21
f(3) = 103 +1 = 31
and so on.
Both functions have similar behavior and answer the given conditions.
Step-by-step explanation:
a box contains one red ball, one purple ball, and one blue ball. two balls are drawn from the box one after the other without replacing the first ball. how many outcomes are possible for this experiment?
There are 6 possible outcomes for this experiment.
The total number of outcomes possible for an experiment of drawing two balls one after the other without replacing the first ball, depends on the number of possible outcomes for the first draw, multiplied by the number of possible outcomes for the second draw, given that the first ball was not replaced.
The total number of ways to choose one ball out of three is 3, and the number of ways to choose the second ball out of two remaining balls is 2. Therefore, the total number of outcomes possible for this experiment is 3 x 2 = 6.
The possible outcomes are:
(Red, Purple), (Red, Blue), (Purple, Red), (Purple, Blue), (Blue, Red) and (Blue, Purple)
It's important to notice that this method is called the Multiplication Rule for counting the total number of outcomes of two or more independent events.
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Joseph has a bag filled with 3 red, 3 green, 9 yellow, and 10 purple marbles. Determine P(not yellow) when choosing one marble from the bag.
8%
24%
36%
64%
Answer:
c, 64 percent
Step-by-step explanation:
3+3+10+9=25
25-9(yellow)=16
25/16=64
Answer: D: 64%
Step-by-step explanation: 3 + 3 + 9 + 10 = 25, 3 + 3 + 10 = 16 (Alternative: 25 - 9) 16 / 25 = 64. So the answer is 64%
Lee made a scale drawing of a city. The scale of the drawing was 1 inch : 8 yards. The actual length of a neighborhood park is 96 yards. How long is the park in the drawing?
Answer:
12 inches
Step-by-step explanation:
Use a proportion.
1 inch is to 8 yards as x inches is to 96 yards
1/8 = x/96
Cross multiply.
8x = 96
x = 12
Answer: 12 inches
Does this equation have any possible values?
x+1/2=x-1/2
Answer: No solution
Step-by-step explanation:
x + 1/2 = x - 1/2
Subtract x from both sides:
1/2 = -1/2
This is not true, so there are no solutions to this equation
Answer:
Step-by-step explanation: multiply one and a half by x then thats ur answer
Four students draw a design for a class flag. Each flag is black and white
Shown below are four designs. Which designs have the same fractions o
black and white? Explain how you know.
Designs have the same fractions o black and white is 16/2
Which designs have the same fractions?
Given,
Four student, each with 2 distinct colors, and no two subsequent flag may share the same color. Hence, the first stripe may be colored in any of 4 different ways.
The second student can be colored in 4 different ways after it is not the same color as the first.
The third flag should not be the same color as the second; it can be colored in 4 different ways.
The fourth flag should not be the same color as the third, allowing for a total of 4 different color combinations. total = 4 * 2 * 2 = 16
designs have the same fractions o black and white is 16/2
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5. Quarterly payments of 300 for 9 years that will start 1 year from now,
What is the period of deferral in the deferred annuity?
help me
Period of deferral in the deferred annuity = 3 periods or 3 quarters.
Given: Quarterly payment of 300 for 9 years that will start 1 year from now.
To find the Period of deferral in the deferred annuity.
A deferment period is an agreed-upon time during which a borrower does not have to pay the lender interest or principal on a loan.
Solution: Formula for Period of deferral
K = nt - 1
K- Period of deferral
n- number of times compounded
t- time of start
K= nt - 1
K= 4(1) - 1
K= 3
Period of deferral = 3 periods / 3 quarters.
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PLEASE HELP!!! I need to know the hypotenuse to this triangle.
The bottom side adjacent to the right triangle is 14.4 by the way. You should solve this using trig.
Answer:
hypotenuse = 14.8
Step-by-step explanation:
Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
[tex]3.2^2 + 14.4^2 = c^2\\10.24 + 207.36 = c^2\\\sqrt{217.6} = c\\c = 14.751...\\c = 14.8[/tex]
a classroom has two rows with nine seats in each row. there are 15 students named s1, . . . , s15, where s1, . . . , s4 always sit in the front row and s5, . . . , s10 always sit in the back row. (the students s11, . . . s15 may sit in either row). in how many ways can the students be seated?
Answer: The front row has 4 fixed seats (s1, s2, s3, s4) and 5 open seats. The back row has 6 fixed seats (s5, s6, s7, s8, s9, s10) and 3 open seats. The remaining students (s11, s12, s13, s14, s15) can be placed in the open seats in the front row or the open seats in the back row in any combination.
The open seats in the front row can be filled by the remaining 5 students in 5! ways.
The open seats in the back row can be filled by the remaining 5 students in 5! ways.
So the total number of ways the students can be seated is (5!)^2 = 54321 * 54321 = 14400
Step-by-step explanation:
4. If 2 is subtracted from three times a number, the result is equal to 5 less than three times
the number. Find the number.
The resulting equation: 3x - 2 = 3x - 5
This equation does not have any true answer, meaning either the question asked is wrong or you have typed this equation wrong.
The only answer you could write for this is No Solution.
Alyssa draws the following model to solve a problem.
Which problem is Alyssa trying to solve?
A. 3 5/8−1 7/8
B. 3 7/8−1 3/4
C. 4 5/8−1 7/8
D. 4 1/2−1 7/8
According the diagram, Alyssa trying to solve the problem 4 5/8 - 1 7/8. So the option C is correct.
Alyssa draws the following model to solve a problem.
We can see on the diagram that there have lock of two colors red and black. Some block are cut in both colors.
The total block of red color = 3
The total block of black color = 13/8
So the total block = 3 + 13/8
The total block = (24 + 13)/8
The total block = 37/8
The total block = 4 5/8
The block cut in color red = 1
The block cut in color black = 7/8
Total cut block = 1 + 7/8
Total cut block = (8 + 7)/8
Total cut block = 15/8
Total cut block = 1 7/8
So the problem should be
= The total block - Total cut block
= 4 5/8 - 1 7/8
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The complete question is given below:
Please help I’m very confused?
By means of angle properties and algebra properties, the measure of the missing angle equals 136°.
How to determine the measure of a missing angle
In this problem we find the representation of two consecutive angles, whose sum of measures equals 180°. The measure of an angle is equal to 44° and the measure of the other one must be determined by using the following algebraic expression:
m ∠ x + 44° = 180°
Now we proceed to solve the expression by algebra properties:
m ∠ x = 180° - 44°
m ∠ x = 136°
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The cost of a fishing pole has risen to $48 this week. Last week's cost was $43 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
11.6%
Step-by-step explanation:
First, we have to find how much it increases
48 - 43 = $5
We know it increases by $5
Then we take
5 divided by 43, then times 100 = 11.6%
So, it increases 11.6%
PLEASE HELP ASAP!!!!!!!!!
Answer:2x
Step-by-step explanation:
Answer: the correct answer would be 2x
Step-by-step explanation:
Which of the following is a right triangle?
55°
70°
55
Triangle A
OA. Triangle D
OB. Triangle A
O C. Triangle C
OD. Triangle B
24°
45°
SAA
90°
45
Triangle C
30°
126
Triangle B
60°
60
60°
Triangle D
Step-by-step explanation:
A right triangle is a triangle that has one angle that measures 90 degrees. Based on the information provided, the following triangles are right triangles:
Triangle A - OA. 55° and 70° are not right angles
Triangle B - OB. 30° and 60° are not right angles
Triangle C - O C. 45° and 45° form a right angle
Triangle D - OD. 60° and 60° form a right angle.
SAA is a mnemonic for solving the triangle, not a triangle itself
24°, 45°, and 126° are not angles that form a triangle as the sum of all angles in a triangle is 180.
Two teammates competed in a long jump competition. Their distances on 4 jumps are
listed in the table. Which statement about the recorded data is true?
Heath had the longest jump of 6 meters in the competition.
What is Comparison Theory?Comparison theory is a psychological theory that proposes that people use social comparisons to better understand their own value and place in society. According to this hypothesis, people compare themselves to others in order to assess themselves, typically focusing on the traits that they have and the qualities that other people have. Individuals utilise the comparison to estimate their own value and how they should conduct in order to achieve approval and acceptance from their peers.
This question requires the use of the Comparison Theory.
This theory states that when presented with two or more items, we can compare them to determine which is larger, smaller, longer, shorter, etc.
In this case, we need to compare the distances of each jump for each teammate in order to determine which one had the longest jump.
Step 1: Look at the distances of each jump for Heath.
Step 2: Look at the distances of each jump for Amari.
Step 3: Compare the distances of each jump for both Heath and Amari.
Step 4: Determine which jump was the longest - Heath's 6 meter jump.
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you may not cross a single broken white or yellow line: When doing so would interfere with traffic.
When turning left into a driveway.
When the car in front of you is disabled.
When passing to the right on a one-way street.
You may not cross a single broken white or yellow line, when doing so would interfere with traffic unless it is safe to do so and without interfering with traffic.
The yellow line on the road serves as a barrier between opposing lanes of traffic as a traffic safety measure. It is intended to alert drivers to the fact that they are moving in the opposite directions and should keep a safe distance while driving.
The yellow line is typically placed in the centre of the road to indicate the separation of traffic. On highways and interstates, the yellow line is frequently used to mark the separation between two lanes of traffic moving in the same direction.
Drivers should always follow the yellow line and never cross it because doing so can be risky and result in accidents. The yellow line can also be used to show when passing other vehicles is dangerous.
On the driver's side, it is prohibited to pass other cars when a yellow line is interrupted by a solid line. Overall, the yellow line is an important safety measure for drivers to be aware of and obey when on the road.
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write a formula that expresses the distance between p and 17
Step-by-step explanation:
The f O U r M U la is 72inc hes
You sell triangular flags made from felt. How much felt do you need to make 60 60 flags?
The cost of making 60 triangular flags with base 3.5feet and height 2.5 feet with making charges of $0.40per square foot is equal to $105.
Flag is triangular in shape.
Base of the flag = 3.5 feet
Height of the flag = 2.5feet
Area of the flag = ( 1/2) base × height
= ( 1/2 )× ( 3.5 ) × ( 2.5)
= 4.375 square feet.
Cost of one square foot flag = $0.40
Cost of making one flag = $ ( 0.40 × 4.375 )
= $ 1.75
Cost of making 60 flags = $ ( 1.75 × 60 )
= $ 105.
Therefore, the cost of making 60 triangular flag is equal to $105.
The given question is incomplete, I answer the question in general according to my knowledge:
You make and sell triangular flags. Each flag has a base of 3.5 feet and a height of 2.5 feet. Fabric for the flags costs $0.40 per square foot. What is the cost to make 60 flags?
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Select all equations that represent the situation.
a) 4 · 2 5= ?
b) ? · 2 5= 4
c) 2 5÷ 4 = ? d)
4 ÷ 2 5= ?
e) ? ÷ 2 5= 4
Answer: b) ? · 2 5= 4
d) 4 ÷ 2 5= ?
e) ? ÷ 2 5= 4
The equations that represent the situation are b) ? · 2 5= 4 , d) 4 ÷ 2 5= ?, e) ? ÷ 2 5= 4
The question is asking for an unknown quantity and it is asking to find it by using the 4 and 25, so the equations that represent the situation are the ones that have 4 and 25 in them and have the unknown quantity on one side of the equation and the known quantity 4 on the other side.
a) 4 · 2 5= ? is not a valid equation as it is asking to multiply 4 and 25, which is known and doesn't have any unknown quantity.
c) 2 5÷ 4 = ? is also not a valid equation as it is asking to divide 25 by 4 and doesn't have any unknown quantity.
Step-by-step explanation:
There are many possible cones with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.
a. Write an equation that represents the volume V as a function of the radius r.
b. Complete this table for the function, giving three possible examples
Volume of the cone with height 18 meters and radius 'r' is given by :
a. Equation to represents the volume of the cone is 6πr²( cubic meters).
b. Three possible examples:
r (meters ) : 2 4 6
V (cubic meters ) : 24π 96π 216π
Height 'h' of the cone is 18meters.
Radius of the cone is 'r' meters.
a. Equation to represents volume of a cone as function 'r'
Volume 'V' of the cone is = ( 1 / 3 )π ×r² × h
Substitute value h = 18 meters we get,
V = ( 1 / 3 )π ×r² × 18
⇒ V = 6πr² cubic meters
b. Three possible examples for different values of 'r'
When r = 2
V = 6π × ( 2)²
⇒ V = 24π cubic meters
When r = 4
V = 6π × ( 4)²
⇒ V = 96π cubic meters
When r = 6
V = 6π × ( 6)²
⇒ V = 216π cubic meters
Therefore, the required volume of the cone with radius 'r' and height 18meters is:
a. Equation to represents volume is 6πr².
b. Table completion:
r (meters ) : 2 4 6
V (cubic meters ) : 24π 96π 216π
The above question is incomplete , the complete question is:
There are many possible cones with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.
a. Write an equation that represents the volume V as a function of the radius r.
b. Complete this table for the function, giving three possible examples.
r : 2 _ _
V: ? ? ?
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What is the difference between 3x^2-4x-5 and 2x^2-7x-3?
Answer:
Shown Below
Step-by-step explanation:
The difference between the two polynomials 3x^2-4x-5 and 2x^2-7x-3 is the result of subtracting the second polynomial from the first one.
3x^2 - 4x - 5 (first polynomial)
(subtraction operator)
2x^2 - 7x - 3 (second polynomial)
= x^2 - 3x - 2 (difference)
So the difference between 3x^2-4x-5 and 2x^2-7x-3 is x^2 - 3x - 2
This is a polynomial with a degree of 2 (quadratic) and the coefficient of x^2 is 1, x is -3 and the constant is -2.
A model of Seattle, Washington space Needle is 20 inches tall The actual Space Needle is approximately 600 feet tall a: what does the 1 inch represent in the model? what is the scale? b: what is the scale factor model ?
Answer: 30
Step-by-step explanation: 600/20=30 so each inch on the scale represents 30 feet in real life.
A father Share Gtty 51, 110 among
children Atta, Abena anel Kojor Kojo has
1/2 time as much as Abena and Abeng
has 3 times
as much as Alta
Find the ratio of their shares.
Find the amount each received.
The ratio of their shares is 1:2:3 and amount is 180.5, 3564, 5371.5 respectively.
To find the amount each received:
Atta received 13.5*(51+110) = 1807.5
Abena received 27*(51+110) = 3564
Kojo received 40.5*(51+110) = 5371.5
The total amount shared is 51 + 110 = 161
The ratio of their shares is 1:2:3, meaning Atta receives 1/6 of the total amount, Abena receives 2/6 of the total amount, and Kojo receives 3/6 of the total amount.
To find the amount each received, we multiply their respective share (1/6, 2/6, and 3/6) by the total amount (161)
Kojo received 3 times as much as Atta, and Atta received 1/2 times as much as Abena.
Atta received 1/6 of the total amount, which is (51 + 110)/6 = 81/6 = 13.5
Abena received 2/6 of the total amount, which is (51 + 110)*2/6 = 162/6 = 27
Kojo received 3/6 of the total amount, which is (51 + 110)*3/6 = 243/6 = 40.5
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For what value of p and q the root of quadratic equation x^2 (2p-4)x-(3q5)=0 vanih
Answer:
A quadratic equation of the form ax^2 + bx + c = 0 has solutions (or roots) that are either real or complex. The solutions of the equation vanish (or become equal to zero) when the equation is equal to zero.
For the equation x^2 (2p-4)x-(3q5)=0 to have a solution that vanishes, the discriminant (b^2 - 4ac) must be equal to zero.
Therefore, the roots of the quadratic equation x^2 (2p-4)x-(3q5)=0 vanish when p = 4 and q = 0
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
The graph that represents the situation is given in the attached image.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A gymnast joined a yoga studio to improve his flexibility and balance.
He pays a monthly fee and a fee per class he attends.
The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
The graph of the linear equation is given in the attached image.
And the graph that is equivalent to the graph is also given in the attached image.
Therefore, the equivalent graph is given in the attached image.
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