Answer: t=2
Step-by-step explanation:
-4t+14= -9t+24
+9t =+9t
5t+14=24
-14=-14
5t=10
5t/5 10/5
t=2
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:
Un empleado de una cafetería tomó 3/8 de un saco de café, lo que corresponde a 1.6875kg ¿de cuantos kilogramos era el saco de café?
Using cross multiplication method, a total of 2.7 kilograms of coffee was in the bag.
What is cross multiplication?Cross multiplying is the process of multiplying the denominator of the second fraction on the other side of the equals to symbol by the numerator of the first fraction on one side of the equals to symbol.
Comparably, the numerator of the second fraction is multiplied by the denominator of the first fraction. Cross multiply is another name for the butterfly method of multiplication. The cross-multiply method is used to find one or more variables in a fraction. Cross multiplying can also be used to compare fractions.
The fraction of 3/8 of a bag of coffee = 1.6875kg
Let, The total mass of the bag of coffee be x, i.e.
3/8 = 1.6875/x
Using Cross-multiplication
3x = 1.6875 × 8
3x = 13.5
x = 13.5/5
x = 2.7kg
Thus, Using cross multiplication method, a Total of 2.7 kilograms of coffee was in the bag.
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English Full question
An employee of a cafeteria took 3/8 of a bag of coffee, which corresponds to 1.6875kg. How many kilograms was the bag of coffee?
You are going on vacation and need to rent a car. You must chose between Hertz and Enterprise.
At Hertz you will be charged a one-time insurance fee of $80, plus $60 per day.
At Enterprise you will be charged a one-time insurance fee of $100, plus $55 per day.
Answer:
what's the question? how many days? 4 day is the breakeven mark.
Step-by-step explanation:
80+60x = 100+55x
5x =20
x=4
for a 4-day rental, it'll be the same.
if longer than 4 days, go with enterprise. shorter than 4 days go with hertz.
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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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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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.
imagine you are painting a series of towers built from cubes. You are going to paint only the exposed faces of the cubes. If the tower you paint has 25 exposed faces, how many cubes are in the tower?
Answer:
101 Faces
Step-by-step explanation:
Hope it helps + get it right
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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PLEASE HELP Graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0.4. In other words, a change of 1 unit in x corresponds to a change of 0.4 units in y.
Graph the line and write the equation of the line.
A proportional relationship between y and x can be represented by a linear equation of the form:
y = kx
where k is the unit rate of change of y with respect to x. Given that the unit rate of change of y with respect to x is 0.4, we can substitute this value for k in the equation:
y = 0.4x
This equation represents the line that shows the proportional relationship between y and x.
To graph this equation, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We can rewrite our equation as:
y = 0.4x + b
Since the y-intercept is the point where the line crosses the y-axis, we can substitute any value of x with 0 and solve for b
y = 0.4x + b
y = 0.4*0 + b
y = b
So the y-intercept is b = 0
Therefore, the slope-intercept form of the equation is y = 0.4x + 0
To graph the line, we can take any two x values and substitute them into the equation, and then plot the corresponding y values on the graph. For example, when x = 0, y = 0.40 + 0 = 0 and when x = 1, y = 0.41 + 0 = 0.4.
We can use these points to plot the line on a graph, it will be a straight line passing through the point (0,0) with a slope of 0.4.
Note: This line is also known as the direct variation equation.
Answer:
Y=0.4X
Step-by-step explanation:
when x=1, Y =0.4
when x=2, Y=0.8
Now you have 2 points, draw a line. voila.
see attached
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
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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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 ASAP!!!!!!!!!
Answer:2x
Step-by-step explanation:
Answer: the correct answer would be 2x
Step-by-step explanation:
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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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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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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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.
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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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.
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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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
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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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]
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.
✓3
After how many minutes will the two pools have the same
amount of water?
minutes
Check
5
Two pools are being filled with water. To start, the first pool contains 654 liters of water and the second pool is empty. Water is being added to the first pool at a
rate of 18.5 liters per minute. Water is being added to the second pool at a rate of 45.75 liters per minute.
How much water will be in each pool when they have the
same amount?
liters
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a. The amount of minutes it will take for the two pools to have thesame amount of water is 24 minutes
b. The amount of water in each pool is 1098liters
What are Simultaneous equations?Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution. Some of the examples of simultaneous equations are: 2x - 4y = 4, 5x + 8y = 3.
Represent the number of minutes it will take the two pool to have thesame amount y be x
therefore ;
y = 654+ 18.5x equation 1
y = 0+ 45.75x equation 2
from equation 2, y = 45.75x
substitute 45.75x for y in equation 1
45.75x = 654+ 18.5x
collect like terms
654 = 45.75x - 18.5x
654 = 27.25x
x = 654/27.25
x= 24minutes
from equation 2,
y = 0 + 45.75 × 24
y = 1098 litres
therefore at 24minutes the first and second pool will have the same volume of water of 1098litres
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The water in each pool when they have the same amount will be 1098 liters.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given.
In this case, two pools are being filled with water. To start, the first pool contains 654 liters of water and the second pool is empty. Water is being added to the first pool at arate of 18.5 liters per minute.
Water is being added to the second pool at a rate of 45.75 liters per minute.
Let the minute be represented by m. The equation will be:
653 + 18.5m = 45.75m
Collect the like terms
45.75m - 18.5 m = 654
27.25m = 654
Divide
m = 654 / 27.25
m = 24 minutes
The water in each pool when they have the same amount will be:
= 45.75 × 24
= 1098 liters
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what is y=12x-35 domain and range
The domain and the range of y = 12x - 35 are the set of all real numbers
How to determine the domain and the range?from the question, we have the following parameters that can be used in our computation:
y = 12x - 25
There is no restriction on the input values, x
So, the domain of y = 12x - 35 is all real numbers, since there is no restriction on the input (x).
The range of y = 12x - 35 is also all real numbers, since the output (y) can be any real value, depending on the input (x).
This can be seen by considering that for any real number x, the output y = 12x - 35 will also be a real number.
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Create a diagram based on the given symbolic statement. Be sure enough information is provided in the diagram to validate each statement. △FUN≅△CAR
The triangle △FUN is congruent to the triangles △CAR. And the diagram is given below.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangles △FUN and △CAR, then we have
∠FUN = ∠CAR = 90°
∠UFN = ∠ACR
FN = CR
Then the triangles △FUN and △CAR are congruent triangles. And the diagram is given below.
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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
how to solve 66 divided by 7 using standard algorithm
Answer: The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers. To solve 66 divided by 7 using the standard algorithm, you can follow these steps:
Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:
66 | 7
--- |
Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.
66 | 7
--- | 0
Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).
66 | 7
--- | 0
0 |
Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.
66 | 7
--- | 0
0 | 6
Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).
66 | 7
--- | 0
0 | 6
| 66
Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.
66 | 7
--- | 09
0 | 6
| 66
Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).
66 | 7
--- | 09
0 | 6
--- | 63
Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
So, 66 divided by 7 = 9 with a remainder of 3
So the answer is 9 R 3
Step-by-step explanation:
The solution is: 66 divided by 7 is 9 with a remainder of 3.
The standard algorithm for division is also known as long division, it is a method for solving division problems that involve larger numbers.
To solve 66 divided by 7 using the standard algorithm, you can follow these steps:
Step 1: Write the dividend (66) and the divisor (7) in a division problem format, like this:
66 | 7
--- |
Step 2: Divide the first digit of the dividend (6) by the divisor (7). Since 6 is less than 7, write a 0 as the first digit of the quotient.
66 | 7
--- | 0
Step 3: Multiply the divisor (7) by the first digit of the quotient (0) and write the product (0) under the first digit of the dividend (6).
66 | 7
--- | 0
0 |
Step 4: Subtract the product (0) from the first digit of the dividend (6) and write the result (6) under the subtraction.
66 | 7
--- | 0
0 | 6
Step 5: Bring down the next digit of the dividend (6) and append it to the result of the subtraction to form a new 2-digit number (66).
66 | 7
--- | 0
0 | 6
| 66
Step 6: Divide the new 2-digit number (66) by the divisor (7) and write the quotient (9) above the line.
66 | 7
--- | 09
0 | 6
| 66
Step 7: Multiply the divisor (7) by the quotient (9) and write the product (63) under the new 2-digit number (66).
66 | 7
--- | 09
0 | 6
--- | 63
Step 8: Subtract the product (63) from the new 2-digit number (66) and write the result (3) under the subtraction.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
Step 9: Write the final result (9) as the quotient and the remainder (3) of the division problem.
66 | 7
--- | 09
0 | 6
--- | 63
| 3
So, 66 divided by 7 = 9 with a remainder of 3
So the answer is 9 R 3.
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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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