The property of equality justifies the given statement is Transitive property of equality.
Given,
The statement:
If, 7x = 28,
then, x = 4
We have to find the property of equality that justifies this statement:
The transitive property of equality formula is given as follows:
If y = z and x = y, x must be z. Where items belong to the same category as x, y, and z. For instance, if a line segment's measurement is represented by "x," then its measurement should also be represented by "y" and "z."
The property of equality that justifies this statement If, 7x = 28,
then, x = 4 is transitive property of equality.
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What is the length of x
Answer:
TN/TS=NM/RS
[tex] \frac{240}{120} = \frac{x}{70 } \\ 120x = 16800 \\ x = 140[/tex]
3. Determine the value of y so that the line
passing through (7, y) and (-1,-3) has a slope of 3/4.
Answer: y=3
Step-by-step explanation:
Slope formula: m=(y2-y1)/(x2-x1)
3/4=(y2-y)/(x2-x1)
3/4=(-3-y)/(-1-7)
3/4=(-3-y)/(-8)
(3/4=(-3-y)/(-8))*(-1) ==> Negate the equation to remove the negative denominator
-3/4=(-3-y)/8
8*(-3/4)=(-3-y)/8 * 8
8*(-3/4)=(-3-y)/8 * 8
-24/4=-3-y
-3-y=-6
-3+3-y=-6+3
-y=-3
y=3
The inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents the focus. Which of the following standard equations represents the parabola in which the base of the bulb is at (1, 5) and top of the bulb is at (1, 1)?
The equation of the parabola that models the situation is given by:
(x - 1)² = -16(y - 5).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
(x - h)² = 4p(y - k).
The focus is located at point (h, k + p).
For this problem, to find the values of the parameters h and k, we have that:
The base is the vertex.The base is at (1,5).Hence:
h = 1, k = 5.
And:
(x - 1)² = 4p(y - 5).
For the focus, and subsequently to find parameter p, we have that:
The top is the focus.The top is at (1,1).Hence:
k + p = 1.
5 + p = 1
p = -4.
Then the equation of the parabola that models this situation is given by:
(x - 1)² = 4p(y - 5).
(x - 1)² = 4(-4)(y - 5).
(x - 1)² = -16(y - 5).
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Find the surface area of the cylinder (I've been crying for 3 days because I can't get over this problem!)
Answer:
SA = 301.44 in²
Step-by-step explanation:
SA = 2πr² + 2πrh ← factor out 2πr from each term
= 2πr(r + h)
substitute r = 4 and h = 8
SA = 2π × 4 × (4 + 8) ← substitute π = 3.14
= 2 × 3.14 × 4 × 12
= 6.28 × 48
= 301.44 in²
1. Then a survey of 30 students and it was found that 17 of them have a cat, based on these results, guess how many students out of 300 students in the school have cats?
2. If one out of 12 students in a school shares their locker, how many students share their locker in a school with 456 students?
3. Sabrine runs 2 km in 30 minutes. At this rate, what would you run in 90 minutes? And at what rate did she run each hour?
Answer:
The answer is 47.5 because in my math exam i got 47.5 in 50
a vineyard has 145 acres of chardonnay grapes. a particular soil supplement requires 5.50 g for every square meter of vineyard. how many kilograms of the soil supplement are required for the entire vineyard? (recall that 1 km2
3230 Kilograms of the soil supplement are required for the entire Vineyard.
Some units that need to be recalled are as follows:
1 km = 1000 m
1 km^2 = 1000000 m^2
1 km^2 = 247 acres
1 kg = 1000 g
Let's tackle the problem now:
A vineyard has 145 acres of Chardonnay grapes.
145 acres = [tex]\frac{145}{247}[/tex]× 1 km^2
145 acres = 145/247 km^2
145 acres ~ 0.587 km^2
A particular soil supplement requires 5.50 grams for every square meter of vineyard
1m^2 → 5.50 gram
1 km^2 = 10^6 →5.50 x 10^6 gram
1 km^2 →5.50 x 10^6 x 10^-3 kg
1 km^2 →5.50 x 10^3 kg
145 acres = 145/247 km^2 →145/247 x 5.50 x 10^3 kg
145 acres → 797500/247 kg
145 acres → 3230 kg
It required 797500/247 kg ~ 3230 kg of the soil supplement for the entire Vineyard.
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2. If a car ragistration number have four symbols the first two of which are
letters and the remainder digits.how many different registration numbers
can be made?
Oa)58500
Ob)62250
Oc)63375
O d)65515
The correct option is a)58500.
The number of different registration number possible when the repetition is not allowed is 58500.
What is meant by the term combination?Selections are another name for combinations. Combinations are the selection of items from a given set of items.
We need not aim to arrange anything here. We intend to choose them. The number of distinct x-selections or combinations from a set of n objects is denoted by ⁿCₓ.Now, according to the given question;
The total number of digits mentioned on the number plate is 4.
The first place is to be filled by letter.
We know that there are total 26 letter. So, there are total 26 possible ways in which the place is filled.
Now, the second place is also to be filled by the letter, but now the letter left are 25. Thus, possible fillings is by 25 letter.
The third position is to be filled by number; there are 10 number (0 - 9) by which the position can be filled.
The fourth position is also to be filled by the number; but now the numbers left are 9.
Thus, the total combination is;
= 26×25×10×9
= 58500
Therefore, there are 58500 possible ways in which the number plate can be formed.
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Jacob signs up to work for 2 5/8 hours at the school carnival. If each work shift is 3/4 hour, how many shifts will Jacob work
3 full shifts of 3/4 hour and 1 half shift of 3/4 hour
Shift work is an employment strategy intended to utilize or give service during each of the seven days of the week's full 24 hours. The day is often divided into shifts, predetermined times when various groups of workers carry out their tasks.
Total work hours = 2.625 hours
Each shift = 0.75 hr
Number of shifts = Total work hours / Each shift
= 2.625 / 0.75
= 3.5
Therefore, He worked three full shifts of three hours each and one half-shift of three hours.
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Which is different? Find “both” answers
Find AC+CB .
Find BC-AC .
Find AB .
Find CA+BC .
The "different" answer is {Blank} The "same" answer is {Blank}.
The different answer is 4 and the same answer is 10.
What is 2-3-7-9-6-7-8-6-5-7-7
Answer:-61
Step-by-step explanation:
Answer:
2-3-7-9-6-7-8-6-5-7-7=-63
Step-by-step explanation:
Hope it helps!!!
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Given directed line segment cd, if point e divides cd three-fourths of the way from c to d, find the coordinates of e.
The coordinates of point E is (-2, -1.5)
How to determine the coordinates of point E?
see in the file attached below
The given parameters are
C = (1, 6)
D = (-3, -4)
The ratio 3/4 can be represented as:
m : n = 3 : 1
So, the coordinate of point E is
E = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have:
E = 1/(3 + 1) * (3 * -3 + 1 * 1, 3 * -4 + 1 * 6)
Evaluate
E = 1/(4) * (-8, -6)
This gives
E = (-2, -1.5)
Hence, the coordinates of point E is (-2, -1.5 )
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Use the following statement to answer questions 10-16.
If a number is greater than -500, then the number is greater than 500.
Determine the truth value of the conditional statement. Explain.
The truth value of the conditional statement is false
How to determine the truth value of the conditional statement?
The conditional statement is given as
“If a number is greater than -500, then the number is greater than 500.”
The above conditional statement is false
This is because not all numbers greater than -500 are greater than 500
for example 450 is greater than -500, but less than 500 that is the number between -500 and 500 will not satisfy the above statement.
Hence, the truth value of the conditional statement is false
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the possibility that experimental results are due to chance, or some factor other than the experimental variable, is measured by the blank
The possibility that experimental results are due to chance, or some factor other than the experimental variable, is measured by the Probability Value.
What is Probability value?Probability value, also called P-value, is defined as:
Under the premise that the null hypothesis is true, the p-value is the likelihood that test findings will be at least as extreme as the result actually observed.
Now,
According to the definition of probability value, the probability that experimental results are due to chance or some factor, can only be measured by probability value as it fits the context most appropriately.To learn more about probability value, refer to the link: https://brainly.com/question/25638875
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You deposit $300 into a savings account that earns interest annually. the function g(x) = 300(1.04)x can be used to find the amount of money in the savings account, g(x), after x years. what is the range of the function in the context of the problem? â„ [0, [infinity]) [300, [infinity]) [0, 300]
The constant percent rate of change is of 4%
Using compound interest, it is found that the constant percent rate of change is of 4%.
The formula for an amount of money invested into compound interest is given by:
[tex]A(t) = A(0)(1+r)^{t}[/tex]
In which:
A(t) is the amount after t years.
A(0) is the initial amount.
r is the constant percent rate of change.
t is the time.
The function is:
[tex]g(x)=300(1.04)^{x}[/tex]
Thus, for the constant percent rate of change:
1+r = 1.04;
r = 0.04;
0.04 × 100% = 4%
The constant percent rate of change is of 4%.
An annual percentage rate is expressed as an hobby charge. It calculates what percentage of the major you will pay every year by using taking things inclusive of month-to-month bills under consideration. APR is also the annual rate of interest paid on investments without accounting for the compounding of interest within that year.
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Answer:
(C) [300, ∞)
Step-by-step explanation:
Got it right on my quiz.
slope intercept form of -5/6x+4
The slope of equation y = -5/6 x + 4 is -5/6 and the slope-intercept form of -5/6x+4 is y = -5/6 x + 4
The slope of a function y = f(x) is given by a formula
slope = y2-y1 / x2- x1
where ( x1 , y1) and (x2, y2) are coordinates of any two points on the line of graph representing y = f(x)
Or we can simply use the slope-intercept form
y = mx+ c
where m is the slope of the given equation and c is the constant
so, in the given equation y = -5/6 x + 4
slope of the equation is -5/6
Hence, The slope of equation y = -5/6 x + 4 simply is -5/6 and the slope intercept form of -5/6x+4 is y = -5/6 x + 4
When you know the slope of the line to be investigated and the point given is also the y intercept, you can utilize the slope intercept formula y = mx + b. (0, b). The y value of the y intercept point is represented by b in the formula.
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Find the values of a and b that complete the mapping diagram.
Value of a and b that completes the mapping diagram will be a=0 and b=1
• Mapping diagram simply means a function that has a special type of relation where the elements of the domain are paired with that of the range.
• Mapping diagram consists of two parallel columns, the first column depicts the domain of the function whereas the second column depicts the range.
• Lines are drawn from first column to second column i.e. from domain to range, to represent the relation between 2 elements.
• Mapping is quite similar to making a flowchart, showing input and output values.
• Point to be noted that every mapping is a relation but every relation is not a mapping.
Value of a and b that completes the mapping diagram will be a=0 and b=1
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Answer: A = 0, and B = 1.
Step-by-step explanation: I put 0, and 1, and it was the perfect answer.
find the sum and express it in it's lowest terms 3/11 + 2/3=
Answer:
[tex]\frac{31}{33}[/tex]
Step-by-step explanation:
You need a common denominator to add. The smallest number that is divisible by both 11 and 3 is 33. Rewrite both fractions with a denominator of 33
[tex]\frac{3}{11}[/tex] x [tex]\frac{3}{3}[/tex] [tex]\frac{3}{3}[/tex] is just another name for 1. We are making an equivalent fraction. Multiple 3 x3 for the top and 11 x 3 for the bottom to get:
[tex]\frac{9}{33}[/tex]
Do the same for [tex]\frac{2}{3}[/tex]
[tex]\frac{2}{3}[/tex] x [tex]\frac{11}{11}[/tex] [tex]\frac{11}{11}[/tex] is just another name for 1. We are making an equivalent fraction. Multiple 2 x 11 for the top and 3 x 11 for the bottom to get:
[tex]\frac{22}{33}[/tex]
Now add these two fractions together:
[tex]\frac{9}{33}[/tex] + [tex]\frac{22}{33}[/tex] = [tex]\frac{31}{33}[/tex]
Math with a key 6 page 15 task 8 pl. For tomorrow
The value of the expressions will be:
1. -13.
2. 4
3. -9
4. 27
5. 0
How to calculate the value?It should be noted that this is an expression. In this case:
minus × minus = plus
plus × minus = minus
1. (-15) - (-2)
= -15 + 2
= -13
2. (-3( - (-7)
= -3 + 7
= 4
3. 4 - 13
= -9
4. 5 - (-22)
= 5 + 22
= 27
5. (-15) - (-15)
= -15 + 15.
= 0
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Ed needed to extend the string on his kite. The current string was seven and three fourths feet. He cut a piece of string that measured 8.5 feet and added it to the existing string. What is the new length of the string?
The new length of the string that Ed have now is 16.25 feet.
What is a fraction ?Fraction is some part of a total quantity.
Ed has a kite and a string of length[tex]7\frac{3}{4}[/tex] feet which is = [tex]\frac{31}{4}[/tex] feet.
He wants to extend the sting length so he added another 8.5 feet which is
= [tex]\frac{17}{2}[/tex] feet.
∴ The total length of the string will become
(31/4) + (17/2) feet.
= (31 + 34)/4 feet.
= 65/4 feet.
= 16.25 feet.
So, after he extended his string it has a length of 16.25 feet.
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Answer:
To find the new length of the string, we need to add the length of the new piece of string to the existing length.
The current string length is 7 and 3/4 feet. This can be written as a mixed number, 7 + 3/4 = 7 3/4.
The new piece of string measures 8.5 feet.
To add these two lengths, we can convert the mixed number to an improper fraction and then add the fractions together.
7 3/4 can be converted to an improper fraction as (7 * 4 + 3) / 4 = 31/4.
Now we can add the fractions:
31/4 + 8.5 = (31/4) + (8.5 * 4/4) = 31/4 + 34/4 = 65/4
To simplify the fraction, we can divide the numerator (65) by the denominator (4) to get the whole number part and the remainder.
65 ÷ 4 = 16 remainder 1
So the new length of the string is 16 1/4 feet.
Therefore, the new length of the string is 16 and 1/4 feet.
Step-by-step explanation:
A perimeter of 400.8 meters the length is 182.5 meters .
Answer: 17.9 meters
Step-by-step explanation:
400.8 meters perimeter,
182.5 meters length,
So, Width= (400.8/2)-182.5
Width= 17.9 meters
3. A focus group was formed to provide opinions for a target market. What type of data is being collected from the focus group?
Qualitative data is being collected from the focus group.
Given that, a focus group was formed to provide opinions for a target market.
What is a focus group?A group of people assembled to participate in a discussion about a product before it is launched, or to provide feedback on a political campaign, television series, etc.
Focus group used to gather qualitative data and in-depth insights, they enable researchers to collect information on anything from products and services to beliefs and perceptions in order to reveal true customer attitudes and opinions.
Therefore, qualitative data is being collected from the focus group.
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Construct a relative frequency histogram for tuition and fees for students at public four-year colleges. write a few sentences describing the distribution of tuition and fees, commenting on center, spread, and shape.
lindsay bedford works at the baseball cap shop. she is paid $6.50 per hour plus $0.45 for each cap she embroiders. how many caps must she embroider to earn at least $85 in an 8-hour day? group of answer choices
Answer:
Step-by-step explanation:
74 caps
The cost of 5 gallons of gasoline is $20. Write an equation to show the relationship between the cost, c, and the gallons of gasoline, g. Enter your equation AND your work or explanation in the box provided.
An equation to show the relationship between the cost, c, and the gallons of gasoline, g is; c = 4g
How to interpret a Linear Equation?
The general form of a linear equation in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are told that the cost of 5 gallons of gasoline is $20. Thus, the cost of one gallon of gasoline = 20/5 = $4 per gallons
Therefore if he cost is c, and the gallons of gasoline is denoted by g, then the formula to find the cost with these letters is;
c = 4g
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Hi, please answer
is 1/24 and 7/19 equivalent????
please thank yoooouuuu
Answer:No this is not equivalent.
Answer:
No
Step-by-step explanation:
Both fractions have been simplified as much as possible and aren't the same. They are not equivalent for this reason.
I wasn't entirely sure how to explain this but I hope this helps!
HURRY PLEASSEEEEE I'M IN CLASS!
What is the distance between -11 and 3? Write an expression then solve.
15 POINTSS
Answer:
Step-by-step explanation:
because the y points are the same, you'd only have to worry about the x points on the coordinate plane. assuming each unit equals 1 count the distance between points a and b or 11 to 4, which would be 7.
The endpoints of CD are C(3,
5) and D(7, 9).
The coordinates of the
midpoint M of CD are
Answer: M(5,7)
Step-by-step explanation:
[tex]\displaystyle\\C(3,5)\ \ \ \ \ D(7,9)\ \ \ \ \ M(x_M,y_M)=?\\\\M(x_M,y_M)=(\frac{3+7}{2},\frac{9+5}{2})\\\\ M(x_M,y_M)=(\frac{10}{2},\frac{14}{2} )\\\\ M(x_M,y_M)=(5,7)[/tex]
61= -9c +7
its asking to solve c please help :)
Answer:
c = -6
Step-by-step explanation:
add 9c to both sides to get 61 + 9c = 7
subtract 61 from both sides to get 9c = -54
divide by 9 to get c = -6
There are 4,500 pounds of fruit in John's store. 1,200 pounds
of the fruit is apples and half as much is mangoes. The weight
of pears is three times the weight of mangoes. If the rest of the
fruits are grapefruits, what is the total weight of grapefruits?
pounds
Help meee pls hhhh help answering now
Answer:
3/8
Step-by-step explanation:
hope this works for you :)
Answer:
the answer is 3/8
Step-by-step explanation:
5/8 + 3/8 = 1