The distributive property to write an equivalent expression.
8(4n+ 3) = 32n + 24
12x-6= 1/2
5x+20= 4
3(x+6)= 3x + 18
7x-35= 5
20p + 16 = 4/5
A distributive property in mathematics is defined:The distributive property states that multiplying the sum of two or more addends by a number yields the same result as multiplying each addend separately by the number and combining the resulting products.
We use distributive property for what purposes?One of the most common properties in arithmetic is the distributive property. The multiplier is applied to each integer inside the parentheses, and the results are added to obtain the answer. This technique is used to simplify and solve multiplication problems.
According to the given data:the distributive property to write an equivalent .
8(4n+ 3)
= 8 * 4n + 3* 8
= 32n + 24
for 12x-6
12x-6 = 0
x = 6/12
x = 1/2
For 5x+20
5x+20 =
x = -4
For 3(x+6)
= 3 * x + 3 * 6
= 3x + 18
For 7x-35
= 35/7
= 5
For 20p + 16
= 20/16
= 5/4
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The vertices of a figure are F(1, 2), G(3,5),and H(3, 2). Rotate the figure 180° about the origin. Find the coordinates of the image.
The coordinates of the vertices after the image is rotated about origin will be -
F(1, 2) → F'(-1, -2)
G(3, 5) → G'(-3, -5)
H(3, 2) → H'(-3, -2)
What is rotation of figure?
A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.
Given are the vertices of a figure as → F(1, 2), G(3,5) and H(3, 2).
Since, it is not given in which direction the figure is rotated, we will consider it to be rotated in anti - clockwise direction about the origin. When we rotate a coordinate point by 180 degrees in counterclockwise direction about the origin, then the point A(x ,y) becomes A'(-x ,-y).
The new coordinates will be -
F(1, 2) → F'(-1, -2)
G(3, 5) → G'(-3, -5)
H(3, 2) → H'(-3, -2)
Therefore, the coordinates of the vertices after the image is rotated about origin will be -
F(1, 2) → F'(-1, -2)
G(3, 5) → G'(-3, -5)
H(3, 2) → H'(-3, -2)
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The length of a rectangle is 2 cm longer than its width.
If the perimeter of the rectangle is 44 cm, find its area.
Answer:
perimeter = 2(b x L)
p° 2(2+20)
= 22X2 =44cm
area = B x W
a = 20x 2 =40 cm²
A number is multiplied by 6, and that product is added to 3. The sun is equal to the product of 3 and 11
Answer:
x = 5
Step-by-step explanation:
3 + x * 6 = 3 * 11
3 + 6x = 33
6x = 30
x = 5
x=0,0.5,1,3,3.5,4,5y= 63,72,75,81,84,90,93calculate the correlation coefficient, r.round answer to the 3 decimal places
In order to find the correlation coefficient r, we can use the formula:
[tex]r=\frac{7\sum ^{}_{}(xy)-\sum ^{}_{}x\sum ^{}_{}y}{\sqrt[]{\lbrack7\sum ^{}_{}x^2-(\sum ^{}_{}x)^2\rbrack\cdot\lbrack7\sum ^{}_{}y^2-(\sum ^{}_{}y)^2\rbrack}}[/tex]where the sum must be taken upon all 7 values of x and y.
So, let's find each term and then use them in the formula:
[tex]\begin{gathered} 7\sum ^{}_{}(xy)=7(0\cdot63+0.5\cdot72+1\cdot75+3\cdot81+3.5\cdot84+4\cdot90+5\cdot93) \\ =7\cdot1473=10311 \end{gathered}[/tex][tex]\begin{gathered} \sum ^{}_{}x\sum ^{}_{}y=(0+0.5+1+3+3.5+4+5)\cdot(63+72+75+81+84+90+93) \\ =17\cdot558=9486 \end{gathered}[/tex][tex]\begin{gathered} 7\sum ^{}_{}x^2-(\sum ^{}_{}x)^2 \\ 7\cdot(0^{2^{}}+0.5^2+1^2+3^2+3.5^2+4^2+5^2)-(0+0.5+1+3+3.5+4+5)^2 \\ 7\cdot63.5-17^2 \\ 444.5-289 \\ 155.5 \end{gathered}[/tex][tex]\begin{gathered} 7\sum ^{}_{}y^2-(\sum ^{}_{}y)^2 \\ 7\cdot(63^2+72^2+75^2+81^2+84^2+90^2+93^2)-(63+72+75+81+84+90+93)^2 \\ 7\cdot45144-558^2 \\ 316008-311364 \\ 4644 \end{gathered}[/tex]Now, we need to use them in the formula to find r:
[tex]r=\frac{10311-9486}{\sqrt[]{155.5\cdot4644}}=\frac{825}{\sqrt[]{722142}}\cong0.9708[/tex]Finally, round the answer to the 3 decimal places, we find
r = 0.971
ASAP FREE PONTS! HELP! The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Use the constraints of the real-world situation to predict the height of the water balloon at 15 seconds. Use complete sentences to support your answer.
The height of the water balloon at 15 seconds based on the potential rupturing effect of the balloon's initial gravitational potential energy on the membrane of the balloon upon impact with the ground and that addition forces are not added, is at the ground level or zero feet.
What is gravitational potential energy?Gravitational potential energy is the energy possessed by a body by virtue of its elevation above ground level.
The points on the path of the water balloon thrown from the building's roof are;
(0, 4), (2, 7), (7, 5), (6, 4), (9, 1), (9.5, 0)
The location of the water balloon, 9.5 seconds after it is thrown off the roof is therefore at the point, h(9.5) = 0 feet, which can be taken as the ground level or base of the building.
According to Newton's third law of motion, which is a physics or natural law, and which states that all bodies remain at rest or continue perpetually in a straight line unless acted upon by a force.
Given that no additional force is specified after the water balloon is thrown from the building, and that a water balloon can be treated as a large drop of water, where the elastic balloon membrane, represents the surface tension holding the large droplet together, we have that the energy of impact of collision of the balloon when it lands, which is obtained from the initial gravitational potential energy of the water balloon, can potentially rupture the membrane, such that the water is spilled and remains on the floor, well after 9.5 seconds, such that at 15 seconds, the height of the balloon remains at ground level.
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how many times larger is a square kilometer than a square dekameter
Answer: It is 10000 times larger
What’s the correct answer answer asap for brainlist
An international company has 29,200 employees in one country. If this represents 31.7% of the company's employees, how many employees does it have in total?Round your answer to the nearest whole number.
Answer:
The total number of employees the company have is;
[tex]92,114[/tex]Explanation:
Given that an international company has 29,200 employees in one country.
If this represents 31.7% of the company's employees.
let n represent the total number of employees the company have;
[tex]31.7\text{\% of n = 29,200}[/tex]Solving for n;
[tex]\begin{gathered} \frac{31.7}{100}n=29,200 \\ 0.317n=29,200 \\ n=\frac{29,200}{0.317} \\ n=92,113.564668 \\ n\approx92,114 \end{gathered}[/tex]Therefore, the total number of employees the company have is;
[tex]92,114[/tex]
A probability experiment consists of rolling a 6-sided die, numbered 1 to 6. Find the probability of the event below.
rolling a number less than 6
According to the solving the Probability of the event below is as:
= 0.8333
What is probability?Probability is the possibility that an event will occur given all the potential outcomes. A decision-maker considers the likelihood of a result to be important. Decisions will be made better as potential outcomes are better understood.
The purpose of probability:Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures as well as the risk of health impacts are related.
According to the given data:The probability of rolling a number less than 6.
There are six sides to the die with numbers on each side of (1, 2, 3, 4, 5, 6)
There is a total of six numbers and five ae below six in value.
So,
P(X < 6) = 5/6
= 0.8333
According to the solving the Probability of the event below is as:
= 0.8333
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I need help with this the question reads before the pandemic Corning planned to make 75 millions vials in 2021 due to the vaccine demand Corning will make d times as many vials write an expression to find how many vials Corning will make in 2021
The solution:
The question says Corning planned to make 75,000,000 vials in 2021.
But due to the demand for the vaccine, Corning decided to make d times as many vials.
We are asked to write an expression to find the number of vials Corning will make in 2021.
So, the required expression is:
[tex]75000000\times d=75000000d\text{ vials}[/tex]Therefore, the correct answer is 75000000d vials.
Sabastian Company has 10,000 shares of $100 par, 2% cumulative preferred stock and 50,000 shares of $50 par common stock. The following amounts were distributed as dividends: Year Amount Year 1 $10,000 Year 2 30,000 Year 3 45,000 Determine the dividends per share for preferred and common stock for each year. If required, round your answers to two decimal places. If your answer is zero, please enter "0".
The dividends per share for preferred and common stock for each year is year 1 $20,000, $10,000; year 2 $30,000, $0 year 3 $30,000, $15,000.
How to determine the Preferred and common stock?Year 1
Preference Shares = Number of shares × Par value ×%
Preference Shares = 10,000 ×100 × 2%
Preference Shares = $20,000
Common Shareholders:
Common Shareholders = $20,000 - $10,000
Common Shareholders = $10,000
Year 2
Preference Shares = $30,000
Common Shareholders = $0
Year 3
Preference Shares = $20,000 + ($20,000 - $10,000)
Preference Shares = $20,000 + $10,000
Preference Shares = $30,000
Common Shareholders:
Common Shareholders = $45,000 - $30,000
Common Shareholders = $15,000
Therefore year 1 has the amount of $20,000 as preferred stock and $10,000 as common stock.
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Evaluate the expression when y=4 and x=6 so what is x+8y
John's utility bills for the last five months are $23.84, $23.87, $20.48, $29.75, and $28.34. Find John's mean utility bill over this period.
Answer:
[tex]\text{ \$25.26}[/tex]Explanation:
Here, we want to get the mean utilit bill over the period
Mathematically, that means we have to find the average of his utility bills in that period
To get this,we have to divide the sum of all these values by the count of these values (5)
Mathematically, we have this as:
[tex]\frac{23.84\text{ + 23.87 +20.48 + 29.75 + 28.34}}{5}=\text{ }\frac{126.28}{5}\text{ = \$25.26}[/tex]PLEASE HELP!!!!!
Answer two questions about Equations AAA and BBB:
A. x/4 + 1 = -3
B. x + 4 = -12
1) How can we get Equation BBB from Equation AAA?
Choose 1 answer:
(Choice A)
Rewrite one side (or both) using the distributive property
(Choice B)
Rewrite one side (or both) by combining like terms
(Choice C)
Multiply/divide only one side by a non-zero constant
(Choice D)
Multiply/divide both sides by the same non-zero constant
Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
(Choice A)
Yes
(Choice B)
No
Answer:
1)D and 2)A
Step-by-step explanation:
1) D
When you dived B by 4 on both sides , you get A
2) A
:]
For the following word problems, create a system of equations and solve by using the substitution method.
We will solve as follows:
*We have the equations:
[tex]9.50A+27.00B=4000[/tex]&
[tex]A+B=200[/tex]We solve then for the second equation [Either for A or B], that is:
[tex]A=200-B[/tex]Now, we replace in the first equation and solve for B:
[tex]9.50(200-B)+27.00B=400\Rightarrow1900-9.50B+27.00B=4000[/tex][tex]=17.5B+1900=4000\Rightarrow17.5B=2100[/tex][tex]\Rightarrow B=120[/tex]Now, we replace the value of B in the second equation:
[tex]A=200-(120)\Rightarrow A=80[/tex]So, the investor has 80 shares on stock A and 120 shares on stock B.
When your grandmother got out of the hospital, she was so excited that she gave you some money. You decided to go to Canada where the exchange rate is 1.06 Canadian dollars to $1 US dollar as of November 2015. You have $10,000 to take with you. How many Canadian dollars do you have to spend? (Show all work using dimension analysis, round to nearest cent if necessary)
Answer:
10,600 Canadian dollars
Step-by-step explanation:
[tex] \frac{1.06}{1} = \frac{x}{10000} [/tex]
[tex]x = 10000(1.06) = 10600[/tex]
The production cost of x computers for a company over one year is $175x + $150,000. To minimize production costs in a given year to $465,000, how
many computers can the company make in that year?
Answer:
I'm pretty sure it's 1800!!
Complete the sentence
Percent means per _______.
Answer:
Percent means parts per hundred.
Step-by-step explanation:
Percent comes from the Latin phrase per centum which means per hundred. The % symbol is used to represent percent.
Example: 54/100 is equal to 54%.
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In the equation y = 3x + 2, the expression f(x) would replace which part of the equation.
In the equation y = 3x + 2, the expression f(x) would replace which part of the equation.
Answer: y will be replaced by the expression f(x).
(-7) -4 evaluate expression
Answer:
28
Step-by-step explanation:
To evaluate this expression, multiply the two numbers.
-7x-4=28
28 is not negative because a negative times a negative is positive.
Hope this helps! :D
What is the slope-intercept equation of the line below?y-intercept = (0, 3)5slope =4
Step-by-step explanation:
the slope-intercept form is
y = ax + b
a is the slope, b is the y- intercept (the y-value when x = 0).
so, the equation is
y = -5/4 x + 3
100 points and brainly for right answer A line includes the points (9,10) and (6,9). What is its equation in point-slope form?
Answer:
y = 1/3x + 7
Step-by-step explanation:
A line includes the points (9,10) and (6,9). What is its equation in point-slope form?
slope = change in rise/change in run
so:
slope = change in y/change in x
you are given two points in (x , y) format, points are: (9,10) and (6,9) [second in each pair are the y values]. Figure change in y and x:
y: 10 - 9 = 1
x: 9 - 6 = 3
so slope =y/x = 1/3
slope intercept form is: y = mx + b where m = slope. Substitute in value previously found for slope:
y = 1/3x + b
Now, you need to find y intercept, or b. Using one of the points given, we will use the first one (9,10), calculate for b:
y = 1/3x + b
10 = 1/3(9) + b
10 = 3 + b
subtract 3 from both sides:
10 - 3 = 3 + b - 3
b = 7
Put this into your equation: y = mx + b
y = 1/3x + 7
Establish the identity.
(sec 0+1)(sec 0-1)= tan 0
Multiply and write the left side expression as the difference of two squares.
- Tan²θ is the left side expression as the difference of two squares in trigonometric ratios.
What do trigonometric ratios represent?
As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. Trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.Review the sine, cosine, tangent, cotangent, secant, and cosecant trigonometric ratios.When calculating unknown distances from known or measured angles in geometric figures, trigonometric functions are used.(sec θ+1)(sec θ-1)= tan² θ
use ( a+ b ) ( a - b) = a² - b²
= 1² - sec²θ { we know that 1 + tan²θ = sec²θ}
= 1 - sec²θ
= - tan²θ
LHS = RHS
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-109-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10 Which of the following inequalities is represented by the number line?
The inequality is x > -3
The second choice is the correct answer.
Help DUE by 10:00 pm help
A regular polygon is shown.
15 sided regular polygon
Determine the measure of one of its angles.
156°
168°
2,340°
2,700°
The measure of the given polygon's angle is 2340°
Polygons are two-dimensional closed objects in geometrical mathematics where n number of line segments cross each other to generate n number of vertices. A triangle is a polygon with three sides, for instance.
In an n-sided polygon, there are n inner angles.
The total of all interior angle measurements in a polygon is always constant and is denoted by the notation "n" for the number of sides in the polygon.
the formula is ;
Sₙ = ( n - 2 ) 180°
Here in question n is given as 15
Thus Sₙ = ( n - 2 ) 180° becomes
Sₙ = ( 15 - 2) 180
13 × 180
= 2340 °
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What do you put in each box
The equivalent expression to 8(t+8) is 8t+64 and the equivalent expression to 8t+8 is 4(2t+2) and 4t+8+4t.
The given expressions are 8(t+8) and 8t+8.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Now, 8(t+8)
Using distributive property a(b+c)=ab+ac, simplify 8(t+8)
That is, 8t+64
Take common factor in 8t+8 is 4(2t+2) and 8t+8=4t+8+4t
Therefore, the equivalent expression to 8(t+8) is 8t+64 and the equivalent expression to 8t+8 is 4(2t+2) and 4t+8+4t.
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f(x) = 3x - 3, find f (-4)
Answer:here x=-4
Step-by-step explanation:
3(-4)-3=-15
A printing service charges a set-up fee of $14.50 for each order and 15 cents more for each copy. The total cost, C (in dollars), for an order of x copies is given by the following function.
C (x) = 0.15x + 14.50
What is the total cost for an order of 30 copies?
Answer: $19
Step-by-step explanation:
Since we want 30 copies, let x=30.
[tex]C(30)=0.15(30)+14.50=19[/tex]
Jen purchased the items shown in the table.
Item Cost ($)
shirt 11.99
shoes 35.50
belt 6.75
socks 3.00
In the city she lives in, the sales tax rate is 7.15%. In another city, the sales tax rate is 6.35%. How much more is she spending if she purchases the items in the city where she lives? Round to the nearest cent.
She spends the cost of $0.46 if she purchases the items in the city where she lives.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The given data below as:
Cost of the shirt = $11.99
Cost of the shoes = $35.50
Cost of the belt = $6.75
Cost of the socks = $3.00
Total cost of the items = 11.99 + 35.50 + 6.75 + 3.00
Total cost of the items = $57.24
In the city she lives in, the sales tax rate is 7.15%.
Total cost of the items with tax of 7.15%
= 57.24 × 7.15/100 + 57.24 = 4.092 + 57.24 = $61.33
In another city, the sales tax rate is 6.35%
Total cost of the items with tax of 6.35%
= 57.24 × 6.35/100 + 57.24 = 3.633+ 57.24 = $60.87
Hence, she spends the cost of $0.46 if she purchases the items in the city where she lives.
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3/4x = 24/3 × fraction ? x = ___ × 4/3× = fraction × 4/3x = ___ or 2 2/3
Given that 3/4x = 2
[tex]\begin{gathered} \frac{3}{4}x\text{ = 2} \\ \text{This can be written as} \\ \frac{3\cdot\text{ x}}{4}\text{ = 2} \\ \frac{3x}{4}\text{ = 2} \\ \text{Cross multiply} \\ 3x\text{ = 2 x }4 \\ 3x\text{ = }8 \\ x\text{ = }\frac{8}{3}\cdot\text{ }\frac{1}{1} \\ \text{x = }\frac{8}{3} \\ x\text{ = 2}\frac{2}{3} \end{gathered}[/tex][tex]undefined[/tex]