If a triangle has an area of 20in every dimension of the triangle is multiplied by a scale factor, and the new triangle has an area of 180in . the scale factor is 3.
Scale factorFirst step is to calculate the area
Area:
Area = New triangle /Old triangle
Area = 180 / 20
Area = 9
Second step is to calculate the ratio of areas
Ratio of areas :
Ratio of areas = 9
Ratio of areas = (3)²
Hence,
Scale factor : 3
Therefore the scale factor is 3.
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The sum of an integer and 2 times the next consecutive integer is -13. Find the value of the greater integer.
Answer:x+x+1=13
2x+1=13
2x=13−1
2x=12
x=
2
12
x=6
x+1=6+1=7
Step-by-step explanation:yes
A construction company is building a new office building with x floors that will have a roof that is 35 feet tall. Each floor of the building will be 10.5 feet high. Which equation can be used to find the total height of the office building, y, with x floors and the roof?
has to be like "y=mx+b"
Answer:
y = 10.5x + 35
Step-by-step explanation:
Since the roof is 35 feet tall, it will be the y-intercept (since it is constant). The number of floors can change, so it will be the x variable.
The final equation is y = 10.5x+35
help past due!
Multiply the polynomials (5a² + 2a − 7) and (3a² − a + 1). Simplify
the answer.
Answer:
C
Step-by-step explanation:
Use the distributive property to solve.
(5a²+2a-7)(3a²-a+1)
=15a⁴-5a³+5a²+6a³-2a²+2a-21a²+7a-7
=15a⁴+a³-18a²+9a-7
Ruby went on a walk that was 10/3 miles long. She stopped to have lunch when she walked 12/25 of her way. How far, in miles, did ruby walk before lunch? Give your answer as a fraction in its simplest form
Fraction - The distance she walked before lunch 214 / 75 miles
What is Fraction ?
A fraction, which also represents a portion of a whole, is a mathematical symbol for any number of equal parts. A fraction, such as one-half, eight-fifths, and three-quarters, indicates the number of components of a specific size when used in conversational English.
Given that,
The distance Ruby has to walk = 10/3miles
The distance left to complete before stopping = 12/25miles
The distance Ruby has to walk before lunch = 10/3 - 12/25
= 250 - 36 / 75
= 214 / 75miles
Hence, she walked 214 / 75 miles before lunch
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x =7, -2, 0, 7
y= 10,0,10,3
Is this a function?
Answer:
Yes
Step-by-step explanation:
Each x-value corresponds with only one y-value.
Tyrell bought n number of shares for s dollars and paid a 3% commission. He sold
the stock for d dollars and paid a flat fee of $15. Which expression below models
Tyrell’s net proceeds algebraically?
The expression that models Tyrell's net proceeds algebraically is d-(1.03ns + 15) .
In the question ,
it is given that ,
Tyrell bought n shares for s dollars
So the price Tyrell paid for shares = $ ns .
Tyrell also paid 3% commission ,
so the total cost price Tyrell paid for shares = price of share + commission
total cost price = ns + 3% of ns
= ns + 0.03ns ....as 3% = 0.03
= 1.03ns ...(i)
Tyrell sold the stocks for d dollars .
Tyrell also paid the flat fee of $15 .
So, the selling price for stocks = d-15 ......(ii)
The Tyrell's Net Proceeds can be calculated using the formula
Net Proceeds = Selling Price - Cost price
Substituting the values of selling price and cost price from (i) and (ii) ,
we get ,
Net Proceeds = (d-15)-(1.03ns)
= d-15-1.03ns
= d-(1.03ns + 15)
Therefore , the expression that models Tyrell's net proceeds algebraically is d-(1.03ns + 15) .
The given question is incomplete , the complete question is
Tyrell bought n number of shares for s dollars and paid a 3% commission. He sold the stock for d dollars and paid a flat fee of $15. Write an expression to model Tyrell’s net proceeds algebraically.
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Which choice is the value of three over five raised to the second power?
three over twenty-five
three over ten
nine over twenty-five
six over seven
The value of three over five raised to the second power is nine over twenty-five.
How can the operation be performed?From the question , we were given that three over five raised to the second power which can be interpreted as (3/5)^2 then we can find the square of the given value so that we can arise at the answer.
In this case , (3/5)^2 = 9/25 which implies that the value of the (3/5)^2 is been found and to calculate the value of (3/5)^2, we will need to find the square of 3 which is the numerator as well as the square of 5 which is the denominator.
Therefore, the third option is correct.
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In Exercises 3 and 4, plot the points in a coordinate plane. Then determine whether
AB and CD are congruent.
3. A(-7, 1), B(-4, 1), C(3, -5), D(3, -2)
4. A(1, -1), B(1, 1), C(3, -4), D(5,-4)
AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.
What is congruency?If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence. In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.So, all coordinates are shown on the graph as follows:
(Refer to the image attached below)
Now, we can see that in the 4th quadrant, two triangles are formed that are ABE and CDE.
We can see that:Then, we can conclude that:
AB ≅ CD (Angle in front of them is similar so, the sides are also similar)Therefore, AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.
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A football team lost 14 yards on their first play then lost another 7 yards on the next play. What integer represents the total change in yards for the two plays?
Answer:
- 21
Step-by-step explanation:
They lost 14 yards, then lost and additional 7 more. You would simply add and make it a negative number due to the key word " lost ".
The equation would look like this: -14 + ( -7 ).
Another way to solve this equation is to multiply. ( + ) x ( - ) = -.
Your equation will the look this this: -14 - 7.
Now you just solve.
Thus, your answer should be - 21.
Hopes the helps!
Have a great day.
Answer: -21
Step-by-step explanation:
.A football team will lose an additional 7 yards if they lost 14 on their first play.
. Since the first play resulted in a loss of 14 yards, the integers that reflect the overall change in yards for the two plays are negative.
.In the second play, we score 14 points but lose 7 yards, which is a loss of 7 points.
.Negative 14 + Negative 7 = Negative 21, which is the overall change in yards.
. Hence, the answer would be -21 yards.
. -21 would be the correct integer that will represent the the total change in yards for the two plays.
Is the relationship between the number of tickets sold and the number of hours proportional? If so, how many tickets were sold in 8 hours?
hours.
1) 3
2) 5
3) 9
Tickets sold
1) 240
2) 400
3) 720
PLS HELP WILL GIVE 20 POINTS AND BRAINLIEST!! ASAP!!!!
Answer:
[tex]\frac{36}{49}[/tex]
Step-by-step explanation:
the pattern identified in the sequence is to add 1/49 after each step in the sequence.
When you add 1/49 to 34/49 you get 35/49, which can be simplified to 5/7.
To get the next value in the sequence just add 1/49 to 35/49, which equals 36/49.
this answer can not be simplified further.
increase 35 %of 78 please help me out
35% more than 78?
35% of 78;
78 x .35 = 27.3
78 + 27.3 = 105.3
.the temperature is -15 degree. then the temperature is 11 degree. what is the degree warmer
Answer: 26
Step-by-step explanation:
If you take 26 minus 11 it gets you -15.
Number lines help a lot with negatives. You can also start with -15 and just start adding numbers starting at a large number and going up or down depending on you answer. Ex. -15 + 30 = 15, -15 + 25 = 10, -15 + 26 = 11.
Given that [tex]\alpha , \beta[/tex], roots of [tex]4x^{2} - x + 1 = 0[/tex], without finding the value of [tex]\alpha , \beta[/tex] ; evaluate
a. [tex]\beta x^{2} +\alpha x^{2} -\alpha \beta[/tex]
b. [tex]\frac{\alpha }{\beta } + \frac{\beta }{\alpha }[/tex]
Considering the product and the sum of the roots of the quadratic function, the numeric value of the expressions are given as follows:
1. [tex]\beta x^2 + \alpha x^2 - \alpha\beta = \frac{1}{4}(x^2 - 1)[/tex]
2. [tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{7}{4}[/tex]
What are the product and the sum of the roots of the quadratic function?A quadratic function is defined according to the following rule:
y = ax² + bx + c.
In which a and b are the coefficients of the equation.
Supposing that the equation has roots [tex]\alpha[/tex] and [tex]\beta[/tex], the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex][tex]\alpha + \beta = -\frac{b}{a}[/tex]In this problem, the equation is:
4x² - x + 1.
Hence the coefficients are:
a = 4, b = -1, c = 1.
Then the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{1}{4}[/tex][tex]\alpha + \beta = \frac{1}{4}[/tex]Then the numeric values for the expressions can be found as follows:
[tex]\beta x^2 + \alpha x^2 - \alpha\beta = x^2(\alpha + \beta) - \alpha\beta = \frac{1}{4}x^2 - \frac{1}{4} = \frac{1}{4}(x^2 - 1)[/tex]
For the second expression:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^2 + \beta^2}{\alpha\beta} = 4(\alpha^2 + \beta^2)[/tex]
The sum of the squares of the roots is:
[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta[/tex]
Hence:
[tex]\alpha^2 + \beta^2 = \frac{1}{16} - \frac{1}{2} = -\frac{7}{16}[/tex]
Then:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{28}{16} = -\frac{7}{4}[/tex]
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David, Eva and Farooq share a sum of money.
1/6
David gets
- of the money and Eva gets -
1
4
- of the money.
Farooq gets the rest of the money.
David gets £2.50
Work out how much money Farooq gets.
Answer:
Farooq gets £8.75
Step-by-step explanation:
Let's represent the amounts obtained by David, Eva and Farooq as D, E and F to make things simpler. Let M be the total amount of money shared
D = 2.50 and represents 1/6 of the total amount of money(M)
So
M/6 = 2.50
Multiply both sides by 6 => M = 2.50 x 6 = £15
Eva gets 1/4th of this so E = 15 x 1/4 = £3.75
David gets £2.50
Together they get £2.50 + £3.75 = £6.25
The balance goes to Farook so F = 15 - 6.25 = £8.75
6. Find the equation for a parabola with vertex (5,-8) containing the point (1,1).
Answer:
[tex]y=\frac{9}{16}(x-5)^2-8[/tex]
Step-by-step explanation:
The equation in vertex form is [tex]y=a(x-5)^2-8[/tex].
Substituting in the coordinates [tex](1,1)[/tex] to solve for [tex]a[/tex],
[tex]1=a(1-5)^2-8 \\ \\ 1=16a-8 \\ \\ 9=16a \\ \\ a=9/16[/tex]
So, the equation is [tex]y=\frac{9}{16}(x-5)^2-8[/tex].
A basketball player attempts 15 baskets in a game. He makes 9 out of the attempted baskets.
Which describes the number of the baskets the player made to the number of baskets the player attempted?
The ratio is 3:5 .
The problem we are dealing with is related to the term ratio, where the ratio is characterized as the comparison of two quantities of the same units that shows how much of one amount is present within the other amount. Ratios can be classified into two sorts. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio indicates how two distinct entities or groups are related. whereas, the part-to-whole proportion indicates the relationship between a particular group to an entirety.The situation we are given is that the player attempted 15 baskets in a game and out of 9 was the number of times he made the attempted baskets.We just need to find the ratio of the number of baskets made to the number of baskets attempted,
= 9:15
Here we divide each by 3
= 9/3: 15/3
=3:5
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two rival dry cleaners both advertise their prices.store a´s prices are modeled by the
expression 20x-8,where x is the number of items brought in.store Bs pricesare modeled by the expression 5(4x+4),where x is the number of items brought in.when do the two stores charge the same rate?select the correct choise below and ,if necessary,fill in the answer to complete your choise.
A) The two stores charge the same when_______items are brought in.
B) The two stores always charge the same rate.
C) The two stores never charge the same rate.
C) The two stores never charge the same rate as per the cost expression of store A and store B.
The each expression of store A and store B represent the total cost charged by them based on the number of items bought. The mentioned expressions will be equated when assuming their total cost to be same. Thus, equating the the expressions.
20x - 8 = 5 (4x + 4)
Performing multiplication on Right Hand Side of the equation
20x - 8 = 20x + 20
Since 20x is present on both the sides, it will be cancelled. The remaining expression will be :
8 = 20, which is a false case as 8 is not equal to 20.
Thus, the equation has no solution and hence, the two stores will never charge the same rate, no matter how many items are bought.
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Find the sum of AP 35+29+23+....... as far as the 15th term
Answer: The answer is y=6x.
"Le Sage" Restaurant charges one price for adults and another for children for their buffet dinner. Raj's family has two adults and three children and their bill was $57 without taxes. Eman's family consists of 3 adults and 2 children and their bill was $63 without taxes. What is the cost of the buffet for an adult and for a child.
Answer:
5763 is the answer because 57 plus 63
Which number is NOT a perfect square?
9
1
4
2
Answer:
2
Step-by-step explanation:
A perfect square is the product of a number multiplied by itself.
So, 9 would be 3 x 3 so that's a perfect square.
1 is 1 x 1, so that is a perfect square.
4 is 2x2, so that is a perfect square.
2 does not have a number that multiplies by itself to equal 2, so it is not a perfect square.
Answer:
d) 2
Step-by-step explanation:
Now we have to,
→ find which is not a perfect square.
Let's solve the problem,
→ √9 = 3
→ √1 = 1
→ √4 = 2
→ √2 = 1.415
Hence, 2 is not a perfect square.
8. Find the greatest number which exactly divides 48 and 140.
Answer:
4
Step-by-step explanation:
Greatest Common Factor or Divisor is 4, because it is the greatest number that divides evenly into all of them.
Hope this helps! :)
Find the value of x in degrees for which d//m
Answer:
x = 31
Step-by-step explanation:
87=2x-25
-25 on each side
62=2x
divide each side by 2
31=x
x=31
Solve for x. 1/4+1/2+x=−3/4 Enter your answer as a fraction in simplest form in the box.
Answer:
yes!! finally a question i can solve:
so,
Step-by-step explanation:
Exact Form:
x = − 3/2
Decimal Form:
x = −1.5
Mixed Number Form:
x = -1 1/2
suppose that a large mixing tank initially holds 400 gallons of water in which 80 pounds of salt have been dissolved. pure water is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. determine a differential equation for the amount of salt a(t) in the tank at time
The differential equation for the amount of salt A(t) in the tank at the time (dA / dT) / (A / 100) = 0, A(0) = 30
It is Given that a large tank holds 400 gallons of water, in which 80 ponds of salt have been dissolved, given that pure water is pumped into the tank at a rate of 8 gallons/min. here we have to find the differential equation for the amount of salt in the tank at the time when the solution is well stirred. we have to multiply both 400 gallons of water and pumped water at the rate of 8 gallons/min.
dA / dT = Rin - Rout
Rin = 0
Rout = A(t) / 400 * 8
= A / 50
So,
dA / dt = Rin - Rout
dA / dt = 0 - A /50
After solving the differential equation we get
A(0) = 30
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If 2y+ 5x = 5 and 4y - x = 21, then what is the value of x + y ?
The value of equation (x + y) will be 1.
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The equation are;
2y + 5x = 5 ... (i)
4y - x = 21 ... (ii)
Now, Solve both the equation and find the value of x and y as;
Multiply by 2 in equation (i) we get;
4y + 10x = 10
Subtract above equation by (ii);
4y + 10x - (4y - x) = 21 - 11
11x = 11
x = 1
And, 2y + 5x = 5
Substitute x = 1;
2y + 5x = 5
2y + 5 = 5
2y = 0
y = 0
So, x + y = 1 + 0 = 1
Thus, The value of (x + y) will be 1.
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A certain grocery store charges a fee of
3% of the total bill to have groceries
delivered. What is the total price the store
charges to deliver $140 worth of groceries
C $144.20
D $140.42
A $154.42
B $149.80
For groceries to be delivered, one particular grocery store charges 3% of the whole purchase price. The total price the store charges to deliver $140 worth of groceries will be $144.20.
What do you mean by percentage?A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although abbreviations "pct.", "pct.", and occasionally "pc" are also used, percent symbol, "%," is frequently used to indicate it. A % lacks dimensions and has no associated unit of measurement.
It should be mentioned that a certain grocery store charges a delivery fee equal to 3% of the entire purchase price.
Consequently, the following is the total the store will charge to deliver $140 worth of groceries:
= Percentage charged × Cost+ Cost
= 3% × $140+$140
= 0.03 × $140+$140
= $4.20+$140
The amount charged is $144.20.
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Need Help Asap Find the measure of a base angle using the Triangle Sum Theorem
Answer:
45°
Step-by-step explanation:
Given:
Angles are (5x+15)°, 3x° and 3x°.To Find:
Measure of base angle.Concept used:
Sum of all interior angles in a triangle is equal to 180° .Using the above concept, we have
5x + 15 + 3x + 3x = 180
11x = 165
x = 165/11
x = 15
So, 3x = 3*15 = 45°
So, the measure of base angle is 45°
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Base \:\: Angle=3x = 45° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Property of Triangle : sum of all interior angles of a triangle is 180°
[tex]\qquad \tt \rightarrow \: 5x + 15 + 3x + 3x = 180[/tex]
[tex]\qquad \tt \rightarrow \: 5x + 3x + 3x + 15 = 180[/tex]
[tex]\qquad \tt \rightarrow \: 11x = 180 - 15[/tex]
[tex]\qquad \tt \rightarrow \:11 x = 165[/tex]
[tex]\qquad \tt \rightarrow \: x = 165 \div 11[/tex]
[tex]\qquad \tt \rightarrow \: x = 15[/tex]
Value of x is 15°, base angle is 3x :
[tex]\qquad \tt \rightarrow \: base \: \: angle = 3x = 3 \times 15 = 45 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Picture attached below, and it's not a rectangle. It's a pentagonsolve a and b
a)
The perimeter is given by
[tex]2x+3+4x+5+3x+15+40[/tex]b)
Then we simplify by summing similar terms we obtain that the expression of the perimeter is
[tex](2x+4x+3x)+(3+5+15+40)[/tex][tex]9x+63[/tex]Write the slope-intercept form of the equation of each line given the slope and y-intercept. Slope = 3/5, y-intercept = 0
Answer:y=3/5x
Step-by-step explanation:
just plug 3/5 in and you don’t need to add the 0