The miles Sophia drove is 60 miles
The distance Sophia drove is represented in fractions.
What is a Fraction?A number is expressed as a quotient where a numerator is divided by a denominator. In a simple fraction, both are integers.
A fraction consists of a numerator and a denominator. An example of a fraction is 1/2 where 1 is the numerator and 2 is the denominator.
In order to determine the miles Sophia drove, the total distance of the trip would be multiplied by the fraction of the time Sophia drove.
Miles Sophia drove = 3/5 x 100
= 60 miles
So sophia drove 60 miles in 500 miles.
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if 3²× = 27 what is x
Answer:
3
Step-by-step explanation:
whenever solving for x, you have to work backwards…like so:
3 squared is 9
27 divided by nine is 3
x=3
To double check the answer, substitute the value that we just found into x
(3x3)x3=27
Answer:
[tex]x=\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]3^{2x}=27[/tex]
Rewrite 27 in exponential form with base 3:
[tex]\implies 3^{2x}=3^3[/tex]
As both exponents have the same base,
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies 2x=3[/tex]
Divide both sides by 2:
[tex]\implies x=\dfrac{3}{2}[/tex]
en un proyecto de innovacion, se deben determinar montos para varios gastos, Se gasta un 25% en equipamiento, un quinto en salarios, un 35% en publicidad, qudando un remanente de $1.500.000 para gastos varios
The amount that's was attributed to the project from the start based on the percentage is $7,500,000.
How to calculate the percentage?From the information given, the remaining percentage will be:
= 100% - (25% + 20% + 35%)
= 100% - 80%
= 20%
Let the total amount be x.
Therefore, 20% of x = 1,500,000
0.2x = 1,500,000
x = 1500000/0.2
x = 7500000
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Sam ran 3 1/4 miles on Tuesday and then ran 2 5/6 miles on Wednesday. How many total miles did Sam run ?
Answer:
6 1/12 miles total
Step-by-step explanation:
3 1/4 = 13/4
2 5/6 = 17/6 to ADD fractions, you must have a common denominator
I will use 12 for these
13/4 = 39/12
17/6 = 34 /12
now you can add and simplify 39/12 + 34/12 = 73/12 = 6 1/12 miles
Dilate ∆ABC about the origin using the scale factor n. Measure and compare the lengths of the sides of the dilated triangle, ∆A'B'C', with those of ∆DEF. Take a screenshot of your dilation, save it, and insert the image below the table.
The attached graph represents the image of the triangles
How to dilate the triangle?To do this, we make use of the following coordinates
A = (1, 0)
B = (5, 0)
C = (1, 6)
The lengths of the triangle are calculated using
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(1-5)^2 + (0 -0)^2} = 4[/tex]
[tex]BC = \sqrt{(1-5)^2 + (6 -0)^2} = 7.2[/tex]
[tex]AC = \sqrt{(1-1)^2 + (6 -0)^2} = 5[/tex]
Using the scale factor of 2, we have the image of the dilation to be:
D = (2, 0)
E = (10, 0)
F = (2, 12)
The lengths of these sides are
DE = 8
EF = 14.4
DF = 10
See attachment for the image of the triangles ABC and DEF
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Please help me!
For a certain company, the cost for producing x items is 50x + 300 and the revenue for selling x items is 90x - 0.5x^2.
The profit that the company makes is how much it takes in (revenue) minus how much it spend (cost). In economic models, one typically assumes that a company wants to maximize its profit or at least wants to make a profit:
Set up an expression for the profit from producing and selling x items
Find two values of x that will create a profit of $300
Using the profit concept, we have that:
The expression is: P(x) = -0.5x² + 40x - 300.A profit of $300 is found with x = 20 and x = 60.What is the profit concept?Profit is given by revenue subtracted by costs.
In this problem, we have that:
The revenue is: R(x) = 90x - 0.5x².The costs are: C(x) = 50x + 300.Hence the expression for the profit is given as follows:
P(x) = R(x) - C(x)
P(x) = 90x - 0.5x² - 50x - 300
P(x) = -0.5x² + 40x - 300.
A profit of $300 is found when P(x) = 300, hence:
300 = -0.5x² + 40x - 300
0.5x² - 40x + 600 = 0.
x² - 80x + 1200 = 0.
(x - 60)(x - 20) = 0.
Hence the values are:
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what is the lcd of 1/4 and 1/6
Answer:
12
Step-by-step explanation:
LCD of 1/4 and 1/6 is the least common denominator that is divisible by 4 and 6 at the same time and is the least.
So it the same to find least common multiple of 4 and 6 that is 12.
The answer is 12.
22POINTS PLEAS ANsewer
Answer:
2y>-y+5
Step-by-step explanation:
because it has a eligible number at the right hand side
What is the domain and range of this graph?
Suppose U = The set of one digit numbers and A = {x: x is an even natural number less than or equal to 9} Describe each of the sets by complete listing method: A'
The sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}
How to list the set elements?The sets are given as:
U = The set of one-digit numbers
A = {x: x is an even natural number less than or equal to 9}
One-digit numbers are numbers 0 - 9.
So, we have
U = {0, 1, 2, 3.....,9}
Natural numbers are numbers from 1.
Even natural numbers can be divided by 2 without remainder'
So, we have
A = {2, 4, 6, 8}
Hence, the sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}
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Answer:
Step-by-step explanation:
Write an equation for the nth term of the arithmetic sequence 8, 3, -2, -7,... Find the 9th term of the sequence.
For what value of y does 125 =
(1/25)^y-1
Answer:
[tex] y = -\dfrac{1}{2} [/tex]
Step-by-step explanation:
I assume that y - 1 is an exponent, and the equation is
[tex] 125 = (\dfrac{1}{25})^{y - 1} [/tex]
[tex] 5^3 = (5^{-2})^{y - 1} [/tex]
[tex] 5^3 = 5^{-2y + 2} [/tex]
[tex] -2y + 2 = 3 [/tex]
[tex] -2y = 1 [/tex]
[tex] y = -\dfrac{1}{2} [/tex]
la longitud del jardín
de Carme es 15 m 24 cm. la longitud del jardín de su amigo es 2 m 98 cm más que el de Carmen . ¿cuál es la longitud del jardín de su amigo?
la longitud del jardín del amigo de Carmen es 18 m 22 cm.
¿Qué es una ecuación?Una ecuación se forma cuando dos expresiones algebraicas se igualan usando un signo igual.
Se da que la longitud de Carme
Se sabe que la longitud del jardín de Carmen es de 15 m 24 cm.
y el largo del jardín de su amigo es 2 m 98 cm más largo que el de Carmen.
Sea La longitud del jardín de Carmen es x m
Entonces la ecuación se convierte en
La longitud del jardín de su amigo = x + 2m 98 cm
ahora ,
x = 15m 24cm
Sustituyendo los valores en la ecuación
La longitud del jardín de su amigo = 15m 24cm + 2m 98 cm
1m = 100cm
La longitud del jardín de su amigo = 17 m 122 cm
as 100 cm = 1m
122 cm = 1 m 22 cm
so ,
La longitud del jardín de su amigo = 18 m 22 cm.
Por lo tanto, la longitud del jardín del amigo de Carmen es 18 m 22 cm.
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ANSWER ASAP, GIVING BRAINLIEST TO FIRST ANSWER!!!
Which linear inequality represents the graph below?
(-3,3)-(0,1)
Answer:
if the red line is included it is a. if the red line is excluded it is C. I believe.
Answer:
A
Step-by-step explanation:
the equation of the line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (0, 1) ← 2 points on the line
m = [tex]\frac{1-3}{0-(-3)}[/tex] = [tex]\frac{-2}{0+3}[/tex] = - [tex]\frac{2}{3}[/tex]
the line crosses the y- axis at (0, 1 ) ⇒ c = 1
y = - [tex]\frac{2}{3}[/tex] x + 1 ← equation of line
the solutions to the inequality lie above the line, including the line, in the shaded area , then
y ≥ - [tex]\frac{2}{3}[/tex] x + 1 → A
Pls answer for brainlest and 50 points PLEASE EXPLAIN
In image
First, let's complete the angles in the triangle. Remember that the sum of the angles in a triangle is 180 degrees.
73 + 90 + x = 180
163 + x = 180
x = 17
So, the angle that completes the triangle is 17 degrees. If we look at that angle in the triangle and the one adjacent to it, we can see that those two angles form a linear pair (or are supplementary, both meaning that they add up to 180 degrees).
17 + x = 180
x = 163
So, 17's supplement is 163 degrees. The 163 degree angle corresponds with angle r, and corresponding angles are congruent.
Therefore, angle r is 163 degrees. The correct answer is option C.
Hope this helps!
need help with this question.
We have this equation:
[tex]\log(x) + \log(x + 99) = 2[/tex]
First, combine both logarithms using the multiplication property and simplify the expression.
[tex]\log[x(x + 99)] = 2[/tex]
[tex]\log[ {x}^{2} + 99x ] = 2[/tex]
Now, use the definition of logarithm to transform the equation.
[tex] {10}^{2} = {x}^{2} + 99x[/tex]
[tex] {x}^{2} + 99x - 100 = 0[/tex]
Finally, use the quadratic formula to solve the equation.
[tex]x = \frac{ -99 ± \sqrt{ {99}^{2} - 4 \times 1 \times ( - 100)} }{2 \times 1} [/tex]
With this, we can say that the solution set is:
x = 1x = -100We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.
What is the simple interest that is missing from the table?
I
?
p
$375
r
2.2%
t
3 years
Answer:
SI =PXRXT/100
Step-by-step explanation:
THIS WOULD HELP YOU
!!!!!!!A dress pattern uses the scale 2 inches : 1 foot.if the model is 12 inches long how long is the dress!!!!!!pls Hurry
Using the scale ratio, the length of the dress is: 6 ft.
How to Apply Scale to Measurement?Given a scale for the dress pattern as, 2 inches : 1 foot, it means 2 inches of the model equals 1 foot of the actual dress.
Therefore, using the scale ratio, let x represent the length of the dress. We would have:
2/1 = 12/x
x = (12 × 1)/2
x = 6 ft.
The length of the dress is: 6 ft.
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Question 18
Which formula is used to find the y-coordinate of the vertex of the quadratic function?
Answer:
[tex]\frac{-D}{4a}[/tex]
Step-by-step explanation:
y-coordinate is [tex]\frac{-D}{4a}[/tex] where a is coefficient of quadratic polynomial (ax^2+bx+c) and D is discriminant of the quadratic equation when you equate it to zero.
PLS HELP ME Solve the following equation: two fifths plus one fifth equals
one fifth,
three tenths,
two fifths,
or three fifths.
it is three fifths,
and it is the answer.
How did I do? for one of the questions I assumed you didnt take in count for the base so I just did lateral area
The area of the exposed surface is 442 square feet
What is a right square pyramid?A right square pyramid is a polyhedron with 5 faces consisting of four triangles and a square base.
Analysis:
The exposed surface is the area of the four triangles.
The perpendicular height of the triangles is same and it is the slant length of the shape = 17ft
Area of 4 triangles = 1/2 bh = 1/2 x 17 x 13 x 4 = 442 square feet.
In conclusion, area of exposed surface is 442 square feet.
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Solve for x: -5(-3x+1)=-45
Answer:
x = -8/3
Step-by-step explanation:
-5(-3x+1)=-45
⇔ 15x - 5 = -45 (left side of the equation expanded)
⇔ 15x = -45 + 5 (add 5 to both sides)
⇔ 15x = -40
⇔ x = -40/15 (Divide both sides by 15)
⇔ x = -8/3 (simplify)
134 A financial analyst believes that if interest rates decrease in a given period then the
probability that the stock market will go up is 0.08. The analyst further believes that
interest rate have a 0.40 chance of decreasing during the period in question. Given the
above information, what is the probability that the market will go up and interes: rate
will go down during the period in question?
The probability that the market will go up and interest rate will go down during the period in question is 0.03.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the market will go up and interest rate will go down = 0.08 X 0.40 = 0.03
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A block is a rectangle that measures 100yards by 76yards. How many times around the block do you have to drive in order to drive one mile?
If block has length 100 yards and breadth 76 yards then we have to drive 5 times to drive one mile.
Given The length of block is 100 yards, the breadth of block is 76 yards.
We have to find number of times we need to drive one mile.
The perimeter of a rectangle= 2(length +breadth)
length is 100 yards
Breadth is 76 yards
perimeter=2(100+76)
=2*176
=352 yards.
We know that 1 mile is equal to 1760 yards.
We have to find number of times to drive 1 mile=1760/352
=5 times.
Hence we have to drive 5 times around the block which have length 100 yards and breadth 76 yards.
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which diagram shows a pair of angle measures that prove lines a and b are parallel?
Answer:
d
Step-by-step explanation:
it's kinda hard to explain
What is the least possible value of (x+1)(x+2)(x+3)(x+4)+2019 where x is a real number?
By completing the square, we have
[tex](x+1)(x+4) = x^2 + 5x + 4 = \left(x+\dfrac52\right)^2 - \dfrac94[/tex]
[tex](x+2)(x+3) = x^2 + 5x + 6 = \left(x + \dfrac52\right)^2 - \dfrac14[/tex]
Then
[tex](x+1)(x+2)(x+3)(x+4) = \left(x+\dfrac52\right)^4 - \dfrac52 \underbrace{\left(x + \dfrac52\right)^2}_{=y} + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = y^2 - \dfrac52 y + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(y - \dfrac54\right)^2 - 1 \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(\left(x + \dfrac52\right)^2 - \dfrac54\right)^2 - 1[/tex]
This product has a minimum of -1 when
[tex]\left(x + \dfrac52\right)^2 - \dfrac54 = 0[/tex]
which has two real solutions; then the minimum of the overall expression is -1 + 2019 = 2018.
Simplify, using the distributive
property.
5f + 16f = (5 +?)f=?f
Applying the distributive property, we would simplify the expression as: 5f + 16f = (5 + 16)f = 21f.
How to Apply the Distributive Property?The distributive property states that, ab + ac = (b + c)a.
Using the distributive property, we have:
5f + 16f
= (5 + 16)f
= 21f
Therefore, 5f + 16f is simplified as 21f.
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What is the end behavior of the function f of x equals negative 2 times the cube root of x? as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0. as x → [infinity], f(x) → [infinity], and as x → –[infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity].
The end behavior of the function is as:
as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
What is end behavior?The end behavior of a function will describe the behavior of the graph of the function at the "ends" of the x-axis.
How do determine the end behavior of a function?By determining the highest degree of the polynomial function. As the highest degree term will grow faster than the other terms as x gets very large or very small, its behavior will dominate the graph.
The graph of the function is f(x)=2∛x
the function leads to infinity so the end behavior of the function is
as [tex]x[/tex]→∞, f(x)→+∞ and as x→-∞, f(x)→+∞
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Factor by Grouping.
The ac product of 35x² + 41x + 12 is
The factors of the ac product that add to 41 are
35x² + 41x + 12 =
Submit Question
x +
)(
and
x +
000
Answer:
The ac product of [tex]35x^2+41x+12[/tex] is 420.
The factors of the ac product that add to 41 are 20 and 21.
[tex]35x^2+41x+12 =[/tex] [tex](7x+4)(5x+3)[/tex]
Step-by-step explanation:
1) The general form of a quadratic is [tex]ax^2 + bx + c[/tex]. Hence, multiplying 35 by 12 gives you the product of ac, which is 420.
2) We need to find two numbers that multiply to 420 and add up to 41 simultaneously. If we pull out the factors of 420, two of them will be 20 and 21, which multiply to 420 as well as add up to 41.
3) Write [tex]41x[/tex] as a sum.
[tex]35x^2+20x+21x+12[/tex]
Now, we can factor them out by grouping.
[tex]35x^2+20x+21x+12\\5x(7x+4)+3(7x+4)[/tex]
Since, [tex]7x +4[/tex] is common in both of the factors, we only take one of the [tex]7x+4[/tex] along with [tex]5x[/tex] and [tex]3[/tex].
[tex](7x+4)(5x+3)[/tex]
Answer:
[tex]\text{The ac product of }\: 35x^2+41x+12 \text{ is }\boxed{420}\:.[/tex]
[tex]\text{The factors of the ac product that add to 41 are }\:\boxed{20} \: \text{ and }\: \boxed{21}\:.[/tex]
[tex]35x^2+41x+12=\left( \: \boxed{5}\:x+\:\boxed{3}\:\right)\left(\: \boxed{7}\:x+\boxed{4}\:\right)[/tex]
Step-by-step explanation:
Given quadratic:
[tex]35x^2+41x+12[/tex]
Factoring quadratics by grouping
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=35 \cdot 12 = 420[/tex]
[tex]\implies b = 41[/tex]
Therefore, the two numbers that multiply to 420 and sum to 41 are:
20 and 21
Rewrite b as the sum of these two numbers:
[tex]\implies 35x^2+20x+21x+12[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 5x(7x+4)+3(7x+4)[/tex]
Factor out the common term [tex](7x+4)[/tex] :
[tex]\implies (5x+3)(7x+4)[/tex]
Conclusion
[tex]\text{The ac product of }\: 35x^2+41x+12 \text{ is }\boxed{420}\:.[/tex]
[tex]\text{The factors of the ac product that add to 41 are }\:\boxed{20} \: \text{ and }\: \boxed{21}\:.[/tex]
[tex]35x^2+41x+12=\left( \: \boxed{5}\:x+\:\boxed{3}\:\right)\left(\: \boxed{7}\:x+\boxed{4}\:\right)[/tex]
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The lsrl after an exponential transformation is log yhat=.4785 + 1.468x. What is the exponential form of the regression?
Answer:
[tex]10^{0.4785+1.468x}=y[/tex]
Step-by-step explanation:
So I'm assuming when you typed "log yhat=.4785 + 1.468x", you meant to write: [tex]log(y)=0.4785+1.468x[/tex]. And generally a logarithm can be written in the form [tex]log_ba=c[/tex] which can then be rewritten as [tex]b^c=a[/tex], but since the log has no base, it's assumed to be 10. So in this case you have the equation:
[tex]log_{10}y=0.4785+1.468x[/tex], which can then be written in exponential form as:
[tex]10^{0.4785+1.468x}=y[/tex]
77 is the product of 7 and diego's height use the variable d to represent diego';s height
Diego's height is 7 units
How to determine Diego's height?The statement is given as:
77 is the product of 7 and Diego's height
This means that:
77 = 7 * d
Divide both sides by 7
d = 11
Hence, Diego's height is 7 units
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