a = hours worked by the first mechanic
b = hours worked by the second mechanic.
since the first mechanic charges $55 per hour, then for "a" hours that'd be a total of 55*a or 55a, likewise, for the second mechanic that'd be a total charge of 80*b or 80b.
we know all hours combined are 15, so then a + b = 15.
we also know that all charges combined are $950, so 55a + 80b = 950.
[tex]\bf \begin{cases} a+b=15\\ \boxed{b}=15-a\\ \cline{1-1} 55a+80b=950 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{55a+80\left( \boxed{15-a} \right)=950} \\\\\\ 55a+1200-80a=950\implies -25a+1200=950\implies -25a=-250 \\\\\\ a=\cfrac{-250}{-25}\implies \blacktriangleright a = 10\blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=15-a\implies }b=15-10\implies \blacktriangleright b=5 \blacktriangleleft[/tex]
What is the solution to the following equation? 4(3x − 6) + 15 = 27 2 3 4 5
Answer:
Hi there!
The answer to this question is 3
Step-by-step explanation:
You first distribute the four into the parenthesis to get: 12x-24+15+ 27
Next you add -24 to 15 to get: -9 your equation should now look like 12x-9=27
Then you add 9 on both side to get 12x=36
Last you divide twelve on both sides to x=3
Answer:
3
Step-by-step explanation:
Which of these is the quadratic parent function
Answer:
Option C (f(x) = x^2)
Step-by-step explanation:
Quadratic Function is a polynomial which has a maximum degree of 2. It is expressed in the form:
f(x) = a + bx + cx^2; where a, b, and c are real numbers.
Any function which has the highest degree of 2 (not more than that) is the quadratic function. Option A illustrates the absolute values function. Option B shows a function which does not match the characteristics of the quadratic equation. Option D shows a linear function. Therefore, Option C (i.e. f(x) = x^2) is the correct choice!!!
he function f(x) = x^2 + 10x - 3 written in vertex form is fx) = (x+5)^2– 28. What are the coordinates of the vertex?
0 (-5, -28)
O (-5, 28)
O (5.-28)
O (5, 28)
Answer:
(- 5, - 28 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = (x + 5)² - 28 ← is in vertex form
with vertex (h, k) = (- 5, - 28)
On a particular day, the wind added 4 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 4 miles per hour from her rate on her return trip. Jaime found that in the same amount of time she could row 48 miles with the wind, she could go only 24 miles against the wind. What is her normal rowing speed with no wind?
Answer:
12 miles per hour
Step-by-step explanation:
Let her normal rowing speed be x
Also note the formula D = RT, where d is distance, R is rate(speed) and T is time
On windy day, her speed is x + 4
On against wind return, her speed is x - 4
With wind, she can go 48 miles in same amount of time when she goes 24 miles against wind. This can be written as:
48 = (x+4)T
24 = (x-4)T
We can write each equation in terms of T and equate both. So we have:
48/x+4 = T
24/x-4 = T
Thus,
[tex]\frac{48}{x+4}=\frac{24}{x-4}\\48(x-4)=24(x+4)\\48x-192=24x+96\\24x=288\\x=\frac{288}{24}\\x=12[/tex]
Thus, Jaime's normal rowing speed is 12 miles per hour
The two triangles below are similar. What is the similarity ratio of ∆ABC to ∆DEF?
A) 3:1
B) 1:3
C) 2:1
D) 1:2
Answer:
Option C is correct
Step-by-step explanation:
The two triangles are similar if there sides are proportional to each other
So, In Triangle ABC and Triangle DEF
AB/DE=BC/EF=AC/FD
according to definition of similar triangles.
We are given AC = 8
and FD = 4
So, AC/FD = 8/4 = 2/1
or 2:1
So, Option C is correct
Answer: Option C
2:1
Step-by-step explanation:
Two triangles are similar if the ratio of their sides is proportional.
In this case we have the triangle ∆ABC and ∆DEF so for the sides of the triangles they are proportional it must be fulfilled that:
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]
In this case we know that:
[tex]AC=8[/tex]
[tex]DF=4[/tex]
Therefore
[tex]\frac{AC}{DF} = \frac{8}{4}\\\\\frac{AC}{DF} = \frac{2}{1}[/tex]
The similarity ratio of ∆ABC to ∆DEF is 2:1
cuales el numero menor que 34.969.387 y mayor que 34.969.385
Has la serie numérica
a= 34.969.385
b = 34.969.386
c = 34.969.387
[tex]a < b < c[/tex]
Which of the following is a trinomial?
Answer:
D
Step-by-step explanation:
A trinomial is an expression consisting of three terms, and D is the only one with 3 terms.
Please give brainliest!
The trinomial among the following expressions is 5x² + 3x + 6
What is a trinomial?A polynomial with three terms is called a trinomial.
How to find which of the following is a trinomial?In order to find the trinomial, we need to find in which of the following expressions, there are 3 terms.Clearly in options A ,B , C there are two terms in all the expressions and hence they are not trinomial.
In option D, the expression is 5x² + 3x + 6, which is having 3 terms
So this is the trinomial.
Option D is correct.
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convert 1.5 miles to feet
Answer: 7,920 feet.
Step-by-step explanation: There are 5,280 feet in a mile. To find how many feet are in 1.5 miles, multiple 1.5 by 5,280.
1.5 x 5,280 = 7,920
There are 7,920 feet in 1.5 miles.
What is a counter example for: If the name of the month begins with a J, then it is a summer month.
Answer:
January
Step-by-step explanation:
January is a counter-example of the name of the month begins with a January then it's a winter month by a season.
The counter example is : January since it begins with the letter J and is a winter month, which is not summer.
What is a counter example?An example that disproves a statement (shows that it is false) is called a counter example.
How to find the counter example for the given examples?According to the problem, the given statement is : If the name of the month begins with a J, then it is a summer month.The counter example will be : January since January is a month that starts with J that is not a summer month
January is the only month that fits this criteria.
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Is (4y-8)cm divided by 2 equals to 4y-8cm over 2 and then a cm or is it (2y-4)cm?
Answer:
(2y-4)cm
Step-by-step explanation:
In the given question we have (4y-8) divided by 2
which can be written mathematically as [tex]\frac{\left ( 4y-8 \right )cm}{2}[/tex]
Now (4y-8) is a quatity with unit cm. and the whole expression is in parentheses. Moreover, two quatity can only be added or subtracted only when their units are same. Therefore 4y and 8 must have same unit that is cm.
Therefore, [tex]\frac{\left ( 4y-8 \right )cm}{2}=(2y-4)cm[/tex] and not anything else
e equation 2x + 3y = 36, when y = 6?
Answer:
x=9
Step-by-step explanation:
Since y=18
The new equation is [tex]2x+3*6=36[/tex]
Moving some terms, it stays like the following:
[tex]2x=36-18[/tex]
solving for x, give us that x=9
evaluate the expression 1.5(p+n) for p= and n =6
Answer:
The answer is 18
Step-by-step explanation:
1.5(p+n) for p= and n =6
As we know the values of p=6 and n=6
Solve it according to the BODMAS rule. According to this rule if we have brackets or parenthesis then first we have to solve or simplify the brackets.
Put the values in the given expression:
1.5(6+6)
Now solve the parenthesis first:
1.5(12)
Now multiply 1.5 by
The answer is 18....
At the mall, buying a pair of shoes and buying a book are independent events.
The probability that a shopper buys shoes is 0.15. The probability that a
shopper buys a book is 0.10.
What is the probability that a shopper buys shoes and a book?
Answer:
0.015
Step-by-step explanation:
The probability two independent events take place is the product of their individual probabilities.
p(shoes & book) = p(shoes) * p(book) = 0.15 * 0.10 = 0.015
Answer:
0.015 ~apex
Step-by-step explanation:
What is the constitutional basis for the expressed powers of the federal
government?
Answer:
Article I, Section 8.
Step-by-step explanation:
The expressed powers of the federal government are given in Article I, Section 8 of the Constitution. This includes the many specific powers which the framers intended for the federal government to have, such as to declare war, regulate commerce, establish post offices, and establish rules of naturalization.
Answer:
They are directly listed in the Constitution.
Transformations were performed on pentagon H as shown in the graph. What types of transformations were performed? Do those transformations result in congruent shapes?
A. Translation and dilation, yes
B. Translation and reflection, no
C. Translation and rotation, yes
D. Translation and dilation, no
How do I do this? Please provide steps.
Answer:
3/5
Step-by-step explanation:
Soh Cah Toa
In some trigonometry classes, this acronym is very important to solving questions like this.
Why?
It tells us the right triangle-definition of these trigonometry functions.
We have that cosine of an angle is equal to tge side that is adjacent to it over the hypotenuse.
So here we are asked to find cos(B).
Lets look at triangle respect to the angle B
The measurement of the side that is opposite is 64.
The measurement of the side that is adjacent is 48.
The measurement of the hypotenuse is 80.
So cos(B)=48/80.
Let's reduce. 48 and 80 have a common factor of 8 so divide numerator and dexter by 8. This gives us:
cos(B)=6/10.
One more step in reducing. Both factors are even so cos(B)=3/5.
what is the equation for the line of reflection?
x=3
y=3
y=x
x=6
Answer:
y=x
Step-by-step explanation:
If you draw the line y=x on the shown graph a and a' are the same distance away from the line. This is the same for all the other points and its prime.
(01.03 MC)
Which of the following is a step in simplifying the expression
(Xy^4/x^-5y^5)^3
[tex]\displaystyle\tt\left(\frac{xy^4}{x^{-5}y^5}\right)^{-3} =\frac{x^{-3}y^{4\cdot(-3)}}{x^{-5\cdot(-3)}y^{5\cdot(-3)}}=\boxed{\tt\frac{x^{-3}y^{-12}}{x^{15}y^{-15}}}[/tex]
Hello I don’t get this, I don’t want the answer I just need someone to teach it to me because it wasn’t in the lesson
Answer:
[tex]3 \le x \le 7[/tex].
Step-by-step explanation:
Hopefully this will help. Let me know in the comments if it doesn't.
The domain is all the x's where the function exists. The function you have starts at x=3 and ends at x=7. There are no breaks in your line between those numbers for x. So your domain is all x's between 3 and 7 ( inclusive).
So that means all values of x that is greater than or equal to 3 and values of x less than or equal to 7.
[tex]3 \le x \le 7[/tex].
Find the measure of angle 2 (27)
The measure of <2 is 45 degree.
What is Angle Sum Property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is always 180 degrees.
From the figure, applying angle sum property
<2 + 45 + 90= 180
<2 + 135=180
<2 = 180- 135
<2 = 45 degree
Thus, the measure of <2 is 45 degree.
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If f(x) = 3x - 2 and g(x) = 2x + 1, find (f+ g)(x).
[tex](f+g)(x)=3x-2+2x+1=5x-1[/tex]
Help asap
The scale of a town map is 1 inch to 3 miles. On the map, a lake and the downtown are 4 inches apart. What is the actual distance between the lake and the downtown?
3/4 mile
1/3 mile
7 miles
12 miles
Answer:
Step-by-step explanation:
The answer is 12 miles, if every inch is 3 miles on the map then 3x4=12.
Answer:
12 miles
Step-by-step explanation:
In order to solve the problem you only have to use the scale of the map, we know that the ratio is 1 inch to 3 miles, so if one inch in the map represent 3 miles on real scale, now we just do a rule of three like this:
[tex]\frac{1 inch}{4 miles}=\frac{3 inches}{x}[/tex]
So now that we have our function we can clear the x to solve the problem:
[tex]x=\frac{3x4}{1}[/tex]
[tex]x=\frac{12}{1}[/tex]
[tex]x=12 miles.[/tex]
By doing this we now know that there are 12 miles from downtown to the lake.
HELP PLEASE REALLY NEED IT
Answer:
x=65
Step-by-step explanation:
The angle with the measurement of 125 degrees is supplementary to the one adjacent to it (sharing the same vertex and on same line).
What that means is that the measurement of the angle adjacent to that angle of 125 degrees is 180-125=55.
So now we know the sum of the interior angles of a triangle add up to be 180 degrees.
That is we have to solve the following equation for x:
x+55+60=180
Add 55 and 60:
x+115=180
Subtract 115 on both side:
x=180-115
Simplify:
x= 65
Evaluate 2^-4 TOOOOOOOOOOONGAAAAAAAAAAAAAA
Answer:
1/16
Step-by-step explanation:
2 ^ -4
The negative puts the number in the denominator
1 / 2^4
1/16
Simplify the expression 43 + 2(3 − 2).
14
16
66
68
Final answer:
To simplify the expression 43 + 2(3 - 2), first solve inside the parentheses (3 - 2 = 1), then multiply by 2 (2 × 1 = 2), and finally add to 43 to get 45.
Explanation:
The question asks to simplify the expression 43 + 2(3 − 2). To simplify, follow the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). First, solve the expression within the parentheses, which is 3 − 2 = 1. Next, multiply the result by 2 (2 × 1 = 2). Lastly, add this result to 43 to get the final answer, 43 + 2 = 45. This process demonstrates how to approach and simplify mathematical expressions using proper order of operations.
Pls help !!!!!!!!!! I need to get this question right
Answer:
B
Step-by-step explanation:
Answer:
He didn't change the direction of the inequality when he divided both sides by -2.
Step-by-step explanation:
Let's go through each step and see.
First step: They distribute and they did so correctly. -4(x+8)=-4x-32.
Second step: They added 2x on both sides.
Third step: They added 32 on both sides.
Fourth step: The divide both sides by -2 correctly but since this is inequality you must flip the sign.
For example 3>2 but if you multiply both sides by -1 or divide both sides by -1 you get -3<-2.
You have to flip the sign whenever you multiply or divide both sides of inequality by negative number.
A city determines that a planned community must have at least 4 acres of developed and open space, and the difference
between the number of developed acres, y, and the number of open acres, x, can be no more than 1. Which graph
represents the system of inequalities for this scenario?
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x -----> the number of open acres
y ----> the number of developed acres
we know that
[tex]x+y \geq 4[/tex] -----> inequality A
[tex]x\leq 1[/tex] ----> inequality B
Remember that
if the number of open acres, x, can be no more than 1. then the number of open acres, x must be less than or equal to 1
Solve the system of equations by graphing
The solution is the shaded area (Note The number of acres cannot be a negative number)
The graph in the attached figure
Answer: It's B
Step-by-step explanation: I just did it on edge 2020
Which logarithmic equation has the same solution as x-4=2^3
Answer:
[tex]log_{3}(x-4)= 3log_{3}(2)[/tex]
Step-by-step explanation:
The given equation is:
[tex]x-4=2^{3}[/tex]
We have to find the logarithmic equation with same solution as the given equation.
If we take the log of both sides, we can get a logarithmic equation. Since the log operation is applied to both sides the solution of the equation will stay the same.
Taking the logarithm to the base 3 of both sides, we get:
[tex]log_{3}(x-4)= log_{3}(2)^{3}\\\\ log_{3}(x-4)= 3log_{3}(2)[/tex]
Answer: The CORRECT answer is C: log2(x-4)=3
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The solution set of n2 − 14n = -45 is [ ]
Answer:
n=5 n=9
Step-by-step explanation:
n^2 − 14n = -45
Add 45 to each side
n^2 − 14n +45 = -45+45
n^2 -14n +45 = 0
Factor the equation
What 2 number multiply to 45 and add to -14
-5*-9 = 45
-5+-9 = -14
(n-5) (n-9) =0
Using the zero product property
n=5 n=9
Francisco’s bank offers car financing for 3,4 or 5 years.if Francisco chooses 3-year financing ,how many monthly payment will he have?
Answer:
How much money the payment is in one year, then divided by 12.
Step-by-step explanation:
To do this, lets say that Francisco's bank earns 120036$ a year.
120036/12=1003$ a month
How much payment in one year, then divided by 12.
Answer:
36 months
Step-by-step explanation:
simple math