19. The function f(x) = 27x – 67.5 has an
* -intercept at (a,0). The function g(x) is
defined in the table below and has an
x-intercept at (b,0). How much greater is the
value of b than the value of a?
Answers
Answer:
First we have the function f(x) = 27*x - 67.5
It has an x-intercept at (a, 0)
This means that:
f(a) = 0 = 27*a - 67.5
Solving the above equation we can find the value of a.
0 = 27*a - 67.5
67.5 = 27*a
67.5/27 = a = 2.5
Now let's look at equation g(x).
It is a linear equation, remember that a linear equation can be written as:
g(x) = y = A*x + B
Where:
A is the slope, and B is the y-intercept.
If the line passes through the points (x₁, y₁) and (x₂. y₂), the slope can be written as:
A = (y₂ - y₁)/(x₂ - x₁)
In this case we can select any two points from the table, for example, I will use the second and third points:
(1, 39) and (2, 32.5)
Then the slope is:
A = (32.5 - 39)/(2 - 1) = -6.5/1 = -6.5
Then the equation is something like:
g(x) = y = -6.5*x + B
B is the y-intercept, to find this value, we can use one of the two points we used before.
For example, (1, 39) means that g(1) = 39
Then:
g(1) = -6.5*1 + B = 39
= B = 39 + 6.5 = 45.5
Then the equation for g(x) is:
g(x) = -6.5*x + 45.5
Now, we know that g(x) has an x-intercept at (b, 0)
this means that:
g(b) = 0 = -6.5*b + 45.5
6.5*b = 45.5
b = 45.5/6.5 = 7
Then the difference between b and a is:
b - a = 7 - 2.5 = 4.5
b is equal to a plus 4.5
And the ratio is:
b/a = 7/2.5 = 2.8
b is 2,8 times larger than a.
Related Questions
exponential function b^y=x can be expressed as
Answers
Answer:
[tex] {b}^{y} = x \\ x = {b}^{y} \\ log_{b}x = y[/tex]
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answers
Step-by-step explanation:
try to factor them anx than set each bracket to 0 the negative one would not work
Answer:
5(−x−2)(x−7)
Step-by-step explanation:
I-Ready help...... AND DON"T SAY USE A CALCULATOR IT SO EZZ I Would if i flip In COULD DU>>>>>A>>>>>S>>>>S>>>>>'S SORRY TO BE mean XD
Answers
Answer:
-0.099
Step-by-step explanation:
0.9 × -0.11 = -0.099
Your pfp is giving me a seizure
You're like 12
And your cringy
""Sorry to be mean XD""
please help me! ill give a brainlest for who answer this
Answers
Answer:
(0,1)
Step-by-step explanation:
Answer:
The coordinates of the point are (0,1)
Step-by-step explanation:
At a grocery store,39 out of 60 customers use a shopping cart. What percent of the customers use a shopping cart?
Answers
Answer:
39 is 65% of 60
65% use a shopping cart.
PLEASE HELP ME ILL GIVE BRAINLIEST
Select the correc answer. Consider function g. 5+2 What is the average rate of change of function g over the interval [-4, 3]
OA. 1/2
OB. -7/2
OC. -1/2
OD. 2
Answers
determine the volume of rectangular prism 6cm 4m 4m
Answers
f(x) = x^2. What is g(x)?
Answers
Answer:
g(x) = 5x^2
Step-by-step explanation:
[-15(-1.5)]+[(-2.5) x 1.25] plz help me out guys
Answers
Answer:
19.375
Step-by-step explanation:
Hope this helps ;)
Answer: 19.375
Step-by-step explanation:
[-15(-1.5)]+[(-2.5) x 1.25]
[22.5]+[-3.125]
22.5-3.125= 19.375
HELP ASAP 50 POINTS
What are the exact solutions of x2 + 5x + 1 = 0 using x equals negative b plus or minus the square root of the quantity b squared minus 4 times a times c all over 2 times a?
x = the quantity of 5 plus or minus the square root of 21 all over 2
x = the quantity of negative 5 plus or minus the square root of 21 all over 2
x = the quantity of 5 plus or minus the square root of 29 all over 2
x = the quantity of negative 5 plus or minus the square root of 29 all over 2
Answers
Answer:
B. x = the quantity of negative 5 plus or minus the square root of 21 all over 2Step-by-step explanation:
x² + 5x + 1 = 0 x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex])/ (2a)x = (- 5 ± [tex]\sqrt{5^2 - 4*1*1}[/tex]) / (2*1)x = (- 5 ± [tex]\sqrt{21}[/tex]) /2Correct choice is B
9 ( x - 5 ) = -108 solve for x
Answers
Answer:
x = -7
Step-by-step explanation:
9 ( x - 5 ) = -108
9x - 45 = -108
add 45 to each side of the equation:
9x = -63
divide both sides by 9:
x = -7
Answer:
x = - 7
Step-by-step explanation:
9(x - 5) = - 108
9x - 45 = - 108
9x - 45 + 45 = - 108 + 45
9x = - 63
9x ÷ 9 = - 63 ÷ 9
x = - 7
Un padre cede al mayor de sus hijos la quinta parte de su capital, al segundo la cuarta parte del mismo y al tercero le da el resto, que son 33,000 euros. ¿Cuál era su capital? ¿Cuánto le correspondió a cada hijo?
Answers
Answer:
El padre tenía un capital de 60,000 euros.
El hijo mayor recibe 12,000 euros.
El hijo segundo recibe 15,000 euros.
El hijo tercero recibe 33,000 euros.
Step-by-step explanation:
Sea [tex]x[/tex] el capital total del padre y [tex]a,b,c[/tex] son las asignaciones a los hijos mayor, segundo y tercero. A continuación, construimos las ecuaciones matemáticas a partir de lo descrito en el enunciado:
Hijo mayor
[tex]a = \frac{1}{5}\cdot x[/tex] (1)
Hijo segundo
[tex]b = \frac{1}{4}\cdot x[/tex] (2)
Hijo tercero
[tex]c = \left(1-\frac{1}{5}-\frac{1}{4}\right)\cdot x = 33000[/tex] (3)
De (3) tenemos que el capital del padre es:
[tex]x = \frac{33000}{1-\frac{1}{5}-\frac{1}{4} }[/tex]
[tex]x = 60000[/tex]
El padre tenía un capital de 60,000 euros.
Por (1) y (2) determinamos los capitales del hijo mayor y el hijo segundo:
[tex]a = \frac{1}{5}\cdot x[/tex]
[tex]x = 12000[/tex]
El hijo mayor recibe 12,000 euros.
[tex]b = \frac{1}{4}\cdot x[/tex]
[tex]b = 15000[/tex]
El hijo segundo recibe 15,000 euros.
Which expression is equivalent to 32 + 16?
(A) 8(4 + 2)
(B) 8(24 + 8)
(C) 7(4 + 2)
(D) 7(24 + 8)
Answers
Brainiest please!!! :)
answer: (A) 8(4+2)
Step-by-step explanation:
I think so BECAUSE I ADD IT ALL UP
Jayden has $0.56 worth of pennies and nickels. He has a total of 20 pennies and nickels altogether. Determine the number of pennies and the number of nickels that Jayden has.
There are ______ pennies and _______ nickels
Answers
Answer:
there are 7 nickels and 13 pennies
PLEASE HELP ME i DONT KNOW how to do this!
Answers
Answer:
It's b
Step-by-step explanation:
It is b or the second option because -2 is equal or greater than A therefore it is option 2
What is the value of X
What is the value of Y
I will crown u and give you 20 extra points
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
4) 35° and x° are vertical angles, so they are congruent to each other. Therefore, x°=35°. Since y°+y°+35°=180° since they are all supplementary to each other, then y°=72.5° when solved.
5) A is true. Think of two adjacent angles measured 60° and 30° that are next to each other. They add up to 90° as well.
B isn't true. Vertical angles are congruent to each other, not supplementary.
C isn't true. The statement contradicts itself. Complementary angles add up to 90° while supplementary angles add up to 180°
A student was interested in purchasing notebooks in bulk to get ready for school. Three stores were offering packages of the kind of notebook the student wanted. The table below shows the offers from each store. Order the stores from the best deal to the worst deal for the notebooks.
Answers
Plz help
What is the next step in this construction?
A. construct a line perpendicular to x p through point a
B.measure the distance from point A to p
C.construct a line parallel to XP through point a
D. construct a transversal line through points a and X
Answers
Answer:
Construct a transversal line through points A and X. i think im not sure
Step-by-step explanation:
For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?
(A) 0.065 (B) 0.335 (C) 0.350 (D) 0.450 (E) 0.665
Answers
Answer:
0.335
Step-by-step explanation:
1. There is a 30 percent chance of a flight being delayed because of icy weather ,then the probability of being delayed is 0.3 and of being not delayed is 0.7.
2. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem, then the probability of being delayed is 0.1 and the probabilty of not being delayed is 0.9.
3. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem (MP), then the probability of being delayed is 0.05 and the probabilty of not being delayed is 0.95. (See attached probability tree)
Delayed of icy weather - 0.3
Delayed of MP when weather is not icy - 0.7·0.05=0.035
Now, if one flight is selected at random from the airport in January, the probability that the flight selected will have at least one of the two types of delays is
0.3+0.035=0.335
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HELP PLEASE:(
Determine if the triangles are congruent by using HL?
Answers
Answer:
whats hl
Step-by-step explanation:
Find m
70°
55°
80°
90°
Answers
Answer:
70°
Step-by-step explanation:
angle subtended by arc is half of arc
The ratio of small dogs two big dogs at the park is 1: 3 which does not represent this ratio A. 3:9 B. 9:27 C. 2:4 D. 30:90
Answers
C(2.4) does not represent this ratio.
Answer:
2:4
Step-by-step explanation:
i did the test
All Questions Are Above
Answers
Answer:
...
Step-by-step explanation:
2. 5.25, because the radius is half the diameter
3. 3 in because the diameter is 2x the radius
4. i.dk this one sorry
Answer:
2. 5.25in
3. 3 in
4. 81.68 or 82
Step-by-step explanation:
The first two are basically multiplication and division. radius is half the diameter, and diameter is the whole of radius. the circumference is 3.14 or [tex]\pi[/tex] x diameter
so you need to add the radius (13) by itself (13+13) to get the diameter (or 13*2) then multiply by 3.14159. (26*3.14159 = 81.68) and if you need to round its 82.
~R3V0
In ΔSTU, the measure of ∠U=90°, the measure of ∠S=31°, and TU = 77 feet. Find the length of US to the nearest tenth of a foot.
Answers
Answer:
US = 128.15 ft
Step-by-step explanation:
tan 31° = 77/US
0.6009 = 77/US
0.6009US = 77
US = 128.15 ft
Answer:
128.7
Step-by-step explanation:
Choose all of the values for x that are solutions to x < -2.
A.x=0
B. x=2
C. x= -2
D.x=-1/2
E. x= -4
Answers
Calcula el área de este hexágono. Datos: -lados 8 cm² -apotema 3'7cm²
Answers
Respuesta:
88,8 cm²
Explicación:
Consideremos un hexágono regular. Su apotema, la distancia más corta entre el centro del hexágono y uno de sus lados, es 3,7 cm y sus lados miden 8 cm.
Primero debemos calcular su perímetro, que es igual a la suma de sus 6 lados.
Perímetro = 8 cm + 8 cm + 8 cm + 8 cm + 8 cm + 8 cm = 48 cm
Luego, podemos calcular el área del hexágono usando la siguiente fórmula:
Area = Perímetro × Apotema / 2
Area = 48 cm × 3,7 cm / 2 = 88,8 cm²
A right triangle has a base of 6 feet, a height of 4 feet, and a slant height of 9 feet. Find the area. *
Answers
PLEASE HELP WITH GEOMETRY IM STUCK!?}
Answers
Answer:
13.8
Step-by-step explanation:
Recall the trigonometric ratios
Sine = Opposite over Hypotenuse (SOH)
Cosine = Adjacent over Hypotenuse (CAH)
Tangent = Opposite over Adjacent (TOA)
Now lets look back at the question
We are given an angle and its adjacent side length (11) and we need to find the hypotenuse
The hypotenuse and adjacent sides corresponds with the trig function cosine so we will use cosine to solve for x
( remember that cosine = adjacent over hypotenuse )
[tex]cos(37)=\frac{11}{x}[/tex]
step 1 multiply each side by x
[tex]cos(37)*x=xcos(37)\\\frac{11}{x} *x=11[/tex]
now we have [tex]xcos(37)=11[/tex]
step 2 divide each side by cos(37)
[tex]\frac{xcos(37)}{cos(37)} =x\\\frac{11}{cos(37)} =13.77349\\[/tex]
we're left with x = 13.77439
Our last step would be to round to the nearest tenth
We would get that the answer is 13.8
Answer:
G) x = 13.8
Step-by-step explanation:
cos 37° = adj/hyp = 11/x
0.7986x = 11
x = 13.8
What is the domain of this function?
Answers
Answer:
-5, -1, 1, 2, 4
Step-by-step explanation:
The domain includes the x-values of the points. Starting from the left, the points are (-5, -5), (-1, 0), (1, 1), (2, 5), (4, -3).
Take the x-values, and the domain is {-5, -1, 1, 2, 4}.
Idil has a smart phone data plan that costs $25 per month that includes 10 GB of
data, but will charge an extra $20 per GB over the included amount. How much
would Idil have to pay in a month where she used 4 GB over the limit? How much
would Idil have to pay in a month where she used went over by x GB?