Step-by-step explanation:
PEMDAS rule
3 -15 = -12
-20 - 4 = -24
-5 + 16 + 1 = 12
= 12/6 which = 2
15 + 5 = 20
35/6 = 5 5/6
Find the vertex of f(x) = 3(x-7)(x+5)
Please show your work.
^^ I’ve been having a bit of trouble with this question :( although it’s simple quadratics is not my strong suit
Answer:
The vertex is at (1, -108).
Step-by-step explanation:
We have the function:
[tex]f(x)=3(x-7)(x+5)[/tex]
And we want to find its vertex point.
Note that this is in factored form. Hence, our roots/zeros are x = 7 and x = -5.
Since a parabola is symmetric along its vertex, the x-coordinate of the vertex is halfway between the two zeros. Hence:
[tex]\displaystyle x=\frac{7+(-5)}{2}=\frac{2}{2}=1[/tex]
To find the y-coordinate, substitute this back into the function. Hence:
[tex]f(1)=3((1)-7)((1)+5)=3(-6)(6)=-108[/tex]
Therefore, our vertex is at (1, -108).
Answer:
vertex (1, -108)
Step-by-step explanation:
First find the zeros
f(x) = 3(x-7)(x+5)
0 = 3(x-7)(x+5)
Using the zero product property
x-7 = 0 x+5 = 0
x = 7 x = -5
The x coordinate of the vertex is the average of the zeros
(7+-5)/2 = 2/2 =1
To find the y coordinate, substitute the x coordinate into the equation
y = 3(1-7)(1+5) = 3(-6)(6) = -108
If x + 10 = 70, what is x?
Answer:
x=60
Step-by-step explanation:
First, you subtract 10 from both sides. Your final answer is 60.
How many fives makes 6 tens
Answer:
12 fives
Step-by-step explanation:
6 tens is 60, so 60÷5 is 12
Answer:
12
Step-by-step explanation: 60 divided by 12 is 5 and 12 times 5 is 60 so there you go.
Date
Prove that sintheta sec theta+costheta cosec theta=
2 cosec 2theta
Answer:
See Below.
Step-by-step explanation:
We want to prove that:
[tex]\displaystyle \sin\theta\sec\theta+\cos\theta\csc\theta = 2\csc2\theta[/tex]
Let secθ = 1 / cosθ and cscθ = 1 / sinθ:
[tex]\displaystyle \frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta}=2\csc2\theta[/tex]
Creat a common denominator. Multiply the first fraction by sinθ and the second by cosθ. Hence:
[tex]\displaystyle \frac{\sin^2\theta}{\sin\theta\cos\theta}+\frac{\cos^2\theta}{\sin\theta\cos\theta}=2\csc2\theta[/tex]
Combine fractions:
[tex]\displaystyle \frac{\sin^2\theta + \cos^2\theta}{\sin\theta\cos\theta}=2\csc2\theta[/tex]
Simplify. Recall that sin²θ + cos²θ = 1:
[tex]\displaystyle \frac{1}{\sin\theta\cos\theta}=2\csc2\theta[/tex]
Multiply the fraction by two:
[tex]\displaystyle \frac{2}{2\sin\theta\cos\theta}=2\csc2\theta[/tex]
Recall that sin2θ = 2sinθcosθ. Hence:
[tex]\displaystyle \frac{2}{\sin2\theta}=2\csc2\theta[/tex]
By definition:
[tex]\displaystyle 2\csc2\theta = 2\csc2\theta[/tex]
Hence proven.
PLS HELP (algebra 1)
solve 4( -15x - 2) + 8
Answer:
-60x
Step-by-step explanation:
Helpppp ,I will mark you brainlist
Answer:
Okay
Step-by-step explanation:
Does every integer have a successor?
Answer:
Yes every integer has a successor and a predecessor
Step-by-step explanation:
help please
1 2 3 4 5 6 7 8 9 10
Answer:
place it 2 3 4 5 6 7 8 9 10 1 then is come 18
Answer:
2 3 4 5 6 7 8 9 10 1 then come 18
Which set of numbers includes only integers?
a.)Negative 5, negative 3 and one-fourth, 1, one-eighth
b.)Negative 3, negative 2, 2, 3
c.)Negative 6, negative 4, negative 2, negative one-half
d.)One-half, two-thirds, StartFraction 6 Over 7 EndFraction, 0
Answer:
a
Step-by-step explanation:
in integer there will negative ,positive or rational number
Thank you very much you can help me with the others that I am uploading to my profile and there is more in case you can please
Answer: y = 2x + 20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
Step-by-step explanation:
Because it's time, it don't have to be just integers. Seconds are fractions of minutes.(0,20) is the y-intercept and there will be no smaller y-values because x(time) cannot go negative.He goes at a rate of a problem per 2 minutes, so 2 is his slope.Answer:
The second one is the answer.
Step-by-step explanation:
Objective: Linear Equation Problems.
Let model the equation given to us.
Vlad spent 20 minutes on his homework already and he complete x math problems every 2 minutes so we represent this as
[tex]y = 2x + 20[/tex]
X can be any real number greater than or equal zero because time isnt negative so anything below zero is wrong.
Y can be any real number but however since Vlad spent 20 mins on his homework already, he must spend over or equal to 20 minutes completing the total homework.
The second one is the answer
What is the median of the data set given below?
19, 22, 46, 24, 37, 16, 19,33
A. 24
B. 23
C, 19
D. 27
Answer:
B. 23
Step-by-step explanation:
16, 19, 19, 22, 24, 33, 37, 46
Median = n/2
= 8/2
= 4//
(22 + 24)÷2 = 46 ÷ 2
= 23
Find slope if a line pass through the original and (3,2)
heyy im not sure if you meant origin instead of original but the origin would be (0,0)
Answer:
2/3
Step-by-step explanation:
the slope form equation is : y2 - y1/ x2-x1 (aka change in y divided by change in x)
so it would be 2-0/ 3-0 = 2/3
the slope is 2/3
A high school held an election for class president. Exactly 1,000 votes were cast and they were all for either Gillian or Clive. Gillian received 100 more votes than Clive. What percent of the 1,000 votes were for Gillian?
Answer: 60%
1000÷2=500
Clive: 500-100= 400
Gillian: 500+100= 600 (Because Gillian has 100 more votes than Clive)
[tex] \frac{600}{1000} \times 100\% = 60\%[/tex]
If Gillian received 100 more votes than Clive, Gillian received 55% of the 1,000 votes.
To determine the percentage of votes for Gillian out of the total 1,000 votes, we need to calculate the proportion of votes that Gillian received.
Given that Gillian received 100 more votes than Clive, we can set up the equation:
Votes for Gillian = Votes for Clive + 100
Let's denote the number of votes for Clive as C. Therefore, the number of votes for Gillian is C + 100.
The total number of votes is 1,000, so we have the equation:
C + (C + 100) = 1,000
Simplifying, we find:
2C + 100 = 1,000
2C = 900
C = 450
Therefore, Clive received 450 votes and Gillian received 450 + 100 = 550 votes.
To calculate the percentage of votes for Gillian, we divide her votes by the total votes and multiply by 100:
(550 / 1,000) * 100 = 55%
To learn more about percentage click on,
https://brainly.com/question/13228217
#SPJ2
Thanks to whoever decides to help
[tex]\displaystyle\ S=Vt=> V=\frac{S}{t }[/tex] in our case, S is d(h) ; and t is t (x), then [tex]\displaystyle\ V=\frac{d(x)}{t(h)}=\bigg(\frac{d}{t} \bigg )(h)=\frac{6h^2-h-1}{2h-1} =\frac{2h^2-h+4h^2-1}{2h-1} =\\\\\\\\\frac{h\underline{(2h-1)}+\underline{(2h-1)}(2h+1)}{2h-1} =\frac{(3h+1)(2h-1)}{2h-1} =\boxed{3h+1}\\\\\\Answer: \boxed{V=3h+1}[/tex]
Can someone help me with this math homework please!
Answer:
#1: (D) all real numbers greater than or equal to -3
#2: (D) It is not a function because there are two different y-values for a single x-value
#3: (A) all real numbers
#4: (B, C)
#5: (B) {y | y = -9, -3, 0, 5, 7}
Step-by-step explanation:
Question 1:
The domain of the function is all the input values, or the x values. The graph extends all the way to right infinitely. However, to the left, it ends at -3. Because the dot is filled, that means the domain INCLUDES -3. So it's (D).
Question 2:
By definiton, a function is a relation between a set of inputs and a set of outputs. However, each input only has ONE output.
If you noticed, there are two points: (4, 4) & (4, -2)
There are two different y-values, 4 & -2, for one x-value, 4.
Question 3:
The graph extends infinitely both directions, so it's all real numbers.
Question 4:
The amount of water DEPENDS on the amount of rice you put in, so the amount of water is the dependent variable. The rice doesn't depend on the amount of water, so it's the independent variable. (By the way, it's not the last option because you need two options)
Question 5:
The range of the function is the y values. So you are only going to put the y values from the coordinate points in the range. Thus, (B) is the answer.
Hope it helps (●'◡'●)
In the past year Maya watched 34 movies that she thought were very good. She watched 40 movies over the whole year. Of the movies she watched, what percentage did she rate as very good?
Answer:
90 percent
Step-by-step explanation:
the fraction is 90/100 so the percentage is 90%
Which polynomial function has x-intercepts –1, 0, and 2 and passes through the point (1, –6)
Answer:
y=3x(x+1)(x-2)=3x^3-3x^2-6x
Step-by-step explanation:
The polynomial function can be written in the form:
y=a(x-x1)(x-x2)(x-x3)
where
x1=-1
x2=0
x3=2
Therefore
y=a(x+1)(x-0)(x-2)=a(x^2+x)(x-2)=a(x^3-x^2-2x)
To find the value for "a" we use the info about the line passing in (1,-6):
-6=a(1-1-2)
a=3
y=3x(x+1)(x-2)=3x^3-3x^2-6x
Answer:
f(x) = 3x3 - 3x2 - 6x
Good luck! :D
Step-by-step explanation:
Please someone quick answer this!!!
To find a probability you take the specific parameters divided by the entire set of possibilities.
For example, the specific parameter here is that the drink must be a medium, (no matter the temperature). So, we would add 48 and 12 to get 60.
And we know that the total number of orders is 100.
So, we should divide 60 by 100, and we get 60%.
If the ordered pairs(a,3)and (2,b) belong to the set {(x,y):y=2x-3},find the value of a,b
Answer:
a=3
b=1
Step-by-step explanation:
3=2a-3 => a=3
b=2*2-3 = 1
a ratio equivalent to 10:15
Answer:
3/2, 6/4, 9/6, 12/8, 15/10, 18/12, 21/14, 24/16, 27/18, 30/20, 33/22, 36/24, 39/26, 42/28, 45/30, 48/32, 51/34, 54/36, 57/38, 60/40
Step-by-step explanation:
Answer:
20 : 30
Step-by-step explanation:
Given Ratio :-
10 : 15Equivalent Ratio :-
10 : 15 10 / 15 10 * 2 / 15 *2 20 / 30 20 : 30Charity and her family are going on vacation to visit family over the summer. Their flight will last 6.94 hours. Charity says, "If we round this number, it is a seven-hour flight." Her sister says, "I think you're wrong. If we round it, it is 6.9-hour flight." Who is correct? Explain your reasoning.
Answer:
Charity is more correct
Step-by-step explanation:
Flight time = 6.94 hours
Charity estimation = 7 hours
Her sister's estimation = 6.9 hours
Charity is more correct if we are to round to the nearest whole hour
6.94 hours is approximately 7 hours
Her sister is only correct if we are to round up to 1 decimal place
6.94 hours is approximately 6.9 hours to 1 decimal place
solve the following simultaneous linear equations by the substitution method.
2p + 3q = 10
p - 2q = -2
Answer:
p = 2 and q = 2
Step-by-step explanation:
hope this helps please like and mark as brainliest
What is the gradient of the graph shown? In its simplest form
Answer:
1
Step-by-step explanation:
the line passes point (-3,0) abd (0, 3)
so, the gradient = (3-0)/(0+3) = 3/3 = 1
Find the length of the mid segment (median)
Answer:
13
Step-by-step explanation:
Median of a trapezoid = sum of 2 bases divided by 2
Bases = 10 and 16
Median = (10 + 16)/2
10 + 16 = 26
26/2 = 13
Median = 13
Six liters of paint will cover 50 square meters. How many square meters will nine liters cover?
Answer:
75 m²Step-by-step explanation:
Six liters of paint will cover 50 square meters.
6L ⇒ 50m²
then,
1L ⇒ 50/6 m²
9L ⇒ 50 × [tex]\frac{9}{6}[/tex] m²
⇒ 75 m²
if you were pouring juice into a cylindrical cup with a 2 inch radius and height of 8 inches. you want to fill it exactly half full, how many cubic inches of juice would you pour
Answer:
You would pour 50.3 in^3 of juice
Step-by-step explanation:
The term ‘cubic’ indicates volume
so in the context of this question, we are to calculate the volume of the cylinder, then we divide by 2
Mathematically, we have the volume of the cylinder as;
V = pi * r^2 * h
r = 2 inch
h = 8 inch
Since we are dividing the volume by 2 (exactly half full)
V = 1/2 * pi * 2^2 * 8
V = 50.3 in^3
Can someone help me with this math homework please!
Answer: h = 14
Step-by-step explanation:
7h-5(3h-8)-56 = -128
7h -15h+40-56 = -128
or, -8h-16= -128
or, -8h = -128 + 16
or, -8h = -112
or, 8h = 112
or, h = 112/8
so, h = 14
Answer:
h = 14
Step-by-step explanation:
We are going to use basic algebra to solve this equation.
First, let's isolate the h variables by moving -56 to the other side:
7h - 5(3h - 8) - 56 = -128
(add 56 to both sides)
7h - 5(3h - 8) = -72
Next, let's distribute the -5 to (3h - 8) by separating it from the equation then adding it back:
7h - 5(3h - 8) = -72
Separation:
-5(3h - 8) --> (-5*3h) + (-5*-8) --> (-15h) + (40)
-15h + 40
Adding it back in:
7h -15h +40 = -72
Next, let's simplify it down by adding like terms, meaning adding 7h & -15h:
7h -15h +40 = -72
(add 7h & -15h)
-8h + 40 = -72
Now we're going to move the 40 to the other side but subtracting 40:
-8h + 40 = -72
(subtract 40 to both sides)
-8h = -112
Finally, we're going to divide both sides by -8
-8h = -112 --> h = 14
The answer is h = 14
(You can double check by plugging 14 into the equation and see if it equals -128, which it does, so it's correct :-) )
Hope it helps (●'◡'●)
5 tons of sand cost $7,200.00. What is the price per pound?
Answer:
$0.72 per pound
Step-by-step explanation:
1 ton = 2000
5 tons = 10000
10000 lb = $7200
7200/10000 = 0.72
0.72 dollars a pound
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
What is the total value of digit 7 in the number 32.8794
Answer:
hundredth
Step-by-step explanation:
numbers after the decimal point start counting from
tenth
hundredth
Answer:
0.07 or 7 hundredths
Step-by-step explanation:
(12.3456)- I'll use this as my example
1-tens place
2-ones place
3- tenths place
4= hundredths place
5-thousandths place
6- im pretty sure its the 10 thousandths place
Una torre de 28.2 m de altura esta situada a la orilla de un rio, desde lo alto del edificio el ángulo de depresión a la orilla opuesta es de 25.2°. Calcular el ancho del río
Answer:
El ancho del río es 59.9 metros.
Step-by-step explanation:
El ancho del río lo podemos calcular con la siguiente relación trigonométrica asumiendo que la torre forma un triángulo rectángulo con el río:
[tex]tan(\theta) = \frac{CO}{CA}[/tex]
En donde:
CA: es el cateto adyacente = Altura de la torre = 28.2 m
CO: es el cateto opuesto = ancho del río =?
θ: es el ángulo adyacente a CA
Dado que el ángulo de depresión (25.2°) está ubicado fuera de la parte superior de la hipotenusa del triángulo que forma la torre con la orilla opuesta del río, debemos calcular el ángulo interno (θ) como sigue:
[tex]\theta = (90 - 25.2)^{\circ} = 64.8 ^{\circ}[/tex]
Ahora, el ancho del río es:
[tex]CO = tan(\alpha)*CA = tan(64.8)*28.2 = 59.9 m[/tex]
Por lo tanto, el ancho del río es 59.9 metros.
Espero que te sea de utilidad!
