Answer:
Step-by-step explanation:
The axis of symmetry is vertical, so the parabola is vertical.
Vertex-form equation for a vertical parabola with vertex (h,k):
y = a(x-h)² + k
axis of symmetry: x = h
Apply your data and solve for h, k, and a.
vertex (-1,7)
h = -1
k = 7
y = a(x+1)² + 7
(0,10) is a point on the parabola
10 = a(0+1)² + 7
a = 3
The equation becomes
y = 3(x+1)² + 7
The Browns scored 13 more points than the Saints. The total of
their scores was 47. How many points did each team score?
Answer:
Saints team scores points = 17
Browns team scores point = 30
Step-by-step explanation:
Let Saints team scores points = x
Browns team scores point = y
As given,
The Browns scored 13 more points than the Saints.
⇒ y = x + 13
Now, given
The total of their scores was 47.
⇒ x + y = 47
⇒x + x + 13 = 47
⇒ 2x = 47 - 13
⇒2x = 34
⇒x= [tex]\frac{34}{2}[/tex] = 17
∴ we get
Saints team scores points = x = 17
Browns team scores point = y = x + 13 = 17 + 13 = 30
Answer:
30 , 17
Step-by-step explanation:
browns have x + 13
saints have y
x+13 + x+y = 47
2x = 34
x=17
17 + y = 47
y=30
The perimeter of an equilateral triangle is 114mm.
State the length of one of its sides
Answer:
Since an equilateral triangle has all three side equal then one of its side is 38mm
The length of one of the sides of the triangle is 38 mm.
What is Perimeter?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Given that all of the sides of an equilateral triangle are equal in length, we may calculate the length of a side by dividing the perimeter by the triangle's total number of sides, which is 3.
As a result, the equilateral triangle's one side has the following length:
114 mm / 3 = 38 mm
Therefore, the equilateral triangle's sides are each 38 mm long.
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Hi Brainly users! I have an 8th-grade math problem for you! Please see the screenshot! :)
Answer:
A) [tex]32\pi[/tex]
Step-by-step explanation:
First, solve the volume of the cylinder. It's about [tex]87.96[/tex]
Next, find the volume of the cone. It's about [tex]12.57[/tex]
Thus, the total volume is [tex]87.96[/tex] [tex]+[/tex] [tex]12.57[/tex], which is about [tex]100.53[/tex]
[tex]100.53[/tex] in terms of [tex]\pi[/tex] is A) [tex]32\pi[/tex]
Hope I helped!
Fred went to an arcade to play video games. He paid $2 for every 11 tokens he bought. He spent a total of $16 on tokens. Which equation can be used to determine t, the number of tokens Fred bought?
Answer:
D
Step-by-step explanation:
Since there are two types of values here: tokens and dollars, we will need to use the same value across numerators and denominators in the ratio.
Choice D has 11 tokens over $2 equals to t tokens over $16. In both fractions the numerator is tokens and denominator is dollars.
Theres the picture! Thank you.
Answer:
B. x = 8√3 ≈ 13.86; y = 8
Step-by-step explanation:
✔️Find x using trigonometric ratio:
Reference angle = 60°
opposite = x
Hypotenuse = 16
Thus:
Sin(60) = x/16
16*sin(60) = x
16*√3/2 = x
8√2 = x
x = 8√3 ≈ 13.86
✔️Find y using Pythagorean Theorem:
y² = 16² - (8√3)²
y² = 256 - 192 = 64
y = √64
y = 8
What is the probability of flipping 4 coins and having exactly three of them land on tails?
A) 1/16
B) 2/16
C) 3/16
D) 4/16
A right triangle has one leg that is 4 more than twice the other. The area of the triangle is 35. Find the length of the sides.
Answer:
one leg = 5
other leg = 14
Step-by-step explanation:
let 'x' = length of shorter leg
let '2x + 4' = length of longer leg
A = 1/2bh
35 = 1/2x · 2x + 4
35 = x² + 4
x² + 4 - 35 = 0
(x + 7)(x - 5) = 0
x = -7 and x = 5
We can eliminate -7 as an answer since a length cannot be negative
Answer:
The shorter leg = 5
The longer leg = 14
The hypotenuse = 14.866.....
Step-by-step explanation:
if we represent the smaller leg as "x" we firstly represent the longer leg as...
Longer leg = 2x + 4
(We can do this based on the question)
Now we need to undersstadn t in a right angle triangle the legs can be used as a height and base. So we can make the following equation.
[tex]A_{triangle} = \frac{bh}{2}[/tex]
Substitute the lengths of the legs as based and height and get...
[tex]A_{triangle} = \frac{(2x + 4)(x)}{2}[/tex]
[tex]35 = \frac{2x^{2} + 4x}{2}[/tex]
[tex]35 = x^{2} + 2x[/tex]
[tex]35 = x(x + 2)[/tex]
From here we can see that x = 5.
Therefore the lengths are as follows...
The shorter leg = x = 5
The longer leg = 2(5) + 4 = 14
The hypotenuse = [tex]\sqrt{5^{2} + 14^{2} }[/tex]
The hypotenuse = [tex]\sqrt{5^{2} +14^{2} }[/tex]
The hypotenuse = 14.866.....
What is the factors for x squared plus 5x - 6
Answer:
=[tex](x-1)(x+6)[/tex]
Step-by-step explanation:
Answer:
[tex]x^{2} +5x-6=(x-1)(x+6)[/tex]
Step-by-step explanation:
A woman can bicycle 80 miles in the same time as it takes her to walk 16 miles. She can ride 8 mph faster than she can walk. How fast can she walk
Answer:
she can walk 2 miles mph
Step-by-step explanation:
because 80 ÷8=10
16÷8=2
Answer:
2 miles p/h.
Step-by-step explanation:
16 miles walk = 80miles bike = 16/80 = 0.2 / 1
0.2 / 1 = 1 / 5 = 2 / 10 as we see 8 difference as we continue the pattern.
2 miles per hour is our answer
What is an equation of the line that passes through the points (1,6) and (1, 2)?
Answer:
x=1
Step-by-step explanation:
Since both lines have 1 as it x value, x=1 is the line
Please help asap!
The graphs of linear functions f and g are shown.
Enter the solution to the equation f(x) = g(x).
9514 1404 393
Answer:
x = -3
Step-by-step explanation:
The solution to the equation ...
f(x) = g(x)
is the x-value where the functions have equal values. That is the x-coordinate of the point where the graphs intersect. The intersection point is (-3, 5), so the solution to the equation is x = -3.
Did I use the right properties to justify each step? 100 points!!
Answer:
You are right I am pretty sure
Jane bought a new car for $30,000. A function that models the value of Jane’s car after t years is v(t)= 5(30,000) (0.85)t . In how many years will the car be worth less than half of what Jane paid for it?
a 2
b 3
c 4
d 5
Answer:
c
Step-by-step explanation:
Answer: C.) 4
-plug 4 in for t
-solve the equation
7. Washcloths were selling for $1.88 each. If 14 1/4 dozen cloths were sold, what was the retail value of the total sales
Answer:
The retail value of the total sales was $311.48
Step-by-step explanation:
14 1/4 dozen cloths were sold
This means that the total number of cloths sold was:
[tex]14*12 + 12*\frac{1}{4} = 168 + 3 = 171[/tex]
Each for $1.88
So the retail value of total sales was.
$1.88*171 = $311.48
The retail value of the total sales was $311.48
what is the simplifed form of the fraction below?
24/30
Answer:
it is 4/5 because you have to divide by 6
For the following exercise, determine the range (possible values) of the random variable, X. A batch of 300 machined parts contains 10 that do not conform to customer requirements. The random variable is the number of parts in a sample of 5 parts that do not conform to customer requirements. Choose the correct answer.
a. The range of X is {0,1,2,3,4,5,6}
b. The range of X is {0,1,2,3,4,5,6}
c. The range of X is {0,1,2,3,4,5,6}
d. The range of X is {0,1,2,3,4,5,6}
e. The range of X is {0,1,2,3,4,5,6}
Answer:
{0,1,2,3,4,5}
Step-by-step explanation:
We are given that
Total number of machine parts=300
Number of defective machine parts=10
Total number of good machine parts=300-10=290
Sample contain parts that do not conform to customer requirement=5
X is a random variable which is the number of parts in a sample of 5 parts that do not conform to customer requirements.
We have to find the correct answer.
The sample contain 5 parts
Therefore, the possible values of random variable X
0,1,2,3,4,5
Hence, the range of X is given by
{0,1,2,3,4,5}
cuales son las fuentes primarias
Answer:
Testigos de primera mano
Answer:
Algunos tipos de fuentes primarias son:
*Documentos originales
*Diarios
*Novelas
*Instrumentos musicales
*Minutas
*Entrevistas
*Poesia
*Apuntes de investigacion
*Noticias
*Fotografias
*Autobiografias
*Cartas
*Discursos
ESPERO QUE TE HAYA SIDO DE AYUDA.
Without graphing, describe the end behavior of the graph of the function.
f(x) = 1 - 2x2-x
Answer:
A
Step-by-step explanation:
When doing function behaviors it would be really helpful if you memorized the picture i've attached below
We can see that we have a negative leading coefficent and an odd degree which means that as x approaches -∞ it's positive and as x approaches ∞ it's negative
This means that the answer is A
of the last 14 contestants on a game show, 7 qualified for the bonus round. Considering this data,
how many of the next 12 contestants would you expect to qualify for the bonus round?
contestants
Help Me Please! I will give 40 points!!
Who is correct?
4^m x 4^5/ 4^n
Cung Pi simplifies to: 4^(m-n+5)
Thuy le simplifies it to: 4^m(n-5)
A. Cung Pi is correct
B. Thuy Le is correct
C. Both of them have equivalent expressions
D. Neither of them are correct
A. Cung Pi is correct. I hope this helps!
Is this possible?
a=b
a²=ab
a²-b²=ab-b²
(a+b)(a-b)=b(a-b)
(a+b)=b
a+a=a
2a=a
2=1
Answer:
No. It is not possible.
Step-by-step explanation:
No, that is not possible.
The problem lies in that [tex]a=b[/tex].
Looking at your fourth line of work, [tex](a+b)(a-b)=b(a-b)[/tex]
You divided by [tex](a-b)[/tex].
And because [tex]a=b[/tex], [tex]a-b=0[/tex]
This means that when you divided by [tex](a-b)[/tex] you divided by zero, which cannot happen.
A server at a restaurant works 5 hours on a weekday and 8 hours on a weekend day. Use the expression to find the number of hours the server works on 4 weekdays and 2 weekend days.
Answer:
20 weekday hours and 16 weekend hours
Step-by-step explanation:
all u do is take 5 hours and multiple them by 4 weekdays so it gives u 20 hours and then u multiple 8 hours by 2 which is 16 hours
Enter the ordered pair that is the solution to the system of equations graphed below.
y = 1/3x +4
y = 2x - 1
Answer:
Step-by-step explanation:
The solution is the coordinates of the point where the lines intersect: (3,5)
Find the value of x. Round to the nearest tenth. x=
27 , 34 , 11 ,
Answer:
x = 13.5
Step-by-step explanation:
x = 11 · (sin 34°) / sin 27°
Answer:
120
Step-by-step explanation:
180-27-34=119
119 round up to nearest 10 = 120
You look up at 1 but you are not soposed to answer the question by looking at 1, if you have nearest 10 to round then always look at the units.
Always look at the second digit of the nearest number that you would round up.
Example:
round 560 to the nearest 100.
The answer would be 600 because 0-4 goes down and 5-9 goes up,
and in this number 5 goes up so the answer would be rounded up.
If the question said round 560 to the nearest 10 then the answer would be the same because the second digit is 0 and 0 goes down so it does not make any difference. If the second digit goes down then you do not need to change your answer the answer would be the same as the question number.
What does tan^2(x) mean
Answer:
Step-by-step explanation:
When the exponent is attached to the trig function like that, its essentially the same thing as taking the entire function to that power.
tan^2(x) = (tanx)^2
In a MBS first year class, there are three sections each including 20 students. In the first section, there are 10 boys and 10 girls, in the second section there are 15 boys and 5 girls, and in the third section, there are 12 boys and 8 girls. Five students are selected at random from each group to form committee of 15 students. What is the probability that all the 15 students selected are girls?
Answer:
[tex]3.52 \times 10^{-9} = 3.52 \times 10^{-7}\%[/tex] probability that all the 15 students selected are girls
Step-by-step explanation:
The selection is from a sample without replacement, so we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
All girls from the first group:
20 students, so [tex]N = 20[/tex]
10 girls, so [tex]k = 10[/tex]
5 students will be selected, so [tex]n = 5[/tex]
We want all of them to be girls, so we find P(X = 5).
[tex]P_1 = P(X = 5) = h(5,20,5,10) = \frac{C_{10,5}*C_{10,5}}{C_{20,5}} = 0.0163[/tex]
All girls from the second group:
20 students, so [tex]N = 20[/tex]
5 girls, so [tex]k = 5[/tex]
5 students will be selected, so [tex]n = 5[/tex]
We want all of them to be girls, so we find P(X = 5).
[tex]P_2 = P(X = 5) = h(5,20,5,5) = \frac{C_{5,5}*C_{15,5}}{C_{20,5}} = 0.00006[/tex]
All girls from the third group:
20 students, so [tex]N = 20[/tex]
8 girls, so [tex]k = 8[/tex]
5 students will be selected, so [tex]n = 5[/tex]
We want all of them to be girls, so we find P(X = 5).
[tex]P_3 = P(X = 5) = h(5,20,5,8) = \frac{C_{8,5}*C_{12,5}}{C_{20,5}} = 0.0036[/tex]
All 15 students are girls:
Groups are independent, so we multiply the probabilities:
[tex]P = P_1*P_2*P_3 = 0.0163*0.00006*0.0036 = 3.52 \times 10^{-9}[/tex]
[tex]3.52 \times 10^{-9} = 3.52 \times 10^{-7}\%[/tex] probability that all the 15 students selected are girls
Write the ratios for sin X, cos X, and tan X. Use the / for a fraction.
Answer:
Step-by-step explanation:
From the right triangle attached in the picture,
sine ratio for the angle X,
[tex]\text{sinX}=\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]=\frac{YZ}{XZ}[/tex]
[tex]=\frac{21}{29}[/tex]
cosine ratio for the angle X,
[tex]\text{cosX}=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]=\frac{XY}{XZ}[/tex]
[tex]=\frac{20}{29}[/tex]
tang ratio for the angle X,
[tex]\text{tanX}=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
[tex]=\frac{21}{20}[/tex]
A company that advertises on websites uses the formula below to estimate the number of people who will click on one of its advertisements, where c is the number of clicks on that advertisement, t is the length of time the advertisement is displayed (in days), and d is the distance from the top of the website to the advertisement (in inches).
c = 152t - 44d
How many clicks would the company estimate to receive from its advertisement that is displayed 7 inches from the top of the website for 18 days? A. 272 B. 2,692 C. 2,428 D. 2,729
Answer:
C. 2428
Step-by-step explanation:
c=152t-44d
Its given that,
t=18, d=7
substituting
c=152(18)-44(7)=2428
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What is the volume of the figure below, in cubic centimeters?
2 rectangular prisms. One prism has a length of 12 centimeters, width of 9 centimeters, and height of 2 centimeters. The other prism has a length of 10 centimeters, width of 9 centimeters, and height of 8 centimeters.
756
936
1,008
1,080
The volume of the rectangular prism is V = 936 cm³
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
To find the volume of the figure, we need to calculate the volumes of the two rectangular prisms separately and then add them together.
The volume of a rectangular prism is given by the formula:
Volume = length x width x height
For the first prism:
Length = 12 centimeters
Width = 9 centimeters
Height = 2 centimeters
Volume of first prism = 12 cm x 9 cm x 2 cm = 216 centimeters³
For the second prism:
Length = 10 centimeters
Width = 9 centimeters
Height = 8 centimeters
Volume of second prism = 10 cm x 9 cm x 8 cm = 720 centimeters³
Now, we add the volumes of the two prisms together to get the total volume of the figure:
216 cubic centimeters + 720 cubic centimeters = 936 centimeters³
Hence , the rectangular prism has volume of 936 cm³
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Can someone explain this to me? I really need help. Thx!
Answer:
3 to the 4th power.
Step-by-step explanation:
Basically, here 3 to the 3rd power is 27. Multiplying it by 3 is only adding another power, making it 81, which is the same answer to 3 to the 4th power if that makes sense.