Answer:
[tex](-2,\, 4)[/tex].
Step-by-step explanation:
To find the vertex of this parabola, start by rewriting it in the vertex form [tex]f(x) = a\, (x - h)^2 + k[/tex].
Start with the original expression:
[tex]f(x) = (x + 2)^2 + 4[/tex].
Note that in the vertex form, the sign in front of [tex]h[/tex] should be a minus. However, in [tex]f(x) = (x + 2)^2 + 4[/tex], the sign in front of [tex]2[/tex] is a plus. Since adding
[tex]f(x) = (x - (-2))^2 + 4[/tex].
Therefore:
[tex]h = -2[/tex],[tex]k = 4[/tex].Hence, [tex](-2,\, 4)[/tex] is the vertex of this parabola.
What is the value of x in the equation 3/4(14x+8)-(1/2x+2)=3/8(4-x)-1/4
Answer:
-37/68
Step-by-step explanation:
3/4(14x+8)-(1/2x+2)=3/8(4-x)-1/4
(21/2x+6)-(1/2+2)=(3/2x-3/8)-1/4
(21/2x-1/2x)+(6-2)=3/2x-3/8-1/4
10x+4=3/2x-5/8
37/8=-17/2x
37/8 (2)=-17/2x(2)
37/4=-17x
37/68=-x
-37/68=x
The product of two irrational numbers is rational.
Answer:
It can be both rational and irrational.
Step-by-step explanation:
The difference of a number and 2 is
_1
3
Answer:
-5/3
Step-by-step explanation:
Let x be the unknown number
2-x = 1/3
Subtract 2 from each side
2-x-2 = 1/3 -2
x = 1/3 -2
Get a common denominator
x = 1/3 - 2 *3/3
x = 1/3 -6/3
x = -5/3
Answer:
5/3
Step-by-step explanation:
2 - n = ⅓
n = 2 - ⅓
n = (2×3 - 1)/3
n = 5/3
step by step plz
3x^2 + 16x + 5
Answer:
3x^2 + 16x + 5
= (3x^2 + 15x) + (x + 5)
= 3x(x + 5) + (x + 5)
= (3x + 1)(x + 5)
Hope this helps!
:)
What is the domain of this exponential function? y=2x
Answer:
x∈R
Step-by-step explanation:
[tex]y=2^{x}[/tex]
2>0
The domain is all real numbers.
x∈R
A college conducted a survey of randomly selected freshmen about their choice of major. The table shows the results of the survey. English 50. Science 35. Engineering 40. Business 45. Education 60. Undecided 50. Other 20. Which inference about all freshmen at this collage is best supported by this information?
Answer:B
Step-by-step explanation:
Answer:b
Step-by-step explanation:
For which equations below is x = -3 a possible solution? Select three options.
|x] = 3
1x1 = -3
1x1 = 3
|-x] = -3
-[x] = -3
Answer:
|x|=3, |-x|=3 and - |x|=-3
Step-by-step explanation:
May I please have Brainliest?
Stay safe!!!!!!!!!!!!
Answer:
What he said hope this helps
Step-by-step explanation:
Please help its in math
Answer:
989 in^2
Step-by-step explanation:
The surface area of the larger cube is
SA = 5 s^2 because she will stain all the sides but the bottom one
SA = 5 * 11^2 = 5*121 = 605
The surface area of the smaller cube is
SA = 6s^2 since she will stain all sides
SA = 6* 8^2 =6*64 =384
Add both surface areas together
605+384
989
Answer:
989 square inches
Step-by-step explanation:
Let's start by finding the surface area of the bottom cube. It has six sides with side length 11, meaning that each side has area 11^2=121. Multiplying this by 5(since she's not staining the bottom), you get 605. For the second sphere, you can calculate this with the expression 6 * 8^2=384. Adding these together, you get a total surface area of 989 square inches. Hope this helps!
The names of 11 boys and 9 girls from your class are put into a hat. What is the probability that the first two names chosen will both be girls?
Show work please and Thanks
Answer:
18/95
Step-by-step explanation:
There are a total of 20 names, 9 of which are girl names.
The probability that the first name is a girl name is 9/20.
Since there's one less girl name in the hat, there are now a total of 19 names, 8 of which are girl names. So the probability that the second name is a girl name is 8/19.
The total probability is (9/20) (8/19) = 18/95.
Find the missing measurement. Photo attached
Answer:
Height Length: ( About ) 3.3 yards; Option B
Step-by-step explanation:
~ We are given the Area of this triangle, so let us apply the area of a triangle formula 1/2 * base * height ~
The base is known the be 4.1 yards, the Area 6.8 yards^2, so let us substitute these values into the formula for a triangle as to solve for height. At the same time let us declare x ⇒ height of the triangle:
6.8 = 1/2 * 4.1 * x,
6.8 = 2.05 * x,
x = 6.8/2.05,
Height Length: ( About ) 3.3 yards
Linda is making a line plot of the data below. 11.25, 12.5, 11.25, 14.125, 10.5, 11.25, 12 Which line plot represents the data correctly? A. Line plot shows a number line from 10 to 15 which is divided into 20 equal parts. 1 dot on 10.5, 3 dots on 11.25, 1 dot on 12, 1 dot on 12.5 and 1 dot on 14.125 is given. B. Line plot shows a number line from 10 to 15 which is divided into 20 equal parts. 1 dot on 10.5, 2 dots on 11.25, 1 dot on 12, 1 dot on 12.5 and 1 dot on 14.125 is given. C. Line plot shows a number line from 10 to 15 which is divided into 20 equal parts. 1 dot on 10.5, 3 dots on 11.25, 1 dot on 12, 1 dot on 12.5 and 1 dot on 13.75 is given. D. Line plot shows a number line from 10 to 15 which is divided into 20 equal parts. 1 dot on 10.5, 3 dots on 11.25, 1 dot on 12 and 1 dot on 14.125 is given.
The plot Line plot shows a number line from 10 to 15 which is divided into 20 equal parts. 1 dot on 10.5, 3 dots on 11.25, 1 dot on 12, 1 dot on 12.5, and 1 dot on 14.125 is given to represent the data correctly.
Linda is making a line plot of the data below.
11.25, 12.5, 11.25, 14.125, 10.5, 11.25, 12.
What is the measurement of 1 foot in inches?
The measurements 12 inches equals 1 foot
The line plot shows a number line from 10 to 15 which is divided into 20 equal parts.
The dot on 10.5, 3 dots on 11.25, 1 dot on 12, 1 dot on 12.5, and 1 dot on 14.125 are given.
If we look, there's a point at 10.5, 3 points at 11.25, a point at 12, a point at 12.5, and finally a point at 14.125.
This covers all the data provided.
Therefore option A is correct.
To learn more about the data plot visit:
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Answer:
I’m sorry I really can’t understand the answers but I think it’s a I did it on my test I have proof down there
Step-by-step explanation:
thanks hope it helps have a nice day
Tia and Ken sold snack bars and magazine subscriptions for the school fundraiser. Tia sold 16 snack bars and 4 magazine subscriptions and raised $132. Ken sold 20 snack bars and 6 magazine subscriptions and raised $190. What was the cost of a snack bar and the cost for a magazine subscription?
Answer:
The value of the snack bar is $ 2 and that of the magazine subscription is 25 $
Step-by-step explanation:
We have a system of two equations and two unknowns, which would be the following:
let "x" be the cost of the snack bar
Let "y" be the cost of the magazine subscription
16 * x + 4 * y = 132
20 * x + 6 * y = 190 => y = (190 - 20 * x) / 6
replacing:
16 * x + 4 * (190 - 20 * x) / 6 = 132
16 * x + 126.66 - 13.33 * x = 132
2.66 * x = 132 - 126.66
x = 5.34 / 2.66
x = 2
for "y":
y = (190 - 20 * 2) / 6
y = 25
Which means that the value of the snack bar is $ 2 and that of the magazine subscription is 25 $
In the right triangle shown, m\angle J = 60^\circm∠J=60 ∘ m, angle, J, equals, 60, degrees and JL = 6\sqrt{3}JL=6 3 J, L, equals, 6, square root of, 3, end square root. How long is JKJKJ, K?
Answer:
[tex]|JK|=3\sqrt{3}[/tex]
Step-by-step explanation:
The diagram of the triangle is drawn and attached,
From trigonometric ratios,
[tex]cos \theta =\frac{Adjacent}{Hypotenuse} \\cos60^\circ =\frac{|JK|}{|JL|}\\ 0.5=\frac{|JK|}{6\sqrt{3} }\\$Cross multiply$\\|JK|=0.5*6\sqrt{3}\\|JK|=3\sqrt{3}[/tex]
Answer:
the proof is in the picture
Step-by-step explanation:
At the state fair, the giant Ferris wheel takes 48 seconds to make one full rotation. The Ferris wheel has a diameter of 60 ft. and the bottom of the wheel is 8 ft. above the ground. If you are the last person on the Ferris wheel and you board at the bottom, which equation below models your height above the ground as a function of time?
Answer: H = 30ft*cos(2*pi*t/48s + pi) + 38ft.
Step-by-step explanation:
We can use a trigonometric function to model this, let's use:
H = A*cos(w*t) +
where A is a constant, w is the frequency, t is time, and h is of the wheel, this is half the diameter plus the distance above the ground:
30ft + 8ft = 38ft.
A is equal to the radius of the wheel, or half the diameter, A = 60ft/2 = 30ft.
we know that the period is 48 seconds, this means that:
cos(w*0) = cos(w*48s) = 1
then w*48s = 2*pi
w = 2*pi/48s
so now function is:
H = 30ft*cos(2*pi*t/48s) + 38ft.
But we also know that, at t= 0, you must be at the bottom of the wheel, so we must ad a phase of pi to the cosine function
H = 30ft*cos(2*pi*t/48s + pi) + 38ft.
So now when t = 0, we have:
H(0) = 30ft*cos(0 + pi) + 38ft. = 8ft.
[tex]\rm H = 30cos \frac{2 \pi t}{48} + 38 \ ft.[/tex] is the obtained equation below model your height above the ground as a function of time.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given data;
A is a constant,
ω is the frequency
t is the passage of time
h is the wheel's height,
d is the diameter
h = d/2
The equation for the SHM is found as;
y = Acosωt
For the given condition the equation is written as;
H = Acosωt
The distance above the ground;
30ft + 8ft = 38ft.
⇒cos(ωt)
⇒cos(w × 48) = 1
⇒ω×48s = 2π
⇒w = 2π/48s
The obtained function is;
[tex]\rm H = 30cos \frac{2 \pi t}{48} + 38 \ ft.[/tex]
We must add a phase of π to the cosine function since we also know that at time t=0, you must be at the bottom of the wheel.
So now when t = 0, we have:
[tex]\rm H(0) = 30ft\times cos(0 + \pi) + 38ft.\\\\\ H(0) = 8 \ ft.[/tex]
To learn more, about equations, refer;
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What is the volume of a sphere whose radius is 6 yards
Answer:
[tex] 904.32 \: {yard}^{3} [/tex]
Step-by-step explanation:
[tex] V_{sphere} = \frac{4}{3} \pi {r}^{3} \\ \\ = \frac{4}{3} \times 3.14 \times {6}^{3} \\ \\ = \frac{4}{3} \times 3.14 \times 216 \\ \\ = \frac{4 \times 3.14 \times 216}{3} \\ \\ = \frac{2,712.96}{3} \\ = 904.32 \: {yard}^{3} [/tex]
Solve the inequality.
5c + 3 ≤ −2
Answer:
c is greater than or equal to -1.
Step-by-step explanation:
Subtract 3 from both sides, divide by 5.
I have attached the work to your problem below.
I hope this helps.
What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)?
O y-4-3(x-1)
0 1-y-3(x-4)
4-4-3(1-x)
1-y, -3(4-x)
Answer:
y-4=3(x-1) A is correct
Step-by-step explanation:
y−y1=m(x−x1) Point slope form
y-4=3(x-1)
Hope this helps! Please mark brainliest :)
Which always yields a cross section that is the same shape and size as the base of the figure
Answer:
a triangular pyramid when sliced parallel to its base
Step-by-step explanation:
what are the steps for this question?
Answer:
1. Add 5 to both sides
2. Divide both sides by 2
3. Take the square root of both sides
4. Subtract 2 from both sides
Step-by-step explanation:
2(x+2)²-5=93
Add 5 to both sides
2(x+2)²=98
Divide both sides by 2
(x+2)²=49
Square root both sides
x+2=7
Subtract 2 from both sides
x=5
Answer:
Let's solve the equation. To do this, we have to get x by itself. Perform the opposite of what is being done to the equation.
1. Add 5 to both sides, since 5 is being subtracted
2(x+2)^2-5=93
2(x+2)^2-5+5=93+5
2(x+2)^2=93+5
2(x+2)^2=98
2. Divide both sides by 2, since 2 is being multiplied
2(x+2)^2=98
2(x+2)^2/2=98/2
(x+2)^2=49
3. Take the square root of both sides, since x+2 is being squared
(x+2)^2=49
√(x+2)^2=√49
x+2=√49
x+2=7
4. Subtract 2 from both sides since 2 is being added
x+2=7
x+2-2=7-2
x=7-2
x=5
Students are voting on the color of T-shirts to wear on their field trip. There are 160 students-65 boys and 95 girls-going or
the field trip. A random sample of students is chosen. Surveying the random sample produced a representative sample of th
population. Which was most likely true of the representative sample?
The representative sample contained all 160 students.
The representative sample contained more boys than girls.
The representative sample contained more girls than boys.
The representative sample contained an equal number of boys and girls.
Answer:
C
Step-by-step explanation:
Because I said so
Will mark as brainliest if correct
Answer:
1.2
Step-by-step explanation:
5*1.2=6
Answer: .9
Step-by-step explanation:
please help...again, i'm tired...still
Answer:
B
Step-by-step explanation:
Since all of the x- coordinates are below -4
What is the distance between (-6. 2) and (8.10) on a coordinate grid?
Answer:
The distance between 2 points is 16.1 units.
Step-by-step explanation:
You have to apply distance formula using coordinates,
[tex]distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
Let (x1,y1) be (-6,2),
Let (x2,y2) be (8,10)
[tex]distance = \sqrt{ {(8 - ( - 6))}^{2} + {(10 - 2)}^{2} } [/tex]
[tex]distance = \sqrt{196 + 64} [/tex]
[tex]distance = \sqrt{260} [/tex]
[tex]distance = 2 \sqrt{65} [/tex]
[tex]distance = 16.1 \: units \: (3s.f)[/tex]
Which point lies on the circle represented by the equation (x + 5)2 + (y − 9)2 = 82?
Answer:
x = −y+45
Step-by-step explanation:
Step 1: Add -2y to both sides.
Step 2: Add 8 to both sides.
Step 3: Divide both sides by 2.
please help 2 questions
Answer:
1) 2002
2) 92
Step-by-step explanation:
1)
First, you need to find the area of the triangular base. The height of the triangle is 7, and the base is 26, meaning that the area is 7*26/2=91. Multiplying this by the length of the prism, you get 2002 cubic meters.
2)
First, you need to find the area of the trapezoidal base. The two bases of the trapezoid have lengths 12 and 11, while the height is 8, meaning that the area is 8*(12+11)/2=92 cubic centimeters.
Hope this helps!
I got 60p and 70p but that doesn't work, so i need help pls. again, pretty simple question but mt brain isn't working
Step-by-step explanation:
let's reffer to:
gumbo (x)
raspberry (y) so,
8x + 9y =14. 3 (1)
6x + 3y = 8.1 (2)
devide (2) by 3
2x + y = 2.7
y = 2.7 - 2x (3)
substitute 3 in 1
8x + 9(2.7 - 2x) = 14.3
8x + 24.3 - 18x = 14.3
10 x = 10
x = 1 (ANS)
and y = 0.7 (ANS)
Answer:
Hello There the correct answer to this is The first one is 1029.6 Because you need to multiply 8 x 9 then it will be 72 and then multiply 72 x 14.30 it will be 1029.6 it will the same the Second one is 145.8 Because you you need to multiply the first one multiply 6 x 3 which that 18 the multiply 18 x 8.10 which that will be 145.8 SO both of these answer are the same.
Hope It Helps!
ItsNobody
a square number whose digits add up to seven.
Answer:
list the squares
1x1=1
2x2=4
3x3=9
4x4=16
16 the answer because 1+6=7
hope this helps if you have any questions you can ask
Step-by-step explanation:
Answer:
4's square number : 16
5's square number : 25
32's square number : 1024
40's square number : 1600
49's square number : 2401
50's square number : 2500
Step-by-step explanation:
I might have missed a few but ...
A special cable has a mean breaking strength of 1131 pounds. The standard deviation of the population is 333 pounds. A researcher selects a sample of 30 cables with a mean of 931 pounds. Can one reject the claim that the mean breaking strength is less than 1131 pounds? (Use the 0.05 level of significance)
Answer:
[tex]z=\frac{931-1131}{\frac{333}{\sqrt{30}}}=-3.290[/tex]
Now we can calculate the p value using the alternative hypothesis:
[tex]p_v =P(z<-3.290)=0.0005[/tex]
Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 1131
Step-by-step explanation:
Information given
[tex]\bar X=931[/tex] represent the sample mean
[tex]\sigma=333[/tex] represent the population standard deviation
[tex]n=30[/tex] sample size
[tex]\mu_o =1131[/tex] represent the value to check
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true mean is less than 1131, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 1131[/tex]
Alternative hypothesis:[tex]\mu <1131[/tex]
The statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Reaplacing we got:
[tex]z=\frac{931-1131}{\frac{333}{\sqrt{30}}}=-3.290[/tex]
Now we can calculate the p value using the alternative hypothesis:
[tex]p_v =P(z<-3.290)=0.0005[/tex]
Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 1131
If x = 3-2√2 ,then find the value of x2 – 1/x2
Answer: - 24√2
Step-by-step explanation: i did the math this is what i got
Hello there!
x^2 - (1/x^2)
x = 3 - 2√2 -- (1)
1/x = 1/( 3-2√2 )
= ( 3 + 2√2 ) / (3 - 2√2 )(3+2√2 )
= ( 3 + 2√2 ) / 3² - ( 2√2 )²
3^2 = 9 and 2√2 ² = 8
= ( 3 + 2√2 ) / ( 9 - 8 )
= ( 3 + 2√2) -- (2)
x - 1/x = 3 - 2√2 - ( 3 + 2√2 )
= 6
= 3 - 2√2 - 3 - 2√2
= - 4√2
x² - 1/x² = ( x + 1/x ) ( x - 1/x )
= 6 × ( - 4√2 )
6 x ( -4√2 ) = -24√2
What is the area of the triangle?
Answer:
= 40
Step-by-step explanation:
A = 1/2bh
A = 1/2 x 10 x 8
A = 1/2 x 80
A = 40