Step-by-step explanation:
let's start with B :
the best way to find the vertex is by transforming the function into the vertex form :
y = a(x - h)² + k
with (h, k) being the vertex.
when doing all the multiplications, we get
y = a(x²-2hx+h²) + k = ax² - 2ahx + ah² + k
let's compare with the irreducible function
ax² = 4x²
a = 4
-2ahx = 8x
-2×4hx = 8x
-8hx = 8x
-8h = 8
-h = 1
h = -1
ah² + k = -5
4×(-1)² + k = -5
4 + k = -5
k = -9
so, the vertex form is
y = 4(x + 1)² - 9
the vertex is (-1, -9)
if the factor of the (x-h)² term is greater than 0, then the parabola opens upward, and if it is less than zero, the parabola opens downward.
out factor is +4, so it opens upward, and the vertex is a minimum.
A
now we know
y = 4(x + 1)² - 9
for the x-intercepts we need to find the x-values that lead to 0 y values.
so,
0 = 4(x + 1)² - 9
9 = 4(x + 1)²
3 = ± 2(x + 1) = ± (2x + 2)
for +(2x + 2) is then
3 = 2x + 2
2x = 1
x = 1/2
for -(2x + 2) is then
3 = -2x - 2
5 = -2x
x = -5/2
so, the x-intercepts are
(-5/2, 0) and (1/2, 0).
C
I know it is a parabola.
i know 3 points : the vertex and the 2 x-interceot points. i could then also calculate the points for x = 0, 1, -1, 2, -2.
and then draw the graph with a curve ruler connecting the points.
How can I find the x value?
How can I explain it?
PLEASE ANSWER THE QUESTION!!!
f(x) = 3x + 2
What is f(5)?
Answer:
17
Step-by-step explanation:
→ f(x) = 3x + 2
→ f(5) = 3(5) + 2
→ 15 + 2
→ 17 is the answer.
Answer:
F(5) = 17
Step-by-step explanation:
to solve, we just need to plug all values of x into 5 as shown
f(x) = 3x + 2
f(5) = (3*5) + 2
then following the format of PEMDAS (explained at footer) we solve the new equation
f(5) = (3*5) + 2
f(5) = 15 + 2
f(5) = 17
therefor F(5) is equal to 17
The PEMDAS format of solving equations:
the term Pemdas stands for the steps involved in solving an equation
Parenthasis (follow PEMDAS within these ( ) first untill in simplest form)
Exponents (such as x^y)
Multiply (any multiplication)
Devide (any devision)
Addition (any addition)
Subtraction (any subtraction)
hpe all this helps you ^^
Help pls I don't understand
Answer:
me too a I don't understand
Two sides of a triangle and an angle between them are given. Construct the triangle. Does the solution exist for any given angle?
A solution exists for constructing a triangle given two sides and the included angle if the triangle inequality theorem is satisfied
We have to draw a line segment to represent one of the given sides of the triangle.
From one endpoint of the line segment, use a protractor to measure the given angle. Mark this angle on the line segment.
Using a compass, set the compass to the length of the other given side of the triangle.
With the compass centered at the endpoint of the line segment, draw an arc that intersects the angle on the line segment.
Draw a line connecting the endpoint of the line segment to the point where the arc intersects the angle.
This line represents the second side of the triangle.
Finally, draw a line connecting the two endpoints of the sides you have constructed. This line completes the triangle.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ2
12x+16y=336
Please help me find y intercept the answer should be 28 but guide me on the steps
I need help! its really hard to do
The scale factor of the dimensions of two similar wood floors is 4:3. It costs $153 to refinish the smaller wood floor. At this rate, how much would it cost to refinish the larger wood floor?
With the given scale factor, The cost to refinish the larger wood floor is $204
How to determine the amount for the larger wood?The scale factor is given as:
Scale factor = 4 : 3
This means that:
x : 153 = 4 : 3
Where x represents the cost to refinish the larger wood floor
Express as fraction
x/153 = 4/3
Multiply both sides by 153
x = 204
Hence, the cost to refinish the larger wood floor is $204
Read more about scale factors at:
https://brainly.com/question/3457976
#SPJ1
4. The equation 2x = - 10 is modeled below.
What is the value of x makes the equation true?
Answer:
x = -5
Step-by-step explanation:
2x = -10 <== divide both sides by 2
/2 /2
x = -5
Check your work:
2x = -10
2(-5) = -10
-10 = -10
This statement is true
Hope this helps!
What type of graph is this ?
Step-by-step explanation:
this isn't a graph of a function, this is just a series of plotted points.
Is it True or false?
Answer: False
Step-by-step explanation: right triangles need two equal angles and one different.
The diameter of a circle is 42 ft. Find its area to the nearest whole number.
Answer:
5539 or 1764[tex]\pi[/tex]
Step-by-step explanation:
to find the area, we need the radius
The radius(R) is half of the diameter(D)
R = D/2
R = 42/2
R = 21
area of a circle(A) = pi x radius[tex]^{2}[/tex]
A = pi( which most times in a problem, equals 3.14) x 42[tex]^{2}[/tex]
A = 3.14 x 1764
A = 5538.96
A(when rounded) = 5539
the scores made by a group of eleventh grade students on the mathematical portion of the SAT are given.
Using the percentage concept, it is found that 33.33% of the students scored 650 or higher in the mathematical portion of the SAT.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
Researching the problem on the internet, it is found that of the 15 students, 5 scored 650 or higher in the mathematical portion of the SAT, hence the percentage is given by:
[tex]P = \frac{5}{15} \times 100\% = 33.33\%[/tex]
More can be learned about percentages at https://brainly.com/question/10491646
#SPJ1
The height of a plant in centimeters is recorded each day for 14 days. The function y = 1.44x + 1.55 is determined to be a good fit for the data. On day 7, the recorded height was 12.32 centimeters. How close is the predicted height to the actual height of the plant (the residual)? A) 0.63 cm B) 0.69 cm C) 1.38 cm Eliminate D) −0.69 cm
The predicted height is close to the actual height of the plant by 0.69 cm
How to determine the closeness in the heights?The equation of the height function of the plant is given as:
y = 1.44x + 1.55
The height on day 7 is calculated as:
y = 1.44 * 7 + 1.55
Evaluate
y = 11.63
The recorded height is given as 12.32
The residual is calculated as:
Residual = Recorded - Predicted
So, we have:
Residual = 12.32 - 11.63
Evaluate
Residual = 0.69
Hence, the predicted height is close to the actual height of the plant by 0.69 cm
Read more about residuals at:
https://brainly.com/question/16180255
#SPJ1
The circle graph shows how Emily spent one hour using her iPhone. How many minutes did Emily spend on research?
Answer:
I don't see a circle graph. Add one and ill edit this answer
Step-by-step explanation:
Add
the
image.
(7 + 1)2 – (11 + 32) ÷ 4. simplify
Answer: 5.25
Step-by-step explanation:
Solve using PEMDAS,
(7 + 1)2 – (11 + 32) ÷ 4
(8)2 - (43) ÷ 4
16 - 10.75 = 5.25
20d + 0.7m = 235
Shelly spent $235 to rent a moving van. The equation above shows the relationship
between the number of days she rented the van, d, and the number of miles she drove
the van, m. If she rented the van for 3 days, how many miles did she drive the van?
The number of miles she drove the van for is 250 miles
Solving linear equationsFrom the question, we are to determine the number of miles Shelly drove the van
The given equation which shows the relationship between the number of days she rented the van, d, and the number of miles she drove the van, m is
20d + 0.7m = 235
Now, if she rented the van for 3 days, that is, d = 3
Putting the value of d = 3 into the equation to determine the value of m
We get
20(3) + 0.7m = 235
60 + 0.7m = 235
0.7m = 235 - 60
0.7m = 175
m = 175 / 0.7
m = 250
Hence, the number of miles she drove the van for is 250 miles
Learn more on Solving linear equations here: https://brainly.com/question/19081972
#SPJ1
How to find maximum and minimum values of a parabola
Answer:
Step-by-step explanation:
Finding max/min: There are two ways to find the absolute maximum/minimum value for f(x) = ax2 + bx + c: Put the quadratic in standard form f(x) = a(x − h)2 + k, and the absolute maximum/minimum value is k and it occurs at x = h. If a > 0, then the parabola opens up, and it is a minimum functional value of f.
A. 611.18 b. 431.59 c. 395.59 d. 1,042.37. ASAP PLEASEE
Answer:
A
Step-by-step explanation:
Place (dlick and drag) one option from each of the lists below Into Its corresponding box to
create an equation of the line that passes through the polnt (1, "10) and is perpandicular to y=-1/3 x +5
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-1}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-1}\implies 3}}[/tex]
so we're really looking for the equation of a line whose slope is 3 and passes through (1 , 10)
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{10})\qquad \qquad \stackrel{slope}{m}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{3}(x-\stackrel{x_1}{1}) \\\\\\ y-10=3x-3\implies y=3x+7[/tex]
The table shows the results of rolling a number cube with sides labeled 1 through 6 several times.
What is the experimental probability of rolling a 3 or a 6?
Enter your answer as a fraction in simplest form in the box.
1 10
2 6
3 4
4 8
5 6
6 6
Total times die rolled =10+6+4+8+6+6=40
Times 3 and 6 appears
4+6=10Experimental probability
P(3 or 6)
10/401/40.25Answer:
[tex]\sf \dfrac{1}{4}[/tex]
Step-by-step explanation:
Experimental probability
Calculated by dividing the number of times an event happens by the total number of trials in an actual experiment.
[tex]\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}[/tex]
Total number of trials = 10 + 6 + 4 + 8 + 6 + 6 = 40
Total number of times rolling a 3 or a 6 = 4 + 6 = 10
[tex]\textsf{Experimental Probability of rolling 3 or 6} = \sf \dfrac{10}{4}=\dfrac{1}{4}[/tex]
find the slope of the line containing the points (-3,2) and (3,7)
[tex]\text{Given that,}~ (x_1,y_1) =(-3,2)~ \text{and}~ (x_2 ,y _2) = (3,7)\\\\\text{Slope,}~ m = \dfrac{y_2 -y_1}{x_2 -x_1}\\\\\\~~~~~~~~~~~~=\dfrac{7-2}{3-(-3)}\\\\\\~~~~~~~~~~~~=\dfrac{5}{3+3}\\\\\\~~~~~~~~~~~~=\dfrac 56[/tex]
Complete the definition of the h(x) so that it is continuous over its domain.
Answer:
A=0
B=2
so we have our question, h (x) x^3, x<0.
a is equal to 0 since that answer was already given.
so now it would be srqt/x over 0 of 4
4 divided by 0 is 0
1/2x x>4
turns into 1/2x x>4/1
cross simplify
the answer to B is 2
Answer:
a=0
b=2
Step-by-step explanation:
Please help, will give brainliest!
Answer:
1.99 x 10 ^20 N
Step-by-step explanation:
Just substitute in the values given
F = (6.67x 10^-11) * (5.97x10^24)(7.36 x 10^22) / ( 3.84 x 10^8) ^2
= 1.99 x 10^20 N
Rectangle pqrs had vertices p(-4,3),q(-2,5),r(3,0) and s(1,-2). the diagonals of the rectangle bisect eachother. atwhich point do the diagonals intersect?
Answer:
Step-by-step explanation:
Simplify the expression. Write your answer as a power.
The simplified expression is
Answer:
Answer = 6^7
Step-by-step explanation:
When multiplying expressions with exponent you add the exponents together. So here you would get 6^13/6^6. However you can simplify this farther since the base (6) is the same. When dividing expressions with exponents you subtract the exponents so the the answer would be 6^7.
Hope that helps! :)
Mr. Brown picks out the time that appears the most to find the
. He arranges the times in increasing order and picks the middle value to find the
.
Green paint can be made by mixing yellow and blue paint in a 2 : 5 ratio
What fraction of the green paint is yellow paint? Give your answer in its
simplest form.
Answer:
4 : 10
Step-by-step explanation:
Answer:
2/7
Step-by-step explanation:
there's seven parts in green (2 yellow and 5 blue)
two of them are yellow
so 2/7 is the fraction
(seven is prime so it's already in simplest form.)
Yuuma applied the steps below to find the product of (–10.2)(–16.4).
Step 1: (–10.2)(–16.4) = (–16.4)(–10.2)
Step 2: = (–16.4)(–10) + (–16.4)(–0.2)
Step 3: = ____________
Step 4: = 167.28
Which expression correctly fills in the blank in Step 3?
(–164) + (–3.28)
164 – 3.28
(–164) + 3.28
164 + 3.28
Answer:
164+3.28
Step-by-step explanation:
(16.4)(10)+(16.4)(0.2)
164+3.28
167.28
In Galton’s height data, the least-squares line for predicting forearm length (y) from height (x) is y = −0.2967 + 0.2738x.
Predict the forearm length of a man whose height is 72 in. Round the answer to three decimal places.
Using the line of best fit, it is found that the prediction of the forearm length of a man whose height is of 72 in is of 19.417 in.
What does the line of best fit state?It states that the predicted forearm length of a person of height x is given by:
y = -0.2967 + 0.2738x.
In this problem, the height is of x = 72 in, hence:
y = -0.2967 + 0.2738(72) = 19.417 in.
More can be learned about line of best fit at https://brainly.com/question/17261411
#SPJ1
Cos(alpha-beta)cos(alpha beta)=cos^2 alpha-cos^2 beta
The equation cos (α - β) × cos (α + β) ≠ cos² α - cos² β. Then the given equation is incorrect.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
The equation is given below.
cos (α - β) × cos (α + β) = cos² α - cos² β
Then show whether the equation is correct or incorrect.
Taking the left-hand side, then we have
[tex]\cos(\alpha-\beta)*\cos(\alpha +\beta) = (\cos \alpha \cos\beta + \sin \alpha \sin \beta ) (\cos \alpha \cos\beta - \sin\alpha \sin\beta )\\\\\cos(\alpha-\beta)*\cos(\alpha +\beta) = \cos ^2 \alpha \cos ^2\beta - \sin ^2 \alpha \sin ^2\beta[/tex]
The left-hand side does not equal to the right-hand side.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ4