Answer:
The turning point is (2,8)
Step-by-step explanation:
we know that
The general equation of the substance's temperature is equal to
[tex]T(x)=(x-h)^{3}+k[/tex]
where
(h,k) is the vertex (turning point)
In this problem we have
[tex]T(x)=(x-2)^{3}+8[/tex]
so
(h,k)=(2,8)
therefore
The turning point is (2,8)
Rachel has a box in the shape of a prism with a square base. The capacity of the box is 150 cubic inches. The height of the box (y) is times the base length of the box (x). Find the approximate height and the length of the box.
A. x = 4 and y = 6
B. x = 5 and y = 7.5
C. x = 4.2 and y = 6.3
D. x = 4.6 and y = 6.9
Answer:
Step-by-step explanation:
What do we know about that prism?
It's a rectangular prism with a square base.
Height: y (from question)
base length: x (from question)
base width: x (from question, since it's a square base).
Total volume: 150 cu inches
The question lacks a relationship between x and y the "is __ times", but we can see from the answer choices that they all show a constant relationship:
y = 1.5 x
The volume of a prism is obtained by multiplying the lengths of its 3 dimensions: V = length * width * height. In our case, we then have
150 = x * x * y
then we replace y by its x-expressed equivalent:
150 = x * x * (1.5x) = 1.5x³
then we isolate x³ by dividing each side by 1.5
x³ = 100, we do the cubic root on each side
x = 4.64
So, answer is D. x = 4.6 and y = 6.9
If you you 4.64 * 4.64 * 6.96 = you get 149.8, which is very close to 150.
the function f(x)= sqrt x is translated left 5 units and up 3 units to create the function g(x). what is the domain of g(x)?
Answer:
the domain is from -5 to infinity
Step-by-step explanation:
f(x+5)+3=√x+5 +3
x+5>0
x>-5
the domain is from -5 to infinity
Answer:
A. {x | x > –5}
the greater than sign should be greater than or equal to
if m
17
27
90
63
** picture is attached below!!
Answer:
Last option: 63
Step-by-step explanation:
You need to observe and analize the triangle XWZ provided in the image attached.
You can observe that the lenght of the side XW of the triangle XWZ is congruent to the lenght of the side ZW. This means that the lenght of the side XW and the lenght of the side ZW are equal.
Therefore, if the measure of the angle ∠X is 63, then the measure of the angle ∠YZW is 63:
[tex]m\angle YZW=m\angle X[/tex]
[tex]m\angle YZW=63[/tex]
This matches with the last option.
solve for x.
3x-12y=27
Answer: x=4y+9
Step-by-step explanation:
All of the variables, 3x, 12y, and 27 can be divided y 3, so we will simplify by dividing the whole equation by 3.
3x/3-12y/3=27/3
Which is equal to....
x-4y=9
Now you can move -4y over to the right side by changing its sign...
x=4y+9
Let the equation be 3x - 12y = 27 then, the value of x = 9 + 4y.
How to find the value of x?Given: 3x - 12y = 27
To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Solve the value of x, then
Add 12y to both sides
3x - 12y + 12y = 27 + 12 y
Simplifying the above equation, we get
3x = 27 + 12y
Divide both sides by 3, then we get
[tex]$\frac{3 x}{3}=\frac{27}{3}+\frac{12 y}{3}$$[/tex]
Therefore, the value of x = 9 + 4y.
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Jodi invested $497.50 in a regular savings account that paid simple interest at a rate of 3.5% per year. How much was her investment worth in one year?
Answer:
17.41
Step-by-step explanation:
497.50 x 0.035
Jodi's investment will earn $17.41 in interest in one year at an interest rate of 3.5%. Therefore, after one year, her investment will be worth $514.91.
Explanation:To find out how much Jodi's investment is worth in one year, we can use the formula for simple interest, which is Interest = Principal x Rate x Time. In this case, the principal is $497.50, the rate is 3.5% (or 0.035 in decimal form), and the time is 1 year.
So, the interest earned in one year would be $497.50 x 0.035 x 1 = $17.41.
To find the total worth of her investment after one year, we add the interest earned to the initial principal. So, $497.50 (the principal) + $17.41 (the interest) = $514.91. Therefore, her investment is worth $514.91 after one year.
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Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)?
AB
CD
FG
HJ
Answer:
HJ
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are the same
so
The slope of the line that is parallel to a line that has a slope of 3 is equal to 3
Verify the slope of the blue and red line , because their slopes are positive
Blue line
we have
C(-3,0),D(3,2)
The slope m is equal to
m=(2-0)/(3+3)
m=2/6
m=1/3
Red line
we have
H(-1,-4),J(1,2)
The slope m is equal to
m=(2+4)/(1+1)
m=6/2
m=3
therefore
The answer is the red line HJ
What is the simplified form of x+6/2x+5 + x+5/x+3
Answer:
Step-by-step explanation:
6/2 evaluates to 3
Multiply x and 3
Multiply x and 1
The x just gets copied along.
The answer is x
x
6/2*x evaluates to 3x
x+6/2*x evaluates to 4x
x+6/2*x+5 evaluates to 4x+5
4x + x = 5x
The answer is 5x+5
x+6/2*x+5+x evaluates to 5x+5
To divide 1 by x
The x just gets copied along in the denominator.
The answer is
5/x evaluates to
The answer is
x+6/2*x+5+x+5/x evaluates to
5 + 3 = 8
The answer is
B
x+6/2*x+5+x+5/x+3 evaluates to
The final answer is
B
Factorise:b+√b-12
An easy one.
Answer:
Step-by-step explanation:
If you let b = x^2 the problem becomes a whole lot easier. Note that x = √b
x^2 + x - 12
Now factor this trinomial.
(x + 4)(x - 3)
Now put b back into the equation
(√b + 4)(√b - 3)
Please help me find this shaded reigon fast
Answer:
=293.7m²
Step-by-step explanation:
Area of the shaded region = area of the circle-area of the minor segment.
The area of the minor segment is calculated as follows.
Area= Area of sector - area of the triangle bound by the radii.
=∅/360πr²-1/2r²sin∅, where r is the radius of the circle and ∅ the obtuse angle bound by the radii.
=130/360×π×11.1²-1/2×11.1²sin130
=93.43m²
Area of the whole circle =πr²
=π×11.1²
=387.08m²
Area of the shaded region
=387.08m²-93.43m²
=293.65m²
≅293.7m² to the nearest tenth.
Use the quadratic formula to solve the equation. 2x^2-6x+1=0 Enter your answers, in simplified radical form, in the boxes.
x=__or x=
please send me image and explain work
Answer:
(3 (pm) sqrt(7))/2
Step-by-step explanation:
First step: Identify a,b, and c
a=2
b=-6
c=1
Second step: Find b^2-4ac (this is called the discriminant-I will call this D)
(-6)^2-4(2)(1)=36-8=28
Third step: Find the square root of the discriminant aka sqrt(D)
sqrt(28)
Let's see if we can simplify sqrt(28)
Here is there a factor of 28 that is a perfect square? How about 4? Yep!
sqrt(28)=sqrt(4)sqrt(7)=2sqrt(7).
Fourth Step: What is -b? If b=-6 then -b=6.
Fifth step: What is 2a? 2(2)=4
So the formula is
x=(-b (pm) sqrt(D))/(2a)
or
x=(step4 (pm) step 3)/(step 5)
x=(6 (pm) 2sqrt(7))/4
Simplify
x=(3 (pm) sqrt(7))/2
*pm means plus or minus
*sqrt( ) means square root of the number that follows in the ( )
Answer:
Just took it!
Step-by-step explanation:
Find the equation of the line graph below in slope intercept form. please show your work. (will make brainiest.)
Answer:
y=2/3x+3
Step-by-step explanation:
the slope is 2 over 3 because you ride 2 up and 3 to the right to get to the next dot and the y intercept is 3 because that's where the line intercepts the y axis.
What is the solution to log 25x = 3?
Answer: x=40
Step-by-step explanation:
The solution to log (25x) = 3 is 40. This is calculated by using log rules.
What are the rules of a logarithmic function?A function that has log terms is said to be a logarithmic function.
Some of the rules for solving log functions are as follows:
The basic form of a logarithmic function is [tex]log_b(m)=n[/tex] ⇒ [tex]m=b^n[/tex].Product rule: [tex]log_b(x)+log_b(y)=log_b(xy)[/tex]Quotient rule: [tex]log_b(x)-log_b(y)=log_b(\frac{x}{y})[/tex]Power rule: [tex]log_b(x)^n=nlog_b(x)[/tex]Identity rule: [tex]log_b(b)=1[/tex] where [tex](b^1=b)[/tex]Finding the solution for the given function:Given that,
log (25x) =3
Using basic form [tex]log_b(m)=n[/tex] ⇒ [tex]m=b^n[/tex]
Here base b=10, m=25x and n=3
Then,
log (25x) =3
⇒ [tex]25x = 10^3[/tex]
⇒ 25x = 1000
⇒ x = 1000/25
∴ x = 40.
Hence the solution of the given function is 40.
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If
[tex] log_{5}(3) = a[/tex]
and
[tex] log_{5}(4)= b[/tex]
then
[tex] log_{15}(2) [/tex]
is?
a)2b/a+1
b)a+b/ab
c)2b-a/2b
d)b/2a+2
e)2a+2/b
[tex]\bf \log_5(3)=a\qquad \qquad \log_5(4)=b\ \\\\\\ \log_5(4)=b\implies \log_5(2^2)=b\implies 2\log_5(2)=b\implies \log_5(2)=\cfrac{b}{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{15}(2)\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_5(2)}{\log_5(15)}}\implies \cfrac{~~\frac{b}{2}~~}{\log_5(3\cdot 5)}\implies \cfrac{~~\frac{b}{2}~~}{\log_5(3)+\log_5(5)} \\\\\\ \cfrac{~~\frac{b}{2}~~}{a+1}\implies \cfrac{b}{2}\cdot \cfrac{1}{a+1}\implies \cfrac{b}{2a+2}[/tex]
A. What is the area of the base? Use complete sentences to explain your reasoning.
B. What is the volume of the prism? Use complete sentences to explain your reasoning.
Answer:
For the first answer (A)
The area of the base is the area of the 8 by 4 rectangle, minus the missing 2 by 2 square in the top-right. This is 8*4-2*2=32-4=28 square centimeters.
For the second answer (B)
The volume of the prism is the base area multiplied by the height, or 28*10=280 cubic centimeters.
Answer:
Area = 28 cm² and Volume = 280 cm³
Step-by-step explanation:
A. Area of the base of the prism = Area of rectangle with dimensions 4 × 8 cm. minus area of a rectangle with dimensions 2×2 cm.
Area = 4 × 8 - 2 × 2
= 32 - 4 = 28 cm²
B. Volume of the given prism = Volume of full prism with dimensions 10 × 4 × 8 cm. minus volume of small prism (missing) having dimensions 2×2×10 cm.
Volume = 10 × 4 × 8 - 2 × 2 × 10
= 320 - 40
= 280 cm³
Area = 28 cm² and Volume = 280 cm³
Which equation can be used to calculate the area of the shaded triangle in the figure below?
Answer:
A
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 14 and h = 4, hence
A = [tex]\frac{1}{2}[/tex] (14 × 4) = 28
In the word "COURSE” what is the probability of choosing a vowel?
Answer:
3 vowel in the word and theres 6 letters so 50% 3/6
Step-by-step explanation:
The range of the function f(x) = x + 5 is {7, 9). What is the function's domain?
Answer:
(2,4)
Step-by-step explanation:
The range is the y values
y = x+5
Let y=7
7 =x+5
Subtract 5
7-5 x+5-5
2=x
Let y= 9
Subtract 5
9-5 x+5-5
4=x
The domain is (2,4)
What is 4 divided by 1/3 write in fractions
Answer:
the answer is 12.
Step-by-step explanation:
the explanation is in the image above
Hope this helps
3. Mr. Terence had 18 boxes containing 36 donuts each. He sold 162 donuts and
repacked the rest into 81 boxes. How many donuts did he put into cach box?
6 donuts. He repacked 6 donuts into each box .
Mr. Terence had 18 boxes containing 36 donuts each, that means:
Total donuts = n° boxes*n° donuts
Total donuts = 18*36 = 648
He had in total 648 donuts.
He sold 162 donuts and repacked the rest into 81 boxes. Then:
Rest donuts = Total donuts - sold donuts
Rest donuts = 648 - 162 = 486
The rest donuts are 486 donuts.
He repacked the rest into 81 boxes, then:
n° donuts (each box) = Rest donuts/n° boxes
n° donuts (each box) = 486/81 = 6
The number of donuts that he put in each box is 6 donuts.
Which graph represents the function g(x) = |x + 4| + 2?
Answer:
Step-by-step explanation:
Graph y = |x|. This graph is v-shaped, opening up, with vertex at (0, 0). Now translate this graph 4 units to the left and 2 units up. The result is the graph of g(x) = |x + 4| + 2.
Next time, please share the possible answer choices. Thanks.
The function g(x) is derived from the function f(x) by translating f(x) graph 4 units to the left and 2 units up
The equation of the function is given as:
[tex]g(x) = |x + 4| + 2[/tex]
The above is an absolute value function, and the equation of the parent function is:
[tex]f(x) = |x|[/tex]
This means that the function g(x) is derived from the function f(x) by translating f(x) graph 4 units to the left and 2 units up
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What is half of a number z
Answer:
[tex]\frac{1}{2} z[/tex]
Step-by-step explanation:
A class of 20 students is visiting the fair today. Each student is 16 years old or younger and will participate in
either the Hay Bale Toss or the Pie Eating Contest. If all 20 students joined the same event, how would the shape
of the histogram change compared to the original?
The histogram would change due to the different distribution of ages when all 20 students join the same event.
Explanation:A histogram is a graphical representation of the distribution of numerical data. It consists of bars, where the length or height of each bar corresponds to the frequency or relative frequency of data within a specific interval or range. Histograms provide insights into data patterns and distributions.
The histogram would change when all 20 students join the same event compared to the original because the distribution of ages would be different. The original histogram would show the number of students participating in each event, while the new histogram would show the number of students in each age group. The new histogram would have different bars representing each age group, and the heights of these bars would be determined by the number of students in each age group.
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Two asteroids are 1000 km apart and are heading straight for each other. One asteroid is travelling at 59 km per second and the other at 41 km per second. How long does it take for them to collide?
Answer:
10 seconds.
Step-by-step explanation:
The velocity at which they are approaching each other = 59 + 41 = 1000 km per second.
Velocity = distance / time
So time = distance / velocity
= 1000 / 100
= 10 seconds.
10 seconds long does it take for them to collide.
Velocity
Velocity exists as the measurement of the amount of distance an object covers in a given amount of time. Here's a term equation that describes the connection between distance, velocity, and time: Velocity equals distance traveled divided by the time it brings to get there.
The velocity at which they exist approaching each other = 59 + 41
= 1000 km per second.
Velocity = distance / time
So, time = distance / velocity
= 1000 / 100
= 10 seconds.
Therefore, 10 seconds long does it take for them to collide.
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Use a transformation to solve the equation. w/4 = 8 can you also leave a detailed explanation on how this equation = 32
Answer:
w=32
Step-by-step explanation:
w/4 = 8
4/1 * w/4 = 8*4
w=32
What is the solution for this equation 3(80-9x)=x-96
Answer:
X=12
Step-by-step explanation:
3(80-9x)=X-96 Distribute 3 through the parenthesis
240-27x=x-96
Move the variable to the left side and change its sign
Move constant to the right side and change its sign
-27x-x+240=-96
collect the like terms
calculate the difference
-28x=-336
Divide both sides of the equation by -28
x=12
Write the following ration as a reduced fraction. Simplify your answer when possible: 14 to 84
Answer:
Hi there!
Since you asked for a simplified fraction, the answer to this question is: 1/6
Step-by-step explanation:
Look at the fraction 14/84, there is a definite similar factor between 14 and 84, 2. So all you do is divide the two numbers by two to reduce the fraction into 7/42
then you divide both 7 and 42 by 7 to get 1/6
Answer:
1/6
Step-by-step explanation:
14 to 84
First lets make it a fraction
14/84
Divide the top and bottom by 14
1/6
Which of the following translates the sentence the difference of three times a number and 20 is 13"?
x x - x - 20 = 13
3x - 20 = 13
3x + 20 = 13
Answer:
3x - 20 = 13
Step-by-step explanation:
it says difference so it cant be the last one and three times a number is 3 x so it cant be the first one leaving the middle.
please mark brainliest
Steven earns extra money babysitting. He charges $25.00 for 4 hours and $37.50 for 6 hours. Write an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represents the amount he charges. The equation is y=
An easy way to solve this problem is divide $23.25 by 3 or $54.25 by 7. Either way, you get $7.75. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:
$7.75x = y
I hope this helped! :)))
Connie has $660,000 she wants to save. If the FDIC insurance limit per
depositor, per bank, is $250,000, which of these ways of distributing her
money between three banks will guarantee that all of her money is insured?
O
A. $220,000 in bank A, $160,000 in bank B, $280,000 in bank C
O
B. $180,000 in bank A, $220,000 in bank B, $260,000 in bank C
O
c. $220,000 in bank A, $300,000 in bank B, $140,000 in bank C
O
D. $180,000 in bank A, $240,000 in bank B, $240,000 in bank C
SUBMIT
Answer:
The answer would be D) $180,000 in bank A, $240,000 in bank B, $240,000 in bank C.
Step-by-step explanation:
You can immediately eliminate A, B and C because the question clearly states that the limit per bank is $250,000.
Answer:
D. $180,000 in bank A, $240,000 in bank B, $240,000 in bank C
Step-by-step explanation:
She needs to deposit less than $250,000 in each bank in order to be able to have that sum of money insured, in this case she could deposit it this way:
$250,000
$250,000
$160,000
But that could be too risky and too on the verge of not being accepted, you she just takes $10,000 out of every $250,000 deposits to make them $240,00, and add it to the $160,000 deposit, so she is left with three deposits of:
$240,000
$240,000
$180,000
And with this she makes sure all of her deposits are insured by staying below the $250,000 limit.
Can someone please help me out
Answer:
3 + 3 + 12 + 8 + 8Step-by-step explanation:
We have:
two triangles with base b = 6 and height h = 1
two rectangles with length l = 4 and width w = 2
one reactangel with length l = 6 and width w = 2.
The formula of an area of a triangle:
[tex]A_T=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A_T=\dfrac{(6)(1)}{2}=3[/tex]
The formula of an area of a rectangle:
[tex]A_R=lw[/tex]
Substitute:
[tex]A_{R_1}=(4)(2)=8\\\\A_{R_2}=(6)(2)=12[/tex]
The surface area of the prism:
[tex]S.A.=A_T+A_T+A_{R_1}+A_{R_1}+A_{R_2}[/tex]
[tex]S.A.=3+3+8+8+12[/tex]