Answer:
165 minutes
Step-by-step explanation:
1hour--> 60 minutes
60+60+45=165 minutes
What is an equation to a line parallel to the line on the graph that passes through (4,15)?
The equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3
How to find equation of a line?The equation of a line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
parallel line have the same slope
(5, 35)(10, 50)
m = 50 - 35 / 10 - 5 = 15 / 5 = 3
Hence,
(4, 15)
y = 3x + b
15 = 3(4) + b
15 - 12 = b
b = 3
Therefore, the equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3
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What are two integers whose sum is -2 and product is -80?
Answer:
We can write:
x + y = -2
xy = -80
We can rewrite the first equation as x = -y - 2 and then plug that into the second equation to get (-y-2) * y = -80 → -y² - 2y = -80 → y² + 2y - 80 = 0 → (y - 8)(y + 10) = 0 → y = 8, -10. Substituting these values into the first equation we get x = -10, 8 so the answer is (x₁, y₁) = (-10, 8) or (x₂, y₂) = (8, -10).
Problem P(x)=x4−3x2+kx−2P(x)=x^4-3x^2+kx-2P(x)=x4−3x2+kx−2P, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, minus, 3, x, squared, plus, k, x, minus, 2 where kkkk is an unknown integer. P(x)P(x)P(x)P, left parenthesis, x, right parenthesis divided by (x−2)(x-2)(x−2)left parenthesis, x, minus, 2, right parenthesis has a remainder of 10101010. What is the value of kkkk? K=k=k=
Answer: k = 4
Step-by-step explanation:
For this division, to determine the value of k, use the Remainder Theorem, which states that:
polynomial p(x) = dividend (x-a) * quotient Q(x) + remainder R(x)
Knowing the degree of quotient is
degree of Q = degree of p(x) - degree of (x-a)
For this case, Q(x) is a third degree polynomial.
Using the theorem:
[tex]x^{4}-3x^{2}+kx-2 = (x-2)(ax^{3}+bx^{2}+cx+d) + 10[/tex]
[tex]x^{4}-3x^{2}+kx-2 = ax^{4} + x^{3}(b-2a)+x^{2}(c-2a)+x(d-2c)-2d+10[/tex]
a = 1
b - 2a = 0 ⇒ b = 2
c - 2b = -3 ⇒ c = 1
-2d + 10 = -2 ⇒ d = 6
d - 2c = k ⇒ k = 4
Therefore, k = 4 and Q(x) = [tex]x^{4} -2x^{2} + 4x + 2[/tex]
Help me with 2a and 2b please
Answer:
Step-by-step explanation:
A∩B={x| x∈a and x∈B}
a) A∩B={4,6}
b) A∩B={ 4,9}
c) A∩B={yellow,green}
what is 25 (10 + 50) - 25?
Answer:
Hey there!
25(10+50)-25
25(60)-25
1500-25
1475
Hope this helps :)
Answer:
The answer is
1475Step-by-step explanation:
25 (10 + 50) - 25
Expand
250 + 1250 - 25
Simplify
We have the final answer as
1475
Hope this helps you
A prism has a volume of 405 cubic inches. A prism has a length of 15 inches, height of h, and width of 4.5 inches. Which is the correct substitution for finding the height of the prism? V = l w h. 405 = 15 + 4.5 + h. V = l w h = 15 times 4.5 times 405 V = l w h = 15 times 4.5 times 15 V = l w h. 405 = 15 times 4.5 times h
Answer:
d) 405 = 15 times 4.5 times h
The height of the prism 'h' = 6 inches
Step-by-step explanation:
Explanation:-
Given Volume of prism
V = 405 cubic inches
Given length of the prism
L = 15 inches
Given width of the prism
W = 4.5 inches
The volume of the prism
V = l w h
405 = 15 ×4.5× h
405 = 67.5 h
Dividing '67.5' on both sides , we get
h = 6 inches
Final answer:-
The height of the prism 'h' = 6 inches
Answer: V = l w h. 405 = 15 times 4.5 times h
Step-by-step explanation:
Given the following :
Volume of prism = 405 in^3
Length = 15 inches
Height = h
Width = 4.5 inches
Recall :
The volume of a prism is the product of the Base and the height.
That is;
Volume = Base × height
However, Base of prism is given by the area of the base shape of the prism.
From our parameters Base shape of the prism is a rectangle.
Therefore, Area of rectangle = Length × width
= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism
Therefore, Volume of prism equals ;
Volume = 15 × 4.5 × h
Volume = 405in^3
Volume = Base × height
405 = 15 × 4.5 × h
5 3/4 divided by 1 1/2
Answer:
[tex] \frac{23}{6} [/tex]Solution,
[tex]5 \frac{3}{4} \div 1 \frac{1}{2} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{23}{4} \div \frac{3}{2} [/tex]
To divide by a fraction, multiply by the reciprocal of that fraction
[tex] \frac{23}{4} \times \frac{2}{3} [/tex]
Reduce the numbers with the GCF 2
[tex] \frac{23}{2} \times \frac{1}{3} [/tex]
Multiply the fraction
[tex] \frac{23}{6} [/tex]
Hope this helps...
Good luck on your assignment...
Solve for x. − 6 ≥ 10 − 8x.
Answer:
2</x or x>/2
Step-by-step explanation:
-6>/10-8x
-10 -10
-16>/-8x
divide both sides by -8
2</x or x>/2
the reason the sign is bc u r dividing by a - number.
Answer:
x ≥ 2
Step-by-step explanation:
-6 ≥ 10 - 8x
Subtract 10 on both parts.
-6 - 10 ≥ 10 - 8x - 10
-16 ≥ -8x
Divide both parts by -8 remembering to reverse sign.
-16/-8 ≤ (-8x)/-8
2 ≤ x
Switch parts.
x ≥ 2
help me again pleasee :(
Erin buys 3 packs of potatoes costing £2 each, 4 packs of carrots for £2 per pack, and 4 turnips costing 90p each. If she pays with a £20 note, how much change would she get in pounds, £?
Answer: £2.4
Step-by-step explanation:
From the question, Erin buys 3 packs of potatoes costing £2 each, 4 packs of carrots for £2 per pack, and 4 turnips costing 90p each.
Total cost of potatoes = 3 × £2 = £6
Total cost of carrots = 4 × £2 = £8
Total cost of turnips = 4 × 90p = £360p = £3.6
The total cost of things bought by Erin will now be:
= £6 + £8 + £3.6
= £17.6
If she pays with a £20 note, she will collect a change of:
= £20 - £17.6
= £2.4
= 2 pounds, 40 pennies.
What is the sum of the measures, in degrees, of the interior angles of an 18-
sided polygon?
A. 2880
B. 3600
C. 3240
D. 3060
Answer:
Option (D)
Step-by-step explanation:
Sum of interior angles of a polygon is represented by the expression,
Sum of interior angles = n(n - 1)×180°
Here n is the number of sides of a polygon
If n = 18,
Sum of 18 sided polygon = (18 - 1) × 180°
= 7 × 180°
= 3060°
Therefore, sum of interior angles of a 18 sided polygon will be 3060°.
Option (D) will be the answer.
Answer:
2880
Step-by-step explanation:
SUM=_-2=
18-2=16
16*180 = 2880 OR
18*160 = 2880 degrees
2/3 - 5bx = bx + 1/3 In the equation shown above, b is a constant. For what value of b = NO SOLUTIONS? A. 5 B. 0 C. -5 D. 2/5
Answer:
B
Step-by-step explanation:
Here, we want to know at what values of b does the equation becomes not solvable
Now looking at the left hand side, we have;
2/(3-5bx) and also the right hand side bx + 1/3
For this expression if we insert b = 0, then automatically x cancels out on both sides of the equation and we shall be left with nothing to solve
Answer:
−5
Step-by-step explanation:
First, we observe that this is a linear equation.
A linear equation in one variable will have no solutions if the equation reduces to an equation of the form:
\blue a x+\red b=\blue c x + \red dax+b=cx+dstart color #6495ed, a, end color #6495ed, x, plus, start color #df0030, b, end color #df0030, equals, start color #6495ed, c, end color #6495ed, x, plus, start color #df0030, d, end color #df0030
where \blue a=\blue ca=cstart color #6495ed, a, end color #6495ed, equals, start color #6495ed, c, end color #6495ed and \red b\neq \red db
=dstart color #df0030, b, end color #df0030, does not equal, start color #df0030, d, end color #df0030.
In this case, the equation will reduce to the statement \red b=\red db=dstart color #df0030, b, end color #df0030, equals, start color #df0030, d, end color #df0030, which is not true for any value of xxx.
Hint #2
Since \red {\dfrac23}\neq \red {\dfrac13}
3
2
=
3
1
start color #df0030, start fraction, 2, divided by, 3, end fraction, end color #df0030, does not equal, start color #df0030, start fraction, 1, divided by, 3, end fraction, end color #df0030 , the equation will have no solutions if \blue b=\blue {-5}b=−5start color #6495ed, b, end color #6495ed, equals, start color #6495ed, minus, 5, end color #6495ed.
Let's check that this is the case. If we add \blue {5}{x}5xstart color #6495ed, 5, end color #6495ed, x to both sides, we get
\begin{aligned} \red{\dfrac23}\blue{-5}x&= \blue{-5} x+\red{\dfrac13}\\\\ \red{\dfrac23}\blue{-5}x+\blue5x&= \blue{-5}x+\blue{-5}x+\red{\dfrac13} \\\\ \red{\dfrac23}&=\red{\dfrac13} \end{aligned}
3
2
−5x
3
2
−5x+5x
3
2
=−5x+
3
1
=−5x+−5x+
3
1
=
3
1
which is not true for any value of xxx, so there are no solutions.
For all other values of b,b,b, comma there will be one solution.
Hint #3
If b=-5b=−5b, equals, minus, 5, the equation will have no solutions.
1. A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
2. Find the perimeter of a circle whose radius is 3.5cm. (Take pi = 22/7)
3. The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
4. What is the coefficient of b in the expression b² - 5b +18
5. Expand (x +2) (9 - x)
7. Find x and y in the simultaneous equations. x + y = 4 3x + y = 8
8. Factorize a² +3ab - 5ab - 15b²
9. The bearing of a staff room from the assembly ground is 195degrees, what is the bearing of the assembly ground from the staff room?
Step-by-step explanation:
68$53++83(-$(7(3($++$
There are 100 sophomores at a school. 85% of them are good students. What would the percent of good students be at school if (round the answer up to the nearest ones) ten “F” students would come to this school?
Answer: subtract 85 with a hundred because you are trying to see how many students out of 100% are good students after that you should get your answer
Step-by-step explanation:
Answer:
77% (rounded)
Step-by-step explanation:
1. Find 85% of 100
100 x 0.85 = 85
SO 85 students out of 100 students are good students.
2. Add the 10 more students to the total number.
100 + 10 = 110 total students
3. Find the percent of good students in the total number of current students.
85/110 = 0.77 * 100 (to convert to percent) = 77%
The graph of f(x) =7x is reflected across the x-axis. write a function g(x) to describe the new graph. G(x)=___
To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.
The Vance family is saving money to buy a new car that costs $12,000. They plan to save $715 per month (m), and they have already saved $645. Which of the following inequalities show the number of months (m) the Vance family could save in order to buy the new car? Select all that apply. A. 715m≥11,355 B. 715m≤11,355 C. 12,000≤715m+645 D. 12,645≤715m
Answer:
C. 12,000≤715m+645
Step-by-step explanation:
You want to have either equal to or more than 12,000
Answecr:
C
Step-by-step explanation:
What is the solution to this equation?
4x-3 + 2x= 33
O A. x= 15
B. x = 18
O c. x = 5
O D. x = 6
Answer:
4x – 3 + 2x = 33
6x = 36
x = 6
D. x = 6
It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of
. The base angle theorem of isosceles trapezoids verifies that angle
is congruent to angle
. We also see that EH ≅ EH by the
property. Therefore, by
, we see that ΔFHE ≅ ΔGEH.
The solution is ΔFHE ≅ ΔGEH. [SAS], i.e. triangle FHE is similar to triangle GEH, by SAS rule.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Given: An Isosceles trapezoid EFGH in which EF =GH
To prove: ΔFHE ≅ ΔGEH
Proof: In Isosceles trapezoid EFGH, Considering two triangles ΔFHE and ΔGEH
1. FE ≅ G H → [ Given]
2. ∠H = ∠E
→ Draw GM⊥HE and FN ⊥EH, and In Δ GMH and ΔFNE,
GH=FE [Given]
∠M+∠N=180°
so, GM║FN and GF║EH, So GFMN is a rectangle.]
∴ GM =FN [opposite sides of rectangle]
∠GMH = ∠FNE [ Each being 90°]
Δ GMH ≅ ΔFNE [ Right hand side congruency]
→∠H =∠E [CPCT]
→ Side EH is common i.e EH ≅ EH .
→ΔFHE ≅ ΔGEH. [SAS]
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help if you can but this is kinda urgent any help is welcome tho
Answer:
(Change in y)/(change in x) is defined as the average rate of change.
For a linear equation:
y = a*x + b
A is the average rate of change, and is called the "slope" of the linear equation, and this is a constant.
Then the sentence will be:
"The average change between two ordered pairs (x,y) is the ratio (change in x)/(change in y)
In a linear function, this is called the slope, and it is constant"
Write the expression in standard form. -3 + yi = x + 6i
Answer:
The expression in standard form is -3 + 6i
Step-by-step explanation:
Writing complex equation in standard form we have;
-3 + yi = x + 6i
We transfer the real and imaginary parts to be on different sides of the equation as follows;
yi - 6i = x + 3
We factorize the imaginary part;
i(y-6) = x + 3
We note that the real portion on the left hand side of the equation is zero, therefore, we have;
i(y-6) + 0= x + 3
x + 3 = 0
Therefore, x = -3
Substituting the value of x in the first equation, we have;
-3 + yi = -3 + 6i
Comparing gives;
y = 6
The expression in standard form is -3 + 6i.
A line goes through points (0, 3) and (6, 12). What would be the slope of this line's perpendicular bisector?
Answer:
the slope of the perpendicular bisector is -2/3
Step-by-step explanation:
The slope of the line joining the two points P1(0,3), P2(6,12) is given by
m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5
The slope m2 of a line perpendicular to the previous line is given by
m1*m2 = -1
solving
m2 = -1/m1 = -1/ (3/2) = -2/3
THerefore the slope of the perpendicular bisector is -2/3
Circle A has radius 5, and Circle B has radius 2. If CD = 12 and is a common
tangent, what is AB?
Answer:
[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]
Step-by-step explanation:
In the attached diagram
CA=CO+OA
CO=DB
Therefore:
5=2+OA
OA=3 Units
The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:
OB=12 units
OA=3 units
Using Pythagoras theorem
[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]
The windows of a downtown office building are arranged so that each floor has 6 fewer windows than the floor below. If the ground floor has 52 windows, how many windows are on the 8th floor?
Answer:
10
Step-by-step explanation:
This is an arithmetic sequence. The common difference is -6, and the first term is 52.
a = 52 − 6(n − 1)
When n = 8:
a = 52 − 6(8 − 1)
a = 52 − 42
a = 10
Which of the following expressions are equivalent to -9/6?
the correct answer is:
A. 9/-6
A study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.) What percentage of the 5000 surveys were returned? Does that response rate appear to be low? In general, what is a problem with a very low response rate? Of the 5000 surveys, nothing% were returned. This response rate ▼ appears does not appear to be low.
Answer:
Of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
Step-by-step explanation:
Given:
Total sample collected = 5000
Survey returned = 700
i) What percentage of the 5000 surveys were returned?
To find percentage returned, we have:
[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]
Percentage returned = 14%
ii) Does that response rate appear to be low?
Yes, the response is significantly low as only 14% is returned out of expected 100%
iii) In general, what is a problem with a very low response rate?
The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.
Therefore, of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
Find the pattern and fill in the missing numbers: 0, …, 9, 18, 30, 45, ...
it is 9
and it is also 54
Answer:
3 and 63.
Step-by-step explanation:
The sequence formula is [tex]\frac{3n(n+1)}{2}[/tex].
Resulting in a sequence of 0, 3, 9, 18, 30, 45, 63.
If a toy rocket is launched vertically upward from ground level with an initial velocity of 120 feet per second, then its height h after t seconds is given by the equation h(t) = -16t^2 + 120t. How long will it take the rocket to return to the ground? Group of answer choices
Answer:
[tex]Time = 7.5\ seconds[/tex]
Step-by-step explanation:
Given
[tex]Equation:\ h(t) = -16t^2 + 120t[/tex]
[tex]Initial\ Velocity = 160ft/s[/tex]
Required:
Determine the time taken to return to the ground
From the equation given; height (h) is a function of time (t)
When the rocket returns to the ground level, h(t) = 0
Substitute 0 for h(t) in the given equation
[tex]h(t) = -16t^2 + 120t[/tex]
becomes
[tex]0 = -16t^2 + 120t[/tex]
Solve for t in the above equation
[tex]-16t^2 + 120t = 0[/tex]
Factorize the above expression
[tex]-4t(4t - 30) = 0[/tex]
Split the expression to 2
[tex]-4t = 0\ or\ 4t - 30 = 0[/tex]
Solving the first expression
[tex]-4t = 0[/tex]
Divide both sides by -4
[tex]\frac{-4t}{-4} = \frac{0}{-4}[/tex]
[tex]t = \frac{0}{-4}[/tex]
[tex]t =0[/tex]
Solving the second expression
[tex]4t - 30 = 0[/tex]
Add 30 to both sides
[tex]4t - 30+30 = 0+30[/tex]
[tex]4t = 30[/tex]
Divide both sides by 4
[tex]\frac{4t}{4} = \frac{30}{4}[/tex]
[tex]t = \frac{30}{4}[/tex]
[tex]t = 7.5[/tex]
Hence, the values of t are:
[tex]t =0[/tex] and [tex]t = 7.5[/tex]
[tex]t =0[/tex] shows the time before the launching the rocket
while
[tex]t = 7.5[/tex] shows the time after the rocket returns to the floor
Calculate the slope of the line going through A(-4,3) and B(0,6) PLEASE ANSWER
Answer:
6-3/0-(-4)
=3/4
Step-by-step explanation:
Given two points of a line to find the slope, we use the formula.y2-y1/x2-x1 hence the answer above. Our xs are x2=0 x=-4 y2=6 y1=3
Need help solving. Prefer you show each step in solving.
Answer:
AB║CD and AD║BC
Step-by-step explanation:
By the property of a parallelogram,
" Consecutive angles of a parallelogram are supplementary"
In the figure attached,
∠DCB and ∠CDA are the supplementary angles. Therefore ABCD will be a parallelogram.
[Given: m(∠DCB) + m(∠CDA) = 180°]
And the pair of opposite sides of the parallelogram ABCD will be parallel.
AD║BC and AB║CD
A box contains 2 dozen pairs of contact lenses ,of which 8 pairs are tinted. A pair of contact lenses is drawn at random from the box.Find the probability that it is not tinted.What is the answer:2/3 2/5
Answer:
[tex]\dfrac{2}{3}.[/tex]
Step-by-step explanation:
It is given that a box contains 2 dozen pairs of contact lenses ,of which 8 pairs are tinted.
1 dozen = 12 units
Total pairs of contact lenses [tex]=2\times 12 = 24[/tex]
Tinted pairs of contact lenses = 8
Pairs of contact lenses not tinted = 24 - 8 = 16
If a pair of contact lenses is drawn at random from the box, then we need to find the probability that it is not tinted.
[tex]P(\text{Not tinted})=\dfrac{\text{Pairs of contact lenses not tinted}}{\text{Total pairs of contact lenses}}[/tex]
[tex]P(\text{Not tinted})=\dfrac{16}{24}[/tex]
[tex]P(\text{Not tinted})=\dfrac{2}{3}[/tex]
Therefore, the required probability is [tex]\dfrac{2}{3}.[/tex]