Answer:
4/21
Step-by-step explanation:
Given:
1/k - 1/4 = 5Subject is k, so the following steps are to solve it for k:
1/k = 5+ 1/4 ⇒ adding 1/4 to both sides1/k = 21/4 ⇒ simplifying the fraction on right sidek = 4/21 ⇒ inverting both sides to get answerAnswer is 4/21
1
9. By what rational number must
26
be divided to get
?
39
Answer:
let the unknown rational number be X.
26/X=39
X=39/26
X=3/2
While you are driving along westward at 55 mi./hr you doze for 1.5 seconds. How far have you traveled during your snooze?
Answer: 0.02291666
Step-by-step explanation:
divide 55 by 60 (minutes)
then by 60 again (seconds)
multiply by 1.5
there you go
The person travelled for 0.0229167 miles.
To calculate the distance, we have to multiply the speed by the time taken.
Distance = Speed × Time
Speed = 55 miles per hour.
Time taken = 1.5 seconds = 0.0004167 hours
Note that 3600 seconds = 1 hour
Therefore, 1.5 seconds = 0.0004167 hours
Then, the distance will be:
= Speed × Time
= 55 × 0.0004167
= 0.0229167 miles
The person travelled for 0.0229167 miles.
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Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the nth term.
5th term is - 26, 16th term is 51
What is the first term of the sequence?
What is the common difference?
What is the recursive formula for the sequence?
an = ,-1+
What is the formula for the nth term
the sequence?
Enter your answer in each of the answer boxes
Answer:
27
Step-by-step explanation:
375 7579 779
Rectangle PQRS has vertices at P-2,5), Q44,5), R(4, -1), and S(-2,-1). What is the area, in square units, of rectangle PQRS? 21 b 35 36 40
Answer:
36 square units.
C
Step-by-step explanation:
Please refer to the provided graph.
So we want to figure out the area of the rectangle. To do so, we simply need to figure out the base and height of the rectangle. We can then multiply them together to acquire the area.
From the graph, we can see that if we find the length of SR and SP, we can use the the base and height, respectively.
Now, we just have to find there lengths. Technically, we could just count. However, I'm going to use the distance formula.
the distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Find the length of SR:
Point S is (-2,-1) while Point R is (4,-1). Let (-2,-1) be x₁ and y₁ and (4,-1) be x₂ and y₂. Therefore:
[tex]d=\sqrt{(4-(-2))^2+(-1-(-1))^2}\\d=\sqrt{(6^2)+(0)^2} \\d=\sqrt{36}=6[/tex]
So, SR is 6.
Now, find the length of SP:
Point S is (-2,-1) while Point P is (-2,5). Let Let (-2,-1) be x₁ and y₁ and (-2,5) be x₂ and y₂. Therefore:
[tex]d=\sqrt{(-2-(-2))^2+(5-(-1))^2}\\d=\sqrt{0^2+6^2}\\ d=\sqrt{36}=6[/tex]
Therefore, SP is also 6.
Now, the area for a rectangle is:
[tex]A=bh[/tex]
Plug in 6 for the base and 6 for the height:
[tex]A=6(6)\\A=36\text{ units}^2[/tex]
Solve the solution
15 - 2(3 - 2x) = 46
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf x = 9.25}}}}[/tex]Step-by-step explanation:
[tex] \sf{15 - 2(3 - 2x) = 46}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{15 - 6 + 4x = 46}[/tex]
Subtract 6 from 15
⇒[tex] \sf{9 + 4x = 46}[/tex]
Move 9 to right hand side and change its sign
⇒[tex] \sf{4x = 46 - 9}[/tex]
Subtract 9 from 46
⇒[tex] \sf{4x = 37}[/tex]
Divide both sides of the equation by 4
⇒[tex] \sf{ \frac{4x}{4} = \frac{37}{4} }[/tex]
Calculate
⇒[tex] \sf{x = 9.25}[/tex]
Hope I helped!
Best regards!!
The solution of the given equation 15 - 2(3 - 2x) = 46 is x = 37/4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
15 - 2(3 - 2x) = 46
Let us first expand the brackets ,
15 - 6 + 4x = 46
Now solving them we get,
9 + 4x = 46
Substracting by 9 both the sides of the equation we get,
⇒4x = 37
Dividing the equation by 4 we get
⇒x = 37/4
Hence,The solution of the given equation 15 - 2(3 - 2x) = 46 is x = 37/4.
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3x = 17 Answer Needed Very soon
Answer:
x=17/3
Step-by-step explanation:
divide both sides by 3 to isolate x
find the perimeter of the quadrant whose radius is 28cm
Answer:
[tex]\huge \boxed{\mathrm{99.98 \ cm}}[/tex]
Step-by-step explanation:
A quadrant is quarter of a circle.
The perimeter of a quarter of a circle is [tex]\frac{2\pi r}{4} +2r[/tex].
The radius [tex]r[/tex] is 28 cm.
[tex]\frac{2\pi (28)}{4} +2(28)= 99.982297...[/tex]
The perimeter of the quadrant with radius 28 cm is approximately 99.98 cm.
Answer:
[tex]\huge\boxed{Perimeter = 99.98\ cm}[/tex]
Step-by-step explanation:
Quadrant is one - fourth of a circle
Perimeter of quadrant = [tex]\frac{2\pi r }{4} + 2r[/tex]
Where r = 28 cm
=> P = [tex]\frac{2(3.14)(28)}{4} + 2(28)[/tex]
=> P = [tex](3.14)(14) + 56[/tex]
=> P = [tex]43.98 + 56[/tex]
=> P = 99.98 cm
Witch relations is a function
So basically everything but choices B and C are functions.
====================================
Explanation:
A. This is a function as there are no repeated input x values. Each input (x) leads to exactly one output (y).B. This is not a function. We have the input 2 lead to more than one output (1 and 4 at the same time)C. This is not a function. Similar to choice B, we have multiple outputs for a given input. In this case, x = 20 has more than one output.D. This is a function. Any x input will produce only one y output. When graphed, it passes the vertical line test.E. This is a function. This graph passes the vertical line test. It is not possible to draw a vertical line through more than one point on the blue curve, so that's what I mean by "passing the vertical line test".F. This is a function. At any given hour (x), there is exactly one temperature (y) possible. The thermometer is not going to produce multiple readings at any one specific moment in time.produce your answer Frombase four to base 10
Answer:
A. 54₁₀
B. 81₁₀
Step-by-step explanation:
To convert from base 4 to base 10, we simply do the following:
A. 312₄ to base 10
312₄ = (3×4²) + (1×4¹) + (2×4⁰)
312₄ = (3×16) + (1×4) + (2×1)
312₄ = 48 + 4 + 2
312₄ = 54₁₀
Therefore, 312₄ is equivalent to 54₁₀.
B. 1101₄ to base 10
1101₄ = (1×4³) + (1×4²) + (0×4¹) + (1×4⁰)
1101₄ = (1×64) + (1×16) + (0×4) + (1×1)
1101₄ = 64 + 16 + 0 + 1
1101₄ = 81₁₀
Therefore, 1101₄ is equivalent to 81₁₀.
The linear scale factor of two similar shapes is in ratio 3:4. If the area of the smaller shape is 72cm square, find the area of the bigger shape.
Answer:
128 cm²
Step-by-step explanation:
Given the scale factor of 2 similar figures is a : b , then
ratio of areas = a² : b²
Here the scale factor = 3 : 4 , thus
ratio of areas = 3² : 4² = 9 : 16
let x be the area of the larger figure then by proportion
[tex]\frac{9}{72}[/tex] = [tex]\frac{16}{x}[/tex] ( cross- multiply )
9x = 1152 ( divide both sides by 9 (
x = 128
Thus area of larger figure is 128 cm²
The required area of the bigger shape is 128 cm².
The linear scale factor of two similar shapes is in ratio 3:4. the area of the smaller shape is 72cm square. To determine the area of the bigger shape.
What is the Ratio?
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Linear scale factor ratio of two similar shapes = 3:4
Let the area of the bigger shape = x²
Area of the smaller shape = 72
Now since the ratio is linear = 3 : 4
squaring the ratio = 3²:4²
= 9:16
Now the ratio of the are = 72: x²
Equating the ratios
72/x² = 9/16
x² = 16/9 * 72
x² = 1.77 * 72
x² = 128
Thus, the required area of the bigger shape is 128 cm².
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Find the volume for the following composite object.
Answer:
[tex] Volume = 7440.16 ft^3 [/tex]
Step-by-step explanation:
Volume of the composite object = volume of cylinder - volume of rectangular prism
Volume of the composite object = πr²h - whl
where,
π = 3.14
r = 14 ft
h = 14 ft
w = 6 ft
l = 14 ft
[tex] Volume = (3.14*14^2*14) - (6*14*14) [/tex]
[tex] Volume = 8616.16 - 1176 [/tex]
[tex] Volume = 7440.16 ft^3 [/tex]
Order least to greatest: 1.5, 1.1, .9, 1, 1.7, 1.25
Answer:
1,1.1,1.25,1.5,1.7,9
find the common ratio of the gemetric sequence -320, 80, -20, 5
Answer:
- 0.25
Step-by-step explanation:
Common ratio
[tex]r = \frac{succeeding \: term}{preceding \: term} \\ = \frac{80}{ - 320} \\ = - \frac{1}{4} \\ = - 0.25[/tex]
Given that :-
Geometric sequence → -320,80,-20,5
To find :-
Common ratio .
Solution :-
Common ratio = ar/a
→ Here a = -320
→ ar = 80
→ Common ratio = 80/-320
→ Common ratio = -1/4Let's check it →
Taking a = 80 and ar = -20
→ Common ratio = -20/80
→ Common ratio = -1/4So common ratio will be -1/4
Melissa was charged $3 each time she
used the ATM at work. She used the
work ATM 24 times in a month. By how
much did her bank account change from
using the ATM at work?
Answer:
Therefore, Melissa will be charged $72 for busing work ATM 24 times in a month
Step-by-step explanation:
Melissa was charged $3 each time she used the ATM at work
She used the work ATM 24 times in a month.
Charge per usage= $3
Number of times of usage= 24
By how much did her bank account change from using the ATM at work
Total charges = charge per usage × Number of times of usage
= 3 × 24
= 72
Total charges = $72
Therefore, Melissa will be charged $72 for busing work ATM 24 times in a month
a fence 2.4m tall,is 10m away from a tree of height 16m.calculate the angle of elevation of the top of the tree from the top of the fence
Answer:
53.67⁰
Step-by-step explanation:
Give the height of the fence to be 2.4 m tall
Height of the tree = 16m
Horizintal distance from the fence to the tree = 10m
Check the diagram in the attachment.
From the attachment, we will need to first calculate the height AB
AC = AB+BC
Given AC = height of the r=tree = 16m
BC is the height of the fence = 2.4m
16 = AB + 2.4
AB = 16-2.4
AB = 13.6m
Using the SOH CAH TOA trig identity on right angled triangle AEB with AB as the opposite and AB and the adjacent as BE
Using TOA;
tan ∝ = opposite/adjacent = AB/BE
∝ is the angle of elevation of the top of the tree from the top of the fence.
tan∝ = 13.6/10
tan∝ = 1.36
∝ = tan⁻¹1.36
∝ = 53.67⁰
Hence the angle of elevation of the top of the tree from the top of the fence is 53.67⁰
Derrick does 29 push-ups in the morning and 36 more push-ups in the evening. If he does the same number of push-ups every day of the week for 4 weeks, about how many push-ups will he do in all?
29 + 36 = 65 total pushups per day.
Multiply pushups per day by 7 days per week:
65 x 7 = 455 total pushups per week
Multiply pushups per week by number of weeks:
455 x 4 weeks = 1,820 total pushups.
Darryl bought nine candy bars for a total of $54. How much did each candy bar cost?
Answer:
$6
Step-by-step explanation:
Divide $54 with 9 canday bars
So, 54/9
=$6
Each candy bar cost $6
|-12+3|= simply the expression
Answer:
|-12+3|=9
Step-by-step explanation:
Hello, -12+3=-9 and then we have to take the absolute value of -9, which is 9.
Thank you
Answer:
9
Step-by-step explanation:
|-12+3|
|-9|
9
what is the value of y^0
Answer:
1
Step-by-step explanation:
Any number that is raised to the power of 0 is 1.
1^0 = 1
323^0 = 1
k^0 = 1
Hope that helped!!! k
Verify the identity. ( 1-sin x)/cosx=cosx/(1+sin x)
Answer:
See below.
Step-by-step explanation:
I'm going to use what I assume is the correct question.
[tex] \dfrac{1 - \sin x}{\cos x} = \dfrac{\cos x}{1 + \sin x} [/tex]
[tex] \dfrac{\cos x}{\cos x} \times \dfrac{1 - \sin x}{\cos x} = \dfrac{\cos x}{1 + \sin x} [/tex]
[tex] \dfrac{\cos x(1 - \sin x)}{\cos^2 x} = \dfrac{\cos x}{1 + \sin x} [/tex]
Now use the identity
[tex] sin^2 x + cos^2 x = 1 [/tex]
[tex] cos^2 x = 1 - sin^2 x [/tex]
We replace [tex] \cos^2 x [/tex] in the left denominator.
[tex] \dfrac{\cos x(1 - \sin x)}{1 - \sin^2 x} = \dfrac{\cos x}{1 + \sin x} [/tex]
Factor the difference of squares in the left side denominator.
[tex] \dfrac{\cos x(1 - \sin x)}{(1 + \sin x)(1 - \sin x)} = \dfrac{\cos x}{1 + \sin x} [/tex]
[tex] \dfrac{\cos x}{1 + \sin x} = \dfrac{\cos x}{1 + \sin x} [/tex]
What is the value of -32+(-4+7)(2)?
0-28
0 -3
O 3
O 15
nunber a that is -27
hope it helps
Answer:
it should be -26
Step-by-step explanation:
-32+(-4+7)(2)
=-32+3×2
=-32+6
=-26
How to solve -3 + 10 - 1
Answer:
6
Step-by-step explanation:
-3+10-1
10-4
=6
hope this helps
Answer:
6
Step-by-step explanation:
You can add -3 and -1 to make -4 and subtract from 10.
-3-1+10= 6
A two digit number is chosen at random. Find the probality that the number is a perfect square
Answer:
[tex]\Large \boxed{\frac{1}{15} }[/tex]
Step-by-step explanation:
The two-digit perfect squares are 16, 25, 36, 49, 64, 81.
There are 6 numbers that are two-digit perfect squares.
There are a total of 90 numbers that have two-digits.
P(two-digit perfect square) = [tex]\frac{6}{90} =\frac{1}{15}[/tex]
The Probability that the number is a perfect square out of two-digit number is chosen at random is [tex]\frac{1}{15}[/tex] .
What is the probability?Probability is a branch of mathematics that deals with the occurrence of a random event.
For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.
Probability formula :
Probability(Event) = Favorable Outcomes/Total Outcomes
According to the question
A two digit number is chosen at random.
Total number of two digit number are from 10 to 99
i.e
=99-10+1 = 90
or Total Outcomes = 90
Total of perfect square of two-digits are: 16,25,36,49,64,81
Total number of perfect square of two-digits = 6
or Favorable Outcomes = 6
Now , The Probability that the number is a perfect square
Probability(Event) = Favorable Outcomes/Total Outcomes
Probability(Event) = [tex]\frac{6}{90}[/tex]
Probability(Event) = [tex]\frac{1}{15}[/tex]
Hence, the Probability that the number is a perfect square out of two-digit number is [tex]\frac{1}{15}[/tex] .
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part 2 of the other set of questions i need help answering and explaning please!
Answer:
top answer is -23
bottom answer is -2
On a coordinate plane, a line goes through (negative 3, 2) and (2, negative 1). A point is at (3, 0). What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)? 3x + 5y = −9 3x + 5y = 9 5x − 3y = −15 5x − 3y = 15
Answer:
5x -3y = 15
Step-by-step explanation:
First find the slope of the line through ( -3,2) and (2,-1)
m = (y2-y1)/(x2-x1)
=( -1-2)/(2--3)
= -3/(2+3)
= -3/5
We want a line that is perpendicular so the slopes will multiply to -1
m * -3/5 = -1
Multiply each side by -5/3
m * -3/5 * -5/3 = -1 *-5/3
m = 5/3
The slope of the perpendicular line is 5/3
We have a slope and a point
Using point slope form
y-y1 = m(x-x1)
y-0 = 5/3( x-3)
y = 5/3( x-3)
Distribute
y = 5/3x -5
Multiply each side by 3
3*y = 3(5/3x -5)
3y = 5x - 15
Subtract 5x from each side
-5x+3y = -15
Multiply each side by -1
5x -3y = 15
Answer:
D. 5x − 3y = 15
May I have brainliest please? :)
What is the slope of a line between (-17,6)and (-18,11)
Answer:
m = -5
Step-by-step explanation:
m = (y₂ - y₁) / (x₂ - x₁)
m = (11 - 6) / (-18 - ( -17))
m = 5 / (-18 + 17)
m = 5 / -1
m = -5
Choose the percent that is equivalent to the number. 0.75 A. 0.75% B. 7.5% C. 0.0075% D. 75%
Answer:75
Step-by-step explanation:
Answer:
D. 75%
Step-by-step explanation:
Hello!
To convert a decimal to a percent we move the decimal point two times to the right
0.75 ⇒ 75%
The answer is D.75%
Hope this helps!
If f(x) x^2 — 5 + 3 and g(x) = 1 — 2x, find f(g(x).
Answer:
f(g(x))= 1-2(x^2-5+3)
Step-by-step explanation:
To do this you would plug in x^2-5+3 into the x for the g(x) so you would get f(g(x))= 1-2(x^2-5+3)
Answer:
4x^2+6x-1
Step-by-step explanation:
the question asks for f(g(x)). this means you have to plug in the value of g(x) into the "x" of f(x). (you should always work inside out.)
if you do that, you get this equation : (-2x+1)^2-5(-2x+1)+3 (i changed the 1-2x into -2x+1) because you plug in the g(x) (in this case, -2x+1) into the x's in the f(x) equation.
first you foil the (-2x+1)^2 and get 4x^2-4x+1.
then you distribute -5(-2x+1) and get +10x-5
and you bring down the 3.
so you have 4x^2-4x+1+10x-5+3 and you combine your like terms and get
4x^2+6x-1
which is your answer!
divide 28 cans of soda into two groups so the ratio is 3 and 4
Answer:
12 and 16 or 12:16
Step-by-step explanation:
The ratio is 3:4. You need the ratio to equal 28. If you multiply 4 by each one, you get:
3 times 4= 12
4 times 4= 16
12+16=28
what is 40% of 20
zdfghj
First write 40% as the decimal .40.
The word "of" tells us to multiply.
So we have (.40)(20) which is 8.
So 40% of 20 is 8.
Answer:
8
Step-by-step explanation:
40% of 20
= 40 × 20/100
= 800/100
= 8/1
= 8
Thus, 40% of 20 is 8