8 -4s = s + 13 Solve for S
Answer:
s = -1
Step-by-step explanation:
8 - 4s = s + 13
-4s - s = 13 - 8
-5s = 5
s = 5/-5
s = -1
probe:
8 - 4*-1 = -1 + 13
8 + 4 = 12
Sarah and Homer each have a cylinder. Sarah's cylinder has a diameter of 9 cm and a height of 4 cm. Homer's cylinder has a diameter of 4 cm and a height of 9 cm. Find the surface area of Sarah's cylinder, in square centimetres. Round your answer to two decimal places. answer fast plz its urgent
Answer:
240.37 cm^2
Step-by-step explanation:
The question is on the mensuration of solids, a cylinder
Given data
height of cylinder h= 4 cm
diameter d= 9 cm
radius = d/2= 9/2= 4.5 cm
we know that the surface area of cylinder is
[tex]SA= 2\pi r h+ 2\pi r^2[/tex]
Substituting our data into the expression we have
[tex]SA= 2*3.142 *4.5* 4+ 2*3.142 4.5^2[/tex]
[tex]SA= 113.12+ 127.25\\\\SA= 240.37 cm^2[/tex]
Therefore the total surface area is 240.37 cm^2
can someone help me please
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ {12.56 \: {mm}^{2} }}}}}}[/tex]Step-by-step explanation:
Given,
Radius ( r ) = 2 mm
pi ( π ) = 3.14
Finding the area of circle having radius of 2 mm
Area of circle [tex] \sf{ = \pi \: {r}^{2} }[/tex]
plug the values
⇒[tex] \sf{3.14 \times {2}^{2} }[/tex]
Evaluate the power
⇒[tex] \sf{3.14 \times 4}[/tex]
Multiply the numbers
⇒[tex] \sf{12.56 \: {mm}^{2} }[/tex]
Hope I helped!
Best regards!!
what is the smallest length that can be divided exactly into equal sections of length 5m, 8m and 12m
Answer:
1m
Step-by-step explanation:
That would be 1 m.
1 is the only whole number which divides exactly into 5, 8 and 12.
(x+4) (x+10)
simplify
Answer:
x^2 + 14x + 40.
Step-by-step explanation:
(x+4) (x+10)
= x(x + 10) + 4(x + 10) ( By the Distributive Law)
= x^2 + 10x + 4x + 40
= x^2 + 14x + 40.
Answer:
x^2+14x+40
Step-by-step explanation:
xx+x*10+4x+4*10= xx+10x+4x+4*10
Then simplify
x^2+14x+40
I hope this helps!
Find the area the sector. A. 38π in² B. 1083π4 in² C. 57π4 in² D. 1083π8 in²
Answer:
[tex]A=135.37\ \text{inch}^2[/tex]
Step-by-step explanation:
Given that,
Radius of circle, r = 19 inch
Angle with sector, [tex]\theta=135^{\circ}[/tex]
We need to find the area of the sector.
The formula is given by :
[tex]A=\dfrac{\theta}{360}\times \pi r^2\\\\A=\dfrac{135}{360}\times \pi (19)^2\\\\A=135.37\ \text{inch}^2[/tex]
So, the area of the sector is [tex]135.37\ \text{inch}^2[/tex].
Which are rational and irrational? Thanks in advance :)
Answer:
[tex]3\frac{1}{2}-rational[/tex]
[tex]\pi -irrational[/tex]
[tex]-\frac{2}{3}-rational[/tex]
[tex]\sqrt{16} -rational[/tex]
[tex]\sqrt{3} -irrational[/tex]
[tex]18-rational[/tex]
[tex]0.625-rational[/tex]
[tex]0.987987987...-rational[/tex]
Step-by-step explanation:
Rational numbers:
-are all numbers you can write as a quotient of integers [tex]\frac{a}{b}[/tex] , [tex]b\neq 0[/tex]
-include terminating decimals. For example, [tex]\frac{1}{8}=0.125[/tex]
-include repeating decimals. For example, [tex]\frac{1}{3} =0.33333....[/tex]
Irrational numbers:
-have decimal representations that neither terminate nor repeat. For example, [tex]\sqrt{2}=1.414213....[/tex]
-cannot be written as quotients of integers
f(x) = 3•2^x
h(x) = 2x - 7
h(f(2)) =
Answer:
17
Step-by-step explanation:
f(x) = 3•2^x
h(x) = 2x-7
f(2) = 3•2^2
= 3•4
= 12
h(f(2)) = 2(12) - 7
= 24 - 7
= 17
what is mid point theorem
Answer:
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Step-by-step explanation:
i don't have an explanation though
Answer:
The theory of midpoint theorem is used in coordinate geometry stating that the midpoint of the line segment is an average of the endpoints. Both the ‘x’ and the ‘y’ coordinates must be known for solving an equation using this theorem. The Mid- Point Theorem is also useful in the fields of calculus and algebra.
Step-by-step explanation:
Od=125
d) f = 120
11. Melissa is buying a sweater. The original cost of the sweater
is $18.00. The sweater is 15% off, and sales tax is 8%. How
much will the sweater cost?
a) $14.08
O b) $12.24
O c) $16.52
O d) $15.30
Answer:
Hey there!
The sweater is selling for 85% of the original price
0.85(18)=15.30
1.08(15.30)=16.52
Let me know if this helps :)
The solution is Option C.
The total cost of the sweater is $ 16.52
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the original cost of the sweater be = $ 18
Let the sales tax percentage be = 8 %
Let the discount of the sweater be = 15 %
So , the equation for the total cost of the sweater is
The cost of the sweater after discount of 15 % is = original cost of the sweater - discount of the sweater x original cost
The cost of the sweater after discount of 15 % is = 18 - ( 15/100 ) x 18
= 18 - 0.15 x 18
= 18 - 2.7
= $ 15.3
Now , the cost of the sweater after sales tax of 8 % is = cost of the sweater after discount + sales tax percentage x cost of the sweater after discount
So , the equation is
The cost of the sweater after sales tax of 8 % is = 15.3 + ( 8/100 ) x 15.3
= 15.3 + 0.08 x 15.3
= 15.3 + 1.224
= $ 16.524
Hence , the total cost of the sweater is $ 16.52
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Q1) If Q is directly proportional to P and Q = 28 when P = 4, (i) express Q in terms of P, (ii) find the value of Q when P = 5, (iii) calculate the value of P when Q = 42.
Answer: i) Q=7*P ii) if P=5 => Q=35 iii) if Q=42 => P=6
Step-by-step explanation:
Q is directly prportional to P that means that
Q/P=k=const ( where k is the prportionality coefficient)
So k= 28/4=7
So i) Q= 7*P
ii) Q=5*7=35 if P=5 =>Q=35
iii) P=42/7=6 if Q=42 => P=6
Help me pleaseee. :)
Answer:
Answer attached below
Since there are no common factors, the only common factor for he eqaution is 1
(✿◡‿◡)
Write an algebraic expression for four times the
square of n.
Answer:
4n^2
Step-by-step explanation:
n to the power of 2 (squared), multiplied by 4
[tex]4n^{2}[/tex]
An algebraic expression is one that is constructed using integer constants, variables, and algebraic operations.
Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, is a basic algebraic operation.
Square of [tex]n=n^{2}[/tex]
Four times the square of [tex]n^{2}[/tex] is equal to [tex]4n^{2}[/tex]
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How to find the solution for 3x-11=x+3 ?
Answer:
7
3 times ? - 11
=
? + 3
? = 7
Step-by-step explanation:
3 times 7 is 21 -11 is 10
7+3 is 10
Both equations has to make 10 so it is the answer of 7
Hope this helps :)
Answer:
[tex]\boxed{x=7 }[/tex]
Step-by-step explanation:
3x - 11 = x + 3
→ Minus x from both sides to isolate the 'x's
2x - 11 = 3
→ Add 11 to both sides to isolate 2x
2x = 14
→ Divide both sides 2 to isolate x
x = 7
Which answer choice is a coefficient in the expression shown below?
2-x
Answer:
Coefficents of 2-x: 2, -1.
The answer is 2 or -1, but I don't have choices.
Answer:
-1
Step-by-step explanation:
The coefficient is the number in front of the variable along with the sign
2 + -1x
The coefficient is -1
Suppose that you could replace the ordered pair
(1.4) to make the relation R (shown left) into a
function. Which ordered pair would work?
O (1,2)
(-1,4)
O (23)
(4, 15)
DONE
Answer:
This is incomplete, but i will answer it in a general way.
A function is something like y = f(x)
You can think in a function like a "machine", that eats an input (x) and transforms it into an output (y).
The functions have a rule: For all the possible inputs, the function can transform them into only one output.
This means that if we have for an input x1.
f(x1) = y1 and f(x1) = y2
So f(x) maps x1 into two different values, y1 and y2, then this is not a function.
Now, you want to change the point (1, 4) of a relationship in order to transform it into a function (so in the relation R we have two points with x = 1, and differet values of y). Then you need to choose the option that in the x-component does not have the same value that one of the other data points of the relation.
What is (f−g)(x)? f(x)=x4−4x2+4 g(x)=x3−2x2+4x−8 Enter your answer in standard form.
Answer:
x4-x3-2x2-4x+12
Step-by-step explanation:
(f-g)(x)=f(x)-g(x)
=> x4-4x2+4-(x3-2x2+4x-8)
=> x4-4x2+4-x3+2x2-4x+8
=> x4-x3-2x2-4x+12
The value of the function (f-g)(x) is [tex]x^4-x^3-2x^2-4x+12[/tex].
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are [tex]f(x)=x^4-4x^2+4[/tex] and g(x)=x³-2x²+4x-8.
Now, (f-g)(x)=f(x)-g(x)
= ([tex]x^4-4x^2+4[/tex])-(x³-2x²+4x-8)
= [tex]x^4-4x^2+4[/tex]-x³+2x²-4x+8
= [tex]x^4-x^3-2x^2-4x+12[/tex]
Therefore, the value of the function (f-g)(x) is [tex]x^4-x^3-2x^2-4x+12[/tex].
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PLEASE HELP An equation in the form y = mx + b is in standard form. True False
Answer: False!
This equation is in slope - intercept form, which is used to calculate and graph a line, and/or find the y - intercept and slope of a line. The standard form would be the equation before it was converted into slope - intercept form.
Hope this helps!
Answer:
False
Step-by-step explanation:
The y=mx+b form is called the slope-intercept form.
● m is the slope
● b is the y-intercept
● x is the variable (the input)
● y is the output
John has a box of nails. The box contains 65 small nails, 40 medium nails, and 45 large nails. Susan has a box of nails that has the same proportion of small, medium, and large nails as John's box. There are 176 medium nails in Susan's box. What is the total number of nails in Susan's box?
Answer:
The total number of nails in Susan's box is 660 nails
Step-by-step explanation:
The given parameters are;
The number of small nails in John's box = 65
The number of medium nails in John's box = 40
The number of large nails in John's box = 45
The number of medium nails in Susan's box = 176
The ratio of the nails in John's box is given as follows;
The ratio of small nails in John's box = 65/(65 + 40 + 45) = 13/30
The ratio of medium nails in John's box = 40/(65 + 40 + 45) = 4/15 = 8/30
The ratio of large nails in John's box = 45/(65 + 40 + 45) = 3/10 = 9/30
Given that the proportion of the nails in John's box and Susan's box are the same, we have;
The ratio of medium nails in Susan's box = 8/30
Therefore;
Where the total number of nails in Susan's box = X, we have;
8/30 × X = 176
X = 176 × 30/8 = 660 nails
The total number of nails in Susan's box = 660 nails.
Using proportions, it is found that the total number of nails in Susan's box was 660.
---------------
John had 65 + 40 + 45 = 150 nails.The proportion of medium nails is: [tex]\frac{40}{150}[/tex]Susan's box has x nails.Of those nails, 176 are medium. Thus, the proportion of medium nails out of the total in Susan's box is of: [tex]\frac[176}{x}[/tex]---------------
Since the proportions are equal:
[tex]\frac{40}{150} = \frac{176}{x}[/tex]
[tex]40x = 150\times176[/tex]
[tex]x = \frac{150\times176}{40}[/tex]
[tex]x = 660[/tex]
The total number of nails in Susan's box was 660.
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12, 6, 0, -6,
What is the common difference in the following arithmetic sequence
Answer:
-6
Step-by-step explanation:
In an arithmetic sequence, the common difference is the difference between each number in the sequence.
In this sequence, the common difference is -6 because from left to right, we can see that the numbers decrease by 6 each time.
For example, 12 - 6 = 6.
Answer:
every step you subtract 6 so the common difference is -6
Andrea ran 4 a miles on
Saturday and 5 miles I
on Sunday. How many
miles did she run in all?
Answer:9
Step-by-step explanation:5+4=9
Write the equation of the line perpendicular to x+2y=6 that passes through (5, 8).
Answer:
y = 2x-2
Step-by-step explanation:
First find the slope of the line
x+2y=6
2y = -x+6
y = -1/2x +3
This is in slope intercept form ( y = mx+b) so -1/2 is the slope
We want a line that is perpendicular so take the negative reciprocal of the slope
- ( 1/ (-1/2)) = 2
The slope of the perpendicular line is 2
y = 2x+b
Substitute the point into the equation
8 = 2(5) +b
8 = 10+b
-2 =b
The equation of the line perpendicular is
y = 2x-2
Answer:
y = 2x - 2
Step-by-step explanation:
x + 2y = 6 can be solved for y (and thus for slope m) as follows:
2y = -x + 6, or y = (-1/2)x + 3.
Any new line perpendicular to this one has a slope that is the negative reciprocal of (-1/2); that would be +2.
Starting from y = mx + b,
Replace x with the given 5, y with the given 8 and m with the calculated +2:
8 = 2(5) + b, or
b = -2
and then the desired equation is
y = 2x - 2
Which of the following variables
is most likely to be used as categorical?
A) Length of a garden hose
B) Recorded rainfall for a day
C) Flower color
D) Weight of books on a shelf
Answer:
C) Flower color.
Step-by-step explanation:
Quantitative variables are things that can be measured. A garden hose's length is measured in meters or feet. You measure the rainfall for a day in millilitres or liters. The weight of books on a shelf is measured in pounds or grams.
Categorical variables are often descriptions, such as C) Flower color.
Hope this helps!
Flower colors, generated from anthocyanins, flavonoids, or carotene which draw bone, trichromats, photoreceptor cells, tri- or tetrachromats butterflies & birds, that are supersensitive, blues, as well as green.
Quantity variables are measurable items.In meters or feet is measured the time of garden plants.The precipitation is calculated in milliliters or liters for one day.Books are assessed in pounds or grams in mass in a rack.That is why categorical variables, such as Flowers color, frequently are descriptions.Therefore, the "Option C" is the only correct answer.
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Hector and Evelyn are solving the following problem. Find x,y, and z in this 45-45-90 triangle.
Answer: A. They are both incorrect
Step-by-step explanation:
x=3√2
y=6
z=3√2
-----------------------
45-45-90=1:1:√2
------------------------
solve for x
x is the side accordingly to 90 in the smaller triangle, so it should be the [45] side times √2
3×√2=3√2
-----------------------
solve for y
y is the side accordingly to 90, so it should be the [45] side times √2
3√2×√2=6
----------------------
solve for z
z is the side accordingly to 45 in the bigger triangle, x is also accordingly to 45 in the bigger triangle
z=x
z=3√2
helpppppppppppppppppp
Answer:
B
Step-by-step explanation:
a negative and a negative makes a positive, so in this case, it would be a positive 4.
Answer: C
Step-by-step explanation: 96 divided by 8 will give 12 and you subtract 12 from 2 to the power of 3 and it will give 4.
2 to the power of 3= 2×2×2=8
(96÷8)-2³=12-2³
=12-8
=4
Create two groups of cards with the SAME SUM using as many cards as possible using the numbers 8 7 6 2 1 3.
Answer:
Explained below.
Step-by-step explanation:
In this case we need to form two group of cards (consisting of any number of cards) having the same sum using the cards numbered as 8, 7, 6, 2, 1, 3.
The possible groups are as follows:
Group 1 Group 2 Sum
{8, 1} {7, 2} 9
{8, 2} {7, 3} 10
{8, 3} {7, 3, 1} 11
{8, 1, 3} {7, 3, 2} 12
{8, 2, 3} {7, 2, 1, 3} 13
{8, 3, 2, 1} {7, 6, 1} 14
And so on.
Which of the following numbers are perfect squares? Choose all that apply. A 27 D 108 B 36 E 121 C 81 F 169
Compare and contrast a line and a line segment I mean how are they different, how are they alike?
Line segment is limited by two endpoints which also define one.
A Line is not limited to but only exists because of those two endpoints.
Hope this helps.
A church spire casts a shadow on the level ground. At the tip of the shadow, the tip of the spire lies 25° upward. Walking 100 m closer, the tip of the spire is at an angle of 55°. What must be the height of the spire in Figure 2?
Answer:
The height of the spire must be 69.24 m
Step-by-step explanation:
The information given are;
The initial angle of elevation of the tip of the spire from the tip of the shadow = 25°
The angle of elevation of the tip of the spire from the tip of the shadow after moving 100 m closer = 55°
The change distance moved closer to the church spire = 100 m
Let the base angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow be 25° and ∠x°
We have;
∠x° and the 55° angle of the ray from the tip of the spire to the tip of the shadow are supplementary angles (angle on a straight line)
Therefore;
∠x° = 180° - 55° = 125°
The calculated angle 125° above, the given 25° and the angle in between the two rays from the tip of the spire to the tip of the shadows are the interior angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow
Let the angle in between the two rays from the tip of the spire to the tip of the shadows = y
Therefore;
125° + y° + 25° = 180 (Angle sum theorem)
y° = 180° - (125° + 25°) = 30°
By sin rule, we have;
100/(sin (30°)) = (The length of the initial ray from the tip of the spire to the tip of the shadow before the shift)/(sin(125°))
Let the length of the initial ray from the tip of the spire to the tip of the shadow before the shift = l
100/(sin (30°)) = l/(sin(125°))
l = (sin(125°))×100/(sin (30°)) = 163.83 m
The height of the spire, by trigonometric ratio = sin(25°) × 163.83 m = 69.24 m
The height of the spire = 69.24 m.
2x² - 7x + 3 = 0 solve the quadratic equations by using the quadratic formula
Answer:
x = 1/2 or 3
Step-by-step explanation:
Compare the given equation to the standard form equation to identify the values of the variables in the formula. Then put those values in the formula and do the arithmetic.
[tex]ax^2+bx+c=0\\\\2x^2-7x+3=0\\\\a=2;\ b=-7;\ c=3\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)}}{2(2)}=\dfrac{7\pm\sqrt{25}}{4}=\dfrac{7\pm 5}{4}\\\\x=\left\{\dfrac{1}{2},3\right\}[/tex]
Answer:
x = 3x =1/2Step-by-step explanation:
[tex]2x^2-7x+3=0\\\\x_1 ,2 =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=2\\\:b=-7\\,\:c=3\\:\quad x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\times\:2\times\:3}}{2\times\:2}\\\\=\frac{7+\sqrt{\left(-7\right)^2-4\times\:2\times\:3}}{2\times\:2}\\\\7+\sqrt{\left(-7\right)^2-4\times\:2\times\:3}=7+\sqrt{25}\\\\=\frac{7+\sqrt{25}}{2\times\:2}\\\\=\frac{7+\sqrt{25}}{4}\\\\\sqrt{25}=5\\\\=\frac{7+5}{4}\\\\=\frac{12}{4}\\\\=3 \\[/tex]
[tex]x=\frac{-\left(-7\right)-\sqrt{\left(-7\right)^2-4\times\:2\times\:3}}{2\times\:2}\\\\=\frac{7-\sqrt{\left(-7\right)^2-4\times\:2\cdot \:3}}{2\times\:2}\\\\7-\sqrt{\left(-7\right)^2-4\times \:2\times\:3}=7-\sqrt{25}\\\\=\frac{7-\sqrt{25}}{2\times \:2}\\\\=\frac{7-\sqrt{25}}{4}\\\sqrt{25}=5\\\\=\frac{7-5}{4}\\=\frac{2}{4}\\\\=\frac{1}{2}[/tex]