Since the weight varies directly, we have that
[tex]156.71=k\times26.64[/tex]where k is the constant of proportinality.
In order to find k, we can divide both sides by 26.64 and get
[tex]\begin{gathered} \frac{156.71}{26.64}=k \\ or\text{ equivalently, } \\ k=\frac{156.71}{26.64} \end{gathered}[/tex]which gives
[tex]k=5.8825[/tex]Once we know the constant of proportionallity, we can write
[tex]213.53=k\times x[/tex]where x denotes the unknown weight on the Moon. Since k is 5.8825, we get
[tex]213.53=5.8825\times x[/tex]Then, by dividing both sides by 5.8825, we obtain
[tex]\begin{gathered} \frac{213.53}{5.8825}=x \\ or\text{ equivalently,} \\ x=\frac{213.53}{5.8825} \end{gathered}[/tex]Therefore, we have
[tex]x=36.299\text{ lb}[/tex]Finally, by rounding to the nearest tenth, the answer is: 36.3 lb
X^3+3x^2+kx-10 and x-1 is a factor what is k
Answer:
6
Step-by-step explanation:
Using the factor theorem, the expression evaluated at [tex]x=1[/tex] will equal [tex]0[/tex].
[tex]1^3+3(1^2)+k(1)-10=0 \\ \\ 1+3+k-10=0 \\ \\ k=6[/tex]
÷5=9i need help please
Answer
The missing number = 45
Explanation
Let the unknown number be x
x ÷ 5 = 9
Multiply both sides by 5
x ÷ 5 × 5 = 9 × 5
x = 45
Hope this Helps!!!
7. Write an equation of the line parallel to y = 8x - 1 that contains (-6, 2). Please write the equation
in slope-intercept form.
Answer:
you have to use the formula of a line passing through a point, so: y-y0=m(x-x0)
We also know that m=8, because it is parallel to the line y=(8=m)x -1
so: y-2=8(x+6)
and you solve it, so:
y-2=8x+48
y=8x+48+2
y=8x+50
Which graph has a slope of ? A coordinate plane with a straight line. The line starts at (negative 5, negative 4) and passes through points at (0, 1) and (4, 5). A coordinate plane with straight line. The line starts at (negative 5, negative 2) and passes through points at (negative 1, 0) and (4, 5). A coordinate plane with straight line. The line starts at (negative 5, negative 1) and passes through points at (negative 2, 0) and (3, 2). A coordinate plane with straight line. The line starts at (negative 4, negative 5) and passes through points at (0, 0) and (4, 5).
Answer: B
Step-by-step explanation:
a model rocket is launched with an initial upward velocity of 175 ft/s the rocket's height is represented by h (in feet) after t seconds is given by the followingh = 175t - 16t^2find all values of t for which the rockets height id 85 feetand i need to round the answer to nearest hundredth
Given relation between height and time is:
[tex]h=175t-16t^2[/tex]Now put the value of h=85 ft in given relation:
[tex]85=175t-16t^2[/tex]Solving it for t:
[tex]\begin{gathered} 16t^2-175t-85=0 \\ t=\frac{175\pm\sqrt[]{(-175)^2-4\times16\times85}}{2\times16} \\ t=\frac{175\pm\sqrt[]{30625-5440}}{32} \\ t=\frac{175\pm\sqrt[]{25185}}{32} \\ t=\frac{175\pm158.6}{32} \\ t=0.51\text{ or }10.43\text{ second} \end{gathered}[/tex]NSWERVariableType ofvariableQuantitative(a) Temperature (in degrees Fahrenheit)Level ofmeasurementNominalOrdinalIntervalRatioCategoricalQuantitative(b) Dosage (in milligrams) of medicationNominalOrdinalIntervalRatioCategoricalQuantitative(C) Exchange on which a stock is traded(NYSE, AMEX, or other)NominalOrdinalIntervalRatioCategorical
We are looking at what type of variables are given. Let's analyze it one by one to check which one suits it best.
(a) Temperature
Temperature is measured by numbers, hence, this is categorized as a quantitative variable. Temperature does not have a non-finite value since it changes as time goes by, hence, the level of measurement for this type of variable is ratio.
Answer: Quantitative and ratio
(b) Dosage of the medication
The dosage of medication is measured in milligrams, which means we are dealing with numbers, hence, this is a quantitative variable. In the case of dosage, we are dealing with fixed values, hence, the level of measurement for this type of variable is interval.
Answer: Quantitative and interval
(c) Stock exchange
Stock exchanges are types of group variables. These are represented as categories, hence, this variable is classified as categorical. The exchanges are ranked in some specific order. When dealing with categorical variables that have rank order, we have ordinal variables.
Answer: Categorical and ordinal
WXYZ~EFGD.13WXYZ26EFGDWhat is the similarity ratio of WXYZ to EFGD?Simplify your answer and write it as a proper fraction, improper fraction, or whole number
STEP - BY - STEP SOLUTION
What to find?
The similarity ratio of WXYZ to EFGD.
Given:
The ratio of WXYZ to EFGD can be determine by taking the ratio of any of the simila side of WXYZ to EFGD.
That is;
[tex]Similarity\text{ ratio=}\frac{WZ}{ED}[/tex]Since EFGD is a rectangle, using the property of the rectangle that state " opposite sides are congruent, we can deduce that ED = EG = 6
Hence,
[tex]similarity\text{ ratio=}\frac{WZ}{ED}=\frac{3}{6}=\frac{1}{2}[/tex]ANSWER
1/2
please help asap please please i’ll give brainliest
Answer:
[tex] C = \dfrac{5}{9}(F - 32) [/tex]
Step-by-step explanation:
[tex] F = \dfrac{9}{5}C + 32 [/tex]
Switch sides to have C on the left side.
[tex] \dfrac{9}{5}C + 32 = F [/tex]
Subtract 32 from both sides.
[tex] \dfrac{9}{5}C = F - 32 [/tex]
Multiply both sides by 5/9.
[tex] \dfrac{5}{9} \times \dfrac{9}{5}C = \dfrac{5}{9} \times (F - 32) [/tex]
[tex] C = \dfrac{5}{9}(F - 32) [/tex]
How would I find the length of the highlighted arc in the circle? Also I need to know how I would right the answer using pi as the symbol
The rule of the length of the arc of a circle is
[tex]L=\frac{x^{\circ}}{360^{\circ}}\times2\pi r[/tex]Where
x is the central angle subtended by the arc
r is the radius of the circle
From the given figure
The radius is 3 units, then
r = 3
The central angle of the highlight arc is a right angle, then
x = 90 degrees
Substitute them in the rule above
[tex]\begin{gathered} L=\frac{90}{360}\times2\times\pi\times3 \\ \\ L=\frac{1}{4}\times6\pi \\ \\ L=\frac{6}{4}\pi \\ \\ L=\frac{3}{2}\pi \\ \\ L=1.5\pi\text{ unit} \end{gathered}[/tex]The length of the highlight arc is 1.5pi units
Which equation represents the same line as the points in the table?
Input (x) Output (y)
−5 5
0 0
7 −7
x=−yx is equal to negative y
y=−x+5y is equal to negative x plus 5
y=−x−7y is equal to negative x minus 7
y=−x
Answer: (c) y = −1/3x −2
Step-by-step explanation:
I know it because I looked on brainly .
A remote-controoled car is traveling at a speed of 4 feet per second. use this rate to complete the equation, where d is the distance in feet that the car travels in t seconds. use equation to find the distance in feet that the car travels in t=8 seconds
Distance travelled by remote controlled car is 32 feet in 8 sec
What is speed ?Speed is the rate and direction of an object's movement, whereas speed is the scalar at which an object moves along a path in time. Velocity is a vector, whereas speed is a scalar integer.
Calculationspeed = 4 feet/sec
distance = d feet
time = t sec
4 = d / t
t = 8 sec
d = 4 *8
d = 32 feet
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b) Solve x + 5x - 14 = 0
f (x) = 6x + 2g (x) = -5- 9
we have
f(x)=6x+2
g(x)=-5x-9
Find out the product
so
f(x)*g(x)=(6x+2)*(-5x-9)
Applying distributive property
f(x)*g(x)=(6x)*(-5x)+(6x)*(-9)+(2)*(-5x)+(2)*(-9)
f(x)*g(x)=-30x^2-54x-10x-18
combine like terms
f(x)*g(x)=-30x^2-64x-18
the answer is the option DList from greatest to least:5.1 , 5 1/5, 5.5 and 5 1/4
Answer:
5.5, 5¼, 5 1/5 and 5.1.
Explanation:
To list the height from greatest to least, we convert each of them to a decimal.
[tex]\text{Suki}=5\frac{1}{5}=5+\frac{1}{5}=5+0.2=5.2[/tex][tex]\text{Also, Amir=5}\frac{1}{4}=5+\frac{1}{4}=5+0.25=5.25[/tex]Therefore, the weights are: 5.1, 5.2, 5.5 and 5.25
Arranging them from greatest to least gives:
5.5, 5.25, 5.2 and 5.1 which is equivalent to: 5.5, 5¼, 5 1/5 and 5.1.
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 3.4 meters, Length = 6.4 meters
Step-by-step explanation:
If the width is [tex]w[/tex], then the length is [tex]w+3[/tex].
[tex]w(w+3)=22\\\\w^2 +3w=22\\\\w^2 +3w-22=0\\ \\ w=\frac{-3 \pm \sqrt{3^2 -4(1)(-22)}}{2(1)}\\\\w \approx 3.4 \text{ } (w > 0)\\\\\implies w+3 \approx 6.4[/tex]
How many miles did a plane travel if it flew 455 miles per hour in 3 hours?
The distance travelled by the plane is 1365 miles.
Given,
Speed of the pane =455 miles per hour
Time taken =3 hours
To find distance covered by the plane use formula,
[tex]speed =\frac{Distance}{Time taken}\\ \\Distance=Speed * time taken\\\\Distance=455*3\\\\Distance=1365 miles[/tex]
Thus, the distance travelled by the plane is 1365 miles.
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A smaller number and a larger number add up to 8 and have a difference of 6. (Let X be the larger number and Y be the smaller number)
If the larger number is x, and the smaller one is y, then what we have is;
[tex]\begin{gathered} x+y=8---(1)\text{ both add up to 8} \\ x-y=6---(2)\text{ both have a difference of 6} \\ \text{From equation (1), make x the subject,} \\ x=8-y \\ \text{Substitute for the value of x into equation (2)} \\ x-y=6 \\ (8-y)-y=6 \\ 8-y-y=6 \\ 8-2y=6 \\ 8-6=2y \\ 2=2y \\ \text{Divide both sides by 2} \\ y=1 \\ \text{If x+y=8, then when y=1} \\ x+1=8 \\ x=8-1 \\ x=7 \end{gathered}[/tex]Therefore, the numbers are 7 and 1
Write a quadratic equation in standard form with the given roots. -4, 6
Answer:
Below
Step-by-step explanation:
With roots -4 and 6
the equation is a * (x+4)(x-6) = 0
'a' can be any real number (I'll choose '1')
Expand to x^2 -2x - 24 = f(x)
a rectangle field is four times as long as it's wide if the length is decreased by 10 ft and the width is increased by 2 ft the perimeter will be 80 ft find the dimensions of the original field the original dimensions are blank feet long by blank feet wide
Let the width of the field = w
∵ The length is four times as the width
∵ The width = w
∴ The length = 4w
∵ The length is decreased by 10 feet
∴ The new length = 4w - 10
∵ The width is increased by 2 feet
∴ The new width = w + 2
The new perimeter is 80 feet
∵ The perimeter of the rectangle = 2(length + width)
[tex]\therefore P=2(4w-10+w+2)[/tex]Let us simplify it
[tex]\begin{gathered} P=2(4w+w-10+2) \\ P=2(5w-8) \\ P=2(5w)-2(8) \\ P=10w-16 \end{gathered}[/tex]Now equate it by 80
[tex]10w-16=80[/tex]Add 16 to both sides
[tex]\begin{gathered} 10w-16+16=80+16 \\ 10w=96 \end{gathered}[/tex]Divide both sides by 10
[tex]\begin{gathered} \frac{10w}{10}=\frac{96}{10} \\ w=9.6 \end{gathered}[/tex]The length is 4 times the width
[tex]\begin{gathered} l=4(9.6) \\ l=38.4 \end{gathered}[/tex]The length is 38.4 feet and the width is 9.6 feet
hi I need to solve for X and Y in this
In this question, we are given two similar triangles ABC and DEF.
Similar triangles:
The triangles are similar if they have congruent corresponding angles and the corresponding sides of triangles are in proportion.
Therefore, the proportion of all sides should be the same. To proportion (k) can be found using:
k = Side AB / side DE
k = 9/6
or
k = 3/2
Similarly, the 'k' should be the same for side BC and side EF. Therefore,
k = side BC/ side EF
Now, put the values in the equation
[tex]\frac{3}{2}=\frac{4x-1}{10}[/tex][tex]3\cdot10\text{ = 2}\cdot(4x-1)[/tex][tex]30\text{ = 8}x-2[/tex][tex]30+2\text{ = 8}x[/tex][tex]32\text{ = 8}x[/tex][tex]x\text{ = }\frac{32}{8}[/tex][tex]x\text{ = 4}[/tex]Therefore, the value of x would be 4.
please help me. I think I have it figured out but I just wanted to double check.
Let's consider triangle ABC
Length AB can be obtained using Pythagoras
[tex]\begin{gathered} AB^2=x^2+y^2 \\ AB\text{ = }\sqrt[]{x^2+y^2} \\ \end{gathered}[/tex]Similarly, we can consider triangle ACD, so that length AD will be obtained through Pythagoras
[tex]\begin{gathered} AD^2=x^2+z^2 \\ AD\text{ = }\sqrt[]{x^2+z^2} \end{gathered}[/tex]Considering triangle ABD, with BD being the hypotenuse
[tex]\begin{gathered} BD^2=AD^2+AB^2 \\ (y+z)^{2\text{ }}=(x^2+z^2)+(x^2+y^2\text{)} \end{gathered}[/tex]Expanding the parentheses
[tex]\begin{gathered} y^2+2yz+z^2=x^2+z^2+x^2+y^2 \\ \\ y^2-y^2+z^2-z^2+2yz=2x^2 \\ 2yz=2x^2 \\ \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{2yz}{2}=\text{ }\frac{2x^2}{2} \\ yz=x^2 \\ \\ x^2\text{ =yz} \\ \\ x\text{ = }\sqrt[]{yz} \end{gathered}[/tex]Option A is correct
Answer:
Let's consider triangle ABCLength AB can be obtained using PythagorasSimilarly, we can consider triangle ACD, so that length AD will be obtained through PythagorasConsidering triangle ABD, with BD being the hypotenuseExpanding the parentheses Divide both sides by 2Option A is correct
Step-by-step explanation:
2. Alonzo built a rectangular sign that measured 2 3/4 feet in length by 1 1/2 feet in width. a. What is the area of the sign?
Area of a rectangle = Length x Breadth
[tex]\begin{gathered} \text{Length = 2}\frac{3}{4} \\ \text{ = }\frac{11}{4} \\ \text{Breadth = 1}\frac{1}{2} \\ \text{ = }\frac{3}{2} \\ \\ \text{Area of a rectangle = }\frac{11}{4}\text{ x }\frac{3}{2} \\ \text{ = }\frac{33}{8} \\ \text{ = 4}\frac{1}{8}feet^2 \end{gathered}[/tex]Noam had a length of
13
1
3
cm
13
3
1
cm13, start fraction, 1, divided by, 3, end fraction, start text, c, m, end text of ribbon and cut
3
1
3
3
3
1
3, start fraction, 1, divided by, 3, end fraction equal-sized strips the full width of the ribbon.
How long is each whole strip?
The length of each strip is 4 cm
In this question, we have been given Noam had a length of 13 1/3 cm of ribbon and cut 3 1/3 equal sized strips the full width of the ribbon.
We need to find the length of each whole strip.
first we convert the improper fraction into a proper fraction.
13 1/3 = 40/3
3 1/3 = 10/3
To find the length of each whole strip, we need to divide 13 1/3 by 3 1/3
i.e., 40/3 ÷ 10/3
= (40/3) / (10/3)
= 40/3 × 3/10
= 40/10
= 4
Therefore, the length of each strip is 4 cm
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Answer:
4
Step-by-step explanation:
Just did it on khan academy.
Suppose you observe a star orbiting the galactic center at a speed of 1400 km/s in a circular orbit with a radius of 14 days light calculate the mass of the object that the star is orbiting
The mass of the object that the star is orbiting is 1.0659 × 10³⁷ kg.
Define mass.One of the fundamental quantities and the most fundamental feature of matter is mass. The quantity of matter in a body is referred to as its mass. The SI unit of mass is the "kilogram," or kg, while there are other units for determining mass, such as grams, pounds, pounds, etc. A good conversion formula can be used to convert any mass unit to another without changing the meaning or essence of the quantity being measured.
Given, the speed of the orbiting star is 1400 km/s.
Converting the speed in meter per second.
speed = 1.4 × 10⁶ m/s
The radius of the circular orbit is 14-day light.
Converting the radius in meters,
radius = 3.626 × 10¹⁴ m
We know that the gravitational constant = 6.67 × 10⁻¹¹ N.m²/kg².
Now, find the mass of the object:
mass = ((1.4 × 10⁶)² × 3.626 × 10¹⁴)/6.67 × 10⁻¹¹
= (1.96 × 10¹² × 3.626 × 10¹⁴)/6.67 × 10⁻¹¹
= (7.10696 × 10²⁶)/6.67 × 10⁻¹¹
= 1.0659 × 10³⁷ kg
Therefore, the mass of the object that the star is orbiting is 1.0659 × 10³⁷ kg.
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help with this question
Shifts on x, where x and k form a binomial, are horizontal shifts. If k is positive, it is a left shift. If k is negative, it is a right shift.
The constant final term of the equation acts in the opposite way. It will be a vertical shift, and positive will mean up, negative will mean down.
So here, where there is a positive horizontal shift of 2 and a negative vertical shift of 7, the function is shifted 2 units to the left and 7 units down.
write the equation that goes through the point (4,-7) and is perpendicular to the line y+6=-2/5(x-1) all i need is slope intercept form.
To find the equation of the line that goes through the point (4, -7) and is perpendicular to the line y + 6 = -2/5 (x - 1), we can use the fact that two lines are perpendicular if their slopes are negative reciprocals of each other.
The slope of the line y + 6 = -2/5 (x - 1) is -2/5, so the slope of the line that is perpendicular to it must be -5/2. We can use this slope and the point (4, -7) to write the equation of the line in slope-intercept form.
To do this, we can use the point-slope formula, which is: y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes, and m is the slope of the line. In our case, the point is (4, -7) and the slope is -5/2, so the equation of the line is: y - (-7) = (-5/2)(x - 4).
We can simplify this equation to get: y + 7 = -5/2 x + 10. Finally, we can rearrange the terms to get the equation in slope-intercept form, which is: y = -5/2 x - 25/2.
Therefore, the equation of the line that goes through the point (4, -7) and is perpendicular to the line y + 6 = -2/5 (x - 1) is y = -5/2 x - 25/2 in slope-intercept form.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y+6=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}(x-1)\qquad \impliedby \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} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies \cfrac{5}{2}}}[/tex]
so we're really looking for the equation of a line whose slope is 5/2 and that it passes through (4 , -7)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{2} \\\\\\ \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}{(-7)}=\stackrel{m}{ \cfrac{5}{2}}(x-\stackrel{x_1}{4}) \implies {\large \begin{array}{llll} y +7= \cfrac{5}{2} (x -4) \end{array}}[/tex]
Answer the question below be sure to mark all answers
Note that:
• All numbers whose final digit is 0 or an even number are divisible by 2
,• All numbers whose final digit is 0 are divisible by 10
,• 498 is divisible by 2 but not divisible by 5 and 10
,• 151 is not divisible by any of 2, 5, or 10
,• 150 is divisible by al of 2, 5, and 10
The complete table is uploaded below
The angle measures in a triangle are (3x+4), (5x), and (7x-4). What is the measure of the largest angle in the triangle?12 degrees40 degrees60 degrees80 degrees
Answer:
80 degrees
Explanation:
The sum of the measures of angles in a triangle is 18 degrees.
Given that the angle measures in a triangle are (3x+4), (5x), and (7x-4), then:
[tex](3x+4)+(5x)+(7x-4)=180^0[/tex]First, we solve the equation for x.
[tex]\begin{gathered} 3x+5x+7x+4-4=180^0 \\ 15x=180^0 \\ x=\frac{180^0}{15} \\ x=12^0 \end{gathered}[/tex]Therefore, the measures of the angles are:
[tex]\begin{gathered} 3x+4=3(12)+4=40^0 \\ 5x=5(12)=60^0 \\ 7x-4=7(12)-4=80^0 \end{gathered}[/tex]The measure of the largest angle in the triangle is 80 degrees.
help please what is 3x plus 94 if x equals 27
Answer: To do that, we divide both sides by 3. Thus, the answer to "3 times what equals 27?" is 9. To double-check our work, multiply 9 by 3 to see that it equals 27.
Step-by-step explanation:
Answer: 175
Step-by-step explanation:
3(27)+94 =
81 + 94 = 175
Which of the following would solve the equation below for x in onestep?10=x-15A. Adding 15 to both sides of the equationB. Adding 10 to both sides of the equationC. Subtracting 15 to both sides of the equationD. Subtracting 10 to both sides of the equation
In order to solve the equation for x, we need to look at the side where the variable is, then, we apply the contrary operations to this operation on both sides.
In this case, x is being subtracted by 15, then we need to eliminate this 15 by adding 15 on both sides
[tex]\begin{gathered} 10+15=x-15+15 \\ 25=x \end{gathered}[/tex]Answer:
A. Adding 15 to both sides of the equation