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
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
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]
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.
Upload your work at the end email to your teacher for full credit. Do not enter any words/spaces. Your answer should be a whole number. Answer:
x = 4
The area of the figure can be found below.
The size of the farm is a rectangle therefore, we use the area of a rectangle to find the area of the farm.
[tex]\begin{gathered} \text{area of the farm=lw} \\ \text{where} \\ l=\text{length} \\ w=\text{width} \\ l=3x+1+2x+4+5x-2=10x+3=10\times4+3=43 \\ w=2x+1+3x=5x+1=5\times4+1=21 \\ \text{area}=43\times21=903unit^2 \end{gathered}[/tex]Combine like terms. -3 + 7x^2- 4x – 5 + 3x^2 – 2x
The expression is given as,
[tex]-3+7x^2-4x-5+3x^2-2x[/tex]Rearranging the like terms,
[tex]7x^2+3x^2-4x-2x-5-3[/tex]Like terms : Terms that have same power of variable.
Simplifying further,
[tex]10x^2-6x-8[/tex]Thus the result of the given expression is,
[tex]10x^2-6x-8[/tex]Answer:
-8 + 10x^2 - 6x
Step-by-step explanation:
(doesn’t have to be in this order)
1. Combine numbers with the x^2
-3 + 10x^2 - 4x - 5 - 2x
2. Combine regular numbers
-8 + 10x^2 - 4x - 2x
3. Combine numbers with the plain x
-8 + 10x^2 - 6x
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
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
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]
i need to know how to solve this question please
ANSWER
w = 6.71 or -6.71
EXPLANATION
List 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.
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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Select the correct answer.
Which equation combines with the given equation to form a system of equations with the solution x = 3 and y = 9?
x + 2y = 21
A.
OB.
O C.
O D.
OE.
4x+6y=64
2x+y = 36
4x + y = 21
-3x + 4y = 33
3x + 2y = 28
The correct option C; 4x + y = 21 is the equation combines with the x + 2y = 21 equation to form a system of equations with the solution x = 3 and y = 9.
What is meany by the term system of equations?simultaneous equations, system of equations Two or more equations must be solved together in algebra, and the solution should first satisfy all of the equations with in system. The number of parameters must equal the amount of unknowns for a system to produce a unique solution.x + 2y = 21 eq .....(i)
The solutions are x = 3 and y = 9.
Put the values of x and y in equation (i),
3 + 2 × 9 = 21
3 + 18 = 21
21 = 21
Now, evaluate every option by substituting the values.
A. 4x + 6y = 64
Put the values of x and y in equation,
4 × 3 + 6 × 9 ≠ 64
48 ≠ 64
In correct option.
B. 2x + y = 36
Put the values of x and y in equation,
2 × 3 + 9 ≠ 36
15 ≠ 36
Incorrect option
C. 4x + y = 21
Put the values of x and y in equation,
4 × 3 + 9 = 21
12 + 9 = 21
21 = 21
Correct option.
Thus, equation combines with the x + 2y = 21 equation to form a system of equations with the solution x = 3 and y = 9 is 4x + y = 21.
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In the given figure, mBJ = 106 and FHJH. Which statement is true?
F
H
G
Figure not drawn to scale
K
106°
OA.
The measure of ZG is 21", and triangle FGH is isosceles.
OB.
The measure of ZG is 56", and triangle FGH is isosceles.
O.C.
The measure of ZG is 21", and triangle FGH is not isosceles.
The measure of ZG is 56", and triangle FGH is not isosceles.
D.
The 106° measure of arc [tex]m\widehat{HJ}[/tex] and the length of the chords [tex]\widehat{FH}[/tex] and [tex]\widehat{JH}[/tex], which are the same, indicates that m∠G = 21° and ΔFGH is not isosceles. The correct option is option C;
C. The measure of ∠G is 21°, and triangle FGH is not isosceles
What is an isosceles triangle?An isosceles triangle is a triangle that have two sides of the same length and two angles of the same measure.
According to the outside angle to a circle theorem, the measure of the outside angle ∠G formed by the secant GJ and the tangent GF is equal to the difference of the measures of the arcs [tex]m\widehat{F'KJ}[/tex], and arc [tex]m\widehat{FH}[/tex] divided by 2.
[tex]m\widehat{F'KJ}[/tex] = 360° - [tex]m\widehat{FH}[/tex] - [tex]m\widehat{HJ}[/tex]
[tex]\widehat{FH}[/tex] = [tex]\widehat{JH}[/tex]
[tex]\widehat{FH}[/tex] ≅ [tex]\widehat{JH}[/tex]
The lengths of the chord intercepted by congruent arcs are congruent.
Therefore; [tex]\widehat{JH}[/tex] ≅ [tex]\widehat{FH}[/tex]
Which indicates;
[tex]m\widehat{JH}[/tex] = 106° = [tex]m\widehat{FH}[/tex]
[tex]m\widehat{F'KJ}[/tex] = 360° - 106° - 106° = 148°
m∠G = ([tex]m\widehat{F'KJ}[/tex] - [tex]m\widehat{FH}[/tex]) ÷ 2
m∠G = (148° - 106°) ÷ 2 = 21°
m∠G = 21°[tex]m\widehat{F'KJ}[/tex] = 148°
m∠FHJ = 148° ÷ 2 = 74° (Angle at the center is twice angle formed at the circumference)
∠FHJ = ∠HFG + ∠G (exterior angle to triangle ΔFGH)
∠HFG = ∠FHJ - ∠G
Therefore; m∠HFG = 74° - 21° = 53°
m∠HFG = 53°
m∠FHG = 180° - 74° = 106° (linear pair angles property)
m∠G ≠ m∠FHG ≠ m∠HFG, therefore, ΔFGH is not isoscelesThe correct option is option C.
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A, B, and C are collinear, and point B lies in between point A and point C. Point D is a point not on the line. Given thatmZABD = (x - 2)° and mZCBD = (5x), find mZCBD.
Answer:
70degrees
Explanation:
The diagrammatical representation of the statement is as shown;
Since the sum of angles on a straight line is 180degrees, then;
m8x+2 + 5x = 180
13x + 2 = 180
13x = 180 + 2
13x = 182
x = 182/13
x = 14
Get mmmmHence the measure of m
What are the coordinates of J A G when reflected over the line y=2?
We can start by plotting the triangle JAG and the line y = 2 to see how we can solve it:
We can see the line y = 2 (red line) over which we have to reflect the point J, A and G.
To do that we have to look at the distance of each point to the line.
This distance will be the distance at which the image point will be located, opposite to the the original point.
As y = 2 is an horizontal line, the distance is vertical and the x-coordinate of the original points and the images will remain equal. Only the y-coordinate will change.
We can sketch the procedure as:
Then, for example, poing G is 1 unit below y = 2, so its image G' will be one unit over the line y = 2, locating at (2,3).
Point J is 2 units above y = 2, so J' will be 2 units below y = 2.
Point A is 3 units above y = 2, so A' will be 3 untis below y = 2
We can plot the remaining points as:
The red triangle is the original triangle and the blue triangle is the image.
Answer:
The coordinates are J'=(1,0), A'=(3,-1) and G'=(2,3).
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 DNoam 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.
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
b) Solve x + 5x - 14 = 0
(G.5d, 1 pt) Determine the range for the measure of AC. А 10 m B 13 m O A. 10
The length of a side must be less than the sum of the other two sides. Here, that means x < 10+13, or x < 23.
In addition, remember that the length of a side must be greater than the difference of the other two sides. That means x > 13 - 10, or x > 3.
Therefore we have two limits for the value of x: 3 and 23.
3 < x < 23
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
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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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
The weight M of an object on the moon varies directly as its weight E on earth. A person whoweighs 156.71 lb on earth weighs 26.64 lb on the moon. How much would a 213.53-lb personweigh on the moon?A 213.53-1b person would weigh___ lb on the moon. (Round to the nearest tenth.)
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
÷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!!!
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 .
State the postulate or theorem, if any, that could be used to prove two triangles
The angle sum property of a triangle the and in isosceles triangle base angles are equal theorem are used.
In the given triangle, the measure of two angles are 67° and 35°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
7a) Using angle sum property of triangle, we get
Now, 67°+35°+x=180°
⇒ 102°+x=180°
⇒ x=180°-102°
⇒ x=78°
7b)
67°+78°+y=180°
⇒ 145°+y=180°
⇒ y=180°-145°
⇒ y=35°
8a) In isosceles triangle base angles are equal.
Here, p=q
50°+p+q=180°
⇒ 50°+p+p=180°
⇒ 2p=130°
⇒ p=65°
So, p=q=65°
8a) Here, c+115°=180°
⇒ c=180°-115°
⇒ c=65°
So, b=c=65°
Now, a+b+c=180°
⇒ a+65°+65°=180°
⇒ a+130°=180°
⇒ a=50°
Hence, the angle sum property of a triangle the and in isosceles triangle base angles are equal theorem are used.
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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
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]