For a direct variation between each point (x, y),
[tex]\begin{gathered} x\propto y \\ x=ky \\ k=\frac{x}{y} \end{gathered}[/tex]For (x₁, y₁) = (3, 12),
[tex]\begin{gathered} k=\frac{3}{12} \\ k=0.25 \end{gathered}[/tex]To find n, consider (n, 8) = (x, y)
[tex]\begin{gathered} x=ky \\ \end{gathered}[/tex]Substituting,
[tex]\begin{gathered} n=0.25\times8 \\ n=2 \end{gathered}[/tex]Therefore, the value of n is 2
Graph quadrilateral ABCD with vertices A(−4,1) B(−3,3) C(0,1) D(−2, 0) and its image after the translation.(x,y)→(x+4, y−2)
To find:
The graph of quadrilateral ABCD and its translation.
Solution:
Plot the points A(−4,1) B(−3,3) C(0,1) D(−2, 0) on the graph and join the points.
The translation is (x,y)→(x+4, y−2). So, the image after translation is given below:
What is the solution of 5/2xminus7=3/4xplus14А. x=-6 B. x=6 C. x= 8 D. x=12
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
[tex]\frac{5}{2}x\text{ - 7 = }\frac{3}{4}x+14[/tex]Step 02:
We must apply algebraic properties.
[tex]\begin{gathered} \frac{5}{2}x-\frac{3}{4}x=14+7 \\ \frac{20x-6x}{8}=21 \\ \frac{14x}{8}=21 \\ 14x=21\cdot8 \end{gathered}[/tex]x = 168 / 14
x = 12
The answer is:
x = 12
what is the ratio of dried fruit to sunflower seeds in the granola recipe?If you need to triple the recipe,will the ratio change?Explain.
We have to the ratio between the dried fruit and the sunflower seeds.
We know that the recipe requires 1/2 cup of dried fruit, and 1/8 of sunflower seeds. The ratio would be
[tex]\frac{\frac{1}{2}\text{fruit}}{\frac{1}{8}seeds}=\frac{1\cdot8}{1\cdot2}=4[/tex]So, the ratio of dried fruit to sunflower seeds in the granola recipe is 4, which means there must be 4 cups of dried fruits per each cup of sunflower seeds.If we triple the recipe, the ratio won't change, because ratios are constant, that way no matter if you do ten times more of the recipe, the result will be the same, because the ratios is the same too.
Are the angles congruent If yes, how do you know?
From the given diagram, notice that DE is congruent to AB, EC is congruent to BC and the angles ABC and DEC are congruent.
Since two sides of the triangles and the included angle are congruent, we know from the SAS congruence theorem that ABC and DEC are congruent.
Therefore, the answer is: yes, the triangles ABC and DEF are congruent due to the SAS theorem.
Which of the following is a simple event?Getting a spade cardGetting a numbered cardAll of the choicesGetting an ace of diamond card
Explanation
A simple event is one that can only happen in one way - in other words, it has a single outcome.
A compound event is more complex than a simple event, as it involves the probability of more than one outcome.
Getting a spade card is a simple event
Also, Getting a numbered card is a simple event
Getting an ace
A rectangular certificate has an area of 35 square inches. Its perimeter is 24 inches. What arethe dimensions of the certificate?
Explanation
Given that the area of the rectangular certificate is 35 inches and its perimeter is 24 inches. Therefore, if L represents the length of the certificate and w represents its width, therefore;
[tex]\begin{gathered} lw=35---1 \\ 2(l+w)=24---2 \end{gathered}[/tex]Therefore, we can say
[tex]l=\frac{35}{w}[/tex]We will substitute the above in equation 2
[tex]\begin{gathered} 2(\frac{35}{w}+w)=24 \\ \frac{70}{w}+2w=24 \\ multiply\text{ though by w} \\ 70+2w^2=24w \\ 2w^2-24w+70=0 \\ 2(w^2-12w+35)=0 \\ w^2-7w-5w+35=0 \\ (w-7)-5(w-7)=0 \\ (w-7)(w-5)=0 \\ w=7\text{ or w=5} \end{gathered}[/tex]Since the width must be shorter than the length therefore the width will be 5 inches.
Hence;
[tex]l=\frac{35}{5}=7[/tex]Answers:
The dimensions are:
Length = 7 inches
Width = 5 inches
What is mZADB in Circle D? 57° 85.5° 28.5° 114°
We want to know the measure of the angle ADB on the circle D.
For doing so, we remember that:
• The measure of an inscribed angle is ,half ,of the measure of the arcs it intercepts.
,• The measure of an arc is ,equal ,to the measure of the central angle it generates (whose vertex is the center of the circle).
In the graph, we see that the angle ACB is inscribed, and thus, the measure of the arc AB is given by:
[tex]\hat{AB}=2m\angle ACB=2\cdot(57^{\circ})=114^{\circ}[/tex]But, the arc AB is equal to the central angle it generates, this is:
[tex]\hat{AB}=m\angle ADB=114^{\circ}[/tex]This means that the measure of ∠ADB is 114°.
Factor completely. 4x^2+44x+72
4(x + 2)(x + 9)
Explanation:4x² + 44x +72
a = 4, b = 44, c = 72
a(c) = 4(72) = 288
The factors of 288 whose sum gives 44 are 36 and 8
4x² + 36x + 8x +72
4x(x + 9) + 8(x + 9)
(4x + 8)(x + 9)
To factorise completely, 4 is common to the first parenthesis:
(4x + 8) = 4(x + 2)
The factorisation of 4x² + 44x +72:
4(x + 2)(x + 9)
Question 5 of 15
Which statement is true?
A. All rational numbers are either integers or whole numbers.
B. All rational numbers can be written as integers.
C. All irrational numbers can be written as integers.
D. All real numbers are either rational or irrational.
Answer:
D. All real numbers are either rational or irrational.
Step-by-step explanation:
You want to know the true statement about the sets of rational, irrational, integer, and whole numbers.
Rational numbersA rational number is one that can be written as the ratio of two integers. All integers and whole numbers are rational, but not all rational numbers are integers.
3 = 3/1 . . . . an integer that is written as a rational number
1/2 . . . . . . . a rational number that is not an integer
Irrational numbersAn irrational number is a number that cannot be written as a ratio of two integers. √2 is an example of an irrational number. Its decimal representation has a fractional part that is never-ending and never-repeating.
The decimal part of any real number either terminates, repeats, or neither. If the number terminates or repeats, it is a rational number. If it doesn't, then it is an irrational number.
D. All real numbers are either rational or irrational.
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Bob reads 1/2 of a 200 page book in 4 days. How long would it take him to read 600 page book
24 days
1) Consider that Bob reads at a regular pace. So, we can write out a pair of ratios. Note that if Bob reads half of a 200 pages book so he does 100 pages in 4 days
[tex]\begin{gathered} pages--------days \\ 100---------4 \\ 600---------x \end{gathered}[/tex]2) So writing out a pair of ratios we have:
[tex]\frac{100}{600}=\frac{4}{x}[/tex]Now, we can cross multiply them:
[tex]\begin{gathered} 100x=600\cdot4 \\ 100x=2400 \\ \frac{100x}{100}=\frac{2400}{100} \\ x=24 \end{gathered}[/tex]how do I solve x without measuring it, i need help with the third question please
Answer:
Explanation:
Based on the given figure, the two angles ( 54° and x) are supplementary.
So, they add up to 180°.
54 + x =180
We subtract 54 from 180 to get the value of x:
x=180-54
Calculate
x= 126°
Therefore, the value of x is 126°.
-4(e+6)(b+3) (-7)-8(v-7)(2n+3)65(c+d)27(3x-1)(e-f)32(-3m+1)(2b-3) (-9)5(s+7)(t+7)36(-2v+4)(m-n) (-3)4e+7e+55-4x-8-3h-2h+6h+97-5y+2+14z+3-2z-z
By using the distribution property in the following algebraic expressions, you obtain:
6) -4(e + 6) = (-4)(e) + (-4)(6) = -4e - 24
7) (b + 3)(-7) = (b)(-7) + (3)(-7) = -7b - 21
8) (2n + 3)6 = (2n)(6) + (3)(6) = 12n + 18
9) 5(c + d) = (5)(c) + (5)(d) = 5c + 5d
10) 27(3x - 1) = (27)(3x) + (27)(-1) = 81x - 27
11) (e - f)(3) = (e)(3) + (-f)(3) = 3e - 3f
where you have taken into account, that each term inside a parenthesis must be multiplied by all terms of the other facto. Furthermore, you took into account the signs multiplcation rule (+ x + = +, - x - = +, - x + = -, + x - = -), and also you mulitiplied coefficients by coefficients for cases in which you have numbers and variables.
7. Write an equation and solve. Round to the nearest hundredth where necessary.
19 is what percent of 40?
Answer:
47.5%
Step-by-step explanation:
Frogs lay spherical eggs that are 1.2 millimeters in diameter. Nutrients are absorbed through the egg's surface. What is the approximate area ofa frog egg's surface?ОА. 15.1 mm2OB. 18.1 mm2OC. 86.8 mm2OD. 4.5 mm2
Surface Area of a Sphere
For a sphere of radius r, the surface area can be calculated as:
[tex]A=4\pi r^2[/tex]A frog's egg has a diameter of d = 1.2 mm. The radius is half the diameter, thus:
r = 1.2 mm/2 = 0.6 mm
Calculating the surface area:
[tex]A=4\pi(0.6mm)^2[/tex][tex]A\approx4.5mm^2[/tex]Choice D
For #'s 12 - 13, find the area of each figure.
Using the distance(d) formula to obtain the length AB,BC,CA.
The distance formula is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given
[tex]\begin{gathered} A\rightarrow(5,-6) \\ B\rightarrow(-5,-3) \\ C\rightarrow(5,6) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} AB=\sqrt{(-5-5)^2+(-3--6)^2}=\sqrt{(-10)^2+(-3+6)^2}=\sqrt{100+3^2}=\sqrt{109} \\ BC=\sqrt{(5--5)^2+(6--3)^2}=\sqrt{10^2+9^2}=\sqrt{100+81}=\sqrt{181} \\ CA=\sqrt{(5-5)^2+(6--6)^2}=\sqrt{0^2+12^2}=\sqrt{144}=12 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} AB=\sqrt{109}=10.44030\approx10.4 \\ BC=\sqrt{181}=13.45362\approx13.5 \\ CA=12 \end{gathered}[/tex]Using Heron's formula to solve for the area
[tex]\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]where,
[tex]\begin{gathered} a=10.4 \\ b=13.5 \\ c=12 \\ \\ s=\frac{10.4+13.5+12}{2}=17.95 \end{gathered}[/tex]Therefore, the area is
[tex]undefined[/tex]Find the coordinates of the midpoint of HX1H4-1X34324
We need to find the midpoint of a segment HX given the endpoints:
H = (4.5, -4.25) and X = (3.25, -2.75)
where we have written the coordinates (initially in mixed number form) in decimal form for ease of handling operations.
4 1/2 = 4.5
-4 1/4 = -4.25
etc.
Now we apply the formula for the midpoint (in the x and y coordinates separately):
x coordinate of midpoint = (4.5 - 3.25)/2 + 3.25 = 3.875
y coordinate of midpoint = (-2.75 - (-4.25))/2 + (-4.25) = -3.5
So we can write the coordinates of themidpoint as:
(3.875, -3.5) or in mixed number form as: (3 7/8, -3 1/2)
Using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true:
___ / ___ = ____ / ____ = ____
The complete equality will be;
⇒ 1 / 2 = 3 / 6 = 4 / 8
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
By using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true.
Now,
All the numbers from 1 to 9 are;
= 1, 2 ,3 , 4, 5, 6, 7, 8, 9
Let a proportion = 1 / 2
Hence, The equivalent ratio of 1/2 are;
= 3 / 6 and 4 / 8
Thus, The complete equality will be;
⇒ 1 / 2 = 3 / 6 = 4 / 8
Learn more about the proportion visit:
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A. Input 3, output 0B. Input 4, output 5C. Input -3, output 0D. Input 2, output 3
The only valid pair is B.
To determine this we need to remember that the input is the value of x and the output is the value of y.
For the input 4, that is x=4, the graph passes through the output is 5, that is y=5. This means that the graph passes through the point (4,5).
The location of a point moved from (1, - 3) to (-2, -1) by translation. Find the translation rule
moved from (1, - 3) to (-2, -1)
x'= x -3
y=
A window shaped like a parallelogram has an area of 31 square feet. The height of the window is 33 feet. How long is the base of the window?
The area of a parallelogram can be determined by multiplying its height by its base following the formula:
[tex]A=h\cdot b[/tex]If you know the area and the height of the parallelogram you can determine the length of the base. To do so, you have to divide the area by the height:
[tex]b=\frac{A}{h}[/tex]We know that the area of the window is A=31ft² and the height is h=33ft, you can calculate the length of the base as follows:
[tex]undefined[/tex]Determine the range for the relation below
Answer:
Assuming the scale of the graph is 1, the range would be just -1
Step-by-step explanation:
The graph is just a single horizontal line, so the range (what y can be) will always be that one constant. It appears that the scale of the graph is by 1s, so the Range would be -1
Question attached!!Answer choices 1. The graph has a relative minimum 2. The graph of the quadratic function has a vertex at (0,5)3. The graph opens up 4. The graph has one x- intercept 5. The graph has a y-intercept at (5,0)6. The axis of symmetry is x=0
Consider the following table:
this table represents the following graph:
According to this graph (parabola), and remembering that an absolute minimum is also a relative minimum:
we can conclude that the correct answer is:
Answer:1. The graph has a relative minimum 2. The graph of the quadratic function has a vertex at (0,5)3. The graph opens up 6. The axis of symmetry is x=0cuatro multiplicado por la suma de ocho y un numero.la suma de nueve y el numero
Definiendo como x al número desconocido.
la suma de ocho y un numero: 8 + x
cuatro multiplicado por la suma de ocho y un numero: 4(8 + x)
la suma de nueve y el numero: 9 +x
la suma de estas dos cantidades es igual a: 4(8 + x) + (9 + x)
These three pizzas are all the same size. Which one has the greatest number of equal pieces?
Given the following question:
It tells us that these pizzas are the same size
We are trying to find out which one of these pizza's have the greatest number of equal pieces.
For first pizza
It's cut up in four different pieces and these four pieces are equal
For the second pizza it is cut up in three different pieces and these three pieces are equal.
For the third pizza it is cut up in two pieces, these pieces are indeed equal.
Again the question is asking us which one has the GREATEST NUMBER of equal pieces
4, 3, 2
4 > 3
4 > 2
= 4
Your answer is the first pizza.
To pay for a 15,300 car, Tony made a down payment of $3900 and took out a loan for the rest. On the loan , he paid monthly payment payment of $252.34 for 4 years.A:what was the total amount Tony end up paying for the car.(including the down payment and monthly payment.B: how much interest did Tony pay on the loan.
Down Payment = 3900
Loan Amount - 15,300 - 3900 = $11,400
Total Paid on Loan = $252.34 (monthly) for 4 years (4 x 12 = 48 months).
So, he paid
[tex]252.34\times48=\$12,112.32[/tex]So, total amount Tony paid for the car is "downpayment (3900) + loan amount with interest (12,112.32)".
So,
[tex]3900+12,112.32=\$16,012.32[/tex]Answer: $16,012.32
B)The interest is the excess amount on the loan.
Loan amount = $11,400
Loan + Interest amount = $12,112.32
Thus, the interest amount is 12,112.32 - 11,400 = $712.32
Answer: $712.32
A committee has raised $230 in fundraising and continues toraise 30 dollars at each event they throw.-- Identify your independent and dependent variables- Write an equation to model the situationDetermine how much money will be raised after 10 events!Answer here:
Let's denote by x = the number of events.
and let's denote by y = the dollars raised.
Because the dollars raised to depend on the number of events, we can say that the dependent variable is y, and the independent variable is x. Now, we have the following data:
first event: 1, and the dollars raised is 230. That is, our first point is:
[tex](x_0,y_0)\text{ = ( 1,230 )}[/tex]second event: 2, and the dollars raised is 230 + 30. That is, our second point is
[tex](x_1,y_1_{\text{ }})=(2,230+30)=(2,260)_{}[/tex]Now, let's calculate the slope of the graph:
[tex]m\text{ = }\frac{y_1-y_0}{x_1-x_0}=\frac{260-230}{2-1}_{}_{}_{}[/tex]that is equivalent to say:
[tex]m\text{ = }\frac{260-230}{2-1}\text{ = }\frac{30}{2}\text{ = 15}[/tex]The equation for a line is y = mx + b. Now, let's calculate b
y = mx + b
so
b = y- mx
but m = 15, so the previous equation is equivalent:
b = y - 15x
if we choose the point (x,y) =(1,230) and we replace it in the previous equation we have:
b = 230- 15(1) = 230 - 15 = 215.
So, our equation of the line is :
y = 15x + 215
if x = 10 events we have :
y = 15(10) + 215 = 365 dollars
then, to the question: how much money will be raised after 10 events?, the answer is 365 dollars.
match the blanks to their missing phrases to complete the proof
blank A: a^2 + b^2 = c^2
blank B: Definition of unit circle
blank C: sin θ = y/1 = y
Explanation:
In order to prove the identity given, we first start with Pythagoras's theorem
[tex]a^2+b^2=c^2[/tex]which is blank a.
Next, we apply the theorem to the circle to get
[tex]x^2+y^2=r^2[/tex]then we make the substitutions.
Since it is a unit circle r = 1 (blank B) and using trigonometry gives
[tex]\cos \theta=\frac{x}{r}=\frac{x}{1}=x[/tex][tex]\boxed{x=\cos \theta}[/tex]and
[tex]\sin \theta=\frac{y}{r}=\frac{y}{1}=y[/tex][tex]\boxed{y=\sin \theta}[/tex]which is blank C.
With the value of x, y and r in hand, we now have
[tex]x^2+y^2=1[/tex][tex]\rightarrow\sin ^2\theta+\cos ^2\theta=1[/tex]Hence, the identity is proved.
What is the value of x?12 units15 units20 units25 units
Explanation
Step 1
set the equations:
we have three rectangles triangles,so
Let
triangle STR and triangle RTQ
so,
a) for triangle STR
let
[tex]\begin{gathered} \text{ hypotenuse: RS} \\ \text{adjacent side;RT}=x \\ \text{opposite side:ST=9} \\ \text{angle:m}\angle R \end{gathered}[/tex]so, we can use the Pythagorean theorem,it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
so
[tex]\begin{gathered} (RS)^2=(ST)^2+(RT)^2 \\ (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \end{gathered}[/tex]b) for triangle RTQ
[tex]\begin{gathered} \text{ hypotenuse: RQ} \\ \text{adjacent side;TQ}=16 \\ \text{opposite side:RT=x} \\ \text{angle:m}\angle Q \end{gathered}[/tex]again, let's use the P.T.
[tex]\begin{gathered} (RQ)^2=(RT)^2+(TQ)^2 \\ (RQ)^2=(x)^2+(16)^2\Rightarrow\text{equation}(2) \end{gathered}[/tex]c)
we know the triangles STR and SQR are similar, so
[tex]m\angle R=m\angle Q[/tex]also,
[tex]\begin{gathered} \tan m\angle R=\tan m\angle Q \\ \frac{oppositeside_R}{\text{adjacent sideR}}=\frac{oppositeside_Q}{\text{adjacent sideQ}} \\ \frac{9}{x}=\frac{SR}{RQ}\rightarrow equation\text{ (3)} \end{gathered}[/tex]finally, we can set a new equation with triangle SQR
d)again, let's use the P.T.
[tex]\begin{gathered} (SQ)^2=(SR)^2+(RQ)^2 \\ \text{replace} \\ (9+16)^2=(SR)^2+(RQ)^2 \\ (25)^2=(SR)^2+(RQ)^2\rightarrow equation(4) \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \\ (RQ)^2=(x)^2+(16)^2\Rightarrow\text{equation}(2) \\ \frac{9}{x}=\frac{SR}{RQ}\rightarrow equation\text{ (3)} \\ (25)^2=(SR)^2+(RQ)^2\rightarrow equation(4) \end{gathered}[/tex]solution:
a)
[tex]\begin{gathered} \text{isolate (x) in equation(1) and (2) and set equal } \\ (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \\ (RS)^2-(9)^2=(x)^2 \\ \text{and} \\ (RQ)^2=(x)^2+(16)^2\Rightarrow\text{equation}(2) \\ (RQ)^2-\mleft(16\mright)^2=(x)^2 \\ (RQ)^2-(16)^2=(x)^2 \\ \text{hence} \\ (RS)^2-(9)^2=(RQ)^2-(16)^2 \\ \text{isolate (RS)}^2 \\ (RS)^2=(RQ)^2-(16)^2+(9^2) \\ (RS)^2=(RQ)^2-175\rightarrow equation(5) \end{gathered}[/tex]b) now using equation (4) and equation(5) we can set system of 2 equations and 2 unknown values, so
[tex]\begin{gathered} (25)^2=(RS)^2+(RQ)^2\rightarrow equation(4) \\ (RS)^2=(RQ)^2-175\rightarrow equation(5) \\ replce\text{ eq(5) into equation (4)} \\ (25)^2=(RS)^2+(RQ)^2\rightarrow equation(4) \\ so \\ (25)^2=(RQ)^2-175+(RQ)^2 \\ 625+175=(RQ)^2+(RQ)^2 \\ 800=2(RQ)^2 \\ \mleft(RQ\mright)^2=\frac{800}{2} \\ (RQ)^2=400 \\ RQ=20 \end{gathered}[/tex]so
RQ=20
now, replace in equation (5) to find RS
[tex]\begin{gathered} (RS)^2=(RQ)^2-175\rightarrow equation(5) \\ (RS)^2=(20)^2-175 \\ (RS)^2=225 \\ RS=\sqrt[]{225} \\ RS=15 \end{gathered}[/tex]RS=15
finally, replace RS in equation (1) to find x
[tex]\begin{gathered} (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \\ (15)^2=(9)^2+(x)^2 \\ 225-81=x^2 \\ 144=x^2 \\ \sqrt[]{144}=\sqrt[]{x^2} \\ 12=x \end{gathered}[/tex]therefore, the answer is
12 unitsI hope this helps yuo
-2x - 14 =-2(Solve for x)
Explanation
[tex]-2x-14=-2[/tex]Step 1
add 14 in both sides,
[tex]\begin{gathered} -2x-14=-2 \\ -2x-14+14=-2+14 \\ -2x=12 \end{gathered}[/tex]Step 2
divide both sides by -2
[tex]\begin{gathered} -2x=12 \\ \frac{-2x}{-2}=\frac{12}{-2} \\ x=-6 \end{gathered}[/tex]I Hope this helps you
0.001×4= Possible answers: a),1/100×4/4 b),1/10×4/1000 c),1/4×4/4 d)1/1000×4/1
Explanation:
0.001×4:
[tex]\begin{gathered} 0.001\text{ = }\frac{1}{1000} \\ we\text{ know these by looking at the place value of the last number.} \\ \text{place value is thousandth} \end{gathered}[/tex][tex]\begin{gathered} 4\text{ = }\frac{4}{1} \\ 0.001\times4\text{ = }\frac{1}{1000}\times\frac{4}{1} \\ \text{(option D)} \end{gathered}[/tex]