Answers
First, find the interest percentage. Divide the amount borrowed by the interest amount.
[tex]\frac{100}{10}=10[/tex]Then, divide the result by 100% to express it as a percentage.
[tex]\frac{10}{100}=0.10[/tex]Once we have the interest percentage as a decimal number, multiply it by the new borrowed amount.
[tex]0.10\times1100=110[/tex]Therefore, you owe $110 at the end of the five weeks.Related Questions
Find the inverse of the function below and sketch by hand a graph of both the function and is inverse on the same coordinate plane. Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded. f(x)=(x+3)^2 with the domain x \geq-3
Answers
In order to find the inverse of f(x), let's switch x by f^-1(x) and f(x) by x in the function, then we solve the resulting equation for f^-1(x).
So we have:
[tex]\begin{gathered} f(x)=(x+3)^2 \\ x=(f^{-1}(x)+3)^2 \\ \sqrt[]{x}=f^{-1}(x)+3 \\ f^{-1}(x)=-3+\sqrt[]{x} \end{gathered}[/tex](The domain of f(x) will be the range of f^-1(x), so the range of f^-1(x) is y >= -3)
In order to graph the function and its inverse, we can use some points that are solutions to each one.
For f(x), let's use (-3, 0), (-2, 1) and (-1, 4).
For f^-1(x), let's use (0, -3), (1, -2) and (4, -1).
Graphing f(x) in red and f^-1(x) in blue, we have:
Graphing it manually, we have:
A rectangular certificate has an area of 35 square inches. Its perimeter is 24 inches. What arethe dimensions of the certificate?
Answers
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
match the blanks to their missing phrases to complete the proof
Answers
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.
For #'s 12 - 13, find the area of each figure.
Answers
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]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.
Answers
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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These three pizzas are all the same size. Which one has the greatest number of equal pieces?
Answers
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.
7. Write an equation and solve. Round to the nearest hundredth where necessary.
19 is what percent of 40?
Answers
Answer:
47.5%
Step-by-step explanation:
Determine the range for the relation below
Answers
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
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
Answers
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
cuatro multiplicado por la suma de ocho y un numero.la suma de nueve y el numero
Answers
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)
Factor completely. 4x^2+44x+72
Answers
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)
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.
Answers
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.
Using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true:
___ / ___ = ____ / ____ = ____
Answers
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:
https://brainly.com/question/870035
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Find the equation of a line in the form y=Mx+b MATH HW
Answers
Using y=mx+b form first we calculate the slope.
We'll use points (0,-8) and (-8,0).
[tex]\begin{gathered} m=(-8-0)\div(0--8) \\ m=-\frac{8}{8} \\ m=-1 \end{gathered}[/tex]Next we calculate our b intercept
[tex]\begin{gathered} 0=-1(-8)+b \\ b=-8 \end{gathered}[/tex]So the equation is y=-x-8
-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
Answers
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.
Are the angles congruent If yes, how do you know?
Answers
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.
The location of a point moved from (1, - 3) to (-2, -1) by translation. Find the translation rule
Answers
moved from (1, - 3) to (-2, -1)
x'= x -3
y=
Graph the following Y=x-4
Answers
Ok, so
We want to find the line:
[tex]y=x-4[/tex]First, remember that a line can be described with the following formula:
[tex]y=mx+b[/tex]Where "m" is its slope and b is its y-intercept.
Based in our equation, we got that m = 1 and b = - 4. So, we have a line with slope = 1, and y-intercept = -4.
To graph it, we have to take two points that lie on the line, and join them. We already know that the line has y-intercept at ( 0 , -4 ), so that's one point.
To find the other point, we could make y = 0 to find the x-intercept as follows:
[tex]\begin{gathered} y=x-4 \\ x-4=0 \\ x=4 \end{gathered}[/tex]Now, we have the x-intercept at (4 , 0) so that's other point.
We join both points:
So that's the graph for y = x-4.
Answer:
Step-by-step explanation:
1. When x is 0, y=-4, so plot the point (0,4) on the graph.
2. When y is 0, x=4, so plot the point (4,0) on the graph.
3. Draw a line between them and you're done.
What is the value of x?12 units15 units20 units25 units
Answers
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
2 The ratio of males to females in the class is 5 to 9. If the lunchroom has the same ratio but 45 females, how many males are in the lunchroom?
Answers
Answer:
Explanation:
From the question, we are given the ratio of males to females in the class as 5 to 9.
Total ratio = 5+9 = 14
Let the total number of student in the class be x. If there are 45 females then;
9/14 * x = 45
9x/14 = 45
Cross multiply;
9x = 14 * 45
x = 14 * 5
x = 70
Hence the total number of student in the class is 70
Get the number of male students;
Total students = Male + Female
70 = Male + 45
Male = 70-45
Male = 25
Answer:
Step-by-step explanation:
To get 45 females, you have to multiply 9 by a number. That number is 5 because 5 times 9 is 45. So what you do here is what you do with the other number, (5), so 5 times 5 is 25. That means there were 25 males in the lunchroom.
Which of the following is a simple event?Getting a spade cardGetting a numbered cardAll of the choicesGetting an ace of diamond card
Answers
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
What is mZADB in Circle D? 57° 85.5° 28.5° 114°
Answers
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°.
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
Answers
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=0Find the probability to generate a 4 digit even number from 1, 2, 3, 5.A.1/4B.1/2C.1D.0
Answers
give the following numbers
1, 2, 3, 5
we were asked to find the probability of generating a 4 digit even number from the numbers give above
recall,
Probabily = Number of possible outcome/Total number of outcomes
Number of possible outcome is = 1
Total number of outcomes is = 4
therefore,
Probability = 1/4
so the probability of generating a 4 digit even number from 1, 2, 3, 5 is 1/4
so the correct option is A which is 1/4
-2x - 14 =-2(Solve for x)
Answers
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
How would I solve 11 I’m confused on it I’m sorry I’m a bit slow
Answers
In order to better understand the question, let's draw an image representing the situation:
We want to find the distance x of this triangle. To do so, we can use the Pythagorean theorem, which states that the length of the hypotenuse squared is equal to the sum of each leg squared.
So we have:
[tex]\begin{gathered} 110^2=55^2+x^2 \\ 12100=3025+x^2 \\ x^2=12100-3025 \\ x^2=9075^{} \\ x=95.26\text{ ft} \end{gathered}[/tex]Rounding to the nearest tenth, we have a distance of 95.3 ft.
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
Answers
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]Bob reads 1/2 of a 200 page book in 4 days. How long would it take him to read 600 page book
Answers
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]An item has a listed price form 45. If the sale tax rate is 9?% how much is the sales tax.
Answers
In order to calculate the sales tax to 45, calculate the 9% of 45, just as follow:
(9/100)(45) = 4.05
Hence, the sales tax is $4.05
how do I solve x without measuring it, i need help with the third question please
Answers
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°.