I have 42 dimes in my piggy bank according to the given condition of 66 coins and amount $10.20 and used the system of equation as well as substitution method.
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations.
What is substitution method?Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations, x+y=7 and x-y=8, we can deduce that x=7-y from the first equation. Applying the substitution method begins with this.
Here,
x+y=66 ......(1)
1 dime values 10 cents.
1 quarter values 25 cents.
10x+25y=1020 ........(2)
x=66-y
10(66-y)+25y=1020
660-10y+25y=1020
15y=360
y=360/15
y=24
x=66-24
x=42
I used the system of equations and the substitution method to determine that I have 42 dime coins in my piggy bank in accordance with the requirement of 66 coins totaling $10.20.
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if [tex] \sqrt{ \times } [/tex]is equal to the coordinate of point D in the diagram above, then X is equal to:
11)
The number line is divided into 5 equal intervals. if the fourth segment is 7, then we would find the distance between each segment
The distance between the fourth segment and the first segment is 7 - - 1 = 8
Since we are considering the distance between segment 1 and segment 4, the distance between each segment would be
8/4 = 2
Thus,
point D = 7 + 2 = 9
If
[tex]\begin{gathered} \sqrt[]{x\text{ }}\text{ = D, then} \\ \sqrt[]{x}\text{ = 9} \\ \text{Squaring both sides of the equation, we have} \\ x=9^2 \\ x\text{ = 81} \end{gathered}[/tex]Option E is correct
A bridge being designed will crossthe river at a right angle. Theequation of the left bank of theriver is y = 2x + 8. The center ofthe bridge will pass through (0, 2).What is the equation of the linerepresenting the bridge?
Let's begin by listing out the information given to us:
Left side: y = 2x + 8
Center of the bridge: (0, 2)
[tex]\begin{gathered} y=2x+8 \\ m=2 \\ \text{However, the bridge is perpendicular to }y=2x+8\colon \\ m(perpendicular)=-\frac{1}{m} \\ m(perpendicular)=-\frac{1}{2} \end{gathered}[/tex]Use the point-slope formula to get the equation of the bridge:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(0,2);m=m(perpendicular)=-\frac{1}{2} \\ y-2=-\frac{1}{2}(x-0) \\ y-2=-\frac{1}{2}x \\ y=-\frac{1}{2}x+2 \\ \\ \therefore\text{ equation of the line representing the bridge is }y=-\frac{1}{2}x+2 \end{gathered}[/tex]Calculate the degree of the angles in the triangles below.
the sum of the internal angles of a triangle is equal to 180, then
[tex]\begin{gathered} 2x+7+5x+12=180 \\ 7x+19=180 \\ 7x+19-19=180-19 \\ 7x=161 \\ \frac{7x}{7}=\frac{161}{7} \\ x=23 \end{gathered}[/tex]so
answer:
angle 1 = 2x + 7 = 2(23) + 7 = 46 + 7 = 53°
angle 2 = 5x = 5(23) = 115°
angle 3 = 12°
Virginia is going to visit 5 cities this summer. She will choose from 8 different cities and the order in which she visits the cities does not matter. How many different city combinations are possible for the summer travelling?
Which angle is coterminal to 128°?A. -52°B. 308C. 232°D. 488°
The coterminal of angle with measure x is x + 360 degrees
Example:
If x = 30 degrees, then
The coterminal of x is 30 + 360 = 390 degrees
The coterminal of 128 degrees is 128 + 360 = 488 degrees
Then the answer is D
Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting (intersect at just one point), or coinciding (intersect at all points)?y = -x + 11, 2y = -2x + 22
Given
The lines,
[tex]\begin{gathered} y=-x+11\text{ \_\_\_\_\_\lparen1\rparen} \\ 2y=-2x+22\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]To find:
Whether the lines are perpendicular, coinciding, intersecting or parallel?
Explanation:
It is given that,
[tex]\begin{gathered} y=-x+11\text{ \_\_\_\_\_\lparen1\rparen} \\ 2y=-2x+22\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]That implies,
Since the slope of the two lines are,
[tex]\begin{gathered} m_1=-1 \\ m_2=\frac{-2}{2}=-1 \\ \therefore m_1=m_2 \end{gathered}[/tex]Hence, the two lines are parallel.
A man realizes he lost the detailed receipt from the store and only has the credit card receipt with theafter-tax total. If the after-tax total was $357.06, and the tax rate in the area is 8.2%, what was the pre-tax subtotal?
Answer: the pre-tax subtotal is $330
Explanation:
Let x represent the pre tax total
If the tax rate in the area is 8.2%, it means that the amount of tax paid is
8.2/100 * x = 0.082x
pretax total + tax = after tax subtotal
Given that after tax subtotal is $357.06, then
x + 0.082x = 357.06
1.082x = 357.06
x = 357.06/1.082
x = 330
the pre-tax subtotal is $330
Use the graph to answer the question.Which statement matches the vector operation shown on the coordinate grid?
We have the correct statement about the vectors in the graph.
We can already see that it is a sum of vectors like:
[tex]v+w=u[/tex]As v has starting point at (-1,0) and ending point at (3,3), we can describe the vector as:
[tex]v=(3-(-1))\hat{i}+(3-0)\hat{j}=4\hat{i}+3\hat{j}[/tex]As w starts at (3, 3) and ends on (5, 2), we can describe it as:w
[tex]w=(5-3)\hat{i}+(2-3)\hat{j}=2\hat{i}-1\hat{j}[/tex]Finally, u starts at (-1,0) and ends at (5,2), so it can be described as:
[tex]u=(5-(-1))\hat{i}+(2-0)\hat{j}=6\hat{i}+2\hat{j}[/tex]Answer: v + w = u for v = 4i + 3j, u = 2i - j and u = 6i + 2j [Option C].
Finding an output of a function from its graphThe graph of a function fis shown below.Find f (0).543-2f(0) =I need help with this math problem.
Given:
Given a graph of the function.
Required:
To find the value of f(0), by using graph.
Explanation:
From the given graph
[tex]f(0)=-4[/tex]Final Answer:
[tex]f(0)=-4[/tex]Look at the graphs and their equations below. Then fill in the information about the coefficients A, B, C, and D.
Given:
Aim:
We need to find the coordinates and The sign of the equation.
Explanation:
[tex]We\text{ know that y=a\mid x\mid is upside and y}\ge\text{0 when a >0 and downside and y}\leq\text{owhen a<0}[/tex]The coefficient of the given functions are
[tex]y=A|x|\text{ is positive}[/tex][tex]y=B|x|\text{ is positive}[/tex][tex]y=C|x|\text{ is negative}[/tex][tex]y=D|x|\text{ is negative}[/tex]The coefficient is closest to zero.
Comparing the graph of y=A|x| and y=B|x|, we get y=A|x| is wider than y=B|x|.
[tex]A
Comparing the graph of y=C|x| and y=D|x|, we get y=D|x| is wider than y=C|x|.
[tex]CComparing the graph of y=A|x| and y=C|x|, we get y=C|x| is wider than y=A|x|.
[tex]C The coefficient is closest to zero y=C|x|.The coefficient with the greatest value.
Comparing the graph of y=B|x| and y=D|x|, we get y=D|x| is wider than y=B|x|.
[tex]D The coefficient with the greatest value is y=B|x|. .Find an equation in standard form of the parabola passing through the points. (2,-20),(-2,-4), (0, -8)
The equation of a parabola in standard form is
[tex]y\text{ }=ax^2\text{ + bx + c}[/tex]So, we have the following equations,
For ( 2, -20) , -20 = a(2)^2 + b (2) + c,
For (-2, -4), -4 = a( -2)^2 + b (-2) + c,
For (0.-8), -8 = a (0) + b (0) + c
Then solving,
4a + 2b + c = -20 .............. equ 1
4a - 2b + c = -4 ................... equ 2
c= -8
put c= -8 in equ 1,
we have
4a + 2b -8 = -20 = 4a + 2b = -12 ------equ 3
put c= -8 in equ 2,
4a - 2b -8 = -4 = 4a - 2b = 4................... equ 4
Solving equ 3 and equ 4, a= -1 , b= -4
so a =-1, b= -4, c= -8
Then substituting the values in
[tex]y=ax^2\text{ + bx + c}[/tex][tex]y=-1(x^2)\text{ + -4(x) + }(-8)[/tex]
So, y= -x^2 -4x-8
1. Jessica finishes her book in 2 1/3
hours. Eric takes 1 1/2
times longer than
Jessica to finish his book.
This model represents the amount of time Jessica takes to finish her
book. It has a width of 1 and a length of 2 1/3
. The model is 2 1/3 out of 3
Proportionately, the number of hours it takes Eric to finish the book as Jessica is 3¹/₂ hours.
What is proportion?Proportion refers to the ratio of the quantity contained in a number or value concerning another value's ratio.
Proportions, like ratios, are fractional values, represented using decimals, fractions, or percentages.
In ratio terms, Eric's reading time is 3¹/₂ hours to Jessica's 2¹/₃ hours, giving an absolute ratio of 3: 2 with a constant proportionality of 1.5 hours.
For instance, the product of Eric's reading time, compared to Jessica's reading time, shows that Jessica does a faster reading than Eric.
The total number of hours it takes Jessica to finish her book = 2¹/₃ hours
The total hours it takes Eric to finish the book = 2¹/₃ hours x 1¹/₂
= 3¹/₂ hours (2¹/₃ x 1¹/₂).
Thus, whereas Jessica takes 2¹/₃ hours to finish the book, in proportion, Eric consumes 3¹/₂ hours reading the same book.
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Complete Question:Jessica finishes her book in 2¹/₃ hours. Eric takes 1¹/₂ times longer than Jessica to finish his book. How long did Eric take to finish the book?
1 4/5 + (2 3/20 + 3/5) use mental math and properties to solve write your answer in simpleist form
Given data:
The given expression is 1 4/5 + (2 3/20 + 3/5).
The given expression can be written as,
[tex]\begin{gathered} 1\frac{4}{5}+(2\frac{3}{20}+\frac{3}{5}_{})=\frac{9}{5}+(\frac{43}{20}+\frac{3}{5}) \\ =\frac{9}{5}+\frac{43+12}{20} \\ =\frac{9}{5}+\frac{55}{20} \\ =\frac{36+55}{20} \\ =\frac{91}{20} \end{gathered}[/tex]Thus, the value of the given expression is 91/20.
Hannah is saving money to buy some lirns. She invests $290 in a savings account that earns 7.6% interest, compounded annually. How much money will she have in her account after 2 years? Answer in dollars and round to the nearest cent.
Principal amount, P= $290.
Rate, r = 0.076
Time, t = 2
Therefore, the total amount in her account after 2 years is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Hence,
[tex]\begin{gathered} A=290(1+0.076)^2 \\ =335.755 \end{gathered}[/tex]Therefore, the amount is 335.80 dollars.
That is, 335 dollars and 80 cents.
if an above ground graden is the shape of triangular pyramid measuring.the base is a right triangle with adjacent lengths measuring 5feet and 8feet. the height of the pyramid is 1.5feet. the organic soil cost $1.20 per cubic foot. how much will it cost to fill the graden fully
Solution
The volume for a triangular pyramid is given by:
[tex]V=\frac{1}{3}Bh[/tex]And the Base is given by:
[tex]B=\frac{1}{2}(5)(8)[/tex]And since h= 1.5 ft we have this:
[tex]V=\frac{1}{6}(5\cdot8)\cdot1.5ft^3=10ft^3[/tex]And then we can find the total cost like this:
[tex]C=10ft^3\cdot\frac{1.2\text{ dollars}}{1ft^3}=12dollars[/tex]Then the final answer would be 12$
Dalia works mowing lawns and babysitting. She earns $8.40 an hour for mowing and $7.90 an hour for babysitting . How much will ahe earn for 7 hours of mowing and 1 hour of babysitting?
Given that she earns $8.40 an hour for mowing then for 7 hours of mowing, the amount earned
= 7 * $8.40
=$58.80
Furthermore, given that she earns $7.90 for baby sitting for an hour
Hence for mowing for 7 hours and baby sitting for 1 hour, the total amount she will earn
= $58.80 + $7.90
= $66.70
Linda's medicine bottlesays "If you will be driving, then youshould not take this medicine." What arethe inverse, converse, and thecontrapositive of this statement?
For two statements p and q, and the compounded statement "If p, then q", we have the following definitions for the inverse, converse, and contrapositive of this compounded statement:
inverse: If not p, then not q.
converse: If q, then p.
contrapositive: If not q, then not p.
So, for the presented statement, i. e., "If you will be driving, then you should not take this medicine" we have:
p: you will be driving
q: you should not take this medicine
Notice that:
not p: you will not be driving
not q: you may take this medicine
Then, using the above definitions, we write:
inverse: If you will not be driving, then you may take this medicine.
converse: If you should not take this medicine, then you will drive.
contrapositive: If you may take this medicine, then you will not be driving.
I need help figuring out which of the following statements is false
EXPLANATION
We can first array the sets in order to match the terms:
X= {15, 22, 33, 44, 89, 165, 1025}
Y= {-5, 15, 33, 88, 99, 150, 160, 1025}
We can see that the common terms are {15,33,1025}, thus the third statement is true.
Now, we can check if the second statement is true or false.
If we put both sets together from smaller to greater and using just one common term, we get the following expression:
X U Y = {-5, 15, 22, 33, 44, 89, 99, 150, 160, 165, 1025}
In conclusion, the second statement is also true.
AnimalPossible Locations Relativeto Ocean's Surface25. Reasoning Suppose you plot the locations ofthe animals on a number line. Which animalwould be represented by the point farthest fromO on the number line? Explain. MP2Bloodbelly comb jellyDeep sea anglerfish-0.8 km- km- 2 kmFanfin anglerfishGulper eel-1.1 km26. Which animal is closest to a depth of -0.7 km?Pacific blackdragon- šo kmSlender snipe eel-0.6 km
Number line
[tex]\ldots-5<-4<-3<-2<\text{ -1< 0<1<2<3<4<5}\ldots[/tex]Let's
[tex]undefined[/tex]solve for x. z=5x-9y
ANSWER:
[tex]x=\frac{z+9y}{5}[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]z=5x-9y[/tex]We solve for x as follows:
[tex]\begin{gathered} z+9y=5x \\ 5x=z+9y \\ x=\frac{z+9y}{5} \end{gathered}[/tex]If the point (-6, 4) is dilated by a scale factor of 1/2, the resulting point is (-3,2).TrueFalse
(-6,4)
Multiply each coordinate by 1/2
( -6 * 1/2 , 4 * 1/2) = (-3,2)
True
Jamal is comparingprices of several different brandsof peanuts. Which brand is thebest buy? Explain.
So we need to figure out which is the best buy. In order to do this we must look at a particular variable: the price per ounce of peanuts. This price is given by dividing the total price of a certain amount of peanuts divided by its weight in ounces. So for the Barrel brand we get:
[tex]\frac{3.39}{10}=0.339[/tex]So the Barrel peanuts cost $0.339 per ounce. For the Mr. Nut peanuts we get:
[tex]\frac{4.54}{14}=0.324[/tex]Then the Mr. Nut peanuts cost $0.324 per ounce. Finally, the price per ounce of the Chip's peanuts is:
[tex]\frac{6.26}{18}=0.348[/tex]Then, the cheapest peanuts are those of the brand Mr. Nut and that is the best buy.
complete the equation of the line through (-1,6) and (,7-2)
The two points given are
A(-1, 6)
B(7, -2)
We shall start by calculating the slope of the line, since we've been given two points.
[tex]\begin{gathered} \text{The slope which is m, is derived as;} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-6}{7-\lbrack-1\rbrack} \\ m=\frac{-8}{7+1} \\ m=\frac{-8}{8} \\ m=-1 \end{gathered}[/tex]Next we shall derive the y-intercept, by inserting the known values into the equation in slope-intercept form.
[tex]\begin{gathered} y=mx+b \\ We\text{ shall use the first set of coordinates, that is (-1, 6)} \\ 6=-1(-1)+b \\ 6=1+b \\ 6-1=b \\ b=5 \end{gathered}[/tex]Having calculated the values of m (the slope) and b (the y-intercept), the equation is now;
[tex]\begin{gathered} y=mx+b \\ y=-1x+5 \\ y=-x+5 \end{gathered}[/tex]Point B is located at -2. Points C and D are each 8 units away from point B. Where are C and D located?
They are located 8 units away, so one has to be away in the left direction and the other one in the right direction
[tex]\begin{gathered} \text{ - 2 - 8 = -10 } \\ \text{ - 2 + 8 = 6} \end{gathered}[/tex]So, C and D are located at -10 and 6
Can someone help me with this geometry question? First box has 3 options: 60,96,48Second box has two options: 480 and 552Third box: 180 and 216
Surface area of a square prism is:
[tex]\begin{gathered} \text{4\lparen ah\rparen= SA square prism} \\ 4(20)(6)\text{= SA square prism} \\ 80(6)\text{= SA square prism} \\ 480=\text{SA square prism} \\ \\ \end{gathered}[/tex]The surface area of the square prism 480.
The surface area for the cube is:
[tex]\begin{gathered} 5a^2=\text{ SA cube} \\ 5(6)^2=\text{ SA cube} \\ 5(36)=\text{ SA cube} \\ 180=\text{ Surface area of the cube} \end{gathered}[/tex]The surface area of the cube is: 180.
The surface area of the pyramid is:
[tex]\begin{gathered} SurfaceAreaPyramid=4bh \\ SAPyramid=\text{4\lparen6\rparen\lparen4\rparen} \\ SAPyramid=\text{ 96} \\ \end{gathered}[/tex]The surface area of the pyramid i 96.
In each geometric figure, we have to remove the inner square faces, since they are not on the surface.
The total surface area is:
[tex]\begin{gathered} SA\text{ cube + SA square prism + SA pyramid= Total SA} \\ 180\text{ + 480 + 96= Total SA} \\ 756=\text{ Total surface area. } \end{gathered}[/tex]The total surface area is 756.
write an equation of each parabola in vertex form. Vertex (3,-2) Point (2,3)
The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .
The equation of parabola with vertex (h,k) is denoted by the equation
y = a(x-h)² + k
In the question ,
it is given that
the vertex of the Parabola is (3,-2) and the point is (2,3)
So, the equation of the parabola with vertex (3,-2) will be
y = a(x-3)² - 2
Since the point (2,3) lies on the parabola ,
So, 3 = a(2-3)² - 2
3 + 2 = a*(-1)²
5 = a
Substituting a in the equation y = a(x-3)² - 2 ,
we get
y = 5(x-3)² - 2
Therefore , The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .
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A college conducted a survey of randomly selected freshmen about their choice of major. The table shows the results of the survey. KS
ONLY F is correct;
Here, we want to select the correct inference from the data presented
f) We want to comapre the number of English freshmen and the undecided
Both have a count of 50; we can see that these values are equal and thus, we conclude that these two are equal
This makes the inference correct
g) Here, we want to compare Education freshmen to science freshmen or others
From the question, the number of education freshmen is 60
The number of science or others is (30+25) = 55
The number for education is greater and not less
This makes this option or inference incorrect
h) Here, we want to comapre Business/Education and Science/Engineering
Business OR Education is = 45 + 60 = 105
Science OR Engineering is = 35 + 40 = 75
Business/Education is greater and this makes this option or inference wrong
j) Here, we want to compare Business and English
Business is 45
English is 50
We can see that English is greater and this makes the inference/option wrong
A pair of bikes cost $89.99 and the sales tax is 8%.What is the total cost of the shoes including tax?
Answer
Total Cost of the bike including tax = $97.1892
Explanation
Cost of the bike = $89.99
Sales Tax = 8% of Cost of bike = 8% (89.99) = 0.08 (89.99) = $7.1992
Total Cost of the bike = (Cost of the bike) + (Sales Tax)
= 89.99 + 7.1992
= $97.1892
Hope this Helps!!!
can you help me? on this math problem. (in the pic)
Given:
(x, y) ==> (1, -6)
m = 5
To write the equation, use the slope intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
To solve for b, substitue 1 for x, -6 for y, and 5 for m in the equation.
Thus we have:
y = mx + b
-6 = 5(1) + b
-6 = 5 + b
Subtract 5 from both sides:
-6 - 5 = 5 - 5 + b
-11 = b
The y-intercept is -11.
Therefore, the equation of the line in slope-intercept form is:
y = 5x - 11
ANSWER:
y = 5x - 11
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
Option is the the. correct answer A
