You have a total of 21 coins, all nickels and dimes. The total value is $1.70. Which of the following is the system of linear equations that represent this scenario? Let n = the number of nickels and let d = the number dimes.
Answers
n = number of nickels
d = number of dimes
1 nickel = 5 cents
1 dime = 10 cents
total number of 21 coins:
n + d = 21
Total value = $1.70
5n + 10 d = 170
Divide by 100
0.05n + 0.10 d = 1.70
Answer:
n + d = 21
0.05n + 0.10 d = 1.70
Related Questions
9(11 - x) = 3(3x -9) what is x
Answers
x = 7
Explanation:9(11 - x) = 3(3x -9)
Expanding the expression:
9(11) - (9x) = 3(3x) -3(9)
99 - 9x = 9x - 27
collect like terms:
99 + 27 = 9x + 9x
126 = 18x
Divide both sides by 18:
126/18 = 18x/18
x = 7
If an item is discounted 30% then what percent of the original price is the sale price? if the organal price of the item is $500 what is the dollar amount of the discount?how much is the sale price ?
Answers
a.) Discount = 30%
Percent of the original price on sale = 100% - 30% = 70%
b.) Original price = $500
Discount = 30%
Dollar amount of the discount = $500 x (30% / 100%) = $500 x 0.30 = $150
c.) The sale price = $500 - (Discount Amount) = $500 - $150 = $350
why you can always solve a right triangle if you know the measures of one side and one acute angle.
Answers
In a right triangle, one angle is always 90.
If you know one acute angle, you automatically know the other (3rd) angle.
3 angles are solved.
Now, comes the sides.
If you already know 1 side, you can easily know another side by using the basic trig identities SIN, COS, or TAN.
When you know 2 sides, the 3rd side can always be find using:
• pythagorean theorem, or
,• again, trigonometric ratios (sin, cos, tan).
Match each expression with its translation.1. 3 na number increased by three2. a +3the quotient of three and a number3. Y-3three times a number4. 3 = xthree subtracted from a number
Answers
A number increased by three:
Every time we read a number, it's an unknown value represented with a letter (x,y, a,n)
increased by three means t
A right triangle is shown in the graph.
right triangle on coordinate plane with hypotenuse labeled t and one endpoint of hypotenuse at r comma s and the other endpoint at x comma y, vertical line from point x comma y and horizontal line from r comma s that meet at right angle of triangle, horizontal dotted line from point r comma s to point s on y axis, horizontal dotted line from point x comma y to point y on y axis, vertical dotted line from point r comma s to point r on x axis, and vertical dotted line from right angle to point x on x axis
Part A: Use the Pythagorean Theorem to derive the standard equation of the circle with center at (r, s) and a point on the circle at (x, y). Show all necessary math work. (3 points)
Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle. (4 points)
Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence. (3 points
Answers
Part a: The standard equation of circle: (x - r)² + (y - s)² = t².
Part b: Domain = {17, -3} and Range = {-14, 6}.
Part c: Point (9, 1) lies inside the circle.
What is termed as the Pythagorean Theorem?The Pythagorean theorem, or Pythagorean theorem, explains the relation between the three sides of such a right-angled triangle. The the hypotenuse's square is equal to the total of the squares of the remaining two sides of a triangle, according to Pythagoras' theorem.For the given question,
The right triangle are given with two of ts vertices as (r, s) and (x, y).
The distance between these two points is 't'.
Part a: The standard equation of the circle.
Centre of circle = (r,s) and
Point on the circle = (x, y)
Using Pythagorean Theorem,
(x - r)² + (y - s)² = t²
Thus, the standard equation of the circle is (x - r)² + (y - s)² = t²
Where, t is the radius of the circle.
Part b: Domain and range.
(r, s) = (7, –4) and t = 10,
For x values in the domain r ± t and y values in the range s ± t, the circle would be defined.
Domain = 7 ± 10 = {17, -3}
Range = -4 ± 10 = {-14, 6}
Part c: Point (9, 1) lies inside or not.
(r, s) = (7, –4) and t = 10
Point (9, 1) = (x, y)
Put the values;
(x - r)² + (y - s)² ≤ t²
(9 - 7)² + (1 + 4)² ≤ 10²
2² + 5² ≤ 10²
4 + 25 ≤ 100
29 ≤ 100
Thus, the points (9, 1) lies inside the circle.
To know more about the Pythagorean Theorem, here
https://brainly.com/question/21332040
#SPJ13
You have two spinners each with three sections of equal size labeled with numbers 1,2,3. You spin both and observe the numbers. Let x be the sum of the two numbers. Find the probability distribution for X.
Answers
From the given problem with two spinners with three sections of equal size labeled as 1, 2, and 3.
Spinner 1 : 1 2 3
Spinner 2 : 1 2 3
The sum is as follows :
1+1 = 2
1+2 = 3
1+3 = 4
2+1 = 3
2+2 = 4
2+3 = 5
3+1 = 4
3+2 = 5
3+3 = 6
There are 9 total outcomes
There are (1) 2,
(2) 3's
(3) 4's
(2) 5's
and
(1) 6
and their corresponding probability can be calculated by :
[tex]\text{probability}=\frac{\text{ quantity}}{\text{ total quantity}}[/tex]Probability of 2 = 1/9
Probability of 3 = 2/9
Probability of 4 = 3/9 or 1/3
Probability of 5 = 2/9
Probability of 6 = 1/9
Construct the probability distribution :
To check if your probability distribution is correct.
The sum of P(X) must be equal to 1
1/9 + 2/9 + 1/3 + 2/9 + 1/9 = 1
Therefore the distribution is correct.
. Math and Science During winter months, freshwater fish sense the water getting colder and swim to the bottoms of lakes and rivers to find warmer water. If a fish 7 swims of the depth of a 32-foot deep lake, how many feet down did the fish swim?[tex]51[/tex]
Answers
The total depth of the lake is:
[tex]32\text{ ft}[/tex]And we need to find how many feet are 7/8 of the depth.
To find how much is 7/8 out of 32 ft what we do is multiply 32 by 7/8:
[tex]32\times\frac{7}{8}[/tex]This multiplication can also be represented as follows:
[tex]\frac{32}{8}\times7[/tex]We start by solving the division:
[tex]4\times7[/tex]and finally, we solve the multiplication:
[tex]4\times7=28[/tex]-->the fish swam 28 ft.
Answer: 28 ft
What it 3 1/8 + 3/4?
Answers
The given expression is:
[tex]\begin{gathered} 3\frac{1}{8}+\frac{3}{4}=3\frac{1+6}{8} \\ =3\frac{7}{8} \end{gathered}[/tex]Therefore, the value of the expression is:
3 7/8
.
Find the area of this trapezoid. Be sure to include the correct un4 cm6 cm4 cm15 cm
Answers
So,
Here we have the following trapezoid:
Remember that the area of a trapezoid can be found if we apply the following formula:
[tex]A=\frac{1}{2}(\text{base}1+\text{base}2)\cdot\text{height}[/tex]Where bases 1 and 2 are the greater and smaller bases respectively.
So, if we replace:
[tex]\begin{gathered} A=\frac{1}{2}(15+4)\cdot4 \\ A=\frac{1}{2}(19)\cdot4 \\ A=9.5\cdot4 \\ A=38 \end{gathered}[/tex]So the area is 38cm^2.
What is the slope of a line parallel to the line whose equation is 5x-3y=18
Answers
Slope and slant both refer to an incline away from a reference surface or line that is generally straight.The definition of slope is "a vertical inclination in an oblique direction"Here, the land abruptly slopes either upward or downhill.
How to Determine a Line's Slope?
slope,The inclination of a line with respect to the horizontal is measured numerically.The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). To determine how much the y coordinates have changed, find the difference.To determine how much the x coordinates have changed, find the difference.Find the slope by dividing y by x.
Y=mx+b, where m is the slope and b is the y-intercept, is the slope-intercept form.
y=mx+b
Change the formula to 3y+18=5x.
−3y+18=5x
From both sides of the equation, deduct 18.
−3y=5x−18
Simplify by multiplying each term in 3y=5x18 by 3.
Subtract 3 from each term in 3y=5x18.
−3y/−3=5x/−3+−18/−3
Make the left side simpler.
Tap to take additional steps:Y= -5X/3+-18/-3
Make the right side simpler.
Tap to take additional steps: y=5x/3+6
Write in the form y=mx+b.
Tap to take additional steps: y=5/3x+6
The slope is- 5/3 using the slope-intercept form.
.
m=−5/3
To learn more about slope refer
https://brainly.com/question/3493733
#SPJ13
The probability that the degree is not a bachelor's given that thr recipient Is male is
Answers
Answer
Probability that the degree is not a bachelor's given that thr recipient Is male = 0.36
Explanation
The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.
For this question,
Number of degrees that are not bachelor's degree given to a male = Number of associate's degree given to a male = 239
Total number of males = 239 + 427 = 666
Probability that the degree is not a bachelor's given that thr recipient Is male = (239/666)
= 0.36
Hope this Helps!!!
You pick a card at random.
1 2 3 4
What is P(factor of 24)?
Write your answer as a percentage rounded to the nearest tenth
Answers
Answer:
100%
Step-by-step explanation:
All of the numbers are factors of 24. So, picking a factor of 24 is guaranteed, so the probability is 1.
This is equal to 100%.
What number is 3/4 of 17
Answers
3/4 of 17 is equal to the product of 3/4 times 17, that is,
[tex]\frac{3}{4}\times17=\frac{3\times17}{4}[/tex]which gives
[tex]\frac{3\times17}{4}=\frac{51}{4}[/tex]in decimal form, the answer is 12.75.
A traffic light weighing 16 pounds is suspended by two cables (see figure). Find the tension in each cable. (Round your answers to one decimal place.) lb (smaller value) lb (larger value)
Answers
Step 1: Draw an image to illustrate the problem
Consider the forces along the horizontal axis.
[tex]\begin{gathered} -T_1\cos \theta_1+T_2\cos \theta_2=0 \\ \text{ therefore} \\ T_2\cos 20^0=T_1\cos 20^0 \end{gathered}[/tex][tex]\text{ Dividing both sides by }\cos 20^0[/tex][tex]\begin{gathered} \frac{T_2\cos20^0}{\cos20^0}=\frac{T_1\cos 20^0}{\cos 20^0} \\ \text{thus} \\ T_2=T_1 \end{gathered}[/tex]Consider the forces along the vertical axis.
[tex]\begin{gathered} T_1\sin 20^0+T_2\sin 20^0-16=0 \\ T_1\sin 20^0+T_1\sin 20^0-16=0\text{ (}T_1=T_2) \\ \text{ Thus} \\ 2T_1\sin 20^0=16 \\ T_1=\frac{16}{2\sin 20^0}\approx23.39\text{ pounds} \end{gathered}[/tex]then T₁ = 23.39 pounds
Since T₁=T₂, then T₂ = 23.39 pounds
Hence, smaller value = 23.4 pounds to one decimal place and
larger value = 23.4 pounds to one decimal place
a normal distribution with u= 40 with o=4 what is the probability of selecting a score greater than x=44?
Answers
We have the following information:'
[tex]\begin{gathered} \mu=40 \\ \sigma=4 \\ x=44 \end{gathered}[/tex]We want to calculate the following probability:
[tex]P(X>44)[/tex]then, using the information that we are given, we havE:
[tex]P(X>44)=P(X-\mu>44-40)=P(\frac{X-\mu}{\sigma}>\frac{44-40}{4})=P(\frac{X-\mu}{\sigma}>1)[/tex]since:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]we have the following:
[tex]P(X>44)=P(Z>1)=0.1587[/tex]therefore, the probability of selecting a score greater than 44 is 15.87%
DEF is a right triangle. If FE= 12 and DE= 5, find DF.
Answers
Answer:
DF = 13
Explanation:
The Pythagoras theorem says that
[tex]FE^2+ED^2=DF^2[/tex]Now in our case,
FE = 12
ED =
Question 1 4 pts Match each quadratic expression that is written as a product with an equivalent expression that is expanded. A. (x + 2)(x + 6) [Choose ] [Choose ] B. (2x + 3)(x + 2) 2x^2 + 10x + 12 X^2 + 12x + 32 C. (X + 8)(x + 4) x^2 + 8x + 12 2x^2 + 12x + 16 D. (x + + 2)(2x + 6) [Choose ]
Answers
(x +2) (x +6) ------> x^2 +8X + 12
(2x + 8) (x +2) -------> 2x^2 +12x + 16
(x +8) (x+4) ------------> x^2 +12x +32
(x + 2) (2x+6) ----------> 2x^2 +10x +12
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
Answers
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.
if RS=2x+6 ST=x+4 and RT= 40 Find RS
Answers
RS + ST = RT
Substituting with data,
2x + 6 + x + 4 = 40
(2x + x) + (6 + 4) = 40
a portion of the graph of f(x) = -x^2 - 2x +8 is shown. which of the following describes all solutions for f(x)?
Answers
Given the function:
[tex]f(x)=-x^2-2x+8[/tex]Let's determine the expression which describes the solution for f(x).
From the graph, we can see the x-values go from -5 to 3.
The expression which describes the solution will be:
[tex](x,-x^2-2x+8),where-5\leq x\leq3[/tex]ANSWER:
[tex](x,-x^{2}-2x+8), where-5\leqslant x\leqslant3[/tex]what is 1 5/8 + 2 1/3=
Answers
1 5/8 + 2 1/3
= 3 23/24
Explanation:1 5/8 + 2 1/3
= 1 + 2 + 5/8 + 1/3
= 3 + 23/24
= 3 23/24
Divide. −3.52−2.2 What is the quotient
Answers
The quotient of - 3.32 / - 2.2 is 8 ÷5.
What is the quotient?Given fraction:
-3.32 / -2.2
First step is to re-write the given fraction which is - 3.52 / - 2.2
3.52 / 2.2
Second step is to convert the decimal to fraction
352 ÷ 100 / 22 ÷10
Third step is to reduce the fraction
reducing 352/100
=(2^5 × 11)/(2^2 × 5^2)
= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]
= (2^3 × 11)/5²
= 88/25
Reducing 22/10
Divide the numerator and denominator by the greatest common divisor
= 22 ÷ 2 / 10 ÷ 2
= 11 /5
Now let determine or find the quotient
88 ÷ 25 × 11 ÷ 5
= 8 ÷ 5
Therefore we can conclude that 8 ÷ 5 is the quotient.
Learn more about quotient here: https://brainly.com/question/11418015
#SPJ1
Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π). The circle's radius is 2 units long and the terminal point is (−1.79,−0.89).The terminal point is how many radius lenghts to the right of the circle's center?h= radii Then, cos−1(h)=Does the number we get in part (b) give us the correct value of θ? Therefore, θ=
Answers
Given the terminal point ( -1.79 , -0.89 )
So, the x- coordintes = -1.79
[tex]\begin{gathered} \theta=\cos ^{-1}h \\ \\ h=-\frac{1.79}{2} \\ \\ \theta=\cos ^{-1}(-\frac{1.79}{2})=206.5^o \end{gathered}[/tex]
Graph the equation. y = 2x 20 N 18 16 14 12 10 8 6 4 N. 0 1 2 3 4 ул 6 10 2. y = 2x
Answers
Make a table, and give values to x.
Solve the equation and obtain y values.
Graph the points and join them:
x = 0
y= 2x = 2 (0) = 0
x= 2
y= 2(2) = 4
x= 4
y= 2(4) = 8
Graph:
find a b c d e f from the picture
Answers
Given data:
The value of a is (3+4+2)=9
The value of b is (5+1+2)=8
The value of c is (1+8+1)=10
The value of d is (
9. Madison needs $10 000.00 in 16 years at an interest rate of 3 %/a compounded monthly. How much should she invest?
Answers
SOLUTION:
Case: Compound interest
Method:
The formula is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]P =?
A= $10 000.00
n = 12
r = 3% or 0.03
t = 16 years
[tex]\begin{gathered} 10000=P(1+\frac{0.03}{12})^{12\times16} \\ 10000=P(1.0025)^{192} \\ 10000=P\times1.6151 \\ P=\frac{10000}{1.6151} \\ P=6191.54 \end{gathered}[/tex]Final answer: To the nearest cent
She should invest $6191.54
Students were divided into 10 teams with 12 on each team. later, the same day students were divided into teams with 3 on each team. how many teams were there then?
Answers
At first, the students were divided into 10 teams with 12 on each of them; we can write this as:
team 1 = 12 students
team 2 = 12 students
team 3 = 12 students
team 4 = 12 students
team 5 = 12 students
team 6 = 12 students
team 7 = 12 students
team 8 = 12 students
team 9 = 12 students
team 10 = 12 students
Sum up the number all the students and this adds up to: 120 students.
Then, the question says these 120 students were divided into teams with 3 students on each team.
This time the number of teams created will be more.
team 1 = 3 students
team 2 = 3 students
teams 3 = 3 students
...
And so on.
In order to get the number of teams, we simply divide the number of students by the number of students in a team.
[tex]\frac{120}{3}=40\text{ teams}[/tex]Therefore, the number of 3 person teams are 40 teams
What percent of 60 is 39?
Answers
Answer:
To find the percent of 60 is 39
Let x be the percent of 60 is 39,
we get,
[tex]\frac{x}{100}\times60=39[/tex]Solving this, we get
[tex]x=\frac{39\times10}{6}[/tex][tex]x=65[/tex]Hence 65 percent of 60 is 39.
Answer is: 65%
Which of the following statements is not true based on the given graph?abd0OlbicasbCO
Answers
The Solution.
From the given number line graph, we can see clearly that the following option are true.
[tex]undefined[/tex]The only option that is not true is
[tex]undefined[/tex]...
>
Question
A triangle with area 40 square inches has a height that is four less than six times the width. Find the width and height of the
triangle
Provide your answer below:
width:
inches, height:
inches
FEEDBACK
MORE INSTRUCTION
Content attribution
SUBMIT
Math
Answers
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the formula for the area of the triangle
[tex]Area=\frac{1}{2}\times base\times height[/tex]STEP 2: Represent the statements to get an equation
[tex]\begin{gathered} width=base \\ From\text{ the statement,} \\ six\text{ times of the width}=6w \\ four\text{ less than six times the width }=6w-4 \\ \therefore height=6w-4 \end{gathered}[/tex]STEP 3: Substitute into the formula in step 1
[tex]\begin{gathered} height=6w-4,width=base=w,Area=40in^2 \\ Area=\frac{1}{2}\times w\times(6w-4) \\ Area=\frac{w(6w-4)}{2}=\frac{6w^2-4w}{2}=40 \end{gathered}[/tex]STEP 4: Cross multiply
[tex]\begin{gathered} 6w^2-4w=40\times2 \\ 6w^2-4w=80 \\ Subtract\text{ 80 from both sides} \\ 6w^2-4w-80=80-80 \\ 6w^2-4w-80=0 \\ Divide\text{ through by 2, we have:} \\ 3w^2-2w-40=0 \\ By\text{ factorization;} \\ 3w^2-12w+10w-40=0 \\ 3w(w-4)+10(w-4)=0 \\ (w-4)(3w+10)=0 \end{gathered}[/tex]STEP 5: Find the values of w
[tex]\begin{gathered} w-4=0,w=0+4,w=4 \\ 3w+10=0,3w=0-10,3w=-10,w=\frac{-10}{3} \\ \\ Since\text{ the width cannot be negative, width=4 inches} \end{gathered}[/tex]STEP 6: Find the height
[tex]\begin{gathered} Recall\text{ from step 2:} \\ h=6w-4 \\ Substitute\text{ 4 for w} \\ h=6(4)-4=24-4=20in \end{gathered}[/tex]Hence,
width = 4 inches
height = 20 inches