We have the next quadratic function given:
[tex]3x^2-9x+2=0[/tex]Mary used the next quadratic formula:
[tex]x=\frac{-b^\pm\sqrt{b^2-4ac}}{2a}[/tex]Replace using the form ax²+bx+c
Where a= 3
b=-9
c=2
Then:
[tex]\begin{gathered} x=\frac{-\lparen-9)\pm\sqrt{\left(-9\right)^2-4\left(3\right)\left(2\right)}}{2\left(3\right)} \\ x=\frac{9\pm\sqrt[]{57}}{6}\frac{}{} \end{gathered}[/tex]Therefore, the correct answer is "x = fraction numerator 9 plus-or-minus square root of 57 over denominator 6 end fraction"
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
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
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The liters in the tank when it is filled to a height of 3.70 is 5,580 liters
The liters that needs to be added to 100% capacity is 480 liters
What is the volume?A right circular cone is a three dimensional object has a flat circular base that tapers to a vertex. The volume of a right circular cone is the amount of space in the right circular cone.
Volume of a cone = 1/3(πr²h)
Where:
π = pi = 3.14r = radius h = heightVolume of the right circular cone when its filled to a height of 3.70 = 1/3 x 3.14 x 3.70 x 1.20² = 5.58 m³
5.58 x 1000 = 5,580 liters
Volume of the right circular cone when it is full = 1/3 x 3.14 x 4 x 1.20² = 6.03 m³
6.03 x 1000 = 6030 liters
Liters that needs to be added to 100% capacity = 6030 liters - 5,580 liters = 480 liters
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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
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.
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What number is 3/4 of 17
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.
find a b c d e f from the picture
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 (
what is 1 5/8 + 2 1/3=
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
Function Notation - TransformationIll send a picture of the question
Given the vertices of the original quadilateral:
(3, 4), (5, 6), (7, 4), and (5, 3)
Vertices of the transformed quadilateral:
(-5, -6), (-3, -4), (-1, -6), and (-3, -7)
Let's describe the transformation rule used for this transformation.
To find the transformation rule, let's find the number of movements in the x-direction and y-direction that would map the original quadilateral to the transformed quadilateral by subtracting the x and y coordinates of the coresponding sides.
We have:
(x, y) ==> (-5 -3, -6 -4) ==> (-8, -10)
(x, y) ==> (-3 -5, -4, -6) ==> (-8, -10)
(x, y) ==> (-1 -7, -6 -4) ==> (-8, -10)
(x, y) ==> (-3 -5, -7 -3) ==> (-8, -10)
For all corresponding sides, we have: (x, y) ==> (-8, -10)
This means there was a shift 8 units to the left, and 10 units downwards.
Therefore, the rule for the transformation shown here is:
(x, y) ==> (x - 8, y - 10)
ANSWER:
B. f(x, y) = (x - 8, x- 10)
The probability that the degree is not a bachelor's given that thr recipient Is male is
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!!!
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?
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
Colin just travelled across Ontario on a road trip. He bought some skis in Blue Mountain for $879.95 plus tax, a boombox in Muskoka for $145.58 including taxes, a souvenir in Niagara Falls for $99.97 plus tax, and some maple syrup in Toronto for $45.14 including tax. Overall, how much HST did Colin pay on his trip? Answer should be rounded off to whole number.
The Harmonized Sales Tax that Colin paid on this trip was of $152.18.
What is the Harmonized Sales Tax?The Harmonized Sales Tax is a rate that a person pays over the values of their purchases.
In the context of this problem, the person traveled on Ontario, where the HST rate is of 13%.
The purchases of the person are given as follows:
Skis in Blue Mountain for $879.95.Boombox in Muskoka for $145.58.Souvenir in Niagara Falls for $99.97.Maple syrup in Toronto for $45.14.The total value of these purchases is given by:
Total value = 879.95 + 145.58 + 99.97 + 45.14 = $1,170.64.
The HST paid is 13% of this amount, hence it is calculated as follows:
HST = 0.13 x 1170.64 = $152.18.
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all you need is in the photo please answer fast please helpppppp DON'T DO STEP BY STEP PUT ONLY THE ANSWER PLEASEEEEEEEEEEEEEEEEEEEEE
Notice that since the residuals are varying from -1 to 1 without a pattern, we have that the line is not a good fit for the data.
Also, some residuals (for 0, 2, 4 and 6) are relatively large compared to the actual data values.
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=
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]
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 ]
(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
9. Madison needs $10 000.00 in 16 years at an interest rate of 3 %/a compounded monthly. How much should she invest?
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
What percent of 60 is 39?
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%
a portion of the graph of f(x) = -x^2 - 2x +8 is shown. which of the following describes all solutions for f(x)?
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]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.
. 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]
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
a normal distribution with u= 40 with o=4 what is the probability of selecting a score greater than x=44?
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%
Divide. −3.52−2.2 What is the quotient
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.
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a. During a basketball practice, Mai attempted 40 free throws and was successful on
25% of them. How many successful free throws did she make?
410
0
free throws
25%
Unit 3, Lesson 11
50%
75% 100% 125% 150%
Answer: 10
1/4 (25%) of 40 is 10, meaning Mai made 10 successful free throws.
Which of the following statements is not true based on the given graph?abd0OlbicasbCO
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]What it 3 1/8 + 3/4?
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
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.
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)
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
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
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%.
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 ?
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
...
>
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
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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
37)You need at least 15 pencils or markers. You want to spend at most $14 onpencils and markers. Pencils p are $0.85 each and markers m are $1.45each. Which system of inequalities models the situation?A) p+m>150.85p+1.45m<14B) p+m>140.85p+1.45m>15C) p+m≥150.85p+1.45m≤14D) p+m≥140.85p+1.45m≤15
Given:
Minimum number of pencils or markers = 15
Maximum amount to spend on pencils and markers = $14
Cost of a pencil = $0.85
Cost of a marker = $1.45
Required: System of inequalities models the situation
Explanation:
Let p denote the number of pencil and m be the number of markers
Since the minimum number of pencils or markers is 15, it gives the inequality
[tex]p+m\geq15[/tex]Since the maximum amount to spend on pencils and markers is $14, it gives the inequality
[tex]0.85p+1.45m\leq14[/tex]Final Answer:
[tex]\begin{gathered} p+m\ge15 \\ 0.85p+1.45m\leqslant14 \end{gathered}[/tex]
DEF is a right triangle. If FE= 12 and DE= 5, find DF.
Answer:
DF = 13
Explanation:
The Pythagoras theorem says that
[tex]FE^2+ED^2=DF^2[/tex]Now in our case,
FE = 12
ED =