Answer:
1 and -3.
Explanation:
Given the quadratic polynomial:
[tex]a^2+2a-3=0[/tex]To use the completing the square method to find the zeros, follow the steps below:
Step 1: Take the constant to the right-hand side.
[tex]a^2+2a=3[/tex]Step 2: Divide the coefficient of a by 2, square it and add it to both sides.
[tex]a^2+2a+(1)^2=3+(1)^2[/tex]Step 3: Write the left-hand side as a perfect square.
[tex](a+1)^2=4[/tex]Step 4: Take the square root of both sides.
[tex]a+1=\pm\sqrt[]{4}[/tex]Step 5: Solve for a.
[tex]\begin{gathered} a=-1\pm\sqrt[]{4} \\ a=-1\pm2 \\ a=-1+2\text{ or }a=-1-2 \\ a=1\text{ or }a=-3 \end{gathered}[/tex]The zeros of the quadratic equation are 1 and -3.
The perimeter of the rectangle blow is 70 units find the length of side PS
The perimeter of the given rectangle is 78 units.
Recall that the perimeter of a rectangle is given by
[tex]P=2(w+l)[/tex]Where w is the width and l is the length of the rectangle.
As you can see from the given figure,
w = 3z + 3
l = 4z + 1
We are asked to find the side length of side PS.
Substitute the given values into the above formula and solve for z.
[tex]\begin{gathered} P=2(w+l) \\ 78=2(3z+3+4z+1_{}) \\ 78=2(7z+4_{}) \\ \frac{78}{2}=(7z+4_{}) \\ 39=7z+4_{} \\ 39-4=7z \\ 35=7z \\ \frac{35}{7}=z \\ 5=z \end{gathered}[/tex]So, the value of z is 5
Finally, the length of side PS is
[tex]\begin{gathered} PS=4z+1 \\ PS=4(5)+1 \\ PS=20+1 \\ PS=21 \end{gathered}[/tex]Therefore, the length of the side PS is 21 units.
factor the expression 120 + 50 using gcf
The given expression is,
[tex]120+50[/tex]The factors of 120 are, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The factors of 50 are, 1, 2, 5, 10, 25, 50
From this, we can infer that, the greatest common factor of 120 and 50 is,
10.
Therefore, we can write,
[tex]120+50=(10\times12)+(10\times5)=10(12+5)=10\times17=170[/tex]The area of a circle is 100 square millimeters. What is the circumference?
Please help me with this rectangle problem they always give me trouble
Hello there. To solve this question, we'll have to remember some properties about rectangles.
A rectangle is a quadrilateral polygon (that is, it has 4 right angles in its corners) and two parallel sides.
The special cases of quadrilaterals are the parallelogram, that has two parallel sides but the angles might not be right angles and the square, in which the sides are equal.
In the case of the rectangle, it has a side with length L and other side, that we call its width, with length W, as in the following drawing:
Its area A can be calculated taking the product between the length and the width, therefore:
[tex]A=L\cdot W[/tex]With this, we can solve this question.
It says that a rectangle is 15 ft longer than it is wide. Its area is 2700 ft². We have to determine its dimensions.
Say this rectangle has width W.
If this rectangle is 15 ft longer than it is wide, it means that
[tex]L=15+W[/tex]Now, we plug this values for the formula of area, knowing that A = 2700:
[tex]\begin{gathered} A=L\cdot W=(15+W)\cdot W \\ \end{gathered}[/tex]Apply the FOIL
[tex]2700=15W+W^2[/tex]In this case, we have a quadratic equation in W.
We'll solve it by completing the square, that is, finding a perfect trinomial square such that we can undo the binomial expansion and solve a simpler quadratic equation.
The binomial expansion (a + b)² gives us
[tex]a^2+2ab+b^2[/tex]So to find the b we need to complete the square, we start dividing the middle term by 2.
In the case of our equation, the middle term has coefficient 15, hence
[tex]b=\dfrac{15}{2}[/tex]Square the number and add it on both sides of the equation, such that
[tex]\begin{gathered} 2700+\left(\dfrac{15}{2}\right)^2=\left(\dfrac{15}{2}\right)^2+2\cdot\dfrac{15}{2}\cdot W+W^2 \\ \\ 2700+\dfrac{225}{4}=\dfrac{11025}{4}=\left(W+\dfrac{15}{2}\right)^2 \end{gathered}[/tex]Take the square root on both sides of the equation, knowing that 11025 = 105²
[tex]W+\dfrac{15}{2}=\sqrt{\dfrac{11025}{4}}=\sqrt{\left(\dfrac{105}{2}\right)^2}=\dfrac{105}{2}[/tex]Subtract 15/2 on both sides of the equation
[tex]W=\dfrac{105}{2}-\dfrac{15}{2}=\dfrac{105-15}{2}=\dfrac{90}{2}=45[/tex]Then we plug this value in the expression for L, hence we get:
[tex]L=15+W=15+45=60[/tex]Notice that multiplying the numbers, we'll get:
[tex]L\cdot W=60\cdot45=2700[/tex]That is exactly the area we had before.
Hence we say that its width equals 45 ft and its length equals 60 ft.
Which ratio is equivalent? 8 cm to 20 mm
Given the ratio:
8 cm to 20 mm
first convert from cm to mm
1 cm = 10 mm
so, 8 cm = 8 * 10 mm = 80 mm
so, the ratio will be :
8 cm to 20 mm = 80 mm to 20 mm =
[tex]\frac{80\operatorname{mm}}{20\operatorname{mm}}=\frac{80}{20}=\frac{8}{2}=\frac{4}{1}=4\colon1[/tex]so, the answer is: 8 cm to 20 mm = 4 : 1
Bonnie is making a dipping sauce. She mixes 150 ml of soy sauce with 100 ml of vinegar.how much soy sauce does Bonnie mixed with every 1 milliliter of vinegar
The question is asking how much soy sauce Bonnie is mixing per every millilter of vinegar. To calculate this ratio, we simply divide the amount of soy sauce she mixed by the total amount of vinegar she used. This leads to
[tex]\frac{150\text{ (soy sauce)}}{100\text{ (vinegar)}}[/tex]which is equals to
[tex]\frac{150}{100}=\frac{30\cdot5}{20\cdot5}=\frac{30}{20}=\frac{3}{2}=1.5[/tex]so Bonnie uses 1.5 ml of soy sauce per every ml of vinegar
When rolling a pair of dice, find the probability that the sum is less than five and even.
In order to obtain the solution for this question, we need to find the sample space for 2 dice, which is given by:
As we can note, there are 36 events and there are 4 events which sum is less than five and even:
Since the probability is defined as the number of possible outcomes divided by the total number of outcomes, we have
[tex]P(\text{ sum less than 5 and even\rparen=}\frac{4}{36}[/tex]By simplifying this result, the answer is:
[tex]P(\text{ less than 5 and even\rparen=}\frac{1}{9}[/tex]What is the range of the function on the graph?у5all real numbers32all real numbers greater than or equal to 0O all real numbers greater than or equal to 1all real numbers greater than or equal to 211-5 -4 -3 -2 -11 + 1 2 3 4 5 X-2--34+-3
Given:
The graph of the function is given.
The range of the function is all y-values or output
Answer:
The answer is D or "all real numbers greater than or equal to 2"
Edge 2023 ✅Use the vertex and intercept to sketch the graph of the quadratic function.
The expression we have is:
[tex]f(x)=9-(x+3)^2[/tex]We need to compare this expression with the Vertex form of the quadratic equation:
[tex]f(x)=a(x-h)^2+k[/tex]Where the vertex is at (h,k).
We rewrite our expression as follows:
[tex]f(x)=-(x-(-3))^2+9[/tex]And we can see that h=-3, and k=9. Thus, the vertex of this quadratic function is at:
[tex](-3,9)[/tex]Also, since we have a negative sign along side the x, that means that the parabola opens down.
And the correct result is:
Option C
Which of the following values have 2 significant figures? Check all that apply.A. 40B.12C.1,200D. 1,001
A and B have 2 significant
3. Lin is solving this system of equations:S 6x – 5y = 343x + 2y = 83. She starts by rearranging the second equation to isolate the y variable: y = 4 -1.5%. She then substituted the expression 4 - 1.5x for y in the first equation, asshown below:--6x – 5(4 – 1.5x) = 346x – 20 – 7.5x = 34-1.5x = 54x = -36y = 4 – 1.5xy = 4 - 1.5 • (-36)y = 58.
We are given the following system of equations:
[tex]\begin{gathered} 6x-5y=34,(1) \\ 3x+2y=8,(2) \end{gathered}[/tex]We are asked to verify if the point (-36, 58) is a solution to the system. To do that we will substitute the values x = -36 and y = 58 in both equations and both must be true.
Substituting in equation (1):
[tex]6(-36)-5(58)=34[/tex]Solving the left side we get:
[tex]-506=34[/tex]Since we don't get the same result on both sides this means that the point is not a solution.
Now, we will determine where was the mistake.
The first step is to solve for "y" in equation (2). To do that, we will subtract "3x" from both sides:
[tex]2y=8-3x[/tex]Now, we divide both sides by 2:
[tex]y=\frac{8}{2}-\frac{3}{2}x[/tex]Solving the operations:
[tex]y=4-1.5x[/tex]Now, we substitute this value in equation (1), we get:
[tex]6x-5(4-1.5x)=34[/tex]Now, we apply the distributive law on the parenthesis:
[tex]6x-20+7.5x=34[/tex]This is where the mistake is, since when applying the distributive law the product -5(-1.5x) is 7.5x and not -7.5x.
Ms Martins has lockers for the students to store their things. The volume of the lockerd is 40 feet if the base is 4 by 2 feet how tall are the lockers
The volume of the lockerd is 40 feet ^3
If the base is 4 feet by 2 feet .
How tall are the lockers?
SOLUTION
Volume = Length x Width x Height
40 = L X 4 x 2
40 = L X 8
Divide both sides by 8
L = 5 feet
The locker is 5 feet
What is the slope of the line descrbed by the equation below?
The given equation of the line is:
[tex]y-5=-3(x-17)[/tex]It is required to determine the slope of the line.
Recall that the point-slope form of the equation of a line is given as:
[tex]y-b=m(x-a)[/tex]Where m is the slope of the line and it passes through the point (a,b).
Notice that the given equation is in the point-slope form.
Notice that the slope is m=-3.
The answer is option A.
2. What is the value of the expression (x - y) when x = 5and y=-1?F.7G.6H. 16K. 36
G.6
In this expression, let's plug it the values already informed to find the answer.
x=5
y= -1
(x-y)
(5-(-1)) = (5+1) =6
Remember that the minus changes the minus inside to plus.
What is the product of the complex numbers below? (4-21)(1+7) O A. 18-301 O B. -10-301 ОО O C. -10 + 261 O D. 18 + 261
Given the complex product:
(4 - 2i)(1 + 7i) =
• First we multiply each parenthesis:
4 + 28i - 2i - 14i²
• Using i² = -1
4 + 28i - 2i + 14 =
18 + 26i
the prism shown has a volume of 798cm3. what is the hight of the prism?the volume is 798cm3 the width is 8cm and the length is 9.5cm
Answer:
Height = 10.5 cm
Explanation:
The volume of a rectangular prism can be calculated as follows:
Volume = Length x Width x Height
So, we can replace the volume by 798, the width by 8, and the length by 9.5:
798 = 8 x 9.5 x Height
798 = 76 x Height
Then, we can solve for the Height dividing both sides by 76:
798/76 = 76 x Height / 76
10.5 = Height
Therefore, the height of the prism is 10.5 cm
Find the unknown value in the proportion. Round to the nearest tenth if needed. 4/3=12/?
Starting with the proportion:
[tex]\frac{12}{?}[/tex]Since it should be equal to 4/3, notice that if we divide both numerator and denominator by 3, then we should get 4 and 3 respectively:
[tex]\frac{12}{?}=\frac{12\div3}{?\div3}=\frac{4}{?\div3}=\frac{4}{3}[/tex]Therefore, ?÷3 is equal to 3.
Which number is equal to 3 when we divide it by 3?
That number is 9. 9÷3=3
Therefore, ?=9.
Can someone help me identify these things this is geometry
(a)
The rays are opposite if angle between the two rays in 180 degree. So ray AB and ray CB is a pair of opposite ray.
(b)
When two line intersect each other then angle lies on opposite side od the intersecting points are termed as vertical angles. So a pair of vertical angle is angle ABD and angle mBC.
(c)
The plane can be named by three points lying on the plane. So other name of plane P is EBC.
(d)
The colinear points always lies in a striaght line. So point A, point B and point C are collinear points.
(e)
The angles whose sum is equal to 180 degree are called linear pair of angle. So angle ABD and angle CBD are linear pair of angles.
Karla says 4 and 4.7 would fall between V17 and 4O FactO Fib
First of all, we have to know the equivalent decimal number to each of them.
[tex]\begin{gathered} 4\frac{2}{3}=\frac{4\cdot3+2}{3}=\frac{12+2}{3}=\frac{14}{3}=4.66666\ldots \\ 4.7 \\ \sqrt[]{17}=4.12310\ldots \\ 4\frac{3}{4}=\frac{4\cdot4+3}{4}=\frac{16+3}{4}=\frac{19}{4}=4.75 \end{gathered}[/tex]Notice that the interval is from 4.12310... to 4.75.
You can observe that 4.7 falls into this interval, and 4.666... also falls into this interval.
Therefore, the numbers Karla indicated fall into the interval she mentioned.The answer is Fact.Let the Universal Set, S, have 52 elements. A and B are subsets of S. Set A contains 26 elements and SetB contains 14 elements. If the total number of elements in either A or B is 27, how many elements are inA but not in B?
ANSWER
Number of elements in A but not in B = 13
EXPLANATION
Step 1: Given that:
n(S) = 52
n(A) = 26
n(B) = 14
n(A U B) = 27
Step2: Using the Venn Diagram
Step 3: Determine the value of n(A n B)
n(A U B) = n(A) + n(B) - n(A n B)
27 = 26 + 14 - n(A n B)
n(A n B) = 40 - 27
n(A n B) = 13
Step 4: Determine the number of elements in A but not in B
n(A - B) = n(A) - n(AnB)
n(A - B) = 26 - 13
n(A - B) = 13
Hence, number of elements in A but not in B = 13
Translate the word sentence into a number sentence5. One thousand is less than a number6. A number is greater than four-fifths7. Five and nine tenths is greater than or equal to a number8. A number is not equal to twelve hundredths 9. Eight plus four is not equal to eleven10. The sum of twelve and five is greater than a number
To translate "One thousand is less than a number" into a number, we can divide the sentence in three parts.
One thousand is less than a number
a b c
Let's translate each part:
(a) One thousand
We have to write the equivalent number: 1000.
(b) is less than
The symbol that represents it is <.
(c) a number
Since we do not know this number, let's assume it is x.
Now, we can put the parts together and write the number sentence.
1000 < x.
Answer: One thousand is less than a number is the same as 1000 < x.
2 Which cookie is the better deal? Oreos $2.98 for 15.5 oz O $ Chips Ahoy $2.50 for 14oz 2b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0,43 or.43, if there is a dollar amount like 1.50, do not add zeros in front) Your answer
Chips ahoy $0.18 per oz.
1) Let's write it down, since the point here is what's the best deal we need to find out the unit rate for each one. Let's set a proportion:
$2.98 ----------- 15.5 oz
x -------------- 1 oz
Cross multiplying it:
15.5x = 2.98 * 1 Divide both sides by 15.5
x= 0.192
So $0.19 per oz.
Chips Ahoy:
$2.50------------14 oz
y --------------1
14y= 2.50
y=0.1785 rounding it to the nearest hundredth 0.18
Then $0.18 per oz
So the better deal, is buying Chips Ahoy.
i need help: question = Which process will create a figure that is congruent to the figure shown?
Solution
Option A
Option A is Congruent because the size of the image is not tampered with, we only rotate, reflect and translate
Option A is correct
Option B
Option B is not congruent because there is a translation of scale factor of 1/2
Option C
Option C is not congruent because the distance between each points and the x-axis are tripled
Option D
Option D is not also congruent because the distance between each points and the x-axis are doubled
Hence, Option A is correct
Solve this using either imaginary or complex numbers equation please!
Explanation: Here we will use two rules to be able to solve our question
First rule (complex numbers):
[tex]\sqrt[]{-1}=i[/tex]Second rule:
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]Step 1: Now we can solve our expression as follows
Final answer: So the final answer is
[tex]i\cdot8\cdot\sqrt[]{3}[/tex]A coach buys a uniform and a basketball for each of the 12 players on the team. Each basketball costs $15. The coach spends a total of $756 for uniforms and basketballs. Write an equation that models the situation with u, the cost of one uniform.Find the cost of one uniform
Equation: 180 + 12u = 756
the cost of one uniform is $48
Explanation:Total number of players = 12
The cost per basketball = $15
Total cost for uniform and basket balls = $756
let the cost of each uniform = u
The equation becomes:
Total number of players(The cost per basketball ) + Total number of players( cost of each uniform)
12($15) + 12(u) = $756
180 + 12u = 756
To get u, we subtract 180 from both sides:
180 - 180 + 12u = 756 - 180
12u = 576
u = 576/12
u = 48
Hence, the cost of one uniform is $48
AC = 12√3. Find BC and AB. Write answer in simplest form.
BC = a
AC = b= 12√3
AB =c
A= 30°
B=60°
C=90°
Using the sine rule
[tex]\frac{\sin\text{ A}}{a}=\frac{\sin B}{b}[/tex]substitute the values into the above
[tex]\frac{\sin30}{a}=\frac{\sin 60}{12\sqrt[]{3}}[/tex][tex]\frac{\frac{1}{2}}{a}=\frac{\frac{\sqrt[]{3}}{2}}{12\sqrt[]{3}}[/tex][tex]\frac{1}{2\times a}=\frac{\sqrt[]{3}}{2\times12\sqrt[]{3}}[/tex][tex]\frac{1}{2a}=\frac{\sqrt[]{3}}{24\sqrt[]{3}}[/tex][tex]\frac{1}{2a}=\frac{1}{24}[/tex]cross multiply
[tex]2a=\text{ 24}[/tex][tex]a=12[/tex]Therefore BC = 12
Let's proceed to find AB
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex][tex]\frac{\sin30}{12}=\frac{\sin 90}{c}[/tex][tex]\frac{\frac{1}{2}}{12}=\frac{1}{c}[/tex][tex]\frac{1}{2\times12}=\frac{1}{c}[/tex][tex]\frac{1}{24}=\frac{1}{c}[/tex]cross-multiply
[tex]c=24[/tex]
In many European stores ,shoe sizes are proportional to the length of the shoe. The table shows examples for some women shoe sizes what is the constant of proportionally
Proportionality: The term proportionality describes any relationship that is always in the same ratio. It is express as :
x = ky, where k is the proportionality constant
Shoes Size are proportional to the length of the shoes
Shoes Size = K (Length of the shoes)
From the given data
1) Shoes size = 37, Length of shoes =9.25
So, equation will be : 37 = k (9.25)
Simplify the equation:
[tex]\begin{gathered} 37\text{ = k(9.25)} \\ k=\frac{37}{9.25} \\ k=4 \end{gathered}[/tex]So, proportionality constant is 4
Answer: Proportionality constant = 4
Seven years ago, Tom bought a house for $80,000, whichappreciated in value at 9% per year due to inflation. If Tomhas 48 more monthly payments of $500 to make to the bankon his 12% mortgage, find his present equity in the house.
The equity will be the value of the house today minus the present value of the remaining mortgage payments.
We can start with the value of the house. If the house was originally valued in $80,000 and appreciated at 9% per year during 7 seven years, we can calculate the present value as:
[tex]\begin{gathered} PV=80000\cdot(1+0.09)^7 \\ PV=80000\cdot1.09^7 \\ PV\approx80000\cdot1.828 \\ PV\approx146243.13 \end{gathered}[/tex]Now we can calculate the present value of the mortgage payments as an annuity.
The payments are monthly (m = 12), with an annual rate of 12% (r = 0.12). The amount paid monthly is $500 and there are 48 remaining payments (m*t = 48), so we can calculate the annuity as:
[tex]\begin{gathered} PV=M\cdot\frac{1-(1+\frac{r}{m})^{-m\cdot t}}{\frac{r}{m}} \\ PV=500\cdot\frac{1-(1+\frac{0.12}{12})^{-48}}{\frac{0.12}{12}} \\ PV=500\cdot\frac{1-(1.01)^{-48}}{0.01} \\ PV\approx500\cdot\frac{1-0.62026}{0.01} \\ PV\approx500\cdot\frac{0.37974}{0.01} \\ PV\approx500\cdot37.974 \\ PV\approx18986.98 \end{gathered}[/tex]Then, if we substract the mortgage present value from the present value of the house, we get the equity:
[tex]\begin{gathered} E=PV_{h\text{ouse}}-PV_{\text{mortgage}} \\ E=146243.13-18986.98 \\ E=127256.15 \end{gathered}[/tex]Answer: the present equity in the house is $127,256.15
A jar contains 10 purple marbles, 2 red marbles, and 5 blue marbles. What is the probability thatrandomly chosen marble is purple? Round the answer to the nearest hundredth of a percent.
EXPLANATION
Let's see the facts:
purple marbles = 10
red marbles = 2
blue marbles = 5
The probability formula is:
[tex]P(X)\text{ = }\frac{n\nu mber\text{ of favourable outcomes}}{\text{Total number of outcomes}}[/tex]The totl number of outcomes is 10+2+5 = 17 marbles
The number of favourable outcomes is equal to 10 because there are 10 purple marbles.
Then, the probability would be:
[tex]P(X)=\frac{10}{17}=\text{ 0.59}[/tex]Probability is 0.5882352941-->0.59 Rounded to the nearest hunderdth--------------->59%.
Answer: The probability is 59% (Rounded to the nearest hunderdth).
The table shows the results of a survey of 100 people selected at randomat an airport. Find the experimental probability that a person selected atrandom is going to City C.AirportDestinationsNumber ofDestination ResponsesCity A24City B44City C12City D12NINISThe experimental probability that a person selected at random is going to City Cis.
we have that
the experimental probability is equal to
P=12/100
P=0.12 or P=12%