Answer:
x= -4
Step-by-step explanation:
adding the two equations,
x+x+y-y=-10+2
2x= -8
x=-4
the function f(x)=2^x and g(x)=f(x)+k if k=2 what can be concluded about the graph of g(x)?
Find the set of values of m for which the line with equation y = mx + 1 and the curve with equation y = 3x^2+ 2x + 4 intersect at two distinct points.
Answer:
Given : line y=mx+4 intersects the curve y=3x2 −4x+7at two distinct points.
To find : set of values of m
Step-by-step explanation:
y = mx + 4
y = 3x² − 4x + 7
Substitute y = mx + 4 to find intersection point
mx + 4 = 3x² − 4x + 7
=> 3x² - x(m + 4) + 3 = 0
(m + 4)² > 4(3)(3)
=> m² + 8m + 16 > 36
=> m² + 8m - 20 > 0
=> (m + 10)(m - 2) > 0
m < - 10 & m > 2
m = (-∞ , - 10) ∪ ( 2 , ∞ )
What is 25.4 x 10 to the 4th power?
Answer:
254,000
Step-by-step explanation:
What is 25.4 x 10 to the 4th power?
Translate:
25.4 * 10⁴
25.4 * 10,000
When multiplying numbers by 10s, 100s, 1,000s, and so on, all you have to do is move the decimals left (for dividing) or right (for multiplying). The number of spaces you move the decimal is based on the number of zeros following the 1. For example, *100 means moving the decimal two times to the right, and /100 means moving the decimal two places to the left. No calculator is really needed.Here, we will be moving the decimal four times to the right:
25.4 * 10,000
254,000
Note: if you're not sure, you can always use a calculator to double check :)
Hope this helps!
Three students are sitting in a playground to make a circular path. They are sitting on the circumference, the co-ordinates of their position on the circle are (1, 2), (3, 4) and (3, 2). Find the co-ordinates of the point equidistant from their position. Also, find the equation of the locus.
The coordinates of the point equidistant from their position is C(x,y) = (2, 3) and the equation of the locus is (x - 2)² + (y - 3)² = 2.
How to derive the equation of the circunference associated with a playground
The center is the point that is equidistant to every point on the circumference. First, we need to determine the coefficients of the general equation of the circle, whose form is described below:
x² + y² + D · x + E · y + F = 0 (1)
We need three distinct points of the circumference to determine one solution.
If we know that (x₁, y₁) = (1, 2), (x₂, y₂) = (3, 4) and (x₃, y₃) = (3, 2), then the system of linear equations is:
D + 2 · E + F = -5 (2)
3 · D + 4 · E + F = - 25 (3)
3 · D + 2 · E + F = - 13 (4)
The solution of the linear system is D = - 4, E = - 6 and F = 11.
Now we proceed to transform the expression into its standard form by completing the squares:
x² + y² - 4 · x - 6 · y + 11 = 0
(x² - 4 · x + 4) + (y² - 6 · y + 9) - 2 = 0
(x - 2)² + (y - 3)² = 2
The coordinates of the point equidistant from their position is C(x,y) = (2, 3) and the equation of the locus is (x - 2)² + (y - 3)² = 2.
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IM STUCK CAN SOMEBODY SOLVE THE EQUATION
Answer:
1.) 400, all you have to do is subtract the two populations and it gives you the amount that it grew by.
2.) it took 2 years, because that is the difference between 2005 and 2007.
3.)if you could tell me the option then that might help? but it grew on an average of 200 students per year.
4.)1002 would be the answer because if it goes down by 200 a year, then you have to subtract 2002-1000 giving you the answer
Step-by-step explanation:
hope this helps.
Which of the following techniques will provide the most consistently correct result?
a
A map is drawn to scale so that a length of 1 centimeter on the map represents an actual distance of 5
kilometers. If two towns are 30 centimeters apart on the map, what is the actual distance between the two
towns?
Answer: 150 kilometers
Step-by-step explanation:
if it's 30 units of 5 kilometers then you multiply it
5x30=150
could i have some super quick quick help? graph part isn't necessary
y=4x²-1
#1
y=(2x)²-1²y=(2x+1)(2x-1)#2
Zeros are 1/2,-1/2
#3
Convert to vertex form y=a(x-h)²+k
y=(4x+0)²-1Vertex(h,k)=(0,-1)
#4
Graph attached
Answer:
i) [tex]y=(2x+1)(2x-1)[/tex]
ii) [tex]x=-\dfrac12, x=\dfrac12[/tex]
iii) (0, -1)
iv) see attached
Step-by-step explanation:
Given quadratic: [tex]y=4x^2-1[/tex]
Factored form
We can use the Difference of Two Squares to factor the given quadratic.
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Therefore,
[tex]a^2=4x^2=(2x)^2\implies a=2x[/tex]
[tex]b^2=1=1^2 \implies b=1[/tex]
So the relation in factored form is:
[tex]y=(2x+1)(2x-1)[/tex]
Zeros
The zeros of the quadratic polynomial are the x-coordinates of the points where the graph intersects the x-axis, i.e. when y = 0
[tex]\implies y=0[/tex]
[tex]\implies (2x+1)(2x-1)=0[/tex]
[tex]\implies (2x+1)=0\implies x=-\dfrac12[/tex]
[tex]\implies (2x-1)=0\implies x=\dfrac12[/tex]
Therefore, the zeros are -1/2 and 1/2
Vertex
The x-coordinate of the vertex is the midpoint of the zeros.
[tex]\textsf{midpoint}=\dfrac{-\frac12+\frac12}{2}=0[/tex]
To find the y-coordinate of the vertex, substitute the found value of x into the given equation:
[tex]\implies y=4(0)^2-1=-1[/tex]
Therefore, the vertex is (0, -1)
Meena buys cookies and apples at the store.
She pays a total of $24.02.
She pays a total of $6.90 for the cookies.
She buys 4 bags of apples that each cost the same amount.
How much does each bag of apples cost?
Answer:
each apple would cost $4,28
The cost of each bag of apples is 4.28 dollars.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that Meena buys cookies and apples at the store.
Meena pays a total amount of $24.02.
She pays a total amount of $6.90 for the cookies.
She buys 4 bags of apples which each cost the same amount.
The total cost of apples = 24.02 - 6.90
= 17.12
Therefore, each bag of apples cost = 17.12/ 4 = 4.28
Hence, the cost of each bag of apples is 4.28 dollars.
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The numbers 32 and 12 are each rounded to the nearest ten and then multiplied to estimate the product. What is the best estimate of 32 × 12 based on this method?
Answer:
300
Step-by-step explanation:
32 rounds to 30.
12 rounds to 10.
30 × 10 = 300
Answer: 300
Answer:
[tex]beinggreat78~here~to~help.[/tex]
So the method is clearly stating that we need to round to the nearest ten, so let's round using the rule set.
If the number is below 5, round down.If the number is 5, round up.If the number is above 5, also round up.This array should help you vision the sequence better.
⇒ [tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
Now, using the rounding ruleset, we have to find what to round to. Since 32 and 12 both have a ones digit below 5, we round down, meaning we now have 30 and 10. The last step is to multiply 30 by 10 to get your estimate.
[tex]30[/tex]
[tex]*~10[/tex]
▬▬
[tex]300[/tex]
With this information, your answer is 300(rounded to nearest ten)!
The outer rectangle is 2 feet by 4 feet. There is a semicircle and isosceles triangle within the rectangle. Find the area of the shaded region to the nearest tenth.
To find the shaded area in an image first calculate the total area of the figure and then subtract the white area from this total.
How to find the area of a shaded area?Determine the total area of the figure, in this case, the are of the rectangle that contains the triangle and the semicircle.Calculate the area of the white region.Substract the non-shaded area to the total area.How to find out the area of different shapes?Rectangle: side x side = 2 x 4 = 8 square feetIsosceles triangle = 1/2 base x heightSemicirle = 1/2 (π x r^2)Note: This question is incomplete because the image of the shaded regions is not provided; due to this, the answer is based on general knowledge.
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Plsss help
Explain how the shapes shown have been sorted.
Answer:
A have no right angles and B had all right angles.
Which is greater -8.5 or -15
Answer:
-8.5
Step-by-step explanation:
this is because the more negative a number is, the less value it is, hence -8.5 is greater than -15.
if books cost $14.99, and there is 5% sales tax, how much is the sales tax on the books?
Answer:
0.7495 or 0.75 sales tax
Step-by-step explanation:
5% of 14.99 is 0.7495. rounded to the nearest tenth it is 0.75
Simplify the expression. Write the answer using scientific notation.
a) 2.52 × 10–3
b) 2.52 × 10–2
c) 2.52 × 10–1
d) 4.3 × 10–2
Answer:
b) 2.52 x 10^(-2)
Step-by-step explanation:
0.7 X 3.6 = 2.52
2.52 X 10^(-2)
What would be the most logical first step for solving this quadratic equation?
x²+2x-11=4
A. Add 11 to both sides
B. Take the square root of both sides
C. Divide both sides by x
D. Subtract 4 from both sides
Answer:
D. Subtract 4 from both sides
Step-by-step explanation:
When you're solving a quadratic equation you want to use the quadratic formula [tex]\frac{-b+ \sqrt[]{b^{2} -4ac } }{2a}[/tex].
To get the quadratic equation into this form, you first need to convert it into [tex]ax^{2} +bx+c=0[/tex] which means the first step would be to subtract 4 on both sides.
Jessica needs 658 cups of flour for her recipe. The box she has only has 78 cup of flour left in it.
How many more cups of flour does she need?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
5 3/4 cups.
Step-by-step explanation:
Subtract the two amounts.
6 5/8 - 7/8
Make 6 5/8 an improper fraction by multiplying the 8 and 6 then adding 5.
8 x 6 = 48
48 + 5 = 53
53/8
53/8 - 7/8 = 46/8
Convert back into a mixed number by dividing.
46/8 = 5 6/8
reduce the fraction
5 3/4
Pamela made a profit of $3250 after selling stocks for $10500 after 4 years. What was her average annual percentage gain?
Pamela's average annual percentage gain was = 7.7%
Calculation of annual percentage gainThe start up capital (P) = $10500
The simple interest (SI) = $3250
Time (T) = 4 years
Rate = ?
But SI = P × T × R /100
Make R the subject of formula,
R = SI × 100/P × T
R = 3250 × 100/ 10500 × 4
R = 325000/ 42000
R = 7.7%
Therefore, Pamela's average annual percentage gain was = 7.7%
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WILL GIVE BRAINLY
Triangle ABC is similar to triangle WYZ.
Select all angles whose cosine equals [tex]\frac{3}{5}[/tex]
Question 1 options:
Angle B
Angle Y
Angle Z
Angle C
Angle A
Angle W
Answer:Angle W and Angle C
Step-by-step explanation:
The angles whose cosine equals 3/5 are <A and <W.
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
We have,
ΔACB and ΔWZY are similar to each other.
Now, Using trigonometry
cosine = Adjacent leg/ Hypotenuse
We have cosine = 3/5
where Adjacent side =3 and Hypotenuse = 5
So, the angle which have Adjacent side 3 in both triangles are
<A and <W.
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How would you write 8^5 as a multiplication expression?
OA 8x5
ОВ.8x8x8x8x8
OC. 5x5x5x5x5x5x5x5
Answer:
The answer is B
Step-by-step explanation:
Because the exponent shows how many times you multiply that number
Example: 8^2 would be 8x8 because it is to the second power
Hopefully this helps
Answer:
Step-by-step explanation:
8•8•8•8•8 is the correct answer
In a school theater performance, 150 tickets were sold, some for $30 and others for $20, how many tickets were sold of each price if the total sale was $3,500?
Answer:
85 tickets for 20 dollars and 60 for 30
Step-by-step explanation:
my smart friend in AP calc said so
A house blueprint has a scale of 1 in. : 6 ft. The length and width of each room in the actual house are shown in the table. Complete the table by finding the length and width of each room on the blueprint.
Answer:
The dimensions of the rooms in the blueprint will be Living room (), Kitchen (), Office (), Bedroom (), Bedroom (), Bathroom ().
Given information:
A house blueprint has a scale of 1 in : 4 ft.
The length and width of each room in the actual house are shown in the table below:
Living room Kitchen Office Bedroom Bedroom Bathroom
Length 20 16 8 8 20 6
width 8 16 16 16 20 8
The scale factor is of 1 in: 4 ft. So, 4 ft of actual length is equivalent to 1 inch in the blueprint.
So, the length and width of the different rooms in te house in the blueprint will be,
Living room Kitchen Office Bedroom Bedroom Bathroom
Length(in) 5 4 2 2 5 1.5
width(in) 2 4 4 4 5 2
Therefore, the dimensions of the rooms in the blueprint will be Living room (), Kitchen (), Office (), Bedroom (), Bedroom (), Bathroom ().
For more details, refer to the link:
brainly.com/question/2305449
Step-by-step explanation:
hope this helps
Jose weighs 12 pounds less than twice what his sister maria weighs. If w respesent maria weight. Which expression shows jose weight
Answer:
2w-12
Step-by-step explanation:
Jose = 2x(Maria's weight) -12
j = 2w -12
Please help me solve this problem
Answer:
See belowStep-by-step explanation:
Since all graphs pass throught the origin, they all have the form of:
y = ax², where a- coefficientThe coefficient of each graph's equation can be calculated based on the given pairs of points.
Each of them calculated for you and attached below.
help me please complete the table at the right by writing the fraction of the day each animal sleeps and an equivalent fraction remember there are 24 hours in a day
Answer:
1 day = 24 hours
Divide each of the "number of hours spent sleeping" by the total number of hours in a day (24). Then divide the numerator and denominator by the highes common factor to reduce the fraction to its simplest equivalent.
[tex]\sf Cat=\dfrac{12}{24}=\dfrac{12 \div 12}{24 \div 12}=\dfrac{1}{2}[/tex]
[tex]\sf Cow=\dfrac{4}{24}=\dfrac{4 \div 4}{24 \div 4}=\dfrac{1}{6}[/tex]
[tex]\sf Squirrel=\dfrac{15}{24}=\dfrac{15 \div 3}{24 \div 3}=\dfrac{5}{8}[/tex]
[tex]\sf Tiger=\dfrac{16}{24}=\dfrac{16 \div 8}{24 \div 8}=\dfrac{2}{3}[/tex]
One side of a rectangle is twelve feet longer than three times another side of the rectangle . Find the sides we also know that the area of the rectangle is 231f * t ^ 2
Answer:
Length: 33 ft
Width or side: 7 ft
Step-by-step explanation:
Check the attachment.
If 12% of a number is 30, find 4% of that number.
Answer:
12 of 40=30 so if you do 4 percent of 40 its 1.4
Step-by-step explanation:
angles A, B, and Y are in quadrants 1, 2, 3 respectively such that:
tan A= 2
tan B= -4/3
cos Y= -1/3
evaluate the following:
1)cos(2B)
2)tan(2A)
3)cos(Y/2)
4)tan(Y/2)
5)sin(B/2)
6)csc(2B)
7)sec(A/2)
Answer:
so the lol is the very nice in the lol morning in the 1098 in 1233 because is use the lol in morning.
help pretty please!
Cyrus lives 11 miles due south of Adriana, Adriana live 19 miles due west of Jane, Jane lives 12 miles due south of Madisyn.
The shortest distance between Cyrus' house and Jane's house is
•21.95
•481.802
•0.52
The shortest distance between Adriana's house and Madisyn's house is
•504.901
•22.47
•44.42
Answer:
A.) 21.95
B.)22.47
Step-by-step explanation:
A.) An easy way to solve this is to use the Pythagorean theorem. Since the only person between Cyrus and Jane is Adriana, we will use her as a measuring point. Adriana's distance to Jane is 19, we will set a = 19, Adriana also is 11 miles away from Cyrus, and we will set b = 11. Now we plug it into the Pythagorean theorem.
[tex]a^2+b^2=c^2\\19^2+11^2=c^2\\\sqrt{482} =\sqrt{c^2}\\ 21.95=c[/tex]
B.) Using the same principle but for Adriana and Madisyn, we will use Jane as she is between them. Adriana is 19 miles from Jane, so we will set a=19, Madisyn is also 12 miles from Jane, so we will set b=12. Plug it for the Pythagorean theorem.
[tex]a^2+b^2=c^2\\19^2+12^2=c^2\\505=c^2\\\sqrt{505}=\sqrt{c^2}\\ 22.47 = c[/tex]
Complete the sentence.
If a section of a cicle graph needs to represent 15%, then its angle measure will be _____ degrees.
Answer:
54
Step-by-step explanation:
We know that a circle is 360 degrees. Therefore, ↓
360° -----------> 100%
x°-----------> 15%
[tex]x = \frac{15}{100} \times 360 \\ = 54[/tex]
Hope this helps =)