Answer:
b. (3, 0.5).
Step-by-step explanation:
x + 2y = 4
2x - 2y = 5
Adding the 2 equations eliminates the y:
3x = 9
x = 3
Substitute fro x in the first equation:
3 + 2y = 4
2y = 1
y = 0.5.
Option B is correct, (3, 0.5) is the solution of the system of equations.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The two equations are
x+2y=4...(1)
2x-2y=5...(2)
Add equation 1 and 2
x+2y+2x-2y=4+5
3x=9
Divide both sides by 3
x=3
3+2y=4
Subtract 3 from both sides
2y=1
y=1/2
y=0.5
Hence, option B is correct, (3, 0.5) is the solution of the system of equations.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
Gregory has 2/3 of an entire pizza. If he gives 1/4 of an entire pizza to his friend Marlene, what fraction of his partial pizza did he give to Marlene?
Gregory has 2/3 of a pizza and gives 1/4 of an entire pizza to Marlene. By converting the fractions to a common denominator, we find that he gives away 3/8 of his portion of the pizza to Marlene.
Explanation:Understanding fractions can sometimes be as easy as picturing how you would slice a pie and share it with friends.
Gregory has 2/3 of an entire pizza and decides to give 1/4 of an entire pizza to his friend Marlene.
To solve how much of his portion Gregory gives to Marlene, we need to figure out what fraction 1/4 represents out of the 2/3 that Gregory has.
If we think of the pizza being cut into 12 slices (since 12 is a common multiple of both 3 and 4), Gregory's 2/3 is equivalent to 8/12 of the pizza because (2/3) × (12/1) = 8/12.
Similarly, 1/4 of the pizza is equivalent to 3/12 of the pizza because (1/4) × (12/1) = 3/12.
Now we know that Gregory aims to give away 3/12 of the pizza, but we want to express this as a part of his original 8/12.
To find out what fraction of his part he gives away, we then calculate (3/12) ÷ (8/12).
When we divide these fractions, we can multiply by the reciprocal of the second fraction:
(3/12) × (12/8), which simplifies to 3/8.
Therefore, Gregory gives away 3/8 of his 2/3 of the pizza to Marlene.
Please help me find the surface area of this right prism. ASAP please. Thank you ~
Answer:
[tex]\large\boxed{V=\dfrac{75\sqrt3}{2}\approx64.95}\\\boxed{S.A.=\dfrac{160+25\sqrt3}{2}}[/tex]
Step-by-step explanation:
The formula of a volume of a prism:
[tex]V=BH[/tex]
B - base area
H - height
In the base we have the equilateral triangle. The formula of an area of an equilateral triangle with side a:
[tex]A=\dfrac{a^2\sqrt3}{4}[/tex]
Substitute a = 5:
[tex]B=\dfrac{5^2\sqrt3}{4}=\dfrac{25\sqrt3}{4}[/tex]
H = 6.
Calculate the volume:
[tex]V=\left(\dfrac{25\sqrt3}{4}\right)(6)=\dfrac{75\sqrt3}{2}[/tex]
The formula of a Surface Area:
[tex]S.A.=2B+PH[/tex]
B - base area
P - perimeter of a base
H - height
Calculate P: [tex]P=5+5+5=15[/tex]
Substitute:
[tex]S.A.=2\left(\dfrac{25\sqrt3}{4}\right)+(15)(6)=\dfrac{25\sqrt3}{2}+80=\dfrac{160+25\sqrt3}{2}[/tex]
1. At a fundraiser dinner, the bill for 4 cups of coffee
and 6 spaghetti specials is $20.50, whereas the bill for 1 cup of coffee and 3 spaghetti
specials is $8.75.
Write
a system of 2 equations to model this problem. Let c stand for the price of a cup of coffee and let s stand for the price of a spaghetti
special.
Use the
substitution method to solve the system of equations.
What
would the bill be for 1 cup of coffee and 1 spaghetti special?
(Pls help!)
1- Writing the system of equations:
The price of a cup of coffee is denoted by c while the price of a spaghetti is denoted by s
We are given that:
4 cups of coffee and 6 spaghetti cost $20.5
This means that:
4c + 6s = 20.5 ................> equation 1
We are also given that:
1 cup of coffee and 3 spaghetti cost $8.75
This means that:
c + 3s = 8.75 .................> equation 2
2- Solving the equations using substitution methods:
From equation 2:
c = 8.75 - 3s ................> I
Substitute with I in equation 1 and solve for s as follows:
4c + 6s = 20.5
4(8.75 - 3s) + 6s = 20.5
35 - 12s + 6s = 20.5
35 - 6s = 20.5
6s = 14.5
s = $2.41667
Substitute with s in I to get c:
c = 8.75 - 3s
c = 8.75 - 3(2.41667) = 1.4999 = $1.5
3- getting price for 1 cup of coffee and 1 spaghetti:
c + s = 1.5 + 2.41667 = $3.91667
Hope this helps :)
|
3. What is the next number in the sequence 20, 10, 5, 5/2
Answer:
[tex]\large\boxed{\dfrac{5}{4}}[/tex]
Step-by-step explanation:
[tex]a_1=20\\\\a_2=\dfrac{20}{2}=10\\\\a_3=\dfrac{10}{2}=5\\\\a_4=\dfrac{5}{2}\\\\a_5=\dfrac{\frac{5}{2}}{2}=\dfrac{5}{2}\cdot\dfrac{1}{2}=\dfrac{5}{4}[/tex]
PLEASE HELP ME ASAP.....
MATHS.
In a triangle ABC, AD is the bisector of angle A ....If AB=5.6cm ,AC=4cm and DC=3cm, find BD and DC
PLS HELP ME
Step-by-step answer:
Given:
In a triangle ABC, AD is the bisector of angle A ....If AB=5.6cm ,AC=4cm and DC=3cm, find BD and DC
This problem can be solved by direct application of the angle bisector theorem, which states that the division of the side opposite to the bisected angles is proportional to the respective sides.
Here we have:
Bisector: AD
Side divided: DC = 3 cm
Length of AB = 5.6
Length of AC = 4.0
Then BD = AB/AC * DC = 5.6/4.0 * 3 = 4.2
BC = BD+DC = 4.2+3 = 7.2
A pair of jeans that originally cost $25.60 is 45% off .what is the sale price for the jeans?
Answer:
Step-by-step explanation:
45% off $25.60
= [tex]\frac{45}{100}[/tex] x $25.60
= $11.52 (Ans)
Answer:
$11.52
Step-by-step explanation:
$25.60 is 25.6 and 40% is 0.40
So do 25.6 * 0.40 and you get your answer of $11.52
Hope this helped ^-^
can some one help me please time
Answer:
The answer would be B. 2x+4 / x
For this case we have that by definition of composition of functions that:
[tex](f_ {0} h_ {0} g) = f (h (g (x)))[/tex]
So:
[tex]h (g (x)) = 4 (x-2) -1 = 4x-8-1 = 4x-9[/tex]
So:
[tex]f (h (g (x))) = \frac {4x-9 + 4} {4x-9} = \frac {4x-5} {4x-9}[/tex]
ANswer:
[tex](f_ {0} h_ {0} g) = \frac {4x-5} {4x-9}[/tex]
Option D
which graph represents the solution of the inequality?
Answer:
The third graph.Step-by-step explanation:
[tex]14\leq2t+18\leq20\qquad\text{subtract 18 from all sides}\\\\14-18\leq2t+18-18\leq20-18\\\\-4\leq2t\leq2\qquad\text{divide all sides by 2}\\\\\dfrac{-4}{2}\leq\dfrac{2t}{2}\leq\dfrac{2}{2}\\\\-2\leq t\leq1\\\\\text{The third graph.}[/tex]
You invest $3000 in an account at 3.5% per year simple interest. How much will
you have in the account at the beginning of the 7th year?
A. $3735
B. $3720
C. $3540
D. $3630
What is square root of -98 + 71
Answer:
= 5.196 i
Step-by-step explanation:
The problem tells us to find the square root of -98 +71
√(-98 + 71)
= √(-27)
Which is an imaginary number
=√(-3^3)
Lets remember that, √(-1) = i
= i*3√(3)
= 5.196 i
Please see attached image for more information
Paul to Ava salaries ratio is 3:4. If Paul's salary is $87,000, what is Ava's salary?
Answer: $116,000
Step-by-step explanation:
Set up a ratio and then cross multiply and divide. See paper attached. (:
Final answer:
Ava's salary is calculated based on the given salary ratio of Paul to Ava (3:4). By dividing Paul's salary by 3, we find out how much one part of the ratio is worth and then multiply by 4 to find Ava's salary to be $116,000.
Explanation:
The question provided asks us to calculate Ava's salary based on the ratio of Paul to Ava's salaries which is 3:4. If Paul's salary is $87,000, we determine Ava's salary using the given ratio. Here is the step-by-step process:
Step 1: Understand the ratio, which tells us that for every 3 parts of Paul's salary, Ava gets 4 parts. This does not tell us the total amount, but how they share the total amount.
Step 2: Since Paul's salary is $87,000, and that represents 3 parts of the total, we divide $87,000 by 3 to find out what 1 part is: $87,000 / 3 = $29,000.
Step 3: Now that we know 1 part is $29,000, we can calculate Ava's salary which is 4 parts: $29,000 X 4 = $116,000.
Ava's salary is therefore $116,000.
The graph of F(x), shown below, has the same shape as the graph of
G(x) = x3, but it is shifted down 1 unit. What is its equation?
F(x) =
Answer:
x^3-1
Step-by-step explanation:
f(x)=g(x)-1 since was shifted down 1 unit x^3-1
f(x)=g(x)+1 would have been a shift up of 1 unit x^3+1
f(x)=g(x-1) shifted right 1 unit (x-1)^3
f(x)=g(x+1) shifted left one unit (x+1)^3
Anyways the answer is f(x)=x^3-1
1. Find the product (13 – x2)(x + 2).
-x3 - 2x2 + 13x + 26
Answer:
The product is -x³ - 2x² + 13x + 26
Step-by-step explanation:
* Lets revise how to find the product of two binomials
- If (ax ± b) and (cx ± d) are two binomials, where a , b , c , d are constant
their product is:
# Multiply (ax) by (cx) ⇒ 1st term in the 1st binomial and 1st term in the
2nd binomial
# Multiply (ax) by (d) ⇒ 1st term in 1st binomial and 2nd term in
2nd binomial
# Multiply (b) by (cx) ⇒ 2nd term in 1st binomial and 1st term in
2nd binomial
# Multiply (b) by (d) ⇒ 2nd term in 1st binomial and 2nd term in
2nd binomial
# (ax ± b)(cx ± d) = cx² ± adx ± bcx ± bd
- Add the terms adx and bcx because they are like terms
* Now lets solve the problem
- There are two binomials (13 - x²) and (x + 2)
- We can find their product by the way above
∵ (13)(x) = 13x ⇒ 1st term in the 1st binomial and 1st term in the
2nd binomial
∵ (13)(2) = 26 ⇒ 1st term in 1st binomial and 2nd term in
2nd binomial
∵ (-x²)(x) = -x³ ⇒ 2nd term in 1st binomial and 1st term in
2nd binomial
∵ (-x²)(2) = -2x² ⇒ 2nd term in 1st binomial and 2nd term in
2nd binomial
∴ The product of (13 - x²)(x + 2) = 13x + 26 - x³ - 2x²
- There is no like terms
- Lets arrange the terms from greatest power to smallest power
∴ The product is -x³ - 2x² + 13x + 26
A parallelogram is transformed according to the rule (x, y) → (x, y). Which is another way to state the transformation?
A. R0, 90°
B. R0, 180°
C. R0, 270°
D. R0, 360°
Answer:
D. R0, 360°
Step-by-step explanation:
Since the transformation is from (x,y) to (x,y), the values stay the same...
It's just like a 360 degrees rotation then, since the end position is identical to the start position.
All other answers would affect at least one of the values to change sign like (-x,y), (x,-y) or (-x,-y)... but a 360 degrees rotation would not.
Can someone help me plz
Answer:
2p, since twice as long would hint to multiplication.
Which of the following equations can be used to find the length of angle LN in the triangle below?
HELP ASAP PLS
Answer:
Option A. [tex]LN^{2}=33^{2}-11^{2}[/tex]
Step-by-step explanation:
we know that
In the right triangle MNL
Applying the Pythagoras Theorem
[tex]MN^{2}=ML^{2} +LN^{2}[/tex]
substitute the values
[tex]33^{2}=11^{2} +LN^{2}[/tex]
[tex]LN^{2}=33^{2}-11^{2}[/tex]
When a factor x − k is raised to an odd power, the graph crosses the x-axis at x = k.
When a factor x − k is raised to an even power, the graph only touches the x-axis at x = k.
Describe the graph of the function g(x) = (x − 1)(x + 4)3(x + 5)2.
The graph:
crossesdoes not intersecttouches the axis at (1, 0).
crossesdoes not intersecttouches the axis at (−4, 0).
crossesdoes not intersecttouches the axis at (−5, 0)
Answer:
The graph of [tex]g(x) = (x - 1) (x + 4)^3(x +5)^2[/tex] crosses the x-axis at (1,0) and (-4, 0). It touches the x-axis at (-5, 0).
Step-by-step explanation:
g(x):
[tex]g(x) = (x - 1) (x - (-4))^3(x - (-5)^2[/tex].
There are three factors:
(x - 1), where k = 1,(x - (-4)), where k = -4, and(x - (-5)), where k = -5.The first and second factors are raised to odd powers. The graph will cross the x-axis at all these two points:
(1, 0) as a result of the factor (x - 1), (-4, 0) as a result of the factor (x - (-4)).The third factor is raised to an even power. The graph will touch the x-axis at that point.
(-5, 0) as a result of the factor (x - (-5)).Answer:
crosses at (1,0)
crosses at (-4,0)
touches at (-5,0)
Got correct on ed
Step-by-step explanation:
8/9 and 7/8 common denominator
Answer: 72
Step-by-step explanation:
Rewriting input as fractions if necessary:
8/9, 7/8
For the denominators (9, 8) the least common multiple (LCM) is 72.
LCM(9, 8)
Therefore, the least common denominator (LCD) is 72.
Rewriting the original inputs as equivalent fractions with the LCD:
64/72, 63/72
At a busy street corner, one of every hundred jaywalkers will be hit when they cross. What is the probability of a jaywalker not being hit if he makes a round trip daily for thirty days? (0.01)30 (0.99)30 (0.9801)30
Answer: Last option
[tex]p = (0.9801) ^ {30}[/tex]
Step-by-step explanation:
the probability of a jaywalker being hit is
[tex]P = \frac{1}{100} = 0.01[/tex].
So the probability of a jaywalker not being hit is:
[tex]P '= 1-0.01[/tex]
[tex]P '= 0.99[/tex]
As in this experiment the probability of each trial is independent then, the probability that it is not a jaywalker will not be hit if it makes a round trip is:
[tex]P '= (0.99) (0.99) = 0.9801[/tex]
[tex]P '= 0.9801[/tex]
If this experiment is repeated for 30 days then the probability that it is not a jaywalker will not be hit if it makes a round trip is:
[tex]p = (0.9801) ^ {30}[/tex]
The diagnals of a parallelogram are congruent. Which could be the parallelogram?
A. Trapezoid
B. Rectangle
C. Kite
D. Rhombus
Answer:
B. Rectangle
Step-by-step explanation:
All rectangles are parallelograms.
What is the value of f(6) in the function below? f(x)=2^x
A. 16
B. 32
C. 12
D. 64
Sam is designing a fence post for his yard. He will need to construct a perpendicular line through the point above the line to make sure the fence post is perpendicular to the ground. Which step should Sam do first to ensure that the fence post model is perpendicular to the ground in the diagram?
A. Place the compass at the point off the ground, and swing an arc on either side of the point.
B. Place the compass at the point off the ground, and swing arcs above and below the ground.
C. Place the compass at the point off the ground, and swing an arc that intersects the ground in one place.
D. Place the compass at the point off the ground, and swing an arc that intersects the ground in two places.
Answer:
Step-by-step explanation:
D is correct. The idea here is to ensure that the point on the post is equidistant from the bottom of the post (where it meets the ground), which in turn ensures that the angle between ground and post is 90° in at least two places on the ground.
The step that Sam must take first in order to make sure that the post of the fence is ⊥ to the bottom of the ground would be:
D). "Place the compass at the point off the ground, and swing an arc that intersects the ground in two places."
In the given situation, Sam is required to locate the compass away from the ground so that the arc created divides the ground into two equal and equidistant places. Since the point framed on the post would be at an equal distance from its bottom, the angle formed among them(post, as well as, ground) would be a right angle or perpendicular.Thus, option D states a true claim regarding the precise placement of the compass to get the desired angle i.e. 90° for at least two locations.Learn more about 'arcs' here:
brainly.com/question/16765779
A. Look at the diagram of the two squares shown below.
The Pythagorean theorem says that for any right triangle, the square of the length of the hypotenuse, c, is equal to the sum of the squares of the lengths of the legs (a and b): a2 + b2 = c2. Explain how the diagram shown above can be used to prove the Pythagorean theorem. Show your work.
B. Look at the small box shown below.
What is the length of the diagonal of the box shown? Leave your answer in radical form. Show your work and explain your steps.
Squares 1 and 2 have the same area because they're both (a+b) on a side.
Each of these squares is covered by four identical right triangle tiles, legs a,b, hypotenuse c.
In the first picture we see the uncovered part of the square, not covered by triangular tiles, is two squares, area [tex]a^2+b^2[/tex].
In the second picture the uncovered part of the square is a smaller square, area [tex]c^2[/tex].
We just moved the tiles around on the square, so the uncovered part is the same in both cases. So
[tex]a^2 + b^2 = c^2[/tex]
--------
The rectangular prism has a bottom rectangular base 6 by 8. So the diagonal is [tex]\sqrt{6^2+8^2}=\sqrt{100}=10[/tex].
The diagonal and the 7 cm side make a right triangle whose hypotenuse is the diagonal of the rectangular prism we seek.
[tex]\sqrt{10^2 + 7^2} = \sqrt{149}[/tex]
Answer: √149
Lota points
44 is 25% of what
Answer:
176
Step-by-step explanation:
To find a number from a known percentage and a number, divide the given number by the percent.
[tex]\frac{v}{p}[/tex]
Where [tex]v[/tex] is the value given and [tex]p[/tex] is the percentage.
[tex]\frac{44}{0.25}=176[/tex]
Answer:
176
Step-by-step explanation:
5(x-4)+3x-9x=6-(2x+5)+8x
Answer:
The value of x is -3
Step-by-step explanation:
We need to solve the given equation and find value of x
5(x-4)+3x-9x=6-(2x+5)+8x
First solving the brackets
5x-20+3x-9x = 6-2x-5+8x
Now combining the like terms,
5x+3x-9x-20 = -2x+8x+6-5
8x-9x-20 = 6x +1
-x-20=6x+1
Now moving x terms on one side and constants on other
6x+x=-20-1
7x = -21
Dividing both sides by 7
7x/7 = -21/7
x = -3
So, the value of x is -3
Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?
Answer:
The graph of his initial step in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=3(4)^{x}[/tex]
This is a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
r is the rate of change
In this problem
a=3 ---> the initial value ( value of the function when the value of x is equal to zero)
b=4
b=1+r ----> 4=1+r ----> r=3 ---> r=300%
therefore
The initial value is the point (0,3)
The graph of his initial step in the attached figure
Calculista · Quality Assurance - seems pretty accurate i was looking at their answer and he went as far as actually graphing it out for everyone... it shure as **** helped me not get confused. Thanks Calculista you got big brain lol!
Select the correct solution set. x + 17 ≤ -3
{x | x ≤ -20}
{x | x ≤ 14}
{x | x ≥ -20}
Answer:
{x | x ≤ -20}
Step-by-step explanation:
x + 17 ≤ -3
Subtract 17 from each side
x + 17-17 ≤ -3-17
x ≤ -20
Answer:
{x | x ≤ -20}
write the equation in logarithmic form e^x=403.429
[tex]x=\ln 403.429[/tex]
Which methods could you use to calculate the y-coordinate of the midpoint of
a vertical line segment with endpoints at (0,0) and (0, 15)
Answer:
Counting by hand
Dividing 15 by 2
Step-by-step explanation:
An image of a parabolic lens is projected onto a graph.The y-intercept of the graph is (0, 90), and the zeros are 5 and 9. Which equation models the function? y = 90(x – 5)(x – 9) y = 2(x – 5)(x – 9) y = 90(x + 5)(x + 9) y = 2(x + 5)(x + 9)
Step-by-step explanation:
If the zeros are 5 and 9, then the equation will have the form:
y = a (x–5) (x–9)
We know the point (0, 90) is on the curve, so we can use this to find the coefficient a:
90 = a (0–5) (0–9)
90 = 45a
a = 2
y = 2 (x – 5) (x – 9)
Answer:
y = 2 (x-5) (x-9)
Step-by-step explanation:
Edge