Answer:
x = 2 and y = -2Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-y=4&\text{add}\ y\ \text{to both sides}\\x+2y=-2\end{array}\right\\\\\left\{\begin{array}{ccc}x=4+y&(1)\\x+2y=-2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(4+y)+2y=-2\qquad\text{combine like terms}\\\\4+(y+2y)=-2\qquad\text{subtract 4 from both sides}\\\\3y=-6\qquad\text{divide both sides by 3}\\\\y=-2\\\\\text{put the value of}\ y\ \text{to (1):}\\\\x=4+(-2)\\\\x=2[/tex]
Martin has 48 blue balloons and 36 orange balloons he separates the balloons into mixed groups of blue and orange there are the same number of blue balloons in each group and the same number of orange balloons I'm each group.what is the leat total number of balloons that could be in each group?
A.)4
B.)7
C.)9
D.)21
Answer: A
48+ 36 = 84
84/4 = 21 groups
there are 21 groups of 4 balloons
50 POINTS! WILL MARK BRAINLIEST, THANK, AND RATE! The volume of a right rectangular prism can be determined by multiplying the base area of the figure by the height. The volume of a right rectangular prism with a base area of 8 square inches is more than 64 cubic inches. The inequality 8h > 64 can be used to model the situation, where h represents the height of the figure. Which is a possible value of h?
A. 2
B. 4
C. 8
D. 12
Answer:
D. 12
Step-by-step explanation:
Answer:
D 12
Step-by-step explanation:
8h > 64
Divide each side by 8
8h/8 > 64/8
h > 8
H must be greater than 8
The only value in your list greater than 8 is 12
The mass of a box with 6 tennis balls is 2 kg 40 g The same box with
10 tennis balls is 3 kg 160g. What is the mass of the empty box!
Answer:
maybe you add then all up
In a survey, 300 adults and children were asked whether they preferred hamburgers or pizza. The survey data are shown in the relative frequency table.
Answer:
D. 40%
Step-by-step explanation:
You can fill in the table completely
[tex]\begin{array}{cccc}&\text{Hamburgers}&\text{Pizza}&\text{Total}\\\text{Adults}&0.24&0.36&0.6\\\text{Children}&0.11&0.29&0.4\\\text{Total}&0.35&0.65&1\end{array}[/tex]
From this table you can state that the probability that a randomly selected person is a child is 0.4 that is 40%.
The percentage of the people surveyed are children is:
40%
Step-by-step explanation:We are given a table as follows:
HAMBURGERS PIZZA TOTAL
ADULTS 0.24 0.36 0.6
CHILDREN 0.11 0.29 0.4
TOTAL 0.35 0.65 1
Now we are asked to find the percent of students that were surveyed.
From the table we may see that the probability of children who were surveyed are:
0.11+0.29=0.40
( since, the second column gives the total of the probability of children)
Hence, in percentage form it is given by:
0.40×100=40%
Hence, the answer is:
40%
Solve using the following quadratic equation for all values of x in simplest form !! Please answer this !!
Answer:
No solution
Step-by-step explanation:
Rearrange into quadratic form: 3x² + 0x - 3 = 0
Quadratic formula: when ax² + bx + c = 0: x = (-b ± √(b² - 4ac))/2a
Plug in: x = 0 ± √(0 - 4*3*3))/2a
From this, we can conclude that this equation has no solution, as 0 - 4*3*3 will definitely be negative, and a negative number can not be square rooted.
If you know that two angles are supplementary angles and you know the measurement of one of the angles, describe how you would find the measurement of the unknown angle.
Since supplementary angles add up to 180°, you would subtracted the measurement that you have from 180°.
Ex.
180-x= y
X being the measurement that you have, and y being the missing measurement.
PLLLLEEEAAAASSSSSEEEE HELP!
Answer:
see explanation
Step-by-step explanation:
The length of the arc is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{90}{360}[/tex] ← r = 1
= 2π × [tex]\frac{1}{4}[/tex] = [tex]\frac{\pi }{2}[/tex] ≈ [tex]\frac{3.14}{2}[/tex] = 1.57
Factorise completely 9a^2-1
Answer:
(3a-1)(3a+1)
Step-by-step explanation:
We can quickly see with this problem that it is the difference of two squares as 9a^2 is (3a)^2 and 1 is 1^2 and therefore can factorise quickly using this rule.
x^2-y^2 = (x-y)(x+y) where x = 3a and y = 1
ANSWER
[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]
EXPLANATION
We want to simplify completely:
[tex]9 {a}^{2} - 1[/tex]
We express the two terms as difference of two squares;
[tex] {(3 {a})^{2} } - {1}^{2} [/tex]
Recall and apply the following identity;
[tex]{x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
We apply this identity to obtain:
[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]
Which equation represents the hyperbola (y -2)^2/4 - (x-2)^2/9=1
in general form?
Answer:
[tex]9y^2-4x^2-36y+16x-16=0[/tex]
Step-by-step explanation:
The given hyperbola has equation:
[tex]\frac{(y-2)^2}{4}-\frac{(x-2)^2}{9}=1[/tex]
We multiply through by 36 to get:
[tex]9(y-2)^2-4(x-2)^2=36[/tex]
We expand to get:
[tex]9(y^2-4y+4)-4(x^2-4x+4)=36[/tex]
[tex]9y^2-36y+36-4x^2+16x-16=36[/tex]
[tex]9y^2-36y-4x^2+16x-16=0[/tex]
The equation of the hyperbola in general form is:
[tex]9y^2-4x^2-36y+16x-16=0[/tex]
Calculate the product matrix for the following matrix multiplication.
Answer:
[tex]\large\boxed{\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right] }[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}8&3\\-7&2\end{array}\right] \cdot\left[\begin{array}{ccc}8&3\\-7&-6\end{array}\right] \\\\=\left[\begin{array}{ccc}(8)(8)+(3)(-7)&(8)(3)+(3)(-6)\\(-7)(8)+(2)(-7)&(-7)(3)+(2)(-6)\end{array}\right] \\\\=\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right][/tex]
Answer:
D
Step-by-step explanation:
43, 6
-70, -33
What is the solution to the matrix equation [2 1 1 0]x=5/10
[2 1 | 1 0 ] • x = [5 | 10]
We multiply by the inverse of
[2 1 | 1 0 ]
det( [2 1 | 1 0] ) = -1
=> [2 1 | 1 0 ]^(-1) = (-1)•[0 -1 | -1 2 ] =
= [0 1 | 1 -2]
=> [2 1 | 1 0 ] • x = [5 | 10]
=> x = [2 1 | 1 0 ]^(-1) • [5 | 10]
=> x = [0 1 | 1 -2] • [5 | 10]
=> x = [0+10 | 5-20]
=> x = [10 | -15]
A bookstore has a sale: Jen wants to buy four books: for $10.00, for $12.00, for $15.00, and for $20.00. What is the smallest she could pay for these books during the sale? By what percent would the sale reduce the total cost of these four books?
Answer:
$47, 17.5%
Step-by-step explanation:
When she buys the $20 book, she can get 40% off either the $15, $12, or $10 book. She'll save the most by getting 40% off the $15 book.
Then, when she buys the $12 book, she'll get %40 off the $10 book.
The total she pays is:
20 + (0.60)(15) + 12 + (0.60)(10)
20 + 9 + 12 + 6
47
Without the discounts, the cost of the books would have been:
20 + 15 + 12 + 10
57
So she saves $10. 10 out of 57 is approximately 17.5%.
recall that the difference between a country's exports and imports is called the country's trade balance. suppose last year the United states had $968 billion in exports and $1658 billion in imports. what would be the u.s. trade balance for that year?
Let's call trade balance b, exports e and imports i.
We now construct formula.
[tex]b=\Delta{ei}=e-i[/tex]
Put in the data from last year.
[tex]b=968-1658=\boxed{-690}[/tex]
U.S trade balance for that year is -690 billion dollars.
if 1000 pencils cost $20 how much would 10 pencils cost
Answer:
20 cents.
Step-by-step explanation:
You can drop 2 zeros from both the price and the amount of pencils. If 1000 pencils costs 20.00 dollars then 10 pencils cost .20 dollars or 20 cents.
Which is the most likely to be the actual proportion of defective toys in the population?
The mean, or average, of the data set is 3 defective toys per sample group. Therefore set 0.3 and 0.5 are the most accurate representations.
Option C) 0.3
How does the greenhouse effect keep the Earth warm? The atmosphere
O
A. causes the winds moving down from the
poles to bend away from the equator
B. contains strong winds that move from west
to east between hot and cold air
O
c. allows uneven heating of the Earth so that
winds blow from high to low pressure
O
D. contains gases that allow light to pass
through, but trap heat
Answer:
D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
Which expression is equivalent to
Answer:
The correct answer is last option
x¹⁶y²²
Step-by-step explanation:
Points to remember
Identities
Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾
Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾
(Xᵃ)ᵇ = Xᵃᵇ
To find the correct answer
It is given an expression {X⁶Y⁸}³/X²Y²
By using identities we can write,
{X⁶Y⁸}³/X²Y² = X⁶ˣ³ Y⁸ˣ³/X²Y²
= X¹⁸Y²⁴/X²Y²
= X⁽¹⁸ ⁻ ²⁾ * Y⁽²⁴ ⁻ ²⁾
= X¹⁶Y²²
Therefore the correct answer is last optionX¹⁶Y²²
What function represented by graph? Answer choices
y=tan 2 theta
y=tan 1/2 theta
y=tan theta
y=tan 1/4 theta
Answer:
[tex]y=\tan \frac{1}{2} \pi[/tex]
Step-by-step explanation:
The given graph has a period of [tex]2\pi[/tex], because the graph repeats after every [tex]2\pi[/tex] units.
The formula for finding the period of a tangent function is
[tex]T=\frac{\pi}{b}[/tex]
We substitute the period to get;
[tex]2\pi=\frac{\pi}{b}[/tex]
This implies that;
[tex]b=\frac{\pi}{2\pi}[/tex]
Therefore[tex]b=\frac{1}{2}[/tex]
Hence the function represented by the graph is
[tex]y=\tan \frac{1}{2} \pi[/tex]
a pet store buys bags of dog food for 30.00 dollars per bag and sells them for 54.00 dollars per bag. What is the percent markup?
Answer:
80%
Step-by-step explanation:
(54-30)/30 *100 = 80%
How far from the base of the house do you need to place a 15 foot ladder so that it exactly reaches the top of a 12 foot wall?
Answer:
9 ft
Step-by-step explanation:
The ladder is 15 foot
The height the ladder reaches from the bottom of the wall is 12 ft
The distance (x) from the bottom of the wall to the foot of the ladder is:
Applying the Pythagorean theorem;
x = [tex]\sqrt{15^2 - 12^2}[/tex] = 9 ft
A 15 foot ladder needs to be placed at a distance of 9 foot from the base of the house so that it exactly reaches the top of a 12 foot wall.
Further Explanation:Right triangle A right triangle is a triangle with one of its angles being 90 degrees or right angle.The triangle has two shorter sides making the right angle and the hypotenuse which is the longest side.Scalene triangleIt is a triangle that with sides and angles that are not equal.Pythagoras Rule According to Pythagoras rule, in a right angled triangle if the squares of the shorter sides are added then they are equivalent to the square of the hypotenuse.That is; [tex]a^{2} + b^{2} =c^{2}[/tex], where a and b are the shorter sides while c is the hypotenuse.In this case;
The ladder, the wall of the house and the ground from the base of the house makes a right angled triangle;Therefore;
Length of the ladder is the hypotenuse which is 15 ftThe wall of the house is one of the leg which is 12 ftWe are going to find the distance of the ladder from the base of the house on the ground which is the other leg.
Using Pythagoras theorem;
[tex]a^{2} + b^{2} = c^{2}[/tex]
Taking the horizontal distance of the ladder from the wall as b
Then;
[tex]b^{2} = c^{2} -a^{2}[/tex]
therefore,
[tex]b^{2} = 15^{2} -12^{2}[/tex]
[tex]b^{2} = 225 -144[/tex]
[tex]b^{2} = 81[/tex]
[tex]b = \sqrt{81} \\b= 9 ft[/tex]
Hence; the ladder needs to be placed at a distance of 9 foot from the base of the house.
Keywords: Right triangle, Pythagoras rule
Learn more about: Pythagoras theorem: brainly.com/question/13035995Right triangle: brainly.com/question/13035995Application of Pythagoras theorem: https://brainly.com/question/11638432Level; High school
Subject: Mathematics
Topic: Pythagoras theorem
Can someone help find the positive and negative coterminal for this problem please. I got either the positive or negative one wrong but I keep getting the same answer separately for both.
Check the picture below.
let's notice that 89/36 => 2 and 17/36, namely 2π or two revolutions and then a bit more, the 17/36 slack, so then -89π/36 = - 2π - 17π/36.
the positive angle will of course be 2π - 17π/36 = 55π/36.
If you are finding the area of a triangle and there are three sides
Answer:
If you're asking for the formula to find the area of a triangle, its:
1/2bh
b = base
h = height
Mr. Case is placing boxes along one of the walls in his attic. If the wall is 11 1⁄3 feet long and each box is 2 1⁄2 feet long, how many boxes can he fit along the attic wall?
He can fit 4 boxes along the wall
In the rhombus, m angle 1 =40. Find m angle 2
ANSWER
40°
EXPLANATION
The opposite sides of a rhombus are parallel.
This implies that, the diagonal is a transversal.
This means that,
m<1 and m<2 are alternate interior angles.
Since alternate interior angles congruent,
m<1 =m<2=40°
The correct choice is C.
What are the factor of 8x^3 - 27?..
Answer:
(x - 3)(4x² + 6x + 9)
Step-by-step explanation:
This is a difference of cubes which factors in general as
a³ - b³ = (a - b)(a² + ab + b²)
8x³ = (2x)³ ⇒ a = 2x
27 = 3³ ⇒ b = 3
Hence
8x³ - 27
= (2x)³ - 3³
= (2x - 3)( (2x)² + (2x × 3) + 3²)
= (2x - 3)(4x² + 6x + 9)
Describe the translation of f(x) = |x|.
f(x) = (x + 51 - 3
5 units left, 3 units down
3 units left, 5 units down
5 units right, 3 units up
3 units right, 5 units up
5 unit to left, 3 units down is the correct answer.
Can someone help me please
Answer: W = 700 divided by a+18
Step-by-step explanation:
a) We can plug in $358 into A(w), since A(w) represents the amount of money Dale needs. So,
358 = 700 - 18w
Subtract: -342 = -18w
Divide: w = 19 weeks
b) We can plug in 6 into w, since w represents the number of weeks Dale saves money. So,
A(w) = 700 - 18(6)
Multiply: A(w) = 700 - 108
Subtract: A(w) = $592
Help me answer this question please
Answer:
D.
Step-by-step explanation:
For this case we have:
Let k> 0:
To graph [tex]y = f (x) + k,[/tex] the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
Let h> 0:
To graph[tex]y = f (x-h)[/tex], the graph moves h units to the right.
To graph [tex]y = f (x + h),[/tex] the graph moves h units to the left.
So, we have:
[tex]y = f (x) = - \sqrt [3] {x}[/tex]
Shifted 7 units up and 4 to the right means:
[tex]k = 1\\h = 4[/tex]
[tex]y = f (x) = - \sqrt [3] {x-4} +7[/tex]
Answer:
Option B
What is the volume, in cubic units, of a pyramid of height 8 and a square base of length 15?
Answer:
900 cuboc unit
Step-by-step explanation:
Volume of pryamid= 1/3× area× height
= 1÷3×15^15×8
= 900cubic unit
For this case we have by definition, that the area of a square base pyramid is given by:
[tex]V = \frac {L ^ 2 * h} {3}[/tex]
Where:
L: It's the side of the square base
h: It's the height of the pyramid
We have that[tex]L = 15 \ units[/tex], then [tex]L ^ 2 = 15 ^ 2 = 225 \ units ^ 2[/tex]
Substituting:
[tex]V = \frac {225 * 8} {3}\\V = 600 \ units ^ 3[/tex]
Finally, the volume of the pyramid is [tex]600 \ units ^ 3[/tex]
Answer:
[tex]600 \ units ^ 3[/tex]
Jenna's family is going on a trip * after driving 72 miles they used 3.2 gallons of gas * After driving 72 miles, they used 3.2 gallons of gas *Her family has 850 miles remaining on their road trip *The gas tank holds 15 gallons They filled the gas tank at the start of the road trip. They plan to only stop to fill up when their gas tank nears empty. There are plenty along the route. HOW MANY ADDITIONAL STOPS FOR GAS WILL THEY NEED TO MAKE TO GET TO THEIR DESTINATION? explain your answer using numbers words and/or pictures
Answer:
2
Step-by-step explanation:
Given Data:
total distance= 850 miles
gas tank holds gas= 15 gallons
mileage = 72/3.2 miles/gallon
if
72 miles uses= 3.2 gallon
then
850 miles uses= x gallons
by cross-multiplication we get
72x=3.2(850)
x=37.778
i.e. 850 miles will use 37.7778 gallon of gas
Asgas tank holds 15 gallons
number of times gas tank is used up= 37.3/15
= 2.518
rounding off
number of times gas tank is used up=3
As they filled the gas tank at the start of the road trip, hence 3-1=2
ADDITIONAL STOPS FOR GAS WILL THEY NEED TO MAKE TO GET TO THEIR DESTINATION =2 !