Answer:
Rita is 20 years old
Step-by-step explanation:
If you add 8 years to Fati's age, (15+8), you get 23. That is Rita's age right now. Now subtract 3 from 23. You get 20. So Rita is 20 years old.
Find the midpoint of the segment with the given endpoints. (-7,2)and(-1,1)
The midpoint is _
Answer:
(-4.5, 1.5) is the midpoint
Step-by-step explanation:
midpoint formula:
([x₁ + x₂] / 2 , [y₁ + y₂] / 2)
(-7 - 1) / 2 = -4.5
(2 + 1) / 2 = 1.5
(-4.5, 1.5) is the midpoint
There are 45 male teachers and 75 female teachersin a school. Find the percentage of male teachers, female teachers in the school.
Answer:
37.5% are male
62.5% are female
Step-by-step explanation:
in total 120 teachers (45 male+75 female)
therefore:
for male
120 - 100%
45 - x% (we need to find x)
by using the butterfly method (or cross multiply) we get:
120x=100*45
x=4500/120=37.5% (male teachers)
we do the same for female but instead of using 45 we will use 75(the quantity of female theachers in school)
120x=100*75
x=7500/120=62.5%
Consider a rectangle whose length, L, is 4 more than twice its width, w. a. Write an expression for L in terms of w. b. Show that the perimeter, P, is equal to = 6 + 8. c. Given the perimeter is 20, find the length and width of the rectangle using your answer to part b.
Answer:
Step-by-step explanation:
a)L=2w+4
b)P=2L+2w
sub L=2w+4,
P=2(2w+4)+2w
P=4w+8+2w
P=6w+8
c) 20=6w+8
12=6w
2=w
L=2(2)+4
=8
Hence,
L=8 and w=2
Plzzz help me im having alot of trouble understanding this question does some one understand if you do plz help fast!!!
1/2 - 3(1/2 + 1)²
(1 + 1/3)² - 2/9
Answer:
1/2 - 3(1/2 + 1)²
simplify the expression (1/2 + 1)
1/2 - 3•(3/2)²
using PEMDAS, we see we have to evaluate the exponent first
(3/2)² = 9/4
rewrite the equation
1/2 - 3 • (9/4)
multiply 3 by (9/4)
1/2 - (27/4)
subtract
-25/4
(1 + 1/3)² - 2/9
simplify the expression (1 + 1/3)
(4/3)² - 2/9
using PEMDAS, we see we have to evaluate the exponent first
(4/3)² = 16/9
rewrite the equation
(16/9) - (2/9)
subtract
14/9
B=(5,6)is a set. From this set make all possible ordered pairs.
5,6 and6,5
Step-by-step explanation:
there is only two ordered pairs of 5,6that is itself and 6,5
Answer:
the two possible orders are 5,6 and 6, 5
Please help me on this question
Answer:
2+7=9
450/9 = 50
2( 50) = 100 no concentrate
7(50) or 450 - 100 = 350 ml water
maria bought gifts for 7 of her friends.she spent $86.66.If she spent the same amount on each of her friends,how much did she spend on each?
Answer:
$12.38
Step-by-step explanation:
total money / total friends = amount per friend
86.66 / 7 = 12.38
Answer:
She spent 12.38 on each gift
Step-by-step explanation:
Take the total amount and divide by the number of gifts purchased
86.66 / 7
12.38
She spent 12.38 on each gift
The altitude of a right square prism is of length 12 and its base has a side of length 8. What is the lateral surface area of this prism?
A. 484 units²
B. 48 units²
C. 192 units²
D. 384 units²
Answer:
D. 384 units²
Step-by-step explanation:
Hey there!
Well a right square prism's bases are squares meaning the area of the base is 64 units².
Meaning 128 "which is the sum of 64+64" needs to be taken out of the SA to find the LSA.
Now we only have 4 sides to find the area of,
h = 12
l/w = 8
A = (12*8) * 4
A = 96 * 4
LSA = 384 units²
Hope this helps :)
The lateral surface area of the given prism of length 12 and its base has a side of length 8 is 384 [tex]units^{2}[/tex]
What is Lateral surface area?The lateral surface area of an object is the total area of its sides excluding its top and the bottom.
What is a right square prism?A right square prism is a prism having four sides as rectangle and two sides as squares as its bases.
How to find the lateral surface area of right square prism?The lateral surface area of right square prism is equal to the area of the four rectangles only. So the formula is as follows:
Lateral surface area=4(length*breadth)
The altitude which is given to us of 12 will be the breadth of the rectangles and the length of base of 8 will be the length of the rectangles. So,
Lateral surface area of right prism=4(12*8)
=4*96
=384
Hence the lateral surface area of right prism of altitude of length 12 and base has a side of length 8 is 384[tex]units^{2}[/tex]
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what value of x makes the equation true
2 (6x-1) = -38
Answer:
[tex] \boxed{\bold{\boxed{ \sf{x = - 3}}}}[/tex]Step-by-step explanation:
[tex] \sf{2(6x - 1) = - 38}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{12x - 2 = - 38}[/tex]
Move constant to right hand side and change it's sign
⇒[tex] \sf{12x = - 38 + 2}[/tex]
Calculate
⇒[tex] \sf{12x = - 36}[/tex]
Divide both sides of the equation by 12
⇒[tex] \sf{ \frac{12x}{12} = \frac{ - 36}{12} }[/tex]
Calculate
⇒[tex] \sf{x = - 3}[/tex]
Hope I helped!
Best regards!!
(x−3)^2+2=8 quadratic
Answer:
x = 3 ± √6.
or 0.55, 5.45 to the nearest hundredth.
Step-by-step explanation:
(x−3)^2+2=8
(x - 3)^2 = 8 - 2 = 6
(x - 3)^2 = 6
Taking square roots of both sides:
x - 3 = +/- √6
x = 3 ± √6.
ㅤ
Given quadratic equation:-
⇢ [tex]\rm{(x - 3) 2 + 2 = 8}[/tex]
ㅤ
Simplifying the given equation:-
ㅤ
1) Simplify both sides of the equation.
⇢ [tex]\rm{x^{2} - 6x + 11 = 8}[/tex]
ㅤ
2) Subtract (8) from both sides, we get:
⇢ [tex]\rm{x^{2} - 6x + 11 - 8 = 8 - 8}[/tex]
⇢ [tex]\rm{x^{2} - 6x + 3 = 0}[/tex]
ㅤ
3) In the equation: (a = 1), (b = -6), (c = 3):
⇢ [tex]\rm{1x^{2} + - 6x + 3 = 0}[/tex]
ㅤ
4) Use quadratic formula:
⇢ [tex]\rm{x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}}[/tex]
⇢ [tex]\rm{x = \dfrac{-(-6) \pm\sqrt{(-6)^{2} - 4 (1) (3)}}{2 \times 1}}[/tex]
⇢ [tex]\rm{x = \dfrac{6 \pm \sqrt{4}}{2}}[/tex]
⇢ [tex]{\boxed{\rm{x = 3 \pm \sqrt{6}}}}[/tex]150 people attend a concert. There were 30 more adults than children at the concert. There were 20 more men than women. What was the ratio of the number of men to the number of women to the number of children?
Answer:
11:7:12
Step-by-step explanation:
take x to be number of women
Total= 150
adults=(x+x+20)= 2x+20
children=(2x+20-30)= 2x-10
men =x+20
women=x
find the value of x
2x-10+x+20+x=150
2x+x+x+20-10+=150
4x+10=150
4x=150-10
4x=140. divide both sides by 4
x=35
thus.
men=(35+20)=55
women=35
children=70-10=60
ratio= 55:35:60.
simplify= 11:7:12
please help me on this
Answer:
Option (3)
Step-by-step explanation:
If a point having coordinates of a point (x, y),
If this point is rotated by an angle of 90 degrees clockwise about the origin then the coordinates of the image will follow the rule,
(x, y) → (y, -x)
If a point A is (3, -9) and this point is following the the same rule, new image point will be,
A(3, -9) → A'(-9, -3)
Option (3) will be the correct option.
What is the ratios 15cm: 5m lowest term?
I really need help with this problem, I don't know how to do it. Please help if you can.
2/3 +y =1/4
Answer:
see below
Step-by-step explanation:
2/3 +y =1/4
Subtract 2/3 from each side
2/3-2/3 +y =1/4-2/3
y = 1/4 -2/3
Get a common denominator
y = 1/4 (3/3) - 2/3 *4/4
= 3/12 - 8/12
=-5/12
or if
2/(y+3) = 1/4
Using cross products
y+3 = 2*4
y+3 = 8
y =8-3
y = 5
Answer:
y = -5/12
Step-by-step explanation:
2/3 + y = 1/4
y = 1/4 - 2/3
y = 3 - 8/ 12
y = -5/12
Is (a-3)(2a^2 + 3a + 3) equivalent to 2(a^3 - 1.5a^2 - 3a - 4.5)
==============================================
Work Shown:
Expand out the first expression to get
(a-3)(2a^2 + 3a + 3)
a(2a^2 + 3a + 3) - 3(2a^2 + 3a + 3)
2a^3 + 3a^2 + 3a - 6a^2 - 9a - 9
2a^3 + (3a^2-6a^2) + (3a-9a) - 9
2a^3 - 3a^2 - 6a - 9
Divide every term by 2 so we can pull out a 2 through the distributive property
2a^3 - 3a^2 - 6a - 9 = 2(a^3 - 1.5a^2 - 3a - 4.5)
This shows that (a-3)(2a^2 + 3a + 3) is equivalent to 2(a^3 - 1.5a^2 - 3a - 4.5)
Answer:
yes
Step-by-step explanation:
(a-3)(2a^2 + 3a + 3) = a(2a^2 + 3a + 3) -3(2a^2 + 3a + 3)
= 2a^3 +3a^2 +3a -6a^2 -9a -9
= 2a^3 +a^2(3 -6) +a(3 -9) -9
= 2a^3 -3a^2 -6a -9
= 2(a^3 -1.5a^2 -3a -4.5) . . . . the form you're asking about
Find the degree of this polynomial. .
[tex] - 5 {u}^{4} [/tex]
Answer:
4
Step-by-step explanation:
The degree of a polynomial is the highest of the degrees of the polynomial's monomials with non-zero coefficients
Find the length of UT¯¯¯¯¯¯¯+CV¯¯¯¯¯¯¯¯. A. 53 B. 4x + 35 C. 65 D. 59
Answer:
UT + CV = 4x + 33
Step-by-step explanation:
Given:
TW = 14
WU = 2x + 2
VW = 2x + 5
WC = 12
Find:
UT + CV
Computation:
UT = TW + WU
UT = 14 + 2x + 2 = 16 + 2x
CV = VW + WC
CV = 2x + 5 + 12 = 2x + 17
UT + CV
16 + 2x + 2x + 17
UT + CV = 4x + 33
b. 2(3x - 5) = 2x + 6
Answer:
x = 4
Step-by-step explanation:
Given
2(3x - 5) = 2x + 6 ( divide both sides by 2 )
3x - 5 = x + 3 ( subtract x from both sides )
2x - 5 = 3 ( add 5 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
Answer:
x = 4
Step-by-step explanation:
2(3x - 5) = 2x + 6
expand- 2(3x-5):6x+10
6x-10= 2x+6
Add 10 to both sides
6x-10+10=2x+6+10
simplify
6x=2x+16
subtract 2x from both sides
6x-2x=2x+16-2x
simplify
4x=16
divide both sides by 4
4x/4=16/4
x=4
Talia is packing a moving box. She has a square-framed poster with an area of 4 square feet. The cube-shaped box has a volume of 14 cubic feet. Will the poster lie flat in the box? Explain?
Answer:
Length of sides of poster = 2 Ft
Length of sides of box = 2.41 Ft
Since the box has a longer side than the poster, the poster will lie flat when placed in the box.
Step-by-step explanation:
In order to determine if the poster will lie flat in the box or not, we will determine the length of the sides of the poster and the box, if the length of the side of the square poster is smaller than that of the box, it will lie flat. This is calculated as follows:
Area of poster = 4 square feet
Area of poster = (Length)²
4 = (Length)²
∴ Length = √(4)
Length of poster = 2 Ft
Volume of box = 14 cubic feet
Volume of box = (Length)³
14 = (Length)³
∴ Length = ∛(14)
Length = 2.41 Ft
∴ Length of sides of poster = 2 Ft
Length of sides of box = 2.41 Ft
Since the box has a longer side than the poster, the poster will lie flat when placed in the box.
If function f has zeros at -3 and 4, which graph could represent function f? A. the graph of a quadratic function y = (1/4)(x+3)(x-4) B. the graph of a quadratic function y = -(1/4)(x-3)(x+4) C. the graph of a quadratic function y = -(x+3)(x+4) D. the graph of a quadratic function y = (x-3)(x-4)
Answer:
A. the graph of a quadratic function y = (1/4)(x+3)(x-4)
Step-by-step explanation:
(1/4)(x+3)(x-4) = 0
x+3 = 0 or x-4 = 0
x = -3 or x = 4
For the others:
B. -(1/4)(x-3)(x+4) = 0
x-3 = 0 or x+4 = 0
x = 3 or x = -4
C. -(x+3)(x+4) = 0
x+3 = 0 or x+4 = 0
Step-by-step explanation:
The graph of function y = 1/4 (x+3)(x-4) gives the zeros at -3 and 4, therefore option (a) is correct.
What is function?A function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
Given that,
The function f has 0 at -3 and 4.
The function f has 0 at -3 and 4 implies that the value of function is 0, when value of x are -3 and 4.
Solve with the help of options,
(a)
y = 1/4 (x + 3)(x - 4)
Substitute x = -3,
y = 1/4 (-3 + 3) (3 + 4)
y = 1/4 x 0 x 7
y = 0
Substitute x = 4,
y = 1/4 (4 + 3)(4 - 4)
y = 1/4 x 7 x 0
y = 0
The value of y is 0 at x = -3 and 4,
Therefore, option (A) is correct option.
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Put these in order from shortest to longest
Answer:
acb
Step-by-step explanation:
The side across from the smallest angle will always be the smallest side. Since 58 is the smallest angle measure, side a must be the smallest. This pattern continues with the other side and angle pairs.
1 An airport employee checked a group of passengers through security on Thursday. On Friday, she checked three times as many passengers, and on Saturday she processed 5,000 passengers through security. In the 3 days, she processed 15,000 passengers. How many did she process on Friday? 10005000300020007500
Answer:7,500
Step-by-step explanation
x + 3x + 5,000 = 15,000
4x - 5,000 = 10,000
4x = 10,000
/4
x = 2,500
On friday, she checked 3x, so she processed 2,500 x 3 = 7,500 passengers.
What is one negative angle that is co-terminal to 150°? *
Answer:
-210 degrees.
Step-by-step explanation:
That is 150 - 360
= -210 degrees.
Which of the following is the correct equation for the distance formula for the points (x1, y1) and (x2, Y2)?
pleaseee help asap!
Answer:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Step-by-step explanation:
A point in a coordinate plane is represented by using its x coordinate and y coordinate. If a point O has a x coordinate (a) and a y coordinate (b), it is represented as O(a, b)
The distance between two points with location at A([tex]x_1,y_1[/tex]) and point B([tex]x_2,y_2[/tex]) is the length of the line AB and is given by the formula:
[tex]D=|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Eduardo counted ten seconds (y) between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles (x) away. What is the equation of the variation?
Answer:
The equation for the variation is:
[tex]\frac{Miles}{thunder\,\,time } =0.2\,\frac{mi}{s}[/tex]
Step-by-step explanation:
The relationship is given by the quotient between the two variables: (1) distance of the storm, and (2) the number of seconds to hear the thunder. That is:
[tex]\frac{Miles}{thunder\,\,time } =\frac{2}{10} =0.2\,\frac{mi}{s}[/tex]
8r - rs when r =6 and s= 5
Answer:
The answer is 18.
Step-by-step explanation:
8r - rs
8×6=48
5×6=30
48-30=18
The perimeter of a rectangle is 72 meters. The width of the rectangle is 4 meters less than its length. Find the length and the width of the rectangle
Answer:
length = 20 meters
width = 16 meters
Step-by-step explanation:
72 = 2(a+b)
a = b-4
a = width
b = length
then:
72 = 2((b-4)+b)
72/2 = b-4+b
36 = 2b - 4
36 + 4 = 2b
40 = 2b
b = 40/2
b = 20
a = b - 4
a = 20 - 4
a = 16
Check:
72 = 2(20+16)
72 = 2*36
The shape of a dome can be modeled by the equation h=2dsquared +100 when h issue height (in feet) of the dome from the floor d feet from its center. How far from the center of the domes is the height 50 feet?
Given that,
The shape of a dome can be modeled by the equation :
[tex]h=2d^2+100[/tex] ....(1)
h is the height of the dome
d is distance from its center
We need to find the distance from the center of the dome if the height is 50 feet. Put h = 50 in equation (1)
[tex]50=2d^2+100\\\\2d^2=100-50\\\\2d^2=50\\\\d^2=25\\\\d=5\ \text{feet}[/tex], neglecting d = -5 feet (as height can't be negative)
So, at a distance of 5 feet from the center of domes the height is 50 feet.
What is the constant proportionality shown on the graph?
Please and Thank you
Answer:
A.
Step-by-step explanation:
Gabe is mapping out important family events. He uses negative numbers to represent time before he was born and positive numbers to represent time after he was born. For example, Gabe's mom was given a special coin in year -20−20minus, 20, and Gabe's sister was born in year 555. What does year 000 represent? Choose 1 answer: Choose 1 answer:
Answer:
Year 0 is represent the year that Gabe was born
Step-by-step explanation:
Gabe is mapping out important family events. He uses negative numbers to represent time before he was born and positive numbers to represent time after he was born. For example, Gabe's mom was given a special coin in year -20, and Gabe's sister was born in year 5. What does year 0 represent?
Answer: Positive numbers represent things that happen after Gabe was born while negative numbers represent things that happened before Gabe was born. The first example in the question meant that Gabe's mom was given a special coin 20 years before he was born while the second example in the question meant that Gabe's sister was born 5 years after he was born.
Year 0 is represent the year that Gabe was born.