Answer:
x (children) = 58
y (students) = 66
z (adults) = 29
Step-by-step explanation:
Step 1: Write system of equations
x + y + z = 153
5x + 7y + 12z = 1100
1/2x = z
The best way to solve the systems of equations is to use an augmented matrix:
Top row: [1 1 1 | 153]
Middle row: [5 7 12 | 1100]
Bottom row: [1/2 0 -1 | 0]
And then put it in RREF form:
Top row: [1 0 0 | 58]
Middle row: [0 1 0 | 66]
Bottom row: [0 0 1 | 29]
Which graph describes the relation (3,1),(-2,1),(0,2),(-2,0)
Answer:
b
Step-by-step explanation:
For one month Siera calculated her home town’s average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function C of F = five-ninths (F minus 32) . What does C(F) represent?
Answer:
The answer is below
Step-by-step explanation:
A function shows relationship between variables usually between inputs (an independent variable) and outputs (a dependent variable).
C(F) = 5/9(F - 32) shows the relationship between C and F. C(F) is the temperature in degree Celsius for any temperature in Fahrenheit. This means that the function C(F) represents the conversion of temperature from Fahrenheit to degree Celsius.
Use the diagram to find the indicated angle measures. m∠1 = degrees m∠2 = degrees m∠3 = degrees
Answer:
m∠1 = 131°
m∠2 = 49°
m∠3 = 112°
Step-by-step explanation:
We find the m∠2 using Vertical Angles Theorem
We find the m∠1 using Definition of a Line
We find the m∠3 also using Vertical Angles Theorem
During a sale, a shop allows 20% discount off the marked price of clothing. What will a customer pay for a dress with a marked price of $30? * 1 point
Answer:
$24
Step-by-step explanation:
Let the full price of $30 be 100%.
If the discount allowed is 20%, then the percentage of the original price that a customer will pay is:
[tex]P=100\%-20\%\\P=80\%[/tex]
80% of a marked price of $30 is:
[tex]80\%*\$30\\\$24[/tex]
A customer will pay $24.
What percentage of students under age 15 travel to school by car? Round to the nearest whole percent. 11% 18% 41% 80%
Answer:
11%
Step-by-step explanation:
We need to fill the missing cells of the table first and are interested in first row for under age 15
1. 152- 65= 87 for the top left cell
2. 165- (87+60)= 18 for car column on same row
now we have number 18 and the total of the first row is 165:
18/165*100%= 10.9%So the first choice- 11% is the answer
Answer:
11% is the pecentage of students under the age of 15 that travel by car to school.
Increase £16470.45 by 3.5% Give your answer rounded to 2 DP pls help
Answer:
$17046.90
Step-by-step explanation:
Write out the equation for increase:
16470.45(1 + 0.035)
16470.45(1.035)
17046.90
Find the surface area of the prism.
Answer:
a). B = 24 yd²
b). h = 8 yd
c). S.A. = 240 yd²
Step-by-step explanation:
Area of the triangular base B = [tex]\frac{1}{2}(\text{Base of the right triangle})(\text{height of the base triangle})[/tex]
= [tex]\frac{1}{2}(8)(6)[/tex]
= 24 yd²
Height of the prism 'h' = distance between the triangular bases
= 8 yd
Perimeter of the triangular base = leg 1 + leg 2 + hypotenuse
= 8 + 6 + 10 = 24 yd
Surface area = 2B + Ph
= (2×24) + (24×8)
= 48 + 192
= 240 square yds
At a frozen yogurt shop, 7/25 of sales are chocolate, 0.09 of sales are mocha, 2/5 of sales are vanilla, and the rest are strawberry. What percent of sales is strawberry?
Answer:
22%.
Step-by-step explanation:
7/25 = 28%
0.09 = 9%
2/5 = 40%
29% + 9% + 40% = 78%
100% - 78% = 22%
And you have your answer. Hope this helped.
Solve the equation by factoring:
x² – 5x = 14
a. x= -2 or 7
b. x= 2 and -7
C. X= -2 or -7
d. x = 2 or 7
Answer:
The two possible solutions are x = 7, or x = -2
which agree with answer a) in the list of options
Step-by-step explanation:
Start by moving all terms to one side of the equal sign, and then factoring out the constant term:
[tex]x^2-5x-14=0[/tex]
The constant term "-14" has ossible factors: (-1), (1) (-2), (2), (-7), (7), (-14), (14) and we look for a pair whose combining results in "-5" (the coefficient of the middle term. We find (-7) and (2) the appropriate factors, so we use then to split the middle term and then factor by grouping:
[tex]x^2-5x-14=0\\x^2-7\,x+2\,x-14=0\\x(x-7)+2(x-7)=0\\(x-7)\,(x+2) = 0[/tex]
Then if the product of these two binomial factors is zero, it means that the first binomial is zero, or the second one is zero. That is:
( x - 7 ) = 0 which means x = 7
or
( x + 2 ) = 0 which means x = -2
So the two possible solutions are x = 7, or x = -2
Answer:
a. -2 or 7Step-by-step explanation:
[tex]x^2-5x=14\\\\x^2-5x-14=0\\\\x^2+2x-7x-14=0\\\\x(x+2)-7(x+2)=0\\\\(x+2)(x-7)=0\\\\x+2=0\quad\vee\quad x-7=0\\\\x=-2\quad\vee\quad x=7[/tex]
What is the scale factor ??
Answer:
3.5
Step-by-step explanation:
63 divided by 18 is 3.5
35 divided by 10 is 3.5
triangle ABC has vertices A(5, 12) B(13, 13) and C (11,5). show that the triangle ABC is. scalene triangle
Answer:
AB =√( (13 - 5)² + (13-12)²) = √(8² + 1²) = √65
BC = √( (13 - 11)² + (13-5)²) = √(2² + 8²) = √68
AC =√( (11 - 5)² + (5-12)²) = √(6² + 7²) = √85
AB ≠ BC ≠ AC ∴ ABC is Scalene
Step-by-step explanation:
A scalene triangle is a triangle in which all the sides are different lengths.
In order to prove that ABC is scalene, we need to calculate the sidelengths and show them to be different.
The line between points A(x₁, y₁) and B(x₂, y₂) can be denoted AB.
the difference in x-coordinate is x₂ - x₁, and the difference in y-coordinates is y₂ - y₁.
this forms a triangle of length x₂ - x₁ and height y₂ - y₁ and the hypotenuse AB can be calculated using pythagoras' theorem:
AB = √((x₂ - x₁)² +(y₂ - y₁)²)
The triangle ABC with vertices A(5, 12) B(13, 13) and C (11,5) is a scalene triangle.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given three vertices of triangle ABC are A(5, 12) B(13, 13) and C (11,5).
We know that in a scalene triangle all the three sides lengths are different.
Let us find distance of AB,BC, CA
Distance=√(x₂-x₁)²+(y₂-y₁)²
A(5,12), B(13, 13)
AB=√(13-5)²+(13-12)²
=√8²+1²=√64+1=√65
B(13, 13) C (11,5).
BC=√(11-13)²+(5-13)²
=√4+64=√68
C (11,5).A(5,12),
CA=√(5-11)²+(12-5)²
=√(-6)²+(7)²
=√36+49=√85
The lengths of triangle ABC are different so the triangle is Scalene.
Hence the triangle ABC with vertices A(5, 12) B(13, 13) and C (11,5) is a scalene triangle.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ2
are the two triangles similar? how do you know
Answer:
yes; by AA~
Step-by-step explanation:
The triangles are similar because vertical angles are congruent and alternate interior angles are both 39 degrees.
The sum of exterior angles of a regular polygon are equal TRUE\FALSE
Answer:
The sum of exterior angles of a regular polygon are equal true that is equals to 360°
Step-by-step explanation:
i hope this will help you :)
Answer:
true
Step-by-step explanation:
The sum of exterior angles of a regular polygon are 360°
What is the slope of the line? x+3y=10
Answer:
m = -1/3
Step-by-step explanation:
First, write the equation in slope-intercept form:
3y = 10 - x
y = 10/3 - x/3
y = 10/3 - 1/3x
Since our slope is the coefficient of the x term, our slope is -1/3.
Find the fourth term in the sequence defined by the following recursive formula.
t1 = 5
tn = 3tn-1 - 12
1) -75
O 2 3
3) -3
4) -21
Answer
Part 1
Step-by-step explanation:
T2=3(5)-12=3
T3=-3
T4=-21
T5=-75
I need help with this what is the answer
Answer:
5
Step-by-step explanation:
if u substitute the x's then u can see that it makes sense
ex. 5(1)+5 = 10 true
ex. 5(5)=5 = 30 true
hope this helps
what are the soultions of 3(x-4) (2x-3)= 0 check all
Answer:
{3/2, 4}
Step-by-step explanation:
Set x - 4 = 0 and solve for x: x = 4 is a solution.
Seet 2x - 3 = 0 and solve for x: 3/2 is another solution.
Find all the missing angle measures. Remember you cannot assume right angles of diameters. Also think about how many degrees are in a triangle. Given: PA and BD are tangents, mCR=18*, mAC=70*, mBE=130*, and mBR=80*. What are angles 1-15
.
this is answer ok? ok :) leleelellelelelelelelel
The number of squares that are required to fill a rectangle of 512 cm by 108 cm, if each square of length 8 cm is _____________. a. 838 b. 864 c. 752 d. 440
Answer:
864
Step-by-step explanation:
512÷8=64
108÷8=13.5
64×13.5=864
Answer:
b) 864 squares
Step-by-step explanation:
A(rectangle) = 512cm x 108cm = 55296 cm²
A(square) = 8cm x 8cm = 64 cm²
Ar/As = 55296cm²/64cm² = 864 squares
What is the distance from the point (3,8) to the point (7,-6)?
Answer: Distance is 14.6
Step-by-step explanation:
[tex]d = √((x2-x1)2 + (y2-y1)2)[/tex]
[tex](x2-x1) = (7 - 3) = 4[/tex]
[tex](y2-y1) = (-6 - 8) = -14[/tex]
add it all together
[tex](4)2 + (-14)2 = 16 + 196 = 212[/tex]
Square 212
[tex]\sqrt{212} =14.5602[/tex]
round to the nearest tenth
=14.6
PLEASE MARK BRAINLIEST
Answer: d=14.6
Step-by-step explanation:
√212=14.5602
round=14.6
Please answer this question now in two minutes
Answer: mKLJ = 60ᴼ
Step-by-step explanation:
MLO and KLJ are vertical angles, which means their measures are congruent.
Melanie began studying a sample of the chemical element einsteinium-253 which naturally loses its mass over time. The relationship between the elapsed time, t, in days, since Melanie started studying the sample, and the total mass remaining in the sample, M(t), in micrograms, is modeled by the following function: M(t)=169⋅(0.96)^t. How much percent does the chemical element lose weight by everyday?
Answer:
The chemical element loses 4% of its weight everyday
Step-by-step explanation:
Here, we are interested in knowing the percentage weight loss of the chemical each day.
The key to answering this is looking at the expression inside the bracket.
We can express M(t) = 169•(0.96)^t as
M(t) = 169•(1-0.04)^t
So what this means is that we need to find the percentage value corresponding to 0.04 since it is a constant term here
Mathematically, 0.04 is same as 4/100, so we can clearly say that the constant percentage loss is 4%
Answer:
0.96
Step-by-step explanation:
The exponential function modeling the mass of the sample is of the form M(t)=A⋅Bt. Therefore, AAA determines the initial mass of the sample (when Clemence began studying it) and BBB determines the daily change in the mass of the sample.
The mass of the sample is multiplied by \it{0.96}0.960, point, 96 every day. Since 0.96<10.96<10, point, 96, is less than, 1, the mass of the sample shrinks by a factor of 0.960.960, point, 96 every day.
Every day, the mass of the sample shrinks by a factor of 0.960.960, point, 96.
Express 11/5 as a MIXED NUMBER?
Answer:
11 / 5 as a mixed number is 2 1/5
Hope this helps you
Answer:
2⅕
Step-by-step explanation:
5x2=10
1 left over 1/5
What is the volume of the cone with a diameter of 4ft and height 4ft round to the nearest cubic foot
Answer:
67
Step - Step - Explanation
Solve the equation below algebraically for the exact value of x. 6 − 23(x + 5) = 4x
Answer:
See below.
Step-by-step explanation:
6 - 23(x+5) = 4x
First, distribute.
6 - 23x - 115 = 4x
Reorder the terms.
6 - 115 - 23x = 4x
Subtract.
-109 -23x = 4x
Add 23x to both sides.
-109 = 27x
Divide by 27.
x = -109/27 (This cannot be simplified)
Which is equal to a rotation of 90°ccw?
A. 180°cw rotation about the origin
В. 270°cw rotation about the origin
C. 180ºccw rotation about the origin
D. 270ºccw rotation about the origin
Answer:
В. 270°cw rotation about the origin
Step-by-step explanation:
We can rotate a total of 360 degrees in a circular pattern.
If we rotate x degrees in one direction, this rotation is equivalent to rotating (360 - x) in the other direction, because we would arrive in the same place.
So if we rotate 90 degrees in the counter clockwise direction, this is equivalent to rotating (360 - 90) = 270 degrees in the opposite direction, that is, in the clockwise direction.
So the correct option is B. -> 270°cw rotation about the origin.
If a ∥ b and _____, then a ∥ c.
Answer:
b || c
Step-by-step explanation:
a can only be parallel to c is if c is parallel to either a or b as both a and b are parallel to each other. By the way || means that they are parallel lines.
simplify -5(3m2 + 7n2) + 8n2
Answer:
-15m² - 27n²Step-by-step explanation:
-5(3m² + 7n²) + 8n²
Expand brackets.
-15m² + -35n² + 8n²
Combine like terms.
-15m² + -27n²
Answer:
[tex]\boxed{\red{= - 3(5 {m}^{2} + 9 {n}^{2} )}}[/tex]
Step-by-step explanation:
[tex] - 5(3 {m}^{2} + 7 {n}^{2} ) + 8 {n}^{2} \\ - 15 {m}^{2} - 35 {n}^{2} + 8 {n}^{2} \\ = - 15 {m}^{2} - 27 {n}^{2} \\ = - 3(5 {m}^{2} + 9 {n}^{2} )[/tex]
Geraldo is driving 504 miles to his grandparents’ house for the holidays. So far he has driven 21 miles in 20.3 minutes. If he continues to drive at this average rate of speed, estimate how long the entire trip will take.
Answer: about 5 hours and 3 min
Step-by-step explanation:
Answer:
about 8 hours and 7 minutes
Step-by-step explanation:
have 60 minutes divided by 20.3 minutes to find the correct ratio to find themph if the speed remained constant. It is about 2.95567 and using this number multiply to 21 to get the miles per hour. the speed is about 62.069 mph. then divide the 504 miles by the mph of the car to find how long it will take to get there. It is about 8 hours 7 minutes and 20 seconds give or take, or 8.12 hours.
Please answer this question in two minutes
Answer:
FGH and BCD
it's obvious.
no common lines between them