Answer:
ur numbers are 2 and -5
Step-by-step explanation:
7x + 3y = -1
x + y = -3......x = -3 - y
7(-3 - y) + 3y = -1
-21 - 7y + 3y = -1
-7y + 3y = - 1 + 21
-4y = 20
y = -20/4
y = -5 <====
x = -3 - y
x = -3 - (-5)
x = -3 + 5
x = 2 <====
Answer: The numbers are 2 and -5
Step-by-step explanation:
7x+3y=-1 ...(equation 1)
x+y=-3 ...(equation 2)
x+y=-3
Broken down, we have x=-3-y
Substitute x=-3-y into equation 1
Then we have 7(-3-y) +3y=-1
Which is -21-7y+3y=-1
which is -21-4y=-1
-4y=-1+21=20
y=-20/4=-5
y=-5
Substitute y=-5 into equation 1
x+y=-3
x-5=-3
x=-3+5=2
x=2
A game designer must decide how to color four buildings that are in a row. Using only the colors yellow, green, red, and blue, each building must be painted with exactly one color. Any two neighboring buildings must be different colors, and the first and last buildings must be different colors. How many ways are there to paint the four buildings?
To determine how many ways to paint the buildings, we consider the choices for each building sequentially, considering the constraints. There are either 36 or 24 combinations, depending on the colors chosen for the first and last buildings. A step-by-step count confirms this range of possibilities.
A systematic approach gives us the general formula: 4 choices for the first building × 3 choices for the second building × 3 choices for the third building × (2 or 3) choices for the fourth building, depending on the first color chosen. This results in a total of 36 or 24 possible combinations, depending on the first and last color's relationship. A careful count avoiding the restrictions on the colors confirms this.
An architect uses a 3-D printer to create the scale model for a house that will be built. In the model the house is 53cm tall . The house will be 624 cm tall. The volume of the model is 0.8125 cubic meter. What is the volume of the house . (Note: 1 cubic meter = 1,000,000 cubic centimeters)
Answer:
The volume of the actual house is 1,324.94 cubic meters
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Height of the scale model = 53 cm
Height of the actual house = 624 cm
Scale of the model = 642/53 = 11.77
Volume of the scale model = 0.8125 cubic meters
2. What is the volume of the house?
For answering the question we have to find the width and the length of the model, then use the scale of the model for calculating the volume of the actual house, this way:
Volume of the scale model = 0.8125 cubic meters
Area of the scale model = Volume of the model/Height of the model
Area of the scale model = 0.8125/0.53
Area of the scale model = 1.533 square meters
Area of the scale model = Length * Width
Area of the scale model = 1.533 * 1
Now, we can calculate, the measurements of the house to calculate its volume:
Height of the actual house = 6.24 meters
Length of the actual house = 1.533 * 11.77 = 18.04 meters
Width of the actual house = 1 * 11.77 = 11.77 meters
Volume of the actual house = 6.24 * 18.04 * 11.77
Volume of the actual house = 1,324.94 cubic meters
There are 9 large bicycles at the store. There are 6 small bicycles at the store. How many bicycles are at the store?
Answer:15
Step-by-step explanation:9+6=15
Answer: 15
Step-by-step explanation:
9+6
1. What is the unit price of shampoo if a
15-ounce bottle costs $2.79?
A. about $0.19 per ounce
B. about $0.29 per ounce
C. about $1.90 per ounce
D. about $5.38 per ounce
-2k = k - 7 - 8 whats the answer
Answer:
−2k=k−7−8
−2k=k+−7+−8
−2k=(k)+(−7+−8)(Combine Like Terms)
−2k=k+−15
−2k=k−15
Step 2: Subtract k from both sides.
−2k−k=k−15−k
−3k=−15
Step 3: Divide both sides by -3.
−3k
−3
=
−15
−3
k=5
Step-by-step explanation:
Given that 2( -x + 4) = 3 , prove that x = 5/2.
Answer: proved
Step-by-step explanation:
-2x+8=3
-2x=3-8
-2x= -5
2x= 5
x=5/2
18.
If z = (5)(11)(28)(38), what is the
greatest prime factor of z?
A. 5
B. 7
C. 11
D. 13
E. 19
Answer:
E. 19
Step-by-step explanation:
z = (5)(11)(2·2·7)(2·19)
z = 2³·5·7·11·19
The greatest prime factor is 19.
A square wall has a surface area of 121ft? What is the length of the wall?
Ans 11ft
Step-by-step explanation:
Sq Area= length * length
Length=√area=√121=11
Point J(-2, 1) and point K(4, 5) form the line segment jk. for the point p that partitions jk in the ratio 3:7 what is the y coordinate of p
Answer:
[tex]\frac{11}{5}[/tex]
Step-by-step explanation:
Using the section formula
[tex]y_{P}[/tex] = [tex]\frac{3(5)+7(1)}{3+7}[/tex] = [tex]\frac{15+7}{10}[/tex] = [tex]\frac{22}{10}[/tex] = [tex]\frac{11}{5}[/tex]
Leon has 16 fewer quarters than dimes. He has 34 quarters.
Use the five-step problem-solving plan.
How many dimes does Leon have?
Enter you answer in the box.
Answer:
A grand total of 50 dimes
Step-by-step explanation:
How do I use the cosine rule for these problems?
Answer:
see explanation
Step-by-step explanation:
Using the Cosine rule
a² = b² + c² - 2abcosA ← Rearranging for cosA gives
cosA = [tex]\frac{b^2+c^2-a^2}{2ab}[/tex]
(a)
let a = 10, b = 7, c = 8 and A = α, then
cosα = [tex]\frac{7^2+8^2-10^2}{2(7)(8)}[/tex] = [tex]\frac{49+64-100}{112}[/tex] = [tex]\frac{13}{112}[/tex], thus
α = [tex]cos^{-1}[/tex]( [tex]\frac{13}{112}[/tex] ) ≈ 83° ( to the nearest degree )
(b)
let the angle opposite side 7 be x
Using the Sine rule
[tex]\frac{10}{sin83}[/tex] = [tex]\frac{7}{sinx}[/tex] ( cross- multiply )
10sinx = 7sin83 ( divide both sides by 10 )
sinx = [tex]\frac{7sin83}{10}[/tex] , thus
x = [tex]sin^{-1}[/tex] ( [tex]\frac{7sin83}{10}[/tex] ) = 44°
The third angle can be found using the sum of angles in a triangle
third angle = 180° - (83 + 44)° = 180° - 127° = 53°
The 3 angles are 83°, 44°, 53°
PLEASE HELP TRYING TO MAKE HONOR ROLL
The sum of two numbers is 36. Their difference is 14. What are the two numbers?
A. -14 and 50
B. -11 and 47
C. 11 and 25
D. 14 and 22
Answer:
it is B. -11 and 47
Step-by-step explanation:
you have to take away 47 and 11 and it equals 36.
Joyce paid $98.00 for an item at the store that was 30 percent off the original price. What was the original price?
Answer:
$127.40
Step-by-step explanation:
$98-30%=$127.4
The SAS Theorem can be used to prove that two triangles are similar.
True
False
Answer:
The answer is true.
I took the quiz! :)
The triangles are simliar by the:
show work please for brainlist
Step-by-step explanation:
BOTH TRIANGLES ARE SIMILAR BY THE AA SIMILARITY POSTULATE.
In first triangle:
Remaining angle = 180° - (70° + 30°)= 80°
In second triangle:
Remaining angle = 180° - (80° + 30°)= 70°
Hence, all the angles of first triangle are congruent to the corresponding angles of the second triangle.
Thus, both the triangles are similar by
THE AA SIMILARITY POSTULATE
The function g(x)=8(4x) is reflected across the x-axis to create f(x).
On a coordinate plane, 2 exponential functions are shown. Function f (x) approaches y = 0 in quadrant 3 and decreases into quadrant 4. It crosses the y-axis at (0, negative 8). Function g (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 8).
What is the equation of f(x)?
f(x)=8(4)x
f(x)=−8(4)x
f(x)=8
f(x)=−8
Answer:
It’s B if you dont want to read all that.
Step-by-step explanation:
The equation of f(x) is f(x) = -8(4x).
Explanation:The equation of the reflected function f(x) can be obtained by changing the sign of the coefficient of g(x), which is 8.
So, the equation of f(x) is f(x) = -8(4x).
Learn more about Reflected functions here:https://brainly.com/question/22702396
#SPJ12
Factor completely 81x^8-1
The complete factorized form for the given expression is [tex]\left(9 x^{4}+1\right)\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]
Step-by-step explanation:
Step 1: Given expression:
[tex]81 x^{8}-1[/tex]
Step 2: Trying to factor as a Difference of Squares
Factoring [tex]81 x^{8}-1[/tex]
As we know the theory that the difference of two perfect squares, [tex]A^{2}-B^{2}[/tex] can be factored into (A+B) (A-B)
from this, when analysing, 81 is the square of 9, [tex]x^{8}[/tex] is the square of [tex]x^{4}[/tex]. Hence, we can write the given expression as,
[tex]\left(9 x^{4}\right)^{2}-1^{2}[/tex]
By using the theory, we get
[tex]\left(9 x^{4}+1\right)\left(9 x^{4}-1\right)[/tex]
Again, we can further factorise the term [tex]\left(9 x^{4}-1\right)[/tex]
[tex]9 x^{4}[/tex] is the square of [tex]3 x^{2}[/tex]. Therefore, it can be expressed as below
[tex]\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]
Now, we can not factorise further the term [tex]\left(3 x^{2}-1\right)[/tex]. Because it will come as [tex]\sqrt{3} x[/tex] (3 is not a square term). Thereby concluding that the complete factorisation for the given expression is [tex]\left(9 x^{4}+1\right)\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]
The cost of some office furniture after a 20% reduction was $3520.00. What was the original price before the furniture was discounted?
Answer:
[tex]\$4,400[/tex]
Step-by-step explanation:
Let
x ----> the original price of the furniture
Remember that
[tex]100\%-20\%=80\%=80/100=0.80[/tex]
we know that
The original price multiplied by 0.80 must be equal to the cost of the furniture after a 20% reduction
so
The linear equation that represent this situation is
[tex]0.80x=3,520.00[/tex]
solve for x
Divide by 0.80 both sides
[tex]x=\$4,400[/tex]
Answer:
4.00
Step-by-step explanation:
What is the average rate of change of the function g(x) = 3(2^x) - 6 over the interval [0,3]?
Final answer:
The average rate of change of the function g(x) = 3(2^x) - 6 over the interval [0,3] is 7. This is found by evaluating g(x) at x = 0 and x = 3 and then dividing the difference by the interval length.
Explanation:
Calculating Average Rate of Change
The average rate of change of a function over an interval is the change in the function's values divided by the change in the independent variable (often x) over that interval. For the function g(x) = 3(2^x) - 6 over the interval [0,3], we first find the values of g(x) at the endpoints of the interval: g(0) and g(3). We then use the formula for average rate of change:
[tex]\[\text{Average Rate of Change} = \frac{g(3) - g(0)}{3 - 0}\][/tex]
Let's compute:
g(0) = 3(2^0) - 6 = 3(1) - 6 = -3g(3) = 3(2^3) - 6 = 3(8) - 6 = 24 - 6 = 18Now we can substitute these values into the formula:
[tex]\[\frac{18 - (-3)}{3 - 0} = \frac{21}{3} = 7\][/tex]
So, the average rate of change of the function g(x) over the interval [0,3] is 7.
What is the reflection of (8, -5) in the Y axis
Answer:
(-8, -5)
Step-by-step explanation:
I plotted the equation on a graph and looked at the reflection and got that.
what is the y-intercept, and what does it represent?
Answer:
The y-intercept is where an equation's graph hits the y-axis. It represents the constant value, when x=0, the intercept is the constant
Step-by-step explanation:
The y-intercept indicates the vertical position where the line or curve intersects the y-axis
The y-intercept refers to the point where a line or curve intersects the y-axis on a graph.
It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.
In the equation of a line in slope-intercept form (y = mx + b), where m represents the slope of the line and b represents the y-intercept, the y-intercept is the constant term (b).
The y-intercept represents the value of the dependent variable (y) when the independent variable (x) is not present or equal to zero.
It is the initial value or starting point of the function or graph.
To learn more on y-intercept click:
https://brainly.com/question/14180189
#SPJ6
Elijah drinks 35 out of 40 ounces of the water in her water bottle what percentage did Elijah drink
Answer:
87.5%
Step-by-step explanation:
35/40=7/8=0.875=87.5%
Amir drove from Jerusalem down to Lowest Place on earth, the Dead Sea descending at a rate of 12 meters per minute he was at sea level after 30 minutes of driving. Graph the relationship between Aamir’s attitude relative to sea level in meters and time inminutes
Answer:
see below for a graph
Step-by-step explanation:
It is convenient to use a point-slope form of the equation of a line for graphing, since we know the slope is -12 m/min and the point is (30, 0) at sea level.
The horizontal axis is minutes; the vertical axis is meters above sea level. The graph cannot extend below -413 meters from sea level, as that is the lowest place on earth.
How many solutions does this equation have?
(15x + 21) / 3
= 5x + 7
Answer:
3*(5*x-7)-(15*x-21)=0
Step-by-step explanation:
3 • (5x - 7) - (15x - 21) = 0
Step 2 :
Equation at the end of step 2 :
0 = 0
Step 3 :
Equations which are always true :
A 6cm section of plastic water pipe has inner diameter of 12cm and outer diameter of 15cm. find the volume of the plastic pipe not the hollow interior to the nearest hundredth
Answer:
The volume of the plastic pipe is 141 cubic centimetre
Step-by-step explanation:
Given:
The Length of the plastic water pipe = 12 cm
The inner Diameter of the plastic water pipe = 12 cm
The outer Diameter of the plastic water pipe = 15 cm
To Find:
the volume of the plastic pipe not the hollow interior to the nearest hundredth = ?
Solution:
The volume of the plastic water pipe can be found by using the volume of the cylinder formula
The Volume of the cylinder = [tex]\pi r^2 h[/tex]
Where
r is the radius
h is the height
Radius r [tex]= \frac{diameter}{2} = \frac{15}{2} = 7.5 cm[/tex]
On substituting the values
The Volume of the cylinder
= [tex]\pi (7.5) (6)[/tex]
= [tex]45 \pi[/tex]
= 141.37 cubic centimetre
= 141 cubic centimetre
Solve n÷6>2. Graph the solution. The solution is?
please help!
Answer:
n>12
Step-by-step explanation:
n/6>2
n>2*6
n>12
The Graph of the inequality is shown below.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have the inequality,
n÷6>2
Multiply both side by 6 we get
(n ÷ 6 ) 6 > 2 x 6
n > 12.
Learn more about Inequality here:
https://brainly.com/question/30228778
#SPJ2
Write the ratio as a fraction in simplest form.
1) 15 girls to 6 boys and question 2) 24 plays for 3 teams
Answer:
Part 1) [tex]\frac{5}{2}[/tex] or [tex]5:2[/tex]
Part 2) [tex]\frac{8}{1}[/tex] or [tex]8:1[/tex]
Step-by-step explanation:
Write the ratio as a fraction in simplest form
Part 1) 15 girls to 6 boys
we know that
To find out the ratio, divide the number of girls by the number of boys
so
[tex]\frac{15}{6}[/tex]
Simplify
Divide by 3 both numerator and denominator
[tex]\frac{5}{2}\ \frac{girls}{boys}[/tex]
Part 2) 24 plays for 3 teams
we know that
To find out the ratio, divide the number of plays by the number of teams
so
[tex]\frac{24}{3}[/tex]
Simplify
Divide by 3 both numerator and denominator
[tex]\frac{8}{1}\ \frac{plays}{team}[/tex]
Final answer:
To simplify the ratios 15 girls : 6 boys and 24 plays : 3 teams, find the greatest common factor and divide both parts of the ratio by it, resulting in the simplest forms rac{5}{2} and 8, respectively.
Explanation:
To write the ratios as fractions in simplest form for the given scenarios:
For the ratio of 15 girls to 6 boys, the fraction would be rac{15}{6}. To simplify, divide both the numerator and the denominator by their greatest common factor (GCF), which is 3. Thus, the simplest form is rac{15 \/ 3}{6 \/ 3} = rac{5}{2}.
For the ratio of 24 plays for 3 teams, the fraction is rac{24}{3}. Again, to simplify, divide both the numerator and the denominator by the GCF, which is 3 in this case. The simplest form is rac{24 \/ 3}{3 \/ 3} = rac{8}{1}, which can also be written simply as 8 since a denominator of 1 implies the value is a whole number.
The dimensions of a 7-cm by 2-cm rectangle are
multiplied by 3. How is the area affected?
Answer:
Step-by-step explanation:
9
Final answer:
Multiplying the dimensions of a rectangle by 3 increases its area by a factor of 9, which is the square of 3. The area of the rectangle goes from 14 cm^2 to 126 cm^2.
Explanation:
When the dimensions of a rectangle are multiplied by a certain factor, the area of the rectangle is affected by the square of that factor. Initially, the area of a 7-cm by 2-cm rectangle is 14 cm2. When the dimensions are each multiplied by 3, the new dimensions become 21 cm by 6 cm. Therefore, the new area is 21 cm imes 6 cm = 126 cm2. The area scales in proportion to the square of the linear dimensions. If we compare the new area to the old area, we see that 126 cm2 / 14 cm2 equals 9, meaning the area has increased by a factor of 9, which is 32, since we multiplied the dimensions by 3. This principle applies generally: when a rectangle's dimensions are scaled by a factor, its area is scaled by the square of that factor.
$65 dress pants 20% discount
Answer:
52
Step-by-step explanation:
65 dollar is price so it has 20 percent discount so,
65× 20% = 13
so,
65- 13
52 dollars
Select all the correct answers.
Which three of these story details can help a reader identify the theme
O
the author's background
O
repetition of ideas
the amount of dialogue
the interaction of story elements
the main conflict
Answer:
ideas and conflict and maybe elements depending on the story