Full question:
For each multiplication expression, sketch an area model. Label the dimensions and the area of each part. Then write an equation showing that the area as a product equals the area as a sum. a. (x+1)(x+2), b. 3(2x+5), c. (2x-3)(x+2), d. (x-1)(y-1), e. -2y(y+3), f. (-x+1)(3x+y-4)
Answer and explanation:
a. (x+1)(x+2)= x×x+x×2+1×x+1×2
The dimensions (length and width) is x+1 and x+2
b. 3(2x+5) = 3×2x+3×5
The dimensions is 3 and 2x+5
c. (2x-3)(x+2)= 2x×x+2x×2-3×x-3×+2
The dimensions are 2x-3 and x+2
d. (x-1)(y-1)= x×y+x×-1-1×y-1×-1
Dimensions are x-1 and y-1
e. -2y(y+3)= -2y×y-2y×3
Dimensions are -2y and y+3
f. (-x+1)(3x+y-4)= -x×3x-x×y-x×-4+1×3x+1×y+1×-4
Dimensions are -x+1 and 3x+y-4
Question 8: Find the equation of the straight line that:
(a) has a gradient of 4 and passes through the point (1, 10)
Answer:
[tex]y=4x+6[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope (also called the gradient) and b is the y-intercept (the value of y when x is 0)
1) Plug the gradient into the equation (b)
[tex]y=mx+b[/tex]
We're given that the gradient of the line is 4. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=4x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=4x+b[/tex]
Plug in the given point (1,10) as (x,y) and solve for b
[tex]10=4(1)+b\\10=4+b[/tex]
Subtract 4 from both sides to isolate b
[tex]10-4=4+b-4\\6=b[/tex]
Therefore, the y-intercept of the line is 6. Plug this back into [tex]y=4x+b[/tex] as b:
[tex]y=4x+6[/tex]
I hope this helps!
answer = y = 4x + 6
y = mx + b
gradient = slope = m = 4
(1,10) = (x,y)
plug in the values
10 = 4 (1) + b
10 = 4 + b
b = 6
y = 4x + 6
Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessary.
Answer:
5.8
Step-by-step explanation:
Y e s .
Using the Distance formula and all.
Find f(2) if f(x) = (x + 1)^2.
9
6
5
Answer:
9
Step-by-step explanation:
f(2)=(2+1)^2
(3)^2
(9)
PLEASE HELP!!! Which choice is a solution to the system of equations below?
A. There are infinitely many solutions
B. (-4, 1)
C. (4, -1)
D. (3, 4)
Answer:
A.
Step-by-step explanation:
4y = 12x + 16
3x = y - 4
=>
y = 3x + 4
using that in the first equation
4(3x+4) = 12x + 16
12x + 16 = 12x + 16
=> both lines/equations are identical, so they have infinitely many solutions.
resolve the factors ( xy+z)^2 (y-xz)^2
Answer:
=x4y2z2−2x3y3z+2x3yz3+x2y4−4x2y2z2+x2z4+2xy3z−2xyz3+y2z2
Make me brainliest
Answer:
x2y-x2z-xy2+xz2+y2z-yz2
step by step
step.1
Equation at the end of step 1:(((x2)•(y-z)(+((y2)•(z-x)))+z2•(x-y)
step2
Equation at the end of step2
(((x2)•(yz))+yz•(z-x))+z2•(x-y)
step.3
equation at the end of step 3.
(x2•(y-z)+y2•(z-x))+z2•(x-y)
step4
trying to factor by pulling out:
factoring: x2y-x2z-xy2+xz2+y2z-yz2
thought fully split the expression at hand into groups,each group having two terms:
group1: y2z-yz2
group 2: x2y-x2z
group 3: xz2-yz2
pull out from each groups separately:
group 1:(x-z)•(-y2)
group 2:(y-z)•(x2)
group 3:(x-y)•(z2)
looking for common sub-expressions:
group 1:(x-z)•(-y2)
group 2:(y-z)•(x2)
group 3:( x-y)•(z2)
bad news !! factoring by pulling out fails:
The groups have no common factor and cannot be added up to form a multiplication.
final result:
x2y-x2z-xy2+xz2+y2z-yz2
Consider the equation: x^2 - 4x + 4 = 2x
Rewrite the equation by completing the square:
Your equation should look like (x+a)^2 = b or (x-c)^2 = d
______
What are the solutions to the equation? (1 right answer!)
Answer:
(x+3)^2=5
Step-by-step explanation:
x^2-4x+4=2x
x^2-6x+4=0
x^2-6x+9-5=0
(x-3)^2-5=0
(x-3)^2=5
Which is a simplified form of the expression 3a + 7 – a – 7?
A. 2a
B. 4a
C. 2a + 14
D. 4a - 14
Answer:
A. 2a
Step-by-step explanation:
imagine an imaginary 1 in front of the a
3a + 7 – 1a – 7
subtract numbers without variables
3a + 7 – a – 7
3a-1a
subtract 1a from 3a
2a
Answer:
A. 2a
Step-by-step explanation:
3a + 7 - a + 7
= 3a - a + 7 - 7
= 2a + 0
= 2a
Grace earned £32,000 last year. She worked for 35 hours a week for 50 weeks. Calculate her pay per hour. Give your answer to 2 decimal places.
Answer:
18.29
Step-by-step explanation:
32000 ÷ 35 ÷ 50 = 18.2857143
Use the distributive property to write the next step in simplifying the numerical expression. Use the asterisk symbol (*) to represent multiplication. Do not multiply factors fully and do not use spaces. 4(x + 9)
Answer:
This is the expression:
4*x+4*9
A new school has x day students and y boarding students.
The fees for a day student are $600 a term.
The fees for a boarding student are $1200 a term.
The school needs at least $720 000 a term.
Show that this information can be written as x + 2y ≥ 1200.
Given:
The fees for a day student are $600 a term.
The fees for a boarding student are $1200 a term.
The school needs at least $720000 a term.
To show:
That the given information can be written as [tex]x + 2y\geq 1200[/tex].
Solution:
Let x be the number of day students and y be the number of boarding students.
The fees for a day student are [tex]\$600[/tex] a term.
So, the fees for [tex]x[/tex] day students are [tex]\$600x[/tex] a term.
The fees for a boarding student are [tex]\$1200[/tex] a term.
The fees for [tex]y[/tex] boarding student are [tex]\$1200y[/tex] a term.
Total fees for [tex]x[/tex] day students and [tex]y[/tex] boarding student is:
[tex]\text{Total fees}=600x+1200y[/tex]
The school needs at least $720000 a term. It means, total fees must be greater than or equal to $720000.
[tex]600x+1200y\geq 720000[/tex]
[tex]600(x+2y)\geq 720000[/tex]
Divide both sides by 600.
[tex]\dfrac{600(x+2y)}{600}\geq \dfrac{720000}{600}[/tex]
[tex]x+2y\geq 1200[/tex]
Hence proved.
2. A rectangle has length 13 and width 10. The length and the width of the rectangle are each
increased by 2. By how much does the area of the rectangle increase? *
50
20
38
35
Annie has set a goal of running at the track three times each week for a total of at least 16 miles per week. On Monday she ran 7.1 miles, and on Wednesday she ran 5.9 miles. If Annie plans to go running again on Friday, what is the minimum number of miles needed to reach her weekly goal?
How do i turn 3/8 into a percent
Factorise this equasion
X^2-5
Answer:
(x - [tex]\sqrt{5}[/tex] )(x + [tex]\sqrt{5}[/tex] )
Step-by-step explanation:
x² - 5 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
x² - 5
= x² - ([tex]\sqrt{5}[/tex] )²
= (x - [tex]\sqrt{5}[/tex] )(x + [tex]\sqrt{5}[/tex] )
Please help me!
Look at this diagram.
Answer:
if you look at carefully the left triangle has two same side. so left-angle of C is 180-130=50 degree 5x+5x+50=180 x=13 degree
Step-by-step explanation:
for right triangle again one angle is 50 degree and other is 6*13-(3)=75 degree so 75+50+(10y+5)=180 degree y=5 degree
Answer:
[tex]x=13\text{ and } y=5[/tex]
Step-by-step explanation:
First, notice that ∠BCD and ∠DCE form a linear pair. Linear pairs sum to 180°. Therefore:
[tex]m\angle BCD + m\angle DCE = 180[/tex]
And since we know that ∠BCD measures 130°:
[tex]m\angle DCE = 180-130=50^\circ[/tex]
And since ∠DCE and ∠BCA are vertical angles:
[tex]\displaystyle \angle DCE \cong \angle BCA[/tex]
Therefore, by definition:
[tex]m\angle DCE = m\angle BCA = 50^\circ[/tex]
Looking at the left triangle, we can see that BC and AC both have one tick mark. This means that they are congruent. Therefore, ΔABC is an isosceles triangle. The two base angles of an isosceles triangle are congruent. Hence:
[tex]m\angle A = m\angle B[/tex]
The interior angles of a triangle must total 180°. So:
[tex]m\angle A + m\angle B +m\angle BCA = 180[/tex]
Substitute in known values:
[tex]m\angle A + m\angle A+ (50)=180[/tex]
Simplify:
[tex]2m\angle A=130[/tex]
Divide both sides by two:
[tex]m\angle A = 65[/tex]
Substitute:
[tex](5x)=65[/tex]
Therefore:
[tex]x=13[/tex]
Similarly, for the triangle on the right, we can write that:
[tex]m\angle D + m\angle E + m\angle DCE = 180[/tex]
Substitute:
[tex](10y+5)+(6x-3)+(50)=180[/tex]
Combine like terms:
[tex]10y+6x+52=180[/tex]
Since we determined that x = 13:
[tex]10y+6(13)+52=180[/tex]
Simplify:
[tex]10y+130=180[/tex]
Therefore:
[tex]10y=50[/tex]
And by dividing both sides by 10:
[tex]y=5[/tex]
Sandra y José son dos amigos que se encuentran en diferentes partes de la ciudad de Lima (Observa el plano), la distancia que los separa en el plano es de 7 cm ellos quisieran saber ¿Cuál es la distancia real en metros que los separa? Sabiendo que el plano ha sido dibujado a escala 1: 20 000.
Respuesta:
1,4 kilometros
Explicación paso a paso:
Dado que :
Distancia que separa a Sandra y José en el mapa = 7cm
Dibujo a escala = 1: 20.000; Esto se puede interpretar en el sentido de que 1 cm en el mapa equivale a 20.000 cm en el suelo.
Por tanto, una distancia de 7 cm en el mapa será:
20.000 * 7 = 140.000 cm en el suelo = distancia real
Por lo tanto, la distancia real = 140.000 cm.
Recordar :
1 cm = 10 ^ -5 km
140000 cm = 1.4 kilometros
Por lo tanto, la distancia real entre Sandra y José es de 1,4 km.
(13+29-2)÷2
show your work
Answer:
[tex](13 + 29 - 2) \div 2 \\ (42 -2 ) \div 2 \\ 40 \div 2 \\ = 20[/tex]
Answer:
(13+29-2)÷240÷220hope it helps.
stay safe healthy and happy..work out the area of a circle with a diameter of 1.8
the median of 2,8,6,10,4,12
Answer: 6
Step-by-step explanation: 6 is a median
Hey there!
To find your mean you have to put the numbers from descending (least/decreasing) to ascending (greater/increasing) order
Median is also understood as the “middle number”
2, 8, 6, 10, 4, 12
= 2, 4, 6, 8, 10, 12
Based on that information, you have in your new data set you have 2 pairs in the middle (6 & 8), so you’ll have to total/average of the number. We have to DIVIDE them by 2 because it’s 2 numbers
6 ends the descending set and 8 starts the ascending set
Median = 6 + 8 / 2
6 + 8 = 14
= 14/2
= 7
Answer: therefore your MEDIAN is most likely 7
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Someone help me please!!!
PLS PLS PLS PLS PLS PLS PLS HELP I DON'T GET IT!!! Write missing monomials to make an identity:
A) (.....+2a)^2=.....+12ab+4*....
B) (3x+.....)^2=....*x^2+.....+49y^2
Answer:
I only have the answer for B
Step-by-step explanation:
This is the answer: 1st blank: 7y
2nd blank: 9
3rd blank: 42xy
Help! This is so hard!
1.4
2.8
3.7 by 10
*Others do by your self*
Step-by-step explanation:
1. 3×4/3= 4
2.⅖×20=8
3.6/5×7/18=7/15
4.10/7×9/5=18/7= 2 4/7. Mixed Fraction
5.4/15×25/8=5/6
6.6×¾= 9/2= 4 1/2. Mixed Fraction
Refer to pictures above
Answer:
6.9
Step-by-step explanation:
Cos ∆ = Adjacent/Hypotenuse
therefore x=12Cos55°
=6.88
=6.9 to the nearest tenth
How would I write this equation? Looking for an answer ASAP.
Answer:
dssadsasdsa
Step-by-step explanation:
ignore this need points for alt
Help pls it’s the last day of summer school
Find the equation of the line through the points (6, -9) and (-2, -1).
find x
(4x - 3) – ( x + 5) = 3(10 - x)
please.....
Answer: 19/3
Step-by-step explanation:
[tex]4x+3-x-5=30-3x\\\\3x-8=30-3x\\\\6x-8=30\\\\6x=38\\\\x=\frac{19}{3}[/tex]
tengo estos problemas de algebra alguien que me atude porfavor !?
Answer:
I think 3 but I am not pretty sure man .
Bonjour,
x est un nombre d'ordinateurs: il est donc un naturel (x € N)
y is the pay cost : y=3*x ==> y€ 3N ⊂ N
Answer last reply : 4.
Write the equation of 2 lines passing through the point (2, 14).
Answer:
Since, the given solution is (2, 14). Therefore, 7x−y=0. Similarly, another equation can be−x+y=−2+14=12. Similarly, another equation can be−2x−y=−2(2)−14=18.
Using the approximation of 5 miles = 8 km
How many km is 12.5 miles?
Answer:
20km is in 12.5miles
Step-by-step explanation:
5miles= 8km
12.5miles=xkm
12.5÷5miles=2.5miles
2.5miles/km
2.5×8km=20km
