Answer:
Distributive property
Step-by-step explanation:
6x – 3x + 9y + 4 + 11 =
First, we combine like terms.
= 3x + 9y + 15
Now we use the distributive property to factor out a common factor.
= 3(x + 3y + 5)
The property can you use to show that 6x – 3x + 9y + 4 + 11 is equivalent to 3(x + 3y + 5) is Distributive property
What is Distributive property
To show that 6x - 3x + 9y + 4 + 11 is equivalent to 3(x + 3y + 5), we can use the distributive property of multiplication over addition.
The distributive property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
6x – 3x + 9y + 4 + 11 =
First, we combine like terms.
= 3x + 9y + 15
Now we use the distributive property to factor out a common factor.
= 3(x + 3y + 5)
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QUESTION 2
Solve for X.
3x + 4 + 2 = 15
Answer:
x=3
Step-by-step explanation:
3x+6 =15
x=3
Answer:
3
Step-by-step explanation:
3x + 6 = 15
3x = 15 - 6 = 9
x = 9/3 = 3
Which of the following is the first step when copying a line segment to construct a new line segment?
a. draw a line segment
b. use a straight edge to connect the point not on the line segment to a point in the arc
c. plot a point not on the original line segment
d. draw an arc
Answer:
The correct option is;
c. Plot a point not on the original line segment
Step-by-step explanation:
The steps to copy a line segment are;
1) Plot a point that will be an endpoint of the new line segment
2) With the compass pin at the beginning of the original line segment, open the compass width to the end of the original line segment
3) With the adjusted compass width from the above step place the compass pin at the plotted point of the new line segment and draw an arc in the region the new line segment is to be located
4) Select a point on the arc where the other end of the new line will be
5) From the selected point from the above step, draw a line to the point plotted as the beginning of the new line segment
6) The length of the line drawn above is the same as the length of the original line segment.
Solve |2x+3/4 |=5 1/2 Please help!!!!
Answer:
=2x+3/4=5.50
x=19/8 or 2 3/8
hope this helps
Step-by-step explanation:
Will give 5 stars, 10 points and maybe brainiest
Answer:
5.25
Step-by-step explanation:
"The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average"
in that case
1.6, 3.2, 3.6, 4.6 , 4.7 , 5.2 , 5.3, 5.4 , 6.1 , 7.8 , 9.0 , 9.5 ,
1st 2nd 3rd 4th 5th 6th 7th . 8th . 9th 10th 11th 12th
as you can seem 5.2 and 5.3 are both in the middle. that means you take the average of those two numbers. so 5.25
Answer:
The median is 5.25
Step-by-step explanation:
Median is found in the middle of numbers.
First you arrange the number from descending to ascending order:
1.6, 3.2, 3.6, 4.6, 4.7, 5.2, 5.3, 5.4, 6.1, 7.8, 9.0, 9.5
There are 12 numbers.
Then find the number that is in the center. In this case, 5.2 and 5.3 are the numbers in the center. You add them together and divide them by 2:
5.2+5.3 = 10.5/2 = 5.25
The median is 5.25
URGENT PLZ!! Drag the correct transformation into the box to match the definition. [BLANK]... moves points across a specified line so that the line is the perpendicular bisector of each line segment connecting corresponding preimage and image points. Translation Rotation Reflection
Answer:
Reflection.
Step-by-step explanation:
Reflection moves points across a specified line so that the line is the perpendicular bisector of each line segment connecting corresponding pre-image and image points.
On the other hand, "Translation" moves points the same distance along lines that are parallel to each other while "Rotation" moves points along concentric circles and through the same angle of rotation.
At an angle of 90°, a line of reflection intersects the line segments connecting corresponding points of the pre-image under a reflection.
Basically, a reflection allows us to flip an object or figure across a line, point or plane without any change in its shape or size.
Hence, to reflect an object or a figure such as a triangle simply means that its mirror image would be produced with respect to a line; this line is generally referred to as the line of reflection.
During summer vacation, Wesley read, on average, 20 pages per night. Now that he has returned to school, he is averaging 65% fewer. How many pages per night is Wesley averaging now?
Answer:
He is currently reading 7 pages per night
Step-by-step explanation:
We can simply the question a little by finding what percent of the original Wesley is currently reading. Instead of saying 65% fewer, we can say he is reading 35% of what he used to read
Now we need to set up a proportion to solve the problem.
35% of 20
35/100=x/20
Cross multiply
35x20=700
700/100=7
He is currently reading 7 pages per night
A professor said 4/5 of his students passed the final examination. If 60 students took the exam, how many passed?
Answer:
Hey there!
We have that 4/5, or 80% of the 60 students passed the exam.
Thus, we have:
0.8(60)=48
48 students passed the exam.
Let me know if this helps :)
Given: D is the midpoint of AB; E is the midpoint of AC.
Prove: DE BC
y
Complete the missing parts of the paragraph proof.
Proof:
To prove that DE and BC are parallel, we need to show
that they have the same slope.
slope of DE = 12-11=_C-C
X2 - x1 a + b - b
A(2b, 2c)
D(b, c)
Ela + bc)
slope of BC =
B(0,0)
C(2a, 0)
Therefore, because
DE 1 BC.
Answer:
The lines DE and BC have the same slope, therefore the two lines, DE and BC, are parallel
Step-by-step explanation:
To prove that DE is parallel to BC, we have;
The slope, m of the lines DE and BC are found from the following equation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where;
(x₁, y₁) and (x₂, y₂) = (b, c) and (a + b + c) for DE, we have;
[tex]Slope, \, m =\dfrac{c - c}{a + b-b} = 0[/tex]
Where we have (x₁, y₁) and (x₂, y₂) = (0, 0) and (2a, 0) for BC, we have;
[tex]Slope, \, m =\dfrac{0 - 0}{2a-0} = 0[/tex]
Therefore, because the lines DE and BC have the same slope, the two lines DE and BC are parallel.
Answer:
slope of DE = 0
slope Bc = 0
slopes are =
Step-by-step explanation:
Simplify the expression 4x-8-2-9x
Answer:
Step-by-step explanation:
4
Answer:
-5x-10
Step-by-step explanation:
first rearrange the expression:
4x-9x-8-2
next combine like terms
-5x-10
thats your answer! hope this helps! :)
PLEASE HELP ME !!!!!!!!!!
if the distance of load from hinge and spring balance are 35 cm and 15 cm respectively. What is the load weight used if the applied force is 4N ?
Answer:
The load weight is 2.29 N
Step-by-step explanation:
We note that at equilibrium, the sum of the moment and the sum of forces about a point is zero, therefore, we have;
∑M =0
∑F = 0
The parameters given are;
The distance of the load from the hinge = 35 cm
The distance of the load from the spring balance = 15 cm
The applied force on the spring balance = 4 N↑
The direction of the applied force on the spring balance = Upwards
Let the weight of the load = W↓
The direction of the weight of the load = Downwards
We use downward negative and upward positive coefficients for the forces
We take moment about the hinge as follows;
Sum of moments equals zero gives;
4 × (35 - 15) - W × 35 = 0
∴ 4 × (35 - 15) = W × 35
4 × 20 = W × 35
W = 4 × 20/35 = 2.29 N
The weight of the load = 2.29 N.
Answer:
The load weight is 2.29 N
hope it helps
I need help with 6 and 7
Answer:
Step-by-step explanation:
6):
Take the small right triangle with the sides 25 and 7.
☆ The Pythagorian theorem ☆
Let x be the third side.
● 25^2 = x^2 + 7^2
Substract 7^2 from both sides
● 25^2 -7^2 = x^2 +7^2 -7^2
● x^2 = 25^2 -7^2
● x^2 = 576
● x = 24 inches
The third that we find is the half of the side of the square.
Multiply it by 2 and get the side of the square.
● 24 × 2 = 48 inches
The perimeter of the square is the side times 4.
● P = 48 × 4
● P = 192 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
7):
Both triangles are righr and they have a khown angle.
Start with the small one and calculte the third angle.
The sum of a triangle angles is 180°
Let B be the third angle.
● B = 180-(90+51) = 39°
That's equal to the second angle of the second's triangle.
So it's an AA similarity.
So:
● x/24 = 7/15
● x = (7/15)×24
● x = 11.2
Jack bought a car for $50,000. He spent $5000 on repairs. He sold the car at a profit of $5000. At what price did he sell the car.
Answer:$60,000
Step-by-step explanation:
If he bought it for $50,000 and then spent $5,000 on repairs then he spent a total of $55,000. For a profit of $5,000 he would need to sell it for $60,000 Because
60,000 - 55,000 = 5,000
Help me please. I need it
Answer/Step-by-step explanation:
Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], to solve each problem.
1. Distance between A(0, 0) and B(-5, 7):
[tex] (0, 0) = (x_1, y_1) [/tex]
[tex] (-5, 7) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(-5 - 0)^2 + (7 - 0)^2} = \sqrt{(-5)^2 + (7)^2} = \sqrt{25 + 49} [/tex]
[tex] AB = \sqrt{74} [/tex]
2. Distance between A(-3, 1) and B(-11, 1):
[tex] (-3, 1) = (x_1, y_1) [/tex]
[tex] (-11, 1) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(-11 - (-3))^2 + (1 - 1)^2} = \sqrt{(-8)^2 + (0)^2} = \sqrt{64 + 0} [/tex]
[tex] AB = \sqrt{64} = 8 [/tex]
3. Distance between A(-3, -2) and B(5, 6):
[tex] (-3, -2) = (x_1, y_1) [/tex]
[tex] (5, 6) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(5 - (-3))^2 + (6 - (-2))^2} = \sqrt{(8)^2 + (8)^2} = \sqrt{64 + 64} [/tex]
[tex] AB = \sqrt{128} = \sqrt{64*2} [/tex]
[tex] AB = 8\sqrt{2} [/tex]
4. Distance between A(-2, -5) and B(-6, 1):
[tex] (-2, -5) = (x_1, y_1) [/tex]
[tex] (-6, 1) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(-6 - (-2))^2 + (1 - (-5))^2} = \sqrt{(-4)^2 + (6)^2} = \sqrt{16 + 36} [/tex]
[tex] AB = \sqrt{52} [/tex]
None of the choices are correct
Determine what type of model best fits the given stituation. Water leaking from a local reservoir at the rate of 500 gallons per hour.
Answer:
Well, in the local reservoir we have an initial amount of water A.
And per hour, the amount of water in the reservoir decreases by 500 gals.
So after t hours, the amount of water in the reservoir is:
W = A - 500gal*t
This is a linear equation, so the model that fits best in the given situation is a linear model.
Where the only thing that you need to take in mind, is that the domain of this model is restricted:
This is because we can not have a negative amount of water in the reservoir, so the maximum value of t accepted is:
W = 0 = A - 500gal*t
t = A/500 hours
So the domain of this linear relation is:
t ∈ {0h, A/500 }
Answer: lin
Step-by-step explanation:
Yazmin is investigating the growth of plants under different conditions for her science class. Once the little sprouts were 1 inch tall, she found that they were growing at a steady rate of about 1/2 inch per day. Write a function that helps Yazmin to see how many days it takes for the plants to reach a given height. Let h = height of the plant (inches), and let d = number of days (days)
Answer:
0.5+d=h
Step-by-step explanation:
If a plant is growing at a steady rate of 0.5 inches (h) in 1 day (d) then after one day your equation should look like: 0.5+1 which would give you the height of the plant in inches. If this is true, then you would keep the height per day the same (0.5) substitute the 1 for d (one day); then your equation would look like this: 0.5+d which would give you the height of the plant in inches (h).
0.5+d=h
The function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.
What is a function?Functions were originally the idealization of how a varying quantity depends on another quantity.
Now it is given that,
Height of sprout = 1 inch
Growth per day = 1/2 inch
Let h = height of the plant (inches), and let d = number of days (days)
∵ Growth per day = 1/2 inch
So, Growth of plant in d days = d * 1/2 = d/2 = 0.5d
Thus, height of the plant, h = 1 + Growth of plant in d days
⇒ h = 1 + 0.5d
Thus, the function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.
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The sum of three consecutive multiples of 7 is 777 find these multiples
let the consecutive multiples be 7(n-1) , 7n and 7(n+1)
so 7(n-1)+7n+7(n+1)=777
or 3n=111,
n=37
252,259,266
[tex]7n+7n+7+7n+14=777\\21n=756\\n=36\\\\7n=252\\7n+7=259\\7n+14=266[/tex]
252,259,266
mrs tay baked some tarts. 25% of the tarts are pineapple tarts and the rest are strawberry tarts. She baked 90 more strawberry tarts than pineapple tarts. How many strawberry tarts did she bake?
Step-by-step explanation:
100 - 25 = 75
75 + 90 = 165
= 165 strawberry .
18. The outside temperature changed - 14 °F over 4 hours. If the temperature changed the same
amount each hour, what was the change in temperature each hour?
The temperature change each hour was
°F.
Answer:
-3.5 °F
Step-by-step explanation:
If the temperature change was the same each hour, we can find the change each hour by dividing -14 by 4.
-14/4= -3.5
= -3.5 °F
What is the correct prime factorization of 24
2^3 * 3^1
Go step by step. 24 = 2 x 12. 12 = 2 x 6. 6 = 2 x 3. We can't factor any more.
Therefore, we have 12 = 2 x 6, and since 6 = 2 x 3, we get 12 = 2 x 2 x 3.
Then 24 = 2 x 12, and 12 = 2 x 2 x 3, so 24 = 2 x 2 x 2 x 3.
There are 3 2's and 1 3's, so it's 2^3 * 3^1.
Hope that helped,
-sirswagger21
Answer:
24=2*12=2*6=2*3
Step-by-step explanation:
I could not draw the tree diagram
to do it you take a prime number it is divisible by and a composite number it is divisible by and you prime factorise the composite number and repeat until you get prime numbers
Simplify 4 to the 2nd power times 4 to the eighth power 
A. 4 to the 16th power
B. 4 to the 10 power
C. 16 to the 16 power
D. 16 to the 10 power
Please help ASAP!!!!!!!!
Answer:
4 to the power of 10.
Step-by-step explanation:
A rule is that x to the power of y + x to the power z of must equal x to the power of z+y.
Answer:
Option B
Step-by-step explanation:
4²×4^8
4^(2+8)
4^10
4 to the 10th power
BRAINLIEST!!
Factor completely 16x2 + 40x + 25. (4x − 5)(4x − 5) (2x − 5)(2x − 5) (2x + 5)(2x + 5) (4x + 5)(4x + 5) And this one please!
Select the polynomial that is a perfect square trinomial. 36x2 − 4x + 16 16x2 − 8x + 36 25x2 + 9x + 4 4x2 + 20x + 25
Answer:
(4x + 5)²
4x² + 20x + 25
Step-by-step explanation:
Step 1: Factor 16x² + 40x + 25
(4x + __)(4x + __)
What multiplies to 25 and adds up to 40 with 4 multiplied as coefficient?
(4x + 5)(4x + 5) or (4x + 5)²
Step 2: Factor perfect square trinomial
36x² - 4x + 16 --> 4(9x² - x + 4) No
16x² - 8x + 36 --> 4(4x² - 2x + 9) No
25x² +9x + 4 --> 25x² + 9x + 4 No
4x² + 20x + 25 --> (2x + 5)(2x + 5) or (2x + 5)² Yes
Answer:
(4x + 5)(4x + 5).
4x^2 + 20x + 25.
Step-by-step explanation:
16x^2 + 40x + 25
= (4x + 5)(4x + 5)
= (4x + 5)^2.
36x^2 − 4x + 16: To be a perfect square trinomial, the factors would have to be (6x + 4) or (6x - 4). Since the value of b is only -4, this is NOT a perfect square trinomial.
16x^2 − 8x + 36: To be a perfect square, factors would have to be (4x + 6) or (4x - 6). Since the value of b is only -4, this is NOT a perfect square.
25x^2 + 9x + 4: To be a perfect square, factors have to be (5x + 2) or (5x - 2). Since b is positive, factors would be (5x + 2)(5x + 2) = 25x^2 + 20x + 4. 20x is not equal to 9x, so this is NOT a perfect square.
4x^2 + 20x + 25: Perfect square would have to have factors (2x + 5) or (2x - 5). b is positive, so factors are (2x + 5)(2x + 5) = 4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25. This IS a perfect square!
Hope this helps!
Z= -3 - 8i Find the angle θtheta (in degrees) that z makes in the complex plane. Round your answer, if necessary, to the nearest tenth. Express θtheta between -180 180 degrees.
The angle is negative to indicate a clockwise rotation.
======================================================
Explanation:
Z = -3 - 8i is in the form z = a+bi with a = -3 and b = -8
In the complex plane the point (a,b) represents the location of z = a+bi
Define three points with the locations
P = (a,b) = (-3,8)
Q = (0,0)
R = (10,0)
The angle PQR is the angle theta we're looking for. This is the angle formed between the positive x axis and the terminal point (a,b)
Use the arctan function to find theta
theta = arctan(b/a)
theta = arctan( (-8)/(-3) )
theta = 69.4439547804166
theta = 69.4 degrees approximately
Note how this theta value is in quadrant Q1, but (a,b) = (-3, -8) is in Q3
So we need to add 180 degrees to adjust this error.
69.4+180 = 249.4
and we're now in the proper quadrant. We would stop here if your teacher did not put the restriction that theta must be between -180 and 180.
However, this restriction is in place so we need to find the difference of 360 and 249.4 to get 360-249.4 = 110.6
-----------
The angle 249.4 degrees is coterminal to -110.6 degrees. They both point in the same direction.
angle 249.4 degrees is found by starting pointing directly east and rotating 249.4 degrees counterclockwise
angle -110.6 degrees is found by starting directly east and rotating 110.6 degrees clockwise.
Check out the diagram below. I used GeoGebra to make the diagram.
At what rate per annum will N250 amount to N330 in 4 years.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{8 \: \% \: }}}}}[/tex]Step-by-step explanation:
Given,
Principal ( P ) = N 250
Time ( T ) = 4 years
Amount ( A ) =N 330
Rate ( R ) = ?
First, finding the Interest :
According to definition of Amount ,
Amount = Principal + Interest
plug the values
⇒[tex] \sf{330 = 250 + I}[/tex]
Move i to left hand side and change it's sign
⇒[tex] \sf{ - I = 250 - 330}[/tex]
Calculate
⇒[tex] \sf{ - I = - 80}[/tex]
Change the signs of the both equation
⇒[tex] \sf{I = 80 }[/tex]
Interest = 80
Finding the rate :
Simple Interest = [tex] \sf{ \frac{PTR}{100} }[/tex]
plug the values
⇒[tex] \sf{80 = \frac{250 \times 4 \times R}{100} }[/tex]
Multiply the numbers
⇒[tex] \sf{80 = \: \frac{1000 \: R}{100} }[/tex]
Apply cross product property
⇒[tex] \sf{1000R = 100 \times 80}[/tex]
Multiply the numbers
⇒[tex] \sf{1000R = 8000}[/tex]
Divide both sides of the equation by 1000
⇒[tex] \sf{ \frac{1000R}{1000} = \frac{8000}{1000} }[/tex]
Calculate
⇒[tex] \sf{R = 8 \: \% \: }[/tex]
Thus, Rate = 8 %
-------------------------------------------------------------------------
Let's learn about Principal , Interest , Time , Rate and Amount :
Principal = The money which is borrowed or deposited is called principal.Interest = The additional amount of money which is paid by borrower to the lender is called interest.Time = The duration of time for which principal us deposited or borrowed is termed as time period.Rate = The condition under which the insterest is charged is called rate.Amount = The sum of principal and Interest is called an amount.Hope I helped!
Best regards!!
Find the product.
7,352 x 48 =
A. 7,400
B. 88,224
C. 352,886
D. 352,896
Answer:
D
Step-by-step explanation:
7 3 5 2
x 4 8
-----------
352,896
Hey There!!~
Because, First thing to do is mulpity 2 x 8 = 16 so, You bring the 6 and bring up the 1. Then, 5 x 8 = 40 + 1 = 41. So, we bring down the 1 and bring up the 4. Then, 3 x 8 = 24 + 4 = 28. Then, The same thing bring down the 8 and let the 2 stay up there. 7 x 8 = 56 + 2 = 58. So, Right now the answer is 58, 816. So, We just completed the first step, But we're are not done yet... 4 x 2 = 8. Then, 5 x 4 = 20. So, we bring down the 0 and bring up the 2. Then, 4 x 3 = 12 + 2 = 14. So, The 4 stay down and 1 goes up. Then, 7 x 4 = 28 + 1 = 29. So, we just completed the second step. The last step is to add 58, 816 + 29, 408 = 352, 896. Hope This helps!!
1. In a right triangle, the lengths of the legs are a and b. Find the length of a hypotenuse, if: a=1, b=1; 2. In a right triangle, the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg, if: c=5, a=3;
Answer:
1. [tex]c = \sqrt{2}[/tex].
2. b = 4.
Step-by-step explanation:
To solve these two questions, keep the Pythagorean Theorem in mind: [tex]a^2 + b^2 = c^2[/tex]. Also remember that measurements cannot be negative, so we will disregard the negative answers.
1. a = 1, and b = 1. c = ?
[tex]1^2 + 1^2 = c^2[/tex]
[tex]1 + 1 = c^2\\[/tex]
[tex]c^2 = 1 + 1\\c^2 = 2\\\sqrt{c^2} = \sqrt{2}\\c = \sqrt{2}[/tex]
2. a = 3, c = 5. b = ?
[tex]3^2 + b^2 = 5^2\\9 + b^2 = 25\\b^2 = 16\\\sqrt{b^2} = \sqrt{16}\\b = 4[/tex]
Hope this helps!
Determine whether or not the given pair of triangles is similar and state how you know.
Is ΔGHI ~ ΔJKI?
Mark all that apply.
Answer:
by SAS. YesStep-by-step explanation:
∠HIG and ∠JIK are vertical angles, so:
m∠HIG = m∠JIK
[tex]\dfrac{GI}{IJ}=\dfrac{7.5}3=2.5\\\\\dfrac{HI}{IK}=\dfrac{2.5}1=2.5[/tex]
[tex]\left\{\dfrac{GI}{IJ}=\dfrac{HI}{IK}\quad\ \wedge\quad m\angle HIG=m\angle JIK\right\}\implies \triangle HIG\sim\triangle JIK\ \ by\ SAS[/tex]
Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
Answer:
y = 0.8x + 10
Step-by-step explanation:
From the given graph,
Graphed line passes through two points (0, 10) and (50, 50)
Let the equation of the given line is,
y = mx + b
Where m = slope of the line
b = y-intercept
Since slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{50-10}{50-0}[/tex]
m = [tex]\frac{4}{5}[/tex] = 0.8
y-intercept of the line 'b' = 10
Therefore, equation of the line of best fit will be,
y = 0.8x + 10
6 times the sum of a number and four is forty- two
Answer:
3
Step-by-step explanation:
6(x+4)=42
x=3
check:
6*(3+4)=42
I REALLY NEED HELP ASAP WITH THESE 2 QUESTIONS!!!!!!!!!
Answer:
4. Meena- 3
Jerry- 6
5a. 5
5b. 6
Step-by-step explanation:
We can use the distance formula to solve all of these.
[tex]\sqrt{(x_{2} } -x_{1} )^2+(y_{2} -y_{1} )^2[/tex]
Plug the numbers in and make sure you understand how i got these answers :) Let me know if you see anything wrong about it, and i will try and fix it.
Always true, sometimes true, never true?
(x-1)(1+3)>0, x<1
