Answer
a)
[tex]{(2b - 5)}^{2} - 36 =( 2b - 11)(2b + 1)[/tex]
b)
[tex]9 - {(7 + 3a)}^{2} = (3a - 4)(3a + 11)[/tex]
c)
[tex]( {4 - 11m)}^{2} - 1 =( 3 - 11m )( 5 - 11m )[/tex]
Explanation
a) The given expresion is
[tex] {(2b - 5)}^{2} - 36[/tex]
We rewrite as difference of two squares
[tex]{(2b - 5)}^{2} - 36 = {(2b - 5)}^{2} - {6}^{2} [/tex]
Recall that:
[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
This implies that:
[tex]{(2b - 5)}^{2} - 36 =( {(2b - 5)} -6)(2b - 5 )+ 6)[/tex]
Or
[tex]{(2b - 5)}^{2} - 36 =( 2b - 5-6)(2b - 5 + 6)[/tex]
This simplifies to give:
[tex]{(2b - 5)}^{2} - 36 =( 2b - 11)(2b + 1)[/tex]
b) The second expression is
[tex]9 - {(7 + 3a)}^{2} [/tex]
We rewrite as perfect squares yo get:
[tex]9 - {(7 + 3a)}^{2} = {3}^{2} - {(7 + 3a)}^{2} [/tex]
This gives:
[tex]9 - {(7 + 3a)}^{2} = ({3} - {(7 + 3a)})({3} + {(7 + 3a)})[/tex]
This implies that
[tex]9 - {(7 + 3a)}^{2} = ({3} - 7 + 3a)({3} + 7 + 3a)[/tex]
We simplify to get:
[tex]9 - {(7 + 3a)}^{2} = (3a - 4)(3a + 11)[/tex]
c) The third expression is:
[tex]( {4 - 11m)}^{2} - 1[/tex]
We obtain the difference of two squares as:
[tex]( {4 - 11m)}^{2} - 1 =( ( {4 - 11m)} - 1 )( ( {4 - 11m)} + 1 )[/tex]
We simplify within the parenthesis to get:
[tex]( {4 - 11m)}^{2} - 1 =( 4 - 11m - 1 )( 4 - 11m+ 1 )[/tex]
We simplify further to get;
[tex]( {4 - 11m)}^{2} - 1 =( 3 - 11m )( 5 - 11m )[/tex]
pls help me with #7!! i don’t understand
A six-sided die is rolled. What is the probability that the number rolled will be an even number or a 6?
Answer:
1/2
Step-by-step explanation:
A six sided die has 1, 2, 3, 4, 5, 6. Out of those numbers, 3 of those are even numbers. Meaning you have a 3/6 chance. This 3/6 can be reduced to 1/2.
The senior classes at High School A and High School B planned separate trips to New York City.
The senior class at High School A rented and filled 4 vans and 6 buses with 360 students. High
School B rented and filled 3 vans and 3 buses with 195 students. Every van had the same
number of students in it as did the buses. Find the number of students in each van and in each
bus.
A deli sells ham subs (h) for $6 each and meatball subs (m) for $8 each. The deli sells less than 40 subs on Monday. The total amount for all sales is less than $200. Which system of inequalities models this situation?
The requried system of inequalities that models this situation 6h + 8m < 200 and h + m < 40.
What is inequality?In mathematics, an inequality is a statement that two values or expressions are not equal. An inequality uses one of the comparison symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).
Here,
Let's use the variables h and m to represent the number of ham and meatball subs sold, respectively. Then the system of inequalities that models this situation is:
h + m < 40 (the deli sells less than 40 subs)
6h + 8m < 200 (the total amount for all sales is less than $200)
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The situation is modeled by the system of inequalities h + m < 40 and 6h + 8m < 200, where h represents the number of ham subs and m represents the number of meatball subs sold.
The deli sells two types of subs: ham subs (h) for $6 each and meatball subs (m) for $8 each. The total number of subs sold on Monday is less than 40, and the total sales amount is less than $200. We are looking to model this situation with a system of inequalities.
To represent the scenario, we can use the following system of inequalities:
h + m < 40 (because the deli sells less than 40 subs)
6h + 8m < 200 (because the total amount for all sales is less than $200)
This system captures the constraints on both the number of subs sold and the total sales amount in dollars.
What is the measure of the angle between two consecutive vertices of a
regular decagon (ten-sided shape)? *
Answer:
36 degrees
Step-by-step explanation:
we know that
The measure of the angle between two consecutive vertices of a regular polygon is given by the formula
[tex]\frac{360^o}{n}[/tex]
where
n is the number of sides
In this problem
n=10 (regular decagon)
so
[tex]\frac{360^o}{10}=36^o[/tex]
Calaculate the value of each expression by writing the decimal factor then writing their products as a decimal
Answer: I need to see it to help ya.
Step-by-step explanation:
What hole do I put it in
@jeff4967
Can you please add a picture
Mike hiked to a lake in 3.5 hours at an average rate of 3 2/5
miles per hour. Pedro hiked the same distance at a rate of 3 4/5
miles per hour. How long did it take Pedro to reach the lake? Round to the hundredths place.
Mike hiked 11.75 miles to the lake which took Pedro approximately 3.09 hours to cover at his speed.
Explanation:The subject of this question is mathematics, more specifically the concept of speed, distance, and time. The first step is to calculate the distance that Mike travels. We know that distance equals speed times time, so Mike traveled 3.5 hours * 3 2/5 miles per hour, which equals 11.75 miles. This is the distance to the lake.
Now, we take the same distance and use Pedro's average speed to figure out how long it took him. Using the formula: Time equals Distance divided by Speed, we can calculate Pedro's time as: Time = 11.75 miles / 3 4/5 miles per hour. To simplify the numerical calculation, we turn 3 4/5 into a decimal form, which is 3.8. So, Time equals 11.75 miles / 3.8 miles per hour. This gives us around 3.09 hours, which we would round to 3.09 hours to the hundredths place.
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What is the solution set of inequality 5-|x+4|<=-3
Answer:
[tex]x \geqslant 4 \: or \: x \leqslant - 12[/tex]
Step-by-step explanation:
The given absolute value inequality is:
[tex]5 - |x + 4| \leqslant - 3[/tex]
Let us subtract 5 from both sides to get:
[tex] - |x + 4| \leqslant - 3 - 5[/tex]
We simplify to get:
[tex] - |x + 4| \leqslant - 8[/tex]
We divide through by -1 to get:
[tex]|x + 4| \geqslant 8[/tex]
By the definition of absolute value function,
[tex](x + 4) \geqslant 8 \: or \: - (x + 4) \geqslant 8[/tex]
Divide through the second inequality by -1 and reverse the inequality sign.
[tex](x + 4) \geqslant 8 \: or \: (x + 4) \leqslant - 8[/tex]
Subtract 4 from both sides of both inequalities.
[tex]x \geqslant 8 - 4 \: or \: x \leqslant - 8 - 4[/tex]
[tex]x \geqslant 4 \: or \: x \leqslant - 12[/tex]
A(3,4),B(5,8),C(7,8) are the vertices of ABC, prove that the line passing through the mid point of AB and AC is parallel to BC
[tex]The \ midpoint \ formula \ of \ the \ line \ segment \\ that \ joins \ the \ two \ points \ (x_{1},y_{1}) \ and \ (x_{2},y_{2}) \ is \\ given \ by \ the \ following \ Midpoint \ Formula:\\ \\ Midpoint=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
Let's name the mid point of [tex]AB[/tex] as [tex]c[/tex]Let's name the mid point of [tex]AC[/tex] as [tex]p[/tex]Then:
[tex]c=(\frac{3+5}{2},\frac{4+8}{2}) \\ \\ c=(\frac{8}{2},\frac{12}{2}) \\ \\ c=(4,6) \\ \\ \\ p=(\frac{3+7}{2},\frac{4+8}{2}) \\ \\ p=(\frac{10}{2},\frac{12}{2}) \\ \\ p=(5,6)[/tex]
So the slope of the line that passes through [tex]c \ and \ p[/tex] is:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m_{cp}=\frac{6-6}{5-4}=0[/tex]
And the slope for BC is:
[tex]m_{BC}=\frac{8-8}{7-5}=0[/tex]
As you can see, both slopes are zero, so these are horizontal lines.
fifteen out of the 60 eighth-graders at sebring junior high are on the track team. what percent of the eight-graders are on the track team?
Answer:
25%
Step-by-step explanation:
You have 60 total, 30 on the track team would be 50%, but there is only 15 on the track them, you cut the 50% in half again which gives 25%.
How much would $200 invested at 5% interest compounded monthly be
worth after 9 years? Round your answer to the nearest cent.
A(t) = P(1+(r/n))^(nt)
Answer:
A = $200(1 + .05/12)¹⁰⁸ = $313.37
What is this answer help pls
Answer:
4 * (3 + 2 ) - 6 ÷ 1 = 14
*, +, -, ÷
Step-by-step explanation:
Remember PEMDAS:
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
So, (3 +2) = 5
5 * 4 = 20
20 ÷ 1 = 20
20 - 6 = 14
Hope I helped! C:
Can you please help me on -6x-3(1+5x)=-8(x-4)+4
Answer:
x=-3
Step-by-step explanation:
-6x-3(1+5x)=-8(x-4)+4
Step 1. Distribute:
-6x-3-15x=-8x+32+4
Step 2. Combine like terms:
-21x-3=-8x+36
Step 3. Add to different sides:
-13x=39
Step 4. Solve for x:
x=-3
-
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
Given Equation:
[tex]-6x-3(1+5x)=-8(x-4)+4[/tex]
[tex]-6x-3(1)-3(5x)=-8(x)-8(-4)+4\\\\-6x-3-15x=-8x+32+4\\\\-6x-15x-3=-8x+36\\\\-21x-3=-8x+36\\\\[/tex]
Adding '[tex]8x[/tex]' both the sides:
[tex]-21x+8x-3=-8x+8x+36\\\\-13x-3=36[/tex]
Adding '3' both the side:
[tex]-13x-3+3=36+3\\\\-13x=39\\\\x=\frac{39}{-13} \\\\[/tex]
[tex]x=-3[/tex]
what is the difference of the fractions below? 3/4-3/5
Answer:
[tex] \frac{3}{4} - \frac{3}{5} = \frac{15}{20} - \frac{12}{20} = \frac{3}{20} [/tex]
Jack has x pence,
Jill has 6 pence less than Jack.
Write down, in terms of x, the number of pence Jill has.
Final answer:
The amount of pence Jill has is written as x - 6, where x is the amount of pence Jack has.
Explanation:
If Jack has x pence, and Jill has 6 pence less than Jack, then the number of pence Jill has is x - 6. To express this in terms of x, we simply subtract 6 from x. So if Jack's amount of pence is represented by x, Jill's amount will be represented by the expression x - 6. It's similar to saying that if you have a certain number of something and someone else has 6 less, you would calculate the other person's amount by taking the number you have and subtracting 6 from it.
There are 50 tooth picks in each box jamie buys 4 boxs for her party platter how many toothpicks does jaime
Jamie has 200 tooth picks for her party platter.
Step-by-step explanation:
1 box = 50 tooth picksTotal number of tooth picks in 4 boxes = 4[tex]\times[/tex]50 = 200 tooth picks.Therefore, Jamie has 200 tooth picks for her party platter.
Blueberries cost 2.25 dollars per pound how many would 10 pints of blueberries cost
The cost of 10 pints of blueberries, given their price per pound ($2.25), is $33.75.
Explanation:The subject of this question is the cost of buying blueberries, given their price per pound. To find out the cost of 10 pints of blueberries, you first need to know how many pounds are in a pint. Given that approximately 1.5 pounds of blueberries make up a pint, you then multiply the number of pints, here 10, by 1.5 to get the total weight in pounds. Therefore, 10 pints is equivalent to 15 pounds of blueberries. You then multiply the total weight (15 pounds) by the cost per pound ($2.25) to get the total cost. Hence, 15 pounds multiplied by $2.25 equals $33.75. So, the cost of 10 pints of blueberries would be $33.75.
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Tommy has 6 more than 3 times the amount of money in his bank account than Judy. Judy has $7500 more than a number in her account. How much money does Judy and Tommy have in each their accounts?
Answer: Judy: n+7500
Tommy: 3(n+7500)+6
Step-by-step explanation:
Tanner calculates the volume of a rectangular prism with dimensions Three-fourths ft by 5 ft by One-half ft. His work is shown below. V = l w h. V = Three-fourths (StartFraction 5 Over 1 EndFraction) (one-half) = StartFraction 3 (5) (1) Over (4) (1) (2) EndFraction = StartFraction 15 Over 6 EndFraction = 2 and one-half. What error did Tanner make? He multiplied the numerators incorrectly. He multiplied the denominators incorrectly. He simplified StartFraction 15 Over 6 EndFraction incorrectly. He wrote 5 as a fraction incorrectly.
Answer:
He multiplied the denominators incorrectly
Step-by-step explanation:
we know that
The volume of a rectangular prism is given by the formula
[tex]V=LWH[/tex]
we have
[tex]L=\frac{3}{4}\ ft\\\\W=\frac{5}{1}\ ft\\\\H=\frac{1}{2}\ ft[/tex]
substitute
[tex]V=(\frac{3}{4})(\frac{5}{1})(\frac{1}{2})=\frac{3*5*1}{4*1*2}=\frac{15}{8}\ ft^3[/tex]
therefore
He multiplied the denominators incorrectly
Answer:
B. He multiplied the denominators incorrectly.
Step-by-step explanation:
I did the test myself. Good luck with the rest of your test! Have a great day/night! <3
-x+5x=48
will give brainlist and thx if correct
Answer:
x=12
Step-by-step explanation:
Answer:
x = 12
Step-by-step explanation:
Given
- x + 5x = 48, that is
4x = 48 ( divide both sides by 4 )
x = 12
Which transformation would not create an image and a pre-image that are CONGRUENT figures?
A
A dilation with a scale factor of 1
B
A translation to the right and up.
C
A dilation with a scale factor of 2.
D
A reflection over the x-axis
Answer:
points
Step-by-step explanation:
Answer:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
Step-by-step explanation:
:0
The diagram shows the position of two towns, Alton and Barking.
The bearing of Barking from Alton is bº.
The bearing of Alton from Barking is 6bº.
No
Calculate the 3-figure bearing of Alton from Barking.
Answer:
216°
Step-by-step explanation:
The difference between the bearing from B to A and the bearing from A to B is 180°. Here, the difference between the two bearings is ...
6b -b = 180°
b = 180°/5 = 36°
6b = 6·36° = 216°
The bearing of Alton from Barking is 216°.
This pattern follows the "multiply by 3" rule. What is the next number in the pattern?
3, 9, 27, 81, ________
A. 243
B. 244
C. 288
D. 343
Answer:
A. 243
Step-by-step explanation:
81 multiplied by 3
Answer:243
Step-by-step explanation: count by 3
Jake thinks that a rhombus is not always a parallelogram.Is jake correct?
Answer:
No, a rhombus is a quadrilateral, with four equal-length sides and opposite sides parallel to each other. All rhombuses are parallelograms, but not all parallelograms are rhombuses. The opposite interior angles of rhombuses are always congruent. A parallelogram is just a four sided closed shape where opposite sides are parallel.
I hope this helps!
A rhombus is always a parallelogram, and its diagonals are perpendicular. Jake is incorrect in his assertion.
A rhombus is indeed always a parallelogram because a parallelogram is a quadrilateral with opposite sides parallel and a rhombus fits this definition.
To show that the diagonals of a rhombus are perpendicular, we use the fact that the scalar product of perpendicular vectors is zero. By representing the diagonals as vectors, we can demonstrate their perpendicularity.
Therefore, Jake is incorrect in thinking that a rhombus is not always a parallelogram - it is a specific type of parallelogram with additional properties.
Which is the simplified form of the expression (6-2.657-3?
Answer: 0.343
Step-by-step explanation:
6-2.657=3.343 subtract 3 you get 0.343
If a study determines the difference in average salary for subpopulations of people with blue eyes and people with brown eyes is NOT significant, then the populations of blue-eyed people and brown-eyed people are ________ different salaries.
unlikely to have
very likely to have
guaranteed to have
guaranteed to not have
Answer:
Unlikely to have.
Step-by-step explanation:
The populations of blue-eyed people and brown-eyed people are unlikely to have different salaries.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Therefore, The populations of blue-eyed people and brown-eyed people are unlikely to have different salaries.
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the distance to the meeting place is 1047 miles if his car gets 29 mpg how many gallons of gas will he need
Answer:
36.1g
Step-by-step explanation:
29mi ..... 1 g
1047mi....x
x=1047×1/29=36.1g
Answer:
36.1 Gallons of gas
Step-by-step explanation:
x= gallons of gas
1047=29x
1047/29=x
36.1=x
36.1 gallons of gas
.Jenny is wrapping a present for her friend's birthday party. The box is 4 in. by 5 in. by 7 in. How much wrapping paper will Jenny need to wrap the present? Enter your answer in the box.
Jenny need 166 square inches of wrapping paper to wrap the present.
Solution:
Length of the box = 4 in
Breadth of the box = 5 in
Height of the box = 7 in
Surface area of the box = 2(lb + bh + lh)
= 2( 4 × 5 + 5 × 7 + 4 × 7)
= 2(20 + 35 + 28)
= 2(83)
Surface area of the box = 166 in²
Hence Jenny need 166 square inches of wrapping paper to wrap the present.
Answer:
166
Step-by-step explanation:
What is 11/15= 8/15-w
Answer: w= 1/5
Step-by-step explanation:
11/15=8/15 -w
-W= 8/15 -11/15
-w= 8-11/15 =-3/15
-w=-3/15
w=3/15= 1/5