The product of the expressions 3a + 5 and 6a - 2 is 18a² + 24a - 10. The distributive property is used to multiply each term in the first expression by each term in the second.
The product of the two expressions 3a + 5 and 2a + 4a - 2 can be found using the distributive property. First, combine like terms in the second expression to simplify it to 6a - 2. Now, to find the product, multiply each term in the first expression by each term in the simplified second expression:
Multiply 3a by 6a to get 18a².
Multiply 3a by -2 to get -6a.
Multiply 5 by 6a to get 30a.
Multiply 5 by -2 to get -10.
Combining these products gives you the final answer: 18a² + 24a - 10.
Triangle ABC has these side measurements: AB = 17 BC = 18 AC = 21 Order the angles of the triangle from largest measure to smallest measure.
Answer:
B, A, C
Step-by-step explanation:
B has the largest angle of 73.677, A has the second largest of 55.345, and C has the smallest angle of 50.977
The order of the angles of the triangle from largest measure to smallest measure. will be ∠B, ∠A, and ∠C.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
Angle obtained from the triangle are;
∠B=73.6°
∠A= 55.345°
∠C =50.977°
As a result, the arrangement of the triangle's angles is from biggest to smallest measure. ∠B, ∠A, and ∠C will be the results.
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if axb=0, then a=0 or b=0
3x=0
Answer:
The given equation is
ax b= 0,
As we see that, it is a linear equation in one variable containing two constant.
So , a≠ 0 [then equation has no meaning.If a=0 , then [tex]0 \times x=0[/tex], which is meaningless]. ∴ a=0 is incorrect.
Similarly , b≠ 0 [ Reason same as above]. ∴b=0 is incorrect.
⇒3 x=0
⇒x=0 is the correct response.
Let me explain by this giving an example
⇒5 x=0
⇒ x=0 but 5≠0
So, x=0 or 3 x=0 is correct response.
15 more than a number b
what is 0.386 0.3 0.683 0.836 from order to greatest to least
0.836, 0.683, 0.386, and then 0.3
Here's the order:
0.300 0.386 0.683 0.836
Nancy wrote the greatest number that can be made using each of these digits exactly once
Plz help me I will show you guys the pic for you guys can help me.....
Answer:
the highest number Nancy made was 985,431
Step-by-step explanation:
if you put Nancy greatest numbers in order from greatest to least it would come out to 9 8 5 4 3 1
Is the equations true, false, open or none of the above?
10x + 5 = 8x + 2
10x + 5 = 8x + 2
Subtract 5 from both sides.
10x = 8x - 3
Subtract 8x from both sides.
2x = -3
Subtract both sides by 2.
x = -1.5
Because we are able to get a value for x, we know that the equation is true, as we can plug the value of x back into the original equation to verify.
10(-1.5) + 5 = 8(-1.5) + 2
-15 + 5 = -12 + 2
-10 = -10 √ this equation is true.
For the equation 10x + 5 = 8x + 2, the statement is true.
The given equation is 10x + 5 = 8x + 2.
The first thing to do is to subtract 5 from both sides.
10x + 5 - 5 = 8x + 2 - 5
10x = 8x - 3
Then, we'll subtract 8x and this will be:
10x - 8x = -3
2x = -3
Divide both side by 2
2x/2 = -3/2
x = -1.5
10x + 5 = 8x + 2,
10(-1.5) + 5 = 8(-1.5) + 2
-15 + 5 = -12 + 2
10 = 10
Therefore, the statement is true
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What is the graph of the inequality
The inequality "x ≤ 5" means that the value of x is going to be less than or equal to the quantity 5.
Because of this, the correct answer on the graph would be a filled in dot (meaning starting at that quantity, rather than one less or one more than), and an arrow pointing to the left.
The value of x could be 5, 4, 3, and so on. Any quantity lower than, and including, 5 is a possible answer for the value of x.
The correct answer is the 2nd option.
Answer:
Graph represented by option B is the correct choice.
Step-by-step explanation:
We have been given an inequality [tex]x\leq 5[/tex]. We are asked to find the graph of the given inequality.
Our given inequality tells that solution is any value of x less than or equal to 5.
Since our given inequality has less than or equal to sign, then the number line will have a solid dot at [tex]x=5[/tex].
Since the values of x are less than or equal to 5, so the solution of the inequality will be numbers less than 5.
Since the numbers on the left side of a number line are less than number on right side, therefore, the graph represented by option B is the correct choice.
Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2) .
Use the polygon tool to graph the dilated figure.
Answer:
The points of the dilated figure would be at (-2, 10), (2, 6), and (-8, 4); an image of the figure is attached.
Step-by-step explanation:
First we translate the center of dilation and figure so the origin becomes the center of dilation.
Since the point (2, 2) is our center of dilation, we must translate it left 2 and down 2 to make the origin the center; this means we map every point
(x, y)→(x-2, y-2)
The scale factor of 2 means that each point will be multiplied by 2; this gives us the rule
(x, y)→(2x-4, 2y-4)
Lastly we will translate the figure right 2 and up 2 to move it back to its original position; this gives us the rule
(x,y)→(2x-4+2, 2y-4+2) = (2x-2, 2y-2)
The first point in the original figure, at the top, is (0, 6). Applying the transformation gives us
(0, 6)→(2*0-2, 2*6-2) = (0-2, 12-2) = (-2, 10)
The point on the right of the pre-image is (2, 4). Applying the transformation rule gives us
(2, 4)→(2*2-2, 2*4-2) = (4-2, 8-2) = (2, 6)
The point on the left of the pre-image is at (-3, 3). Applying the transformation rule, we have
(-3, 3)→(-3*2-2, 3*2-2) = (-6-2, 6-2) = (-8, 4)
Answer:
Here is the correct answer
Step-by-step explanation:
I hope this helps!
Antoine has a carnival booth at the school fair where students randomly select a ping pong ball from a can. He wants to place 5 red ping pong balls an n blue ping pong balls in the can. He also wants the probability of randomly choosing a blue ping pong ball to be 3/5.
Part A:
Write an equation that can be used to model this situation.
Part B:
Solve the equation and interpret the solution in terms of the context, determining if the solution is viable.
Answer:
(a)[tex]5n=3n+15[/tex]
(b)[tex]n=7.5[/tex]
Solution is not viable
Step-by-step explanation:
(a)
Total number of red ping pong balls[tex]=5[/tex]
Total number of red ping pong balls[tex]=n[/tex]
Now, probability of an event [tex]=\frac{Number of favourable events}{Total number of events}[/tex]
Then, theprobability of randomly choosing a blue ping pong ball is
[tex]=\frac{n}{n+5}[/tex]
Given that this probability is[tex]=\frac{3}{5}[/tex]
Thus, we have that,
[tex]\frac{n}{n+5}= \frac{3}{5}\\ 5n=3(n+5)\\5n=3n+15[/tex]
(b)
Solving, the above equation,
[tex]5n=3n+15\\2n=15\\n=7.5[/tex]
This solution is not viable as, number of ping pong ball must be an integer and not a decimal number.
Three girls made necklaces using beads. Jamie used 5 times as many beads as Carmen did. Allison used 8 more than 3 times as many beads as Carmen did. The total number of beads used by the three girls was 143. Which equation can be solved to find the number of beads (n) that Carmen used to make her necklace?
Amos has 12 action,15 comedy,and 9 drama DVDs .Find the ratios of action DVDs to the number of DVDs
Answer:
derp
Step-by-step explanation:
derp lol
Which statement best completes the sentence below? If the measure of /_4 is 70^o, then the measure of /_8 is _________________. A 110^o because /_4 and /_8 are supplementary angles. B 70^o because /_4 and /_8 are alternate exterior angles. C 110^o because /_4 and /_8 are corresponding angles. D 70^o because /_4 and /_8 are corresponding angles.
Answer:
As given, measure of angle 4 is 70°
Then what would be the measure of ∠8.
Following cases comes into consideration
1. If ∠4 and ∠8 are supplementary angles i.e lie on same side of Transversal, then
∠4 + ∠8=180°
⇒70°+∠8=180° [∠4=70°]
⇒∠8=180°-70°
⇒∠8=110°
2nd possibility
But if these two angles i.e ∠4 and ∠8 forms a linear pair.Then
⇒ ∠4 + ∠8=180°
⇒70°+∠8=180° [∠4=70°]
⇒∠8=180°-70°
⇒∠8=110°
3rd possibility
If ∠4 and ∠8 are alternate exterior angles.
then, ∠4 = ∠8=70°
4th possibility
If If ∠4 and ∠8 are corresponding angles.
then, ∠4 = ∠8=70°
Out of four options given Option A[ 110° because ∠4 and ∠8 are supplementary angles], Option B[70° because ∠4 and ∠8 are alternate exterior angles.] and Option D[70° because ∠4 and ∠8 are corresponding angles.] are Correct.
$40.50 that two friends earned mowing a lawn. They want to share the money equally.
Hello AskMeBosh...again
Since we know that there are 2 friends, and 40.50 is going to be split
We would do 40.50 divided by 2
40.50/2
= 20.25
:)
can someone plz answer this . its due tomorrow
Circumference of Earth = Pi* Diameter= 3.1415926536X7926Miles=24,900.3Miles
the height h increased by 6 inches
"Height h increased by 6" can be displayed as:
h + 6
Plz help me I don’t get is show your work
Commission earned is 6% at a show store; original cost of shoes: $125
125 x .06 = 7.5
6% of $125 is $7.50
What is the approximate value of 200,000 x 200
it would be 40000000 because there there are 7 zeroes and then you and then you multiply the two twos together and then put it in the front.
Answer:
the approximate value of 200,000 x 200 is 40,000,000
Step-by-step explanation:
the approximate value of 200,000 x 200
To find the approximate value we multiply 200,000 times 200
WE have two zeros in 200. so when we multiply we add two zeros
now we multiply the numbers
2 times 2 gives us 4
[tex]200,000 \ times \ 200= 40,000,000[/tex]
So the approximate value of 200,000 x 200 is 40,000,000
Monday's dog Rex. Weighed 80 pounds a year ago now he weighs 92 pounds what us the percent increase in his weight
First we find increase in weight
Increase in weight is =92-80 = 12
To find percentage increase in weight we use formula =( increase / actual) ×100
Percentage increase =( 12÷80)×100= 15 %
The answer is about 4%
What is 27÷2356 with the work
27÷2356=
27 goes into 235 8 times which is 216
235-216 is 19
U bring down the 6 which makes 196
27 goes into 196 7 times which is 189
196-189=7
So the answer is 87 reminder 7
how do write 3 to 4 2 other ways?
The ratio "3 to 4" can also be written as "3:4". Typically, though, we write it as "3/4" like a fraction. Those are the three main ways to write out ratios ( a to b, a:b, or a/b).
find the slope 3x+5y=29
Answer: [tex]-\frac{3}{5}[/tex]
Step-by-step explanation:
If you solve for y, then it will be in y = mx + b format where m is the slope.
3x + 5y = 29
-3x -3x
5y = -3x + 29
[tex]\frac{5y}{5} = \frac{-3x}{5} + \frac{29}{5}[/tex]
[tex]y = \frac{-3}{5}x + \frac{29}{5}[/tex]
m = [tex]-\frac{3}{5}[/tex]
To find the slope of the line for the equation 3x+5y=29, rewrite it in slope-intercept form y=mx+b. After isolating y, you'll find that the slope m is -3/5.
Explanation:To find the slope of the line represented by the equation 3x + 5y = 29, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we solve for y:
Subtract 3x from both sides to get 5y = -3x + 29.Divide every term by 5 to isolate y on one side, resulting in y = -3/5x + 29/5.Now, the equation is in slope-intercept form, and we can easily identify the slope as -3/5. This means there is a decrease of 3 on the vertical axis for every increase of 5 on the horizontal axis. Thus, the slope of the line is -3/5.
what is 3ft to 4yd as a ratio as a fraction in simplest form
i think it is 1:4 or as a fration it is 1/4
You are packaging expansion packs for the game of checkers. The table below lists the number of each part needed per expansion pack, as well as the number of each part that you have available.
Part Number in each pack Number available
People marker 6 287
6-sided die 3 143
Teleporter marker 7 341
You make as many expansion packs as you can. With the parts remaining, you could make 1 more expansion pack if you had:
A) 1 more people marker and 1 more die.
B) 1 more die and 1 more teleporter marker.
C) 1 more teleporter marker and 1 more people marker.
D) 2 more people markers.
E) 2 more teleporter markers
Answer: Option (A)1 more people marker and 1 more die.
Step-by-step explanation:
We have to pack expansion packs for the game of checkers in such a way such that there should be enough cards as per requirement.
So for that we have to find packs of each item by dividing each pack by part numbers and what is left after as remainder.
People marker =287 =6(47) + 5 ( as each pack of people marker contains 6 items)
6-sided die =143 = 3(47) + 2 (as each pack of 6- sided die contains 3 items)
Teleport-er marker=341 = 7(48) + 5 (as each pack contains 7 teleport-er marker)
So we can see that for 48th pack we have enough Teleport-er marker just we need one People marker and one 6-sided die. which is option A.
Given the quantities of game components available, we can form 47 complete expansion packs. We can form another pack if we had 1 more 6-sided die and 1 more people marker. Thus, the correct answer is option A.
Explanation:To answer the question, we first need to calculate how many complete expansion packs can be made with the available components:
People marker: We would divide the total number of available markers (287) by the number needed for each pack (6). Thus, a total of 47 full packs can be made with an extra 5 markers left over. 6-sided die: Dividing the total number of dice available (143) by the number needed for each pack (3), we get 47 full packs with 2 dice left over. Teleporter marker: Divided by 7 (the amount needed per pack), the 341 available teleporter markers would result in 48 full packs with 5 markers left over.
Given the available quantities, we can make a total of 47 complete packs. However, we'd have enough components to complete one more pack if we had 1 more die and 1 more people marker. Therefore, the correct answer is option A.
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I need help please!!!!!!!
Solve for number nine !! Please help me !!!!
Basically you subtract the amount of people who rode in cars so and divide the number you get by the number of buses.
404-5=399
399/7=57 kids on each bus
12 more than m machines
the equation would be m+12 because it stands for 12 more than m number of machines.
8(a+b) when a is 5 and b is 3
Substitute 5 and 3 for a and b in the original expression.
8(a+b)
8(5+3)
Using the rules of PEMDAS, solve the inside of the parentheses first, then multiply accordingly.
8(8)
The final answer is 64.
(w+14)/(4w+6)=(3)/(4) show work plz
Answer:
w = -1.44 and w = -14.06
Step-by-step explanation:
That "(3) / (4)" in (w+14)/(4w+6)=(3)/(4) looks fishy. Assuming that you really meant 3/4, then we have (w+14)/(4w+6)=3/4.
Mult. both sides by 4 to remove the fraction: 4(w+14)/(4w+6) = 3.
Multiply out (w+14)/(4w+6): 4w^2 + 6w + 56w + 84. Combine the w terms, obtaining 4w^2 + 62w + 84. Then the original equation becomes:
4w^2 + 62w + 84 = 3, or 4w^2 + 62w + 81 = 0.
This is a quadratic equation, with a = 4, b = 62 and c = 81. The two roots (values of
w) are as follows:
-62 plus or minus √(62^2-4(4)(81)
----------------------------------------------------------
8
-62 plus or minus √(2548) -62 plus or minus 50.48
w = ------------------------------------------- = ---------------------------------------
8 8
Simplifying, we get w = -1.44 and w = -14.06
To solve the algebraic equation (w+14)/(4w+6) = 3/4, we clear the fractions, combine like terms, and isolate the variable w, which gives us the solution w = 4.75.
To solve the equation (w+14)/(4w+6) = 3/4, we first clear the fractions by multiplying both sides by the least common denominator, which is 4(4w+6). This eliminates the denominators and gives us:
4(w + 14) = 3(4w + 6)
Distribute the 4 on the left side and the 3 on the right side:
4w + 56 = 12w + 18
Next, we want to get all the terms with w on one side and the constant terms on the other. Subtract 4w and 18 from both sides:
4w + 56 - 4w - 18 = 12w + 18 - 4w - 18
This simplifies to:
38 = 8w
Divide both sides by 8 to isolate w:
w = 38 / 8
Finally, simplify the fraction to find the value of w:
w = 4.75
Given:2PQ=PR prove: Q is the midpoint of PR
Answer:
Using definition of midpoint, Q is the mid point of PR.
Step-by-step explanation:
Given 2PQ=PR
And Q lies on the line PR (It should be given in the problem itself else we have to assume it to prove "Q is the midpoint of PR").
Then PR=PQ+QR using segment addition postulate.
Let us plugin PR in given equation.
2PQ=PQ+QR
Subtract PQ from both sides.
2PQ-PQ=PQ+QR-PQ
PQ=QR
Since Q lies on the line PR and PQ=QR, Q is the mid point of PR.
Hence proved.
In geometry, if 2PQ=PR, point Q is the midpoint of PR. This is because the given condition implies that the length of segment PQ is half of the length of the whole segment PR, meaning Q divides PR into two segments of equal lengths.
Explanation:In Geometry, the statement 2PQ=PR is the given condition. Prior to your question, we are assuming that PQ and QR are line segments. This would imply that P, Q, and R all lie on the same line, with P and R being the endpoints and Q somewhere between them.
Now, the provided condition (2PQ=PR) means that the length of segment PQ is half of the length of the whole segment PR. If we assume segment PQ is 'a' units long, then 2PQ would be '2a' units long. According to the equation, PR is also '2a' units long.
By definition, the midpoint of a line segment is the point that divides the segment into two segments of equal length. Since PQ is half of PR, point Q would divide PR into two equal segments, PQ and QR, both being 'a' units in length. Therefore, Q is the midpoint of PR.
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