Answer: The correct answer is: [D]: " (x - 5) "
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Step-by-step explanation:
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First, let's try to "factor out" the given trinomial:
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" 5x² - 5x - 100 " ;
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We can "factor out" a "5" ;
since among the three (3) terms in this trinomial,
We have: 5x² , 5x, and 100 ;
Note that not all of these 3 terms have a variable in them;
→ Consider the value; "100" .
Note that the remaining two (2) terms have the same variable, "x" ;
→ 5x² ; and 5x " ;
Note that each of these 2 (two) terms have a coefficient of "5" ;
Note that the other term, "100" ; is divisible "evenly" by "5" ;
→ that is; when the term, "100", is divided by "5" ; the result is an integer; {specially, " 100 ÷ 5 = 20 " .}.
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So: Let us being by "factoring out" a "5" ;
Given the trinomial: " 5x² - 5x - 100 " ;
→5(x² - 1x - 20) ; or: 5(x² - x - 20) ;
→ At this point, although this trinomial express is not completely
"factored out" ;
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Let us consider: Do either of these two (2) factors appear among the answer choices given:
1) " 5" ; or: 2) "(x² - x - 20)" ?? No!
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Let us continue.
We have: 5(x² - x - 20) ;
→ We can write as: " 5 (x² - 1x - 20) " ;
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Now, let see if we can further "factor out" the:
→ (x² - 1x - 20) ;
Now, note the " -20" ; and the " -1x " ;
→ What two (2) factors of: "-20" ; add up to "-1" ? ;
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Let us consider the factor of "-20" :
-20, 1 : -20 + 1 = -19 ; -19 =? -1 ? No.
20, -1 : 20 + (-1) = 20 - 1 = 19 ; 19 =? -1 ? No.
10, -2 : 10 + (-2) = 10 - 2 = 8 ; 8 =? -1 ? No.
-10, 2 : -10 + 2 = -8 ; -8 =? -1 ? No.
-4, 5 : - 4 + 5 = 5 + (-4) = 5 - 4 = 1 ; 1 =? -1 ? No.
4, -5 : 4 + (-5) = -5 + 4 = -1 ; -1 =? -1 ? Yes!
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So, we have +4 and -5 ;
(+4) * (-5) = -20 ;
(+4) + (-5) = -5 + (+4) = -5 + 4 = -1 ;
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So, we factor out:
→ (x² - 1x - 20) ;
that is: " (x² - x - 20) " ;
into:
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" (x + 4) (x - 5) " ;
and to factor out: " 5x² - 5x - 100 " ;
we bring down the "5" ; and write as:
→ " 5 (x + 4) (x - 5) " ,
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So:
We have three (3) factors when the trinomial expression is "factored out":
→ 5 ; (x + 4) ; and: (x - 5) ;
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→ Among these three factors, the only one that appears as a given answer choice is:
→ " (x - 5) " ;
→ which is our answer:
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→ Answer choice: [D]: " (x - 5) " .
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Hope this answer is helpful to you!
Best wishes!
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the sum of 21and 4 doubled
Answer:
50
Step-by-step explanation:
21 + 4 = 25
25 × 2 = 50
Rate as brainliest
What is the solution set of (x | x>-5) V{xl x<5)?
A) numbers except -5 and 5
B)the numbers between -5 and 5
C)the empty set
D)all real numbers
Answer:
I believe the answer to this is D. All Real Numbers. I had the same question and this is what I picked.
Hope it helps!
Find x and y in the figures below
Answer:
There are no figures below...
Step-by-step explanation:
can you divided 14 shirt into 2 equal piles why or why not
Answer:
Yes you can because 14 is a even number.
Step-by-step explanation:
First you divide 14 by 2 to get two equal piles and boom there's your answer.
Yes, you can divide 14 shirts into 2 equal piles, due to the fact that 14 is an even number.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
The solution is as simple as dividing 14 by 2 to produce two equal piles.
⇒ 14/2
⇒ 7
Thus, you can divide 14 shirts into 2 equal piles, due to the fact that 14 is an even number.
Learn more about Arithmetic operations here:
brainly.com/question/25834626
#SPJ2
Evaluate |-6| + 34| + |-5|– 0x6.
0 or 18 or 23 or 25
What is the image point of (-6, -9) after translation left 1 unit and down 5 units?
The original point (-6, -9) is shifted 1 unit to the left and 5 units down to reach the new position (-7, -14).
To find the image point after translating the point (-6, -9) left 1 unit and down 5 units, we subtract the translation values from the coordinates of the original point.
For the horizontal translation (left 1 unit), we subtract 1 from the x-coordinate:
New x-coordinate = -6 - 1 = -7
For the vertical translation (down 5 units), we subtract 5 from the y-coordinate:
New y-coordinate = -9 - 5 = -14
Therefore, the image point after the translation is (-7, -14).
This means that the original point (-6, -9) is shifted 1 unit to the left and 5 units down to reach the new position (-7, -14).
This translation is a geometric operation commonly used in mathematics and computer graphics to move objects or points in a coordinate plane.
Writing in Math Describe a situation in which it would be better
to round to the nearest ten rather than to the nearest hundred
or thousand.
Answer:
the number 151
Step-by-step explanation:
this because if you round 151 to the nearest hundread it would give you 200 but if you round it to the nearest ten ot would give you 150 which is closer to the actual number than 200.
How would you write 77.7% as a decimal?
Convert 2. 17 years into minutes
2.17 years is 1140552 Minutes
Answer:
wait do u want me to convert 17 years or 2.17 years
ill do both
17=8.935e+6
2.17=1140552
Step-by-step explanation:
A coffee shop uses 4 liters of milk every day.
a. If there are 15 liters of milk in the refrigerator, after how many days will more milk need to be purchased? Explain how you know.
b. If only half as much milk is used each day, after how many days will more milk need to be purchased?
Answer:
explained
Step-by-step explanation:
a. daily requirement of milk = 4 liters
15 liters of milk is present
this 15 liters of milk will be used up in [tex]\frac{15}{4}[/tex] days
= 3(3/4) days , so after 3 days only more milk will be required to purchase.
b. daily milk consumption is reduced to half = 2 liters
Now, 15 liters of milk will be used up in [tex]\frac{15}{2}[/tex]= 7.5 or 7(1/2) days.
Hence now milk will be purchased after 7 days.
The product of two consecutive even integers is 168. Find the integers.
Final answer:
To find two consecutive even integers whose product is 168, we set up and solved the equation n(n + 2) = 168, which yielded n = 12 and n + 2 = 14. Hence, the integers are 12 and 14.
Explanation:
The product of two consecutive even integers being 168 requires us to set up an algebraic equation. Let's denote the first even integer as n. Since we are dealing with consecutive even integers, the next integer would be n + 2. The product of these integers is given to be 168, so our equation is n * (n + 2) = 168.
Expanding this we get n^2 + 2n - 168 = 0. Factoring the quadratic equation, we find that (n + 14)(n - 12) = 0. Therefore, the values of n that satisfy this equation are -14 and 12. We are interested in the positive solution since integer sizes are always positive, so the first integer is 12. Consequently, the second integer is 12 + 2 = 14. Therefore, the two consecutive even integers are 12 and 14.
Alfredo is employed on an assembly line. He receives 35 cents for each part that he works on. If he works on more than 150 parts, his employer will pay him 40 cents for each part over 150. Yesterday, Alfredo worked on 210 parts. How much did he earn?
SHOW ALL WORK
Answer:
$76.50
Step-by-step explanation:
Let's split this up.
First, we will do the 150 parts. But, we need to subtract so that we know how many parts he worked on over 150.
So...
210-150=60
Now that we know how many parts he worked on over 150, let's multiply.
.35*150=52.50
Now, let's multiply what he did over 150.
.40*60=24
Finally, we have to add his pay up.
52.50+24.00=76.50
Making your answer...
$76.50
Hope this helps!!!
Brady
I need help with 19 please help and if you can tell me step by step or show your work please!!!
Answer:
This will occur again in 15 more days.
Step-by-step explanation:
Simply divide 15 by 3, which equals 5, in which makes it the least common multiple of 5 and 3.
Tn+1=35-2Tn, T1=5 what is T20?
Answer: 3,495,265
Step-by-step explanation:
[tex]T_{n+1}=35-2T_n\quad and\quad T_1=5, then\\T_{1+1}=35-2(T_1)\implies T_2=35-2(5)\implies T_2=25\\T_{2+1}=35-2(T_2)\implies T_3=35-2(25)\implies T_3=-15\\T_{3+1}=35-2(T_3)\implies T_4=35-2(-15)\implies T_4=65\\T_{4+1}=35-2(T_4)\implies T_5=35-2(65)\quad \implies T_5=-95\\T_{5+1}=35-2(T_5)\implies T_6=35-2(-95)\implies T_6=225\\.\qquad \qquad \qquad \qquad \qquad \qquad \downarrow\\.\qquad \qquad \qquad \qquad \qquad \qquad \downarrow\\.\qquad \qquad \qquad \qquad \qquad \qquad \downarrow[/tex]
[tex]T_{18+1}=35-2(T_{18})\implies T_{19}=35-2(873,825)\implies T_{19}=-1,747,615\\T_{19+1}=35-2(T_{19})\implies T_{20}=35-2(-1,747,615)\implies T_{20}=3,495,265[/tex]
Find the values of x and y.
x + 7i = y − yi
Answer: X = y - yi - 7i
Y = (x + 7i)/(1 - i)
Step-by-step explanation: for the case of (X) you only need to pass the 7i to the other side with the subtraction sign (-7i), then we get this equation:
x + 7i = y − yi
X = y - yi - 7i
in the case of the (Y), first we select the common multiple.
y - yi = y(1 - i)
if we replace it in the original expression, we get the following equation:
x + 7i = y(1 - i)
after that you can pass the value (1 - i) to the other side dividing,
Y = (x + 7i)/(1 - i)
Answer:
x=y-yi-7i
y=ix+x-7+7i
2
Step-by-step explanation:
12x+7<-11 or 5x-8>40
Answer:
[tex]\large\boxed{x<-1\dfrac{1}{2}\ or\ x>9\dfrac{3}{5}\to x\in\left(-\infty,\ -1\dfrac{1}{2}\right)\ \cup\ \left(9\dfrac{3}{5},\ \infty\right)}[/tex]
Step-by-step explanation:
[tex]12x+7<-11\qquad\text{subtrct 7 from both sides}\\\\12x+7-7<-11-7\\\\12x<-18\qquad\text{divide both sides by 12}\\\\\dfrac{12x}{12}<\dfrac{-18}{12}\\\\x<-\dfrac{18:6}{12:6}\\\\x<-\dfrac{3}{2}\\\\x<-1\dfrac{1}{2}\\===========================[/tex]
[tex]5x-8>40\qquad\text{add 8 to both sides}\\\\5x-8+8>40+8\\\\5x>48\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}>\dfrac{48}{5}\\\\x>\dfrac{48}{5}\\\\x>9\dfrac{3}{5}\\===========================[/tex]
[tex]x<-1\dfrac{1}{2}\ or\ x>9\dfrac{3}{5}[/tex]
EMERGENCY Add using the number line.
−9+6
Drag and drop the word Sum to the correct value on the number line.
On a number line, suppose point E has a coordinate of 2, and EGequals5. What are the possible coordinates of point G?
Answer:
-3, 7
Step-by-step explanation:
EG = 5, so the distance between E and G is five.
G can be 5 units to the right of E:
2 + 5 = 7
G has coordinate 7.
G can be 5 units to the left of E:
2 - 5 = -3
G has coordinate -3.
Answer: -3, 7
Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y
Answer:
Well, there are x amounts of white flower and 6 cups of wheat flower.
So the total flower is x + 6
Given that is the total, the equation you would use is:
y=x+6
The constraints are as follows:
y can only be > 6
And if y=0, x would have to be -6 (which is impossible)
Answer:
D) y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.
Step-by-step explanation:
Got it right on my test
6 1/2 cups equals how many ounces
Answer:
52 ounces
Step-by-step explanation:
multiply the volume value by 8
To convert 6 1/2 cups to ounces, multiply the number of cups by 8 (since 1 cup equals 8 ounces). Six cups equal 48 ounces, and half a cup equals 4 ounces, which totals to 52 ounces. Therefore, 6 1/2 cups is equal to 52 ounces.
Explanation:To convert 6 1/2 cups to ounces, we first need to understand the relationship between cups and ounces. A cup is a unit of volume commonly used in cooking to measure liquids, and it is equivalent to 8 ounces. To find out how many ounces are in 6 1/2 cups, we multiply the number of cups by the number of ounces in one cup.
Here is the step-by-step conversion:
We know that 1 cup = 8 ounces.Therefore, 6 cups would be 6 x 8 ounces, which is 48 ounces.For the half cup remaining, we just take half of the ounces in one cup: 1/2 x 8 ounces = 4 ounces.Now, we add the amount of ounces from the 6 full cups to the ounces from the half cup to get the total: 48 ounces + 4 ounces = 52 ounces.So, 6 1/2 cups equals 52 ounces.
What are the coordinates of the vertices of the pre-image given? ry= −x ◦ T1, −2(x, y)
A
B
C (3, 4)
D
Answer:
Hence, the coordinates of pre-image are:
A(1,6) , B(0,4) , C(3,4) , D(2,6)
Step-by-step explanation:
We have to find the coordinates of the vertices of the pre-image given?
Ry= −x ◦ T_1, −2(x, y)
i.e. we have to find the composition of reflection along the line y=-x and translation with the rule:
(x,y) → (x+1,y-2)
Now we have coordinates of A",B",C" and D" as:
A"(-4,-2)
B"(-2,-1)
C"(-2,-4)
D"(-4,-3)
Now we are asked to find the coordinates of the pre-image.
Also when any point is reflected along y=-x then the point is transformed to:
(x,y) → (-y,-x)
Let A,B,C and D are the points of the pre-image.
Hence, the coordinates of the pre-image are given as:
so, the transformation is given as:
A→A'→A"
B→B'→B"
C→C'→C"
D→D'→D"
Where A',B',C',D' represents the transformation after translation and A",B",C",D" represents the transformation after reflection as well.
The coordinates of A' are (2,4)
B' are (1,2)
C' are (4,2)
and D' are (3,4)
Now, the coordinates of pre-image are given as:
A'(x,y) → A(x-1,y+2)=A(1,6)
B'(x,y) → B(x-1,y+2)=B(0,4)
C'(x,y) → C(x-1,y+2)=C(3,4)
and D'(x,y) → D(x-1,y+2)=D(2,6)
Hence, the coordinates of pre-image are:
A(1,6) , B(0,4) , C(3,4) , D(2,6)
Answer its A (1,6) B (0,4) C (3,4) D (2,6)
Step-by-step explanation:
What is the constant of variation, k, of the direct variation, y=kx, through (5,8)
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{5}~,~\stackrel{y}{8})\qquad \implies 8=k(5)\implies \cfrac{8}{5}=k[/tex]
Point B, located at (-5, -8), is rotated 360°. What are the coordinates of point B'?
A.(5, 8)
B.(-5, 8)
C.(5, -8)
D.(-5, -8)
Answer: D
Step-by-step explanation:
If it is rotates 360 degrees it lands back where it started.
Two quadrilaterals are similar. The length of the row longest sides of the first quadrilateral are 40in and 60in. The lengths of the three shortest sides of the second quadrilateral are 5in, 12in, and 16in. Find the unknown lengths of the sides of these two figures .
Answer:
The sides of the first quadrilateral are 60 in, 40 in, 30 in and 12,5 in
The sides of the second quadrilateral are 24 in, 16 in, 12 in and 5 in
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
Arrange the sides of each quadrilateral from largest to smallest
First quadrilateral Second quadrilateral
Longest side=60 in Longest side=c in
Second side=40 in Second side=16 in
Third side= a in Third side= 12 in
Fourth side=b in Fourth side=5 in
so
[tex]\frac{60}{c}=\frac{40}{16}=\frac{a}{12}=\frac{b}{5}[/tex]
Find the value of c
[tex]\frac{60}{c}=\frac{40}{16}[/tex]
[tex]c=60(16)/40[/tex]
[tex]c=24\ in[/tex]
Find the value of a
[tex]\frac{40}{16}=\frac{a}{12}[/tex]
[tex]a=40(12)/16[/tex]
[tex]a=30\ in[/tex]
Find the value of b
[tex]\frac{40}{16}=\frac{b}{5}[/tex]
[tex]b=40(5)/16[/tex]
[tex]b=12.5\ in[/tex]
Final answer:
To find the unknown sides of the two similar quadrilaterals, we calculate the scale factor using known side lengths, then apply this factor to determine the missing side lengths, resulting in 7.5 inches for the second quadrilateral and 128 inches for the first quadrilateral.
Explanation:
The subject of this question is finding the unknown lengths of the sides of two similar quadrilaterals. To determine the lengths, we first need to identify the scale factor that relates the two quadrilaterals. Given that the two longest sides of the first quadrilateral are 40 inches and 60 inches, and that the three shortest sides of the second quadrilateral are 5 inches, 12 inches, and 16 inches we can determine that the quadrilaterals must have been scaled by a factor that relates these sides.
To find the scale factor, we divide one of the known sides of the first quadrilateral by the corresponding side of the second. Let's use the sides 40in and 5in for this purpose: Scale factor = 40in / 5in = 8.
Now, to find the length of the unknown side of the second quadrilateral, we would multiply the length of the corresponding side of the first quadrilateral by the inverse of the scale factor, which in this case is 1/8. Conversely, to find the missing length of the first quadrilateral, we take the known length of the second quadrilateral and multiply it by the scale factor.
To find the unknown length of the longest side of the second quadrilateral, we multiply the length of the longest side of the first quadrilateral (which could be either 40in or 60in) by the inverse of the scale factor: Unknown longest side of second quadrilateral = 60in ×(1/8) = 7.5in.
Similarly, the unknown third side of the first quadrilateral is found by multiplying the third known side of the second quadrilateral by the scale factor: Unknown third side of first quadrilateral = 16in ×8 = 128in.
Therefore, the unknown sides of the two figures are 7.5in for the second quadrilateral and 128in for the first quadrilateral.
Which of the following is equal to the expression when x does not equal -2 or 3?
Answer:
at first we should simplify each equation by find its roots
(x^2+5x+6) =
(x+2) (x+3)
(x^2-x-6)=
(x-3) (x+2)
sox^2+5x+6÷x^2-x-6=
(x+2)(x+3)÷(x-3)(x+2)=
A(x+3) ÷(x-3)
Answer:
x+3/x-3
Step-by-step explanation:
The rule for pattern is ad 6.The first term is 5. The first term is 5.Write the first Five terms in the patterns
Answer:
5, 11, 17, 23, 29
Step-by-step explanation:
5+6=11+6=17+6=23+6=29
Simplify the expression -3/8 -1/10
The answer would be "-3/8 + -1/10."
Simplify means to reduce so in this case we aren't solving the question we are reducing it into simpler terms.
[tex]-\frac{3}{8} -\frac{1}{10}[/tex]
According to the rules of KCC (Keep Change Change) you would have to turn the subtraction sign into a addition sign and make the positive 1/10 into a negative.
[tex]-\frac{3}{8} +-\frac{1}{10}[/tex]
The equation cannot be reduce no further therefore that would be your answer.
Hope this helps.
What is 2/15,1/5,3/5 in least to greatest
Answer:
Step-by-step explanation:
Least: 2/15 , 1/5 , 3/5 -greatest
Answer:
2/15,1/5=3/15,3/5=9/15
Step-by-step explanation:
Look at the answer it is from least to greatest
36÷(1-|2-7|)
what's the answer?work
Answer:
-9
Step-by-step explanation:
36 ÷ (1 - |2 - 7|) =
Start with the calculation inside the absolute value.
= 36 ÷ (1 - |-5|)
Now take the absolute value of -5 which is 5.
= 36 ÷ (1 - 5)
Do the operation inside the parentheses, 1 - 5 = -4.
= 36 ÷ (-4)
Finally divide. Remember that positive divided by negative is negative.
= -9
|-17|= how do you do this
Answer:
17
Step-by-step explanation:
anything in absolute value brackets is going to be positive. Absolute value is the distance of that specific number on the number line from 0. so ex: -3 is 3 units away from 0 so therefore, the answer is 3.