Answer:
-7, 14
Step-by-step explanation:
We start by writing this in the form $x^2 + bx + c = 0$, so we subtract 98 from both sides of the equation.
This gives us $x^2 - 7x - 98 = 0$. We proceed by factoring $x^2 - 7x - 98$, so we seek numbers that multiply to $-98$ and add to $-7$. We find that $7$ and $-14$ work.
Thus, our equation becomes $(x + 7)(x - 14) = 0$. We can now apply the fact that if the product of two real numbers is zero, then at least one of the real numbers must be 0.
Solving $x + 7 = 0$ and $x - 14 = 0$, we find that the solutions are $\boxed{x =-7~\text{and}~x = 14}$.
The value of the equation is given by x = 14 or x = -7
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
x² - 7x = 98 be equation (1)
Subtracting 98 on both sides of the equation , we get
x² - 7x - 98 = 0
Now , on simplifying the equation , we get
x² - 14x + 7x - 98 = 0
Taking x as the common factor of the equation , we get
x ( x - 14 ) + 7 ( x - 14 ) = 0
On further simplification , we get
( x + 7 ) ( x - 14 ) = 0
Now , the two solutions to the equation is
( x + 7 ) = 0
Subtracting 7 on both sides of the equation , we get
x = -7
( x - 14 ) = 0
Adding 14 on both sides of the equation , we get
x = 14
Therefore , the value of A is 14 or - 7
Hence , the equation x² - 7x - 98 = 0 has the solutions of 14 and -7
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A beetle that Hannah observed was too small to draw at its actual size. Hannah decided to make a scale drawing of the beetle as shown above. The beetle in the drawing is 7.62 cm long and 3.81 cm wide. The scale factor of her drawing is 3. Part A: Find the actual length of the beetle Hannah observed. Show all work. Part B: Find the actual width of the beetle Hannah observed. Show all work. Part C: The actual length of each of the beetle's antennae is 0.2 cm. What is the size of each antenna on Hannah's scale drawing? Show all work.
Answer:
[tex]Actual\ Length = 2.54\ cm[/tex]
[tex]Actual\ Width = 1.27\ cm[/tex]
[tex]Scale\ Length = 0.6\ cm[/tex] --- Beetle's antennae
Step-by-step explanation:
Given
The following scale measurements
[tex]Length = 7.62cm[/tex]
[tex]Width = 3.81cm[/tex]
[tex]Scale\ Factor = 3[/tex]
Solving (a): The actual length.
We simply divide the scale length by the scale factor.
[tex]Actual\ Length = \frac{Scale\ Length}{Scale\ Factor}[/tex]
[tex]Actual\ Length = \frac{7.62cm}{3}[/tex]
[tex]Actual\ Length = 2.54\ cm[/tex]
Solving (b): The actual width.
We simply divide the scale width by the scale factor.
[tex]Actual\ Width = \frac{Scale\ Width}{Scale\ Factor}[/tex]
[tex]Actual\ Width = \frac{3.81\ cm}{3}[/tex]
[tex]Actual\ Width = 1.27\ cm[/tex]
Solving (c):
Given: Actual Length of the beetle's antennae is 0.2 cm.
Required: Determine the scale measurement.
This is solved using:
[tex]Actual\ Length = \frac{Scale\ Length}{Scale\ Factor}[/tex]
[tex]0.2\ cm = \frac{Scale\ Length}{3}[/tex]
[tex]Scale\ Length = 0.2cm * 3[/tex]
[tex]Scale\ Length = 0.6\ cm[/tex]
please help, i’m so confused ahhh
Answer: x = 3. the length of side ST is 14.
Step-by-step explanation:
Since both sides are equal, we can use the equation 3x + 5 = 5x - 1.
To start the problem, we subtract 3x from each side which makes our equation 5 = 2x - 1.
The next step would be to simplify the equation by adding 1 to each side which makes our equation 6 = 2x.
We then need to simplify the equation to x = 3.
This means the answer to 9 is x = 3.
For the next problem, since we already know the value of x, we substitute its value which in this case would be 3. This leaves us with an equation of 9 + 5, which equals 14.
This means the length of side ST is 14.
Decide whether enough information is given to prove that the triangles are congruent. If so, state the theorem you would use
not enough information provided
yes; AAS Congruence Theorem
yes; SAS Congruence Theorem
yes; SSS Congruence Theorem
Answer:
Yes; AAS Congruence Theorem
Proof:
In [tex]\triangle ABC[/tex] and [tex]\triangle QRS[/tex]:
[tex]\angle BAC = \angle RQS[/tex] (given)
[tex]\angle ABC = \angle QRS[/tex] (given)
[tex]AC =QS[/tex] (given)
∴ [tex]\triangle ABC \cong \triangle QRS[/tex] (AAS)
There is enough information to prove that the two triangles are congruent through the AAS congruence theorem.
Hope this helps :)
Is the relation shown below a function? Use the graph below to justify your response.
(0, 0), (2, 0), (2, 2), and (3, 4)
Answer:
yes it is a function there is no graph so I cant justify it
The relation is not a function.
Relations
Relations that are functions will pass the vertical line test
Points
The points are given as:
(0,0), (2,0), (2,2), and (3,4)
GraphsNext, we plot the points on the graph (see attachment).
From the graph, we can see that a vertical line passes through points (2,0) and (2,2).
Hence, the relation is not a function.
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Rick has a piece of lumber that is 12 feet long. He cuts it into pieces that are each 3/4 of a foot long. How many pieces of 3/4 foot lumber will he be able to make?
Answer:
He will be able to make 16 pieces of lumber
Step-by-step explanation:
If x = 12 units, y = 4 units, and h = 8 units, find the area of the rhombus shown above using decomposition. A. 16 square units B. 96 square units C. 128 square units D. 32 square units
The area of the rhombus will be 96 square units. Then the correct option is B.
The missing diagram is attached below.
What is the area of the rhombus?Let a be the length and h be the height of the rhombus.
Then the area will be
Area = a × h square units
If x = 12 units, y = 4 units, and h = 8 units.
Then the area of the rhombus will be
A = 12 × 8
A = 96 square units.
Then the correct option is B.
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Answer:
96
Step-by-step explanation:
A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 4 milliliters of compound
B. If a chemist wants to make 621 milliliters of the drug, how many milliliters of compound A are needed?
Answer:
884
Step-by-step explanation:
We know the ratio of A to B is 5:8
let x = the multiplier
then
5x = amt of compound A
and
8x = amt of compound B
:
5x + 8x = 884
13x = 884
x = 884/13
x = 68 is the multiplier
therefore
5(68) = 340 millilters of compound A needed
:
:
Confirm our answer. Find the amt of B
8(68) = 544 ml of B
340 + 544 = 884
Write an equivalent fractions for 3/7 and 1/3 using 21 as the common denominator
Answer:
9/21 & 7/21
Step-by-step explanation:
Equivalent fraction for [tex]\frac{3}{7}[/tex] and [tex]\frac{1}{3}[/tex] using 21 using as the common denominator are [tex]\frac{9}{21} ,\frac{7}{21}[/tex].
What are equivalent fraction?"Equivalent fraction is fraction with different numerator or denominator
that represents the same value or proportion of the whole."
What is common denominator?"Common denominator is the same denominator of all the fraction"
We have to write an equivalent fractions for [tex]\frac{3}{7}[/tex] and [tex]\frac{1}{3}[/tex] using 21 as common denominator.
As we know when we multiply [tex]7[/tex] by [tex]3[/tex] to get [tex]21[/tex]
and we have to multiply [tex]3[/tex] by [tex]7[/tex] to get [tex]21[/tex]
⇒[tex]\frac{3}{7}=\frac{3}{7}[/tex]×[tex]\frac{3}{3}=\frac{9}{21}[/tex]
⇒[tex]\frac{1}{3}=[/tex][tex]\frac{1}{3}[/tex]×[tex]\frac{7}{7}=\frac{7}{21}[/tex]
Hence, Equivalent fraction for [tex]\frac{3}{7}[/tex] and [tex]\frac{1}{3}[/tex] using 21 as common denominator are [tex]\frac{9}{21} ,\frac{7}{21}[/tex].
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Choose the best graph that represents the linear equation:
6x = y + 8
Graph A
On a coordinate plane, a line goes through (negative 2, 4) and (0, negative 8).
Graph B
On a coordinate plane, a line goes through (0, negative 8) and (2, 4).
Graph C
On a coordinate plane, a line goes through (negative 2, negative 4) and (0, 8).
Graph D
On a coordinate plane, a line goes through (0, 8) and (2, negative 4).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D
Which equation is represented by the graph below?
Shannon graphed the system of equations. 7x – 4y= –8 y = y equals StartFraction 3 over 4 EndFraction x minus 3.x – 3 A coordinate grid with 2 lines. The first line passes through (0, negative 3) and (negative 4, negative 6). The second line passes through (0, negative 2) and (negative 4, negative 6). The lines appear to cross at about negative 5 and between negative 6 and negative 8.What of the following best describes the geography English colonists found when they first began to arrive in North America?
Answer:
its (-5 -5.9)
Step-by-step explanation:
i got id right on edg
Translate: the difference of x and 13, added to 12
Answer:
12+(x-13)
Step-by-step explanation:
the difference of x and 13 is subtraction and then added to 12 is addition.
1. Natasha worked at a diner for $10per hour last week and already had $42 in her bank account? She paid $206 for a prom dress. The equations 206 = 42 + 10h represents this problem. How many hour did she work to pay for the prom dress?
2. Translate the following sentence into a mathematics equation. The sum of 10 and five time a number is the same as the difference of the number and 6
Answer:she worked 17 hours
Step-by-step explanation: 10×17=170+42=212
Answer:
She worked 16.4 hours
Step-by-step explanation:
The equation below is the equation of a line in point slope form, what is the x-
coordinate of the point?
y+5=—3 (x+6)
Answer:
Step-by-step explanation:
X=-x^2+x-5
Solve the following equation: 3x + 6 = 9
Answer:
Step-by-step explanation:
3x+6=9
3x=9-6
3x=2
x=1.5
Answer:
x=1
Step-by-step explanation:
Subtract 6 from both sides of the equation, leaving 3x=3.
We put both sides over 3 to divide.
We are left with x=3
To test this, we substitute x with 1.
3(1)+6=9
3+6=9
9=9
What is the approximate area of the circle shown below?
OA. 30 cm2
OB. 39 cm2
DC. 121 cm2
OD. 19.5 cm2
Please help ASAP!
Answer:
C. 121cm2
Step-by-step explanation:
The area of a circle is pir^2.
Let pi be rounded to 3.14 and r = 6.2cm
6.2^2*3.14 = 120.76, which rounds to 121cm2
Answer:
C) 21 cm²Step-by-step explanation:
area of a circle = π r²
= π (6.2)²
≈ 21 cm²
Evaluate. -2 1/4 -(-3 2/5).
Answer:
1 3/20
Step-by-step explanation:
1. Make them all into fractions:
-8/4 -1/4 -(-15/5 -2/5)
2. Add like-terms:
-9/4 -(-17/5)
3. A negative times a negative makes a positive:
-9/4 +17/5
4. Identify the least common denominator (LCD):
20
5. Apply:
-9x5/4x5 +17x4x/5x4
6. Solve:
-45/20 +68/20
7. Result:
23/20, simplified 1 3/20
PLEASE HELP!!!
In order to get a good workout on your treadmill, you figure you have to run 528 feet in one minute. What are the possible numbers of miles you have to run in 20 minutes to exceed this rate? (Hint: 1 mile = 5280 feet)
________________________________________
PLEASE PROVIDE AN EXPLANATION, thank you!
Also, the math should include an inequality. Please show how the answer was gotten with an INEQUALITY. It will help, thank you!
What happens to the graph of f(x) when it is multiplied
by a number between - 1 and 0?
[Image: Vertical number line ranging from negative 5 to 5.]
On this number line, zero represents sea level. Plot the following points based on the description provided.
• -3 1/2
[Image: Vertical number line ranging from negative 5 to 5.]
On this number line, zero represents sea level. Plot the following points based on the description provided.
• opposite of –5
Answer:
Positive 5.
Step-by-step explanation:
Opposite of negative 5 is positive 5.
The point will be on the positive side, which is above sea level. So it will be on 5 above the zero.
Answer:positive 5
Step-by-step explanation:
Rita filled 2/5 of a jug with fruit juice. She then added 200 ml of milk to make a milkshake. At this stage, the ratio of the fruit juice to milk is 3:2
how much more liquid can the jug hold?
a)250 ml
b)300 ml
c)400 ml
d)450 ml
Answer:
250ml understand the concept please
The jug can hold 250 ml more liquid.
Let the jug can hold x ml liquid.
Given Rita filled 2/5 of a jug with fruit juice.
So, the amount of fruit juice is = 2/5 of x = 2x/5.
Then she added 200 ml milk.
Given the ratio of the fruit juice to milk is 3:2.
So,
[tex]\frac{2x}{5}:200=3:2\\\frac{\frac{2x}{5} }{200}=\frac{3}{2}\\2( \frac{2x}{5})=600\\\frac{4x}{5}=600\\ x=\frac{600*5}{4}\\x=750[/tex]
So the amount of fruit juice = [tex]\frac{2}{5}*750=300[/tex] ml.
Total amount of fruit juice and milk = 300+200=500 ml.
So the jug will hold = 750 - 500 =250 ml more.
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What does the statement T(20) = T(c) mean?
A savings account increases from $200 to $208. What is the percent increase of the
savings account?
Answer:
4%
Step-by-step explanation:
8/200 = 0.04
There are 5 hockey games and 7 football games happening in the upcoming month. You decide to attend 3 games by picking at random. What is the probability that you pick 3 football games? Leave your answer as a simplified fraction.
Answer:
1/4
Step-by-step explanation:
5 plus 7 equals to 12
3 football games
3/12=1/4
Cheddar cheese costs $4.25 per pound. Which equation best represents y, the total cost of x pounds of cheddar
cheese?
A. x = 4.25 + y
B. x = 4.25y
C. y = 4.25+ x
D. y = 4.25x
I will MARK brainlist!
Answer:
D
Step-by-step explanation:
4.25 × the amount of cheese you buy (x) equals the total cost (y)
Answer:
D. y = 4.25x
Step-by-step explanation:
You multiple the price per pound by the number of pounds. Can I have brainliest? Thanks!
I’ll mark you brainlist write in y=mx+b form
Answer:
y=-1/8x +4
Step-by-step explanation:
1. First, write the equation in point-slope form: y-y1=m(x-x1)
y-1=-1/8(x-24)
2. Distribute -1/8 to x and -24
-1/8 times x = -1/8x
-1/8 times -24 = 3
y-1=-1/8x+3
3. Add 1 to both sides
y=-1/8x +4
If Mitch bicycles at an avenger speed of 18 miles per hour,how long will it take him to cover 76.5 miles?
Answer:
b
Step-by-step explanation:
Which of the following is the slope of the line that passes through (-3,5) and (1, 15)?
Answer: 5/2
Step-by-step explanation: slope is the change in y over the change in x (y2-y1/x2-x1)
A rectangular prism has a height of 15 centimeters. The base of the prism has an area of 22 square centimeters. What is the volume of the prism?
Answer:
330cm^3
Step-by-step explanation:
22 only has 2 factors 11&2. So take 11•2•15=330 Doing it as 22•1•15 works as well.
What is the slope of the line shown?