Answer:
Step-by-step explanation:
exponential equation has the same base on each side, the exponents must be equal. This also applies when the exponents are algebraic expressions. Therefore, we can solve many exponential equations by using the rules of exponents to rewrite each side as a power with the same base. Then we use the fact that exponential functions are one-to-one to set the exponents equal to one another and solve for the unknown.
7. Francis made 7 withdrawals of
$75 each from his bank account.
What was the overall change in
his account?
Answer: -$525
Step-by-step explanation:
7x = how many times he withdrew money * how much money he withdrew.
7 * 75 = $525
Francis ended up removing $525 from his bank account, if we assume that he started off with $0- then the change would be -525 dollars.
Which set of values is a function?
a.
(6,-5) (7, -3) (8, -1) (9, 1)
b.
(9,5) (10,5) (9,-5) (10,-5)
c.
(3,4) (4,-3) (7,4) (3, 8)
d.
(2, -2) (5, 9) (5, -7) (1, 4)
Answer:
Its A
Step-by-step explanation:
Had it on quizziz
What’s the answer to this
Answer:
√3
Step-by-step explanation:
√1 is an imaginary number, not lying anywhere on a real numberline
√2 is an irrational number
√3 is an irrational number, but can be expressed as a fraction; 3=31=62=124 (so yes, it is a rational number)
√5 is an irrational algebric number
Use properties to rewrite the given equation. Which equations have the same solution as x + + x = – x? Check all that apply.
x + = – x
18x + 20 + 30x = 15 – 6x
18x + 20 + x = 15 – 6x
24x + 30x = –5
12x + 30x = –5
Answer:
options (a), (b), (c), and (e) have the same solution as the solution of 3/5 x + 2/3 + x = 1/2 -1/5x.
Step-by-step explanation:
The given equation is
3/5 x + 2/3 + x = 1/2 -1/5x
First, rearrange the equation to have constant terms and the terms having variable on the separate side.
3/5 x + x +1/5x= 1/2 - 2/3
9/5 x = -1/6
x= -1/6 ÷ 9/5
x= -1/6 x 5/9
x= -5/54 ...(i)
Now, find the solution of all the options in the similar way:
(a) 8/5 x +2/3 = 1/2 -1/5 x
8/5 x + 1/5 x = 1/2 - 2/3
9/5 x = -1/6
x= -1/6 ÷ 9/5
x= -1/6 x 5/9
x= -5/54 which is same as the solution of the mentioned equation. [ from equation (i)]
(b) 18x + 20 + 30x = 15 – 6x
18x+30x+6x = 15 -20
54x=-5
x= -5/54 which is same as the solution of the mentioned equation. [from equation (i)]
(c) 18x + 20 + x = 15 – 6x
18x+x+6x = 15 -20
25x=-5
x= -5/25 which is not the same as the solution of the mentioned equation. [ from equation (i)]
(d) 24x + 30x = –5
54x = -5
54x=-5
x= -5/54 which is same as the solution of the mentioned equation. [ from equation (i)]
(e) 12x + 30x = –5
42x = -5
42x=-5
x= -5/42 which not is same as the solution of the mentioned equation. [ from equation (i)].
Hence, options (a), (b), (c), and (e) have the same solution as the solutions of the given equation.
Find the value of c that makes the equation a perfect square trinomial.
x^2+8x+c
Answer:
16
Step-by-step explanation:
(x + 4)(x + 4)
x² + 4x + 4x + 16
x² + 8x + 16
If the m<4 is 110 degrees, what is m<1 ? (Give number value only.)
Answer:
70
Step-by-step explanation:
I'm not entirely sure, but lines b and a look congruent and vertical angles are congruent and measure 1, 4 would be 180 degrees.
∆ABC is translated 2 units down and 1 unit to the left. Then it is rotated 90° clockwise about the origin to form ∆A′B′C′. The coordinates of vertex A′ of ∆A′B′C′ are . The coordinates of vertex B′ of ∆A′B′C′ are . The coordinates of vertex C′ of ∆A′B′C′ are .
Answer:
A'(-2, 1), B'(1, 0), C'(-1, 0)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.
If a point X(x, y) is translated a units right and b units down, the new location is X'(x + a, y + b) whereas if a point X(x, y) is translated a units left and b units up, the new location is X'(x - a, y - b).
If a point X(x, y) is rotated 90° clockwise about the origin, the new location is X'(y, -x)
From the image attached, ∆ABC is at A(0, 0), B(1,3) C(1, 1)
If ∆ABC is translated 2 units down and 1 unit to the left (x - 1, y - 2), the vertices would be A*(-1, -2), B*(0, 1), C*(0, -1)
If it is then rotated 90° clockwise about the origin, the new location is A'(-2, 1), B'(1, 0), C'(-1, 0)
Answer:
The coordinates of vertex A′ of ∆A′B′C′ are (-2, 1) .
The coordinates of vertex B′ of ∆A′B′C′ are (1, 0) .
The coordinates of vertex C′ of ∆A′B′C′ are (-1, 0) .
Step-by-step explanation:
10.7+(-3.5) help plz
7.2
Step-by-step explanation:Hi there !
10.7 + (-3.5) =
= 10.7 - 3.5
= 7.2
Good luck !
A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 3 feet, 55 feet away from the player. The height $y$ (in feet) of a second hockey puck is modeled by $y=x\left(0.15-0.001x\right)$ , where $x$ is the horizontal distance (in feet). Compare the distances traveled by the hockey pucks before hitting the ground.
Answer:
Second puck travels farther
Step-by-step explanation:
Maximum height of first puck = 3 feet
The height of a second hockey puck is modeled by:
[tex]y=x\left(0.15-0.001x\right)[/tex]
[tex]y=0.15x-0.001x^2[/tex]
To find maximum height of second puck
[tex]y'=0.15-0.002x[/tex]
Equate the derivative equals to 0
0.15-0.002x=0
[tex]\frac{0.15}{0.002}=x[/tex]
75 = x
At x = 75
[tex]y=0.15(75)-0.001(75)^2=5.625[/tex]
So, The maximum height of second puck is greater than first puck
So, Second puck travels farther
find the DIFFERENCE between 901.28 and 375.54
Answer:
Pretty sure its 525.74
1-(2x+4)=4x+5 solution
Find the product 0.025 x 7
A. 0.0175
B: 0.175
C. 1.75
D. 17.5
Answer:
b
Step-by-step explanation:
used a calucator
joe needs to transfer 28 quarts of oil into containers joe calculated that he needs 112 containers but he made a mistake in his calculations identify and correct his error
This question is incomplete
Complete Question
Joe needs to transfer 28 quarts of oil into gallons containers joe calculated that he needs 112 containers but he made a mistake in his calculations identify and correct his error
Joe's error:
28 quarts × 4 quarts/ 1 gallon
= 28 quarts/1 × 4 quarts/ 1 gallon
= (28 × 4)/ ( 1 × 1) = 112 gallons
Answer:
7 gallons is the correct answer
Joe needs to transfer 28 quarts of oil into 7 gallons
Step-by-step explanation:
Joe's error:
28 quarts × 4 quarts/ 1 gallon
= 28 quarts/1 × 4 quarts/ 1 gallon
= (28 × 4)/ ( 1 × 1) = 112 gallons
Correcting Joe's error, we have:
4 quarts = 1 gallon
28 quarts = x
Cross Multiply
4 quarts × x = 28 quarts × 1 gallon
x = 28 quarts × 1 gallon/ 4 quarts
x = 7 gallons
= 28 quarts/x gallons × 1 gallon/4 quarts
= (28 × x)/ ( 1 /4) = 7 gallons
Therefore, Joe needs to transfer 28 quarts of oil into 7 gallons
Solve for AB. Round your answer to the nearest tenth if necessary.
Answer:
See Below
Step-by-step explanation:
You want to find AB.
They give the equation for AB, BC, and AC
AC - BC = AB
substitute the equations
(30) - (8x + 3) = 6x + 8
30 - 8x - 3 = 6x + 8
27 - 8x = 6x + 8
+8x +8x
27 = 14x + 8
-8 -8
19 = 14x
19/14 = 14x/14
1.3571428 = x
0.1 = tenth
1.4 = x
Substitute x into the equation for AB
6(1.4) + 8
16.4
[tex]\bold{Hello!}\\\bold{Your~Answer~Is~Below!}[/tex]
______________________________
[tex]\bold{Solution~Steps:}[/tex]
[tex]1.)~First~you~need~to~make~an~equation:[/tex]
[tex]\bold{30-8x+3=6x+8}[/tex][tex]\bold{You~do~this~by~using~all~the~information~available~and~set~it~up~to~solve~for~AB.}[/tex][tex]2.)~Add~30~and~3~to~get~33:[/tex]
[tex]\bold{33-8x=6x+8}[/tex][tex]3.)~Subtract~6x~from~both~sides:[/tex]
[tex]\bold{33x-8x-6x=8}[/tex][tex]\bold{Causes~signs~to~change~and~the~equation~gets~rearranged.}[/tex][tex]4.)~Combine -8x~and~-6x:[/tex]
[tex]\bold{-8x-(-6x)=-14x}[/tex][tex]\bold{33-14x=8}[/tex][tex]5.)~Subtract~33~from~both~sides:[/tex]
[tex]\bold{33-33=Cancels~out}[/tex][tex]\bold{8-33=-25}[/tex][tex]5.)~Divide~both~sides~by~-14:[/tex]
[tex]\bold{-14x}[/tex] ÷ [tex]\bold{-14=x}[/tex][tex]\bold{-25}[/tex] ÷ [tex]\bold{-14=-1.78571429}[/tex][tex]6.)~Simplify:[/tex]
[tex]\bold{1.78571429}~(Take~Away~the~Negative!)[/tex][tex]\bold{1.8}~(Round~to~the~Nearest~Tenth!)[/tex][tex](To~Round~look~at~that~number~in~the~tenth~place:~7,\\~now~look~to~the~number~to~the~right:~8.~\\\\So~if~that~number~is~greater~than~or~equal~to~5,~then~you~round~up.\\If~that~number~is~less~than~or~equal~to~5,~then~you~round~down.)[/tex]
______________________________
[tex]\bold{Answer:}[/tex]
[tex]\bold{AB=1.8}[/tex]______________________________
[tex]\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~-TotallyNotTrillex}[/tex]
What is the equation of the line that passes through the point (5, 1) and has a slope
of 1?
Answer:
y=1x-4
Step-by-step explanation:
Point Slope Formula: y=m(x-x1)+y
y=1(x-5)+1
1x-5+1
y=1x-4 (y=mx+b)
Write the rate as a unit rate.
5 shirts cost $75.00
Answer:
$15.00 per shirt.
Step-by-step explanation:
A unit rate has one as it's denominator.
[tex]\frac{\text{dollars}}{\text{shirt}}=\frac{75}{5}=\frac{75/5}{5/5}=\frac{15}{1}[/tex]
Each shirt should be $15.00.
Hope this helps.
so you do five shirts divided by 75 dollars then the answer will be 0.06667 shirts per dollar
Write the slope-intercept form of the equation of each line given the slope and y-intercept.
1) Slope = 6, y-intercept = 5
2) Slope = -1/3, y-intercept = 1
Answer:
1.) y= 6x+5
2.) y= -1/3x+1
Step-by-step explanation:
Slope Intercept Form is y=mx+b,
where slope is m
the y-intercept is b
So I just plugged in the slope and y-int to get the equation
A teacher gathered data about the number of hours her students spent studying for a test and their resulting test grades. She found that on average, for every 30 minutes studied, the grade increased by 8 points. Which statements about this relationship are true? Check all that apply.
The data set would have a linear association.
The data set would have a nonlinear association.
The data set would have a positive correlation.
The data set would have a negative correlation.
Every student earns 16 more points for each additional hour they study.
Students that study more tend to earn better grades on the test.
The scenario described exhibits a linear relationship between the number of study hours and test grade as seen in the constant rate of change in grade per increase in study hours. Hence, the following statements are true ;
The data set would have a linear association.The data set would have a positive correlation.Students that study more tend to earn better grades on the test.Since test grade tends to increase as the number of study hours increases, these shows that there is a positive relationship between the variables. Hence, students who take in more hours of study tend to have better test grade.
Learn more : https://brainly.com/question/18618957
Answer:
a,c,f
Step-by-step explanation:
The equation is z=8+6x-px and you're solving for x
Answer:
p= 6x−z+8 /x
Step-by-step explanation:
Answer:
x= z-8/6-p
it says my answer is to short so i'm going to write a bunch or words
PLEASE HELP AND SHOW WORK PLS
Pocndnsmwntjjwbsnsns. Dhaka be d
Answer: m = 4
Step-by-step explanation: 2x4+5=13, 2x4=8 and 8+5=13.
Which statements describe a parabola? Check all that apply. A parabola is the set of all points equidistant from the directrix and focus. The fixed line is called the vertex of a parabola. The focus is a fixed point inside the parabola. The line of symmetry intersects the focus and directrix. The line of symmetry and the directrix are perpendicular. The parabola intersects the directrix.
Answer:
A parabola is the set of all points equidistant from the directrix and focus.
The line of symmetry intersects the focus and directrix
The line of symmetry and the directrix are perpendicular
Step-by-step explanation:
A parabola is the set of all points in a plane that are equidistant from a fixed point (focus) and a line (directrix).
The fixed line of a parabola is known as the directrix of the parabola.
The line of symmetry is a line that passes through the focus and is perpendicular to the directrix. The line of symmetry divides the parabola.
The directrix of a parabola does not intersect touch the parabola
Answer:
1,3,4,5 are correct
Step-by-step explanation:
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose α = 2.6 and β = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to four decimal places.) at most 250 less than 250 more than 300 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) (c) What value is such that exactly 50% of all specimens
Answer:
a
P(X \le 250 ) = 0.7564 [/tex] , [tex]P(X < 250 ) = 0.7564 [/tex] ,
[tex]P(X < 300 ) = 0.09922 [/tex]
b
[tex]P(100 < X < 250 ) =0.644 [/tex]
c
[tex] x = 192.1 [/tex]
Step-by-step explanation:
From the question we are told that
The value for [tex]\alpha = 2.6[/tex]
The value for [tex]\beta = 220[/tex]
Generally the Weibull distribution function is mathematically represented as
[tex]F( x , \alpha , \beta ) = \left \{ 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x < 0} \atop { 1- e^{-(\frac{x}{\beta } )^{\alpha } }}\ \ \ \ \ \ x \ge 0} \right[/tex]
Generally the probability that a specimen's lifetime is at most 250 is mathematically represented as
[tex]P(X \le 250 ) = F(250, 2.7 , 220 )[/tex]
[tex]P(X \le 250 )=1 - e^{- (\frac{250}{220} )^{2.7}}[/tex]
[tex]P(X \le 250 ) = 1 - 0.2436[/tex]
[tex]P(X \le 250 ) = 0.7564 [/tex]
Generally the probability that a specimen's lifetime is less than 250
[tex]P(X < 250 ) = F(250, 2.7 , 220 )[/tex]
[texP(X < 250 ) =1 - e^{- (\frac{250}{220} )^{2.7}}[/tex]
[tex]P(X < 250 ) = 1 - 0.2436[/tex]
[tex]P(X < 250 ) = 0.7564 [/tex]
Generally the probability that a specimen's lifetime is more than 300
[tex]P(X > 300 ) = 1- p(X \le 300 )[/tex]
[tex]P(X > 300 ) = 1- F(300, 2.7 , 220 )[/tex]
[texP(X < 300) =1- [1 - e^{- (\frac{300}{220} )^{2.7}}][/tex]
[tex]P(X < 300 ) = 0.09922 [/tex]
Generally the probability that a specimen's lifetime is between 100 and 250 is
[tex]P(100 < X < 250 ) = P(X < 250) - P(X < 100)[/tex]
=> [tex]P(100 < X < 250 ) =F(250 , 2.7 , 220 ) - F(100 , 2.7 , 220 ) [/tex]
=> [tex]P(100 < X < 250 ) =(1 - e^{-(\frac{250}{220})^{2.7}}) - (1 - e^{-(\frac{100}{220})^{2.7}}) [/tex]
=> [tex]P(100 < X < 250 ) = (1 - 0.244 ) - (1- 0.888)[/tex]
=> [tex]P(100 < X < 250 ) =0.644 [/tex]
Generally the value such that exactly 50% of all specimens
[tex]P(X > x) = 1-P(X < x) = 0.50[/tex]
=> [tex]P(X > x) = 1- (1 - e^{- (\frac{x}{220}) ^{2.7}}) = 0.50[/tex]
=> [tex] P(X> x ) = e^(- \frac{x}{20})^{2.7} = 0.50 [/tex]
=> [tex] P(X> x ) = (- \frac{x}{20})^{2.7} = ln0.50 [/tex]
=> [tex] P(X> x ) = \frac{x}{20} =[ -ln0.50 ] ^{frac{1}{2.7}}[/tex]
=> [tex] x = 220[ -ln0.50 ] ^{frac{1}{2.7}}[/tex]
=> [tex] x = 192.1 [/tex]
Which types of dilation are the given scale factors?
Select Expansion or Contraction to correctly describe the type of dilation for each given scale factor.
-5/4
3/8
-1.2
.5
Answer:
- 5/4: Englargement
3/8: Reduction
- 1.2: Englargement
.5: Reduction
Step-by-step explanation:
Any number from 1 up is an enlargement. Any number from 0 - 0.9 is a reduction. The same goes for negatives. Any number from -1 down is an enlargement. Any number from 0 - -0.9 is a reduction.
Function or not a function?
Answer:
fuction
Step-by-step explanation:
Esmeralda and Genevieve are both planting square gardens. Esmeralda's garden is 25 square feet and
Genevieve's is 4 square yards. Convert their garden sizes to the same units (feet) to determine who's garden has a
larger area. (1 point)
Genevieve's garden is 12 square feet and thus, has a smaller area than Esmeralda's
Genevieve's garden is 16 square feet and thus has a smaller area than Esmeralda's
O Genevieve's garden is 25 square feet, and thus has the exact same area as Esmeralda's
Genevieve's garden is 36 square feet, and thus, has a larger area than Esmeralda's
Answer:
Genevieve's garden is 12 square feet and thus, has a smaller area than Esmeralda's
Step-by-step explanation:
Given:
Esmeralda's garden = 25 square feet
Genevieve's garden = 4 square yards
Convert Genevieve's units (yards) to feet
Yards to feet
1 yard = 3 feet
4 yards = 4 * 3 feet
4 yards = 12 feet
Genevieve's garden = 12 square feet
Genevieve's garden is 12 square feet and thus, has a smaller area than Esmeralda's
Answer:
The answer is: Genevieve's garden is 36 square feet, and thus, has a larger area than Esmeralda's
Step-by-step explanation:
8^ 1/3 what is it simplified
Step-by-step explanation:
Simplifying mixed numbers
Following are the steps to simplify mixed fractions: Find the highest common factor (HCF) of numerator and denominator of the fraction part. Divide both the numerator and the denominator by HCF. The whole number part will remain the same.
Answer:
8^1/3= 2
:-))))
Martin borrowed $2700 from a bank. If he pays a fixed amount for 9 months, how much money does he have to pay per month to clear his debts? Represent the quotient as a rational number.
A. -800/1
B. – 500/1
C. 300/1
D. -100/1
Answer:
300/1
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
2700÷9=300
so,he have to pay 300 per month.
Please help fast
If you drew lines to model the verbal statement, the equation, and the table that you created in the three parts of question 1, would you get the
same line for all three? Explain
Answer:
The resulting line will be the same for all three because the verbal statement, the equation, and the table all represent the same situation. They just do it in different ways.
Answer:
The resulting line will be the same for all three because the verbal statement, the equation, and the table all represent the same situation. They just do it in different ways.
Step-by-step explanation:
8v-34= 6(v-4)
Solve for v
Answer:
v=5
Step-by-step explanation: