Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
Logarithmic functionGiven the log function expressed as:
log(x-3) + logx=1
According to the law of logarithm, addition becomes product to have:
log x(x -3) = log₁₀10
x² - 3x = 10
x² - 3x -10 = 0
x² - 5x + 2x - 10 = 0
x(x-5) + 2(x-5) = 0
(x+2)(x-5)=0
x = -2 and 5
Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
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a candy bar is in the shape of a triangular prisim the volume of the box is 2400 cubic centimeters. what is the height of the base
The height of the base will be 15 cm. The candy bar has a 2400 cubic centimeter box with a triangular prism form to it.
What is the definition of a triangular prism?Join the edges of three rectangles. Now, from both ends, seal their triangle mouths. A triangular prism is a name for the form.
The complete question is;
"A candy bar is in the shape of a triangular prism the volume of the box is 2400 cubic centimeters. It is shown with a base of the triangle labeled 16 cm, the sides of triangles labeled 17 cm, and the length of the box equal to 20 cm. what is the height of the base triangular prism"
The volume of the triangular prism;
[tex]\rm V = \frac{1}{2}\times b \times h\times l\\\\ 2400 \ cm^3 = \frac{1}{2}\times 16 \ cm \times h\times 20 \ cm \\\\ h = 15 \ cm[/tex]
Hence, the height of the base will be 15 cm.
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Jim thinks of a number (n). He adds 5 to the
number then multiplies the result by 7.
(a) Write this as a expression.
The answer Jim gets is 91.
(b) Work out the number Jim thought of.
Show all your
working.
Answers + Step-by-step explanation :
a) the equation should be:
7(n + 5) = 91 since you first add 5 to n and then multiply it by 7. The answer is 91 so that is on the other side of the equal sign
b) we can solve our equation to find for n, the number jim thought of
7(n + 5) = 91
I will use the distributive property.
7n + 35 = 91
Subtract 35 on both sides
7n = 56
Now divide 7 on both sides to find n
n = 8
The number Jim was thinking of was 8! this should be correct, hope this helps!
What is a 10% margin increase on 1,810.69?
Answer:
1991.759
Step-by-step explanation:
1810.69×%10=181.069
1810.69+181.069=1991.759
As seen in the diagram below, Hawa is building a walkway with a width of a feet to go
around a swimming pool that measures 19 feet by 6 feet. If the total area of the pool
and the walkway will be 770 square feet, how wide should the walkway be?
Answer:
8 feet
Step-by-step explanation:
you have to calculate :(19+2x)(6+2x)=770
you will get X1=8,X2= negetive some value but measurement cant be negative .if you put X=8 you'll find LHS=RHS
Answer:
[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex] or [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]
Step-by-step explanation:
So first you need to find the area of the swimming pool:
19*6 = 114
Next you add the area of the swimming pool and the area of the walkway:
114 + 770 = 884
After this you solve for x using this equation:
(19 +2x) * (6 + 2x) = 884
This would normally find the area of the whole swimming pool area and the walkway but because we know that we can use it to solve for x.
The step-by-step is this:
[tex]4x^{2} +50x+114=884[/tex]
[tex]4x^2+50x+114-884=884-884[/tex]
[tex]4x^2+50x+114-884=0[/tex]
Now we'll use the quadratic formula to simplify it farther:
[tex]x= \frac{-(50) + \sqrt{(50)^2-4(4)(-770)} }{2(4)}[/tex]
[tex]x=\frac{-50 + or - \sqrt{14820} }{8}[/tex]
[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex] or [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]
A vacuum cleaner costs $140. If the sales tax rate is 6%, what is the amount of sales tax? What is the total cost of the vacuum cleaner with sales tax?
The values in the table define the function f(x). If g(x) is the inverse of f(x), what is the value of g(1)? x f(x) -1 -3 1 -1 4 1 6 4 7 6 A. 1 B. 2 C. 3 D. 4 E. 5
The value of g(1) is 4 because (x, y) satisfy the function f(x) then (y, x) will satify the function g(x) option (D) 4 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we know if the f(x) has inverse function g(x)
Let (x, y) satisfy the function f(x) then (y, x) must satify the function g(x)
f(x) has ordered pair = (4, 1)
Then g(x) has (1, 4)
g(1) = 4
Thus, the value of g(1) is 4 because (x, y) satisfy the function f(x) then (y, x) will satify the function g(x) option (D) 4 is correct.
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If point d is placed on AC how will the measure of DAB relate to the measure of CAB
Angle DAB will be equal to angle CAB
What is trigonometry?
Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
AC is a straight line and forms one of the sides of the triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.
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Linda needs 2/5 of an ounce of salt to make 1 cup of dip for her fries. How many cups of dip will she be able to make if she has 40 ounces of salt?
Step-by-step explanation:
2/5 oz. for 1 cup
40 oz for x cups
2/5x = 40
x = 100 cups
In parallelogram MNPQ if m/PQM = 140°
find m/MNP.
Answer: 140
Step-by-step explanation:
A parallelogram means the sides are parallel, so PQM would have the same angle as MNP since they are opposite, just like NPQ and QMN.
Answer: 140°
Detailed Explanation with Figure:
In a Parallelogram, the Opposite Angles are Equal. Therefore, ∠PQM = ∠MNP, which is equal to 140°.
Here’s the Figure :-
The lengths represented by BE, EC, and CD on the diagram were determined to be 1800 feet, 200 feet, and 500 feet,
What is the length, in feet, across the lake?
Fill in the blank by entering only a number as your answer.
The length of lake is 4500 feet.
What is Triangle?A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices. A triangle with three vertices P, Q, and R is represented as △PQR.
Here, In ΔABE and ΔDCE
∠ABE = ∠DCE { each 90⁰ }
∠AEB = ∠CED { vertically opposite angle}
By AA similarity, we get
ΔABE ≈ ΔDCE
Now, AB/CD = BE/CE
AB/500 = 1800/200
AB/500 = 9
AB = 9 X 500
AB = 4500 feet.
Thus, the length of lake is 4500 feet.
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Half the product of two numbers is 36 if one number is 9 what is the other number
Answer:
x=9
y=?
36= 1/2(x*y)
36 *2 = 2* 1/2 (9*y)
72 = 9*y
72/9= 9*y/9
8=y
The other number is 8.
Instructions: Simplify the algebraic expression:
[tex]-\frac{1}{2} (32x-10y)[/tex]
Easy Problem for you guys to solve!
The measure of an angle is 10 more than two-thirds of that of its complement. Find the angle and its complement.
On a coordinate plane, a right triangle has points A (negative 5, negative 6), B (negative 5, negative 2), C (negative 2, negative 2).
Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line?
a rise of 6 and a run of 8
a rise of 8 and a run of 6
a rise of 6 and a run of 5
a rise of 5 and a run of 6
A rise of 8 and a run of 6. Then the correct option is B.
What is a coordinate geometry?Coordinate geometry is the study of geometry using the points in space.
On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).
The distance between AB will be
AB² = (-5 + 5)² + (-2 + 4)²
AB² = 4²
AB = 4
The distance between BC will be
BC² = (-2 + 5)² + (-2 + 2)²
BC² = 3²
BC = 3
Then the rise and run will be
rise / run = 4 / 3
Then this can be written as
rise / run = 8 / 6
Then the correct option is B.
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HELP! WILL GIVE BRAINLEST
Examine the following diagram: in the photo I attached of the question
What is the measure of DBC?
2°
6°
41°
49°
Answer:
Option C: 41
Step-by-step explanation:
<ABD+<CBD=90
<ABD=8x+1
<CBD=6x+5
(8x+1)+(6x+5)=90
Combine like terms
(8x+6x)+(1+5)=90
14x+6=90
14x=90-6
14x=84
divide both sides by 14
x=6
Now we plug that value into <DBC = 6x+5
6(6)+5=
36+5
41
Let's take this problem step by step:
∠ABC is 90 degrees
⇒ made up of two angles ⇒ ∠ABD and ∠DBC
⇒ in mathematical equation form:
[tex]ABD + DBC= ABC[/tex]
Since ∠ABD = 8x + 1 and ∠DBC = 6x+5
[tex]8x + 1+6x + 5=90\\14x+6=90\\14x=84\\x=6[/tex]
Let's plug it into ∠DBC = 6x+5
∠DBC = 6x+5 = 6(6)+5=41
Answer: ∠DBC = 41
Hope that helps!
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m∠DFG=(2x+6)° and m∠EFG=(3x−11)°. Find the value of x.
The figure shows straight angle D F E that consists of two angles, D F G and E F G.
Answer:
x = 37
Step-by-step explanation:
A straight angle is 180 degrees. That means ∠DFG & ∠EFG have to add together to be 180.
2x + 6 + 3x - 11 = 180 Combine like terms
5x - 5 = 180 Add 5 to both sides
5x = 185 Divide by 5
x = 37
∠DFG = 80°
∠EFG = 100°
can someone help me?
Answer:
think of each T in the original equation as an empty box, like this:
P( ) = 2( )² + ( ) - 7
when it says p(some number), it means replace all Ts in the equation with that number.
P( 0 ) = 2( 0 )² + ( 0 ) - 7 = 0 + 0 - 7 = -7
do the same for the rest <:)
for the second part, it's the same concept: every T is replaced with what's inside the parentheses.
so P( -t ) = 2( -t )² + ( -t ) - 7 = 2t² - t - 7
and so on and so forth.
Expression -2(x + 4)
Sentence
Symbol
operation
Answer:
c
Step-by-step explanation:
Suppose a simple random sample of size n = 36 is obtained from a population that is skewed right with μ = 75 and o = 24. What is P x > 80 ? Suppose a simple random sample of size n = 36 is obtained from a population that is skewed right with μ = 75 and o = 24. What is P x > 80 ?
Using the normal distribution, it is found that the probability that the sample mean is above 80 is of 0.1056 = 10.56%.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters are given as follows:
[tex]\mu = 75, \sigma = 24, n = 36, s = \frac{24}{\sqrt{36}} = 4[/tex].
The probability that the sample mean is above 80 is one subtracted by the p-value of Z when X = 80, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{80 - 75}{4}[/tex]
Z = 1.25
Z = 1.25 has a p-value of 0.8944.
1 - 0.8944 = 0.1056.
0.1056 = 10.56% probability that the sample mean is greater than 80.
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Which statement accurately describes the movement of an object under a translation vector (-3)? The object moves 2 units down and then 3 units The object moves 2 units to the right and then 3 units down. The object moves 2 units up and then 3 units to the left. D. The object moves 2 units to the left and then 3 units up. A. C.
The object moves 2 units to the left and then 3 units up.
Translation of vectorsTranslation is a transformation technique used to change the position of an object on the xy-plane.
Given the translation vector (-2, 3), this translation shows a movement of an object to the left by 2units and 3 units in the upward direction
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Rita needs to make a total of 60 deliveries this week. So far she has completed 27 of them. What percentage of her total deliveries has Rita completed?
Answer:
35
Step-by-step explanation:
Percent= (part ÷ whole)x100=21/60x100=(0.35)x100=35%
PLEASE HELP!!!!! ASAP
[tex]\text{Let's factor this quadratic.}\\\text{ We can start by thinking of two numbers such that,}\\\text{ if they are multiplied together, the product is 9}\\\text{if they're added together, the sum is -10, the middle term.}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{These numbers are -9 and -1.}\\\text{Checkup::}\\\text{-9*(-1)=9 and -9+(-1)=-10. The answer is good}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now, write these numbers as factors::}\\\text{(x-9)(x-1)=0 (make sure that the equation is \textbf{set to zero})}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now we can solve these mini equations in terms of x::}\\\text{x-9=0; \, x=9}\\\text{x-1=0; x=1}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Our factors are:: \textsl{9 and 1}}[/tex]
Answer:
x=1
Step-by-step explanation:
A
D
4
324
OX+0
+
54324
-2
-3
&
B
h
23
X
Which rule describes the x-coordinates in the translation?
A
27
image
Answer:
x + 6
Step-by-step explanation:
consider the x- coordinates of the right angle
x- coordinate of A = - 4
x- coordinate of B = 2
then
| 2 - (- 4) | = | 2 + 4 | = | 6 | = 6
the x- coordinate has been shifted 6 units to the right , so the rule is
x + 6
cosA/secA+sinA/cosecA=1
Step-by-step explanation:
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The measure of an angle is 1/2 the measure of its supplement find the measure of each supplement. Help
Answer:
।बवछॅनछॅठै रटटृ रटटृरटॅलठट
Determine the correct equation of the following graph.
The equation of the given sine graph is gotten as; y = 4 sin [(0.4(x + 2.5)] - 1
How to find the equation of a sine graph?
We know that the general formula for equation of a sine graph is;
y = A sin [(B(x - D)] + C
where;
A is Amplitude
Period = 2π/B.
Phase Shift = -C/B.
Vertical Shift = D.
From the graph;
A = 4
B = 2π/5π = 2/5
C = -1
D = -5/2
Thus;
y = 4 sin [(0.4(x + 2.5)] - 1
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21. You and your sister have been saving and decide to buy a PlayStation 5 together. You need $500 to buy the PlayStation. Together you have $850 saved up. Since you have more money, you contribute 50% of your savings and your sister contributes 75% of hers toward the $500 cost. How much do each of you have saved individually?
Answer:
I have $550; my sister has $300.
Step-by-step explanation:
Let the amount I have be x.
Let the amount my sister has be y.
We have a total of $850, so
x + y = 850
50% of my amount plus 75% of my sister's amount equals $500.
0.5x + 0.75y = 500
We have a system of two equations:
x + y = 850
0.5x + 0.75y = 500
Multiply the second equation by 2 and subtract the first equation from it.
0.5y = 150
y = 300
x + y = 850
x + 300 = 850
x = 550
Answer: I have $550; my sister has $300.
find the five ratoinal numbers between -2/3 and -1
Answer:
-31/30, -32/30, -33/30, -45/30, -49/30.
Step-by-step explanation:
-2/3 and -1 make denominators 30
-60/30 and -30/30
put any five
The roof of a house rises 9 ft over a run of 12 ft.
Determine the height of a vertical brace placed
8 ft from the low end of the roof.
The height of a vertical brace placed 8 ft from the low end of the roof is 6 feet.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Slope of roof = ratio of rise to run = rise / run = 9/12 = 3/4
If the brace is placed 8 ft from the low end of the roof, hence:
height of brace = slope * 8 = 3/4 * 8 = 6 ft
The height of a vertical brace placed 8 ft from the low end of the roof is 6 feet.
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On tax-free weekend, Ben buys school supplies totaling $47.50. He has a sale coupon for 15% off his entire purchase. What will Ben final cost be after the 15% discount?
