Answer:
X = 3, -1; B
Step-by-step explanation:
Use log properties, log 5 on both sides, log 5 of 25 is 2 that times the exponent, so 2*x = 2x, and on the other side, log 5 and base of 5 cancels. So 2x = x^2 -3, which can be solved using factoring:
x^2 -2x -3 = (x-3)(x+1) = 0, x=3,-1
The value of x in 25ˣ = 5ˣ²⁻³ is x =3 or x = -1.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given that the equation is 25ˣ = 5ˣ²⁻³.
To solve the equation, take logs on both sides, we get,
x log(25) = (x²- 3)log5
2x log 5 = (x²- 3) log5
2x = x²-3
x²- 2x -3 = 0
Now, factorize the quadratic equation,
we get,
x² - 3x + x - 3 = 0
x(x- 3) + 1(x - 3) = 0
x = 3 or -1.
Therefore, x = 3 or x = -1.
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Distribute to create an equivalent expression with the fewest symbols possible.
4(5+y)
Answer:
20 + 4y
Step-by-step explanation:
To have to fewest symbols possible, we must simplify the expression by multiplying 4 into the numbers within the parenthesis. Doing so we get:
[tex]4(5+y) = 4 * 5 + 4 * y = 20 + 4y[/tex]
Answer: 20+4y
Step-by-step explanation:
Hi, let me help you.
What we should do to simplify this expression is to "distribute" 4.
The parentheses around 5+y tell us to multiply 4 times both 5 and y. This is shown below.
[tex]\multimap\quad \tt 4\cdot5+4\cdot y[/tex]
[tex]\multimap\quad\tt 20+4y[/tex] is what we obtain upon multiplying
________________
Hope I helped. Best wishes.
Reach far. Aim high. Dream big.
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Which of the following phrases does not translate to n - 5?
1. the difference between a number and five
2. a number decreased by five
3. a number subtracted from five
4. a number minus five
Answer:
3
Step-by-step explanation:
The table lists the average monthly cost to workers for family health insurance for various years.
a) Use a graphing calculator to fit a regression line to the data.
b) Predict the average monthly cost to workers for family health insurance in 2021, and compare the value with $510.37, which
is obtained using the points (1,338) and (4,385).
c) Find the correlation coefficient for the regression line, and determine whether the line fits the data closely.
Answer:
5 dollars :)
Step-by-step explanation:
ig
Smith rides his cycle at the speed of 10 mile per hour. How many miles smith travels in 4 hours ?
Answer:
40 miles
Step-by-step explanation:
10X4
The answer is 40 miles
-------------------------------------------------------
If he consistently rides ten mph (miles per hour) for 4 hours (4*10) he would have ridden 40 miles.
What is the value of the element in row 1, column 1 of matrix x? [4 y 0 1] x= [y 4]
The value of the element in row 1, column 1 of matrix x is; y.
What is the value of the element in row 1, column 1 of matrix x?According to the task content, it follows that matrix x is defined as; x= [y 4].
In essence, it follows that the matrix x contains one row and 2 columns. Therefore, the element in row 1, column 1 of matrix x is; y.
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Answer: A
Step-by-step explanation:
The two right-angled triangles below are
similar, which means that they have the
same angles.
a) Write down the value of sin as a
fraction in its simplest form.
b) Work out the length x.
8 cm
3 cm
16 cm
X
Not drawn accurately
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \tt{sin(\Theta) = \cfrac{3}{8}} [/tex]
[tex]\qquad \tt \rightarrow \: x = 6\:\: cm[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \sin( Theta) = \cfrac{Opposite \:\: side}{Hypotenuse}[/tex]
[tex]\qquad \tt \rightarrow \: \sin( \Theta) = \cfrac{3}{8} [/tex]
since the Triangles are similar, ratio of their corresponding sides are equal :
[tex]\qquad \tt \rightarrow \: \sin( \Theta) = \cfrac{3}{8} = \dfrac{x}{16} [/tex]
[tex]\qquad \tt \rightarrow \:x = 16 \sdot \cfrac{3}{8}[/tex]
[tex]\qquad \tt \rightarrow \: x = 2 \sdot3[/tex]
[tex]\qquad \tt \rightarrow \: x = 6 \: \: cm[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Since the two right-angled triangles have the same angles, the values are; ai. sin θ= 3/8ii. sin θ= x/16b. x = 6cm
How to determine the valueUsing the sine trigonometric identity expressed as;
sin θ = opposite/hypotenuse
Then, we have that for the first triangle;
sin θ= 3/8
For the bigger triangle;
sin θ= x/16b.
Then, since we have that the sine identity is;
sin θ= x/16
But sin θ= 3/8
Divide the values and find the sine inverse in
θ= 0. 375θ = 22. 0 degrees
x = 0. 375 (16)
Multiply
x = 6 cm
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Table I contains outputs of the function f(x)=b^xf(x)=b
x
I need help
Answer: Table 1: Answer = 1. 404
Table 3 Answer = 1.66
Step-by-step explanation: i hope it's right if not, tell me
How many four-digit odd numbers less than 6000 can be formed using the digits 2, 3, 4, 5, 6, and 8?
Answer:
288
Step-by-step explanation:
First position choice: 4 numbers
Second 6 numbers
Third 6
Fourth 6
TOTAL 4 digit numbers 4 * 6 * 6 * 6 = 864 combos
2 out of 6 of these will end in 3 or 5 (thus making an odd number)
864 * 2/6 = 288 such numbers
In a rectangle the length of diagonal AC is given by (20x+12)&BDis (14x+24)cm find AC&BD
Answer:
52cm, based on my understanding of the question.
Step-by-step explanation:
See attached image. Please confirm my understanding of the question.
I need help for the question in the pic please help. thank you
Answer:
The value of x is 117° by using Alternative interior angle theorem
Step-by-step explanation:
Alternative interior angle theorem: It states that the angles made by transverse between two parallel lines are congruent.
as in figure
Angle A = 42°
Angle B = 108°
Angle C = x
Angle D = 51°
draw two parallel lines passing through B and C .
According to Alternative interior angle theorem angle B is written as 42° + 66°
and angle C is written as x1 + x2 .
Now x1 = 51° as x1 and D are alternative angles
And similarly x2 = 66°
As x = x1 + x2
Therefore x = 51° + 66° = 117°
The value of x is 117°
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2. Estimate the square root to the nearest integer. 5 4 6 7
ggggggggggggggggggggggg
y = 1/4x + 5, (−1, 6)
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given: y = 1/4x + 5, (−1, 6)
we can plug in the point (−1, 6)
6 = 1/4(-1) + 5
6 = -1/4 + 5
6 = 4.75
6 does not equal 4.75 so this point is not on the line
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By solving the equation a = 2 - 9a, the value of a will be:-
A- 2/5
B- 3/5
C- 1/5
D- 1/2
C- 1/5
Step-by-step explanation:
a = 2 - 9a
10a = 2
a = 2/10
a = 1/5
Hope u got it (◠‿・)—☆
Find the total surface area of a regular pyramid with a square base if each edge of the base is 16 inches, the slant height of one side is 17 inches, and the altitude is 15 inches.
Answer:
the answer you're looking for is 60 inches
The perimeter of the base is 4 s since it is a square.
p = 4(16) = 64 inchesThe area of the base is s².
B = 16² = 256 inches ²[tex]\boldsymbol{CST=\dfrac{1}{2}(64)(17)+256=544+256=800 \ inches^{2} }[/tex]
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
What is sin and cos
Sin and cos are trigonometry functions used to find measurements in a right triangle.
[tex]\displaystyle sin=\frac{\text{opposite side}}{hypotenuse}[/tex]
[tex]\displaystyle cos=\frac{\text{adjacent side}}{hypotenuse}[/tex]
An investment group compares returns on an account against the function represented in the table, where x is the time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the table?
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
The function over the interval is an increasing exponential function.
What is quadratic function?A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".
The complete question is
An investment group compares returns on an account
against the function represented in the table, where x is the
time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the
table?
х
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
an increasing exponential function
0
5
f(x)
10,000
12,201.90
14,888.64
22,167.15
10
20
A decreasing quadratic function is the vertex of the parabola lies on the axis parabola. So, time in years change does not give maximum total return on investment.
For increasing quadratic equation, the graph increasing at one side of the axis and decreases at other side.
For, Exponential function
When the exponential function then it shows total return on investment is not maximum.
When the exponential function is increasing it shows time goes, total return on investment is maximum.
Hence, the exponential function is increasing.
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Can you answer the question
well if its asking for an exponent then its (-5)⁴
HELPPPPPPPPPPPPPPPPP PLEASE
which property is illustrated for all expressions a and b if a=b then b=a
Answer:
Symmetric property
Question 20 The sports budget for cricket, football, and netball was divided in the ratio 5: 3:2, respectively. The total sports budget is $1.200,000. How much money will netball receive? A. B. C. D. + O A OB O C O D $120,000 $240,000 $360,000 $600,000 Question 20 The sports budget for cricket , football , and netball was divided in the ratio 5 : 3 : 2 , respectively . The total sports budget is $ 1.200,000 . How much money will netball receive ? A. B. C. D. + O A OB O C O D $ 120,000 $ 240,000 $ 360,000 $ 600,000
Using proportions, it is found that the amount that netball will receive is of:
B. $240,000
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Due to the ratios, the proportion of funding that is destined to netball is given by:
[tex]p = \frac{2}{5 + 3 + 2} = \frac{2}{10} = 0.2[/tex]
Hence, out of $1.200,000, the amount destined to netball is:
A = 0.2 x $1.200,000 = $240,000.
Which means that option B is correct.
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Pls help me solve this equation
Answer:
a
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (6, 4 ) into the partial equation
4 = 2 + c ⇒ c = 4 - 2 = 2
y = [tex]\frac{1}{3}[/tex] x + 2 ← equation of line
this is not the answer i was looking for
What number is exactly between 3.8 and 4.1
The mid-point of the numbers 3.8 and 4.1 will be 3.95.
What is the midpoint of line segment AB?Let C be the mid-point of the A and B.
C = (A + B) / 2
The numbers are given below.
3.8 and 4.1
Then the mid-point of the numbers 3.8 and 4.1 will be
C = (3.8 + 4.1) / 2
C = 7.9 / 2
C = 3.95
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Estimate
12.4 × 18
—————-
0.012
Answer: 12.4 x 18
-------------- = 18600
0.012
Isabella has a dozen apples of the same size and a dozen
watermelons of the same size. Isabella uses her juicer to extract 15
ounces of watermelon juice from 3 watermelons and 5 ounces of
apple juice from 9 apples. She makes a watermelon-apple juice
blend from an equal number of watermelons and apples. What
percent of the blend is watermelon juice?
90 per cent of the blend is watermelon juice.
Given that, Isabella has a dozen apples of the same size and a dozen watermelons of the same size.
Isabella uses her juicer to extract 15 ounces of watermelon juice from 3 watermelons and 5 ounces of apple juice from 9 apples.
We need to find what per cent of the blend is watermelon juice.
What is per cent?The percentage is a relative value indicating the hundredth part of any quantity. One per cent (symbolized 1%) is the hundredth part; thus, 100 per cent represents the entirety and 200 per cent specifies twice the given quantity.
Given that, she makes a watermelon-apple juice blend from an equal number of watermelons and apples.
So if she takes 9 apples, she can extract 5 ounces of juice.
By taking the same number of watermelons, that is 9 she can extract 15×3=45 ounces of juice.
Per cent of watermelon juice in the blend=45/50 ×100= 90%
Therefore, 90 per cent of the blend is watermelon juice.
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Which function is shown in the graph below?
Answer: c
Step-by-step explanation:
It has been given that the point (3,1) is on the graph.
And in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option C
$9,500 is invested in an account earning 9.1% interest (APR), compounded
quarterly. Write a function showing the value of the account after t years, where t
annual growth rate can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage
growth per year (APY), to the nearest hundredth of a percent.
Answer:
$100.5000
Step-by-step explanation:
becuse $9,500 is fived and it got it
A population can be divided into two subgroups that occur with probabilities 60% and 40%, respectively. An event A occurs 30% of the time in the first subgroup and 50% of the time in the second subgroup. What is the unconditional probability of the event A, regardless of which subgroup it comes from
The unconditional probability of the event A, regardless of which subgroup it comes from is 38%
How to determine the probability?Let the events be represented as:
A ⇒ The event A happeningB ⇒ First subgroupC ⇒ Second subgroupSo, we have:
P(B) = 60%
P(C) = 40%
P(A | B) = 30%
P(A | C) = 50%
The probability is then calculated as:
P = P(A | B) * P(B) + P(A | C) * P(C)
Substitute known values
P = 30% * 60% + 50% * 40%
Evaluate the product
P = 38%
Hence, the probability is 38%
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can someone please help meee
Step-by-step explanation:
Well the first 3 you just plug in the value of x which results in.
a. f(0) = 7(0)^2 + 3(0) - 2
f(0) = -2
b. f(2) = 7(2)^2 + 3(2) - 2
f(2) = 7(4) + 6 - 2
f(2) = 28 + 4
f(2) = 32
c. f(-2) = 7(-2)^2 + 3(-2) - 2
f(-2) = 7(4) - 6 - 2
f(-2) = 28 - 8
f(-2) = 20
for the last ones it's essentially the same thing except the value a is not known
d. f(a+1) = 7(a+1)^2 + 3(a+1) - 2
f(a+1) = 7(a^2 + 2a + 1) + 3a + 3 - 2
f(a+1) = 7a^2 +14a + 7 + 3a + 1
f(a+1) = 7a^2 + 17a + 8
c. f(-a) = 7(-a)^2 + 3(a) - 2
f(-a) = 7a^2 + 3a - 2
A box contains
toffee, coffee, orange, mint and hazelnut
flavour chocolates.
The ratio of toffee: coffee: orange : mint chocolates is 5:4:2:3
The
probability of picking a hazelnut chocolate i5 g
How many hazelnut chocolates are in the box?
The probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1
How to determine the probabilityNote that the ratios = 5:4:2:3
toffee: coffee: orange: mint chocolates = 5:4:2:3:1
Total ratio = 15
Probability of picking a hazelnut chocolate = ratio of hazelnut chocolates/ total ratio
Probability of picking a hazelnut chocolate = [tex]\frac{1}{15}[/tex]
The number of hazelnut chocolates in the box is gotten from the ratio which is 1
Therefore, the probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1
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