Answer:
x = 3 , x = -5
Step-by-step explanation:
Given x^2 +2x=15 add 1 to both sides to get:
x^2 + 2x + 1 =16
(x+1)^2 = 16
x + 1 = ± [tex]\sqrt{16}[/tex] = ± 4
x = -1 ± 4
x = 3 or x = -5
In the diagram below, if the measure of < C = 45°, and side AB = 16, then side AC =
Select one:
a. 8
b. 32
c. 16/2
d. 16
Answer:
C
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{16}{AC}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
AC = 16[tex]\sqrt{2}[/tex] → C
The measure of the side of a triangle AC is [tex]16\sqrt{2}[/tex] cm.
Given that, ∠45° and AB=16 cm.
We need to find the measure of side AC.
How do use trigonometric ratios to find the measure of the sides of a triangle?There are three steps:
Choose which trigonometric ratio to use. Choose either sin, cos, or tan by determining which side you know and which side you are looking for.Substitute your information into the trigonometric ratio.Solve the resulting equation to find the length of the side.Now, [tex]sin \ C=\frac{AB}{AC}[/tex] (∵ sinα=Opposite/Hypotenuse)
[tex]sin 45^{o} =\frac{16}{AC} \\[/tex]
[tex]\implies \frac{1}{\sqrt{2} } =\frac{16}{AC}[/tex]
[tex]\implies AC=16\sqrt{2}[/tex] cm
Therefore, the measure of the side of a triangle AC is [tex]16\sqrt{2}[/tex] cm.
To learn more about trigonometric ratios visit:
https://brainly.com/question/14746686.
#SPJ2
Which of the following statements must be true based on the diagram below?
(Diagram is not to scale.)
Answer:
i dont know
Step-by-step explanation:
i dont kow
Enda has job offers at two companies. One company offers a starting salary of $75,000 with a raise of $2,500 each year. The other company offers a starting salary of $55,000 with a raise of $5,000 each year. In how many years would Brenda's salary be the same with both companies? What will the salary be?
Answer:
8 years
Salary: $95000
Step-by-step explanation:
Write an equation to model the salary and its raise per year. Add the base salary to the raise per year salary times (x). Where the parameter (x) represents the number of years spent in the company.
Company (1):
75000 + 2500x
Company (2):
55000 + 5000(x)
One is asked at which year will the salaries be the same. Equate the two expressions and solve for the variable (x):
75000 + 2500x = 55000 + 5000(x)
Inverse operations:
75000 + 2500x = 55000 + 5000x
20000 + 2500x = 5000x
20000 = 2500x
8 = x
Substitute (x) into any one of the experssions and simplify to solve the epxression,
55000 + 5000(x)
x = 8
= 55000 + 5000(8)
= 55000 + 40000
= 95000
subtract the following polynomial (4x+7)-(x+1)
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]\sf{(4x+7)-(x+1) }[/tex] [tex]\sf{4x+7-x-1 }[/tex] [tex]\sf{4x-x+7-1 }[/tex] [tex]\sf{3x+6 }[/tex]The measure of two complementary angles are 2x degree and 3x degree, then value of x is
Answer:
2x+3x=90
or ,5x=90
or,x=90/5
X=18
Answer:
90/5=18 degrees
Step-by-step explanation:
please help !!!
12. JKL = ONM by SAS. Select one set of corresponding parts that could be marked congruent by CPCTC.
Answer:
D
Step-by-step explanation:
The statement of congruency shows which vertices are corresponding.
Answer: D
a handbag was purchased for Rs.280/- and sold for Rs.350/- calculate profit%
Answer:
profit is 25%
Step-by-step explanation:
profit%=sp-cp/cp×100%
=350-280/280×100%
=0.25×100
=25%
pls help me both questions
with explanation sum
9514 1404 393
Answer:
3) x = 55, y = 123, z = 123
4) x = 276°
Step-by-step explanation:
3)Angles P and Q are alternate interior angles, so are congruent.
P = Q
3x -42° = 2x +13°
x = 55° . . . . . . . . . . . add 42°-2x
Then Q = 2x +13 = 2(55°) +13° = 123°.
Angles Y, P, Q, and Z are all congruent, so all have the same measure.
Y = Z = 123°
__
4)If you draw a horizontal line parallel to AB and CD through point O, then small angle POQ is divided into parts that are congruent with angles APO and CQO. That is, small angle POQ = 48° +36° = 84°.
Large angle POQ is then 360° -84° = 276°
Pam and Amanda and Mike work at different clothing stores. Amanda made twice what Pam earned and Julie
made $90 more than Amanda. If their total earnings for a week are $995, how much did each person make?
Answer:
Pam: $181
Amanda: $362
Julie: $452
Step-by-step explanation:
(What does Mike have to do with this problem?)
Let a = Amanda's pay
Let p = Pam's pay
Let j = Julie's pay
"Amanda made twice what Pam earned"
a = 2p
"Julie made $90 more than Amanda"
j = a + 90
j = 2p + 90
Pam earned p
Total salary
a + p + j = 2p + p + 2p + 90
Total salary
$995
2p + p + 2p + 90 = 995
5p = 905
p = 181
a = 2p = 2(181) = 362
j = 2p + 90 = 362 + 90 = 452
Answer:
Pam: $181
Amanda: $362
Julie: $452
3 9. There are 180 girls in a mixed school. the ratio of girls to boys is 4:3 find the otal number of students in the school (a) 25 students (b) 315 students (c) 360 students 405 students of the binary numbers:
The ratio 4:3 means for every 4 girls there are 3 boys.
Divide total girls by 4, multiply that by 3 to get total boys:
180/4 = 45 x 3 = 135
There are 135 boys
For total students add boys and girls:
180 + 135 = 315 total students
Find the mean of first 5 prime numbers.
Answer:
5.6
Step-by-step explanation:
First five prime numbers:
[tex]2,3,5,7,11[/tex]
Add them up:
[tex]2+3+5+7+11=28[/tex]
Calculate the mean:
[tex]\frac{28}{5} =5.6[/tex]
Answer:
8.5
Step-by-step explanation:
We need to find the mean of first five prime numbers . We know that the first five prime numbers are ,
[tex]\sf\longrightarrow First \ 5 \ Prime\ numbers \ = 2, 3, 5 ,7,11 [/tex]
We know that mean is ,
[tex]\sf\longrightarrow Mean =\dfrac{Sum \ of \ observations}{Number\ of\ observations } [/tex]
Substitute the respective values ,
[tex]\sf\longrightarrow Mean =\dfrac{ 2+3+5+7}{2}[/tex]
Add the numbers in numerator ,
[tex]\sf\longrightarrow Mean =\dfrac{ 17}{2} [/tex]
Divide ,
[tex]\sf\longrightarrow\boxed{\blue{\sf Mean = 8.5 }} [/tex]
Hence the mean is 8.5
what is the answer to this
Answer:
Step-by-step explanation:
Let E= {prime numbers less than 30} Work out n(E)
Answer:
10
Step-by-step explanation:
E={2,3,5,7, 11, 13, 17, 19, 23, 29}
therefore,
n(E)={10}
Answer:
10 if I recall correctly
.
A football is punted from a height of 2.75 ft above the ground, with an initial velocity of 48 feet per
second. The motion of the football can be modeled by the equation h = -16t2 + 48t +2.75, where
h represents the height of the football, in feet, and t represents the timelin seconds.
If the football is caught 5.25 ft above the ground, approximately how long did it remain in the air?
Roundyour answer to the nearest hundredth of a second.
Answer:
Step-by-step explanation:
The position function for this is given as
[tex]h(t)=-16t^2+48t+2.75[/tex] where h(t) is the height of the football at any time t. If the ball is caught at 5.25 feet, that h(t) value is 5.25 since we are looking for the time the ball was in the air from its initial 2.75 feet to 5.25 feet, when it was caught.
[tex]5.25=-16t^2+48t+2.75[/tex] and set this equal to 0:
[tex]-16t^2+48t-2.5=0[/tex] and factor.
When we factor we get
t = .05 and t = 2.95 in seconds.
That first time tell us how long it takes to go from the initial height of 2.75 to a point 2.5 feet higher, 5.25. To get get back down to the 5.25 foot height on the other side of the vertex, is 2.95 seconds. So the total time the ball was in the air was 3 seconds exactly.
Add-ons Helplast edit was seconds ago
10 BI VA
+
GO
5
2
E A monthly service fee to download ebooks is $4.96 plus $3.99 per book downloaded White an
equation that represents the total cost, c, in a month when books are downloaded Explain how
yos gation represents the greem
Graph
Create a graph for
select the right one
Answer:
W
Step-by-step explanation:
9^(-1/2)*9^(3/2)=(1/3)*(3^3)=3^2=9
Instructions: Point T is the centroid. Find TE if XE= 21.
Answer:
TE = 7
Step-by-step explanation:
The centroid divides a median in this ratios 1/3 and 2/3. In particular
XT = 2/3 XE
XT = 2/3 * 21
XT = 14
TE = 7
CA Geometry A Illuminate Credit 4 FF.pdf
all 4 pls
Answer:
1) HL=LJ=63
(ZJ)²=16²+63²
(ZJ)²=256+3969
ZJ=√4425
ZJ= 65
2)HJ=HL+LJ
= 63+63
HJ=126
3) XC=XA=8
4) BE=AB/2=20/2=10
OAmalOHopeO
5x
If f(x) = 5x and g(x)= 5x/3, find f(x) divided by g(x).
A. 1/3
B. 3
C. 3/25x^2
D. 25x^2/3
i think its b Step-by-step explanation:
[tex] \frac{5x}{ \frac{5x}{3} } = \frac{15x}{5x} = 3[/tex]
Please tell me the answer to this question. Give a step by step explanation as well.
Answer:
15d^2 +7d-4
Step-by-step explanation:
(5d+4)(3d-1)
FOIL
first 5d*3d = 15d^2
outer 5d(-1) = -5d
inner 4*3d = 12d
last 4*-1 = -4
Add together
15d^2 -5d+12d -4
15d^2 +7d-4
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]\sf{(5d+4)(3d-1) }[/tex] [tex]\sf{ 5d(3d-1)+4(3d-1) }[/tex] [tex]\sf{15d^2-5d+12d-4 }[/tex] [tex]\sf{15d^2+(-5+12)d-4 }[/tex] [tex]\sf{ 15d^2+7d-4 }[/tex][tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
I would like to know the answer please
Answer:
2x^2+10x+2
Step-by-step explanation:
12x^2 +5x+1 - ( 10x^2 -5x-1)
Distribute the minus sign
12x^2 +5x+1 - 10x^2 +5x+1
Combine like terms
2x^2+10x+2
the polygons in each pair are similar. Find the missing side length
Answer:
Since they are similar, 45/27=30/18=x/24. x=40
[tex]\sqrt{2} \frac{7}{8}[/tex]
Answer:
[tex]\sqrt{2\frac{7}{8} } =\\\sqrt{\frac{25}{8} } =\\\sqrt{\frac{25*2}{16} } =[/tex]
±5√2/4
what is the volume if the radius is 7m and the height is 9m.
What is the slope of a line with points (5, 1) and (8,3)?
A. m= 3/2
B. m=2/3
C. m=-3/2
D.m=-2/3
Answer:
2/3
Step-by-step explanation:
If we know two points we can find the slope using
m = ( y2-y1)/(x2-x1)
= ( 3 -1)/(8 - 5)
= 2/3
Jessica purchased a DVD that was on sale for 12% off. The sales tax in her county is 3%. Let y represent the original price of the DVD. Write an expression
that can be used to determine the final cost of the DVD. HELP URGENTLY PLEASE
Answer:
If u add the number it will show u te answer which is 7
Step-by-step explanation:
The number - 7/5 is ___ than- 1 1/5 because -7/5 lies___ 5-1 /1 on a vertical number line
first question answers grater or less
second question answers greater or less
The number - 7/5 is LESS than -1 1/5
because -7/5 lies GREATER 5-1 /1 on a vertical number line.
Which points have an x value less than zero? (last answer choice says (D,J,E)
Answer:
CDJ
Step-by-step explanation:
Answer:
Choice C. C,D,J
Step-by-step explanation:
When it asks for x-values less than zero (x<0), a point that lies on the y-axis is not included.Every other option has a point lying on the y-axis or greater than zero.Una empresa textil dedicada a la confección y venta de pantis Glamour realiza la siguiente promoción de sus productos: para pedidos de hasta una decena, el par de pantis Glamour de cualquier tamaño lo vende a S/. 5. Pero si se hacen pedidos mayores a una decena de pares, cada par de media tiene un valor de S/. 3.
Respuesta:
S / 25
S / 45
S / 75
Explicación paso a paso:
Dado :
Para pedidos de hasta una docena; par de pantimedias Glamour Costo S / 5
Para pedidos de más de una docena; par de pantimedias Glamour Costo S / 3
Función de costo:
Para x ≤ 12
Costo, C = 5x
Para x> 12
Costo, C = 3x
Costo de 5 pedidos:
x = 5
Costo, C = 5 (5) = S / 25
Costo de 15 pedidos:
x = 15
Costo, C = 3 (15) = S / 45
Costo de 25 pedidos:
x = 25
Costo, C = 3 (25) = S / 75
Write the set of non-negative integers in the inequality 2x < 4.
Answer:
The set [tex]S[/tex] of non-negative integers in the inequality [tex]2x < 4[/tex] is
[tex]S = \{0, 1\}[/tex]
Step-by-step explanation:
The non-negative integers are given as [tex]\mathbb{Z}_{\ge 0} = \{ 0, 1, 2, \ldots \}[/tex]
For the inequality [tex]2x < 4[/tex], we have
[tex]2x < 4 \implies x < \dfrac{4}{2} \implies x < 2[/tex]
Therefore,
[tex]x\in \mathbb{R}:x\in(\infty, 2)[/tex]
Note: 2 is not included
The integers are
[tex]\ldots -2, -1, 0, 1[/tex]
And the non-negative integers are
[tex]0, 1[/tex]
